  Complex diseases can be modeled as damage to intracellular networks that
results in abnormal cell behaviors. Network-based dynamic models such as
Boolean models have been employed to model a variety of biological systems
including those corresponding to disease. Previous work designed compensatory
interactions to stabilize an attractor of a Boolean network after single node
damage. We generalize this method to a multinode damage scenario and to the
simultaneous stabilization of multiple steady state attractors. We classify the
emergent situations, with a special focus on combinatorial effects, and
characterize each class through simulation. We explore how the structural and
functional properties of the network affect its resilience and its possible
repair scenarios. We demonstrate the method's applicability to two
intracellular network models relevant to cancer. This work has implications in
designing prevention strategies for complex disease.


  We address the nature of the Mott transition in the Hubbard model at
half-filling using cluster Dynamical Mean Field Theory (DMFT). We compare
cluster DMFT results with those of single site DMFT. We show that inclusion of
the short range correlations on top of the on-site correlations, already
treated exactly in single site DMFT, do not change the nature of the transition
between the paramagnetic metal and the paramagnetic Mott insulator, which
remains first order. However, the short range correlations reduce substantially
the critical $U$ and modify the shape of transition lines. Moreover, they lead
to very different physical properties of the metallic and insulating phases
near the transition, in particular in the region of the phase diagram where the
two solutions coexist. Approaching the transition from the metallic side, we
find an anomalous metallic state with very low coherence scale at temperatures
as low as $T=0.01t$. The insulating state is characterized by the relatively
narrow Mott gap with pronounced peaks at the gap edge.


  Transformer-based visual trackers have demonstrated significant progress
owing to their superior modeling capabilities. However, existing trackers are
hampered by low speed, limiting their applicability on devices with limited
computational power. To alleviate this problem, we propose HiT, a new family of
efficient tracking models that can run at high speed on different devices while
retaining high performance. The central idea of HiT is the Bridge Module, which
bridges the gap between modern lightweight transformers and the tracking
framework. The Bridge Module incorporates the high-level information of deep
features into the shallow large-resolution features. In this way, it produces
better features for the tracking head. We also propose a novel dual-image
position encoding technique that simultaneously encodes the position
information of both the search region and template images. The HiT model
achieves promising speed with competitive performance. For instance, it runs at
61 frames per second (fps) on the Nvidia Jetson AGX edge device. Furthermore,
HiT attains 64.6% AUC on the LaSOT benchmark, surpassing all previous efficient
trackers.


  Let $X$ be a projective Frobenius split variety over an algebraically closed
field with splitting $\theta : F_* \O_X \to \O_X$. In this paper we give a
sharp bound on the number of subvarieties of $X$ compatibly split by $\theta$.
In particular, suppose $\sL$ is a sufficiently ample line bundle on $X$ (for
example, if $\sL$ induces a projectively normal embedding) with $n = \dim
H^0(X, \sL)$. We show that the number of $d$-dimensional irreducible
subvarieties of $X$ that are compatibly split by $\theta$ is less than or equal
to ${n \choose d+1}$. This generalizes a well known result on the number of
closed points compatibly split by a fixed splitting $\theta$. Similarly, we
give a bound on the number of prime $F$-ideals of an $F$-finite $F$-pure local
ring.
  Compatibly split subvarieties are closely related to log canonical centers.
Our methods apply in any characteristic, and so we are also able to bound the
possible number of log canonical centers of a log canonical pair $(X, \Delta)$
passing through a closed point $x \in X$. Specifically, if $n$ is the embedding
dimension of $X$ at $x$, then the number of $d$-dimensional log canonical
centers of $(X, \Delta)$ through $x$ is less than or equal to ${n \choose d}$.


  Extra-large deformations in ultra-soft elastic materials are ubiquitous, yet
systematic studies and methods to understand the mechanics of such huge strains
are lacking. Here we investigate this complex problem systematically with a
simple experiment: by introducing a heavy bead of radius $a$ in an
incompressible ultra-soft elastic medium. We find a scaling law for the
penetration depth ($\delta$) of the bead inside the softest gels as $\delta
\sim a^{3/2}$. While this result is inconsistent with an ideal neo-Hookean
model of elastic deformation, according to which the displacement fields must
diverge, it is vindicated by an original asymptotic analytic model developed in
this article. This model demonstrates that the observed relationship is
precisely at the demarcating boundary of what would be required for the field
variables to either diverge or converge. This correspondence between a unique
mathematical prediction and the experimental observation ushers in new insights
into the behavior of the deformations of strongly non-linear materials.


  Existing communication systems exhibit inherent limitations in translating
theory to practice when handling the complexity of optimization for emerging
wireless applications with high degrees of freedom. Deep learning has a strong
potential to overcome this challenge via data-driven solutions and improve the
performance of wireless systems in utilizing limited spectrum resources. In
this chapter, we first describe how deep learning is used to design an
end-to-end communication system using autoencoders. This flexible design
effectively captures channel impairments and optimizes transmitter and receiver
operations jointly in single-antenna, multiple-antenna, and multiuser
communications. Next, we present the benefits of deep learning in spectrum
situation awareness ranging from channel modeling and estimation to signal
detection and classification tasks. Deep learning improves the performance when
the model-based methods fail. Finally, we discuss how deep learning applies to
wireless communication security. In this context, adversarial machine learning
provides novel means to launch and defend against wireless attacks. These
applications demonstrate the power of deep learning in providing novel means to
design, optimize, adapt, and secure wireless communications.


  Abelian complexity of a word $\mathbf{u}$ is a function that counts the
number of pairwise non-abelian-equivalent factors of $\mathbf{u}$ of length
$n$. We prove that for any $c$-balanced Parry word $\mathbf{u}$, the values of
the abelian complexity function can be computed by a finite-state automaton.
The proof is based on the notion of relative Parikh vectors. The approach works
for any function $F(n)$ that can be expressed in terms of the set of relative
Parikh vectors corresponding to the length $n$. For example, we show that the
balance function of a $c$-balanced Parry word is computable by a finite-state
automaton as well.


  This work addresses the study of two-dimensional electron gas in a
perpendicular magnetic field in the presence of both Rashba and Dresselhaus
spin-orbit (SO) interactions, with effective Zeeman coupling. Exact analytical
expressions are found for the eigenvalue problem giving the Landau levels and
the associated eigenstates, thanks to an appropriate method of parametrization
used to quantize the physical system. Such a system exhibits interesting
properties of quaternions for which vector coherent states are built.
Similarity with the Weyl-Heisenberg group and some relevant properties of these
vectors are discussed.


  Entangled multipartite states are resources for universal quantum
computation, but they can also give rise to ensembles of unitary
transformations, a topic usually studied in the context of random quantum
circuits. Using several graph state techniques, we show that these resources
can `derandomize' circuit results by sampling the same kinds of ensembles
quantum mechanically, (analogously to a quantum random number generator).
Furthermore, we find simple examples that give rise to new ensembles whose
statistical moments exactly match those of the uniformly random distribution
over all unitaries up to order $t$, while foregoing adaptive feed-forward
entirely. Such ensembles -- known as $t$-designs -- often cannot be
distinguished from the `truly' random ensemble, and so they find use in many
applications that require this implied notion of pseudorandomness.


  We report a clear anomaly in the rf response of a tunnel-diode resonator
measured in borocarbide crystals in dc fields along the $c-$axis. We associate
the anomaly in the dynamic magnetic susceptibility, $\chi$, with a structural
transition in the vortex lattice. $\chi$ is sensitive to the Campbell
penetration depth $\lambda_{C}$ of the rf perturbation into the mixed state.
$\lambda_{C}$ depends on the vortex lattice elastic moduli, which in turn
depend on the vortex lattice structure. The high-field transition line is
clearly mapped and shown to behave in agreement with theory.


  We prove a version of Dedekind's Transposition Principle that holds in
lattices of equivalence relations.


  Clustering is one of the major tasks in data mining. In the last few years,
Clustering of spatial data has received a lot of research attention. Spatial
databases are components of many advanced information systems like geographic
information systems VLSI design systems. In this thesis, we introduce several
efficient algorithms for clustering spatial data. First, we present a
grid-based clustering algorithm that has several advantages and comparable
performance to the well known efficient clustering algorithm. The algorithm has
several advantages. The algorithm does not require many input parameters. It
requires only three parameters, the number of the points in the data space, the
number of the cells in the grid and a percentage. The number of the cells in
the grid reflects the accuracy that should be achieved by the algorithm. The
algorithm is capable of discovering clusters of arbitrary shapes. The
computational complexity of the algorithm is comparable to the complexity of
the most efficient clustering algorithm. The algorithm has been implemented and
tested against different ranges of database sizes. The performance results show
that the running time of the algorithm is superior to the most well known
algorithms (CLARANS [23]). The results show also that the performance of the
algorithm do not degrade as the number of the data points increases.


  We consider the moduli space of stable vector bundles on curves embedded in
P_2 with Hilbert polynomial 3m+1 and construct a compactification of this space
by vector bundles. The result is a blow up of the Simpson moduli space
M_{3m+1}(P_2).


  For any 3-manifold M and any nonnegative integer g, we give here examples of
metrics on M each of which has a sequence of embedded minimal surfaces of genus
g and without Morse index bounds. On any spherical space form S^3/Gamma we
construct such a metric with positive scalar curvature. More generally we
construct such a metric with Scal>0 (and such surfaces) on any 3-manifold which
carries a metric with Scal>0. In all but one of these examples the Hausdorff
limit will be a singular minimal lamination. The singularities being in each
case exactly two points lying on a closed leaf (the leaf is a strictly stable
sphere).


  In view of the node importance in weighted networks, weighted expected method
(WEM), was proposed in this paper, which take an advantages of uncertain graph
algorithm. First, a weight processing method is proposed based on the
relationship between the weight of edges and the intensity of contact between
nodes, and the calculation method of the contribution of the weight of edges to
the node importance is defined, even if there are two converse situations in
the reality. Then, because of the use of dynamic programming method, which
reduces the complexity of computational time to a linear level, WEM will be
more suitable for the calculation in large weighted networks. Owning to its
features of calculating, WEM can, to the greatest extent, ensure a precise
order of node essential scores for each node. The node connectivity experiment
and SIR simulation experiment show that the WEM has higher accuracy and
relatively low time complexity.


