  We present the discovery with the QUIJOTE line survey of the cations HC5N+
and HC7N+ in the direction of TMC-1. Seven lines with half-integer quantum
numbers from J=25/2-23/2 to 37/2-35/2 have been assigned to HC5N+ and eight
lines from J=55/2-53/2 to 71/2-69/2 to HC7N+. Both species have inverted 2Pi
ground electronic states with very good estimates for their B0 and AS0
constants based on optical observations. The lines with the lowest J of HC5N+
exhibit multiple components due to the hyperfine structure introduced by the H
and N nuclei. However, these different components collapse for the higher J. No
hyperfine structure is found for any of the lines of HC7N+. The derived
effective rotational and distortion constants for HC5N+ are Beff = 1336.662+/-
0.001 MHz and Deff = 27.4+/-2.6 Hz, while for HC7N+ they are Beff =
567.85036+/-0.00037 MHz and Deff = 4.01+/-0.19 Hz. From the observed
intensities, we derived Trot = 5.5+/-0.5K and N = (9.9+/-1.0)x 1010 cm-2 for
HC5N+, while we obtained Trot = 8.5+/-0.5K and N = (2.3+/-0.2)x1010 cm-2 for
HC7N+. The HC5N/HC5N+, C5N/HC5N+, C5N-/HC5N+, HC7N/HC7N+, HC5N+/HC7N+, and
C7N-/HC7N+ abundance ratios are 670+/-80, 4.8+/-0.8, 1.2+/-0.2, 1000+/-150,
4.2+/-0.5, and 2.2+/-0.2, respectively. We have run chemical modelling
calculations to investigate the formation and destruction of these new cations.
We find that these species are mainly formed through the reactions of H2 and
the cations C5N+ and C7N+, and by the reactions of H+ with HC5N and HC7N, while
they are mostly destroyed through a reaction with H2 and a dissociative
recombination with electrons. Based on the underestimation of the abundances of
HC5N+ and HC7N+ by the chemical model by a factor around 20, we suggest that
the rate coefficients currently assumed for the reactions of these cations with
H2 could be too high by the same factor, something that will be worth
investigating.


  A recent breakthrough by Ambainis, Balodis, Iraids, Kokainis, Pr\=usis and
Vihrovs (SODA'19) showed how to construct faster quantum algorithms for the
Traveling Salesman Problem and a few other NP-hard problems by combining in a
novel way quantum search with classical dynamic programming. In this paper, we
show how to apply this approach to the minimum Steiner tree problem, a
well-known NP-hard problem, and construct the first quantum algorithm that
solves this problem faster than the best known classical algorithms. More
precisely, the complexity of our quantum algorithm is
$\mathcal{O}(1.812^k\poly(n))$, where $n$ denotes the number of vertices in the
graph and $k$ denotes the number of terminals. In comparison, the best known
classical algorithm has complexity $\mathcal{O}(2^k\poly(n))$.


  Propagation of the strong shock in the flat expanding Friedman universe is
investigated using methods of dimension and similarity. Exact analytic solution
of self-similar equations is obtained, determining dependences of the radius
and velocity of the shock wave on time and radius. It is obtained, that in the
expanding medium the velocity of shock decreases as $\sim t^{-1/5}$, what is
slower than the shock velocity in the static uniform medium $\sim t^{-3/5}$.
The radius of the shock wave in the expanding self-gravitating medium increases
$\sim t^{4/5}$, more rapidly than the shock wave radius in the uniform
non-gravitating medium $\sim t^{2/5}$. So, the shock propagates in the
direction of decreasing density with larger speed, that in the static medium,
due to accelerating action of the decreasing density, even in the presence of a
self-gravitation.


  We investigate the Ricci Dark Energy (RDE) in the braneworld models with a
Gauss-Bonnet term in the Bulk. We solve the generalized Friedmann equation on
the brane analytically and find that the universe will finally enter into a
pure de Sitter spacetime in stead of the big rip that appears in the usual 4D
Ricci dark energy model with parameter $\alpha<1/2$. We also consider the
Hubble horizon as the IR cutoff in holographic dark energy model and find it
can not accelerate the universe as in the usual case without interacting.


  Our goal is to study $p$-adic local systems on a rigid-analytic variety with
semistable formal model. We prove that such a local system is semistable if and
only if so are its restrictions to the points corresponding to the irreducible
components of the special fiber. For this, the main body of the paper concerns
analytic prismatic $F$-crystals on the absolute logarithmic prismatic site of a
semistable $p$-adic log formal scheme. Analyzing Breuil-Kisin log prisms, we
obtain a prismatic purity theorem and deduce the above purity theorem for
semistable local systems.


