  Successful incorporation of the spin degree of freedom in semiconductor
technology requires the development of a new paradigm allowing for a scalable,
non-destructive electrical detection of the spin-polarization of injected
charge carriers as they propagate along the semiconducting channel. In this
paper we report the observation of a spin-injection Hall effect (SIHE) which
exploits the quantum-relativistic nature of spin-charge transport and which
meets all these key requirements on the spin detection. The two-dimensional
electron-hole gas photo-voltaic cell we designed to observe the SIHE allows us
to develop a quantitative microscopic theory of the phenomenon and to
demonstrate its direct application in optoelectronics. We report an
experimental realization of a non-magnetic spin-photovoltaic effect via the
SIHE, rendering our device an electrical polarimeter which directly converts
the degree of circular polarization of light to a voltage signal.


  Recently, a class of objects, known as $\Lambda$-polytopes, were introduced
for classically simulating universal quantum computation with magic states. In
$\Lambda$-simulation, the probabilistic update of $\Lambda$ vertices under
Pauli measurement yields dynamics consistent with quantum mechanics. Thus, an
important open problem in the study of $\Lambda$-polytopes is characterizing
its vertices and determining their update rules. In this paper, we obtain and
describe the update of all degenerate vertices of $\Lambda_{2}$, the $2$-qubit
$\Lambda$ polytope. Our approach exploits the fact that $\Lambda_{2}$ projects
to a well-understood polytope $\text{MP}$ consisting of distributions on the
Mermin square scenario. More precisely, we study the ``classical" polytope
$\overline{\text{MP}}$, which is $\text{MP}$ intersected by the polytope
defined by a set of Clauser-Horne-Shimony-Holt (CHSH) inequalities. Owing to a
duality between CHSH inequalities and vertices of $\text{MP}$ we utilize a
streamlined version of the double-description method for vertex enumeration to
obtain certain vertices of $\overline{\text{MP}}$.


  Deep reinforcement learning (RL) algorithms typically parameterize the policy
as a deep network that outputs either a deterministic action or a stochastic
one modeled as a Gaussian distribution, hence restricting learning to a single
behavioral mode. Meanwhile, diffusion models emerged as a powerful framework
for multimodal learning. However, the use of diffusion policies in online RL is
hindered by the intractability of policy likelihood approximation, as well as
the greedy objective of RL methods that can easily skew the policy to a single
mode. This paper presents Deep Diffusion Policy Gradient (DDiffPG), a novel
actor-critic algorithm that learns from scratch multimodal policies
parameterized as diffusion models while discovering and maintaining versatile
behaviors. DDiffPG explores and discovers multiple modes through off-the-shelf
unsupervised clustering combined with novelty-based intrinsic motivation.
DDiffPG forms a multimodal training batch and utilizes mode-specific Q-learning
to mitigate the inherent greediness of the RL objective, ensuring the
improvement of the diffusion policy across all modes. Our approach further
allows the policy to be conditioned on mode-specific embeddings to explicitly
control the learned modes. Empirical studies validate DDiffPG's capability to
master multimodal behaviors in complex, high-dimensional continuous control
tasks with sparse rewards, also showcasing proof-of-concept dynamic online
replanning when navigating mazes with unseen obstacles.


  Choose a polynomial $f$ uniformly at random from the set of all monic
polynomials of degree $n$ with integer coefficients in the box $[-L,L]^n$. The
main result of the paper asserts that if $L=L(n)$ grows to infinity, then the
Galois group of $f$ is the full symmetric group, asymptotically almost surely,
as $n\to \infty$.
  When $L$ grows rapidly to infinity, say $L>n^7$, this theorem follows from a
result of Gallagher. When $L$ is bounded, the analog of the theorem is open,
while the state-of-the-art is that the Galois group is large in the sense that
it contains the alternating group (if $L< 17$, it is conditional on the general
Riemann hypothesis). Hence the most interesting case of the theorem is when $L$
grows slowly to infinity.
  Our method works for more general independent coefficients.


  The beta-conjugates of a base of numeration $\beta > 1$, $\beta$ being a
Parry number, were introduced by Boyd, in the context of the R\'enyi-Parry
dynamics of numeration system and the beta-transformation. These
beta-conjugates are canonically associated with $\beta$. Let $\beta > 1$ be a
real algebraic number. A more general definition of the beta-conjugates of
$\beta$ is introduced in terms of the Parry Upper function $f_{\beta}(z)$ of
the beta-transformation. We introduce the concept of a germ of curve at
$(0,1/\beta) \in \mathbb{C}^{2}$ associated with $f_{\beta}(z)$ and the
reciprocal of the minimal polynomial of $\beta$. This germ is decomposed into
irreducible elements according to the theory of Puiseux, gathered into
conjugacy classes. The beta-conjugates of $\beta$, in terms of the Puiseux
expansions, are given a new equivalent definition in this new context. If
$\beta$ is a Parry number the (Artin-Mazur) dynamical zeta function
$\zeta_{\beta}(z)$ of the beta-transformation, simply related to
$f_{\beta}(z)$, is expressed as a product formula, under some assumptions, a
sort of analog to the Euler product of the Riemann zeta function, and the
factorization of the Parry polynomial of $\beta$ is deduced from the germ.


  We describe pairs (p,n) such that n-dimensional affine space is fibered by
pairwise skew p-dimensional affine subspaces. The problem is closely related
with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon
theory of composition of quadratic forms.


  Angle \theta_13 is one of the two unknown neutrino mixing parameters to be
determined. Its value may determine the future trend of the neutrino physics.
We propose to measure sin^22\theta_13 with a sensitivity better than 0.01 (90%
C.L) at the Daya Bay reactor power plant.


  We examine indivisibility for classes of graphs. We show that the class of
hereditarily $\alpha$-sparse graphs is indivisible if and only if $\alpha > 2$.
Additionally, we show that the following classes of graphs are indivisible:
perfect graphs, cographs, and chordal graphs, and the following classes of
graphs are not indivisible: threshold graphs, split graphs, and
distance-hereditary graphs.


  We present a complex data handling system for the COMPASS tokamak, operated
by IPP ASCR Prague, Czech Republic [1]. The system, called CDB (Compass
DataBase), integrates different data sources as an assortment of data
acquisition hardware and software from different vendors is used. Based on
widely available open source technologies wherever possible, CDB is vendor and
platform independent and it can be easily scaled and distributed. The data is
directly stored and retrieved using a standard NAS (Network Attached Storage),
hence independent of the particular technology; the description of the data
(the metadata) is recorded in a relational database. Database structure is
general and enables the inclusion of multi-dimensional data signals in multiple
revisions (no data is overwritten). This design is inherently distributed as
the work is off-loaded to the clients. Both NAS and database can be implemented
and optimized for fast local access as well as secure remote access. CDB is
implemented in Python language; bindings for Java, C/C++, IDL and Matlab are
provided. Independent data acquisitions systems as well as nodes managed by
FireSignal [2] are all integrated using CDB. An automated data post-processing
server is a part of CDB. Based on dependency rules, the server executes, in
parallel if possible, prescribed post-processing tasks.


  This thesis explores open-sourced machine learning (ML) model explanation
tools to understand whether these tools can allow a layman to visualize,
understand, and suggest intuitive remedies to unfairness in ML-based
decision-support systems. Machine learning models trained on datasets biased
against minority groups are increasingly used to guide life-altering social
decisions, prompting the urgent need to study their logic for unfairness. Due
to this problem's impact on vast populations of the general public, it is
critical for the layperson -- not just subject matter experts in social justice
or machine learning experts -- to understand the nature of unfairness within
these algorithms and the potential trade-offs. Existing research on fairness in
machine learning focuses mostly on the mathematical definitions and tools to
understand and remedy unfair models, with some directly citing user-interactive
tools as necessary for future work. This thesis presents FairLay-ML, a
proof-of-concept GUI integrating some of the most promising tools to provide
intuitive explanations for unfair logic in ML models by integrating existing
research tools (e.g. Local Interpretable Model-Agnostic Explanations) with
existing ML-focused GUI (e.g. Python Streamlit). We test FairLay-ML using
models of various accuracy and fairness generated by an unfairness detector
tool, Parfait-ML, and validate our results using Themis. Our study finds that
the technology stack used for FairLay-ML makes it easy to install and provides
real-time black-box explanations of pre-trained models to users. Furthermore,
the explanations provided translate to actionable remedies.


  Schizophrenic patients suffer from hallucination which its causality is not
yet fully understood. This paper attempts to approach this mystery from the
perspective of quantum mechanical theories. A novel approach has been adopted
to demonstrate the hallucination as a time evolution of percepts basis states
in the Hilbertian consciousness which are desynchronised from the time in real
world. The method also extends his approach to predict mind and brain
modulation through the correlation and coupling of consciousness and it reaches
a clinically hypothetical outcome of inducing consciousness into a brain which
is not conscious.


  Given a pattern x of length m and a text y of length n, both over an ordered
alphabet, the order-preserving pattern matching problem consists in finding all
substrings of the text with the same relative order as the pattern. It is an
approximate variant of the well known exact pattern matching problem which has
gained attention in recent years. This interesting problem finds applications
in a lot of fields as time series analysis, like share prices on stock markets,
weather data analysis or to musical melody matching. In this paper we present
two new filtering approaches which turn out to be much more effective in
practice than the previously presented methods. From our experimental results
it turns out that our proposed solutions are up to 2 times faster than the
previous solutions reducing the number of false positives up to 99%


  We propose a notion of continuous path for locally finite metric spaces,
taking inspiration from the recent development of A-theory for locally finite
connected graphs. We use this notion of continuity to derive an analogue in Z^2
of the Jordan curve theorem and to extend to a quite large class of locally
finite metric spaces (containing all finite metric spaces) an inequality for
the \ell^p-distortion of a metric space that has been recently proved by
Pierre-Nicolas Jolissaint and Alain Valette for finite connected graphs.