  We introduce the notion of a bicollapsible 2-complex. This allows us to
generalize the hyperbolicity of one-relator groups with torsion to a broader
class of groups with presentations whose relators are proper powers. We also
prove that many such groups act properly and cocompactly on a CAT(0) cube
complex.


  In this paper, after reviewing some of the most important concepts about Dark
Matter (DM) and methods of its registration, in particular by using SQUIDs, we
focus on two main problems. First, the possible mechanism of magnetic moment
origin for DM particles, in the form of neutralino, is discussed: the presence
of a magnetic moment means the existence of a new kind of interaction, whose
corresponding cross section is estimated. Second, a simple uniform model for DM
and Dark Energy (DE) is proposed. Two types of devices based on SQUID, in
particular the SQUID-paramagnetic absorber and the SQUID-magnetostrictor
systems, both suitable for investigations of above problems, are considered.


  This paper focuses on the frozen set design for precoded polar codes decoded
by the successive cancellation list (SCL) algorithm. We propose a novel frozen
set design method, whose computational complexity is low due to the use of
analytical bounds and constrained frozen set structure. We derive new bounds
based on the recently published complexity analysis of SCL decoding with near
maximum-likelihood (ML) performance. To predict the ML performance, we employ
the state-of-the-art bounds relying on the code weight distribution. The bounds
and constrained frozen set structure are incorporated into the genetic
algorithm to generate optimized frozen sets with low complexity. Our simulation
results show that the constructed precoded polar codes of length 512 have a
superior frame error rate (FER) performance compared to the state-of-the-art
codes under SCL decoding with various list sizes.


  Semantic segmentation is one of the most fundamental problems in computer
vision with significant impact on a wide variety of applications. Adversarial
learning is shown to be an effective approach for improving semantic
segmentation quality by enforcing higher-level pixel correlations and
structural information. However, state-of-the-art semantic segmentation models
cannot be easily plugged into an adversarial setting because they are not
designed to accommodate convergence and stability issues in adversarial
networks. We bridge this gap by building a conditional adversarial network with
a state-of-the-art segmentation model (DeepLabv3+) at its core. To battle the
stability issues, we introduce a novel lookahead adversarial learning (LoAd)
approach with an embedded label map aggregation module. We focus on semantic
segmentation models that run fast at inference for near real-time field
applications. Through extensive experimentation, we demonstrate that the
proposed solution can alleviate divergence issues in an adversarial semantic
segmentation setting and results in considerable performance improvements (+5%
in some classes) on the baseline for three standard datasets.


  In this paper we associate to each multivariate polynomial $f$ that is
homogeneous relative to a subset of its variables a series of polynomial
families $P_\lambda (f)$ of $m$-tuples of homogeneous polynomials of equal
degree such that the circuit size of any member in $P_\lambda (f)$ is bounded
from above by the circuit size of $f$. This provides a method for obtaining
lower bounds for the circuit size of $f$ by proving $(s,r)$-(weak) elusiveness
of the polynomial mapping associated with $P_\lambda (f)$. We discuss some
algebraic methods for proving the $(s,r)$-(weak) elusiveness. We also improve
estimates in the normal homogeneous-form of an arithmetic circuit obtained by
Raz in \cite{Raz2009} which results in better lower bounds for circuit size
(Lemma \ref{lem:cor38}, Remark \ref{rem:cor38}).
  Our methods yield non-trivial lower bound for the circuit size of several
classes of multivariate homogeneous polynomials (Corollary \ref{cor:412},
Example \ref{ex:bi}).


  This paper is concerned with the Rayleigh-Taylor instability for the
nonhomogeneous incompressible Navier-Stokes equations with Navier-slip boundary
conditions around a steady-state in an infinite slab, where the Navier-slip
coefficients do not have defined sign and the slab is horizontally periodic.
Motivated by [18], we extend the result from Dirichlet boundary condition to
Navier-slip boundary conditions. Our results indicate the factor that "heavier
density with increasing height" still plays a key role in the instability under
Navier-slip boundary conditions.


  Cluster cool cores possess networks of line-emitting filaments. These
filaments are thought to originate via uplift of cold gas from cluster centers
by buoyant active galactic nuclei (AGN) bubbles, or via local thermal
instability in the hot intracluster medium (ICM). Therefore, the filaments are
either the signatures of AGN feedback or feeding of supermassive black holes.
Despite being characterized by very short cooling times, the filaments are
significant H$\alpha$ emitters, which suggests that some process continuously
powers these structures. Many cool cores host diffuse radio mini halos and AGN
injecting radio plasma, suggesting that cosmic rays (CRs) and magnetic fields
are present in the ICM. We argue that the excitation of Alfv\'en waves by CR
streaming, and the replenishment of CR energy via accretion onto the filaments
of high plasma-$\beta$ ICM characterized by low CR pressure support, can
provide the adequate amount of heating to power and sustain the emission from
these filaments. This mechanism does not require the CRs to penetrate the
filaments even if the filaments are magnetically isolated from the ambient ICM
and it may operate irrespectively of whether the filaments are dredged up from
the center or form in situ in the ICM. This picture is qualitatively consistent
with non-thermal line ratios seen in the cold filaments. Future X-ray
observations of the iron line complex with XARM, Lynx, or Athena could help to
test this model by providing constraints on the amount of CRs in the hot plasma
that is cooling and accreting onto the filaments.


  We investigate the morphology of the colour-magnitude diagram (CMD) of the
open cluster NGC 2509 in comparison with other Galactic open clusters of
similar age using Gaia photometry. At $\sim900$ Myr Galactic open clusters in
our sample all show an extended main sequence turn off (eMSTO) with the
exception of NGC 2509, which presents an exceptionally narrow CMD. Our analysis
of the Gaia data rules out differential extinction, stellar density, and
binaries as a cause for the singular MSTO morphology in this cluster. We
interpret this feature as a consequence of the stellar rotation distribution
within the cluster and present the analysis with MIST stellar evolution models
that include the effect of stellar rotation on which we based our conclusion.
In particular, these models point to an unusually narrow range of stellar
rotation rates ($\Omega/\Omega_{\rm{crit,ZAMS}} = [0.4, 0.6]$) within the
cluster as the cause of this singular feature in the CMD of NGC 2509.
Interestingly, models that do not include rotation are not as good at
reproducing the morphology of the observed CMD in this cluster.


  We analyze in this work the energy transfer process of accelerated charges,
the mass fluctuations accompanying this process, and their inertial properties.
Based on a previous work, we use here the dipole antenna, which is a very
convenient framework for such analysis, for analyzing those characteristics. We
show that the radiation process can be viewed by two energy transfer processes:
one from the energy source to the charges and the second from the charges into
the surrounding space. Those processes, not being in phase, result in mass
fluctuations. The same principle is true during absorption. We show that in a
transient period between absorption and radiation the dipole antenna gains mass
according to the amount of absorbed energy and loses this mass as radiated
energy. We rigorously prove that the gain of mass, resulting from electrical
interaction has inertial properties in the sense of Newton's third low. We
arrive to this result by modeling the reacting spacetime region by an electric
dipole.


  We prove that for a generic sub-Riemannian and reversible sub-Finsler metrics
defined on a fixed co-rank 1 distribution, all strictly normal periodic orbits
are non-degenerate.


  Instead of analog electronic circuits and components, digital controllers
that are capable of active multi-resonant piezoelectric shunting are applied to
elastic metamaterials integrated with piezoelectric patches. Giving thanks to
the introduced digital control technique, shunting strategies with transfer
functions that can hardly be realized with analog circuits is possible now. As
an example, the "pole-zero" method is developed to design single- or
multi-resonant bandgaps by adjusting poles and zeros in the transfer function
of piezoelectric shunting directly. Large simultaneous attenuations in up to
three frequency bands at deep subwavelength scale (with the normalized
frequency as low as 0.077) are achieved. The underlying physical mechanism is
attributed to the negative group velocity of flexural wave within bandgaps. As
digital controllers can be readily adapted via wireless broadcasting, the
bandgaps can be tuned easily instead of tuning the electric components in
analog shunting circuits one by one manually. The theoretical results are well
verified experimentally with the measured vibration transmission properties
where large insulations of up to 20dB in low-frequency ranges are observed.


  We study the stability for the direct acoustic scattering problem with
sound-hard scatterers with minimal regularity assumptions on the scatterers.
The main tool we use for this purpose is the convergence in the sense of Mosco.
  We obtain uniform decay estimates for scattered fields and we investigate how
a sound-hard screen may be approximated by thin sound-hard obstacles.


  Context: Understanding the source of systematic errors in photometry is
essential for their calibration. Aims: We investigate how photometry performed
on difference images can be influenced by errors in the photometric scale
factor. Methods: We explore the equations for difference image analysis (DIA)
and we derive an expression describing how errors in the difference flux, the
photometric scale factor and the reference flux are propagated to the object
photometry. Results: We find that the error in the photometric scale factor is
important, and while a few studies have shown that it can be at a significant
level, it is currently neglected by the vast majority of photometric surveys
employing DIA. Conclusions: Minimising the error in the photometric scale
factor, or compensating for it in a post-calibration model, is crucial for
reducing the systematic errors in DIA photometry.


  Entity Resolution (ER) is the problem of determining when two entities refer
to the same underlying entity. The problem has been studied for over 50 years,
and most recently, has taken on new importance in an era of large,
heterogeneous 'knowledge graphs' published on the Web and used widely in
domains as wide ranging as social media, e-commerce and search. This chapter
will discuss the specific problem of named ER in the context of personal
knowledge graphs (PKGs). We begin with a formal definition of the problem, and
the components necessary for doing high-quality and efficient ER. We also
discuss some challenges that are expected to arise for Web-scale data. Next, we
provide a brief literature review, with a special focus on how existing
techniques can potentially apply to PKGs. We conclude the chapter by covering
some applications, as well as promising directions for future research.


  We report extensive photometry of the dwarf nova V660 Herculis. During our
campaign, lasting from August 2003 to November 2004, we recorded one bright
eruption which turned out to be a superoutburst lasting about 15 days and
having amplitude of ~4.5 mag. Clear superhumps with a mean period of Psh =
0.080924(18) days were present during all nights of the superoutburst. The
period of the superhumps was not stable and in the interval covered by our
observations it decreased with a rate of -4.0(1.4) * 10^{-5}.
  Basing on our data and the known orbital period of the binary (Thorstensen
and Fenton 2003) we calculate the period excess of 3.4 +/- 0.1%, which is
typical for an SU UMa star at this orbital period. This value indicates that
the mass ratio of the system is q=0.154.


