  A subset of blazars emit TeV gamma rays which annihilate and pair produce on
the extragalactic background light. We have argued in Broderick et al. (2011,
Paper I) that plasma beam instabilities can dissipate the pairs' energy
locally. This heats the intergalactic medium and dramatically increases its
entropy after redshift z~2, with important implications for structure
formation: (1) This suggests a scenario for the origin of the cool core
(CC)/non-cool core (NCC) bimodality in galaxy clusters and groups. Early
forming galaxy groups are unaffected because they can efficiently radiate the
additional entropy, developing a CC. However, late forming groups do not have
sufficient time to cool before the entropy is gravitationally reprocessed
through successive mergers - counteracting cooling and raising the core entropy
further. Hence blazar heating works different than feedback by active galactic
nuclei, which balances radiative cooling but is unable to transform CC into NCC
clusters due to the weak coupling to the cluster gas. (2) We predict a
suppression of the Sunyaev-Zel'dovich power spectrum on angular scales smaller
than 5' due to the globally reduced central pressure of groups and clusters
forming after z~1. (3) Our redshift dependent entropy floor increases the
characteristic halo mass below which dwarf galaxies cannot form by a factor of
~10 (50) at mean density (in voids) over that found in models that include
photoionization alone. This prevents the formation of late forming dwarf
galaxies (z<2) with masses ranging from 10^{10} to 10^{11} M_sun for redshifts
z~2 to 0, respectively. This may help resolve the "missing satellite problem"
in the Milky Way and the "void phenomenon" of the low observed abundances of
dwarf satellites compared to cold dark matter simulations and may bring the
observed early star formation histories into agreement with galaxy formation
models. (abridged)


  We are looking for a holographic explanation of nuclear forces, especially
the attractive forces. Recently, the repulsive hard core of a nucleon-nucleon
potential was obtained in the Sakai-Sugimoto model, and we show that a
generalized version of that model -- with an asymmetric configuration of the
flavor D8 branes -- also has an attractive potential. While the repulsive
potential stems from the Chern-Simons interactions of the U(2) flavor gauge
fields in 5D, the attractive potential is due to a coupling of the gauge fields
to a scalar field describing fluctuations of the flavor branes' geometry. At
intermediate distances r between baryons -- smaller than R_KK=O(1)/M_{omega
meson} but larger than the radius rho=R_KK/sqrt('t Hooft coupling) of the
instanton at the core of a baryon -- both the attractive and the repulsive
potentials behave as 1/r^2, but the attractive potential is weaker: Depending
on the geometry of the flavor D8 branes, the ratio C=-V_attr/V_rep ranges from
0 to 1/9. The 5D scalar fields also affect the isovector tensor and spin-spin
forces, and the overall effect is similar to the isoscalar central forces:
V(r)->(1-C)*V(r).
  At longer ranges $r\gtrsim R_{\rm KK}$, we find that the attractive potential
decays faster than the repulsive potential, so the net potential is always
repulsive. This unrealistic behavior may be peculiar to the Sakai-Sugimoto-like
models, or it could be a general problem of the large N_c limit inherent in
holography.


  We propose a class of N=2 supersymmetric nonlinear sigma models on the
Ricci-flat Kahler manifolds with O(n) symmetry.


  The stability of high vs. low spin states of transition metal complexes has
been interpreted by ligand field theory, which is a perturbation theory of the
electron-electron interaction. The present first principles calculation of a
series of five cobalt complexes shows that the electron-electron interaction
energy difference between the two states (i) exhibits the opposite trend to the
total energy difference as the ligand nuclear charge varies, and (ii) is three
or four orders of magnitude greater than the total energy difference. A new
interpretation of the crossover of high and low spin states is given in terms
of the chemical bonding.


  In this paper, we show the equivalency between the existence of fast neutrino
flavor instability and that of neutrino flavor lepton number (NFLN) crossings,
which indicates that an NFLN angular distribution takes both signs. The
veracity of this proposition has been uncertain and sometimes controversial
despite its indispensability in the flavor evolutions of dense neutrinos. This
study clarifies that the occurrence of an NFLN crossing is both necessary and
sufficient for fast instability.


  We survey recent progress in the study of $G_{2}$-structure Laplacian
coflows, that is, heat flows of co-closed $G_{2}$-structures. We introduce the
properties of the original Laplacian coflow of $G_{2}$-structures as well as
the modified coflow, reviewing short-time existence and uniqueness results for
the modified coflow and well as recent Shi-type estimates that apply to a more
general class of $G_{2}$-structure flows.


  We discuss possible studies of parton distributions at the proposed 50-GeV PS
facility. First, comments are given in general on the importance of large-x
physics for finding new physics. Second, polarized deuteron reactions are
discussed in connection with new structure functions which are specific for a
spin-1 hadron. Third, if the polarized proton-deuteron Drell-Yan process is
studied at the facility, it could provide information on the light-antiquark
flavor asymmetry in the polarized distributions.


  The Orlik-Solomon algebra of a matroid M is the quotient of the exterior
algebra on the points by the ideal I(M) generated by the boundaries of the
circuits of the matroid. There is an isomorphism between the Orlik-Solomon
algebra of a complex matroid and the cohomology of the complement of a complex
arrangement of hyperplanes. In this article a generalization of the
Orlik-Solomon algebras, called X-algebras, are considered. These new algebras
include, apart from the Orlik-Solomon algebras, the Orlik-Solomon-Terao algebra
of a set of vectors and the Cordovil algebra of an oriented matroid. To encode
an important property of the "no broken circuit bases" of the
Orlik-Solomon-Terao algebras, Andras Szenes has introduced a particular type of
bases, the so called "diagonal bases". This notion extends naturally to
X-algebras. We give a survey of the results obtained by the authors concerning
the construction of Groebner bases of I(M) and diagonal bases of Orlik-Solomon
type algebras and we present the combinatorial analogue of an ``iterative
residue formula'' introduced by Szenes.


  Replicated tree data structures are extensively used in collaborative
applications and distributed file systems, where clients often perform move
operations. Local move operations at different replicas may be safe. However,
remote move operations may not be safe. When clients perform arbitrary move
operations concurrently on different replicas, it could result in various bugs,
making this operation challenging to implement. Previous work has revealed bugs
such as data duplication and cycling in replicated trees. In this paper, we
present an efficient algorithm to perform move operations on the distributed
replicated tree while ensuring eventual consistency. The proposed technique is
primarily concerned with resolving conflicts efficiently, requires no
interaction between replicas, and works well with network partitions. We use
the last write win semantics for conflict resolution based on globally unique
timestamps of operations. The proposed solution requires only one compensation
operation to avoid cycles being formed when move operations are applied. The
proposed approach achieves an effective speedup of 68.19$\times$ over the
state-of-the-art approach in a geo-replicated setting on Microsoft Azure
standard instances at three different continents.


  We elucidate the origin of the phonon-mediated superconductivity in
2$H$-NbS$_2$ using the ab initio anisotropic Migdal-Eliashberg theory including
Coulomb interactions. We demonstrate that superconductivity is associated with
Fermi surface hot spots exhibiting an unusually strong electron-phonon
interaction. The electron-lattice coupling is dominated by low-energy
anharmonic phonons, which place the system on the verge of a charge density
wave instability. We also provide definitive evidence for two-gap
superconductivity in 2$H$-NbS$_2$, and show that the low- and high-energy peaks
observed in tunneling spectra correspond to the $\Gamma$- and $K$-centered
Fermi surface pockets, respectively. The present findings call for further
efforts to determine whether our proposed mechanism underpins superconductivity
in the whole family of metallic transition metal dichalcogenides.


  We present a time-local existence theorem of the initial value problem for a
third-order dispersive evolution equation for open curves on compact almost
Hermitian manifolds arising in the geometric analysis of vortex filaments. This
equation causes the so-called loss of one-derivative since the target manifold
is not supposed to be a K\"ahler manifold. We overcome this difficulty by using
a gauge transformation of a multiplier on the pull-back bundle to eliminate the
bad first order terms essentially.


  One spin excitation states are involved in the transmission of quantum states
and entanglement through a quantum spin chain, the localization properties of
these states are crucial to achieve the transfer of information from one
extreme of the chain to the other. We investigate the bipartite entanglement
and localization of the one excitation states in a quantum $XX$ chain with one
impurity. The bipartite entanglement is obtained using the Concurrence and the
localization is analyzed using the inverse participation ratio. Changing the
strength of the exchange coupling of the impurity allows us to control the
number of localized or extended states. The analysis of the inverse
participation ratio allows us to identify scenarios where the transmission of
quantum states or entanglement can be achieved with a high degree of fidelity.
In particular we identify a regime where the transmission of quantum states
between the extremes of the chain is executed in a short transmission time
$\sim N/2$, where $N$ is the number of spins in the chain, and with a large
fidelity.


  Speech separation aims to separate multiple speech sources from a speech
mixture. Although speech separation is well-solved on some existing English
speech separation benchmarks, it is worthy of more investigation on the
generalizability of speech separation models on the accents or languages unseen
during training. This paper adopts meta-learning based methods to improve the
transferability of speech separation models. With the meta-learning based
methods, we discovered that only using speech data with one accent, the native
English accent, as our training data, the models still can be adapted to new
unseen accents on the Speech Accent Archive. We compared the results with a
human-rated native-likeness of accents, showing that the transferability of
MAML methods has less relation to the similarity of data between the training
and testing phase compared to the typical transfer learning methods.
Furthermore, we found that models can deal with different language data from
the CommonVoice corpus during the testing phase. Most of all, the MAML methods
outperform typical transfer learning methods when it comes to new accents, new
speakers, new languages, and noisy environments.