  It is proposed that a family of Jackiw-Teitelboim supergravites, recently
discussed in connection with matrix models by Stanford and Witten, can be given
a complete definition, to all orders in the topological expansion and beyond,
in terms of a specific combination of minimal string theories. This
construction defines non-perturbative physics for the supergravity that is
well-defined and stable. The minimal models come from double-scaled complex
matrix models and correspond to the cases $(2\Gamma{+}1,2)$ in the
Altland-Zirnbauer $(\boldsymbol{\alpha},\boldsymbol{\beta})$ classification of
random matrix ensembles, where $\Gamma$ is a parameter. A central role is
played by a non-linear `string equation' that naturally incorporates $\Gamma$,
usually taken to be an integer, counting e.g., D-branes in the minimal models.
Here, half-integer $\Gamma$ also has an interpretation. In fact,
$\Gamma{=}{\pm}\frac12$ yields the cases $(0,2)$ and $(2,2)$ that were shown by
Stanford and Witten to have very special properties. These features are
manifest in this definition because the relevant solutions of the string
equation have special properties for $\Gamma{=}{\pm}\frac12$. Additional
special features for other half-integer $\Gamma$ suggest new surprises in the
supergravity models.


  We review investigations of the electron-phonon interaction (EPI) in metal
diborides MeB_2 (Me=Zr, Nb, Ta, Mg) by point-contact (PC) spectroscopy. For
transition metal compounds the PC EPI functions were recovered and EPI
parameter $\lambda\lesssim 0.1$ were estimated. The data are consistent with
the measured surface phonon dispersion curves. The low $\lambda$ value
questions some reports about superconductivity in these compounds. Contrary,
EPI in superconducting MgB_2 films manifests also in the PC spectra itself by
virtue of an elastic EPI contribution to the excess current determined by the
energy dependence of the superconducting order parameter. To analyse the phonon
features in the PC spectra of MgB$_2$ a two-band model is exploited and the
proximity effect in the {\bf k}-space is suggested.


  We discuss the recent constraints on the nuclear equation of state from
pulsar mass measurements and from subthreshold production of kaons in heavy-ion
collisions. While recent pulsar data points towards a hard equation of state,
the analysis of the heavy-ion data allows only for soft equations of state. We
resolve the apparent contradiction by considering the different density regimes
probed. We argue that future measurements of global properties of low-mass
pulsars can serve as an excellent cross-check to heavy-ion data.


  A decade ago bit-string physics predicted that the baryon/photon ratio at the
time of nucleogenesis $\eta= 1/256^4$ and that the dark matter/baryonic matter
ratio $\Omega_{DM}/\Omega_B= 12.7$. Accepting that the normalized Hubble
constant is constrained observationally to lie in the range $0.6 < h_0 < 0.8$,
this translates into a prediction that $0.325 > \Omega_M > 0.183 $. This and a
prediction by E.D.Jones, using a model-independent argument and ideas with
which bit-string physics is not inconsistent, that the cosmological constant
$\Omega_{\Lambda}=0.6\pm 0.1$ are in reasonable agreement with recent
cosmological observations, including the BOOMERANG data.


  Social networks are the natural space for the spreading of information and
influence and have become a media themselves. Several models capturing that
diffusion process have been proposed, most of them based on the Independent
Cascade (IC) model or on the Linear Threshold (LT) model. The IC model is
probabilistic while the LT model relies on the knowledge of an actor to be
convinced, reflected in an associated individual threshold.
  Although the LT-based models contemplate an individual threshold for each
actor in the network, the existing studies so far have always considered a
threshold of 0.5 equal in all actors (i.e., a simple majority activation
criterion).
  Our main objective in this work is to start the study on how the
dissemination of information on networks behaves when we consider other options
for setting those thresholds and how many network actors end up being
influenced by this dissemination. For doing so, we consider a recently
introduced centrality measure based on the LT model, the Forward Linear
Threshold Rank (FLTR). We analyze experimentally the ranking properties for
several networks in which the influence resistance threshold follows different
schemes. Here we consider three different schemes: (1) uniform, in which all
players have the same value; (2) random, where each player is assigned a
threshold u.a.r. in a prescribed interval; and (3) determined by the value of
another centrality measure on the actor. Our results show that the selection
has a clear impact on the ranking, even quite significant and abrupt in some
cases. We conclude that the social networks ranks that provide the best
assignments for the individual thresholds are PageRank and FLTR.


  We consider an example of a system with two degrees of freedom admitting
separation of variables but having a subset of codimension 1 on which the
2-form defining the symplectic structure degenerates. We show how to use
separation of variables to calculate the exact topological invariant of
non-degenerate singularities and singularities appearing due to the symplectic
structure degeneration. New types of non-orientable 3-atoms are found.


  Let $G$ be a compact abelian group, let $\mu$ be the corresponding Haar
measure, and let $\hat G$ be the Pontryagin dual of $G$. Further, let $C_p$
denote the Schatten class of operators on some separable infinite dimensional
Hilbert space, and let $L^p(G;C_p)$ denote the corresponding Bochner space. If
$G\ni\theta\mapsto A_\theta$ is the mapping belonging to $L^p(G;C_p)$ then,
$$\sum_{k\in\hat
G}\left\|\int_G\overline{k(\theta)}A_\theta\,\mathrm{d}\theta\right\|_p^p\le\int_G\|A_\theta\|_p^p\,\mathrm{d}\theta,\qquad
p\ge2$$ $$\sum_{k\in\hat
G}\left\|\int_G\overline{k(\theta)}A_\theta\,\mathrm{d}\theta\right\|_p^p\le\left(\int_G\|A_\theta\|_p^q\,\mathrm{d}\theta\right)^{p/q},\qquad
p\ge2.$$ $$\sum_{k\in\hat
G}\left\|\int_G\overline{k(\theta)}A_\theta\,\mathrm{d}\theta\right\|_p^q\le\left(\int_G\|A_\theta\|_p^p\,\mathrm{d}\theta\right)^{q/p},\qquad
p\le2.$$
  If $G$ is a finite group, the previous comprises several earlier obtained
generalizations of Clarkson-McCarthy inequalities (e.g. $G=\mathbf{Z}_n$ or
$G=\mathbf{Z}_2^n$), as well as the original inequalities, for
$G=\mathbf{Z}_2$.
  Other related inequalities are also obtained.


  We analyze the coherent formation of molecular BEC from an atomic BEC, using
a parametric field theory approach. We point out the transition between a
quantum soliton regime, where atoms couple in a local way - to a classical
soliton domain, where a stable coupled-condensate soliton can form in three
dimensions. This gives the possibility of an intense, stable atom-laser output.


  Spectral line and continuum observations of the ionized and molecular gas in
G20.08-0.14 N explore the dynamics of accretion over a range of spatial scales
in this massive star-forming region. Very Large Array observations of NH_3 at
4'' angular resolution show a large-scale (0.5 pc) molecular accretion flow
around and into a star cluster with three small, bright HII regions. Higher
resolution (0.4'') observations with the Submillimeter Array in hot core
molecules (CH_3CN, OCS, and SO_2) and the VLA in NH_3, show that the two
brightest and smallest HII regions are themselves surrounded by smaller scale
(0.05 pc) accretion flows. The axes of rotation of the large- and small-scale
flows are aligned, and the timescale for the contraction of the cloud is short
enough, 0.1 Myr, for the large-scale accretion flow to deliver significant mass
to the smaller scales within the star formation timescale. The flow structure
appears to be continuous and hierarchical from larger to smaller scales.
  Millimeter radio recombination line (RRL) observations at 0.4" angular
resolution indicate rotation and outflow of the ionized gas within the
brightest HII region (A). The broad recombination lines and a continuum
spectral energy distribution (SED) that rises continuously from cm to mm
wavelengths, are both characteristic of the class of HII regions known as
"broad recombination line objects". The SED indicates a density gradient inside
this HII region, and the RRLs suggest supersonic flows. These observations are
consistent with photoevaporation of the inner part of the rotationally
flattened molecular accretion flow.
  We also report the serendipitous detection of a new NH_3 (3,3) maser.


  Based on a series of lattice calculations we determine the ratio FK/Fpi in
QCD. With experimental data from kaon decay and nuclear double beta decay, we
obtain a precise determination of |Vus|. Our simulation includes 2+1 flavours
of sea quarks, with three lattice spacings, large volumes and a simulated pion
mass reaching down to about 190 MeV for a full control over the systematic
uncertainties.


  In this study we consider relations between companies in Poland taking into
account common branches they belong to. It is clear that companies belonging to
the same branch compete for similar customers, so the market induces
correlations between them. On the other hand two branches can be related by
companies acting in both of them. To remove weak, accidental links we shall use
a concept of threshold filtering for weighted networks where a link weight
corresponds to a number of existing connections (common companies or branches)
between a pair of nodes.


  Online meta-learning has recently emerged as a marriage between batch
meta-learning and online learning, for achieving the capability of quick
adaptation on new tasks in a lifelong manner. However, most existing approaches
focus on the restrictive setting where the distribution of the online tasks
remains fixed with known task boundaries. In this work, we relax these
assumptions and propose a novel algorithm for task-agnostic online
meta-learning in non-stationary environments. More specifically, we first
propose two simple but effective detection mechanisms of task switches and
distribution shift based on empirical observations, which serve as a key
building block for more elegant online model updates in our algorithm: the task
switch detection mechanism allows reusing of the best model available for the
current task at hand, and the distribution shift detection mechanism
differentiates the meta model update in order to preserve the knowledge for
in-distribution tasks and quickly learn the new knowledge for
out-of-distribution tasks. In particular, our online meta model updates are
based only on the current data, which eliminates the need of storing previous
data as required in most existing methods. We further show that a sublinear
task-averaged regret can be achieved for our algorithm under mild conditions.
Empirical studies on three different benchmarks clearly demonstrate the
significant advantage of our algorithm over related baseline approaches.


  In this work we give a few new Strichartz estimates of radial solutions to
the wave equation. These Strichartz estimates still use $L^p L^q$ type norms in
each channel-like region $\{(x,t): |t|+2^k < |x| < |t|+2^{k+1}\}$, with weaker
restrictions on $p, q$ than the classic ones, but combine these localized norms
together in the way of an $l^2$ space. We also give an application of these
Strichartz estimates on the well-posedness theory of non-linear wave equations.


