  Chapter 2 will begin with introduction of Agricultural Robotics. There will
be a literature review of the mechanical structure, vision and control
algorithms. In chapter 3 we will discuss the methodology in detail using block
diagrams and flowcharts. The results of the tested and the proposed algorithms
will also be displayed. In chapter 4 we will discuss the results in detail and
how they are of significance in our work. In chapter 5 we will conclude our
work and discuss some future perspectives. In appendices we will provide some
background information necessary regarding this project.


  Can we increase chances for a scientific breakthrough by get trained in
discovery-oriented thinking?


  The topology of a single-particle band structure plays a fundamental role in
understanding a multitude of physical phenomena. Motivated by the connection
between quantum walks and such topological band structures, we demonstrate that
a simple time-dependent, Bloch-oscillating quantum walk enables the direct
measurement of topological invariants. We consider two classes of
one-dimensional quantum walks and connect the global phase imprinted on the
walker with its refocusing behavior. By disentangling the dynamical and
geometric contributions to this phase we describe a general strategy to measure
the topological invariant in these quantum walks. As an example, we propose an
experimental protocol in a circuit QED architecture where a superconducting
transmon qubit plays the role of the coin, while the quantum walk takes place
in the phase space of a cavity.


  Atkinson developed a strategy which splits solution of a PDE system into
homogeneous and particular solutions, where the former have to satisfy the
boundary and governing equation, while the latter only need to satisfy the
governing equation without concerning geometry. Since the particular solution
can be solved irrespective of boundary shape, we can use a readily available
fast Fourier or orthogonal polynomial technique O(NlogN) to evaluate it in a
regular box or sphere surrounding physical domain. The distinction of this
study is that we approximate homogeneous solution with nonsingular general
solution RBF as in the boundary knot method. The collocation method using
general solution RBF has very high accuracy and spectral convergent speed and
is a simple, truly meshfree approach for any complicated geometry. More
importantly, the use of nonsingular general solution avoids the controversial
artificial boundary in the method of fundamental solution due to the
singularity of fundamental solution.


  The radiative corrections to the pure leptonic decay $D_s{\longrightarrow}
{\ell}{{\nu}}_{\ell}$ up-to one-loop order is presented. We find the virtual
photon loop corrections to $D_s{\longrightarrow} {\tau}{{\nu}}_{\tau}$ is
negative and the corresponding branching ratio is larger than $3.51\times
10^{-3}$. Considering the possible experimental resolutions, our prediction of
the radiative decay $D_s{\longrightarrow} {\tau}{{\nu}}_{\tau}\gamma$ is not so
large as others, and the best radiative channel to determine the $V_{cs}$ or
$f_{D_s}$ is $D_s{\longrightarrow} {\mu}{{\nu}}_{\mu}{\gamma}$.


  We give a necessary and sufficient criterion for an operator in a nest
algebra to belong to a proper two-sided ideal of that algebra. Using this
result, we describe the strong radical of a nest algebra, and give a general
description of the maximal two-sided ideals.


  We present the threshold resummation for the cross section for
electroproduction of heavy quarks. We work to next-to-leading logarithmic
accuracy, and in single-particle inclusive kinematics. We provide
next-to-leading and next-to-next-to-leading order expansions of our resummed
formula, and examine numerically the quality of these finite order
approximations. For the case of charm we study their impact on the structure
function $F_2$ and its differential distribution with respect to the charm
transverse momentum.


  We report a magnetostriction study of a perovskite $\rm{LaCoO}_{3}$ above 100
T using our state-of-the-art strain gauge to investigate an interplay between
electron correlations and spin crossover. There has been a controversy
regarding whether two novel phases in $\rm{LaCoO}_{3}$ at high magnetic fields
result from crystallizations or Bose-Einstein condensation during spin
crossover as manifestations of localization and delocalization in spin states,
respectively. We show that both phases are crystallizations rather than
condensations, and the two crystallizations are different, based on the
observations that the two phases exhibit as magnetostriction plateaux with
distinct heights. The crystallizations of spin states have emerged manifesting
the localizations and interactions in spin crossover with large and cooperative
lattice changes.


  We consider the safety evaluation of discrete time, stochastic systems over a
finite horizon. Therefore, we discuss and link probabilistic invariance with
reachability as well as reach-avoid problems. We show how to efficiently
compute these quantities using dynamic and linear programming.


  Given a set of integers W, the Partition problem determines whether W can be
divided into two disjoint subsets with equal sums. We model the Partition
problem as a system of polynomial equations, and then investigate the
complexity of a Hilbert's Nullstellensatz refutation, or certificate, that a
given set of integers is not partitionable. We provide an explicit construction
of a minimum-degree certificate, and then demonstrate that the Partition
problem is equivalent to the determinant of a carefully constructed matrix
called the partition matrix. In particular, we show that the determinant of the
partition matrix is a polynomial that factors into an iteration over all
possible partitions of W.


  Three-dimensional smooth compact toric varieties (SCTV) admit SU(3)
structures, and may thus be relevant for string compactifications, if they have
even first Chern class (c1). This condition can be fulfilled by infinitely many
SCTVs, including CP3 and CP1 bundles over all two-dimensional SCTVs. We show
that as long as c1 is even, toric SU(3) structures can be constructed using a
method proposed in arXiv:1005.2194. We perform a systematic study of the
parametric freedom of the resulting SU(3) structures, with a particular focus
on the metric and the torsion classes. Although metric positivity constrains
the SU(3) parameters, we find that every SCTV admits several toric SU(3)
structures and that parametric choices can sometimes be made to match
requirements of string vacua. We also provide a short review on the constraints
that an SU(3) structure must meet to be relevant for four-dimensional,
maximally symmetric N=1 or N=0 string vacua.


  The paper is withdrawn due to an error in Section 3.2. The remaining of the
results are included in the preprint solv-int/9605004.


  In the last decade, the study of cosmic microwave background (CMB) data has
become one of the most powerful tools to study and understand the Universe.
More precisely, measuring the CMB power spectrum leads to the estimation of
most cosmological parameters. Nevertheless, accessing such precious physical
information requires extracting several different astrophysical components from
the data. Recovering those astrophysical sources (CMB, Sunyaev-Zel'dovich
clusters, galactic dust) thus amounts to a component separation problem which
has already led to an intense activity in the field of CMB studies. In this
paper, we introduce a new sparsity-based component separation method coined
Generalized Morphological Component Analysis (GMCA). The GMCA approach is
formulated in a Bayesian maximum a posteriori (MAP) framework. Numerical
results show that this new source recovery technique performs well compared to
state-of-the-art component separation methods already applied to CMB data.


  We discuss the axioms for vertex algebras and their modules, using formal
calculus. Following certain standard treatments, we take the Jacobi identity as
our main axiom and we recall weak commutativity and weak associativity. We
derive a third, companion property that we call "weak skew-associativity." This
third property in some sense completes an $\mathcal{S}_{3}$-symmetry of the
axioms, which is related to the known $\mathcal{S}_{3}$-symmetry of the Jacobi
identity. We do not initially require a vacuum vector, which is analogous to
not requiring an identity element in ring theory. In this more general setting,
one still has a property, occasionally used in standard treatments, which is
closely related to skew-symmetry, which we call "vacuum-free skew-symmetry." We
show how certain combinations of these properties are equivalent to the Jacobi
identity for both vacuum-free vertex algebras and their modules. We then
specialize to the case with a vacuum vector and obtain further replacement
axioms. In particular, in the final section we derive our main result, which
says that, in the presence of certain minor axioms, the Jacobi identity for a
module is equivalent to either weak associativity or weak skew-associativity.
The first part of this result has previously appeared and been used to show the
(nontrivial) equivalence of representations of and modules for a vertex
algebra. Many but not all of our results appear in standard treatments; some of
our arguments are different from the usual ones.


  The solutions of the two-dimensional multicomponent Yajima-Oikawa system that
have the functional arbitrariness are constructed by using the Darboux
transformation technique. For the zero and constant backgrounds, different
types of solutions of this system, including the lumps, line rogue waves,
semi-rational solutions and their higher-order counterparts, are considered.
Also, the generalization of the lump solutions (namely, appearing or
disappearing lumps) is obtained in the two-component case under the special
choice of the arbitrary functions. Then, the suitable ansatz is used to find
the further generalization of these lumps (appearing-disappearing lumps or
rogue lumps).


  The long-term evolution of the internal, strong magnetic fields of neutron
stars needs a specific numerical modelling. The diversity of the observed
phenomenology of neutron stars indicates that their magnetic topology is rather
complex and three-dimensional simulations are required, for example, to explain
the observed bursting mechanisms and the creation of surface hotspots. We
present MATINS, a new three dimensions numerical code for magneto-thermal
evolution in neutron stars, based on a finite-volume scheme that employs the
cubed-sphere system of coordinates. In this first work, we focus on the crustal
magnetic evolution, with the inclusion of realistic calculations for the
neutron star structure, composition and electrical conductivity assuming a
simple temperature evolution profile. MATINS follows the evolution of strong
fields (1e14-1e15 Gauss) with complex non-axisymmetric topologies and dominant
Hall-drift terms, and it is suitable for handling sharp current sheets. After
introducing the technical description of our approach and some tests, we
present long-term simulations of the non-linear field evolution in realistic
neutron star crusts. The results show how the non-axisymmetric Hall cascade
redistributes the energy over different spatial scales. Following the
exploration of different initial topologies, we conclude that during a few tens
of kyr, an equipartition of energy between the poloidal and toroidal components
happens at small-scales. However, the magnetic field keeps a strong memory of
the initial large-scales, which are much harder to be restructured or created.
This indicates that large-scale configuration attained during the neutron star
formation is crucial to determine the field topology at any evolution stage.


  We study the entanglement detection by using mutually unbiased measurements
and provide a quantum separability criterion that can be experimentally
implemented for arbitrary $d$-dimensional bipartite systems. We show that this
criterion is more effective than the criterion based on mutually unbiased
bases. For isotropic states our criterion becomes both necessary and
sufficient.