  The rapid development of wireless sensor networks (WSNs) is the significant
incentive to contribute in the vulnerable applications such as cognitive radio
(CR). This paper proposes a Stackelberg game approach to enhance the WSN-based
CR security against the spectrum sensing data falsification (SSDF) attack and
conserve the consequent lost power consumption. The attack aims to corrupt the
spectrum decision by imposing interference power to the delivered reports from
the sensor nodes (SNs) to the fusion center (FC) to make a protection level
below a specific threshold. The proposed model utilizes the intelligent
Stackelberg game features along with the matched filter (MF) to maximize the
number of protected reports sent by the SNs to the FC leading to accurate
decision of the spectrum status. Furthermore, the TDMA protocol is utilized to
resolve the complexity of employing MF for the spectrum detection to avoid the
collision between the delivered reports. The proposed model aims to enhance the
number of correctly received reports at the FC, and hence manage the lost
energy of reports retransmission due to the malicious attack effect. Moreover,
the model can conserve the lost power of the failure communication attempts due
to the SSDF attack impact. Simulation results indicate the improved performance
of the proposed protection model along with the MF over the six different
environments against the SSDF attack as compared to two defense schemes,
namely, random and equal weight defense strategies.


  Optimization algorithms appear in the core calculations of numerous
Artificial Intelligence (AI) and Machine Learning methods, as well as
Engineering and Business applications. Following recent works on the
theoretical deficiencies of AI, a rigor context for the optimization problem of
a \textit{black-box} objective function is developed. The algorithm stems
directly from the theory of probability, instead of a presumed inspiration,
thus the convergence properties of the proposed methodology are inherently
stable. In particular, the proposed optimizer utilizes an algorithmic
implementation of the $n$-dimensional inverse transform sampling as a search
strategy. No control parameters are required to be tuned, and the trade-off
among exploration and exploitation is by definition satisfied. A theoretical
proof is provided, concluding that only falling into the proposed framework,
either directly or incidentally, any optimization algorithm converges in the
fastest possible time. The numerical experiments, verify the theoretical
results on the efficacy of the algorithm apropos reaching the optimum, as fast
as possible.


  Linear codes with few weights have significant applications in secret sharing
schemes, authentication codes, association schemes, and strongly regular
graphs. There are a number of methods to construct linear codes, one of which
is based on functions. Furthermore, two generic constructions of linear codes
from functions called the first and the second generic constructions, have
aroused the research interest of scholars. Recently, in \cite{Nian}, Li and
Mesnager proposed two open problems: Based on the first and the second generic
constructions, respectively, construct linear codes from non-weakly regular
plateaued functions and determine their weight distributions.
  Motivated by these two open problems, in this paper, firstly, based on the
first generic construction, we construct some three-weight and at most
five-weight linear codes from non-weakly regular plateaued functions and
determine the weight distributions of the constructed codes. Next, based on the
second generic construction, we construct some three-weight and at most
five-weight linear codes from non-weakly regular plateaued functions belonging
to $\mathcal{NWRF}$ (defined in this paper) and determine the weight
distributions of the constructed codes. We also give the punctured codes of
these codes obtained based on the second generic construction and determine
their weight distributions. Meanwhile, we obtain some optimal and almost
optimal linear codes. Besides, by the Ashikhmin-Barg condition, we have that
the constructed codes are minimal for almost all cases and obtain some secret
sharing schemes with nice access structures based on their dual codes.


  Spatially-resolved NMR is used to probe the magnetism in and around the
vortex core of nearly optimally-doped Tl_2Ba_2CuO_{6+\delta} (T_c=85K). The NMR
relaxation rate T_1^{-1} at ^{205}Tl site, at which antiferromagnetic (AF)
fluctuation can be monitored sensitively, provides a direct evidence that the
AF spin correlation is significantly enhanced in the vortex core region. In the
core region Cu spins show a local AF ordering with moment ~ 0.1\mu_B parallel
to the layers at T_N=20K. Above T_N the core region is in the paramagnetic
state which is a reminiscence of the state above the pseudogap temperature
(T*=120K), indicating that the pseudogap disappears within the core.


  Estimating dynamic correlation between a pair of time series is of importance
in many applications. We present new estimators for the dynamic correlation
between a pair of correlated Brownian motions and separately for dynamic
correlation between a pair of correlated Geometric Brownian motions. We show
that, as the sample size increases, all estimators presented in this paper
converge in probability to the underlying true dynamic correlation.


  Recent work has shown that additive threat models, which only permit the
addition of bounded noise to the pixels of an image, are insufficient for fully
capturing the space of imperceivable adversarial examples. For example, small
rotations and spatial transformations can fool classifiers, remain
imperceivable to humans, but have large additive distance from the original
images. In this work, we leverage quantitative perceptual metrics like LPIPS
and SSIM to define a novel threat model for adversarial attacks.
  To demonstrate the value of quantifying the perceptual distortion of
adversarial examples, we present and employ a unifying framework fusing
different attack styles. We first prove that our framework results in images
that are unattainable by attack styles in isolation. We then perform
adversarial training using attacks generated by our framework to demonstrate
that networks are only robust to classes of adversarial perturbations they have
been trained against, and combination attacks are stronger than any of their
individual components. Finally, we experimentally demonstrate that our combined
attacks retain the same perceptual distortion but induce far higher
misclassification rates when compared against individual attacks.


  It is proposed four dimensional curved space-time with de-Sitter group of
motion. Theory contain free dimension constants of length, impulse and action.
Under infinite values of these parameters theory pass to usual Minkowski
space-time with Poincare group of motion. In modified space gauge invariant
field theory is constructed.


  Self-supervised (SSL) models have shown great performance in various
downstream tasks. However, they are typically developed for limited languages,
and may encounter new languages in real-world. Developing a SSL model for each
new language is costly. Thus, it is vital to figure out how to efficiently
adapt existed SSL models to a new language without impairing its original
abilities. We propose adaptation methods which integrate LoRA to existed SSL
models to extend new language. We also develop preservation strategies which
include data combination and re-clustering to retain abilities on existed
languages. Applied to mHuBERT, we investigate their effectiveness on speech
re-synthesis task. Experiments show that our adaptation methods enable mHuBERT
to be applied to a new language (Mandarin) with MOS value increased about 1.6
and the relative value of WER reduced up to 61.72%. Also, our preservation
strategies ensure that the performance on both existed and new languages
remains intact.


  Intelligent reflecting surfaces (IRS) consist of configurable meta-atoms,
which can alter the wireless propagation environment through design of their
reflection coefficients. We consider adaptive IRS control in the practical
setting where (i) the IRS reflection coefficients are attained by adjusting
tunable elements embedded in the meta-atoms, (ii) the IRS reflection
coefficients are affected by the incident angles of the incoming signals, (iii)
the IRS is deployed in multi-path, time-varying channels, and (iv) the feedback
link from the base station (BS) to the IRS has a low data rate. Conventional
optimization-based IRS control protocols, which rely on channel estimation and
conveying the optimized variables to the IRS, are not practical in this setting
due to the difficulty of channel estimation and the low data rate of the
feedback channel. To address these challenges, we develop a novel adaptive
codebook-based limited feedback protocol to control the IRS. We propose two
solutions for adaptive IRS codebook design: (i) random adjacency (RA), which
utilizes correlations across the channel realizations, and (ii) deep neural
network policy-based IRS control (DPIC), which is based on a deep reinforcement
learning. Numerical evaluations show that the data rate and average data rate
over one coherence time are improved substantially by the proposed schemes.


  Answering a question of Wilf, we show that if $n$ is sufficiently large, then
one cannot cover an $n \times p(n)$ rectangle using each of the $p(n)$ distinct
Ferrers shapes of size $n$ exactly once. Moreover, the maximum number of
pairwise distinct, non-overlapping Ferrers shapes that can be packed in such a
rectangle is only $\Theta(p(n)/ \log n).$


  We examine phantom dark energy models derived from a scalar field with a
negative kinetic term for which V(phi) approaches infinity asymptotically. All
such models can be divided into three classes, corresponding to an equation of
state parameter w with asymptotic behavior w -> -1, w -> w_0 < -1, and w ->
infinity. We derive the conditions on the potential V(phi) which lead to each
of these three types of behavior. For models with w -> -1, we derive the
conditions on V(phi) which determine whether or not such models produce a
future big rip. Observational constraints are derived on two classes of these
models: power-law potentials with V(phi) = lambda phi^alpha (with alpha
positive or negative) and exponential potentials of the form V(phi) = beta
e^{lambda phi^alpha}. It is shown that these models spend more time in a state
with Omega_m ~ Omega_phi than do corresponding models with a constant value of
w, thus providing a more satisfactory solution to the coincidence problem.


  We investigate the use of orbital-optimized references in conjunction with
single-reference coupled-cluster theory with single and double substitutions
(CCSD) for the study of core excitations and ionizations of 18 small organic
molecules, without any use of response theory or equation-of-motion formalisms.
Three schemes are employed to successfully address the convergence difficulties
associated with the coupled-cluster equations, and the spin contamination
resulting from the use of a spin symmetry-broken reference, in the case of
excitations. In order to gauge the inherent potential of the methods studied,
an effort is made to provide reasonable basis set limit estimates for the
transition energies. Overall, we find that the two best-performing schemes
studied here for Delta-CCSD are capable of predicting excitation and ionization
energies with errors comparable to experimental accuracies. The proposed
Delta-CCSD schemes seem to fare better than the widely used equation-of-motion
CCSD (EOM-CCSD) with core-valence separation protocol, with statistical errors
being reduced by more than a factor of two when compared to FC-CVS-EOM-CCSD.


  Let $R$ be a commutative ring. An $R$-module $M$ is said to be $w$-split if
Ext$_{R}^1(M,N)$ is a GV-torsion $R$-module for all $R$-modules $N$. It is
known that every projective module is $w$-split, but the converse is not true
in general. In this paper, we study the w-split dimension of a flat module. To
do so, we introduce and study the so-called $w$-copure (resp., strongly
$w$-copure) projective modules which is in some way a generalization of the
notion of copure (resp., strongly copure) projective modules. An $R$-module $M$
is said to be $w$-copure projective (resp., strongly $w$-copure projective) if
Ext$_{R}^1(M,N)$ (resp., Ext$_{R}^n(M,N)$) is a GV-torsion $R$-module for all
flat $R$-modules $N$ and any $n\geq1$.


  The consequences of the shear-induced alpha effect to the long-term
modulation of magnetic activity are examined with the help of the axisymmetric
numerical dynamo model that includes the self-consistent description of the
angular momentum balance, heat transport and magnetic field generation in the
spherical shell. We find that the shear contributions to alpha effect can
complicate the long-term behaviour of the large-scale magnetic activity and
differential rotation in nonlinear dynamo. Additionally we consider the impact
secular magnetic activity variations to the secular modulations of the solar
luminosity and radius.