  Despite numerous efforts to ensure large language models (LLMs) adhere to
safety standards and produce harmless content, some successes have been
achieved in bypassing these restrictions, known as jailbreak attacks against
LLMs. Adversarial prompts generated using gradient-based methods exhibit
outstanding performance in performing jailbreak attacks automatically.
Nevertheless, due to the discrete nature of texts, the input gradient of LLMs
struggles to precisely reflect the magnitude of loss change that results from
token replacements in the prompt, leading to limited attack success rates
against safety-aligned LLMs, even in the white-box setting. In this paper, we
explore a new perspective on this problem, suggesting that it can be alleviated
by leveraging innovations inspired in transfer-based attacks that were
originally proposed for attacking black-box image classification models. For
the first time, we appropriate the ideologies of effective methods among these
transfer-based attacks, i.e., Skip Gradient Method and Intermediate Level
Attack, for improving the effectiveness of automatically generated adversarial
examples against white-box LLMs. With appropriate adaptations, we inject these
ideologies into gradient-based adversarial prompt generation processes and
achieve significant performance gains without introducing obvious computational
cost. Meanwhile, by discussing mechanisms behind the gains, new insights are
drawn, and proper combinations of these methods are also developed. Our
empirical results show that the developed combination achieves >30% absolute
increase in attack success rates compared with GCG for attacking the
Llama-2-7B-Chat model on AdvBench.


  We investigate the alignment of international attention of news media
organizations within 193 countries with the expressed international interests
of the public within those same countries from March 7, 2016 to April 14, 2017.
We collect fourteen months of longitudinal data of online news from Unfiltered
News and web search volume data from Google Trends and build a multiplex
network of media attention and public attention in order to study its
structural and dynamic properties. Structurally, the media attention and the
public attention are both similar and different depending on the resolution of
the analysis. For example, we find that 63.2% of the country-specific media and
the public pay attention to different countries, but local attention flow
patterns, which are measured by network motifs, are very similar. We also show
that there are strong regional similarities with both media and public
attention that is only disrupted by significantly major worldwide incidents
(e.g., Brexit). Using Granger causality, we show that there are a substantial
number of countries where media attention and public attention are dissimilar
by topical interest. Our findings show that the media and public attention
toward specific countries are often at odds, indicating that the public within
these countries may be ignoring their country-specific news outlets and seeking
other online sources to address their media needs and desires.


  The Abnormally Weighting Energy (AWE) hypothesis consists of assuming that
the dark sector of cosmology violates the weak equivalence principle (WEP) on
cosmological scales, which implies a violation of the strong equivalence
principle for ordinary matter. In this paper, dark energy (DE) is shown to
result from the violation of WEP by pressureless (dark) matter. This allows us
to build a new cosmological framework in which general relativity (GR) is
satisfied at low scales, as WEP violation depends on the ratio of the ordinary
matter over dark matter densities, but at large scales, we obtain a general
relativity-like theory with a different value of the gravitational coupling.
This explanation is formulated in terms of a tensor-scalar theory of
gravitation without WEP for which there exists a revisited convergence
mechanism toward GR. The consequent DE mechanism build upon the anomalous
gravity of dark matter (i) does not require any violation of the strong energy
condition $p<-\rho c^2/3$, (ii) offers a natural way-out of the coincidence
problem thanks to the non-minimal couplings to gravitation, (iii) accounts
fairly for supernovae data from various very simple couplings and with density
parameters very close to the ones of the concordance model $\Lambda CDM$,
therefore suggesting an explanation to its remarkable adequacy. Finally, (iv)
this mechanism ends up in the future with an Einstein-de Sitter expansion
regime once the attractor is reached.


  This paper studies a new mobile edge computing (MEC) setup where an unmanned
aerial vehicle (UAV) is served by cellular ground base stations (GBSs) for
computation offloading. The UAV flies between a give pair of initial and final
locations, during which it needs to accomplish certain computation tasks by
offloading them to some selected GBSs along its trajectory for parallel
execution. Under this setup, we aim to minimize the UAV's mission completion
time by optimizing its trajectory jointly with the computation offloading
scheduling, subject to the maximum speed constraint of the UAV, and the
computation capacity constraints at GBSs. The joint UAV trajectory and
computation offloading optimization problem is, however, non-convex and thus
difficult to be solved optimally. To tackle this problem, we propose an
efficient algorithm to obtain a high-quality suboptimal solution. Numerical
results show that the proposed design significantly reduces the UAV's mission
completion time, as compared to benchmark schemes.


  We demonstrate plasmon-enhanced photoconduction in Au bowtie nanojunctions
containing nanogaps overlaid with an amorphous Ge film. The role of plasmons in
the production of nanogap photocurrent is verified by studying the unusual
polarization dependence of the photoresponse. With increasing Ge thickness, the
nanogap polarization of the photoresponse rotates 90 degrees, indicating a
change in the dominant relevant plasmon mode, from the resonant transverse
plasmon at low thicknesses to the nonresonant "lightning rod" mode at higher
thicknesses. To understand the plasmon response in the presence of the Ge
overlayer and whether the Ge degrades the Au plasmonic properties, we
investigate the photothermal response (from the temperature-dependent Au
resistivity) in no-gap nanowire structures, as a function of Ge film thickness
and nanowire geometry. The film thickness and geometry dependence are modeled
using a cross-sectional, finite element simulation. The no-gap structures and
the modeling confirm that the striking change in nanogap polarization response
results from redshifting of the resonant transverse mode, rather than
degradation in the Au/Ge properties. We note remaining challenges in
determining the precise mechanism of photocurrent production in the nanogap
structures.


  We deal with strongly competing multispecies systems of
  Lotka-Volterra type with homogeneous Neumann boundary conditions in
dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that,
as the competition rate grows indefinitely, the system reaches a state of
coexistence of all the species in spatial segregation. Furthermore, the limit
configuration is a local minimizer for the associated free energy.


  We propose a new proof technique that aims to be applied to the same problems
as the Lov\'asz Local Lemma or the entropy-compression method. We present this
approach in the context of non-repetitive colorings and we use it to improve
upper-bounds relating different non-repetitive numbers to the maximal degree of
a graph. It seems that there should be other interesting applications to the
presented approach.
  In terms of upper-bound our approach seems to be as strong as
entropy-compression, but the proofs are more elementary and shorter. The
application we provide in this paper are upper bounds for graphs of maximal
degree at most $\Delta$: a minor improvement on the upper-bound of the
non-repetitive number, a $4.25\Delta +o(\Delta)$ upper-bound on the weak total
non-repetitive number and a $
\Delta^2+\frac{3}{2^\frac{1}{3}}\Delta^{\frac{5}{3}}+ o(\Delta^{\frac{5}{3}})$
upper-bound on the total non-repetitive number of graphs. This last result
implies the same upper-bound for the non-repetitive index of graphs, which
improves the best known bound.


  We prove that the local height of a point on a Drinfeld module can be
computed by averaging the logarithm of the distance to that point over the
torsion points of the module. This gives rise to a Drinfeld module analog of a
weak version of Siegel's integral points theorem over number fields and to an
analog of a theorem of Schinzel's regarding the order of a point modulo certain
primes.


  In the first part of this manuscript, I present the results on the properties
of the interstellar medium and the stellar content of galaxies at z=0.6, from a
representative sample of distant galaxies observed with the long slit
spectrograph VLT/FORS2. This study has been realized in the framework of the
ESO large program IMAGES "Intermediate MAss Galaxy Evolution Sequences", which
aims to investigate the evolution of the main global properties of galaxies up
to z~0.9. I discuss the implications of the observed chemical enrichment of the
gas on the scenarios of galaxy formation. I also propose a new method to
estimate reliable stellar masses in starburst galaxies using broadband
photometry and their total star-formation rate.
  In a second part, I present a new method to extract, with high accuracy, the
sky in spectra acquired with a fiber-fed instrument. I have developed this code
in the Framework of the phase A of an instrument proposed for the E-ELT:
OPTIMOS-EVE. This is a multi-fiber spectrograph able to observe at optical and
infrared wavelengths simultaneously.
  In the third part, I show preliminary results from the CENTRA GEPI- survey at
Calar Alto Observatory to study nearby galaxies, hosts of type Ia supernovae,
using integral field spectroscopy. I present the first 2D maps of the gas and
stellar populations of SNe Ia hosts. The results allow us to directly access
the host properties in the immediate vicinity of the SNe Ia. This is a crucial
step to investigate eventual correlations between galaxy properties and SNe Ia
events and evolution, leading to systematic effects on the derivation of the
cosmological parameters.


  The conjecture about relation between infinite-dimensional Grassmannian and
string theory is based on the fact that moduli spaces of algebraic curves are
embedded into Grassmannian via Krichever construction. We describe a
multidimensional analog of Krichever construction, that can be used in the
attempt to relate Grassmannian to membranes.


  Given a pattern $w$ and a text $t$, the speed of a pattern matching algorithm
over $t$ with regard to $w$, is the ratio of the length of $t$ to the number of
text accesses performed to search $w$ into $t$. We first propose a general
method for computing the limit of the expected speed of pattern matching
algorithms, with regard to $w$, over iid texts. Next, we show how to determine
the greatest speed which can be achieved among a large class of algorithms,
altogether with an algorithm running this speed. Since the complexity of this
determination make it impossible to deal with patterns of length greater than
4, we propose a polynomial heuristic. Finally, our approaches are compared with
9 pre-existing pattern matching algorithms from both a theoretical and a
practical point of view, i.e. both in terms of limit expected speed on iid
texts, and in terms of observed average speed on real data. In all cases, the
pre-existing algorithms are outperformed.


  In this paper we study homological stability for spaces ${\rm
Hom}(\mathbb{Z}^n,G)$ of pairwise commuting $n$-tuples in a Lie group $G$. We
prove that for each $n\geqslant 1$, these spaces satisfy rational homological
stability as $G$ ranges through any of the classical sequences of compact,
connected Lie groups, or their complexifications. We prove similar results for
rational equivariant homology, for character varieties, and for the
infinite-dimensional analogues of these spaces, ${\rm Comm}(G)$ and ${\rm
B_{com}} G$, introduced by Cohen-Stafa and Adem-Cohen-Torres-Giese
respectively. In addition, we show that the rational homology of the space of
unordered commuting $n$-tuples in a fixed group $G$ stabilizes as $n$
increases. Our proofs use the theory of representation stability - in
particular, the theory of ${\rm FI}_W$-modules developed by
Church-Ellenberg-Farb and Wilson. In all of the these results, we obtain
specific bounds on the stable range, and we show that the homology isomorphisms
are induced by maps of spaces.