  Long-range ferroelectric crystalline order usually fades away as the spatial
dimension decreases, hence there are few two-dimensional (2D) ferroelectrics
and far fewer one-dimensional (1D) ferroelectrics. Due to the depolarization
field, low-dimensional ferroelectrics rarely possess the polarization along the
direction of reduced dimensionality. Here, using first-principles density
functional theory, we explore the structural evolution of nanoribbons of
varying widths constructed by cutting the 2D sheet of ferroelectric
$\alpha$-III$_2$IV$_3$ (III=Al, Ga, In; VI=S, Se, Te). We discover a
one-dimensional ferroelectric nanothread (1DFENT) of ultrasmall diameter with
both axial and radial polarization, potentially enabling ultra-dense data
storage with a 1D domain of just three unit cells being the functional unit.
The polarization in 1DFENT of Ga$_2$Se$_3$ exhibits an unusual piezoelectric
response: a stretching stress along the axial direction will increase both
axial and radial polarization, referred to as auxetic piezoelectric effect.
Utilizing the intrinsically flat electronic bands, we demonstrate the
coexistence of ferroelectricity and ferromagnetism in 1DFENT and a
counterintuitive charge-doping-induced metal-to-insulator transition. The
1DFENT with both axial and radial polarization offers a counterexample to the
Mermin--Wagner theorem in 1D and suggests a new platform for the design of
ultrahigh-density memory and the exploration of exotic states of matter.


  Correlations between high life expectancy and low lifespan inequality are
frequently observed. A recent article seeks to explain this phenomenon by
proposing that a mortality improvement maps to life expectancy and relative
lifespan equality through the same weights w(x), with an extra weight W(x)
applied for relative lifespan equality, specific for the equality indicator
used. From statistical theory, the claim that changes of life expectancy and
lifespan (in)equality map through the same weights is unexpected.
  The current note explains this phenomenon by showing that W(x) undoes (part
of) w(x). Thus, while the change in relative lifespan equality is proportional
to the product of both weights, w(x)W(x), it is proportional to neither w(x)
nor W(x). As a result, some simplification is possible that gives way to an
intuitive understanding and a more direct interpretation of the perturbation
analysis proposed.


  Observations of exoplanet atmospheres have revealed the presence of cloud
particles in their atmospheres. 3D modelling of cloud formation in atmospheres
of extrasolar planets coupled to the atmospheric dynamics has long been a
challenge. We investigate the thermo-hydrodynamic properties of cloud formation
processes in the atmospheres of hot Jupiter exoplanets. We simulate the dynamic
atmosphere of HD 189733b with a 3D model that couples 3D
radiative-hydrodynamics with a kinetic, microphysical mineral cloud formation
module designed for RHD/GCM exoplanet atmosphere simulations. Our simulation
includes the feedback effects of cloud advection and settling, gas phase
element advection and depletion/replenishment and the radiative effects of
cloud opacity. We model the cloud particles as a mix of mineral materials which
change in size and composition as they travel through atmospheric
thermo-chemical environments. All local cloud properties such as number
density, grain size and material composition are time-dependently calculated.
Gas phase element depletion as a result of cloud formation is included in the
model. In-situ \textit{effective medium theory} and Mie theory is applied to
calculate the wavelength dependent opacity of the cloud component. We present a
3D cloud structure of a chemically complex, gaseous atmosphere of the hot
Jupiter HD 189733b. Mean cloud particle sizes are typically sub-micron
(0.01-0.5 $\mu$m) at pressures less than 1 bar with hotter equatorial regions
containing the smallest grains. Denser cloud structures occur near terminator
regions and deeper ($\sim$ 1 bar) atmospheric layers. Silicate materials such
as MgSiO$_{3}$[s] are found to be abundant at mid-high latitudes, while
TiO$_{2}$[s] and SiO$_{2}$[s] dominate the equatorial regions.


  Open data is an emerging paradigm to share large and diverse datasets --
primarily from governmental agencies, but also from other organizations -- with
the goal to enable the exploitation of the data for societal, academic, and
commercial gains. There are now already many datasets available with diverse
characteristics in terms of size, encoding and structure. These datasets are
often created and maintained in an ad-hoc manner. Thus, open data poses many
challenges and there is a need for effective tools and techniques to manage and
maintain it. In this paper we argue that software maintenance and reverse
engineering have an opportunity to contribute to open data and to shape its
future development. From the perspective of reverse engineering research, open
data is a new artifact that serves as input for reverse engineering techniques
and processes. Specific challenges of open data are document scraping, image
processing, and structure/schema recognition. From the perspective of
maintenance research, maintenance has to accommodate changes of open data
sources by third-party providers, traceability of data transformation
pipelines, and quality assurance of data and transformations. We believe that
the increasing importance of open data and the research challenges that it
brings with it may possibly lead to the emergence of new research streams for
reverse engineering as well as for maintenance.


  We consider the problem of quantifying the Pareto optimal boundary in the
achievable rate region over multiple-input single-output (MISO) interference
channels, where the problem boils down to solving a sequence of convex
feasibility problems after certain transformations. The feasibility problem is
solved by two new distributed optimal beamforming algorithms, where the first
one is to parallelize the computation based on the method of alternating
projections, and the second one is to localize the computation based on the
method of cyclic projections. Convergence proofs are established for both
algorithms.


  We consider the problem of learning co-occurrence information between two
word categories, or more in general between two discrete random variables
taking values in a hierarchically classified domain. In particular, we consider
the problem of learning the `association norm' defined by A(x,y)=p(x,
y)/(p(x)*p(y)), where p(x, y) is the joint distribution for x and y and p(x)
and p(y) are marginal distributions induced by p(x, y). We formulate this
problem as a sub-task of learning the conditional distribution p(x|y), by
exploiting the identity p(x|y) = A(x,y)*p(x). We propose a two-step estimation
method based on the MDL principle, which works as follows: It first estimates
p(x) as p1 using MDL, and then estimates p(x|y) for a fixed y by applying MDL
on the hypothesis class of {A * p1 | A \in B} for some given class B of
representations for association norm. The estimation of A is therefore obtained
as a side-effect of a near optimal estimation of p(x|y). We then apply this
general framework to the problem of acquiring case-frame patterns. We assume
that both p(x) and A(x, y) for given y are representable by a model based on a
classification that exists within an existing thesaurus tree as a `cut,' and
hence p(x|y) is represented as the product of a pair of `tree cut models.' We
then devise an efficient algorithm that implements our general strategy. We
tested our method by using it to actually acquire case-frame patterns and
conducted disambiguation experiments using the acquired knowledge. The
experimental results show that our method improves upon existing methods.


  A combination of hierarchical tree-like data structures and data access
patterns from fast multipole methods and hierarchical low-rank approximation of
linear operators from H-matrix methods appears to form an algorithmic path
forward for efficient implementation of many linear algebraic operations of
scientific computing at the exascale. The combination provides asymptotically
optimal computational and communication complexity and applicability to large
classes of operators that commonly arise in scientific computing applications.
A convergence of the mathematical theories of the fast multipole and H-matrix
methods has been underway for over a decade. We recap this mathematical
unification and describe implementation aspects of a hybrid of these two
compelling hierarchical algorithms on hierarchical distributed-shared memory
architectures, which are likely to be the first to reach the exascale. We
present a new communication complexity estimate for fast multipole methods on
such architectures. We also show how the data structures and access patterns of
H-matrices for low-rank operators map onto those of fast multipole, leading to
an algebraically generalized form of fast multipole that compromises none of
its architecturally ideal properties.


  We follow the life of a generic primordial perturbation mode (scalar or
tensor) subject to modified dispersion relations (MDR), as its proper
wavelength is stretched by expansion. A necessary condition ensuring that
travelling waves can be converted into standing waves is that the mode starts
its life deep inside the horizon and in the trans-Planckian regime, then leaves
the horizon as the speed of light corresponding to its growing wavelength
drops, to eventually become cis-Planckian whilst still outside the horizon, and
finally re-enter the horizon at late times. We find that scalar modes in the
observable range satisfy this condition, thus ensuring the viability of MDR
models in this respect. For tensor modes we find a regime in which this does
not occur, but in practice it can only be realised for wavelengths in the range
probed by future gravity wave experiments if the quantum gravity scale
experienced by gravity waves goes down to the PeV range. In this case
travelling---rather than standing---primordial gravity waves could be the
tell-tale signature of MDR scenarios.


  In this work we generalize the idea of a gravitational phase transition or
GPT at late times to allow for a modified gravity scenario in the early
universe as well. The original GPT was shown to simultaneously relax the $H_0$
and $\sigma_8$ tensions and {\it Planck} internal inconsistencies. However, the
primary results from GPT predictions implied disagreement with the data from
the baryonic acoustic oscillations (BAO). Here we investigate whether the
generalized GPT scenario could address the Hubble tension in the presence of
the BAO data as well. We find that, despite the vastly enlarged gravitational
parameter space, the BAO data strongly prefer the $\Lambda$CDM paradigm with a
low inferred Hubble constant, $68.03\pm 0.76 $ km/s/Mpc, in tension with the
local $H_0$ measurements from Riess et al., $H_0=74.03\pm 1.42$ km/s/Mpc. This
failure of the generalized GPT scenario to host the P18-BAO-R19 trio is of
significance and noticeably shrinks the space of possible gravitational
solutions to the Hubble tension.


  Most successful models of inflation in supergravity have a shift symmetry for
the inflaton and contain a stabilizer field coupled to the inflaton in a
particular way. We argue that the natural interpretation of the stabilizer,
from the viewpoint of the shift symmetry, is a three-form multiplet. Its
coupling to the inflaton is uniquely determined by the shift symmetry and the
invariance under three-form gauge transformations and has a natural string
theory interpretation.


  The effect of stellar scintillation on the accuracy of photometric
measurements is analyzed. We obtain a convenient form of estimaton of this
effect in the long exposure regime, when the turbulence shift produced by the
wind is much larger than the aperture of the telescope. A simple method is
proposed to determine index $S_3$ introduced by perture of the Kenyon et al.
(2006), directly from the measurements with the Multi Aperture Scintillation
Sensor (MASS) without information on vertical profile of the wind. The
statistics $S_3$ resulting from our campaign of 2005 -- 2007 at Maidanak
observatory is presented. It is shown that these data can be used to estimate
high-altitude winds at pressure level 70 -- 100 mbar. Comparison with the wind
speed retrieved from the NCEP/NCAR global models shows a good agreement. Some
prospects for retrieval of the wind speed profile from the MASS measurements
are outlined.