  Situations in which immediate self-interest and long-term collective interest
conflict often require some form of influence to prevent them from leading to
undesirable or unsustainable outcomes. Next to sanctioning, social influence
and social structure, it is possible that strategic solutions can exist for
these social dilemmas. However, the existence of strategies that enable a
player to exert control in the long-run outcomes can be difficult to show and
different situations allow for different levels of strategic influence. Here,
we investigate the effect of threshold nonlinearities on the possibilities of
exerting unilateral control in finitely repeated n-player public goods games
and snowdrift games. These models can describe situations in which a collective
effort is necessary in order for a benefit to be created. We identify
conditions in terms of a cooperator threshold for the existence of generous,
extortionate and equalizing zero-determinant (ZD) strategies. Our results show
that, for both games, the thresholds prevent equalizing ZD strategies from
existing. In the snowdrift game, introducing a cooperator threshold has no
effect on the region of feasible extortionate ZD strategies. For extortionate
strategies in the public goods game, the threshold only restricts the region of
enforceable strategies for small values of the public goods multiplier.
Generous ZD strategies exist for both games, but introducing a cooperator
threshold forces the slope more towards the value of a fair strategy, where the
player has approximately the same payoff as the average payoff of his
opponents.


  Steady laminar flows through porous media spontaneously generate Lagrangian
chaos at pore scale, with qualitative implications for a range of transport,
reactive and biological processes. The characterization and understanding of
mixing dynamics in these opaque environments is an outstanding challenge. We
address this issue by developing a novel technique based upon high-resolution
imaging of the scalar signature produced by push-pull flows through porous
media samples. Owing to the rapid decorrelation of particle trajectories in
chaotic flows, the scalar image measured outside the porous material is
representative of in-situ mixing dynamics. We present a theoretical framework
for estimation of the Lyapunov exponent based on extension of Lagrangian
stretching theories to correlated aggregation. This method provides a full
characterization of chaotic mixing dynamics in a large class of porous
materials.


  Hurewicz proved completely metrizable Menger spaces are /sigma-compact. We
extend this to Cech-complete Menger spaces and consistently to projective
Menger metrizable spaces. On the other hand, it is consistent that there is a
co-analytic Menger space that is not /sigma-compact.


  Many systems, including biological tissues and foams, are made of highly
packed units having high deformability but low compressibility. At two
dimensions, these systems offer natural tesselations of plane with fixed
density, in which transitions from ordered to disordered patterns are often
observed, in both directions. Using a modified Cellular Potts Model algorithm
that allows rapid thermalization of extensive systems, we numerically explore
the order-disorder transition of monodisperse, two-dimensional cellular systems
driven by thermal agitation. We show that the transition follows most of the
predictions of Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory
developed for melting of 2D solids, extending the validity of this theory to
systems with many-body interactions. In particular, we show the existence of an
intermediate hexatic phase, which preserves the orientational order of the
regular hexagonal tiling, but looses its positional order. In addition to
shedding light on the structural changes observed in experimental systems, our
study shows that soft cellular systems offer macroscopic systems in which KTHNY
melting scenario can be explored, in the continuation of Bragg's experiments on
bubble rafts.


  Production of $c\bar c$ pairs in elementary hadron-hadron collisions is
introduced in a simulation of relativistic heavy ion collisions. Coalescence of
charmed quarks and antiquarks into various charmonium states is performed and
the results are compared to PHENIX J$/\psi$ Au+Au data. The $\chi$ and $\psi$'
bound states must be included as well as the ground state J$/\psi$, given the
appreciable feeding from the excited states down to the J$/\psi$ via gamma
decays. Charmonium coalescence is found to take place at relatively late times:
generally after $c$($\bar c$)-medium interactions have ceased. Direct
production of charmonia through hadron-hadron interactions, {\it ie.} without
explicit presence of charm quarks, occurring only at early times, is suppressed
by collisions with comoving particles and accounts for some $\sim 5\%$ of the
total J$/\psi$ production. Coalescence is especially sensitive to the level of
open charm production, scaling naively as $n_{c\bar c}^2$. The J$/\psi$
transverse momentum distribution is dependent on the charm quark transverse
momentum distribution and early charm quark-medium interaction, thus providing
a glimpse of the initial collision history.


  A proof is given for the Fourier transform for functions in a quantum
mechanical Hilbert space on a non-compact manifold in general relativity. In
the (configuration space) Newton-Wigner representation we discuss the spectral
decomposition of the canonical operators and give a proof of the
Parseval-Plancherel relation and the Born rule for linear superposition. We
then discuss the representations of pure quantum states and their dual vectors,
and construct the Fock space and the associated quantum field theory for
Bose-Einstein and Fermi-Dirac statistics.


  The transfer of high-precision optical frequency signals over free-space
links, particularly between ground stations and satellites, will enable
advances in fields ranging from coherent optical communications and satellite
Doppler ranging to tests of General Relativity and fundamental physics. We
present results for the actively stabilized coherent phase transfer of a 193
THz continuous wave optical frequency signal over horizontal free-space links
150 m and 600 m in length. Over the 600 m link we achieved a fractional
frequency stability of 8.9e-18 at one second of integration time, improving to
1.3e-18 at an integration time of 64 s, suitable for transmission of optical
atomic clock signals. The achievable transfer distance is limited by
deep-fading of the transmitted signal due to atmospheric turbulence. We also
estimate the expected additional degradation in stability performance for
frequency transfer to Low Earth Orbit.