  We briefly review the diagonalization of quantum Hamiltonians using the
quasi-sparse eigenvector (QSE) method. We also introduce the technique of
stochastic error correction, which systematically removes the truncation error
of the QSE result by stochastically sampling the contribution of the remaining
basis states.


  In this paper, the reachability of dimension-bounded linear systems is
investigated.Since state dimensions of dimension-bounded linear systems vary
with time, the expression of state dimension at each time is provided.A method
for judging the reachability of a given vector space is proposed. In addition,
this paper proves that the t-step reachable subset is a linear space, and gives
a computing method. The t-step reachability of a given state is verified via a
rank condition. Furthermore, annihilator polynomials are discussed and used to
illustrate the relationship between the invariant space and the reachable
subset after the invariant time point t*. The inclusion relation between
reachable subsets at times t*+i and t*+j is shown via an example.


  The oscillating inflation model recently proposed by Damour and Mukhanov is
investigated with a non-minimal coupling. Numerical study confirms an
inflationary behavior and the density perturbation is obtained. A successful
inflation requires the gravity-dilaton coupling to be small.


  It is known that ab initio molecular dynamics (AIMD) simulations of liquid
water, based on the generalized gradient approximation (GGA) to density
functional theory (DFT), yield structural and diffusive properties in
reasonable agreement with experiment only if artificially high temperatures are
used in the simulations. The equilibrium density, at normal conditions, of DFT
water has been recently shown by Schmidt et al. [J. Phys. chem. B, 113, 11959
(2009)] to be underestimated by different GGA functionals for exchange and
correlation, and corrected by the addition of interatomic pair potentials to
describe van derWaals (vdW) interactions. In this contribution we present a
DFTAIMD study of liquid water using several GGA functionals as well as the van
der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92,
246401(2004)]. As expected, we find that the density of water is grossly
underestimated by GGA functionals. When a vdW-DF is used, the density improves
drastically and the experimental diffusivity is reproduced without the need of
thermal corrections. We analyze the origin of the density differences between
all the functionals. We show that the vdW-DF increases the population of
non-H-bonded interstitial sites, at distances between the first and second
coordination shells. However, it excessively weakens the H-bond network,
collapsing the second coordination shell. This structural problem is partially
associated to the choice of GGA exchange in the vdW-DF. We show that a
different choice for the exchange functional is enough to achieve an overall
improvement both in structure and diffusivity.


  We report on Chandra X-ray observations of four candidate low-mass black hole
(<10^6Msun) active galactic nuclei (AGNs) that have the estimated Eddington
ratios among the lowest (~10^(-2)) found for this class. The aims are to
validate the nature of their AGNs and to confirm the low Eddington ratios that
are derived from the broad H_alpha line, and to explore this poorly studied
regime in the AGN parameter space. Among them, two objects with the lowest
significance of the broad lines are also observed with Multi-Mirror Telescope,
and the high-quality optical spectra taken confirm them as Seyfert 1 AGNs and
as having small black hole masses. X-ray emission is detected from the nuclei
of two of the galaxies, which is variable on timescales of 10^3s, whereas no
significant (or only marginal at best) detection is found for the remaining
two. The X-ray luminosities are on the order of 10^(41) ergs/s or even lower,
on the order of 10^(40) ergs/s for non-detections, which are among the lowest
regimes ever probed for Seyfert galaxies. The low X-ray luminosities, compared
to their black hole masses derived from H_alpha, confirm their low accretion
rates assuming typical bolometric corrections. Our results hint at the
existence of a possibly large population of under-luminous low-mass black holes
in the local universe. An off-nucleus ultra-luminous X-ray source (ULX) in one
of the dwarf galaxies is detected serendipitously, with a luminosity
(6-9)x10^(39) ergs/s in 2-10 keV.


  When placed on rough hydrophobic surfaces, water droplets of diameter larger
than a few millimeters can easily form pearls, as they are in the Cassie-Baxter
state with air pockets trapped underneath the droplet. Intriguingly, a natural
evaporating process can drive such a Fakir drop into a completely wetting
(Wenzel) state. Our microscopic observations with simultaneous side and bottom
views of evaporating droplets upon transparent hydrophobic microstructures
elucidate the water-filling dynamics and the mechanism of this
evaporation-triggered transition. For the present material the wetting
transition occurs when the water droplet size decreases to a few hundreds of
micrometers in radius. We present a general global energy argument which
estimates the interfacial energies depending on the drop size and can account
for the critical radius for the transition.


  We investigate the history of galactic feedback and chemical enrichment
within a sample of 15 X-ray bright groups of galaxies, on the basis of the
inferred Fe and Si distributions in the hot gas and the associated metal masses
produced by core-collapse and type Ia supernovae (SN). Most of these cool-core
groups show a central Fe and Si excess, which can be explained by prolonged
enrichment by SN Ia and stellar winds in the central early-type galaxy alone,
but with tentative evidence for additional processes contributing to core
enrichment in hotter groups. Inferred metal mass-to-light ratios inside r_500
show a positive correlation with total group mass but are generally
significantly lower than in clusters, due to a combination of lower global ICM
abundances and gas-to-light ratios in groups. This metal deficiency is present
for products from both SN Ia and SN II, and suggests that metals were either
synthesized, released from galaxies, or retained within the ICM less
efficiently in lower-mass systems. We explore possible causes, including
variations in galaxy formation and metal release efficiency, cooling-out of
metals, and gas and metal loss via AGN- or starburst-driven galactic winds from
groups or their precursor filaments. Loss of enriched material from filaments
coupled with post-collapse AGN feedback emerge as viable explanations, but we
also find evidence for metals to have been released less efficiently from
galaxies in cooler groups and for the ICM in these to appear chemically less
evolved, possibly reflecting more extended star formation histories in less
massive systems. Some implications for the hierarchical growth of clusters from
groups are briefly discussed.


  Recent numerical simulations of coalescences of highly spinning massive black
hole binaries (MBHBs) suggest that the remnant can suffer a recoil velocity of
the order of few thousands km/s. We study here, by means of dedicated
simulations of black holes build--up, how such extreme recoils could affect the
cosmological coalescence rate of MBHBs, placing a robust lower limit for the
predicted number of gravitational wave (GW) sources detectable by future
space--borne missions (such as LISA). We consider two main routes for black
hole formation: one where seeds are light remnants of Population III stars
(~10^2 \msun), and one where seeds are much heavier (>~10^4 \msun), formed via
the direct gas collapse in primordial nuclear disks. We find that extreme
recoil velocities do not compromise the efficient MBHB detection by LISA. If
seeds are already massive and/or relatively rare, the detection rate is reduced
by only ~15%. The number of detections drops substantially (by ~60%) if seeds
are instead light and abundant, but in this case the number of predicted
coalescences is so high that at least ~10 sources in a three year observation
are guaranteed.


  The light-cone Hamiltonian approach is applied to the super D2-brane, and the
equivalent area--preserving and U(1) gauge-invariant effective Lagrangian,
which is quadratic in the U(1) gauge field, is derived. The latter is
recognised to be that of the three-dimensional U(1) gauge theory, interacting
with matter supermultiplets, in a special external induced supergravity metric
and the gravitino field, depending on matter fields. The duality between this
theory and 11d supermembrane theory is demonstrated in the light-cone gauge.


  We bound the symbol length of elements in the Brauer group of a field $K$
containing a $C_m$ field (for example any field containing an algebraically
closed field or a finite field), and solve the local exponent-index problem for
a $C_m$ field $F$. In particular, for a $C_m$ field $F$, we show that every $F$
central simple algebra of exponent $p^t$ is similar to the tensor product of at
most $len(p^t,F)\leq t(p^{m-1}-1)$ symbol algebras of degree $p^t$. We then use
this bound on the symbol length to show that the index of such algebras is
bounded by $(p^t)^{(p^{m-1}-1)}$, which in turn gives a bound for any algebra
of exponent $n$ via the primary decomposition. Finally for a field $K$
containing a $C_m$ field $F$, we show that every $F$ central simple algebra of
exponent $p^t$ and degree $p^s$ is similar to the tensor product of at most
$len(p^t,p^s,K)\leq len(p^t,L)$ symbol algebras of degree $p^t$, where $L$ is a
$C_{m+ed_L(A)+p^{s-t}-1}$ field.


  We study the correlation functions in the branched polymer model. Although
there are no correlations in the grand canonical ensemble, when looking at the
canonical ensemble we find negative long range power like correlations. We
propose that a similar mechanism explains the shape of recently measured
correlation functions in the elongated phase of 4d simplicial gravity.


  We consider Lorentz-symmetry properties of the ghost-free massive gravity
theory proposed by de Rham, Gabadadze, and Tolley. In particular, we present
potentially observable effects in gravitational-wave propagation and in
Newton's law, including Lorentz-violating signals.


  Bayesian models that can handle both over and under dispersed counts are rare
in the literature, perhaps because full probability distributions for dispersed
counts are rather difficult to construct. This note takes a first look at
Bayesian Conway-Maxwell-Poisson generalized linear models that can handle both
over and under dispersion yet retain the parsimony and interpretability of
classical count regression models. The focus is on providing an explicit
demonstration of Bayesian regression inferences for dispersed counts via a
Metropolis-Hastings algorithm. We illustrate the approach on two data analysis
examples and demonstrate some favourable frequentist properties via a
simulation study.


  We prove that the image of a finely holomorphic map on a fine domain in
$\mathbb{C}$ is pluripolar subset of $\mathbb{C}^{n}$. We also discuss the
relationship between pluripolar hulls and finely holomorphic function.