  4D face reconstruction from a single camera is a challenging task, especially
when it is required to be performed in real time. We demonstrate a system of
our own implementation that solves this task accurately and runs in real time
on a commodity laptop, using a webcam as the only input. Our system is
interactive, allowing the user to freely move their head and show various
expressions while standing in front of the camera. As a result, the put forward
system both reconstructs and visualises the identity of the subject in the
correct pose along with the acted facial expressions in real-time. The 4D
reconstruction in our framework is based on the recently-released Large-Scale
Facial Models (LSFM) \cite{LSFM1, LSFM2}, which are the largest-scale 3D
Morphable Models of facial shapes ever constructed, based on a dataset of more
than 10,000 facial identities from a wide range of gender, age and ethnicity
combinations. This is the first real-time demo that gives users the opportunity
to test in practice the capabilities of the recently-released Large-Scale
Facial Models (LSFM)


  Future wireless networks require the ability to actively adjust the wireless
environment to meet strict performance indicators. Reconfigurable Intelligent
Surface (RIS) technology is gaining attention for its advantages of low power
consumption, cost-effectiveness, and ease of deployment. However, existing
channel models for RIS often ignore important properties, such as the
impairment in the RIS's switch component and the polarization efficiency among
antennas, limiting their practical use. In this paper, we propose a new channel
model for RIS that considers these ignored properties, including the reflected
field, scattered field, and antenna resonant mode. We verify the proposed model
through the practical implementation of a 4 x 4 RIS array with patch antennas
in the 3.5 GHz band, using a phase shifter as the switch component of a RIS
element. The equivalent model of the phase shifter is also formulated and
incorporated into the channel model. We propose a blind controlling algorithm
to discuss the properties of our channel model and emphasize the importance of
considering polarization and tracking mechanisms for the controlling algorithm.
Our channel model is an improvement over existing models and can be used in the
practical design of RIS technology. The proposed algorithm provides a practical
approach to controlling the wireless environment, suitable for various wireless
applications.


  We introduce an optimization technique to discriminate signal and background
in any phenomenological study based on the cut and count-based method. The core
ideas behind this algorithm is the introduction of a ranking scheme that can
quantitatively assess the relative importance of various observables involved
in a new physics process, and a more methodical way of choosing what cuts to
impose. The technique is an iterative process that works with the help of the
MadAnalysis5 interface. Working in the context of a simple BSM scenario with a
heavy Higgs boson that decays to four leptons via ZZ, we demonstrate how
automating the cut and count process in this specific way results in an
enhanced discovery potential compared with the more traditional way of imposing
cuts.


  Larger multi-qubit quantum gates allow shallower, more efficient quantum
circuits, which could decrease the prohibitive effect of noise on algorithms
for noisy intermediate-scale quantum (NISQ) devices and fault-tolerant error
correction schemes. Such multi-qubit gates can potentially be generated by
time-independent Hamiltonians comprising only physical (one- and two-local)
interaction terms. Here, we present an algorithm that finds the strengths of
the Hamiltonian terms by using the direction of the geodesic to the target
quantum gate on the Riemannian manifold of $\mathrm{SU}(2^n)$ for $n$ qubits.
Differential programming is used to determine how the Hamiltonian terms should
be updated in order to follow the geodesic to the target unitary as closely as
possible. We numerically compare our geodesic algorithm to gradient descent
methods and show that it finds solutions with considerably fewer steps for
standard multi-qubit gates such as Toffoli and Fredkin. The geodesic algorithm
is then used to find previously unavailable multi-qubit gates implementing high
fidelity parity checks, which could be used in a wide array of quantum codes
and increase the clock speed of fault-tolerant quantum computers.


  We provide an explicit expression for the first order $q$-difference system
for the Jackson integral of symmetric Selberg type. The $q$-difference system
gives a generalization of $q$-analog of contiguous relations for the Gauss
hypergeometric function. As a basis of the system we use a set of the symmetric
polynomials introduced by Matsuo in his study of the $q$-KZ equation. Our main
result is an explicit expression for the coefficient matrix of the
$q$-difference system in terms of its Gauss matrix decomposition. We introduce
a class of symmetric polynomials called interpolation polynomials, which
includes Matsuo's polynomials. By repeated use of three-term relations among
the interpolation polynomials we compute the coefficient matrix.


  The aim of the MIMAC project is to detect non-baryonic Dark Matter with a
directional TPC using a high precision Micromegas readout plane. We will
describe in detail the recent developments done with bulk Micromegas detectors
as well as the characterisation measurements performed in an
Argon(95%)-Isobutane(5%) mixture. Track measurements with alpha particles will
be shown.


  We develop a detailed regularity theory of $-\Delta +b\cdot\nabla$ in
$L^p(\mathbb R^d)$, for a wide class of vector fields. The $L^p$-theory allows
us to construct associated strong Feller process in $C_\infty(\mathbb R^d)$.
Our starting object is an operator-valued function, which, we prove, coincides
with the resolvent of an operator realization of $-\Delta + b\cdot \nabla$, the
generator of a holomorphic $C_0$-semigroup on $L^p(\mathbb R^d)$. Then the very
form of the operator-valued function yields crucial information about
smoothness of the domain of the generator.


  I present the reconstruction of the involvement of Karl Popper in the
community of physicists concerned with foundations of quantum mechanics, in the
1980s. At that time Popper gave active contribution to the research in physics,
of which the most significant is a new version of the EPR thought experiment,
alleged to test different interpretations of quantum mechanics. The genesis of
such an experiment is reconstructed in detail, and an unpublished letter by
Popper is reproduced in the present paper to show that he formulated his
thought experiment already two years before its first publication in 1982. The
debate stimulated by the proposed experiment as well as Popper's role in the
physics community throughout 1980s is here analysed in detail by means of
personal correspondence and publications.


  We propose the simplest possible renormalizable extension of the Standard
Model - the addition of just one singlet scalar field - as a minimalist model
for non-baryonic dark matter. Such a model is characterized by only three
parameters in addition to those already appearing within the Standard Model: a
dimensionless self-coupling and a mass for the new scalar, and a dimensionless
coupling, \lambda, to the Higgs field. If the singlet is the dark matter, these
parameters are related to one another by the cosmological abundance constraint,
implying that the coupling of the singlet to the Higgs field is large, \lambda
\sim O(0.1 - 1). Since this parameter also controls couplings to ordinary
matter, we obtain predictions for the elastic cross section of the singlet with
nuclei. The resulting scattering rates are close to current limits from both
direct and indirect searches. The existence of the singlet also has
implications for current Higgs searches, as it gives a large contribution to
the invisible Higgs width for much of parameter space. These scalars can be
strongly self-coupled in the cosmologically interesting sense recently proposed
by Spergel and Steinhardt, but only for very low masses (< 1 GeV), which is
possible only at the expense of some fine-tuning of parameters.


  We present exact analytic results for the energy of a SU(N) repulsive Fermi
gas as a function of the spin-channel occupation at second order in the gas
parameter. This is an extension of an old result that now incorporates the
degree of polarization of the system. Therefore, the magnetic properties of the
gas can be obtained, free from numerical uncertainties. For spin 1/2 we find
that second-order corrections change the itinerant ferromagnetic transition
from continuous to first-order. Instead, for spin larger than 1/2 the phase
transition is always of first-order type. The transition critical density
reduces when the spin increases, making the phase transition more accessible to
experiments with ultracold dilute Fermi gases. Estimations for Fermi gases of
Yb and Sr with spin 5/2 and 9/2, respectively, are reported.


  I summarize current knowledge of galaxy formation with emphasis on the
initial conditions provided by the Lambda CDM cosmology, integral constraints
from cosmological quantities, and the demographics of high-redshift
protogalaxies. Tables are provided summarizing the number density, star
formation rate and stellar mass per object, cosmic star formation rate and
stellar mass densities, clustering length and typical dark matter halo masses
for Lyman break galaxies, Lyman alpha emitting galaxies, Distant red galaxies,
Sub-millimeter galaxies, and Damped Lyman alpha absorption systems. I also
discuss five key unsolved problems in galaxy formation and prognosticate
advances that the near future will bring.


  We present Loc-NeRF, a real-time vision-based robot localization approach
that combines Monte Carlo localization and Neural Radiance Fields (NeRF). Our
system uses a pre-trained NeRF model as the map of an environment and can
localize itself in real-time using an RGB camera as the only exteroceptive
sensor onboard the robot. While neural radiance fields have seen significant
applications for visual rendering in computer vision and graphics, they have
found limited use in robotics. Existing approaches for NeRF-based localization
require both a good initial pose guess and significant computation, making them
impractical for real-time robotics applications. By using Monte Carlo
localization as a workhorse to estimate poses using a NeRF map model, Loc-NeRF
is able to perform localization faster than the state of the art and without
relying on an initial pose estimate. In addition to testing on synthetic data,
we also run our system using real data collected by a Clearpath Jackal UGV and
demonstrate for the first time the ability to perform real-time global
localization with neural radiance fields. We make our code publicly available
at https://github.com/MIT-SPARK/Loc-NeRF.


  The purpose of this dissertation is to study the intersection theory of the
moduli spaces of stable maps of degree two from two-pointed, genus zero nodal
curves to arbitrary-dimensional projective space. Toward this end, first the
Betti numbers of \bar{M}_{0,2}(P^r,2) are computed using Serre polynomials and
equivariant Serre polynomials. Then, specializing to the space
\bar{M}_{0,2}(P^1,2), generators and relations for the Chow ring are given.
Chow rings of simpler spaces are also described, and the method of localization
and linear algebra is developed. Both tools are used in finding the relations.
It is further demonstrated that no additional relations exist among the
generators, so that a presentation for the Chow ring A^*(\bar{M}_{0,2}(P^1,2))
is obtained. As a further check of the presentation, it is applied to give a
new computation of the previously known genus zero, degree two, two-pointed
gravitational correlators of P^1.
  Portions of this work also appear in math.AG/0501322 and math.AG/0504575, but
the dissertation contains significantly more background and detail for those
who may be interested in these. The dissertation is preserved in original form
except for spacing changes, elimination of some front and end materials,
additions to some references, and correction of typos in Proposition 11.