  A brain-computer interface (BCI) based on the motor imagery (MI) paradigm
translates one's motor intention into a control signal by classifying the
Electroencephalogram (EEG) signal of different tasks. However, most existing
systems either (i) use a high-quality algorithm to train the data off-line and
run only classification in real-time, since the off-line algorithm is too slow,
or (ii) use low-quality heuristics that are sufficiently fast for real-time
training but introduces relatively large classification error. In this work, we
propose a novel processing pipeline that allows real-time and parallel learning
of EEG signals using high-quality but possibly inefficient algorithms. This is
done by forging a link between BCI and core-sets, a technique that originated
in computational geometry for handling streaming data via data summarization.
  We suggest an algorithm that maintains the representation such coreset
tailored to handle the EEG signal which enables: (i) real time and continuous
computation of the Common Spatial Pattern (CSP) feature extraction method on a
coreset representation of the signal (instead on the signal itself) , (ii)
improvement of the CSP algorithm efficiency with provable guarantees by
applying CSP algorithm on the coreset, and (iii) real time addition of the data
trials (EEG data windows) to the coreset.
  For simplicity, we focus on the CSP algorithm, which is a classic algorithm.
Nevertheless, we expect that our coreset will be extended to other algorithms
in future papers. In the experimental results we show that our system can
indeed learn EEG signals in real-time for example a 64 channels setup with
hundreds of time samples per second. Full open source is provided to reproduce
the experiment and in the hope that it will be used and extended to more
coresets and BCI applications in the future.


  Broad Absorption Line Regions - BALR are composed of a number of successive
independent absorbing density layers. Using the GR model, we analyze the UV Si
IV ({\lambda}{\lambda}1393.755 - 1402.770), O IV ({\lambda}1401.156) and C IV
({\lambda}{\lambda}1548.187 - 1550.772) resonance lines in the spectra of a
certain QSO and discuss the results concerning its kinematic properties
(rotational, radial and random velocities).


  We present a sufficient condition of the complete position flocking theorem
for the Cucker-Smale type model on the unit sphere with an inter-particle
bonding force. For this second order dynamical system derived in [Choi, S.-H.,
Kwon, D. and Seo, H.: Cucker-Smale type flocking models on a sphere. arXiv
preprint arXiv:2010.10693, 2020] by using the rotation operator in three
dimensional sphere, we obtain an exponential decay estimate for the diameter of
agents' positions as well as time-asymptotic flocking for a class of initial
data. The sufficient condition for the initial data depends only on the
communication rate and inter-particle bonding parameter but not the number of
agents. The lack of momentum conservation and the curved space domain make it
difficult to apply the standard methodology used in the original Cucker-Smale
model. To overcome this and obtain a uniform position alignment estimate, we
use an energy dissipation property of this system and transform the
Cucker-Smale type flocking model into an inhomogeneous system of differential
equations of which solution contains the position and velocity diameters. The
coefficients of the transformed system are controlled by the communication rate
and a uniform upper bound of velocities obtained by the energy dissipation.


  Our current understanding of the core-collapse supernova explosion mechanism
is incomplete, with multiple viable models for how the initial shock wave might
be energized enough to lead to a successful explosion. Detection of a
gravitational-wave signal emitted in the initial few seconds after stellar
core-collapse would provide unique and crucial insight into this process. With
the Advanced LIGO and Advanced Virgo detectors expected to approach their
design sensitivities soon, we could potentially detect this signal from a
supernova within our galaxy. In anticipation of such a scenario, we study how
well the BayesWave algorithm can recover the gravitational-wave signal from
core-collapse supernova models in simulated advanced detector noise, and
optimize its ability to accurately reconstruct the signal waveforms. We find
that BayesWave can confidently reconstruct the signal from a range of supernova
explosion models in Advanced LIGO-Virgo for network signal-to-noise ratios
$\gtrsim 30$, reaching maximum reconstruction accuracies of $\sim 90\%$ at SNR
$\sim 100$. For low SNR signals that are not confidently recovered, our
optimization efforts result in gains in reconstruction accuracy of up to
$20-40\%$, with typical gains of $\sim 10\%$.


  A wide range of geophysical methods is used for the exploration of deep
geothermal resources. It aimsat characterizing the deep fractured network and
its capacity for fluid/heat extraction. This relieshowever on the capacity of
geophysical techniques to 1) image the geometry of the fractured networkbut
also 2) characterize the petro-physical properties of the fracture network and
matrix. The challengeis however that the geophysical inverse problem is
ill-posed and multi-scale.To overcome these challenges, we propose here to take
a multi-physics and multi-scale approach of thegeophysical/petro-physical
inverse problem. To do so, we are developing iteratively petro-physical
andgeophysical models that can explain the observables at the different scales.
In this paper, we report outthe results of the first iteration phase of this
research project that consists in building an initial petrophysical model from
well logs and prior geological knowledge, and single-domain inversion
ofgeophysical data. We applied this methodology to the Upper Rhine Graben where
a wealth ofknowledge and dataset on deep fractured formations are available.


  Let $f : X \to S$ be a family of smooth projective algebraic varieties over a
smooth connected quasi-projective base $S$, and let $\mathbb{V} = R^{2k} f_{*}
\mathbb{Z}(k)$ be the integral variation of Hodge structure coming from degree
$2k$ cohomology it induces. Associated to $\mathbb{V}$ one has the so-called
Hodge locus $\textrm{HL}(S) \subset S$, which is a countable union of "special"
algebraic subvarieties of $S$ parametrizing those fibres of $\mathbb{V}$
possessing extra Hodge tensors (and so conjecturally, those fibres of $f$
possessing extra algebraic cycles). The special subvarieties belong to a larger
class of so-called weakly special subvarieties, which are subvarieties of $S$
maximal for their algebraic monodromy groups. For each positive integer $d$, we
give an algorithm to compute the set of all weakly special subvarieties $Z
\subset S$ of degree at most $d$ (with the degree taken relative to a choice of
projective compactification $S \subset \overline{S}$ and very ample line bundle
$\mathcal{L}$ on $\overline{S}$). As a corollary of our algorithm we prove
conjectures of Daw-Ren and Daw-Javanpeykar-K\"uhne on the finiteness of sets of
special and weakly special subvarieties of bounded degree.


  A sequence of earthquakes occurred between the end of August 2016 and the end
of October 2016 in Central Italy causing significant damage and major
disruption in a wide area. The sequence of events is composed of five events
with magnitude between Mw 5.5 to 6.5. As a consequence, numerous residential
buildings in the affected area was not particularly resistant to the shaking,
resulting in the collapse and heavy damage. With a particular focus on masonry
infilled steel frames, this paper evaluates the seismic performance of an
infilled moment-resisting steel frame located in Amatrice, Central Italy, which
suffered significant damage during the August 2016 Central Italy earthquake.
The aim is to investigate the effect of the masonry infill to the seismic
performance of the building. The three-dimensional (3D) frame building is
modeled using the Opensees software, where the beam and column elements are
modeled by using a nonlinear hinge model and the infill is idealized as
diagonal struts with nonlinear hysteretic behavior. Nonlinear static and
dynamic analyses are performed for both bare and infill frames in order to
assess the effect of the masonry infill on the overall seismic response and
confirm the actual damage pattern surveyed in the aftermath of the 2016 Central
Italy earthquake of the case study.


  Echo State Networks (ESNs) are known for their fast and precise one-shot
learning of time series. But they often need good hyper-parameter tuning for
best performance. For this good validation is key, but usually, a single
validation split is used. In this rather practical contribution we suggest
several schemes for cross-validating ESNs and introduce an efficient algorithm
for implementing them. The component that dominates the time complexity of the
already quite fast ESN training remains constant (does not scale up with $k$)
in our proposed method of doing $k$-fold cross-validation. The component that
does scale linearly with $k$ starts dominating only in some not very common
situations. Thus in many situations $k$-fold cross-validation of ESNs can be
done for virtually the same time complexity as a simple single split
validation. Space complexity can also remain the same. We also discuss when the
proposed validation schemes for ESNs could be beneficial and empirically
investigate them on several different real-world datasets.


  We discuss local Sasakian immersion of Sasaki-Ricci solitons (SRS) into fiber
products of homogeneous Sasakian manifolds. In particular, we prove that SRS
locally induced by a large class of fiber products of homogeneous Sasakian
manifolds are, in fact, $\eta$-Einstein. The results are stronger for
immersions into Sasakian space forms. Moreover, we show an example of a
K\"ahler-Ricci soliton on $\mathbb C^n$ which admits no local holomorphic
isometry into products of homogeneous bounded domains with flat K\"ahler
manifolds and generalized flag manifolds.


  Spin reversal in magnetic nanomolecules and nanoclusters is considered. A
method is suggested allowing, from one side, to keep for long time magnetic
polarization in a metastable state and, from the other side, for starting the
reversal process at any required time. This method can find applications for
the operation of storage memory devices and for the regulation of processes in
spintronics.


  The role of heterogeneity in the plastic flow of thin ferrite specimens is
investigated in this study. This is done through a recently introduced quasi-2D
experimental-numerical framework that allows for a quantitative comparison of
the deformation fields of metal microstructures between experiments and
simulations at a high level of detail and complexity. The method exploits
samples that are locally ultra-thin ("2D") and hence have a practically uniform
microstructure through their thickness. This allows testing more complex
loading conditions compared to uniaxial micromechanical experiments while
avoiding the complexity of an unknown subsurface microstructure, which limits
comparisons between experiments and simulations in traditional integrated
approaches at the level of the polycrystalline microstructure. The present
approach enables to study the effect of microstructural features such as grain
boundaries. To study the role of stochastic fluctuations, a constitutive model
is employed which introduces random heterogeneity into a crystal plasticity
model. A detailed analysis of the simulations is performed at the level of
individual slip systems. Since both experimental and numerical results are
susceptible to stochastic fluctuations, the outcomes of many simulations are
compared to the experimentally obtained result. This comparison allows us to
determine how a single experiment relates to an ensemble of simulations.
Additionally, results obtained with a conventional crystal plasticity model are
considered. The analysis reveals that the heterogeneity in the plasticity model
is essential for accurately capturing the deformation mechanisms.


  A profound manifestation of topologically non-trivial states of matter is the
occurrence of fractionally charged elementary excitations. The quantum spin
Hall insulator state is a fundamentally novel quantum state of matter that
exists at zero external magnetic field. In this work, we show that a magnetic
domain wall at the edge of the quantum spin Hall insulator carries one half of
the unit of electron charge, and we propose an experiment to directly measure
this fractional charge on an individual basis. We also show that as an
additional consequence, a rotating magnetic field can induce a quantized dc
electric current, and vice versa.