  A linear chain of connected electron sites with two asymmetric sinks, one
attached to each end, is used as a simple model of quantum electron transfer in
photosynthetic bio-complexes. For a symmetric initial population in the middle
of the chain, it is expected that electron transfer is mainly directed towards
the strongest coupled sink. However, we show that quantum effects radically
change this intuitive "classical" mechanism, so that electron transfer can
occur through the weaker coupled sink with maximal efficiency. Using this
capability, we show how to design a quantum switch that can transfer an
electron to the left or right branch of the chain, by changing the coupling to
the sinks. The operational principles of this quantum device can be understood
in terms of superradiance transitions and subradiant states. This switching,
being a pure quantum effect, can be used as a witness of wave--like behaviour
of excitations in molecular chains. When realistic data are used for the
photosystem II reaction center, this quantum biological switch is shown to
retain its reliability, even at room temperature.


  Structural failures are often caused by catastrophic events such as
earthquakes and winds. As a result, it is crucial to predict dynamic stress
distributions during highly disruptive events in real time. Currently available
high-fidelity methods, such as Finite Element Models (FEMs), suffer from their
inherent high complexity. Therefore, to reduce computational cost while
maintaining accuracy, a Physics Informed Neural Network (PINN), PINN-Stress
model, is proposed to predict the entire sequence of stress distribution based
on Finite Element simulations using a partial differential equation (PDE)
solver. Using automatic differentiation, we embed a PDE into a deep neural
network's loss function to incorporate information from measurements and PDEs.
The PINN-Stress model can predict the sequence of stress distribution in almost
real-time and can generalize better than the model without PINN.


  We explore the possibility of extracting information about lattice dynamics
in simple crystal structures from the neutron pair-density function (PDF)
through inverse data analysis. Contrary to the claims by Dimitrov, Louca, and
Roeder [Phys.Rev. B 60, 6204 (1999)], and in agreement with recent work by
Reichardt and Pintschovius [Phys.Rev. B 63, 174302 (2001)], we find that the
PDF alone is not sufficient for constructing accurate phonon dispersions in the
entire Brillouin zone in systems with complex lattice dynamics. However, our
numerical simulations show that for monatomic fcc and bcc crystal structures it
is, in principle, possible to obtain phonon moments of complex metals as well
as phonon frequencies of simple metals within a few percent accuracy.


  In this work, we study how to use sampling to speed up mechanisms for
answering adaptive queries into datasets without reducing the accuracy of those
mechanisms. This is important to do when both the datasets and the number of
queries asked are very large. In particular, we describe a mechanism that
provides a polynomial speed-up per query over previous mechanisms, without
needing to increase the total amount of data required to maintain the same
generalization error as before. We prove that this speed-up holds for arbitrary
statistical queries. We also provide an even faster method for achieving
statistically-meaningful responses wherein the mechanism is only allowed to see
a constant number of samples from the data per query. Finally, we show that our
general results yield a simple, fast, and unified approach for adaptively
optimizing convex and strongly convex functions over a dataset.


  We use data from the HST Coma Cluster Treasury program to assess the richness
of the Globular Cluster Systems (GCSs) of 54 Coma ultra-diffuse galaxies
(UDGs), 18 of which have a half-light radius exceeding 1.5 kpc. We use a
hierarchical Bayesian method tested on a large number of mock datasets to
account consistently for the high and spatially varying background counts in
Coma. These include both background galaxies and intra-cluster GCs (ICGCs),
which are disentangled from the population of member GCs in a probabilistic
fashion. We find no candidate for a GCS as rich as that of the Milky Way, our
sample has GCSs typical of dwarf galaxies. For the standard relation between
GCS richness and halo mass, 33 galaxies have a virial mass
$M_{vir}\leq10^{11}M_\odot$ at 90% probability. Only three have
$M_{vir}>10^{11}M_\odot$ with the same confidence. The mean colour and spread
in colour of the UDG GCs are indistinguishable from those of the abundant
population of ICGCs. The majority of UDGs in our sample are consistent with the
relation between stellar mass and GC richness of 'normal' dwarf galaxies. Nine
systems, however, display GCSs that are richer by a factor of 3 or more (at 90%
probability). Six of these have sizes $\lesssim1.4$ kpc. Our results imply that
the physical mechanisms responsible for the extended size of the UDGs and for
the enhanced GC richness of some cluster dwarfs are at most weakly correlated.


  Visual localization is the task of estimating a 6-DoF camera pose of a query
image within a provided 3D reference map. Thanks to recent advances in various
3D sensors, 3D point clouds are becoming a more accurate and affordable option
for building the reference map, but research to match the points of 3D point
clouds with pixels in 2D images for visual localization remains challenging.
Existing approaches that jointly learn 2D-3D feature matching suffer from low
inliers due to representational differences between the two modalities, and the
methods that bypass this problem into classification have an issue of poor
refinement. In this work, we propose EP2P-Loc, a novel large-scale visual
localization method that mitigates such appearance discrepancy and enables
end-to-end training for pose estimation. To increase the number of inliers, we
propose a simple algorithm to remove invisible 3D points in the image, and find
all 2D-3D correspondences without keypoint detection. To reduce memory usage
and search complexity, we take a coarse-to-fine approach where we extract
patch-level features from 2D images, then perform 2D patch classification on
each 3D point, and obtain the exact corresponding 2D pixel coordinates through
positional encoding. Finally, for the first time in this task, we employ a
differentiable PnP for end-to-end training. In the experiments on newly curated
large-scale indoor and outdoor benchmarks based on 2D-3D-S and KITTI, we show
that our method achieves the state-of-the-art performance compared to existing
visual localization and image-to-point cloud registration methods.


  The dynamical response of an atomic Bose-Einstein condensate manipulated by
an integrated atom optics device such as a microtrap or a microfabricated
waveguide is studied. We show that when the miniaturization of the device
enforces a sufficiently high condensate density, three-body interactions lead
to a spatial modulational instability that results in a fundamental limit on
the coherent manipulation of Bose-Einstein condensates.


  We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic
trap, modeled by an anisotropic harmonic potential. We evaluate the wave
function and the energy of the Bose Einstein condensate as a function of the
particle number, both for positive and negative scattering length. The results
for the transverse and vertical size of the cloud of atoms, as well as for the
kinetic and potential energy per particle, are compared with the predictions of
approximated models. We also compare the aspect ratio of the velocity
distribution with first experimental estimates available for $^{87}$Rb. Vortex
states are considered and the critical angular velocity for production of
vortices is calculated. We show that the presence of vortices significantly
increases the stability of the condensate in the case of attractive
interactions.


  We consider the family of polynomials $p_{n}\left( x;z\right) ,$ orthogonal
with respect to the inner product \[ \left\langle f,g\right\rangle =
\int_{-z}^{z} f\left( x\right) g\left( x\right) e^{-x^{2}} \,dx. \] We show
some properties about the coefficients in their 3-term recurrence relation,
connections between $p_{n}\left( x;z\right) $ and $p_{n}^{\prime}\left(
x;z\right) ,$ a second order differential equation satisfied by $p_{n}\left(
x;z\right) ,$ and an electrostatic interpretation of their zeros.


  We discuss joint temporal and contemporaneous aggregation of $N$ independent
copies of random-coefficient AR(1) process driven by i.i.d. innovations in the
domain of normal attraction of an $\alpha$-stable distribution, $0< \alpha \le
2$, as both $N$ and the time scale $n$ tend to infinity, possibly at a
different rate. Assuming that the tail distribution function of the random
autoregressive coefficient regularly varies at the unit root with exponent
$\beta > 0$, we show that, for $\beta < \max (\alpha, 1)$, the joint aggregate
displays a variety of stable and non-stable limit behaviors with stability
index depending on $\alpha$, $\beta$ and the mutual increase rate of $N$ and
$n$. The paper extends the results of Pilipauskait\.e and Surgailis (2014) from
$\alpha = 2$ to $0 < \alpha < 2$.


  RR Lyrae (RRL) are old, low-mass radially pulsating variable stars in their
core helium burning phase. They are popular stellar tracers and primary
distance indicators, since they obey to well defined period-luminosity
relations in the near-infrared regime. Their photometric identification is not
trivial, indeed, RRL samples can be contaminated by eclipsing binaries,
especially in large datasets produced by fully automatic pipelines.
Interpretable machine-learning approaches for separating eclipsing binaries
from RRL are thus needed. Ideally, they should be able to achieve high
precision in identifying RRL while generalizing to new data from different
instruments. In this paper, we train a simple logistic regression classifier on
Catalina Sky Survey (CSS) light curves. It achieves a precision of 87% at 78%
recall for the RRL class on unseen CSS light curves. It generalizes on
out-of-sample data (ASAS/ASAS-SN light curves) with a precision of 85% at 96%
recall. We also considered a L1-regularized version of our classifier, which
reaches 90% sparsity in the light-curve features with a limited trade-off in
accuracy on our CSS validation set and -- remarkably -- also on the
ASAS/ASAS-SN light curve test set. Logistic regression is natively
interpretable, and regularization allows us to point out the parts of the light
curves that matter the most in classification. We thus achieved both good
generalization and full interpretability.


  In this note, we answer affirmatively the question if a warped product of a
compact manifold with a line as an ancient solution to the Ricci flow is
trivial. We also consider the global behavior of the Type III warping product
Ricci flow.


  In this work we analyze the finite-size effects on the structural properties
and on the polarization of the rhombohedral phase of HfO$_2$ subjected to a
biaxial compressive strain. We show how the presence of surface charges affects
the polarization, leading to a strong reduction with respect to its bulk value.
This reduction can be ascribed to two mechanisms: the coupling between
compressive strain and the phase-transition order parameter; the changes in the
ferroelectric distortion. We give two alternative explanations of this
phenomenon: from an atomistic point of view, analyzing the evolution of the
bond lengths, and from a symmetry-analysis point of view, considering the
changes in the amplitude of the symmetry-allowed distortions, when a slab
configuration is considered. These results are independent on the
slab-thickness in the considered range, suggesting the absence of a critical
thickness for ferroelectricity in HfO$_2$, in agreement with the proposed
improper nature of hafnia ferroelectricity.


  In the field of gestural action recognition, many studies have focused on
dimensionality reduction along the spatial axis, to reduce both the variability
of gestural sequences expressed in the reduced space, and the computational
complexity of their processing. It is noticeable that very few of these methods
have explicitly addressed the dimensionality reduction along the time axis.
This is however a major issue with regard to the use of elastic distances
characterized by a quadratic complexity. To partially fill this apparent gap,
we present in this paper an approach based on temporal down-sampling associated
to elastic kernel machine learning. We experimentally show, on two data sets
that are widely referenced in the domain of human gesture recognition, and very
different in terms of quality of motion capture, that it is possible to
significantly reduce the number of skeleton frames while maintaining a good
recognition rate. The method proves to give satisfactory results at a level
currently reached by state-of-the-art methods on these data sets. The
computational complexity reduction makes this approach eligible for real-time
applications.