  The role of $CPT$ invariance and consequences for bipartite entanglement of
neutral (K) mesons are discussed. A relaxation of $CPT$ leads to a modification
of the entanglement which is known as the $\omega$ effect. The relaxation of
assumptions required to prove the $CPT$ theorem are examined within the context
of models of space-time foam. It is shown that the evasion of the EPR type
entanglement implied by $CPT$ (which is connected with spin statistics) is
rather elusive. Relaxation of locality (through non-commutative geometry) or
the introduction of decoherence by themselves do not lead to a destruction of
the entanglement. So far we find only one model which is based on non-critical
strings and D-particle capture and recoil that leads to a stochastic
contribution to the space-time metric and consequent change in the neutral
meson bipartite entanglement. The lack of an omega effect is demonstrated for a
class of models based on thermal like baths which are generally considered as
generic models of decoherence.


  Despite the rapid development and great success of machine learning models,
extensive studies have exposed their disadvantage of inheriting latent
discrimination and societal bias from the training data. This phenomenon
hinders their adoption on high-stake applications. Thus, many efforts have been
taken for developing fair machine learning models. Most of them require that
sensitive attributes are available during training to learn fair models.
However, in many real-world applications, it is usually infeasible to obtain
the sensitive attributes due to privacy or legal issues, which challenges
existing fair-ensuring strategies. Though the sensitive attribute of each data
sample is unknown, we observe that there are usually some non-sensitive
features in the training data that are highly correlated with sensitive
attributes, which can be used to alleviate the bias. Therefore, in this paper,
we study a novel problem of exploring features that are highly correlated with
sensitive attributes for learning fair and accurate classifiers. We
theoretically show that by minimizing the correlation between these related
features and model prediction, we can learn a fair classifier. Based on this
motivation, we propose a novel framework which simultaneously uses these
related features for accurate prediction and enforces fairness. In addition,
the model can dynamically adjust the regularization weight of each related
feature to balance its contribution on model classification and fairness.
Experimental results on real-world datasets demonstrate the effectiveness of
the proposed model for learning fair models with high classification accuracy.


  Recently, the theory of quantum error control codes has been extended to
subsystem codes over symmetric and asymmetric quantum channels -- qubit-flip
and phase-shift errors may have equal or different probabilities. Previous work
in constructing quantum error control codes has focused on code constructions
for symmetric quantum channels. In this paper, we develop a theory and
establish the connection between asymmetric quantum codes and subsystem codes.
We present families of subsystem and asymmetric quantum codes derived, once
again, from classical BCH and RS codes over finite fields. Particularly, we
derive an interesting asymmetric and symmetric subsystem codes based on
classical BCH codes with parameters $[[n,k,r,d]]_q$, $[[n,k,r,d_z/d_x]]_q$ and
$[[n,k',0,d_z/d_x]]_q$ for arbitrary values of code lengths and dimensions. We
establish asymmetric Singleton and Hamming bounds on asymmetric quantum and
subsystem code parameters; and derive optimal asymmetric MDS subsystem codes.
Finally, our constructions are well explained by an illustrative example.
  This paper is written on the occasion of the 50th anniversary of the
discovery of classical BCH codes and their quantum counterparts were derived
nearly 10 years ago.


  We present a definition of intersection homology for real algebraic varieties
that is analogous to Goresky and MacPherson's original definition of
intersection homology for complex varieties.


  In this paper we give solutions of certain diophantine equations related to
triangular and tetrahedral numbers and propose several problems connected with
these numbers.
  The material of this paper was presented in part at the 11th International
Workshop for Young Mathematicians - NUMBER THEORY, Krak\'{o}w, 14th-20th
september 2008.


  Long duration gamma-ray bursts (GRBs) and broad-line, type Ic supernovae
(SNe) are strongly connected. We aim at characterizing SN 2013dx, associated
with GRB\,130702A, through sensitive and extensive ground-based observational
campaigns in the optical-IR band.
  We monitored the field of the Swift GRB 130702A (redshift z = 0.145) using
the 8.2-m VLT, the 3.6-m TNG and the 0.6-m REM telescopes during the time
interval between 4 and 40 days after the burst. Photometric and spectroscopic
observations revealed the presence of the associated Type Ic SN 2013dx. Our
multi-band photometry allowed the construction of a bolometric light curve.}
  The bolometric light curve of SN 2013dx resembles that of 2003dh (associated
with GRB 030329), but is ~10% faster and ~25% dimmer. From this we infer a
synthesized 56Ni mass of ~0.2 solar masses. The multi-epoch optical
spectroscopy shows that the SN 2013dx behavior is best matched by SN 1998bw,
among the other well-known low-redshift SNe associated with GRBs and XRFs, and
by SN 2010ah, an energetic Type Ic SN not associated with any GRB. The
photospheric velocity of the ejected material declines from ~2.7X10^4 km/s at 8
rest frame days from the explosion, to ~3.5X10^3 km/s at 40 days. These values
are extremely close to those of SN1998bw and 2010ah. We deduce for SN 2013dx a
kinetic energy of ~35X10^51 erg, and an ejected mass of ~7 solar masses. This
suggests that the progenitor of SN2013dx had a mass of ~25 solar masses, i.e.,
15-20% less massive than that of SN 1998bw.
  Finally, we performed a study of the SN 2013dx environment, through
spectroscopy of the closeby galaxies. 9 out of the 14 inspected galaxies lie
within 0.03 in redshift from z=0.145, indicating that the host of GRB
130702A/SN 2013dx belongs to a group of galaxies, an unprecedented finding for
a GRB-associated SN and, to our knowledge, for long GRBs in general.


  Collective modes of exotic quantum fluids reveal underlying physical
mechanisms responsible for emergent complex quantum ground states. We observe
unexpected new collective modes in the fractional quantum Hall (FQH) regime:
intra-Landau-level plasmons in the second Landau level measured by resonant
inelastic light scattering. The plasmons herald rotational-symmetry-breaking
phases in tilted magnetic fields and reveal long-range translational invariance
in these phases. The fascinating dependence of plasmon features on filling
factor provide new insights on interplays between topological quantum Hall
order and nematic electronic liquid crystal phases. A marked intensity minimum
in the plasmon spectrum at Landau level filling factor v = 5/2 strongly
suggests that this paired state, which could support non-Abelian excitations,
overwhelms competing nematic phases, unveiling the robustness of the 5/2
superfluid state for small tilt angles. At v = 7/3, a sharp and strong plasmon
peak that links to emerging macroscopic coherence supports the proposed model
of a FQH nematic state at this filling factor.


  In this note, we investigate how well we can reconstruct the best rank-$r$
approximation of a large matrix from a small number of its entries. We show
that even if a data matrix is of full rank and cannot be approximated well by a
low-rank matrix, its best low-rank approximations may still be reliably
computed or estimated from a small number of its entries. This is especially
relevant from a statistical viewpoint: the best low-rank approximations to a
data matrix are often of more interest than itself because they capture the
more stable and oftentimes more reproducible properties of an otherwise
complicated data-generating model. In particular, we investigate two agnostic
approaches: the first is based on spectral truncation; and the second is a
projected gradient descent based optimization procedure. We argue that, while
the first approach is intuitive and reasonably effective, the latter has far
superior performance in general. We show that the error depends on how close
the matrix is to being of low rank. Both theoretical and numerical evidence is
presented to demonstrate the effectiveness of the proposed approaches.


  We develop a new method of computing radiation reaction for a point particle
interacting with massless scalar and vector fields in curved space-time. It is
based on the analysis of field Green's functions with both points lying on the
particle world-line and does not require integration of the field stresses
outside the world line as was used in the DeWitt-Brehme approach, thus leading
to a substantial simplification of the problem. We start with space-time of an
arbitrary dimension and show that the Hadamard expansion of the massless scalar
and vector Green's functions contain only integer inverse powers of the Synge
world function in even dimensions and only half-integer in the odd dimensions.
The even-dimensional case then is treated in detail. We analyze divergencies,
calculate higher-derivative counterterms, and find a recurrent formula for the
local parts of the reaction force in neighboring dimensions. Higher-dimensional
curved space counterterms are not simply the covariant generalizations of the
flat ones, but contain additional curvature-dependent terms. We illustrate our
formalism in four and six dimensions. In the first case we rederive the results
of DeWitt-Brehme-Hobbs in a simpler way, in the second case we give a covariant
generalization of the Kosyakov equation. The local part of the reaction force
is found to contain a term proportional to the Riemann tensor which is absent
in four dimensions.


  Nuclear and neutron matters are investigated in the low density region, well
below the nuclear saturation density. Microscopic calculations, based on the
Bethe-Brueckner approach with a few realistic nucleon-nucleon potentials, are
compared with the predictions of a set of phenomenological effective
interactions, mostly employed in nuclear structure studies. An energy
functional is constructed on the basis of the microscopic bulk EoS and applied
to a selection of nuclei throughout the mass table. The results provide a
microscopic basis for a link between nuclear surface behaviour and neutron EoS
previously observed with phenomenological effective forces. Possible effects of
pairing on asymmetric nuclear matter are also analyzed in detail. The results
are expected to illuminate the physical mechanisms which determine the
behaviour of the surface density tail in exotic nuclei.


  In the present paper we give numerical estimations of the plasma ion electric
microfield mixing dynamics rate. This rate was deduced from a quantum atomic
density matrix formalism and corresponds to the mixing dynamics effect of
energy levels by the plasma ion electric microfield. The rate in question is to
be added to the usual collisional-radiative model for the modeling of
dielectronic satellites originating from multi-excited atomic configurations to
diagnose high density plasma regimes generated by the interaction of X-ray free
electron lasers (XFEL's) with solid density matter. The obtained numerical
values of this rate are compared to usual relaxation atomic rates of the
collisional-radiative model in the case of three atomic energy levels of the
doubly excited 2l2l' configuration of helium-like aluminium (Z = 13): 2p^2
1D_2, 2s2p 1P_1 and 2p2 1S_0. The comparison is made for different values of
the electronic density n_e (10^+20, 10^+22, 10^+23, 10^+24 cm^-3) and for the
electronic temperature T_e = 500 eV. The numerical result shows that at high
densities this rate is at the same order of magnitude as usual
collisional-radiative rates and even exceed them in certain cases. This
demonstrates the potential role of this rate for a better understanding of the
heating mechanism underlying the evolution of a solid state matter to a plasma.


  Fitting a simplifying model with several parameters to real data of complex
objects is a highly nontrivial task, but enables the possibility to get
insights into the objects physics. Here, we present a method to infer the
parameters of the model, the model error as well as the statistics of the model
error. This method relies on the usage of many data sets in a simultaneous
analysis in order to overcome the problems caused by the degeneracy between
model parameters and model error. Errors in the modeling of the measurement
instrument can be absorbed in the model error allowing for applications with
complex instruments.