  We propose a spectral viscosity method (SVM) to approximate the
incompressible Euler equations driven by a multiplicative noise. We show that
SVM solution converges to a dissipative measure-valued martingale solution.
These solutions are weak in the probabilistic sense i.e. the probability space
and the driving Wiener process are an integral part of the solution. We also
exhibit weak (measure-valued)-strong uniqueness principle. Moreover, we
establish strong convergence of approximate solutions to the regular solution
of the limit system at least on the lifespan of the latter, thanks to the weak
(measure-valued)--strong uniqueness principle for the underlying system.


  The initial and boundary conditions of the Galactic star formation in
molecular clouds are not well understood. In an effort to shed new light on
this long-standing problem, we measured properties of dense cores and
filamentary structures in the Vela C molecular cloud, observed with Herschel.
We applied the getsf extraction method to separate the components of sources
and filaments from each other and their backgrounds, before detecting,
measuring, and cataloging the structures. The cores and filamentary structures
constitute 40% of the total mass of Vela C, most of the material is in the
low-density molecular background cloud. We selected 570 reliable cores, of
which 149 are the protostellar cores and 421 are the starless cores. Almost 78%
of the starless cores were identified with the gravitationally bound prestellar
cores. The exponent of the CMF (alpha = 1.35) is identical to that of the
Salpeter IMF. We selected 68 filaments with at least one side that appeared not
blended with adjacent structures. The filament widths are in the range of 0.15
pc to 0.63 pc, and have a median value of W = 0.3(0.11) pc. The surface
densities of filaments are well correlated with their contrasts and linear
densities. Within uncertainties of the filament instability criterion, many
filaments may well be both supercritical and subcritical. A large fraction of
filaments may definitely be considered supercritical, in which are found 94
prestellar cores, 83 protostellar cores, and only 1 unbound starless core.
Taking into account the uncertainties, the supercritical filaments contain only
prestellar and protostellar cores. Our findings support the idea that there
exists a direct relationship between the CMF and IMF and that filaments play a
key role in the formation of prestellar cores, which is consistent with the
previous Herschel results.


  A fluid droplet may exhibit self-propelled motion by modifying the wetting
properties of the substrate. We propose a novel model for droplet propagation
upon a terraced landscape of ordered layers formed as a result of surface
freezing driven by the contact angle dependence on the terrace thickness.
Simultaneous melting or freezing of the terrace edge results in a joint
droplet-terrace motion. The model is tested numerically and compared to
experimental observations on long-chain alkane system in the vicinity of the
surface melting point.


  The aim of these notes is to provide a self-contained review of why it is
generically a problem when a solution of a theory possesses ghost fields among
the perturbation modes. We define what a ghost field is and we show that its
presence is associated to a classical instability whenever the ghost field
interacts with standard fields. We then show that the instability is more
severe at quantum level, and that perturbative ghosts can exist only in low
energy effective theories. However, if we don't consider very ad-hoc choices,
compatibility with observational constraints implies that low energy effective
ghosts can exist only at the price of giving up Lorentz-invariance or locality
above the cut-off, in which case the cut-off has to be much lower that the
energy scales we currently probe in particle colliders. We also comment on the
possible role of extra degrees of freedom which break Lorentz-invariance
spontaneously.


  We give an example of a convex body whose centroid and Santal\'o point are
"far apart".


  Recent works investigated the generalization properties in deep neural
networks (DNNs) by studying the Information Bottleneck in DNNs. However, the
mea- surement of the mutual information (MI) is often inaccurate due to the
density estimation. To address this issue, we propose to measure the dependency
instead of MI between layers in DNNs. Specifically, we propose to use
Hilbert-Schmidt Independence Criterion (HSIC) as the dependency measure, which
can measure the dependence of two random variables without estimating
probability densities. Moreover, HSIC is a special case of the Squared-loss
Mutual Information (SMI). In the experiment, we empirically evaluate the
generalization property using HSIC in both the reconstruction and prediction
auto-encoding (AE) architectures.


  A Basarab-Kuhlmann style language L_RV is introduced in the
Hrushovski-Kazhdan integration theory. The theory ACVF of algebraically closed
valued fields formulated in this language admits quantifier elimination. In
this paper, using well-known facts in the theory of valued fields, we give a
straightforward proof of this fact. We also show that two expansions of ACVF,
one with a section of the entire RV-sort and the other with a section of the
residue field, admit quantifier elimination. Thereafter we show that, in terms
of certain minimality conditions, the three theories are distinct
geometrically.


  Potential effects of sublimation of water ice from very slowly moving
millimeter-sized and larger grains, a product of activity at ~10 AU or farther
from the Sun driven presumably by annealing of amorphous water ice, are
investigated by comparing 2I/Borisov with a nominal Oort Cloud comet of equal
perihelion distance of 2 AU. This comparison suggests that the strongly
hyperbolic motion of 2I mitigates the integrated sublimation effect. The
population of these grains near the nucleus of 2I is likely to have been
responsible for the comet appearing excessively bright in pre-discovery images
at 5-6 AU from the Sun, when the sublimation rate was exceedingly low, as well
as for the prominent nuclear condensation more recently. All grains smaller
then 2-3 cm across had been devolatilized by mid-October 2019 and some
subjected to rapid disintegration. This left only larger chunks of the initial
icy-dust halo contributing to the comet's suspected hyperactivity. Sublimation
of water ice from the nucleus has been increasing since the time of discovery,
but the rate has not been high enough to exert a measurable nongravitational
acceleration on the orbital motion of 2I/Borisov.


  Aperture synthesis observations of CO(J=1-0) emission and near-infrared
broad-band photometry of the non-barred Seyfert galaxy NGC 5033 (D = 18.7 Mpc)
were performed. Our 3".9 x 3".6 resolution CO observations reveal a perturbed
distribution and the kinematics of molecular gas in the center of NGC 5033; we
find the characteristic gaseous features that are widely observed in barred
spiral galaxies, such as two bright CO peaks near the center (separated by ~
3'' or 270 pc from the nucleus), two offset ridges of CO emission emanating
from the CO peaks, and a CO ring (with a radius of ~ 14'' or 1.3 kpc).
Double-peaked velocity profiles are also evident near the two CO peaks,
implying that these CO peaks are orbit crowding zones in a barred/oval
potential. Although NIR data only give an upper limit of the possible bar
lengths, due to a large inclination of the NGC 5033 disk (i = 68 deg), our CO
data clearly suggests the presence of a small (the semi-major axis of about
12'' - 15'' or 1.1 - 1.4 kpc) nuclear bar (or oval structure) in the center of
the ``non-barred'' galaxy NGC 5033. Our results demonstrate that
high-resolution CO imaging-spectroscopy is useful to search for nuclear bars,
even in highly inclined systems where isophoto fitting techniques are not
applicable. We find that the gas mass-to-dynamical mass ratio, M_gas/M_dyn, is
small (< 1%) within a radius of 2'' or 180 pc, in contrast to starburst nuclei.
This implies that the starburst does not cohabitate in the type-1.5 Seyfert
nucleus of N GC 5033.


  In this paper, we compute the number of covers of curves with given branch
behavior in characteristic p for one class of examples with four branch points
and degree p. Our techniques involve related computations in the case of three
branch points, and allow us to conclude in many cases that for a particular
choice of degeneration, all the covers we consider degenerate to separable
(admissible) covers. Starting from a good understanding of the complex case,
the proof is centered on the theory of stable reduction of Galois covers.


  We study the chaotic dynamics of graphene structures, considering both a
periodic, defect free, graphene sheet and graphene nanoribbons (GNRs) of
various widths. By numerically calculating the maximum Lyapunov exponent, we
quantify the chaoticity for a spectrum of energies in both systems. We find
that for all cases, the chaotic strength increases with the energy density, and
that the onset of chaos in graphene is slow, becoming evident after more than
$10^4$ natural oscillations of the system. For the GNRs, we also investigate
the impact of the width and chirality (armchair or zigzag edges) on their
chaotic behavior. Our results suggest that due to the free edges the chaoticity
of GNRs is stronger than the periodic graphene sheet, and decreases by
increasing width, tending asymptotically to the bulk value. In addition, the
chaotic strength of armchair GNRs is higher than a zigzag ribbon of the same
width. Further, we show that the composition of ${}^{12}C$ and ${}^{13}C$
carbon isotopes in graphene has a minor impact on its chaotic strength.


  We employ machine learning techniques to investigate the volume minimum of
Sasaki-Einstein base manifolds of non-compact toric Calabi-Yau 3-folds. We find
that the minimum volume can be approximated via a second order multiple linear
regression on standard topological quantities obtained from the corresponding
toric diagram. The approximation improves further after invoking a
convolutional neural network with the full toric diagram of the Calabi-Yau
3-folds as the input. We are thereby able to circumvent any minimization
procedure that was previously necessary and find an explicit mapping between
the minimum volume and the topological quantities of the toric diagram. Under
the AdS/CFT correspondence, the minimum volumes of Sasaki-Einstein manifolds
correspond to central charges of a class of 4d N=1 superconformal field
theories. We therefore find empirical evidence for a function that gives values
of central charges without the usual extremization procedure.


  With the continuous increase of internet usage in todays time, everyone is
influenced by this source of the power of technology. Due to this, the rise of
applications and games Is unstoppable. A major percentage of our population
uses these applications for multiple purposes. These range from education,
communication, news, entertainment, and many more. Out of this, the application
that is making sure that the world stays in touch with each other and with
current affairs is social media. Social media applications have seen a boom in
the last 10 years with the introduction of smartphones and the internet being
available at affordable prices. Applications like Twitch and Youtube are some
of the best platforms for producing content and expressing their talent as
well. It is the goal of every content creator to post the best and most
reliable content so that they can gain recognition. It is important to know the
methods of achieving popularity easily, which is what this paper proposes to
bring to the spotlight. There should be certain parameters based on which the
reach of content could be multiplied by a good factor. The proposed research
work aims to identify and estimate the reach, popularity, and views of a
YouTube video by using certain features using machine learning and AI
techniques. A ranking system would also be used keeping the trending videos in
consideration. This would eventually help the content creator know how
authentic their content is and healthy competition to make better content
before uploading the video on the platform will be ensured.