  We construct a DGP inspired braneworld scenario where a scalar field
non-minimally coupled to the induced Ricci curvature is present on the brane.
First we investigate the status of gravitational potential with non-minimal
coupling and observational constraints on this non-minimal model. Then we
further deepen the idea of embedding of FRW cosmology in this non-minimal
setup. Cosmological implications of this scenario are examined with details and
the quintessence and late-time expansion of the universe within this framework
are examined. Some observational constraints imposed on this non-minimal
scenario are studied and relation of this model with dark radiation formalism
is determined with details.


  Small wind projects encounter difficulties to be efficiently deployed, partly
because wrong way data and information are managed. Ontologies can overcome the
drawbacks of partially available, noisy, inconsistent, and heterogeneous data
sources, by providing a semantic middleware between low level data and more
general knowledge. In this paper, we engineer an ontology for the wind energy
domain using description logic as technical instrumentation. We aim to
integrate corpus of heterogeneous knowledge, both digital and human, in order
to help the interested user to speed-up the initialization of a small-scale
wind project. We exemplify one use case scenario of our ontology, that consists
of automatically checking whether a planned wind project is compliant or not
with the active regulations.


  This dissertation aims to provide a comprehensive account of set theory with
urelements. In Chapter 1, I present mathematical and philosophical motivations
for studying urelement set theory and lay out the necessary technical
preliminaries. Chapter 2 is devoted to the axiomatization of urelement set
theory, where I introduce a hierarchy of axioms and discuss how ZFC with
urelements should be axiomatized. The breakdown of this hierarchy of axioms in
the absence of the Axiom of Choice is also explored. In Chapter 3, I
investigate forcing with urelements and develop a new approach that addresses a
drawback of the existing machinery. I demonstrate that forcing can preserve,
destroy, and recover the axioms isolated in Chapter 2 and discuss how Boolean
ultrapowers can be applied in urelement set theory. Chapter 4 delves into class
theory with urelements. I first discuss the issue of axiomatizing urelement
class theory and then explore the second-order reflection principle with
urelements. In particular, assuming large cardinals, I construct a model of
second-order reflection where the principle of limitation of size fails.


  Phase retrieval is the nonlinear inverse problem of recovering a true signal
from its Fourier magnitude measurements. It arises in many applications such as
astronomical imaging, X-Ray crystallography, microscopy, and more. The problem
is highly ill-posed due to the phase-induced ambiguities and the large number
of possible images that can fit to the given measurements. Thus, there's a rich
history of enforcing structural priors to improve solutions including sparsity
priors and deep-learning-based generative models. However, such priors are
often limited in their representational capacity or generalizability to
slightly different distributions. Recent advancements in using denoisers as
regularizers for non-convex optimization algorithms have shown promising
performance and generalization. We present a way of leveraging the prior
implicitly learned by a denoiser to solve phase retrieval problems by
incorporating it in a classical alternating minimization framework. Compared to
performant denoising-based algorithms for phase retrieval, we showcase
competitive performance with Fourier measurements on in-distribution images and
notable improvement on out-of-distribution images.


  In the last decades, a very important breakthrough has been brought in the
elementary particle physics by the discovery of the phenomenon of the neutrino
oscillations, which has shown neutrino properties beyond the Standard Model.
But a full understanding of the various aspects of the neutrino oscillations is
far to be achieved. In this paper the theoretical background of the neutrino
oscillation phenomenon is described, referring in particular to the
paradigmatic models. Then the various techniques and detectors which studied
neutrinos from different sources are discussed, starting from the pioneering
ones up to the detectors still in operation and to those in preparation. The
physics results are finally presented adopting the same research path which has
crossed this long saga. The problems not yet fixed in this field are discussed,
together with the perspectives of their solutions in the near future.


  Multi-person pose estimation is an important but challenging problem in
computer vision. Although current approaches have achieved significant progress
by fusing the multi-scale feature maps, they pay little attention to enhancing
the channel-wise and spatial information of the feature maps. In this paper, we
propose two novel modules to perform the enhancement of the information for the
multi-person pose estimation. First, a Channel Shuffle Module (CSM) is proposed
to adopt the channel shuffle operation on the feature maps with different
levels, promoting cross-channel information communication among the pyramid
feature maps. Second, a Spatial, Channel-wise Attention Residual Bottleneck
(SCARB) is designed to boost the original residual unit with attention
mechanism, adaptively highlighting the information of the feature maps both in
the spatial and channel-wise context. The effectiveness of our proposed modules
is evaluated on the COCO keypoint benchmark, and experimental results show that
our approach achieves the state-of-the-art results.


  We show that every infinite graph which is locally finite and connected
admits a translation-like action by $\mathbb{Z}$ such that the distance between
a vertex $v$ and $v\ast 1$ is uniformly bounded by 3. This action can be taken
to be transitive if and only if the graph has one or two ends. This strengthens
a theorem by Brandon Seward.
  Our proof is constructive, and thus it can be made computable. More
precisely, we show that a finitely generated group with decidable word problem
admits a translation-like action by $\mathbb{Z}$ which is computable, and
satisfies an extra condition which we call decidable orbit membership problem.
  As an application we show that on any finitely generated infinite group with
decidable word problem, effective subshifts attain all effectively closed
Medvedev degrees. This extends a classification proved by Joseph Miller for
$\mathbb{Z}^{d},$ $d\geq1$.


  We study the dissipative dynamics of a two-level system under ultrastrong
driving when the frequency and strength of the exciting field exceed
significantly the transition frequency. We find three qualitatively different
regimes of such dynamics: 1) the collapse and revival of oscillations in the
population difference, 2) the simple exponential decay of the oscillations
resulting in their steady state with the finite amplitude, and 3) the
steady-state stabilization of the equally populated levels. The nonmonotonic
Bessel-function-like dependence on the driving strength is also predicted for
the decay rate of these oscillations. The features of this dependence are
determined by the relative rates of energetic relaxation and pure dephasing.


  In this paper we study the everywhere H\"older continuity of the minima of a
class of vectorial integral functionals


  Triplet loss is a widely adopted loss function in ReID task which pulls the
hardest positive pairs close and pushes the hardest negative pairs far away.
However, the selected samples are not the hardest globally, but the hardest
only in a mini-batch, which will affect the performance. In this report, a hard
batch mining method is proposed to mine the hardest samples globally to make
triplet harder. More specifically, the most similar classes are selected into a
same mini-batch so that the similar classes could be pushed further away.
Besides, an adversarial scene removal module composed of a scene classifier and
an adversarial loss is used to learn scene invariant feature representations.
Experiments are conducted on dataset MSMT17 to prove the effectiveness, and our
method surpasses all of the previous methods and sets state-of-the-art result.


  In deep CNN based models for semantic segmentation, high accuracy relies on
rich spatial context (large receptive fields) and fine spatial details (high
resolution), both of which incur high computational costs. In this paper, we
propose a novel architecture that addresses both challenges and achieves
state-of-the-art performance for semantic segmentation of high-resolution
images and videos in real-time. The proposed architecture relies on our fast
spatial attention, which is a simple yet efficient modification of the popular
self-attention mechanism and captures the same rich spatial context at a small
fraction of the computational cost, by changing the order of operations.
Moreover, to efficiently process high-resolution input, we apply an additional
spatial reduction to intermediate feature stages of the network with minimal
loss in accuracy thanks to the use of the fast attention module to fuse
features. We validate our method with a series of experiments, and show that
results on multiple datasets demonstrate superior performance with better
accuracy and speed compared to existing approaches for real-time semantic
segmentation. On Cityscapes, our network achieves 74.4$\%$ mIoU at 72 FPS and
75.5$\%$ mIoU at 58 FPS on a single Titan X GPU, which is~$\sim$50$\%$ faster
than the state-of-the-art while retaining the same accuracy.


  Strong nonlinear materials have been sought after for decades for
applications in telecommunications, sensing, and quantum optics. Gallium-doped
zinc oxide is a II-VI transparent conducting oxide that shows promising
nonlinearities similar to indium tin oxide and aluminum-doped zinc oxide for
the telecommunications band. Here we explore its nonlinearities in the epsilon
near zero (ENZ) region and show n2,eff values on the order of 4.5x10-3 cm2GW-1
for IR pumping on 200-300 nm thin films. Measuring nonlinear changes in
transmission and reflection with a white light source probe in the near-IR
while exciting in the near-IR provides data in both time and wavelength. Three
films varying in thickness, optical loss, and ENZ crossover wavelength are
numerically modeled and compared to experimental data showing agreement for
both dispersion and temporal relaxation. In addition, we discuss optimal
excitation and probing wavelengths occur around ENZ for thick films but are
red-shifted for thin films where our model provides an additional degree of
freedom to explore. Obtaining accurate nonlinear measurements is a difficult
and time-consuming task where our method in this paper provides experimental
and modeled data to the community for an ENZ material of interest.


  The control of a robot for manipulation tasks generally relies on object
detection and pose estimation. An attractive alternative is to learn control
policies directly from raw input data. However, this approach is time-consuming
and expensive since learning the policy requires many trials with robot actions
in the physical environment. To reduce the training cost, the policy can be
learned in simulation with a large set of synthetic images. The limit of this
approach is the domain gap between the simulation and the robot workspace. In
this paper, we propose to learn a policy for robot reaching movements from a
single image captured directly in the robot workspace from a camera placed on
the end-effector (a hand-eye camera). The idea behind the proposed policy
learner is that view changes seen from the hand-eye camera produced by actions
in the robot workspace are analogous to locating a region-of-interest in a
single image by performing sequential object localisation. This similar view
change enables training of object reaching policies using
reinforcement-learning-based sequential object localisation. To facilitate the
adaptation of the policy to view changes in the robot workspace, we further
present a dynamic filter that learns to bias an input state to remove
irrelevant information for an action decision. The proposed policy learner can
be used as a powerful representation for robotic tasks, and we validate it on
static and moving object reaching tasks.