  We study the time evolution of the entropy of a collapsing spherical domain
wall, from the point of view of an asymptotic observer, by investigating the
entropy of the entire system (i.e. domain wall and radiation) and induced
radiation alone during the collapse. By taking the difference, we find the
entropy of the collapsing domain wall, since this is the object which will form
a black hole. We find that for large values of time (times larger than
$t/R_s\approx8$), the entropy of the collapsing domain wall is a constant,
which is of the same order as the Bekenstein-Hawking entropy.


  This paper is devoted to bifurcations of periodic solutions of nonlinear
measure differential equations with a parameter. Main tools are nonlinear
generalized differential equations (in the sense of Kurzweil) and the Kurzweil
gauge type generalized integral. We continue the research started by the first
author under the supervision of the second one.


  Let M be a commutative monoid. We provide an explicit first-order formular
that defines the variety generated by M in the lattice of commutative semigroup
varieties.


  We prove the Lieb-Schultz-Mattis theorem in $d$-dimensional spin systems
exhibiting $SO(3)$ spin rotation and lattice translation symmetries in the
presence of interactions decaying as $\sim 1/r^\alpha$ with distance $r$. Two
types of Hamiltonians are considered: Type I comprises long-range spin-spin
couplings, while Type II features long-range couplings between $SO(3)$
symmetric local operators. For spin-$\frac{1}{2}$ systems, it is shown that
Type I cannot have a unique ground state with a nonzero excitation gap when the
interaction decays sufficiently fast, i.e., when $\alpha>\max(3d,4d-2)$. For
Type II, the condition becomes $\alpha>\max(3d-1,4d-3)$. In $1d$, this
ingappability condition is improved to $\alpha>2$ for Type I and $\alpha>0$ for
Type II by examining the energy of a state with a uniform $2\pi$ twist.
Notably, in $2d$, a Type II Hamiltonian with van der Waals interaction is
subject to the constraint of the theorem.


  Motivated by applications in hyperspectral imaging we investigate methods for
approximating a high-dimensional non-negative matrix $\mathbf{\mathit{Y}}$ by a
product of two lower-dimensional, non-negative matrices $\mathbf{\mathit{K}}$
and $\mathbf{\mathit{X}}.$ This so-called non-negative matrix factorization is
based on defining suitable Tikhonov functionals, which combine a discrepancy
measure for $\mathbf{\mathit{Y}}\approx\mathbf{\mathit{KX}}$ with penalty terms
for enforcing additional properties of $\mathbf{\mathit{K}}$ and
$\mathbf{\mathit{X}}$. The minimization is based on alternating minimization
with respect to $\mathbf{\mathit{K}}$ or $\mathbf{\mathit{X}}$, where in each
iteration step one replaces the original Tikhonov functional by a locally
defined surrogate functional. The choice of surrogate functionals is crucial:
It should allow a comparatively simple minimization and simultaneously its
first order optimality condition should lead to multiplicative update rules,
which automatically preserve non-negativity of the iterates. We review the most
standard construction principles for surrogate functionals for Frobenius-norm
and Kullback-Leibler discrepancy measures. We extend the known surrogate
constructions by a general framework, which allows to add a large variety of
penalty terms. The paper finishes by deriving the corresponding alternating
minimization schemes explicitely and by applying these methods to MALDI imaging
data.


  In the current galaxy formation scenarios, two physical phenomena are invoked
to build disk galaxies: hierarchical mergers and more quiescent external gas
accretion, coming from intergalactic filaments. Although both are thought to
play a role, their relative importance is not known precisely. Here we consider
the constraints on these scenarios brought by the observation-deduced star
formation history on the one hand, and observed dynamics of galaxies on the
other hand: the high frequency of bars and spirals, the high frequency of
perturbations such as lopsidedness, warps, or polar rings.
  All these observations are not easily reproduced in simulations without
important gas accretion. N-body simulations taking into account the mass
exchange between stars and gas through star formation and feedback, can
reproduce the data, only if galaxies double their mass in about 10 Gyr through
gas accretion. Warped and polar ring systems are good tracers of this
accretion, which occurs from cold gas which has not been virialised in the
system's potential. The relative importance of these phenomena are compared
between the field and rich clusters. The respective role of mergers and gas
accretion vary considerably with environment.


  We theoretically formulate and experimentally demonstrate the design of
metagratings (MGs) composed of periodic rectangular grooves in a metallic
medium, intended for perfect anomalous reflection. Using mode matching, a
semianalytical scheme for analysis and synthesis of such MGs, containing
multiple, arbitrarily arranged, grooves per period, is derived. Following the
typical MG design approach, we use this formalism to identify the relevant
Floquet-Bloch (FB) modes and conveniently formulate constraints for suppression
of spurious scattering, directly tying the structure's geometrical degrees of
freedom (DOFs) to the desired functionality. Solving this set of constraints,
in turn, yields a detailed fabrication-ready MG design, without any full-wave
optimization. Besides providing means to realize highly-efficient beam
deflection with all-metallic formations, we show that the rectangular
(two-dimensional) groove configuration enables \emph{simultaneous} manipulation
of both transverse electric (TE) and transverse magnetic (TM) polarized fields,
unavailable to date with common, printed-circuit-board-based, microwave MGs. In
addition, we highlight a physical limitation on the TE-polarization
performance, preventing the ability to achieve perfect anomalous reflection in
any desired angle. These capabilities are verified using three MG prototypes,
produced with standard computer numerical control (CNC) machines, demonstrating
both single- and dual-polarized control of multiple diffraction modes. These
results enable the use of MGs for a broader range of applications, where
dual-polarized control is required, or all-metallic devices are preferable
(e.g., spaceborne systems or at high operating frequencies).


  We introduce a class of densely defined, unbounded, 2-Hochschild cocycles
([PT]) on finite von Neumann algebras $M$. Our cocycles admit a coboundary,
determined by an unbounded operator on the standard Hilbert space associated to
the von Neumann algebra $M$. For the cocycles associated to the
$\Gamma$-equivariant deformation ([Ra]) of the upper halfplane
$(\Gamma=PSL_2(\mathbb Z))$, the "imaginary" part of the coboundary operator is
a cohomological obstruction - in the sense that it can not be removed by a
"large class" of closable derivations, with non-trivial real part, that have a
joint core domain, with the given coboundary.


  We introduce clustered millimeter wave networks with invoking non-orthogonal
multiple access~(NOMA) techniques, where the NOMA users are modeled as Poisson
cluster processes and each cluster contains a base station (BS) located at the
center. To provide realistic directional beamforming, an actual antenna array
pattern is deployed at all BSs. We propose three distance-dependent user
selection strategies to appraise the path loss impact on the performance of our
considered networks. With the aid of such strategies, we derive tractable
analytical expressions for the coverage probability and system throughput.
Specifically, closed-form expressions are deduced under a sparse network
assumption to improve the calculation efficiency. It theoretically demonstrates
that the large antenna scale benefits the near user, while such influence for
the far user is fluctuant due to the randomness of the beamforming. Moreover,
the numerical results illustrate that: 1) the proposed system outperforms
traditional orthogonal multiple access techniques and the commonly considered
NOMA-mmWave scenarios with the random beamforming; 2) the coverage probability
has a negative correlation with the variance of intra-cluster receivers; 3) 73
GHz is the best carrier frequency for near user and 28 GHz is the best choice
for far user; 4) an optimal number of the antenna elements exists for
maximizing the system throughput.


  We summarize and reanalyze observations bearing upon missing galactic
baryons, where we propose a consistent picture for halo gas in L >~ L*
galaxies. The hot X-ray emitting halos are detected to 50-70 kpc, where
typically, M_hot(<50 kpc) ~ 5E9 Msun, and with density n \propto r^-3/2. When
extrapolated to R200, the gas mass is comparable to the stellar mass, but about
half of the baryons are still missing from the hot phase. If extrapolated to
1.9-3 R200, the baryon to dark matter ratio approaches the cosmic value.
Significantly flatter density profiles are unlikely for R < 50 kpc and they are
disfavored but not ruled out for R > 50 kpc. For the Milky Way, the hot halo
metallicity lies in the range 0.3-1 solar for R < 50 kpc. Planck measurements
of the thermal Sunyaev-Zeldovich effect toward stacked luminous galaxies
(primarily early-type) indicate that most of their baryons are hot, near the
virial temperature, and extend beyond R200. This stacked SZ signal is nearly an
order of magnitude larger than that inferred from the X-ray observations of
individual (mostly spiral) galaxies with M_* > 10^11.3 Msun. This difference
suggests that the hot halo properties are distinct for early and late type
galaxies, possibly due to different evolutionary histories. For the cooler gas
detected in UV absorption line studies, we argue that there are two absorption
populations: extended halos; and disks extending to ~50 kpc, containing most of
this gas, and with masses a few times lower than the stellar masses. Such
extended disks are also seen in 21 cm HI observations and in simulations.


  Multidimensional reactive flow models of accreted hydrogen rich envelopes on
top of degenerate cold white dwarfs are very effective tools for the study of
critical, non spherically symmetric, behaviors during the early stages of nova
outbursts. Such models can shed light both on the mechanism responsible for the
heavy element enrichment observed to characterize nova envelope matter and on
the role of perturbations during the early stages of ignition of the runaway.
The complexity of convective reactive flow in multi-dimensions makes the
computational model itself complex and sensitive to the details of the
numerics. In this study, we demonstrate that the imposed outer boundary
condition can have a dramatic effect on the solution. Several commonly used
choices for the outer boundary conditions are examined. It is shown that the
solutions obtained from Lagrangian simulations, where the envelope is allowed
to expand and mass is being conserved, are consistent with spherically
symmetric solutions. In Eulerian schemes which utilize an outer boundary
condition of free outflow, the outburst can be artificially quenched.