  We consider the smooth inverse mean curvature flow of strictly convex
hypersurfaces with boundary embedded in $\mathbb{R}^{n+1},$ which are
perpendicular to the unit sphere from the inside. We prove that the flow
hypersurfaces converge to the embedding of a flat disk in the norm of
$C^{1,\beta},$ $\beta<1.$


  We analyze the behavior of the Euclidean algorithm applied to pairs (g,f) of
univariate nonconstant polynomials over a finite field F_q of q elements when
the highest-degree polynomial g is fixed. Considering all the elements f of
fixed degree, we establish asymptotically optimal bounds in terms of q for the
number of elements f which are relatively prime with g and for the average
degree of gcd(g,f). The accuracy of our estimates is confirmed by practical
experiments. We also exhibit asymptotically optimal bounds for the average-case
complexity of the Euclidean algorithm applied to pairs (g,f) as above.


  Blockchain stores information into a chain of "blocks", whose integrity is
usually guaranteed by Proof of Work (PoW). In many blockchain applications
(including cryptocurrencies), users compete with each other to win the
ownership of the blocks, a process commonly referred as "mining". Mining
activities consume huge amount of power, while the outcome appears to be
useless besides validating a block. Here we discuss the requirements of
designing a new PoW algorithm. We also propose a PoW scheme to help solve
high-dimension, non-linear optimization problems. Simulation experiments of
blockchains generated by three miners solved an instance of Traveling Salesman
Problem (TSP), a well-known NP-hard problem. The revised scheme enables us to
address difficult scientific questions as a byproduct of mining.


  We show for every prime $p$ that there exists a Camina pair $(G,N)$ where $N$
is a $p$-group and $G$ is not $p$-closed.


  Many-particle quantum systems with intermediate anyonic exchange statistics
are supported in one spatial dimension. In this context, the anyon-anyon
mapping is recast as a continuous transformation that generates shifts of the
statistical parameter $\kappa$. We characterize the geometry of quantum states
associated with different values of $\kappa$, i.e., different quantum
statistics. While states in the bosonic and fermionic subspaces are always
orthogonal, overlaps between anyonic states are generally finite and exhibit a
universal form of the orthogonality catastrophe governed by a fundamental
statistical factor, independent of the microscopic Hamiltonian. We characterize
this decay using quantum speed limits on the flow of $\kappa$, illustrate our
results with a model of hard-core anyons, and discuss possible experiments in
quantum simulation.


  Dirac's quantization of the Maxwell theory on non-commutative spaces has been
considered. First class constraints were found which are the same as in
classical electrodynamics. The gauge covariant quantization of the non-linear
equations of electromagnetic fields on non-commutative spaces were studied. We
have found the extended Hamiltonian which leads to equations of motion in the
most general gauge covariant form. As a special case, the gauge fixing approach
on the basis of Dirac's brackets has been investigated. The problem of the
construction of the wave function and physical observables have been discussed.


  Harmonicity of holomorphic maps between various subclasses of almost contact
metric manifolds is discussed. Consequently, some new results are obtained.
Also some known results are recovered, some of them are generalized and some of
them are corrected.


  The Change detection based on analysis and samples are analyzed. Land
use/cover change detection based on SDM is discussed.


  In recent years, several authors have used probabilistic graphical models to
learn expression modules and their regulatory programs from gene expression
data. Here, we demonstrate the use of the synthetic data generator SynTReN for
the purpose of testing and comparing module network learning algorithms. We
introduce a software package for learning module networks, called LeMoNe, which
incorporates a novel strategy for learning regulatory programs. Novelties
include the use of a bottom-up Bayesian hierarchical clustering to construct
the regulatory programs, and the use of a conditional entropy measure to assign
regulators to the regulation program nodes. Using SynTReN data, we test the
performance of LeMoNe in a completely controlled situation and assess the
effect of the methodological changes we made with respect to an existing
software package, namely Genomica. Additionally, we assess the effect of
various parameters, such as the size of the data set and the amount of noise,
on the inference performance. Overall, application of Genomica and LeMoNe to
simulated data sets gave comparable results. However, LeMoNe offers some
advantages, one of them being that the learning process is considerably faster
for larger data sets. Additionally, we show that the location of the regulators
in the LeMoNe regulation programs and their conditional entropy may be used to
prioritize regulators for functional validation, and that the combination of
the bottom-up clustering strategy with the conditional entropy-based assignment
of regulators improves the handling of missing or hidden regulators.


  This study aims to review and get information on the different mobile game
applications and the possibility of being a supplementary tool for learning to
enhance and empower the e-Learning aspect of a Technical Education and Skills
Development Authority. It is reviewed to help in the development of the
eLearning department of TESDA. The study aims to facilitate the reorganization
of the E-learning program of TESDA by using a method called Game Based
Learning. To accomplish this target, different applications will be reviewed to
give an idea on how game-based learning is being used as a supplementary
learning tool for different subject areas. This paper will focus on TESDA
language Skills institute and Technical-Vocational program since there are a
lot of reviews for main subject areas but only few in this field. The database
to be used in the methodology is Google Scholar, inclusion and exclusion
criteria used is that article should be within the span of five years and
should be game based learning mobile applications. Will be selecting 4
applications as a representation since it is an informational review. No need
to indicate the other applications as this is just a basis for future studies.
Mobile games have such a powerful instructional potential, by which teaching
can be revolutionized, which output is acquiring the praise and judgment of
academic professionals and educators. After this review, future studies can be
made to support this study like reviewing from other databases like Web of
Science and Scopus to support the foundation made on this review. The review
will open further studies to help TESDA administrator in using mobile games as
a supplementary learning tool for their e-learning.


  One way to analyse the behaviour of machine learning models is through local
explanations that highlight input features that maximally influence model
predictions. Sensitivity analysis, which involves analysing the effect of input
perturbations on model predictions, is one of the methods to generate local
explanations. Meaningful input perturbations are essential for generating
reliable explanations, but there exists limited work on what such perturbations
are and how to perform them. This work investigates these questions in the
context of machine listening models that analyse audio. Specifically, we use a
state-of-the-art deep singing voice detection (SVD) model to analyse whether
explanations from SoundLIME (a local explanation method) are sensitive to how
the method perturbs model inputs. The results demonstrate that SoundLIME
explanations are sensitive to the content in the occluded input regions. We
further propose and demonstrate a novel method for quantitatively identifying
suitable content type(s) for reliably occluding inputs of machine listening
models. The results for the SVD model suggest that the average magnitude of
input mel-spectrogram bins is the most suitable content type for temporal
explanations.


  We have studied the dissipative dynamics of a driven electronic spin trapped
in a quantum dot. We consider the dissipative mechanism as due to the indirect
coupling of the electronic spin to acoustic phonons via the
spin-orbit/electron-phonon couplings. Using an effective spectral function of
the dissipative phonon bath, we evaluated the expectation values of the spin
components through the Bloch-Redfield theory. We show that due to a sharp bath
resonance present in the effective spectral function, with typical energy much
smaller than the electronic confinement energy, the dissipative spin has a rich
dynamical behavior that helps us to determine some features of the spin-bath
coupling. We also quantify the effects produced by the sharp bath resonance,
and thus indicate the best regimes of operation in order to achieve the longest
relaxation times for the spin.


  WWe define the notion of a random metric space and prove that with
probability one such a space is isometricto the Urysohn universal metric space.
The main technique is the study of universal and random distance matrices; we
relate the properties of metric (in particulary universal) space to the
properties of distance matrices. We show the link between those questions and
classification of the Polish spaces with measure (Gromov or metric triples) and
with the problem about S_{\infty}-invariant measures in the space of symmetric
matrices. One of the new effects -exsitence in Urysohn space so called
anarchical uniformly distributed sequences. We give examples of other
categories in which the randomness and universality coincide (graph, etc.).


  This paper proposes a novel non-intrusive system failure prediction technique
using available information from developers and minimal information from raw
logs (rather than mining entire logs) but keeping the data entirely private
with the data owners. A neural network based multi-class classifier is
developed for failure prediction, using artificially generated anonymous data
set, applying a combination of techniques, viz., genetic algorithm (steps),
pattern repetition, etc., to train and test the network. The proposed mechanism
completely decouples the data set used for training process from the actual
data which is kept private. Moreover, multi-criteria decision making (MCDM)
schemes are used to prioritize failures meeting business requirements. Results
show high accuracy in failure prediction under different parameter
configurations. On a broader context, any classification problem, beyond
failure prediction, can be performed using the proposed mechanism with
artificially generated data set without looking into the actual data as long as
the input features can be translated to binary values (e.g. output from private
binary classifiers) and can provide classification-as-a-service.


  We discuss a relation between the
  QCD thermodynamics obtained from a statistical analysis of particle
production in heavy ion collisions at SPS and RHIC energies and recent LGT
results at finite chemical potential. We show that basic thermodynamic
properties obtained from the phenomenological statistical operator of a hadron
resonance gas that describes particle yields in heavy ion collisions are
consistent with recent LGT results. We argue that for $T\leq T_c$ the equation
of state derived from
  Monte--Carlo simulations of two quark--flavor QCD at finite chemical
potential can be well described by a hadron resonance gas when using the same
set of approximations as used in LGT calculations. We examine the influence of
a finite quark mass on the position of the deconfinement transition in
temperature and chemical potential plane.


  We compare estimates of atmospheric precipitation during the Martian
Noachian-Hesperian boundary 3.8 Gyr ago as calculated in a radiative-convective
column model of the atmosphere with runoff values estimated from a
geomorphological analysis of dendritic valley network discharge rates. In the
atmospheric model, we assume CO2-H2O-N2 atmospheres with surface pressures
varying from 20 mb to 3 bar with input solar luminosity reduced to 75% the
modern value.
  Results from the valley network analysis are of the order of a few mm d-1
liquid water precipitation (1.5-10.6 mm d-1, with a median of 3.1 mm d-1).
Atmospheric model results are much lower, from about 0.001-1 mm d-1 of snowfall
(depending on CO2 partial pressure). Hence, the atmospheric model predicts a
significantly lower amount of precipitated water than estimated from the
geomorphological analysis. Furthermore, global mean surface temperatures are
below freezing, i.e. runoff is most likely not directly linked to
precipitation. Therefore, our results strongly favor a cold early Mars with
episodic snowmelt as a source for runoff.
  Our approach is challenged by mostly unconstrained parameters, e.g.
greenhouse gas abundance, global meteorology (for example, clouds) and
planetary parameters such as obliquity- which affect the atmospheric result -
as as well as by inherent problems in estimating discharge and runoff on
ancient Mars, such as a lack of knowledge on infiltration and evaporation rates
and on flooding timescales, which affect the geomorphological data.
Nevertheless, our work represents a first step in combining and interpreting
quantitative tools applied in early Mars atmospheric and geomorphological
studies.