  We define the "entropy of ignorance" which quantifies the entropy associated
with ability to perform only a partial set of measurement on a quantum system.
For a parton model the entropy of ignorance is equal to a Boltzmann entropy of
a classical system of partons. We analyze a calculable model used for
describing low x gluons in Color Glass Condensate approach, which has
similarities with the parton model of QCD. In this model we calculate the
entropy of ignorance in the particle number basis as well as the entanglement
entropy of the observable degrees of freedom. We find that the two are similar
at high momenta, but differ by a factor of order unity at low momenta. This
holds for the Renyi as well as von Neumann entropies. We conclude that the
entanglement does not seem to play an important role in the context of the
parton model.


  In this letter, active control of near-field radiative heat transfer (NFRHT)
between two isotropic materials is realized by a coating-twisting method. The
two slabs are coated with graphene gratings, and then the NFRHT can be not only
enhanced, but also weakened, by tuning the twisted angle between the two
gratings. The physical mechanism is attributed to the modes coupled by the
graphene gratings and the isotropic material, which can vary with the twisted
angle. The proposed method is also applicable for other kinds of anisotropic
films, and may provide a way to realize high-precision nanoscale thermal
management, nimble thermal communications and thermal switch.


  The transport properties of high-performance thin-film transistors (TFT) made
with a regio-regular poly(thiophene) semiconductor (PQT-12) are reported. The
room-temperature field-effect mobility of the devices varied between 0.004
cm2/V s and 0.1 cm2/V s and was controlled through thermal processing of the
material, which modified the structural order. The transport properties of TFTs
were studied as a function of temperature. The field-effect mobility is
thermally activated in all films at T<200 K and the activation energy depends
on the charge density in the channel. The experimental data is compared to
theoretical models for transport, and we argue that a model based on the
existence of a mobility edge and an exponential distribution of traps provides
the best interpretation of the data. The differences in room-temperature
mobility are attributed to different widths of the shallow localized state
distribution at the edge of the valence band due to structural disorder in the
film. The free carrier mobility of the mobile states in the ordered regions of
the film is the same in all structural modifications and is estimated to be
between 1 and 4 cm2/V s.


  In a hybrid optomechanical setup consisting of a two-level atom in a cavity
with a pendular end-mirror, the interplay between the light field's radiation
pressure on the mirror and the dipole interaction with the atom can lead to a
blockade effect, which manifests itself in a suppression of Rabi oscillations
in the atomic population. This effect is present when the system is in the
single photon strong coupling regime and has an analogy in the photon blockade
of optomechanics.


  In 1964 R.Gangolli published a L\'{e}vy-Khintchine type formula which
characterised $K$ bi-invariant infinitely divisible probability measures on a
symmetric space $G/K$. His main tool was Harish-Chandra's spherical functions
which he used to construct a generalisation of the Fourier transform of a
measure. In this paper we use generalised spherical functions (or Eisenstein
integrals) and extensions of these which we construct using representation
theory to obtain such a characterisation for arbitrary infinitely divisible
probability measures on a non-compact symmetric space. We consider the example
of hyperbolic space in some detail.


  The movement of ionic solutions is an essential part of biology and
technology. Fluidics, from nano- to micro- to microfluidics, is a burgeoning
area of technology which is all about the movement of ionic solutions, on
various scales. Many cells, tissues, and organs of animals and plants depend on
osmosis, as the movement of fluids is called in biology. Indeed, the movement
of fluids through channel proteins (that have a hole down their middle) is
fluidics on an atomic scale. Ionic fluids are complex fluids, with energy
stored in many ways. Ionic fluids flow driven by gradients of concentration,
chemical and electrical potential, and hydrostatic pressure. Each flow is
classically described by its own field theory, independent of the others, but
of course, in reality every gradient drives every kind of flow to a varying
extent. Combining field equations is tricky and so the theory of complex fluids
derives the equations, rather than assumes their interactions. When field
equations are derived, rather than assumed, their variables are consistent.
That is to say all variables satisfy all equations under all conditions with
one set of parameters. Here we treat a classical osmotic cell in this spirit,
using a sharp interface method to derive boundary conditions consistent with
all flows and fields. We allow volume to change with concentration, since
changes of volume are a property of ionic solutions known to all who make them
in the laboratory. We consider flexible and inflexible membranes. We show how
to combine the energetics of the membrane with the energetics of the
surrounding complex fluids. The results seem general but need application to
specific situations of technological, biological and experimental importance
before the consequences of consistency can be understood.


  We study the transient phenomena appearing in a subgap region of the double
quantum dot coupled in series between the superconducting and normal metallic
leads, focusing on the development of the superconducting proximity effect. For
the uncorrelated nanostructure we derive explicit expressions of the
time-dependent occupancies in both quantum dots, charge currents, and electron
pairing induced on individual dots and between them. We show that the initial
configurations substantially affect the dynamical processes, in which the
in-gap bound states emerge upon coupling the double quantum dot to
superconducting reservoir. In particular, the superconducting proximity effect
would be temporarily blocked whenever the quantum dots are initially singly
occupied. Such {\it triplet}/{\it Andreev blockade} has been recently reported
experimentally for double quantum dots embedded in the Josephson [D. Bouman et
al., Phys. Rev. B 102, 220505 (2020)] and Andreev [P. Zhang et al.,
arXiv:2102.03283 (2021)] junctions. We also address the role of correlation
effects within the lowest-order decoupling scheme and by the time-dependent
numerical renormalization group calculations. Competition of the repulsive
Coulomb interactions with the superconducting proximity effect leads to
renormalization of the in-gap quasiparticles, speeding up the quantum
oscillations and narrowing a region of transient phenomena, whereas the
dynamical Andreev blockade is well pronounced in the weak inter-dot coupling
limit. We propose feasible methods for detecting the characteristic time-scales
that could be observable by the Andreev spectroscopy.


  The fifth generation and beyond wireless communication will support vastly
heterogeneous services and use demands such as massive connection, low latency
and high transmission rate. Network slicing has been envisaged as an efficient
technology to meet these diverse demands. In this paper, we propose a dynamic
virtual resources allocation scheme based on the radio access network (RAN)
slicing for uplink communications to ensure the quality-of-service (QoS). To
maximum the weighted-sum transmission rate performance under delay constraint,
formulate a joint optimization problem of subchannel allocation and power
control as an infinite-horizon average-reward constrained Markov decision
process (CMDP) problem. Based on the equivalent Bellman equation, the optimal
control policy is first derived by the value iteration algorithm. However, the
optimal policy suffers from the widely known curse-of-dimensionality problem.
To address this problem, the linear value function approximation (approximate
dynamic programming) is adopted. Then, the subchannel allocation Q-factor is
decomposed into the per-slice Q-factor. Furthermore, the Q-factor and
Lagrangian multipliers are updated by the use of an online stochastic learning
algorithm. Finally, simulation results reveal that the proposed algorithm can
meet the delay requirements and improve the user transmission rate compared
with baseline schemes.


  We formalize the simulation paradigm of cryptography in terms of category
theory and show that protocols secure against abstract attacks form a symmetric
monoidal category, thus giving an abstract model of composable security
definitions in cryptography. Our model is able to incorporate computational
security, set-up assumptions and various attack models such as colluding or
independently acting subsets of adversaries in a modular, flexible fashion. We
conclude by using string diagrams to rederive the security of the one-time pad
and no-go results concerning the limits of bipartite and tripartite
cryptography, ruling out e.g., composable commitments and broadcasting.


  Time series imputation remains a significant challenge across many fields due
to the potentially significant variability in the type of data being modelled.
Whilst traditional imputation methods often impose strong assumptions on the
underlying data generation process, limiting their applicability, researchers
have recently begun to investigate the potential of deep learning for this
task, inspired by the strong performance shown by these models in both
classification and regression problems across a range of applications. In this
work we propose MADS, a novel auto-decoding framework for time series
imputation, built upon implicit neural representations. Our method leverages
the capabilities of SIRENs for high fidelity reconstruction of signals and
irregular data, and combines it with a hypernetwork architecture which allows
us to generalise by learning a prior over the space of time series. We evaluate
our model on two real-world datasets, and show that it outperforms
state-of-the-art methods for time series imputation. On the human activity
dataset, it improves imputation performance by at least 40%, while on the air
quality dataset it is shown to be competitive across all metrics. When
evaluated on synthetic data, our model results in the best average rank across
different dataset configurations over all baselines.


  We consider a pure U(1) quantum gauge field theory on a general Riemannian
compact four manifold. We compute the partition function with Abelian Wilson
loop insertions. We find its duality covariance properties and derive
topological selection rules. Finally, we show that, to have manifest duality,
one must assume the existence of twisted topological sectors besides the
standard untwisted one.


  This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense
of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group
$\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every
intrinsic $L$-Lipschitz graph over a subset of a $k$-dimensional horizontal
subgroup $\mathbb{V}$ of $\mathbb{H}^n$ can be extended to an intrinsic
$L'$-Lipschitz graph over the entire subgroup $\mathbb{V}$, where $L'$ depends
only on $L$, $k$, and $n$. We further prove that $1$-dimensional intrinsic
$1$-Lipschitz graphs in $\mathbb{H}^n$, $n\in \mathbb{N}$, admit corona
decompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants.
This complements results that were known previously only in the first
Heisenberg group $\mathbb{H}^1$. The main difference to this case arises from
the fact that for $1\leq k<n$, the complementary vertical subgroups of
$k$-dimensional horizontal subgroups in $\mathbb{H}^n$ are not commutative.