  We introduce a methodology for robust Bayesian estimation with robust
divergence (e.g., density power divergence or {\gamma}-divergence), indexed by
a single tuning parameter. It is well known that the posterior density induced
by robust divergence gives highly robust estimators against outliers if the
tuning parameter is appropriately and carefully chosen. In a Bayesian
framework, one way to find the optimal tuning parameter would be using evidence
(marginal likelihood). However, we numerically illustrate that evidence induced
by the density power divergence does not work to select the optimal tuning
parameter since robust divergence is not regarded as a statistical model. To
overcome the problems, we treat the exponential of robust divergence as an
unnormalized statistical model, and we estimate the tuning parameter via
minimizing the Hyvarinen score. We also provide adaptive computational methods
based on sequential Monte Carlo (SMC) samplers, which enables us to obtain the
optimal tuning parameter and samples from posterior distributions
simultaneously. The empirical performance of the proposed method through
simulations and an application to real data are also provided.


  In this contribution we present the design of a resonant slow extraction
based on the radio frequency knock-out (RF-KO) scheme, where we make use of the
transverse resonance islands bucket (TRIB) optics. The generation of the TRIB
optics is presented in two example lattices, that are considered for the
potential upgrade of the current booster ring for the PETRA synchrotron
radiation source at DESY. Simulations show an extraction efficiency in excess
of 98% with a septum blade thickness of \SI{30}{\micro\meter}.


  A strictly linear evolution of the cosmological expansion scale factor is a
characteristic feature in several classes of alternative gravity theories as
also in the standard (big-bang) model with specially chosen equations of state
of matter. Such an evolution has no free parameters as far as the classical
cosmological tests are concerned and should therefore be easily falsifiable. In
this article we demonstrate how such models present very good fits to the
current supernovae 1a data. We discuss the overall viability of such models.


  Previously, a quantum "tidal" mechanism of polarization of the atoms of He-II
was proposed, according to which, as a result of interatomic interaction, each
atom of He-II acquires small fluctuating dipole and multipole moments, oriented
chaotically on the average. In this work, we show that, in the presence of a
temperature or density gradient in He-II, the originally chaotically oriented
tidal dipole moments of the atoms become partially ordered, which results in
volume polarization of He-II. It is found that the gravitational field of the
Earth induces electric induction U =10(-7)V in He-II (for vessel dimensions of
the order of 10 cm). We study also the connection of polarization and
acceleration, and discuss a possible nature of the electric signal dU = kdT/2e
observed by A.S. Rybalko in experiments with second sound.


  We report the detection of $\sim$ 1500 RR Lyrae of Bailey type ab located in
the Sagittarius dwarf galaxy (Sgr). These variables have been detected on two
ESO Schmidt fields centred on (l,b)=(3.1 deg,-7.1 deg) and (6.6 deg, -10.8
deg), covering an area of $\sim$50 square degree. We present a surface density
map of Sgr based on the spatial distribution of these RRab, allowing us to
trace its structure in a region that was still almost unexplored between b=-14
deg and b=-4 deg. We present the results of the fit of different models to the
density profile of Sgr. The best fit to the core of Sgr is an exponential with
a scale length of 4.1 deg along the major axis. When we look at the extension
of Sgr we find a break (significant at the $\sim2\sigma$ level) in the slope of
the surface density along the main axis of Sgr. The nearly flat (or at least
very slowly decreasing) profile in the outer region of Sgr shows that this
dwarf galaxy is probably extending even further out our fields.


  There is significant interest in the models for production of short gamma-ray
bursts. Until now, the number of known short gamma-ray bursts with
multi-wavelength afterglows has been small. While the {\it Fermi} Gamma-Ray
Burst Monitor detects many gamma-ray bursts relative to the Neil Gehrels {\it
Swift} Observatory, the large localization regions makes the search for
counterparts difficult. With the Zwicky Transient Facility recently achieving
first light, it is now fruitful to use its combination of depth ($m_\textrm{AB}
\sim 20.6$), field of view ($\approx$ 47 square degrees), and survey cadence
(every $\sim 3$ days) to perform Target of Opportunity observations. We
demonstrate this capability on GRB 180523B, which was recently announced by the
{\it Fermi} Gamma-Ray Burst Monitor as a short gamma-ray burst. ZTF imaged
$\approx$ 2900\,square degrees of the localization region, resulting in the
coverage of 61.6\,\% of the enclosed probability over 2 nights to a depth of
$m_\textrm{AB} \sim 20.5$. We characterized 14 previously unidentified
transients, and none were found to be consistent with a short gamma-ray burst
counterpart. This search with the Zwicky Transient Facility shows it is an
efficient camera for searching for coarsely-localized short gamma-ray burst and
gravitational-wave counterparts, allowing for a sensitive search with minimal
interruption to its nominal cadence.


  The bioinformatical methods to detect lateral gene transfer events are mainly
based on functional coding DNA characteristics. In this paper, we propose the
use of DNA traits not depending on protein coding requirements. We introduce
several semilocal variables that depend on DNA primary sequence and that
reflect thermodynamic as well as physico-chemical magnitudes that are able to
tell apart the genome of different organisms. After combining these variables
in a neural classificator, we obtain results whose power of resolution go as
far as to detect the exchange of genomic material between bacteria that are
phylogenetically close.


  The content of this paper is the noted transcription of the documents (232
letters and 25 documents) which make up the Fondo Gian Antonio Maggi stored at
the Library of the Department of Mathematics of the University of Milan. The
documents cover the period 1885-1937.
  La corrispondenza qui riprodotta (232 lettere e 25 documenti) compone il
Fondo Gian Antonio Maggi conservato presso la Biblioteca del Dipartimento di
Matematica (Universita' degli Studi di Milano). I documenti coprono il periodo
1885-1937.


  We study the fundamental limits to the expressive power of neural networks.
Given two sets $F$, $G$ of real-valued functions, we first prove a general
lower bound on how well functions in $F$ can be approximated in $L^p(\mu)$ norm
by functions in $G$, for any $p \geq 1$ and any probability measure $\mu$. The
lower bound depends on the packing number of $F$, the range of $F$, and the
fat-shattering dimension of $G$. We then instantiate this bound to the case
where $G$ corresponds to a piecewise-polynomial feed-forward neural network,
and describe in details the application to two sets $F$: H{\"o}lder balls and
multivariate monotonic functions. Beside matching (known or new) upper bounds
up to log factors, our lower bounds shed some light on the similarities or
differences between approximation in $L^p$ norm or in sup norm, solving an open
question by DeVore et al. (2021). Our proof strategy differs from the sup norm
case and uses a key probability result of Mendelson (2002).


  Liquid argon time projection chambers (LArTPCs) are now a standard detector
technology for making accelerator neutrino measurements, due to their high
material density, precise tracking, and calorimetric capabilities. An electric
field (E-field) is required in such detectors to drift ionized electrons to the
anode to be collected. The E-field of a TPC is often approximated to be uniform
between the anode and the cathode planes. However, significant distortions can
appear from effects such as mechanical deformations, electrode failures, or the
accumulation of space charge generated by cosmic rays. The latter is
particularly relevant for detectors placed near the Earth's surface and with
large drift distances and long drift time. To determine the E-field in situ, an
ultraviolet (UV) laser system is installed in the MicroBooNE experiment at
Fermi National Accelerator Laboratory. The purpose of this system is to provide
precise measurements of the E-field, and to make it possible to correct for 3D
spatial distortions due to E-field non-uniformities. Here we describe the
methodology developed for deriving spatial distortions, the drift velocity and
the E-field from UV-laser measurements.


  Person re-identification has achieved great progress with deep convolutional
neural networks. However, most previous methods focus on learning individual
appearance feature embedding, and it is hard for the models to handle difficult
situations with different illumination, large pose variance and occlusion. In
this work, we take a step further and consider employing context information
for person search. For a probe-gallery pair, we first propose a contextual
instance expansion module, which employs a relative attention module to search
and filter useful context information in the scene. We also build a graph
learning framework to effectively employ context pairs to update target
similarity. These two modules are built on top of a joint detection and
instance feature learning framework, which improves the discriminativeness of
the learned features. The proposed framework achieves state-of-the-art
performance on two widely used person search datasets.


  (Abridged) Neutrino heating may drive core-collapse supernova explosions.
Although it is known that the stalled accretion shock turns into explosion when
the neutrino luminosity from the collapsed core exceeds a critical value
(L_crit) (the "neutrino mechanism"), the physics of L_crit, as well as its
dependence on the properties of the proto-neutron star (PNS) and changes to the
microphysics has never been systematically explored. We solve the
one-dimensional steady-state accretion problem between the PNS surface and the
accretion shock. We quantify the deep connection between the solution space of
steady-state accretion flows with bounding shocks and the neutrino mechanism.
We show that there is a maximum, critical sound speed above which it is
impossible to maintain accretion with a standoff shock, because the shock jump
conditions cannot be satisfied. The physics of this critical sound speed is
general and does not depend on a specific heating mechanism. For the simple
model of pressure-less free-fall onto a shock bounding an isothermal accretion
flow with sound speed c_T, we show that if c_T^2/v_escape^2 > 3/16 explosion
results. We generalize this result to the more complete supernova problem,
showing explicitly that the same physics determines L_crit. We find that the
critical condition for explosion can be written as c_S^2/v_escape^2 = 0.19,
where c_S is the adiabatic sound speed. This "antesonic" condition describes
L_crit over a broad range in accretion rate and microphysics. We show that the
addition of the accretion luminosity (L_acc) reduces L_crit non-trivially. As
in previous work, we find that L_crit is always significantly higher than the
maximum possible value of L_acc. Finally, we provide evidence that the
reduction in L_crit seen in recent multi-dimensional simulations results from a
reduction in the efficiency of cooling, rather than an increase in the heating
rate.


  We propose a class of conservative discontinuous Galerkin methods for the
Vlasov-Poisson system written as a hyperbolic system using Hermite polynomials
in the velocity variable. These schemes are designed to be systematically as
accurate as one wants with provable conservation of mass and possibly total
energy. Such properties in general are hard to achieve within other numerical
method frameworks for simulating the Vlasov-Poisson system. The proposed scheme
employs discontinuous Galerkin discretization for both the Vlasov and the
Poisson equations, resulting in a consistent description of the distribution
function and electric field. Numerical simulations are performed to verify the
order of accuracy and conservation properties.