  Due to the limited number of photons, directly imaging planets requires long
integration times with a coronagraphic instrument. The wavefront must be stable
on the same time scale, which is often difficult in space due to thermal
variations and other mechanical instabilities. In this paper, we discuss the
implications on future space mission observing conditions of our recent
laboratory demonstration of a dark zone maintenance (DZM) algorithm. The
experiments are performed on the High-contrast imager for Complex Aperture
Telescopes (HiCAT) at the Space Telescope Science Institute (STScI). The
testbed contains a segmented aperture, a pair of continuous deformable mirrors
(DMs), and a lyot coronagraph. The segmented aperture injects high order
wavefront aberration drifts into the system which are then corrected by the DMs
downstream via the DZM algorithm. We investigate various drift modes including
segmented aperture drift, all three DMs drift simultaneously, and drift
correction at multiple wavelengths.


  Serverless computing has emerged as a popular cloud deployment paradigm. In
serverless, the developers implement their application as a set of chained
functions that form a workflow in which functions invoke each other. The cloud
providers are responsible for automatically scaling the number of instances for
each function on demand and forwarding the requests in a workflow to the
appropriate function instance. Problematically, today's serverless clouds lack
efficient support for cross-function data transfers in a workflow, preventing
the efficient execution of data-intensive serverless applications. In
production clouds, functions transmit intermediate, i.e., ephemeral, data to
other functions either as part of invocation HTTP requests (i.e., inline) or
via third-party services, such as AWS S3 storage or AWS ElastiCache in-memory
cache. The former approach is restricted to small transfer sizes, while the
latter supports arbitrary transfers but suffers from performance and cost
overheads. This work introduces Expedited Data Transfers (XDT), an
API-preserving high-performance data communication method for serverless that
enables direct function-to-function transfers. With XDT, a trusted component of
the sender function buffers the payload in its memory and sends a secure
reference to the receiver, which is picked by the load balancer and autoscaler
based on the current load. Using the reference, the receiver instance pulls the
transmitted data directly from the sender's memory. XDT is natively compatible
with existing autoscaling infrastructure, preserves function invocation
semantics, is secure, and avoids the cost and performance overheads of using an
intermediate service for data transfers. We prototype our system in
vHive/Knative deployed on a cluster of AWS EC2 nodes, showing that XDT improves
latency, bandwidth, and cost over AWS S3 and ElasticCache.


  Target speech separation refers to extracting the target speaker's speech
from mixed signals. Despite the recent advances in deep learning based
close-talk speech separation, the applications to real-world are still an open
issue. Two main challenges are the complex acoustic environment and the
real-time processing requirement. To address these challenges, we propose a
temporal-spatial neural filter, which directly estimates the target speech
waveform from multi-speaker mixture in reverberant environments, assisted with
directional information of the speaker(s). Firstly, against variations brought
by complex environment, the key idea is to increase the acoustic representation
completeness through the jointly modeling of temporal, spectral and spatial
discriminability between the target and interference source. Specifically,
temporal, spectral, spatial along with the designed directional features are
integrated to create a joint acoustic representation. Secondly, to reduce the
latency, we design a fully-convolutional autoencoder framework, which is purely
end-to-end and single-pass. All the feature computation is implemented by the
network layers and operations to speed up the separation procedure. Evaluation
is conducted on simulated reverberant dataset WSJ0-2mix and WSJ0-3mix under
speaker-independent scenario. Experimental results demonstrate that the
proposed method outperforms state-of-the-art deep learning based multi-channel
approaches with fewer parameters and faster processing speed. Furthermore, the
proposed temporal-spatial neural filter can handle mixtures with varying and
unknown number of speakers and exhibits persistent performance even when
existing a direction estimation error. Codes and models will be released soon.


  Semi-supervised Laplacian regularization, a standard graph-based approach for
learning from both labelled and unlabelled data, was recently demonstrated to
have an insignificant high dimensional learning efficiency with respect to
unlabelled data (Mai and Couillet 2018), causing it to be outperformed by its
unsupervised counterpart, spectral clustering, given sufficient unlabelled
data. Following a detailed discussion on the origin of this inconsistency
problem, a novel regularization approach involving centering operation is
proposed as solution, supported by both theoretical analysis and empirical
results.


  In this article we consider commuting graphs of involution conjugacy classes
in the affine Weyl group of type $\tilde C_n$. We show that where the graph is
connected the diameter is at most $n+2$.


  Regularized system identification is the major advance in system
identification in the last decade. Although many promising results have been
achieved, it is far from complete and there are still many key problems to be
solved. One of them is the asymptotic theory, which is about convergence
properties of the model estimators as the sample size goes to infinity. The
existing related results for regularized system identification are about the
almost sure convergence of various hyper-parameter estimators. A common problem
of those results is that they do not contain information on the factors that
affect the convergence properties of those hyper-parameter estimators, e.g.,
the regression matrix. In this paper, we tackle problems of this kind for the
regularized finite impulse response model estimation with the empirical Bayes
(EB) hyper-parameter estimator and filtered white noise input. In order to
expose and find those factors, we study the convergence in distribution of the
EB hyper-parameter estimator, and the asymptotic distribution of its
corresponding model estimator. For illustration, we run Monte Carlo simulations
to show the efficacy of our obtained theoretical results.


  We report a direct correlation between carrier mobility and Raman topography
of epitaxial graphene (EG) grown on silicon carbide (SiC). We show the Hall
mobility of material on the Si-face of SiC [SiC(0001)] is not only highly
dependent on thickness uniformity but also on monolayer strain uniformity. Only
when both thickness and strain are uniform over a significant fraction (> 40%)
of the device active area does the mobility exceed 1000 cm2/V-s. Additionally,
we achieve high mobility epitaxial graphene (18,100 cm2/V-s at room
temperature) on the C-face of SiC [SiC(000-1)] and show that carrier mobility
depends strongly on the graphene layer stacking. These findings provide a means
to rapidly estimate carrier mobility and provide a guide to achieve very high
mobility in epitaxial graphene. Our results suggest that ultra-high mobilities
(>50,000 cm2/V-s) are achievable via the controlled formation of uniform,
rotationally faulted epitaxial graphene.


  In this article, we propose sampled-data H-infinity design of digital filters
that cancel the continuous-time effect of coupling waves in a single-frequency
full-duplex relay station. In this study, we model a relay station as a
continuous-time system while conventional researches treat it as a
discrete-time system. For a continuous-time model, we propose digital
feedforward and feedback cancelers based on the sampled-data control theory to
cancel coupling waves taking intersample behavior into account. Simulation
results are shown to illustrate the effectiveness of the proposed method.


  Cartesian products of graphs and hypergraphs have been studied since the
1960s. For (un)directed hypergraphs, unique \emph{prime factor decomposition
(PFD)} results with respect to the Cartesian product are known. However, there
is still a lack of algorithms, that compute the PFD of directed hypergraphs
with respect to the Cartesian product.
  In this contribution, we focus on the algorithmic aspects for determining the
Cartesian prime factors of a finite, connected, directed hypergraph and present
a first polynomial time algorithm to compute its PFD. In particular, the
algorithm has time complexity $O(|E||V|r^2)$ for hypergraphs $H=(V,E)$, where
the rank $r$ is the maximum number of vertices contained in an hyperedge of
$H$. If $r$ is bounded, then this algorithm performs even in
$O(|E|\log^2(|V|))$ time. Thus, our method additionally improves also the time
complexity of PFD-algorithms designed for undirected hypergraphs that have time
complexity $O(|E||V|r^6\Delta^6)$, where $\Delta$ is the maximum number of
hyperedges a vertex is contained in.


  The $q$-Coloring problem asks whether the vertices of a graph can be properly
colored with $q$ colors. Lokshtanov et al. [SODA 2011] showed that $q$-Coloring
on graphs with a feedback vertex set of size $k$ cannot be solved in time
$\mathcal{O}^*((q-\varepsilon)^k)$, for any $\varepsilon > 0$, unless the
Strong Exponential-Time Hypothesis (SETH) fails. In this paper we perform a
fine-grained analysis of the complexity of $q$-Coloring with respect to a
hierarchy of parameters. We show that even when parameterized by the vertex
cover number, $q$ must appear in the base of the exponent: Unless ETH fails,
there is no universal constant $\theta$ such that $q$-Coloring parameterized by
vertex cover can be solved in time $\mathcal{O}^*(\theta^k)$ for all fixed $q$.
We apply a method due to Jansen and Kratsch [Inform. & Comput. 2013] to prove
that there are $\mathcal{O}^*((q - \varepsilon)^k)$ time algorithms where $k$
is the vertex deletion distance to several graph classes $\mathcal{F}$ for
which $q$-Coloring is known to be solvable in polynomial time. We generalize
earlier ad-hoc results by showing that if $\mathcal{F}$ is a class of graphs
whose $(q+1)$-colorable members have bounded treedepth, then there exists some
$\varepsilon > 0$ such that $q$-Coloring can be solved in time
$\mathcal{O}^*((q-\varepsilon)^k)$ when parameterized by the size of a given
modulator to $\mathcal{F}$. In contrast, we prove that if $\mathcal{F}$ is the
class of paths - some of the simplest graphs of unbounded treedepth - then no
such algorithm can exist unless SETH fails.


  We examine the influence of microwave photoexcitation on the amplitude of
Shubnikov-de Haas (SdH) oscillations in a two dimensional GaAs/AlGaAs electron
system in a regime where the cyclotron frequency, $\omega_{c}$, and the
microwave angular frequency, $\omega$, satisfy $2 \omega \le \omega_{c} \le 3.5
\omega$. A SdH lineshape analysis indicates that increasing the incident
microwave power has a weak effect on the amplitude of the SdH oscillations, in
comparison to the influence of modest temperature changes on the dark-specimen
SdH effect. The results indicate negligible electron heating under modest
microwave photoexcitation, in good agreement with theoretical predictions.


  The transverse polarization observed in the inclusive production of Lambda
hyperons in the high energy collisions of unpolarized hadrons is tackled by
considering a new set of spin and kT dependent quark fragmentation functions.
Simple phenomenological expressions for these new ``polarizing fragmentation
functions'' are obtained by a fit of the data on Lambda's and Lambdabar's
produced in p-N processes.