  We present an analysis of an avian flu model that yields insight into the
role of different transmission routes in the recurrence of avian influenza
epidemics. Recent modelling work on avian influenza in wild bird populations
takes into account demographic stochasticity and highlights the importance of
environmental transmission in determining the outbreak periodicity, but only
for a weak between-host transmission rate. We determine the relative
contribution of environmental and direct transmission routes to the intensity
of outbreaks. We use an approximation method to simulate noise sustained
oscillations in a stochastic avian flu model with environmental and direct
transmission routes. We see that the oscillations are governed by the product
of a rotation and a slowly varying standard Ornstein-Uhlenbeck process (i.e.,
mean-reverting process). The intrinsic frequency of the damped deterministic
version of the system predicts the dominant period of outbreaks. We show, using
analytic computation of the intrinsic frequency and theoretical power spectral
density, that the outbreak periodicity can be explained in terms of either or
both types of transmission.The amplitude of outbreaks tends to be high when
both types of transmission are strong.


  We describe a mechanism of spin transfer between individual quantum dots that
does not require tunneling. Incident circularly-polarized photons create
inter-band excitons with non-zero electron spin in the first quantum dot. When
the quantum-dot pair is properly designed, this excitation can be transferred
to the neighboring dot via the Coulomb interaction with either {\it
conservation} or {\it flipping} of the electron spin. The second dot can
radiate circularly-polarized photons at lower energy. Selection rules for spin
transfer are determined by the resonant conditions and by the strong spin-orbit
interaction in the valence band of nanocrystals. Coulomb-induced energy and
spin transfer in pairs and chains of dots can become very efficient under
resonant conditions. The electron can preserve its spin orientation even in
randomly-oriented nanocrystals.


  The collision of water and elastic liquid drops with a thin cylinder (thread)
is studied. The droplet flight trajectory and the cylinder axis are mutually
perpendicular. Attention is focused on the difference between collisions of
water drops and drops of elastic fluids. In the experiments, the drop diameter
was 3 mm, the diameter of horizontal stainless steel cylinders was 0.4 and 0.8
mm. The drops were formed by slowly pumping liquid through a vertical stainless
steel capillary with an outer diameter of 0.8 mm, from which droplets were
periodically detached under the action of gravity. The droplet velocity before
collision was defined by the distance between the capillary cut and the target
(cylinder); in experiments, this distance was approximately 5, 10, and 20 mm.
The drop velocities before impact are estimated in the range of 0.2-0.5 m/s.
The collision process was monitored by high-speed video recording methods with
a frame rate of 240 and 960 Hz. The test liquids were water and aqueous
solutions of polyacrylamide of molecular weight 11 million and concentrations
of 100 and 1000 ppm (PAM-100 and PAM-1k). Experiments have shown that,
depending on the drop impact height and polymer concentration, different
scenarios of a drop collision with a thin cylinder are possible: a short-term
recoil of a drop from an obstacle, a drop flowing around a cylindrical obstacle
while maintaining the continuity of the drop, the breakup of a drop into two
secondary drops, one of which can continue flight and the other one is captured
by the cylinder, or both secondary droplets continue to fly, the drop also can
be captured by the cylinder, until the impact of the next drop(s) forces the
accumulated drop detach from the cylinder. Numerical modeling satisfactorily
reproduces the phenomena observed in the experiment.


  We present the full basis of effective operators relevant for dark matter
direct detection, up to and including operators of mass dimension seven. We
treat the cases where dark matter is either a Dirac fermion, a Majorana
fermion, a complex scalar, or a real scalar, allowing for dark matter to
furnish a general representation of the electroweak gauge group. We describe
the algorithmic procedure used to obtain the minimal set of effective operators
and provide the tree-level matching conditions onto the effective theory valid
below the electroweak scale.


  Deep learning has improved performance on many natural language processing
(NLP) tasks individually. However, general NLP models cannot emerge within a
paradigm that focuses on the particularities of a single metric, dataset, and
task. We introduce the Natural Language Decathlon (decaNLP), a challenge that
spans ten tasks: question answering, machine translation, summarization,
natural language inference, sentiment analysis, semantic role labeling,
zero-shot relation extraction, goal-oriented dialogue, semantic parsing, and
commonsense pronoun resolution. We cast all tasks as question answering over a
context. Furthermore, we present a new Multitask Question Answering Network
(MQAN) jointly learns all tasks in decaNLP without any task-specific modules or
parameters in the multitask setting. MQAN shows improvements in transfer
learning for machine translation and named entity recognition, domain
adaptation for sentiment analysis and natural language inference, and zero-shot
capabilities for text classification. We demonstrate that the MQAN's
multi-pointer-generator decoder is key to this success and performance further
improves with an anti-curriculum training strategy. Though designed for
decaNLP, MQAN also achieves state of the art results on the WikiSQL semantic
parsing task in the single-task setting. We also release code for procuring and
processing data, training and evaluating models, and reproducing all
experiments for decaNLP.


  The problem of numerical differentiation can be thought of as an inverse
problem by considering it as solving a Volterra equation. It is well known that
such inverse integral problems are ill-posed and one requires regularization
methods to approximate the solution appropriately. The commonly practiced
regularization methods are (external) parameter-based like Tikhonov
regularization, which have certain inherent difficulties like choosing an
optimal value of the regularization parameter, especially in the absence of
noise information, which is a non-trivial task. An attractive alternative is
iterative regularization, where one minimizes an associated functional in a
regularized fashion (i.e., stopping at an appropriate iteration). However, in
most of the regularization methods the associated minimizing functional
contains the noisy data directly, and hence, the recovery gets affected. In
this paper, we propose an iterative regularization method where the minimizing
functional does not contain the noisy data directly. The advantage, in addition
to circumventing the use of noisy data directly, is that the sequence of
functions (or curves) constructed during the descent process does not converge
strongly to the noise data, rather weakly and hence, avoids overfitting.
Furthermore, this method is very robust to extreme noise level in the data as
well as to errors with non-zero mean. To demonstrate the effectiveness of the
new method we provide some examples comparing the numerical results obtained
from our method with results obtained from some of the popular regularization
methods such as Tikhonov regularization, total variation, smoothing spline and
the polynomial regression method.


  Nuclear magnetic resonance (NMR) experiments on single crystals of
HgBa$_{2}$CuO$_{4+\delta}$ are presented that identify two distinct
temperature-dependent spin susceptibilities: one is due to a spin component
that is temperature-dependent above the critical temperature for
superconductivity ($T_{\rm c}$) and reflects pseudogap behavior; the other is
Fermi-liquid-like in that it is temperature independent above $T_{\rm c}$ and
vanishes rapidly below $T_{\rm c}$. In addition, we demonstrate the existence
of a third, hitherto undetected spin susceptibility: it is temperature
independent at higher temperatures, vanishes at lower temperatures (below
$T_0\neq T_{\rm c}$), and changes sign near optimal doping. This susceptibility
either arises from the coupling between the two spin components, or it could be
given by a distinct third spin component.


  The curved space-time around current loops and solenoids carrying arbitrarily
large steady electric currents is obtained from the numerical resolution of the
coupled Einstein-Maxwell equations in cylindrical symmetry. The artificial
gravitational field associated to the generation of a magnetic field produces
gravitational redshift of photons and deviation of light. Null geodesics in the
curved space-time of current loops and solenoids are also presented. We finally
propose an experimental setup, achievable with current technology of
superconducting coils, that produces a phase shift of light of the same order
of magnitude than astrophysical signals in ground-based gravitational wave
observatories.


  Flux-resolved X-ray spectroscopy is widely adopted to investigate the
spectral variation of a target between various flux levels. In many cases it is
done through horizontally splitting a single light curve into multiple flux
levels with certain count rate threshold(s). In this work we point out there
are two hidden biases in this approach which could affect the spectral analyses
under particular circumstances. The first is that, when Poisson fluctuations of
the source counts in light curve bins are non-negligible compared with the
intrinsic variation, this approach would over-estimate (under-estimate) the
intrinsic average flux level of the high (low) state. The second bias is that,
when the Poisson fluctuations of the background count rate is non-negligible,
the background spectrum of the high (low) state would be under-estimated
(over-estimated), thus yielding biased spectral fitting parameters. We take
NuSTAR spectra for example to illustrate the effects of the biases, and
particularly, how the measurements of the coronal temperature in AGNs would be
biased. We present a toy method to assess the significance of such biases, and
approaches to correct for them when necessary.


  In this article we introduce $K$-type block matrices which include two new
classes of block matrices namely block triangular $K$-matrices and hidden block
triangular $K$-matrices. We show that the solution of linear complementarity
problem with $K$-type block matrices can be obtained by solving a linear
programming problem. We show that block triangular $K$-matrices satisfy least
element property. We prove that hidden block triangular $K$-matrices are $Q_0$
and processable by Lemke's algorithm. The purpose of this article is to study
properties of $K$-type block matrices in the context of the solution of linear
complementarity problem.


  A theoretical study is reported of the molecular-to-atomic transition in
solid hydrogen at high pressure. We use the diffusion quantum Monte Carlo
method to calculate the static lattice energies of the competing phases and a
density-functional-theory-based vibrational self-consistent field method to
calculate anharmonic vibrational properties. We find a small but significant
contribution to the vibrational energy from anharmonicity. A transition from
the molecular Cmca-12 direct to the atomic I4_1/amd phase is found at 374 GPa.
The vibrational contribution lowers the transition pressure by 91 GPa. The
dissociation pressure is not very sensitive to the isotopic composition. Our
results suggest that quantum melting occurs at finite temperature.


  An important class of decidable first-order logic fragments are those
satisfying a guardedness condition, such as the guarded fragment (GF). Usually,
decidability for these logics is closely linked to the tree-like model property
- the fact that satisfying models can be taken to have tree-like form. Decision
procedures for the guarded fragment based on the tree-like model property are
difficult to implement. An alternative approach, based on restricting
first-order resolution, has been proposed, and this shows more promise from the
point of view of implementation. In this work, we connect the tree-like model
property of the guarded fragment with the resolution-based approach. We derive
efficient resolution-based rewriting algorithms that solve the Quantifier-Free
Query Answering Problem under Guarded Tuple Generating Dependencies (GTGDs) and
Disjunctive Guarded Tuple Generating Dependencies (DisGTGDs). The Query
Answering Problem for these classes subsumes many cases of GF satisfiability.
Our algorithms, in addition to making the connection to the tree-like model
property clear, give a natural account of the selection and ordering strategies
used by resolution procedures for the guarded fragment. We also believe that
our rewriting algorithm for the special case of GTGDs may prove itself valuable
in practice as it does not require any Skolemisation step and its theoretical
runtime outperforms those of known GF resolution procedures in case of fixed
dependencies. Moreover, we show a novel normalisation procedure for the widely
used chase procedure in case of (disjunctive) GTGDs, which could be useful for
future studies.