  In this paper we present results on convergence and Ces\`{a}ro summability of
Multiple Fourier series of functions of bounded generalized variation.


  We report on the construction, operation experience, and preliminary
background measurements of an InGrid detector, i.e. a MicroMegas detector with
CMOS pixel readout. The detector was mounted in the focal plane of the Abrixas
X-Ray telescope at the CAST experiment at CERN. The detector is sensitive to
soft X-Rays in a broad energy range (0.3--10 keV) and thus enables the search
for solar chameleons. Smooth detector operation during CAST data taking in
autumn 2014 has been achieved. Preliminary analysis of background data
indicates a background rate of $1-5\times
10^{-5}\,\mathrm{keV}^{-1}\mathrm{cm}^{-2}\mathrm{s}^{-1}$ above 2 keV and
$\sim 3\times 10^{-4}\,\mathrm{keV}^{-1}\mathrm{cm}^{-2}\mathrm{s}^{-1}$ around
1 keV. An expected limit of $\beta_\gamma \lesssim 5\times 10^{10}$ on the
chameleon photon coupling is estimated in case of absence of an excess in solar
tracking data. We also discuss the prospects for future operation of the
detector.


  A fundamental hypothesis for the interpretation of the measured large-scale
line-of-sight peculiar velocities of galaxies is that the large-scale cosmic
flows are irrotational. In order to assess the validity of this assumption, we
estimate, within the frame of the gravitational instability scenario, the
amount of vorticity generated after the first shell crossings in large-scale
caustics. In the Zel'dovich approximation the first emerging singularities form
sheet like structures. Here we compute the expectation profile of an initial
overdensity under the constraint that it goes through its first shell crossing
at the present time. We find that this profile corresponds to rather oblate
structures in Lagrangian space. Assuming the Zel'dovich approximation is still
adequate not only at the first stages of the evolution but also slightly after
the first shell crossing, we calculate the size and shape of those caustics and
their vorticity content as a function of time and for different cosmologies.
The average vorticity created in these caustics is small: of the order of one
(in units of the Hubble constant). To illustrate this point we compute the
contribution of such caustics to the probability distribution function of the
filtered vorticity at large scales. We find that this contribution that this
yields a negligible contribution at the 10 to 15 $h^{-1}$Mpc scales. It becomes
significant only at the scales of 3 to 4 $h^{-1}$Mpc, that is, slightly above
the galaxy cluster scales.


  Quark lepton universality inherent in grand unified theories based on
$SO(10)$ gauge group generically leads to hierarchical neutrino masses. We
propose a specific ansatz for the structure of Yukawa matrices in $SO(10)$
models which differ from this generic expectations and lead to quasi degenerate
neutrinos through the type-I seesaw mechanism. Consistency of this ansatz is
demonstrated through a detailed fits to fermion masses and mixing angles all of
which can be explained with reasonable accuracy in a model which uses the Higgs
fields transforming as $10,120$ and $\overline{126}$ representations of
$SO(10)$. The proposed ansatz is shown to follow from an extended model based
on the three generations of the vector like fermions and an $O(3)$ flavour
symmetry. Successful numerical fits are also discussed in earlier proposed
models which used combination of the type-I and type-II seesaw mechanisms for
obtaining quasi degenerate neutrinos. Large neutrino mixing angles emerge as a
consequence of neutrino mass degeneracy in both these cases.


  Vapor growth of semiconductors is analyzed using recently obtained dependence
of the adsorption energy on the electron charge transfer between the surface
adsorbed species and the bulk [Krukowski et al. J. Appl. Phys. 114 (2013)
063507, Kempisty et al. ArXiv 1307.5778 (2013)]. Ab initio calculations were
performed to study the physical properties of GaN(0001) surface in ammonia-rich
conditions, i.e. covered by mixture of NH3 molecules and NH2 radicals. The
Fermi level is pinned at valence band maximum (VBM) and conduction band minimum
(CBM) for full coverage by NH3 molecules and NH2 radicals, respectively. For
the crossover content of ammonia of about 25% monolayer (ML), the Fermi level
is unpinned. It was shown that hydrogen adsorption energy depends on the doping
in the bulk for the unpinned Fermi level, i.e. for this coverage. Surface
structure thermodynamic and mechanical stability criteria are defined and
compared. Mechanical stability of the coverage of such surfaces was checked by
determination of the desorption energy of hydrogen molecules. Thermodynamic
stability analysis indicates that initally equilibrium hydrogen vapor partial
pressure steeply increases with NH3 content to attain the crossover NH3/NH2
coverage, i.e. the unpinned Fermi level condition. For such condition the
entire range of experimentally accessible pressures belongs showing that vapor
growth of semiconductor crystals occurs predominantly for unpinned Fermi level
at the surface, i.e. for flat bands. Accordingly, adsorption energy of most
species depends on the doping in the bulk that is basis of the possible
molecular scenario explaining dependence of the growth and the doping of
semiconductor crystals on the doping in the bulk


  Constraints on the required flatness of the scalar potential $V(\phi)$ for a
cousin-model to extended inflation are studied. It is shown that, unlike
earlier results, Induced-gravity Inflation can lead to successful inflation
with a very simple lagrangian and $\lambda \sim 10^{-6}$, rather than
$10^{-15}$ as previously reported. A second order phase transition further
enables this model to escape the \lq big bubble' problem of extended inflation,
while retaining the latter's motivations based on the low-energy effective
lagrangians of supergravity, superstring, and Kaluza-Klein theories.


  We demonstrate that memory in an $N$-qubit system subjected to decoherence,
is a potential resource for the slow-down of the entanglement decay. We show
that this effect can be used to retain the sub shot-noise sensitivity of the
parameter estimation in quantum interferometry. We calculate quantum Fisher
information, which sets the ultimate bound for the precision of the estimation.
We also derive the sensitivity of such a noisy interferometer, when the phase
is either estimated from the measurements of the population imbalance or from
the one-body density.


  We study the instantaneous inference of an unbounded planar flow from sparse
noisy pressure measurements. The true flow field comprises one or more
regularized point vortices of various strength and size. We interpret the true
flow's measurements with a vortex estimator, also consisting of regularized
vortices, and attempt to infer the positions and strengths of this estimator
assuming little prior knowledge. The problem often has several possible
solutions, many due to a variety of symmetries. To deal with this ill-posedness
and to quantify the uncertainty, we develop the vortex estimator in a Bayesian
setting. We use Markov-chain Monte Carlo and a Gaussian mixture model to sample
and categorize the probable vortex states in the posterior distribution,
tailoring the prior to avoid spurious solutions. Through experiments with one
or more true vortices, we reveal many aspects of the vortex inference problem.
With fewer sensors than states, the estimator infers a manifold of
equally-possible states. Using one more sensor than states ensures that no
cases of rank deficiency arise. Uncertainty grows rapidly with distance when a
vortex lies outside of the vicinity of the sensors. Vortex size cannot be
reliably inferred, but the position and strength of a larger vortex can be
estimated with a much smaller one. In estimates of multiple vortices their
individual signs are discernible because of the non-linear coupling in the
pressure. When the true vortex state is inferred from an estimator of fewer
vortices, the estimate approximately aggregates the true vortices where
possible.


  We study the spin excitation spectra of the two-dimensional spin-$1/2$
Heisenberg model with a checkerboard structures using stochastic analytic
continuation of the imaginary-time correlation function obtained from a quantum
Monte Carlo simulation. The checkerboard models have two different
antiferromagnetic nearest-neighbor interactions $J_{1}$ and $J_{2}$, and the
tuning parameter $g$ is defined as $J_{2}/J_{1}$. The dynamic spin structure
factors are systematically calculated in all phases of the models as well as at
the critical points. To give a full understanding of the dynamic spectra, spin
wave theory is employed to explain some features of numerical results,
especially for the low-energy part. When $g$ is close to $1$, the features of
the spin excitation spectra of each checkerboard model are roughly the same as
those of the original square lattice antiferromagnetic Heisenberg model, and
the high-energy continuum among them is discussed. In contrast to the other
checkerboard structures investigated in this paper, the $3\times 3$
checkerboard model has distinctive excitation features, such as a gap between a
low-energy gapless branch and a gapped high-energy part that exists when $g$ is
small. The gapless branch in this case can be regarded as a spin wave in
N$\mathrm{\acute{e}}$el order formed by a "block spin" in each $3\times 3$
plaquette with an effective exchange interaction originating from
renormalization. One unexpected finding is that the continuum also appears in
this low-energy branch.


  We revisit quantum phase estimation algorithms for the purpose of obtaining
the energy levels of many-body Hamiltonians and pay particular attention to the
statistical analysis of their outputs. We introduce the mean phase direction of
the parent distribution associated with eigenstate inputs as a new
post-processing tool. By connecting it with the unknown phase, we find that if
used as its direct estimator, it exceeds the accuracy of the standard majority
rule using one less bit of resolution, making evident that it can also be
inverted to provide unbiased estimation. Moreover, we show how to directly use
this quantity to accurately find the energy levels when the initialized state
is an eigenstate of the simulated propagator during the whole time evolution,
which allows for shallower algorithms. We then use IBM Q hardware to carry out
the digital quantum simulation of three toy models: a two-level system, a
two-spin Ising model and a two-site Hubbard model at half-filling.
Methodologies are provided to implement Trotterization and reduce the
variability of results in noisy intermediate scale quantum computers.