  Continuous Spontaneous Localization (CSL) is one possible explanation for
dynamically induced collapse of the wave-function during a quantum measurement.
The collapse is mediated by a stochastic non-linear modification of the
Schrodinger equation. A consequence of the CSL mechanism is an extremely tiny
violation of energy-momentum conservation, which can, in principle, be detected
in the laboratory via the random diffusion of a particle induced by the
stochastic collapse mechanism. In a paper in 2003, Collett and Pearle
investigated the translational CSL diffusion of a sphere, and the rotational
CSL diffusion of a disc, and showed that this effect dominates over the ambient
environmental noise at low temperatures and extremely low pressures (about
ten-thousandth of a pico-Torr). In the present paper, we revisit their analysis
and argue that this stringent condition on pressure can be relaxed, and that
the CSL effect can be seen at the pressure of about a pico-Torr. A similar
analysis is provided for diffusion produced by gravity-induced decoherence,
where the effect is typically much weaker than CSL. We also discuss the CSL
induced random displacement of a quantum oscillator. Lastly, we propose
possible experimental set-ups justifying that CSL diffusion is indeed
measurable with the current technology.


  We consider a macroscopic two-sate system based on persistent current states
of a Bose-Einstein condensate (BEC) of interacting neutral atoms confined in a
ring with a weak Josephson link. We demonstrate that macroscopic superpositions
of different BEC flows are energetically favorable in this system. Moreover, a
macroscopic two-state dynamics emerges in the low energy limit. We also
investigate fundamental limitations due to the noise inherent to the
interacting BEC of Josephson-ring geometry. We show that the coherent
macroscopic dynamics is readily measurable for an experimentally accessible
range of parameters.


  We re-examine the implications of allowing fermion fields to propagate in the
five-dimensional bulk of the Randall-Sundrum (RS) localized gravity model. We
find that mixing between the Standard Model top quark and its Kaluza Klein
excitations generates large contributions to the rho parameter and consequently
restricts the fundamental RS scale to lie above 100 TeV. To circumvent this
bound we propose a `mixed' scenario which localizes the third generation
fermions on the TeV brane and allows the lighter generations to propagate in
the full five-dimensional bulk. We show that this construction naturally
reproduces the observed m_c / m_t and m_s / m_b hierarchies. We explore the
signatures of this scenario in precision measurements and future high energy
collider experiments. We find that the region of parameter space that addresses
the hierarchies of fermion Yukawa couplings permits a Higgs boson with a mass
of 500 GeV and remains otherwise invisible at the LHC. However, the entire
parameter region consistent with electroweak precision data is testable at
future linear colliders. We briefly discuss possible constraints on this
scenario arising from flavor changing neutral currents.


  The manner in which probability amplitudes of paths sum up to form wave
functions of a harmonic oscillator, as well as other, simple 1-dimensional
problems, is described. Using known, closed-form, path-based propagators for
each problem, an integral expression is written that describes the wave
function. This expression conventionally takes the form of an integral over
initial locations of a particle, but it is re-expressed here in terms of a
characteristic momentum associated with motion between the endpoints of a path.
In this manner, the resulting expression can be analyzed using a generalization
of stationary-phase analysis, leading to distributions of paths that exactly
describe each eigenstate. These distributions are valid for all travel times,
but when evaluated for long times they turn out to be real, non-negative
functions of the characteristic momentum. For the harmonic oscillator in
particular, a somewhat broad distribution is found, peaked at value of momentum
that corresponds to a classical energy which in turn equals the energy
eigenvalue for the state being described.


  A method is presented to estimate the region of attraction (ROA) of
stochastic systems with finite second moment and uncertainty-dependent
equilibria. The approach employs Polynomial Chaos (PC) expansions to represent
the stochastic system by a higher-dimensional set of deterministic equations.
We first show how the equilibrium point of the deterministic formulation
provides the stochastic moments of an uncertainty-dependent equilibrium point
of the stochastic system. A connection between the boundedness of the moments
of the stochastic system and the Lyapunov stability of its PC expansion is then
derived. Defining corresponding notions of a ROA for both system
representations, we show how this connection can be leveraged to recover an
estimate of the ROA of the stochastic system from the ROA of the PC expanded
system. Two optimization programs, obtained from sum-of-squares programming
techniques, are provided to compute inner estimates of the ROA. The first
optimization program uses the Lyapunov stability arguments to return an
estimate of the ROA of the PC expansion. Based on this result and user
specifications on the moments for the initial conditions, the second one
employs the shown connection to provide the corresponding ROA of the stochastic
system. The method is demonstrated by two examples.


  We derive some properties of the Nambu-Goldstone boson coupling in theories
that have CP violation and Majorana masses. We show explicitly that its
diagonal coupling to a Majorana fermion is pseudoscalar not scalar. This
clarifies some confusion in the literature. Some potentially useful
off-diagonal properties are also derived. We also show, in the process, that
the Goldstone theorem often produces interesting and nontrivial identities in
matrix theory which may be hard to prove otherwise.


  Despite increasing data from population-wide sequencing studies, the risk for
recessive disorders in consanguineous partnerships is still heavily debated. An
important aspect that has not sufficiently been investigated theoretically, is
the influence of inbreeding on mutation load and incidence rates when the
population sizes change. We therefore developed a model to study these dynamics
for a wide range of growth and mating conditions. In the phase of population
expansion and shortly afterwards, our simulations show that there is a drop of
diseased individuals at the expense of an increasing mutation load for random
mating, while both parameters remain almost constant in highly consanguineous
partnerships. This explains the empirical observation in present times that a
high degree of consanguinity is associated with an increased risk of autosomal
recessive disorders. However, it also states that the higher frequency of
severe recessive disorders with developmental delay in inbred populations is a
transient phenomenon before a mutation-selection balance is reached again.


  While the photonic community is being occupied with exotic concepts
portending a grand future and fame if not a fortune, I respectfully entertain
the possibility that a humble concept of simply increasing refractive index by
a modest factor may have a far greater payoff in many walks of life. With that
in mind, I explore why higher index materials have not yet materialized, and
point out a few tentative directions for the search of these elusive materials,
be they natural or artificial.


  We address crystals of non-attractive colloidal spheres freely expanding into
particle-free environ-ments and melting during dilution. This problem has been
studied in two dimensions, both numeri-cally and in experiments on colloidal
model crystals. Here, we place three-dimensional drops of aqueous colloidal
charged sphere suspensions in a colloid-free, deionized aqueous environment.
Initially in a shear-molten state, they rapidly crystallize to a fine-grained
polycrystalline material of body centred cubic structure. They stabilize their
spherical shape within a few seconds. We over-come the challenges provided by
drop turbidity and use a combination of optical methods to follow the drop
evolution. The crystal ball shows a nearly fourfold increase of the volume
followed by slow shrinkage due to melting, which is nearly linear in time.
Exploiting coherent multiple-scattering by (110) Bragg reflecting crystals,
time-dependent density profiles were recorded within the drop interior. These
show a continuously flattening radial density gradient. Our experimental
situation is close to the isothermal three-dimensional expansion of a spherical
crystallite as described by a theoretical model based on dynamical density
functional theory. We obtain an overall good agree-ment of measured and
calculated expansion curves at most probed densities. We anticipate that our
study opens novel experimental and theoretical access to a long-standing
condensed matter issue.


  Due to the fluctuation of throughput under various network conditions, how to
choose a proper bitrate adaptively for real-time video streaming has become an
upcoming and interesting issue. Recent work focuses on providing high video
bitrates instead of video qualities. Nevertheless, we notice that there exists
a trade-off between sending bitrate and video quality, which motivates us to
focus on how to get a balance between them. In this paper, we propose QARC
(video Quality Awareness Rate Control), a rate control algorithm that aims to
have a higher perceptual video quality with possibly lower sending rate and
transmission latency. Starting from scratch, QARC uses deep reinforcement
learning(DRL) algorithm to train a neural network to select future bitrates
based on previously observed network status and past video frames, and we
design a neural network to predict future perceptual video quality as a vector
for taking the place of the raw picture in the DRL's inputs. We evaluate QARC
over a trace-driven emulation. As excepted, QARC betters existing approaches.


  We compare the spectra of Dynnikov matrices with the spectra of the train
track transition matrices of a given pseudo-Anosov braid on the finitely
punctured disk, and show that these matrices are isospectral up to roots of
unity and zeros under some particular conditions.


  The energy losses of a small black hole passing through the Earth are
examined. In particular, we investigate the excitations in the frequency range
accessible to modern acoustic detectors. The main contribution to the effect is
given by the coherent sound radiation of the Cherenkov type.


  Charge and spin transport in a junction involving two triplet superconductors
and a ferromagnetic barrier are studied. We use Bogoliubov-de Gennes
wavefunctions to construct the Green's function, from which we obtain the
Josephson currents in terms of the Andreev reflection coefficients. We focus on
the consequences of a finite barrier width for the occurrence of 0-\pi
transitions and for the spin currents, and examine the appropriateness of the
common \delta-function approximation for the tunneling region.


  Tunnelling impurities in metals have been known for some time to have the
potential for exhibiting Kondo-like physics. However previous models based on
an impurity hopping between two equivalent positions have run into trouble due
to the existence of relevant operators that drive the system away from the
non-Fermi-liquid Kondo fixed point. In the case of an impurity hopping among
positions with higher symmetry, such as triangular symmetry, it is shown here
that the non-Fermi-liquid behavior at low temperatures can be generic. Using
various bosonization techniques, the fixed point is shown to be {\em stable}.
However, unlike the conventional two-channel Kondo (2CK) model, it has {\em
four} leading irrelevant operators, implying that while the form of the
singular temperature dependence of physical quantities is similar to the 2CK
model, there will not be simple universal amplitude ratios. The phase diagram
of this system is analyzed and a critical manifold is found to separate the
non-Fermi-liquid from a conventional Fermi liquid fixed point. Generalization
to higher symmetries, such as cubic, and the possibility of physical
realizations with dynamic Jahn-Teller impurities is discussed.


  In this paper, we develop a tropical analog of the classical flag variety
that we call the flag Dressian. We find relations, which we call "tropical
incidence relations", for when one tropical linear space is contained in
another, and show that the flag Dressian is a tropical prevariety. In the case
of 2-step flag Dressians, which we call "tropical incidence prevarieties", we
find an equivalence between points in this space and induced subdivisions of a
hypersimplex, generalizing two parts of an equivalence given by D. Speyer for
tropical linear spaces. We attempt to generalize the third part of Speyer's
equivalence to concordant matroids and obtain some partial results.


  In this work we study the problem of rope sway dynamics control for elevator
systems. We choose to actuate the system with a semi-active damper mounted on
the top of the elevator car. We propose nonlinear controllers based on Lyapunov
theory, to actuate the semi-active damper and stabilize the rope sway dynamics.
We study the stability of the proposed controllers, and test their performances
on a numerical example.