  Continuous-variable (CV) photonic states are of increasing interest in
quantum information science, bolstered by features such as deterministic
resource state generation and error correction via bosonic codes.
Data-efficient characterization methods will prove critical in the fine-tuning
and maturation of such CV quantum technology. Although Bayesian inference
offers appealing properties -- including uncertainty quantification and
optimality in mean-squared error -- Bayesian methods have yet to be
demonstrated for the tomography of arbitrary CV states. Here we introduce a
complete Bayesian quantum state tomography workflow capable of inferring
generic CV states measured by homodyne or heterodyne detection, with no
assumption of Gaussianity. As examples, we demonstrate our approach on
experimental coherent, thermal, and cat state data, obtaining excellent
agreement between our Bayesian estimates and theoretical predictions. Our
approach lays the groundwork for Bayesian estimation of highly complex CV
quantum states in emerging quantum photonic platforms, such as quantum
communications networks and sensors.


  We consider the energy current correlation function for the FPU-beta lattice.
For small non-linearity one can rely on kinetic theory. The issue reduces then
to a spectral analysis of the linearized collision operator. We prove thereby
that, on the basis of kinetic theory, the energy current correlations decay in
time as t^(-3/5). It follows that the thermal conductivity is anomalous,
increasing as N^(2/5) with the system size N.


  For a general class of SO(4) symmetric backgrounds in type II-supergravity,
we show that the action of non-Abelian T-duality can be described via
consistent truncation to seven dimensional theories with seemingly massive
modes. As such, any solution to these theories uplifts to both massive type IIA
and IIB supergravities presenting an invertible map between the two. For
supersymmetric backgrounds, we show that for spinors transforming under SO(4)
the non-Abelian T-duality transformation breaks the original supersymmetry by
half. We use these mappings to generate the non-Abelian T-duals of the
maximally supersymmetric pp-wave, the Lin, Lunin, Maldacena geometries and
spacetimes with Lifshitz symmetry.


  We review distributed algorithms for transmitting data ($n$ real numbers)
under a broadcast communication model, as well as for maximum finding and for
sorting. Our interest is in the basics of recursive formulas and corresponding
asymptotics as ${n\to\infty}$. The emphasis is on concrete examples rather than
general theory.


  We investigate the general properties of lattice spin models with emerging
fermionic excitations. We argue that fermions always come in pairs and their
creation operator always has a string-like structure with the newly created
particles appearing at the endpoints of the string. The physical implication of
this structure is that the fermions always couple to a nontrivial gauge field.
We present exactly soluble examples of this phenomenon in 2 and 3 dimensions.
Our analysis is based on an algebraic formula that relates the statistics of a
lattice particle to the properties of its hopping operators. This approach has
the advantage that it works in any number of dimensions - unlike the
flux-binding picture developed in FQH theory.


  We solve a supersymmetric matrix model with a general potential. While matrix
models usually describe surfaces, supersymmetry enforces a cancellation of
bosonic and fermionic loops and only diagrams corresponding to so-called
branched polymers survive. The eigenvalue distribution of the random matrices
near the critical point is of a new kind.


  We propose a new lapse function that simplifies the Hamiltonian constraint,
describing the interior of the black hole in terms of the Ashtekar-Barbero
variables, into a more straightforward form. The new Hamiltonian leads to
different equations of motion than those found in the literature, but through a
suitable transformation between temporal parameters, it is found that such a
choice leads us to the classical solutions of the Schwarzschild metric, still
preserving the physical singularity. In order to resolve this singularity, and
inspired by the minimal uncertainty approach, we modify the classical algebra
between the dynamic variables of the model, imposing an effective dynamics
within the black hole. As a consequence, one of the dynamic variables, denoted
by $p_b$, acquires a minimum value at the singularity $t=0$, and on the other
hand, the variable related to the radius of the 2-sphere, $p_c$, leads to the
resolution of the classical singularity of the black hole by replacing it with
a bounce that connects the interior of the black hole with the interior of the
white hole. This bounce occurs in the Planck-scale region, where a new event
horizon manifests. Upon crossing this horizon, the nature of the interval
changes from spatial to temporal outside the white hole.


  A theory of electron spin-flip Raman scattering (SFRS) is presented that
describes the Raman spectral signals shifted by both single and twice the
electron Zeeman energy under nearly resonant excitation of the heavy hole
excitons in semiconductor nanoplatelets. We analyze the spin structure of
photoexcited intermediate states, derive compound matrix elements of the
spin-flip scattering and obtain polarization properties of the one- and
two-electron SFRS common for all the intermediate states. We show that, in the
resonant scattering process under consideration, the complexes "exciton plus
localized resident electrons" play the role of main intermediate states rather
than tightly bound trion states. It is demonstrated that, in addition to the
direct photoexcitation (and similar photorecombination) channel, there is
another indirect channel contributing to the SFRS process. In the indirect
channel, the photohole forms the exciton state with the resident electron
removed from the localization site while the photoelectron becomes localized on
this site. The theoretical results are compared with recent experimental
findings for ensembles of CdSe nanoplatelets.


  Wind erosion is a destructive mechanism that completely dissolves a weakly
bound object like a planetesimal into its constituent particles, if the
velocity relative to the ambient gas and the local gas pressure are
sufficiently high. In numerical simulations we study the influence of such wind
erosion on pebble and planetesimal accretion by a planetary body up to $10
R_\mathrm{Earth}$. Due to the rapid size reduction of an in-falling small body,
the accretion outcome changes significantly. Erosion leads to a strong decrease
in the accretion efficiency below a threshold size of the small body on the
order of 10 m. This slows down pebble accretion significantly for a given size
distribution of small bodies. The threshold radius of the small body increases
with increasing planet radius and decreases with increasing semi-major axis.
Within the parameters studied, an additional planetary atmosphere (up to 1 bar)
is of minor importance.


  Measuring robustness is a fundamental task for analyzing the structure of
complex networks. Indeed, several approaches to capture the robustness
properties of a network have been proposed. In this paper we focus on spectral
graph theory where robustness is measured by means of a graph invariant called
Kirchhoff index, expressed in terms of eigenvalues of the Laplacian matrix
associated to a graph. This graph metric is highly informative as a robustness
indicator for several realworld networks that can be modeled as graphs. We
discuss a methodology aimed at obtaining some new and tighter bounds of this
graph invariant when links are added or removed. We take advantage of real
analysis techniques, based on majorization theory and optimization of functions
which preserve the majorization order (Schurconvex functions). Applications to
simulated graphs show the effectiveness of our bounds, also in providing
meaningful insights with respect to the results obtained in the literature.


  Let $G$ be a Garside group endowed with the generating set $\mathcal{S}$ of
non-trivial simple elements, and let $H$ be a parabolic subgroup of $G$. We
determine a transversal $T$ of $H$ in $G$ such that each $\theta \in T$ is of
minimal length in its right-coset, $H \theta$, for the word length with respect
to $\mathcal{S}$. We show that there exists a regular language $L$ on
$\mathcal{S} \cup \mathcal{S}^{-1}$ and a bijection $\mathrm{ev} : L \to T$
satisfying $\mathrm{lg} (U) = \mathrm{lg}_\mathcal{S}( \mathrm{ev}(U))$ for all
$U \in L$. From this we deduce that the coset growth series of $H$ in $G$ is
rational. Finally, we show that $G$ has fellow projections on $H$ but does not
have bounded projections on $H$.


  It is believed that the multiple M5-branes are described by the non-abelian
(2,0) theory and have the non-local structure. In this note we investigate the
non-abelian (2,0) theory in loop space which incorporates the non-local
property. All fields will be formulated as loop fields and the two-form
potential becomes a part of connection. We make an ansatz for field
supersymmetry transformation with a help of Lie 3-algebra and examine the
closure condition of the transformation to find the field equations. However,
the closure conditions lead to several complex terms and we have not yet found
a simple form for some constrain field equations. In particular, we present the
clear scheme and several detailed calculations in each step. Many useful
$\Gamma$ matrix algebras are derived in the appendix.


  We propose an efficient first-order method, based on the alternating
direction method of multipliers (ADMM), to solve the homogeneous self-dual
embedding problem for a primal-dual pair of semidefinite programs (SDPs) with
chordal sparsity. Using a series of block eliminations, the per-iteration cost
of our method is the same as applying a splitting method to the primal or dual
alone. Moreover, our approach is more efficient than other first-order methods
for generic sparse conic programs since we work with smaller semidefinite
cones. In contrast to previous first-order methods that exploit chordal
sparsity, our algorithm returns both primal and dual solutions when available,
and a certificate of infeasibility otherwise. Our techniques are implemented in
the open-source MATLAB solver CDCS. Numerical experiments on three sets of
benchmark problems from the library SDPLIB show speed-ups compared to some
common state-of-the-art software packages.


  This paper considers deep neural networks for learning weakly dependent
processes in a general framework that includes, for instance, regression
estimation, time series prediction, time series classification. The $\psi$-weak
dependence structure considered is quite large and covers other conditions such
as mixing, association,$\ldots$ Firstly, the approximation of smooth functions
by deep neural networks with a broad class of activation functions is
considered. We derive the required depth, width and sparsity of a deep neural
network to approximate any H\"{o}lder smooth function, defined on any compact
set $\mx$. Secondly, we establish a bound of the excess risk for the learning
of weakly dependent observations by deep neural networks. When the target
function is sufficiently smooth, this bound is close to the usual
$\mathcal{O}(n^{-1/2})$.


  Within the scope of our recent approach for Efficient Unsupervised
Constitutive Law Identification and Discovery (EUCLID), we propose an
unsupervised Bayesian learning framework for discovery of parsimonious and
interpretable constitutive laws with quantifiable uncertainties. As in
deterministic EUCLID, we do not resort to stress data, but only to
realistically measurable full-field displacement and global reaction force
data; as opposed to calibration of an a priori assumed model, we start with a
constitutive model ansatz based on a large catalog of candidate functional
features; we leverage domain knowledge by including features based on existing,
both physics-based and phenomenological, constitutive models. In the new
Bayesian-EUCLID approach, we use a hierarchical Bayesian model with
sparsity-promoting priors and Monte Carlo sampling to efficiently solve the
parsimonious model selection task and discover physically consistent
constitutive equations in the form of multivariate multi-modal probabilistic
distributions. We demonstrate the ability to accurately and efficiently recover
isotropic and anisotropic hyperelastic models like the Neo-Hookean, Isihara,
Gent-Thomas, Arruda-Boyce, Ogden, and Holzapfel models in both elastostatics
and elastodynamics. The discovered constitutive models are reliable under both
epistemic uncertainties - i.e. uncertainties on the true features of the
constitutive catalog - and aleatoric uncertainties - which arise from the noise
in the displacement field data, and are automatically estimated by the
hierarchical Bayesian model.