  We introduce an intrinsic Ly\alpha\ emission line profile reconstruction
method for high-$z$ quasars (QSOs). This approach utilises a covariance matrix
of emission line properties obtained from a large, moderate-$z$ ($2 \leq z \leq
2.5$), high signal to noise (S/N > 15) sample of BOSS QSOs. For each QSO, we
complete a Monte Carlo Markov Chain fitting of the continuum and emission line
properties and perform a visual quality assessment to construct a large
database of robustly fit spectra. With this dataset, we construct a covariance
matrix to describe the correlations between the high ionisation emission lines
Ly\alpha, C IV, Si IV + O IV] and C III], and find it to be well approximated
by an $N$-dimensional Gaussian distribution. This covariance matrix
characterises the correlations between the line width, peak height and velocity
offset from systemic while also allowing for the existence of broad and narrow
line components for Ly\alpha\ and C IV. We illustrate how this covariance
matrix allows us to statistically characterise the intrinsic Ly\alpha\ line
solely from the observed spectrum redward of 1275\AA. This procedure can be
used to reconstruct the intrinsic Ly\alpha\ line emission profile in cases
where Ly\alpha\ may otherwise be obscured. Applying this reconstruction method
to our sample of QSOs, we recovered the Ly\alpha\ line flux to within 15 per
cent of the measured flux at 1205\AA\ (1220\AA) ~85 (90) per cent of the time.


  We present the first results of a larger study into the stellar abundances
and chemical trends in long-lived dwarf stars in the solar neighbourhood that
belong to (based on their kinematics) the thin and thick galactic disk,
respectively. We confirm that the trends of alpha-elements in the thin and
thick disk are distinct (this has previously been shown for Mg by Fuhrmann
1998, but e.g. Chen et al. 2000 claimed the trends to follow smoothly upon each
other). We find that the thick disk show the typical signature of contribution
from SN Ia (i.e. the ``knee'') to the enrichment of the interstellar gas out of
which the later generations of thick disk stars formed. The trend starts out as
[Mg/Fe] ~0.35 at [Fe/H] ~ -0.7 and continue on this level with increasing
[Fe/H] until -0.4 dex where a decline in [Mg/Fe] starts and steadily continues
down to 0 dex at solar metallicity. The same is true for the other
alpha-elements (e.g. Si). Using ages from the literature we find that the thick
disk in the mean is older than the thin disk. Combining our results with other
observational facts we suggest that the most likely formation scenario for the
thick disk is, still, a violent merger event. We also suggest that there might
be tentativeevidence for diffusion of orbits in todays thin disk (based on
kinematics in combination with elemental abundances).


  Recent work suggests that changing Convolutional Neural Network (CNN)
architecture by introducing a bottleneck in the second layer can yield changes
in learned function. To understand this relationship fully requires a way of
quantitatively comparing trained networks. The fields of electrophysiology and
psychophysics have developed a wealth of methods for characterising visual
systems which permit such comparisons. Inspired by these methods, we propose an
approach to obtaining spatial and colour tuning curves for convolutional
neurons, which can be used to classify cells in terms of their spatial and
colour opponency. We perform these classifications for a range of CNNs with
different depths and bottleneck widths. Our key finding is that networks with a
bottleneck show a strong functional organisation: almost all cells in the
bottleneck layer become both spatially and colour opponent, cells in the layer
following the bottleneck become non-opponent. The colour tuning data can
further be used to form a rich understanding of how colour is encoded by a
network. As a concrete demonstration, we show that shallower networks without a
bottleneck learn a complex non-linear colour system, whereas deeper networks
with tight bottlenecks learn a simple channel opponent code in the bottleneck
layer. We further develop a method of obtaining a hue sensitivity curve for a
trained CNN which enables high level insights that complement the low level
findings from the colour tuning data. We go on to train a series of networks
under different conditions to ascertain the robustness of the discussed
results. Ultimately, our methods and findings coalesce with prior art,
strengthening our ability to interpret trained CNNs and furthering our
understanding of the connection between architecture and learned
representation. Code for all experiments is available at
https://github.com/ecs-vlc/opponency.


  The temperature in most parts of a protoplanetary disk is determined by
irradiation from the central star. Numerical experiments of Watanabe \& Lin
(2008) suggested that such disks, also called `passive disks', suffer from a
thermal instability. Here, we use analytical and numerical tools to elucidate
the nature of this instability. We find that it is related to the flaring of
the optical surface, the layer at which starlight is intercepted by the disk.
Whenever a disk annulus is perturbed thermally and acquires a larger scale
height, disk flaring becomes steeper in the inner part, and flatter in the
outer part. Starlight now shines more overhead for the inner part and so can
penetrate into deeper layers; conversely, it is absorbed more shallowly in the
outer part. These geometric changes allow the annulus to intercept more
starlight, and the perturbation grows. We call this the irradiation
instability. It requires only ingredients that are known to exist in realistic
disks, and operates best in parts that are both optically thick and
geometrically thin (inside 30AU, but can extend to further reaches when, e.g.,
dust settling is considered). An unstable disk develops travelling thermal
waves that reach order-unity in amplitude. In thermal radiation, such a disk
should appear as a series of bright rings interleaved with dark shadowed gaps,
while in scattered light it resembles a moving staircase. Depending on the gas
and dust responses, this instability could lead to a wide range of
consequences, such as {\w ALMA rings and gaps,} dust traps, vertical
circulation, vortices and turbulence.


  Imaging data from the Sloan Digital Sky Survey is used to measure the
empirical size-richness relation for a large sample of galaxy clusters. Using
population subtraction methods, we determine the radius at which the cluster
galaxy number density is 200/Omega_m times the mean galaxy density, without
assuming a model for the radial distribution of galaxies in clusters. If these
galaxies are unbiased on Mpc scales, this galaxy-density-based R_200 reflects
the characteristic radii of clusters. We measure the scaling of this
characteristic radius with richness over an order of magnitude in cluster
richness, from rich clusters to poor groups. We use this information to examine
the radial profiles of galaxies in clusters as a function of cluster richness,
finding that the concentration of the galaxy distribution decreases with
richness and is systematically lower than the concentrations measured for dark
matter profiles in N-body simulations. Using these scaled radii, we investigate
the behavior of the cluster luminosity function, and find that it is well
matched by a Schechter function for galaxies brighter than M_r = -18 only after
the central galaxy has been removed. We find that the luminosity function
varies with richness and with distance from the cluster center, underscoring
the importance of using an aperture that scales with cluster mass to compare
physically equivalent regions of these different systems. We note that the
lowest richness systems in our catalog have properties consistent with those
expected of the earliest-forming halos; our cluster-finding algorithm, in
addition to reliably finding clusters, may be efficient at finding fossil
groups.


  We present the higher order QCD corrections to the fragmentation functions
and the corresponding cross sections.


  We introduce fusion-based quantum computing (FBQC) - a model of universal
quantum computation in which entangling measurements, called fusions, are
performed on the qubits of small constant-sized entangled resource states. We
introduce a stabilizer formalism for analyzing fault tolerance and computation
in these schemes. This framework naturally captures the error structure that
arises in certain physical systems for quantum computing, such as photonics.
FBQC can offer significant architectural simplifications, enabling hardware
made up of many identical modules, requiring an extremely low depth of
operations on each physical qubit and reducing classical processing
requirements. We present two pedagogical examples of fault-tolerant schemes
constructed in this framework and numerically evaluate their threshold under a
hardware agnostic fusion error model including both erasure and Pauli error. We
also study an error model of linear optical quantum computing with
probabilistic fusion and photon loss. In FBQC the non-determinism of fusion is
directly dealt with by the quantum error correction protocol, along with other
errors. We find that tailoring the fault-tolerance framework to the physical
system allows the scheme to have a higher threshold than schemes reported in
literature. We present a ballistic scheme which can tolerate a 10.4%
probability of suffering photon loss in each fusion.


  Continuous variable entanglement is a fundamental resource for many quantum
information tasks. Important protocols like superactivation of zero-capacity
channels and finite-size quantum cryptography that provides security against
most general attacks, require about 10 dB two-mode squeezing. Additionally,
stable phase control mechanisms are necessary but are difficult to achieve
because the total amount of optical loss to the entangled beams needs to be
small. Here, we experimentally demonstrate a control scheme for two-mode
squeezed vacuum states at the telecommunication wavelength of 1550 nm. Our
states exhibited an Einstein-Podolsky-Rosen covariance product of 0.0309 \pm
0.0002, where 1 is the critical value, and a Duan inseparability value of 0.360
\pm 0.001, where 4 is the critical value. The latter corresponds to 10.45 \pm
0.01 dB which reflects the average non-classical noise suppression of the two
squeezed vacuum states used to generate the entanglement. With the results of
this work demanding quantum information protocols will become feasible.


  The equation for the hard pomeron with a running coupling introduced on the
basis of the bootstrap requirement is solved numerically. Two supercritical
pomerons are found with the intercept minus 1 of the leading one of the order
0.35-0.5 and that of the subleading one half as large. The contribution of
multipomeron exchanges is found to be essential only at extremely high energies
of the order of 100 TeV. Comparison of the cross-sections and structure
functions to the present experimental data seems to indicate that the
asymptotical regime has not yet been achieved.


  Networked embedded systems typically leverage a collection of low-power
embedded systems (nodes) to collaboratively execute applications spanning
diverse application domains (e.g., video, image processing, communication,
etc.) with diverse application requirements. The individual networked nodes
must operate under stringent constraints (e.g., energy, memory, etc.) and
should be specialized to meet varying application requirements in order to
adhere to these constraints. Phase-based tuning specializes system tunable
parameters to the varying runtime requirements of different execution phases to
meet optimization goals. Since the design space for tunable systems can be very
large, one of the major challenges in phase-based tuning is determining the
best configuration for each phase without incurring significant tuning overhead
(e.g., energy and/or performance) during design space exploration. In this
paper, we propose phase distance mapping, which directly determines the best
configuration for a phase, thereby eliminating design space exploration. Phase
distance mapping applies the correlation between the characteristics and best
configuration of a known phase to determine the best configuration of a new
phase. Experimental results verify that our phase distance mapping approach,
when applied to cache tuning, determines cache configurations within 1 % of the
optimal configurations on average and yields an energy delay product savings of
27 % on average.


  Let G be an arithmetic Kleinian group, and let O be the associated hyperbolic
3-orbifold or 3-manifold. In this paper, we prove that, in many cases, G is
large, which means that some finite index subgroup admits a surjective
homomorphism onto a non-abelian free group. This has many consequences,
including that O has infinite virtual first Betti number and G has
super-exponential subgroup growth.
  Our first result, which forms the basis for the entire paper, is that G is
commensurable with a lattice containing the Klein group of order 4. Our second
result is that if G has a finite index subgroup with first Betti number at
least 4, then G is large. This is known to hold for many arithmetic lattices.
In particular, we show that it is always the case when G contains A_4, S_4 or
A_5. Our third main result is that the Lubotzky-Sarnak conjecture and the
geometrisation conjecture together imply that any arithmetic Kleinian group G
is large. We also give a new 'elementary' proof that arithmetic Kleinian groups
do not have the congruence subgroup property, which avoids the use of the
Golod-Shafarevich inequality.