  We give a general constructive proof for hierarchical coordinatizations
(Lagrange Decompositions) of permutation groups. The generalization originates
from the investigation of how the subgroup chains of finite permutation groups
yield different coordinate systems. The study is motivated by the practical
needs and the verification of an existing computational implementation. Large
scale machine calculated examples are also presented.


  It is generally known that the holomorphic anomaly equations in topological
string theory reflect the quantum mechanical nature of the topological string
partition function. We present two new results which make this assertion more
precise: (i) we give a new, purely holomorphic version of the holomorphic
anomaly equations, clarifying their relation to the heat equation satisfied by
the Jacobi theta series; (ii) in cases where the moduli space is a Hermitian
symmetric tube domain $G/K$, we show that the general solution of the anomaly
equations is a matrix element $\IP{\Psi | g | \Omega}$ of the
Schr\"odinger-Weil representation of a Heisenberg extension of $G$, between an
arbitrary state $\bra{\Psi}$ and a particular vacuum state $\ket{\Omega}$.
Based on these results, we speculate on the existence of a one-parameter
generalization of the usual topological amplitude, which in symmetric cases
transforms in the smallest unitary representation of the duality group $G'$ in
three dimensions, and on its relations to hypermultiplet couplings, nonabelian
Donaldson-Thomas theory and black hole degeneracies.


  The author finds geodesics, shortest arcs, cut locus, and conjugate sets for
left-invariant sub-Riemannian metric on the Lie group $SO_0(2,1)$ under the
condition that the metric is right-invariant relative to the Lie subgroup
$SO(2)\subset SO_0(2,1)$.


  We investigate the Schwarzschild-Anti-deSitter (SAdS) and SdS BH
thermodynamics in 5d higher derivative gravity. The interesting feature of
higher derivative gravity is the possibility for negative (or zero) SdS (or
SAdS) BH entropy which depends on the parameters of higher derivative terms.
The appearence of negative entropy may indicate a new type instability where a
transition between SdS (SAdS) BH with negative entropy to SAdS (SdS) BH with
positive entropy would occur or where definition of entropy should be modified.


  The splitting processes of bremsstrahlung and pair production in a medium are
coherent over large distances in the very high energy limit, which leads to a
suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We continue
study of the case when the coherence lengths (formation lengths) of two
consecutive splitting processes overlap, avoiding soft-emission approximations.
Previous work made a ``nearly-complete'' calculation of the effect of
overlapping formation times on gluonic splittings such as $g \to gg \to ggg$
(with simplifying assumptions such as an infinite QCD medium and the
large-$N_c$ limit). In this paper, we extend those previous rate calculations
from nearly-complete to complete by including processes involving the exchange
of longitudinally-polarized gluons. In the context of Lightcone Pertubation
Theory, used earlier for the ``nearly-complete'' calculation, such exchanges
are instantaneous in lightcone time and have their own diagrammatic
representation.


  We report on experiments exploring the interplay between the topology of the
complex network of dependent components in a large-scale data-centre, and the
robustness and scaling properties of that data-centre. In a previous paper [1]
we used the SPECI large-scale data-centre simulator [2] to compare the
robustness and scaling characteristics of data-centres whose dependent
components are connected via Strogatz-Watts small-world (SW) networks [3],
versus those organized as Barabasi-Albert scale-free (SF) networks [4], and
found significant differences. In this paper, we present results from using the
Klemm-Eguiliz (KE) construction method [5] to generate complex network
topologies for data-centre component dependencies. The KE model has a control
parameter {\mu}\in[0,1]\inR that determines whether the networks generated are
SW (0<{\mu}<<1) or SF ({\mu}=1) or a "hybrid" network topology part-way between
SW and SF (0<{\mu}<1). We find that the best scores for system-level
performance metrics of the simulated data-centres are given by "hybrid" values
of {\mu} significantly different from pure-SW or pure-SF.


  We show that under certain conditions one-dimensional dielectric lattice
possesses total omnidirectional reflection of incident light. The predictions
are verified experimentally using Na3AlF6/ZnSe multilayer structure developed
by means of standard optical technology. The structure was found to exhibit
reflection coefficient more then 99% in the range of incident angles 0-86
(degree) at the wavelength of 632.8 nm for s-polarization. The results are
believed to stimulate new experiments on photonic crystals and controlled
spontaneous emission.


  Energies and transition probabilities for low lying states in $^{134}$Ba and
$^{104$Ru were calculated within a hybrid model.The ground and the first $2^+$
states are described alternatively as a harmonic and anharmonic vibrator states
while the remaining states as states with E(5) symmetry. One concludes that a
gradual setting of the 'critical' potential yields a better agreement with the
experimental data. Very good agreement with the data is obtained for
$^{104}$Ru. Comparing the present results with those of E(5) symmetry, it is
conspicuous that the present formalism add corrections to the E(5) formalism by
bringing the predictions closer to the experimental data. Analytical
relationship between the states with U(5) symmetry and those given by the E(5)
description is established.


  We present a workable model for the fermion-photon vertex, which is expressed
solely in terms of functions that appear in the fermion propagator and
independent of the angle between the relative momenta, and does not explicitly
depend on the covariant-gauge parameter. It nevertheless produces a critical
coupling for dynamical chiral symmetry breaking that is practically independent
of the covariant-gauge parameter and an anomalous magnetic moment distribution
for the dressed fermion that agrees in important respects with realistic
numerical solutions of the inhomogeneous vector Bethe-Salpeter equation.


  Based on Smale mean value conjecture \textit{[Bull. Amer. Math. Soc., 1981]}
and Dubinin-Sugawa dual mean value conjecture \textit{[Proc. Japan Acad. Ser. A
Math. Sci., 2009]} we formulate the following conjectures.
  \textbf{C*-algebraic Smale Mean Value Conjecture : Let $\mathcal{A}$ be a
commutative C*-algebra. Let $P(z)= (z-a_1)\cdots (z-a_n)$ be a polynomial of
degree $n\geq 2$ over $\mathcal{A}$, $a_1, \dots, a_n \in \mathcal{A}$. If
$z\in\mathcal{A}$ is not a critical point of $P$, then there exists a critical
point $w\in \mathcal{A}$ of $P$ such that \begin{align*}
  \frac{\|P(z)-P(w)\|}{\|z-w\|}\leq 1 \|P'(z)\| \end{align*} or \begin{align*}
  \frac{\|P(z)-P(w)\|}{\|z-w\|}\leq \frac{n-1}{n}
\|P'(z)\|=\frac{\operatorname{deg} (P)-1}{\operatorname{deg} (P)} \|P'(z)\|.
  \end{align*}}
  \textbf{C*-algebraic Dubinin-Sugawa Dual Mean Value Conjecture : Let
$\mathcal{A}$ be a commutative C*-algebra. Let $P(z)= (z-a_1)\cdots (z-a_n)$ be
a polynomial of degree $n\geq 2$ over $\mathcal{A}$, $a_1, \dots, a_n \in
\mathcal{A}$. If $z\in \mathcal{A}$ is not a critical point of $P$, then there
exists a critical point $w\in \mathcal{A}$ of $P$ such that
  \begin{align*}
  \frac{\|P'(z)\|}{\operatorname{deg} (P)} =\frac{\|P'(z)\|}{n} \leq
\frac{\|P(z)-P(w)\|}{\|z-w\|}. \end{align*}} We show that (even a strong form
of) C*-algebraic Smale mean value conjecture and C*-algebraic Dubinin-Sugawa
dual mean value conjecture hold for degree 2 C*-algebraic polynomials over
commutative C*-algebras.


  We use Fra\" iss\' e theoretic methods to construct a universal and
ultrahomogeneous abelian separable metric group. We show that such a group is a
universal abelian Polish group, thus we provide another proof of a result
already discovered by Shkarin. We then construct universal and ultrahomogeneous
abelian periodic metric groups with bounded exponents; it follows that these
groups are also universal objects for the corresponding classes of abelian
Polish groups.


  We present a general procedure for determining possible (nonuniform) magnetic
fields such that the Pauli equation becomes quasi-exactly solvable (QES) with
an underlying $sl(2)$ symmetry. This procedure makes full use of the close
connection between QES systems and supersymmetry. Of the ten classes of
$sl(2)$-based one-dimensional QES systems, we have found that nine classes
allow such construction.


  By using the supersymmetry method we derive an explicit expression for the
parametric correlation function of densities of eigenphases $\theta_a$ of the
S-matrix in a chaotic quantum system with broken time-reversal symmetry coupled
to continua via M equivalent open channels;$\,\,a=1,..,M$ .We use it to find
the distribution of derivatives of these eigenphases over the energy
("phaseshift times") as well as over an arbitrary external parameter.We also
find the parametric correlations of Wigner-Smith delay times


  Let $H = (V,E)$ be a hypergraph with vertex set $V$ and edge set $E$ of order
$\nH = |V|$ and size $\mH = |E|$. A transversal in $H$ is a subset of vertices
in $H$ that has a nonempty intersection with every edge of $H$. A vertex hits
an edge if it belongs to that edge. The transversal game played on $H$ involves
of two players, \emph{Edge-hitter} and \emph{Staller}, who take turns choosing
a vertex from $H$. Each vertex chosen must hit at least one edge not hit by the
vertices previously chosen. The game ends when the set of vertices chosen
becomes a transversal in $H$. Edge-hitter wishes to minimize the number of
vertices chosen in the game, while Staller wishes to maximize it. The
\emph{game transversal number}, $\tau_g(H)$, of $H$ is the number of vertices
chosen when Edge-hitter starts the game and both players play optimally. We
compare the game transversal number of a hypergraph with its transversal
number, and also present an important fact concerning the monotonicity of
$\tau_g$, that we call the Transversal Continuation Principle. It is known that
if $H$ is a hypergraph with all edges of size at least~$2$, and $H$ is not a
$4$-cycle, then $\tau_g(H) \le \frac{4}{11}(\nH+\mH)$; and if $H$ is a
(loopless) graph, then $\tau_g(H) \le \frac{1}{3}(\nH + \mH + 1)$. We prove
that if $H$ is a $3$-uniform hypergraph, then $\tau_g(H) \le \frac{5}{16}(\nH +
\mH)$, and if $H$ is $4$-uniform, then $\tau_g(H) \le \frac{71}{252}(\nH +
\mH)$.