  Wood deformation, in particular when subject to compression, exhibits
scale-free avalanche-like behavior as well as structure-dependent localization
of deformation. We have taken three-dimensional (3D) x-ray tomographs during
compression with constant stress rate loading. Using digital volume
correlation, we obtain the local total strain during the experiment and compare
it to the global strain and acoustic emission. The wood cells collapse layer by
layer throughout the sample starting from the softest parts, i.e., the spring
wood. As the damage progresses, more and more of the softwood layers throughout
the sample collapse, which indicates damage spreading instead of localization.
In 3D, one can see a fat-tailed local strain rate distribution, indicating that
inside the softwood layers, the damage occurs in localized spots. The observed
log-normal strain distribution is in agreement with this view of the
development of independent local collapses or irreversible deformation events.
A key feature in the mechanical behavior of wood is then in the complex
interaction of localized deformation between or among the annual rings.


  The spin-density wave (SDW) can be considered as a pair of charge density
waves (CDWs), one composed only of electrons with up-spins and the other only
of electrons with down-spins. The high-temperature superconductivity found in
cuprates and pnictides may then be ascribed to BCS-type pairing between these
SDWs, which is then no longer simple Cooper pairing between independent singlet
electrons but rather involves collective interaction between Cooper pairs. The
pseudo-gap may also be understood to originate from this BCS-type gap of the
CDW system, in which the parameters are identical to those in the original BCS
scheme, except that the electron-electron interaction is multiplied by a factor
NCDW, which represents the number of electrons of the same spin direction that
belong to a single CDW branch that comprises half the SDW. The superconducting
gap then becomes an s dx2-y2-type gap. This gap may be calculated by assuming a
modified BCS-like scheme that takes into account the contributions of the CDWs.
These CDWs may be driven spatially into a checkerboard-shaped (or striped) form
of superconductivity, depending on whether the CDW is two- or one-dimensional.
The origin of the nodal gap may also be ascribed to the CDWs.


  The post-helium burning evolution of stars from 7 to 11 solar masses is
complicated by the lingering effects of degeneracy and off-center ignition.
Here stars in this mass range are studied using a standard set of stellar
physics. Two important aspects of the study are the direct coupling of a
reaction network of roughly 220 nuclei to the structure calculation at all
stages and the use of a sub grid model to describe the convective bounded flame
that develops during neon and oxygen burning. Below 9.0 solar masses,
degenerate oxygen-neon cores form that may become either white dwarfs or
electron-capture supernovae. Above 10.3 solar masses the evolution proceeds
"normally" to iron-core collapse, without composition inversions or degenerate
flashes. Emphasis here is upon the stars in between which typically ignite
oxygen burning off center. After oxygen burns in a convectively bounded flame,
silicon burning ignites in a degenerate flash that commences closer to the
stellar center and with increasing violence for stars of larger mass. In some
cases the silicon flash is so violent that it could lead to the early ejection
of the hydrogen envelope. This might have interesting observable consequences.
For example, the death of a 10.0 solar mass star could produce two
supernova-like displays, a faint low energy event due to the silicon flash, and
an unusually bright supernova many months later as the low energy ejecta from
core collapse collides with the previously ejected envelope. The potential
relation to the Crab supernova is discussed.


  We provide quantitative inductive estimates for Green's functions of matrices
with (sub)expoentially decaying off diagonal entries in higher dimensions.
Together with Cartan's estimates and discrepancy estimates, we establish
explicit bounds for the large deviation theorem for non-self-adjoint Toeplitz
operators. As applications, we obtain the modulus of continuity of the
integrated density of states with explicit bounds and the pure point spectrum
property for analytic quasi-periodic operators. Moreover, our inductions are
self-improved and work for perturbations with low complexity interactions.


  We numerically evolve spherically symmetric solutions to the linear wave
equation on some expanding Friedmann-Lema\^itre-Robertson-Walker (FLRW)
spacetimes and study the respective asymptotics for large times. We find a
quantitative relation between the expansion rate of the underlying background
universe and the decay rate of linear waves, also in the context of
spatially-hyperbolic spacetimes, for which rigorous proofs of decay rates are
not generally known. A prominent role in the decay mechanism is shown to be
played by tails, i.e. scattered waves propagating in the interior of the
lightcone.


  Let $E/F$ be a quadratic unramified extension of non-archimedean local fields
and $\mathbb H$ a simply connected semisimple algebraic group defined and split
over $F$. We establish general results (multiplicities, test vectors) on $\HH
(F)$-distinguished Iwahori-spherical representations of $\HH (E)$. For discrete
series Iwahori-spherical representations of $\HH (E)$, we prove a numerical
criterion of $\HH (F)$-distinction. As an application, we classify the $\HH
(F)$-distinguished discrete series representations of $\HH (E)$ corresponding
to degree $1$ characters of the Iwahori-Hecke algebra.


  The TeV blazar Ton 599 has exhibited a peculiar flare in 2017 November. The
temporal variation of the source is studied using simultaneous $\gamma$-ray
data from $\textit{Fermi}$ Large Area Telescope and radio data from Owens
Valley Radio Observatory's 40 m telescope, over the period of nine years. Four
major flaring periods are observed in the $\gamma$-ray energy band of 0.1-300
GeV. These periods are studied on a shorter timescale and modeled with a
time-dependent function containing exponential rising and decaying components.
The physical parameters of the jet are estimated numerically and compared with
those reported in the literature. During the fourth flare a bunch of high
energy photons ($>$10 GeV) were detected. The two highest energy photons having
an energy of 76.9 GeV and 61.9 GeV are detected on MJD 58059.0 and 58073.3,
respectively. This observation possibly constrains the $\gamma$-ray emission
region to lie near outer edge or outside the broad line region of size
$\sim$0.08 pc. The variation of equivalent width of a Mg-II line is studied
using the spectroscopic data from Steward observatory. It was observed that the
equivalent width of the line varies inversely with the underlying power-law
continuum.


  Generalizing Feingold-Frenkel's construction we use Weyl bosonic fields to
construct toroidal Lie algebras of types $A_n, B_n$, $C_n$ and $D_n$ of level
$-1, -2, -1/2$ and -2 respectively. In particular, our construction also gives
new bosonic construction for the orthogonal Lie algebras in the cases of affine
Lie algebras.


  In compact and dense star-forming clouds a global star cluster wind could be
suppressed. In this case the stellar feedback is unable to expel the leftover
gas from the cluster. Young massive stars remain embedded into a dense residual
gas and stir it moving in the gravitational well of the system. Here we present
a self-consistent model for the molecular gas distribution in such young,
enshrouded stellar clusters. It is assumed that the cloud collapse terminates
and the star formation ceases when a balance between the turbulent pressure and
gravity and between the turbulent energy dissipation and regeneration rates is
established. These conditions result in an equation that determines the
residual gas density distribution that, in turn, allows one to determine the
other characteristics of the leftover gas and the star formation efficiency. It
is shown that model predictions are in good agreement with several
observationally determined properties of cloud D1 in nearby dwarf spheroidal
galaxy NGC 5253 and its embedded cluster.


  The Linnik phenomenon concerning the repelling effect of Siegel's zeros is
extended to L-functions in a family wider than hitherto considered.


  An elementary introduction is presented to the study of hadron structure
using lattice QCD. Following a brief review of relevant aspects of path
integrals, the discrete lattice path integral is presented for gluon and quark
fields and used to calculate physical observables. Essential aspects of
instanton physics are reviewed, and it is shown how the instanton content is
extracted from lattice gluon configurations. Finally, both comparison of
results including all gluons with those including only instantons and the study
of quark zero modes associated with instantons and their contributions to
hadronic observables are used to show the dominant role of gluons in hadron
structure.


  In this study, we propose AniPortrait, a novel framework for generating
high-quality animation driven by audio and a reference portrait image. Our
methodology is divided into two stages. Initially, we extract 3D intermediate
representations from audio and project them into a sequence of 2D facial
landmarks. Subsequently, we employ a robust diffusion model, coupled with a
motion module, to convert the landmark sequence into photorealistic and
temporally consistent portrait animation. Experimental results demonstrate the
superiority of AniPortrait in terms of facial naturalness, pose diversity, and
visual quality, thereby offering an enhanced perceptual experience. Moreover,
our methodology exhibits considerable potential in terms of flexibility and
controllability, which can be effectively applied in areas such as facial
motion editing or face reenactment. We release code and model weights at
https://github.com/scutzzj/AniPortrait


  In this paper we assess the performances of different analytical
prescriptions for the effective-one-body (EOB) radiation reaction along generic
planar orbits using exact numerical result in the test-mass limit. We consider
three prescriptions put forward in the recent literature: (i) the quasicircular
prescription (QC), (ii) the QC with second post-Newtonian (2PN) order
noncircular corrections (QC2PN), and (iii) the QC corrected by the noncircular
Newtonian prefactor (NCN). The analytical fluxes are then compared against the
exact fluxes that are computed by solving the Teukolsky equation with a
test-mass source in geodesic motion. We find that the NCN prescription is the
most accurate for both eccentric and hyperbolic orbits and it is in robust
agreement also for large values of the eccentricity. This result carries over
to the comparable masses, as we discuss for a numerical-relativity (NR) case
study. We also demonstrate that, while the EOB/NR waveform unfaithfulness is a
necessary check for the precision of EOB models, the direct comparison of
EOB/NR fluxes is a more stringent and informative test to select the best
prescription. Finally, we propose an improved radiation reaction, NCN2PN, that
includes noncircular 2PN corrections, in resummed form, as a further
multiplicative contribution and that is valid for any mass ratio.


  A critical analysis of the relativistic formulation of matter reveals some
surprising inconsistencies and paradoxes. Corrections are discovered which lead
to the long-sought-after equality of the gravitational and inertial masses,
which are otherwise different in general relativity.
  Realizing the potentially great impact of the discovered corrections, an
overview of the situation is provided resulting from the newly discovered
crisis, amid the evidences defending the theory.


  We present our multicolour photometric data of the primary and secondary
eclipses of OW Gem that took place in 1995, 2002, and 2006, as well as the new
radial-velocity data collected since 1993 by R. F. Griffin and A. Duquennoy.
The Wilson-Devinney code was used for the simultaneous solution of both
photometric and spectroscopic data. A complete set of orbital and physical
parameters of the components was obtained. The pair of values, eccentricity
e=0.5286 and argument of periastron omega=140.73 degree, give better
compatibility of the moment of the secondary minimum with the observations
compared to previous estimates.