  Context: In agile transformations, there are many challenges such as
alignment between agile practices and the organizational goals and strategies
or issues with shifts in how work is organized and executed. One very important
challenge but less considered and treated in research are cultural challenges
associated with an agile mindset. Although research shows that cultural clashes
and general organizational resistance to change are part of the most
significant agile adoption barriers. Objective: We identify challenges that
arise from the interplay between agile culture and organizational culture. In
doing so, we tackle this field and come up with important contributions for
further research regarding a problem that practitioners face today. Method:
This is done with a mixed-method research approach. First, we gathered
qualitative data among our network of agile practitioners and derived in sum 15
challenges with agile culture. Then, we conducted quantitative data by means of
a questionnaire study with 92 participants. Results: We identified 7 key
challenges out of the 15 challenges with agile culture. These key challenges
refer to the technical agility (doing agile) and the cultural agility (being
agile). The results are presented in type of a conceptual model named the Agile
Cultural Challenges (ACuCa). Conclusion: Based on our results, we started
deriving future work aspects to do more detailed research on the topic of
cultural challenges while transitioning or using agile methods in software
development and beyond.


  We study many-body quantum dynamics of $\delta$-interacting bosons confined
in a one-dimensional ring. Main attention is payed to the transition from the
mean-field to Tonks-Girardeau regime using an approach developed in the theory
of interacting particles. We analyze, both analytically and numerically, how
the Shannon entropy of the wavefunction and the momentum distribution depend on
time for a weak and strong interactions. We show that the transition from
regular (quasi-periodic) to irregular ("chaotic") dynamics coincides with the
onset of the Tonks-Girardeau regime. In the latter regime the momentum
distribution of the system reveals a statistical relaxation to a steady state
distribution. The transition can be observed experimentally by studying the
interference fringes obtained after releasing the trap and letting the boson
system expand ballistically.


  Constraints are set on the Higgs boson decay width, Gamma_H, using off-shell
production and decay to ZZ in the four-lepton (4l), or two-lepton-two-neutrino
(2l2nu) final states. The analysis is based on the data collected in 2012 by
the CMS experiment at the LHC, corresponding to an integrated luminosity L =
19.7 fb^{-1} at sqrt(s) = 8 TeV. A maximum-likelihood fit of invariant mass and
kinematic discriminant distributions in the 4l case and of transverse mass or
missing energy distributions in the 2l2nu case is performed. The result of it,
combined with the 4l measurement near the resonance peak, leads to an upper
limit on the Higgs boson width of Gamma_H < 4.2 x Gamma_H^SM at the 95%
confidence level, assuming Gamma_H^SM = 4.15 MeV.


  Periodic boundary conditions have not a unique implementation in magnetic
systems where all spins interact with each other through a power law decaying
interaction of the form $1/r^\alpha$, $r$ being the distance between spins. In
this work we present a comparative study of the finite size effects oberved in
numerical simulations by using first image convention and full infinite of
periodic boundary conditions in one and two-dimensional spin systems with those
type of interactions, including the ferromagnetic, antiferromagnetic and
competitive interactions cases. Our results show no significative differences
between the finite size effects produced by both types of boundary conditions
when the low temperature phase has zero global magnetization, while it depends
on the ratio $\alpha/d$ for systems with a low temperature ferromagnetic phase.
In the last case the first image convention gives much more stronger finite
size effects than the other when the system enters into the classical regime
$\alpha/d \leq 3/2$.


  We study the $r$-near neighbors reporting problem ($r$-NN), i.e., reporting
\emph{all} points in a high-dimensional point set $S$ that lie within a radius
$r$ of a given query point $q$. Our approach builds upon on the
locality-sensitive hashing (LSH) framework due to its appealing asymptotic
sublinear query time for near neighbor search problems in high-dimensional
space. A bottleneck of the traditional LSH scheme for solving $r$-NN is that
its performance is sensitive to data and query-dependent parameters. On
datasets whose data distributions have diverse local density patterns, LSH with
inappropriate tuning parameters can sometimes be outperformed by a simple
linear search.
  In this paper, we introduce a hybrid search strategy between LSH-based search
and linear search for $r$-NN in high-dimensional space. By integrating an
auxiliary data structure into LSH hash tables, we can efficiently estimate the
computational cost of LSH-based search for a given query regardless of the data
distribution. This means that we are able to choose the appropriate search
strategy between LSH-based search and linear search to achieve better
performance. Moreover, the integrated data structure is time efficient and fits
well with many recent state-of-the-art LSH-based approaches. Our experiments on
real-world datasets show that the hybrid search approach outperforms (or is
comparable to) both LSH-based search and linear search for a wide range of
search radii and data distributions in high-dimensional space.


  We consider spin-polarized electrons in a single Landau level on a cylinder
as the circumference of the cylinder goes to infinity. This gives a model of
interacting electrons on a circle where the momenta of the particles are
restricted and there is no kinetic energy. Quantum Hall states are exact ground
states for appropriate short range interactions, and there is a gap to
excitations. These states develop adiabatically from this one-dimensional
quantum Hall circle to the bulk quantum Hall states and further on into the
Tao-Thouless states as the circumference goes to zero. For low filling
fractions a gapless state is formed which we suggest is connected to the Wigner
crystal expected in the bulk.


  We consider the modified Korteweg-de Vries equation. Given a self-similar
solution, and a subcritical perturbation of any size, we prove that there
exists a unique solution to the equation which behaves at blow-up time as the
self-similar solution plus the perturbation. To this end, we develop the first
robust analysis in spaces of functions with bounded Fourier transforms. To
begin, we prove the local well-posedness in subcritical spaces through an
appropriate restriction norm method. As this method is not sufficient to
capture the critical self-similar dynamics, we develop an infinite normal form
reduction (INFR) to derive time-dependent a priori $L^\infty$ bounds in
frequency variables. Both approaches rely on frequency-restricted estimates,
which are specific positive multiplier estimates capable of capturing the
oscillatory nature of the equation. As a consequence of our analysis, we also
prove local well-posedness for small subcritical perturbations of self-similar
solutions at positive time.


  Spammer detection on social network is a challenging problem. The rigid
anti-spam rules have resulted in emergence of "smart" spammers. They resemble
legitimate users who are difficult to identify. In this paper, we present a
novel spammer classification approach based on Latent Dirichlet
Allocation(LDA), a topic model. Our approach extracts both the local and the
global information of topic distribution patterns, which capture the essence of
spamming. Tested on one benchmark dataset and one self-collected dataset, our
proposed method outperforms other state-of-the-art methods in terms of averaged
F1-score.


  White blood cells, also known as leukocytes are group of heterogeneously
nucleated cells which act as salient immune system cells. These are originated
in the bone marrow and are found in blood, plasma, and lymph tissues.
Leukocytes kill the bacteria, virus and other kind of pathogens which invade
human body through phagocytosis that in turn results immunity. Detection of a
white blood cell count can reveal camouflaged infections and warn doctors about
chronic medical conditions such as autoimmune diseases, immune deficiencies,
and blood disorders. Segmentation plays an important role in identification of
white blood cells (WBC) from microscopic image analysis. The goal of
segmentation in a microscopic image is to divide the image into different
distinct regions. In our paper, we tried to propose a novel instance
segmentation method for segmenting the WBCs containing both the nucleus and the
cytoplasm, from bone marrow images.


  Domain randomization (DR) is a successful technique for learning robust
policies for robot systems, when the dynamics of the target robot system are
unknown. The success of policies trained with domain randomization however, is
highly dependent on the correct selection of the randomization distribution.
The majority of success stories typically use real world data in order to
carefully select the DR distribution, or incorporate real world trajectories to
better estimate appropriate randomization distributions. In this paper, we
consider the problem of finding good domain randomization parameters for
simulation, without prior access to data from the target system. We explore the
use of gradient-based search methods to learn a domain randomization with the
following properties: 1) The trained policy should be successful in
environments sampled from the domain randomization distribution 2) The domain
randomization distribution should be wide enough so that the experience similar
to the target robot system is observed during training, while addressing the
practicality of training finite capacity models. These two properties aim to
ensure the trajectories encountered in the target system are close to those
observed during training, as existing methods in machine learning are better
suited for interpolation than extrapolation. We show how adapting the domain
randomization distribution while training context-conditioned policies results
in improvements on jump-start and asymptotic performance when transferring a
learned policy to the target environment.


  In this paper we propose a generalization of N=4 three dimensional AdS
supergravity to the noncommutative case. This is a supersymmetric version of
the results presented in hep-th/0201103. We show that it continues to admit an
N=4 supersymmetric solution which is the noncommutative couterpart of AdS_3
space. Some other solutions are also discussed.


  We show that if the closure of a smooth pseudoconvex domain admits a
"sufficiently nice" Stein neighborhood basis, then the d-bar Neumann problem on
the domain is globally regular.


  One crucial aspect of 3D head avatar reconstruction lies in the details of
facial expressions. Although recent NeRF-based photo-realistic 3D head avatar
methods achieve high-quality avatar rendering, they still encounter challenges
retaining intricate facial expression details because they overlook the
potential of specific expression variations at different spatial positions when
conditioning the radiance field. Motivated by this observation, we introduce a
novel Spatially-Varying Expression (SVE) conditioning. The SVE can be obtained
by a simple MLP-based generation network, encompassing both spatial positional
features and global expression information. Benefiting from rich and diverse
information of the SVE at different positions, the proposed SVE-conditioned
neural radiance field can deal with intricate facial expressions and achieve
realistic rendering and geometry details of high-fidelity 3D head avatars.
Additionally, to further elevate the geometric and rendering quality, we
introduce a new coarse-to-fine training strategy, including a geometry
initialization strategy at the coarse stage and an adaptive importance sampling
strategy at the fine stage. Extensive experiments indicate that our method
outperforms other state-of-the-art (SOTA) methods in rendering and geometry
quality on mobile phone-collected and public datasets.