  Due to its angular dependency, Cerenkov light has long been considered a
contamination signal in plastic scintillating dosimeters. In this study, we
propose a novel approach designed to take advantage of this angular dependency
to perform a direct measurement of an external beam radiation angle of
incidence. A Cerenkov probe composed of a 10-mm long filtered sensitive volume
of clear PMMA optical fibre was built. Both filtered and raw Cerenkov signals
from the transport fibre were collected through a single 1-mm diameter
transport fibre. An independent PSD composed of 10-mm BCF12 scintillating fibre
was also used for simultaneous dose measurements. A first series of
measurements aimed at validating the ability to account for the Cerenkov
electron energy spectrum dependency by simultaneously measuring the deposited
dose. A cylindrical phantom was then used to obtain an angular calibration
curve for fixed dose irradiations and perform incident angle measurements using
electron and photon beams. The beam nominal energy was found to have a
significant impact on the shapes of the angular calibration curves obtained for
irradiation angle measurements. This can be linked to the electron energy
spectrum dependency of the Cerenkov emission cone. Irradiation angle
measurements exhibit an absolute mean error of 1.86{\deg} and 1.02{\deg} at 6
and 18 MV, respectively. Similar results were obtained with electron beams and
the absolute mean error reaches 1.97, 1.66, 1.45 and 0.95 degrees at 9, 12, 16
and 20 MeV, respectively. Reducing the numerical aperture of the Cerenkov probe
leads to an increased angular dependency for the lowest energy while no major
changes were observed at higher energy. This allowed irradiation angle
measurements at 6 MeV with a mean absolute error of 4.82{\deg}. The detector
offers promising perspectives for external beam radiotherapy and brachytherapy
applications.


  In this work, we study the dynamics of a spatially heterogeneous single
population model with the memory effect and nonlinear boundary condition. By
virtue of the implicit function theorem and Lyapunov-Schmidt reduction,
spatially nonconstant positive steady state solutions appear from two trivial
solutions, respectively. By using bifurcation analysis, the Hopf bifurcation
associated with one spatially nonconstant positive steady state is found to
occur. The results complement the existing ones. Specifically, it is found that
with the interaction of spatial heterogeneity and nonlinear boundary condition,
when the memory term is stronger than the interaction of the interior reaction
term and the boundary one, the memory-based diffusive model has a single
stability switch from stability to instability, with the increase of the
delayed memory value. Therefore, the memory delay will lead to a single
stability switch of such memory-based diffusive model and consequently the Hopf
bifurcation will happen in the model.


  We present a census of photometrically detected rotation periods for white
dwarf stars. We analyzed the light curves of 9285 white dwarf stars observed by
the Transiting Exoplanet Survey Satellite (TESS) up to sector 69. Using Fourier
transform analyses and the TESS localize software, we detected variability
periods for 318 white dwarf stars. The 115 high probability likely single white
dwarfs in our sample have a median rotational period of 3.9 hours and a median
absolute deviation of 3.5 h. Our distribution is significantly different from
the distribution of the rotational period from asteroseismology, which exhibits
a longer median period of 24.3 hours and a median absolute deviation of 12.0 h.
In addition, we reported non-pulsating periods for three known pulsating white
dwarfs with rotational period previously determined by asteroseismology: NGC
1501, TIC 7675859, and G226-29. We also calculated evolutionary models that
include six angular momentum transfer mechanisms from the literature throughout
evolution in an attempt to reproduce our findings. Our models indicate that the
temperature-period relation of most observational data is best fitted by models
with low metallicity, probably indicating problems with the computations of
angular-momentum loss during the high-mass-loss phase. Our models also generate
internal magnetic fields through the Tayler-Spruit dynamo.


  A very short review on phenomenological aspects of supersymmetry with
violated R-parity at e+e- colliders is given. We present specific examples of a
search for supersymmetric particles with violating R-parity couplings at a 500
GeV~e+e- linear collider. The signal extraction, and the mass measurement in
the case of a pair production of the lightest neutralino, are performed with
the help of Monte Carlo simulation.


  We investigate the localization of four-dimensional metastable gravity in
supersymmetric dilatonic domain walls through massive modes by considering
several scenarios in the model. We compute corrections to the Newtonian
potential for small and long distances compared with a crossover scale given in
terms of the dilatonic coupling. 4D gravity behavior is developed on the brane
for distance very much below the crossover scale, while for distance much
larger, the 5D gravity is recovered. Whereas in the former regime gravity is
always attractive, in the latter regime due to non-normalizable unstable
massive graviton modes present on the spectrum, in some special cases, gravity
appears to be repulsive and signalizes a gravitational confining phase which is
able to produce an inflationary phase of the Universe.


  Photon interactions at the LHC result in striking final states with much
lower hadronic activity in the central detectors than for pp interactions. In
addition, the elastic exchange of a photon leads to a proton scattered at
almost zero-degree angle. Tagging photon interactions relies on either the use
of large rapidity gaps or on the detection of the scattered proton using very
forward detectors. The studies related to such detectors are presented,
including their characterization, their acceptance and reconstruction
performance. Limitations due to the LHC beamline misalignment and possible
solutions are also given.


  The non-stationary evolution of observable quantities in complex systems can
frequently be described as a juxtaposition of quasi-stationary spells. Given
that standard theoretical and data analysis approaches usually rely on the
assumption of stationarity, it is important to detect in real time series
intervals holding that property. With that aim, we introduce a segmentation
algorithm based on a fully non-parametric approach. We illustrate its
applicability through the analysis of real time series presenting diverse
degrees of non-stationarity, thus showing that this segmentation procedure
generalizes and allows to uncover features unresolved by previous proposals
based on the discrepancy of low order statistical moments only.


  A comprehensive new approach is presented for deriving probability densities
of physical properties characterizing lens or source that constitute an
observed galactic microlensing event. While previously encountered problems are
overcome, constraints from event anomalies and model parameter uncertainties
can be incorporated into the estimate. Probability densities for given events
need to be carefully distinguished from the statistical distribution of the
same parameters among the underlying population from which the actual lenses
and sources are drawn. Using given model distributions of the mass spectrum,
the mass density, and the velocity distribution of Galactic disk and bulge
constituents, probability densities of lens mass, distance, and the effective
lens-source velocities are derived, where the effect on the distribution that
arises from additional observations of annual parallax or finite-source
effects, or the absence of significant effects, is shown. The presented
formalism can also be used to calculate probabilities for the lens to belong to
one or another population and to estimate parameters that characterize
anomalies. Finally, it is shown how detection efficiency maps for binary-lens
companions in the physical parameters companion mass and orbital semi-major
axis arise from values determined for the mass ratio and dimensionless
projected separation parameter, including the deprojection of the orbital
motion for elliptical orbits. Compared to the naive estimate based on 'typical
values', the detection efficiency for low-mass companions is increased by
mixing in higher detection efficiencies for smaller mass ratios (i.e. smaller
masses of the primary).


  The geproci property is a recent development in the world of geometry. We
call a set of points $Z\subseteq\mathbb{P}_k^3$ an $(a,b)$-geproci set (for
GEneral PROjection is a Complete Intersection) if its projection from a general
point $P$ to a plane is a complete intersection of curves of degrees $a\leq b$.
Nondegenerate examples known as grids have been known since 2011. Nondegenerate
nongrids were found starting in 2018, working in characteristic 0. Almost all
of these new examples are of a special kind called half grids.
  Before the work in this paper -- based partly on the author's thesis -- only
a few examples of geproci nontrivial non-grid non-half grids were known and
there was no known way to generate more. Here, we use geometry in the positive
characteristic setting to give new methods of producing geproci half grids and
non-half grids.


  A $t$-bar visibility representation of a graph assigns each vertex up to $t$
horizontal bars in the plane so that two vertices are adjacent if and only if
some bar for one vertex can see some bar for the other via an unobstructed
vertical channel of positive width. The least $t$ such that $G$ has a $t$-bar
visibility representation is the bar visibility number of $G$, denoted by
$b(G)$. We show that if $H$ is a spanning subgraph of $G$, then $b(H)\le
b(G)+1$. It follows that $b(G)\le \lceil n/6\rceil+1$ when $G$ is an $n$-vertex
graph. This improves the upper bound obtained by Chang et al. (SIAM J. Discrete
Math. 18 (2004) 462).


  Given a division ring K containing the field k in its center and A,B two
finite subsets of K\{0}, we give some analogues of Pl\"unnecke and Kneser
theorems for the dimension of the k-linear span of the Minkowski product AB in
terms of the dimensions of the k-linear spans of A and B. These Pl\"unnecke
type estimates are then generalized to the case of associative algebras. We
also obtain an analogue in the context of division rings of a theorem by Tao
classifying the sets of small doubling in a group.


  Szegedy's quantum walk is a quantization of a classical random walk or Markov
chain, where the walk occurs on the edges of the bipartite double cover of the
original graph. To search, one can simply quantize a Markov chain with
absorbing vertices. Recently, Santos proposed two alternative search algorithms
that instead utilize the sign-flip oracle in Grover's algorithm rather than
absorbing vertices. In this paper, we show that these two algorithms are
exactly equivalent to two algorithms involving coined quantum walks, which are
walks on the vertices of the original graph with an internal degree of freedom.
The first scheme is equivalent to a coined quantum walk with one walk-step per
query of Grover's oracle, and the second is equivalent to a coined quantum walk
with two walk-steps per query of Grover's oracle. These equivalences lie
outside the previously known equivalence of Szegedy's quantum walk with
absorbing vertices and the coined quantum walk with the negative identity
operator as the coin for marked vertices, whose precise relationships we also
investigate.


  We generalize Berger and Moerdijk's results on axiomatic homotopy theory for
operads to the setting of enriched symmetric monoidal model categories, and
show how this theory applies to orthogonal spectra. In particular, we provide a
symmetric fibrant replacement functor for the positive stable model structure.