  Much attention has been drawn to quantum computing and the exponential
speed-up in computation the technology would be able to provide. Various claims
have been made about what aspect of quantum mechanics causes this speed-up.
Formulations of quantum computing have traditionally been made in orthodox
(Copenhagen) and sometimes many-worlds quantum mechanics. We will aim to
understand quantum computing in terms of de Broglie-Bohm Pilot-Wave Theory by
considering different simple systems that may function as a basic quantum
computer. We will provide a careful discussion of Pilot-Wave Theory and
evaluate criticisms of the theory. We will assess claims regarding what causes
the exponential speed-up in the light of our analysis and the fact that
Pilot-Wave Theory is perfectly able to account for the phenomena involved in
quantum computing.


  This paper proposes a new distance metric between clusterings that
incorporates information about the spatial distribution of points and clusters.
Our approach builds on the idea of a Hilbert space-based representation of
clusters as a combination of the representations of their constituent points.
We use this representation and the underlying metric to design a
spatially-aware consensus clustering procedure. This consensus procedure is
implemented via a novel reduction to Euclidean clustering, and is both simple
and efficient. All of our results apply to both soft and hard clusterings. We
accompany these algorithms with a detailed experimental evaluation that
demonstrates the efficiency and quality of our techniques.


  The eavesdropper technique nowadays is already improved from the theoretical
perspective to the experimental perspective. The technique now more focusing on
the loopholes of the components used such as modulator, laser, and detector.
These all components actually are the classical component which normally being
used in the communication system. The technique called "blinding detector"
introduce by Vadim Makarov et. al. exploit the unavailability of a true
single-photon detector. The detector behavior which is avalanche photodiode
(APD) is being used in almost all quantum system and exploiting its
vulnerability towards the quantum attacks which is limit the potential to
detect the presence of the eavesdropper attack.


  We prove, using $p$-adic Hodge theory for open algebraic varieties, that for
a smooth projective variety over a subfield $k\subset\mathbb C$ which is of
finite type over $\mathbb Q$, the complex abel jacobi map vanishes if the etale
abel jacobi map vanishes. This implies that for a smooth projective morphism
$f:X\to S$ of smooth complex algebraic varieties over $k\subset\mathbb C$ which
is of finite type over $\mathbb Q$ and $Z\in\mathcal Z^d(X,n)^{f,\partial=0}$
an algebraic cycle flat over $S$ whose cohomology class vanishes on fibers, the
zero locus of the etale normal function associated to $Z$ is contained in the
zero locus of the complex normal function associated to $Z$. From the work of
Saito or Charles, we deduce that the zero locus of the complex normal function
associated to $Z$ is defined over the algebraic closure $\bar k$ of $k$ if the
zero locus of the etale normal function associated to $Z$ is not empty. We also
prove an algebraicity result for the zero locus of an etale normal function
associated to an algebraic cycle over a field of finite type over $\mathbb Q$.
By the way, for a smooth morphism $f:X\to S$ of smooth algebraic varieties over
a field of finite type over $\mathbb Q$, we embed the locus of Hodge-Tate
classes of $f$ inside the locus of Hodge classes of $f$.


  Damped mechanical systems with various forms of damping are quantized using
the path integral formalism. In particular, we obtain the path integral kernel
for the linearly damped harmonic oscillator and a particle in a uniform
gravitational field with linearly or quadratically damped motion. In each case,
we study the evolution of Gaussian wavepackets and discuss the characteristic
features that help us distinguish between different types of damping. For
quadratic damping, we show that the action and equation of motion of such a
system has a connection with the zero dimensional version of a currently
popular scalar field theory. Furthermore we demonstrate that the equation of
motion (for quadratic damping) can be identified as a geodesic equation in a
fictitious two-dimensional space.


  High Tc superconductivity in FeAs-based multilayers (pnictides), evading
temperature decoherence effects in a quantum condensate, is assigned to a
Feshbach resonance (called also shape resonance) in the exchange-like interband
pairing. The resonance is switched on by tuning the chemical potential at an
electronic topological transition (ETT) near a band edge, where the Fermi
surface topology of one of the subbands changes from 1D to 2D topology. We show
that the tuning is realized by changing i) the misfit strain between the
superconducting planes and the spacers ii) the charge density and iii) the
disorder. The system is at the verge of a catastrophe i.e. near a structural
and magnetic phase transition associated with the stripes (analogous to the 1/8
stripe phase in cuprates) order to disorder phase transition. Fine tuning of
both the chemical potential and the disorder pushes the critical temperature Ts
of this phase transition to zero giving a quantum critical point. Here the
quantum lattice and magnetic fluctuations promote the Feshbach resonance of the
exchange-like anisotropic pairing. This superconducting phase that resists to
the attacks of temperature is shown to be controlled by the interplay of the
hopping energy between stripes and the quantum fluctuations. The
superconducting gaps in the multiple Fermi surface spots reported by the recent
ARPES experiment of D. V. Evtushinsky et al. arXiv:0809.4455 are shown to
support the Feshbach scenario.


  Recent intriguing discussion of heat death by Kutrovatz is critically
examined. It is shown that there exists another way of answering the heat death
puzzle, already present in the ancient philosophical tradition. This
alternative route relies not only on the final duration of time (which has been
re-discovered in modern times), but also on the notion of observational
self-selection, which has received wide publicity in the last several decades
under the title of the anthropic principle(s). Although the questions Kutrovatz
raises are important and welcome, there are several errors in his treatment of
cosmology which marr his account of the entire topic. In addition, the nascent
discipline of physical eschatology holds promise of answering the basic
explanatory task concerning the future evolution of the universe without
appealing to metaphysics. This is a completely novel feature in the history of
science, in contradistinction to the historical examples discussed.


  A generalized approach to Wang-Landau simulations, macroscopically
constrained Wang-Landau, is proposed to simulate the density of states of a
system with multiple macroscopic order parameters. The method breaks a
multidimensional random-walk process in phase space into many separate,
one-dimensional random-walk processes in well-defined subspaces. Each of these
random walks is constrained to a different set of values of the macroscopic
order parameters. When the multi-variable density of states is obtained for one
set of values of field-like model parameters, the density of states for any
other values of these parameters can be obtained by a simple transformation of
the total system energy. All thermodynamic quantities of the system can then be
rapidly calculated at any point in the phase diagram. We demonstrate how to use
the multi-variable density of states to draw the phase diagram, as well as
order-parameter probability distributions at specific phase points, for a model
spin-crossover material: an antiferromagnetic Ising model with ferromagnetic
long-range interactions. The field-like parameters in this model are an
effective magnetic field and the strength of the long-range interaction.


  We show that in electron-hole bilayers with excitonic order arising from
conduction and valence bands formed by atomic orbitals that have different
parities, nonzero interlayer tunneling leads to a second order Josephson
effect. This means the interlayer electrical current is related to the phase of
the excitonic order parameter as $J = J_c \sin2\theta$ instead of $J = J_c \sin
\theta$, and that the system has two degenerate ground states at $\theta=0,
\pi$ that can be switched by an interlayer voltage pulse. When generalized to a
three dimensional stack of alternating electron-hole planes or a two
dimensional stack of chains, AC Josephson effect implies that electric field
pulses perpendicular to the layers and chains can steer the order parameter
phase between the two degenerate ground states, making these devices ultrafast
memories. The order parameter steering also applies to the excitonic insulator
candidate Ta$_2$NiSe$_5$.


  This paper provides details of the massless three-loop three-point integrals
calculation at the symmetric point. Our work aimed to extend known two-loop
results for such integrals to the three-loop level. Obtained results can find
their application in regularization-invariant symmetric point
momentum-subtraction (RI/SMOM) scheme QCD calculations of renormalization group
functions and various composite operator matrix elements. To calculate
integrals, we solve differential equations for auxiliary integrals by
transforming the system to the $\varepsilon$-form. Calculated integrals are
expressed through the basis of functions with uniform transcendental weight. We
provide expansion up to the transcendental weight six for the basis functions
in terms of harmonic polylogarithms with six-root of unity argument.


  We report on the discovery of two new molecules, HCCCHCCC and HCCCCS, towards
the starless core TMC-1 in the Taurus region from the QUIJOTE line survey in
the 31.1-50.2 GHz frequency range. We identify a total of twenty-nine lines of
HCCCHCCC and six rotational transitions of HCCCCS. The rotational quantum
numbers range from Ju=10 up to 15 and Ka <=2 for HCCCHCCC and Ju=21/2 up to
31/2 for HCCCCS. We derived a column density for HCCCHCCC of
N=(1.3+/-0.2)x10^11 cm-2 with a rotational temperature of 6+/-1 K, while for
HCCCCS we derived N=(9.5+/-0.8)x10^10 cm-2 and Trot =10+/-1 K. The abundance of
HCCCHCCC is higher than that of its recently discovered isomer, l-H2C6. If we
compare HCCCCS with its related molecules, HCS and HCCS, we obtain abundance
ratios HCS/HCCCCS=58 and HCCS/HCCCCS=7.2. We investigated the formation of
these two molecules using chemical modelling calculations. The observed
abundances can be accounted for by assuming standard gas-phase formation routes
involving neutral-neutral reactions and ion-neutral reactions.


  It is well-known that three-boson systems show the Efimov effect when the
two-body scattering length $a$ is large with respect to the range of the
two-body interaction. This effect is a manifestation of a discrete scaling
invariance (DSI). In this work we study DSI in the $N$-body system by analysing
the spectrum of $N$ identical bosons obtained with a pairwise gaussian
interaction close to the unitary limit. We consider different universal ratios
such as $E_N^0/E_3^0$ and $E_N^1/E_N^0$, with $E_N^i$ being the energy of the
ground ($i=0$) and first-excited ($i=1$) state of the system, for $N\le16$. We
discuss the extension of the Efimov radial law, derived by Efimov for $N=3$, to
general $N$.


  The equation for the charge vertex $\gamma$ of the $t-J$ model is derived and
solved in leading order of an 1/N expansion, working directly in terms of
Hubbard operators. Various quantities which depend crucially on $\gamma$ are
then calculated, such as the life time and the transport life time of electrons
due to a charge coupling to other degrees of freedom and the charge-charge
correlation function. Our results show that the static screening of charges and
the dynamics of charge fluctuations depend only weakly on $J$ and are mainly
determined by the constraint of having no double occupancies of sites.