  We give an outlook, how to realize the ideas of complex scaling from
Grothaus, Vogel and Streit to phase space path integrals in the framework of
White Noise Analysis. The idea of this scaling method goes back to Doss.
Therefore we extend the concept complex scaling to scaling with suitable
bounded operators.


  The resource theory of contextuality considers resourceful objects to be
probabilistic data-tables, known as correlations or behaviors, that fail to
have an explanation in terms of Kochen-Specker noncontextual models. In this
work, we advance this resource theory, considering free operations to be
noncontextual wirings (NCW). We show that all such wirings form a convex set.
When restricted to Bell scenarios, we show that such wirings are not equivalent
to local operations assisted by a common source of classical shared randomness
(LOSR). The set of all NCW operations contains LOSR, but is strictly larger. We
also prove several elementary facts about how different resources can be
converted via NCW. As a concrete example, we show that there are pairs of
behaviors that cannot be converted one into the other using NCW. Since resource
conversion mathematically induces a pre-order over the set of all behaviors,
our results reveal the intricate ordering induced by NCW in scenarios beyond
Bell scenarios.


  The properties of the Milky Way's nuclear stellar disc give crucial
information on the epoch of bar formation. Mira variables are promising bright
candidates to study the nuclear stellar disc, and through their period-age
relation dissect its star formation history. We report on a sample of $1782$
Mira variable candidates across the central $3\times3\,\mathrm{deg}^2$ of the
Galaxy using the multi-epoch infrared VISTA Variables in Via Lactea (VVV)
survey. We describe the algorithms employed to select candidate variable stars
and then model their light curves using periodogram and Gaussian process
methods. By combining with WISE, 2MASS and other archival photometry, we model
the multi-band light curves to refine the periods and inspect the amplitude
variation between different photometric bands. The infrared brightness of the
Mira variables means many are too bright and missed by VVV. However, our sample
follows a well-defined selection function as expected from artificial star
tests. The multi-band photometry is modelled using stellar models with
circumstellar dust that characterise the mass loss rates. We demonstrate how
$\gtrsim90$ per cent of our sample is consistent with O-rich chemistry.
Comparison to period-luminosity relations demonstrates that the bulk of the
short period stars are situated at the Galactic Centre distance. Many of the
longer period variables are very dusty, falling significantly under the O-rich
Magellanic Cloud and solar neighbourhood period-luminosity relations and
exhibit high mass-loss rates of
$\sim2.5\times10^{-5}M_\odot\,\mathrm{yr}^{-1}$. The period distribution
appears consistent with the nuclear stellar disc forming
$\gtrsim8\,\mathrm{Gyr}$ ago although it is not possible to disentangle the
relative contributions of the nuclear stellar disc and the contaminating bulge.


  The proliferation of Large Language Models (LLMs), such as ChatGPT, has
raised concerns about their potential impact on academic integrity, prompting
the need for LLM-resistant exam designs. This article investigates the
performance of LLMs on exams and their implications for assessment, focusing on
ChatGPT's abilities and limitations. We propose guidelines for creating
LLM-resistant exams, including content moderation, deliberate inaccuracies,
real-world scenarios beyond the model's knowledge base, effective distractor
options, evaluating soft skills, and incorporating non-textual information. The
article also highlights the significance of adapting assessments to modern
tools and promoting essential skills development in students. By adopting these
strategies, educators can maintain academic integrity while ensuring that
assessments accurately reflect contemporary professional settings and address
the challenges and opportunities posed by artificial intelligence in education.


  The general problem is studied on a simple example. A quantum particle in an
infinite one-dimensional well potential is considered.
  Let the boundaries of well changes in a finite time $T$. The standard methods
for calculating probability of transition from an initial to the final state
are in general inapplicable since the states of different wells belong to
different Hilbert spaces.
  If the final well covers only a part of the initial well (and, possibly, some
outer part of the configuration space), the total probability of the transition
from any stationary state of the initial well into {\bf all} possible states of
the final well is less than 1 at $T\to 0$. If the problem is regularized with a
finite-height potential well, this missing probability can be understood as a
non-zero probability of transitions into the continuous spectrum, despite the
fact that this spectrum disappears at the removal of regularization. This
phenomenon ("transition to nowhere'') can result new phenomena in some
fundamental problems, in particular at description of earlier Universe.
  We discuss also how to calculate the probabilities of discussed transitions
at final $T$ for some ranges of parameters.


  We discuss the wavelength dependence of angular diameters of M giants from an
observational perspective. Observers cannot directly measure an optical-depth
radius for a star, despite this being a common theoretical definition. Instead,
they can use an interferometer to measure the square of the fringe visibility.
We present new plots of the wavelength-dependent centre-to-limb variation (CLV)
of intensity of the stellar disk as well as visibility for Mira and non-Mira M
giant models. We use the terms ``CLV spectra'' and ``visibility spectra'' for
these plots. We discuss a model-predicted extreme limb-darkening effect (also
called the narrow-bright-core effect) in very strong TiO bands which can lead
to a misinterpretation of the size of a star in these bands. We find no
evidence as yet that this effect occurs in real stars. Our CLV spectra can
explain the similarity in visibilities of R Dor (M8IIIe) that have been
observed recently despite the use of two different passbands. We compare
several observations with models and find the models generally under-estimate
the observed variation in visibility with wavelength. We present CLV and
visibility spectra for a model that is applicable to the M supergiant alpha
Ori.


  Non-orthogonal multiple access (NOMA) is capable of serving different numbers
of users in the same time-frequency resource element, and this feature can be
leveraged to carry additional information. In the orthogonal frequency division
multiplexing (OFDM) system, we propose a novel enhanced NOMA scheme, called
NOMA with informative envelope (NOMA-IE), to explore the flexibility of the
envelope of NOMA signals. In this scheme, data bits are conveyed by the
quantified signal envelope in addition to classic signal constellations. The
subcarrier activation patterns of different users are jointly decided by the
envelope former. At the receiver, successive interference cancellation (SIC) is
employed, and we also introduce the envelope detection coefficient to eliminate
the error floor. Theoretical expressions of spectral efficiency and energy
efficiency are provided for the NOMA-IE. Then, considering the binary phase
shift keying modulation, we derive the asymptotic bit error rate for the
two-subcarrier OFDM subblock. Afterwards, the expressions are extended to the
four-subcarrier case. The analytical results reveal that the imperfect SIC and
the index error are the main factors degrading the error performance. The
numerical results demonstrate the superiority of the NOMA-IE over the OFDM and
OFDM-NOMA, especially in the high signal-to-noise ratio (SNR) regime.


  In this paper we present a martingale related to the exit measures of
super-Brownian motion. By changing measure with this martingale in the
canonical way we have a new process associated with the conditioned exit
measure. This measure is shown to be identical to a measure generated by a
non-homogeneous branching particle system with immigration of mass. An
application is given to the problem of conditioning the exit measure to hit a
number of specified points on the boundary of a domain. The results are similar
in flavor to the "immortal particle" picture of conditioned super-Brownian
motion but more general, as the change of measure is given by a martingale
which need not arise from a single harmonic function.


  We show that for a class of $C^2$ quasiperiodic potentials and for any
Diophantine frequency, the Lyapunov exponents of the corresponding
Schr\"odinger cocycles are uniformly positive and weak H\"older continuous as
function of energies. As a corollary, we also obtain that the corresponding
integrated density of states (IDS) is weak H\"older continous. Our approach is
of purely dynamical systems, which depends on a detailed analysis of asymptotic
stable and unstable directions. We also apply it to more general
$\mathrm{SL}(2,\mathbb R)$ cocycles, which in turn can be applied to get
uniform positivity and continuity of Lyapuonv exponents around unique
nondegenerate extremal points of any smooth potential, and to a certain class
of $C^2$ Szeg\H o cocycles.


  A braiding operation defines a real-space renormalization group for anyonic
chains. The resulting renormalization group flow can be used to define a
quantum scaling limit by operator-algebraic renormalization. It is illustrated
how this works for the Ising chain, also known as transverse-field Ising model.
In this case, the quantum scaling limit results in the vacuum state of the
well-known Ising CFT. Distinguishing between the braiding and its inverse is
directly related to the chiral sectors of the Ising CFT. This has direct
implications for the simulation of CFTs on topological quantum computers.


  We study the relativistic formulation of a classical time-dependent
nonholonomic Lagrangian mechanics from the perspective of moving frames. We
also introduce time-dependent $G$-Chaplygin systems with affine constraints,
which are natural objects for the invariant formulation of nonholonomic systems
with symmetries. As far as the author is aware, the Hamiltonization problem for
time-dependent constraints has not yet been studied. As a first step in this
direction, we consider a rolling without sliding of a balanced disc of radius
$r$ over a vertical circle of variable radius $R(t)$. We modify the Chaplygin
multiplier method and prove that the reduced system becomes the usual
Lagrangian system with respect to the new time.


  In this work we study the ice-water interface under coexistence conditions by
means of molecular simulations using the TIP4P/2005 water model. Following the
methodology proposed by Hoyt and co-workers [J. J. Hoyt, M. Asta and A. Karma,
Phys. Rev. Lett., 86, 5530, (2001)] we measure the interfacial free energy of
ice with liquid water by analysing the spectrum of capillary fluctuations of
the interface. We get an orientationally averaged interfacial free energy of
27(2) mN/m, in good agreement with a recent estimate obtained from simulation
data of the size of critical clusters [E. Sanz, C. Vega, J. R. Espinosa, R.
Caballero-Bernal, J. L. F. Abascal and C. Valeriani, JACS, 135, 15008, (2013)].
We also estimate the interfacial free energy of different planes and obtain
27(2), 28(2)and 28(2) mN/m for the basal, the primary prismatic and the
secondary prismatic planes respectively. Finally, we inspect the structure of
the interface and find that its thickness is of approximately 4-5 molecular
diameters. Moreover, we find that when the basal plane is exposed to the fluid
the interface alternates regions of cubic ice with regions of hexagonal ice.