  Unsupervised image-to-image translation aims at learning a mapping between
two visual domains. However, learning a translation across large geometry
variations always ends up with failure. In this work, we present a novel
disentangle-and-translate framework to tackle the complex objects
image-to-image translation task. Instead of learning the mapping on the image
space directly, we disentangle image space into a Cartesian product of the
appearance and the geometry latent spaces. Specifically, we first introduce a
geometry prior loss and a conditional VAE loss to encourage the network to
learn independent but complementary representations. The translation is then
built on appearance and geometry space separately. Extensive experiments
demonstrate the superior performance of our method to other state-of-the-art
approaches, especially in the challenging near-rigid and non-rigid objects
translation tasks. In addition, by taking different exemplars as the appearance
references, our method also supports multimodal translation. Project page:
https://wywu.github.io/projects/TGaGa/TGaGa.html


  The most successful method used so far to search for extrasolar planets is
the radial velocity technique, where periodical shifts on the measured emission
from a star provide evidence for an orbiting planet. This method has been used
on large telescopes with large and expensive instrumentation, only enabling a
small amount of observing time per star. We have developed a compact
spectrograph fed by one or several single-mode fibres that avoids the need for
complex fibre scrambling or gas absorption cells for calibration. In principle,
this will enable planet searches around bright stars over the next few years.
We aim to pave the way for large networks of small telescopes searching for
Earth-like planets. At a resolving power of R~50000, I have characterized this
spectrograph, determined its stability and the fidelity required for a
simultaneous calibration source.


  The LUMINEU is designed to investigate the possibility to search for
neutrinoless double beta decay in $^{100}$Mo by means of a large array of
scintillating bolometers based on ZnMoO$_4$ crystals enriched in $^{100}$Mo.
High energy resolution and relatively fast detectors, which are able to measure
both the light and the heat generated upon the interaction of a particle in a
crystal, are very promising for the recognition and rejection of background
events. We present the LUMINEU concepts and the experimental results achieved
aboveground and underground with large-mass natural and enriched crystals. The
measured energy resolution, the $\alpha/\beta$ discrimination power and the
radioactive internal contamination are all within the specifications for the
projected final LUMINEU sensitivity. Simulations and preliminary results
confirm that the LUMINEU technology can reach zero background in the region of
interest (around 3 MeV) with exposures of the order of hundreds
kg$\times$years, setting the bases for a next generation $0\nu2\beta$ decay
experiment capable to explore the inverted hierarchy region of the neutrino
mass pattern.


  We study the out-of-equilibrium evolution of a strongly interacting quantum
spin chain which is mapped on a system of hard rods that are coherently
deposited on and removed from a lattice. We show that this closed quantum
system approaches an equilibrium steady state which strongly resembles a
microcanonical ensemble of classical hard rods. Starting from the fully
coherent evolution equation we derive a Master equation for the evolution of
the number of hard rods on the lattice. This equation does not only capture
properties of the equilibrium state but also describes the dynamical
non-equilibrium evolution into it for the majority of initial conditions. We
analyze this in detail for hard rods of varying size.


  In the centre of mass frame, we have studied theoretically the $Z$-boson
resonant production in the presence of an intense laser field via the weak
process $e^+e^- \to \mu^+\mu^-$. Dressing the incident particles by a
Circularly Polarized laser field (CP-laser field), at the first step, shows
that for a given laser field's parameters, the $Z$- boson cross section
decreases by several orders of magnitude. We have compared the the Total Cross
Section (TCS) obtained by using the scattering matrix method with that given by
the Breit-Wigner approach in the presence of a CP-laser field and the results
are found to be very consistent. This result indicates that Breit-Wigner
formula is valid not only for the laser-free process but also in the presence
of a CP-laser field. The dependence of the laser-assisted differential cross
section on the Centre of Mass Energy (CME) for different scattering angles
proves that it reaches its maximum for small and high scattering angles. At the
next step and by dressing both incident and scattered particles, we have shown
that the CP-laser field largely affects the TCS, especially when its strength
reaches $10^{9}\,V.cm^{-1}$. This result confirms that obtained for the elastic
electron-proton scattering in the presence of a CP-laser field [I. Dahiri et
al., arXiv:2102.00722v1]. It is interpreted by the fact that heavy interacting
particles require high laser field's intensity to affect the collision's cross
section.


  In this paper I discuss what, according to my long experience, every computer
scientist should know from logic. We concentrate on issues of modeling,
interpretability and levels of abstraction. We discuss what the minimal toolbox
of logic tools should look like for a computer scientist who is involved in
designing and analyzing reliable systems. We shall conclude that many classical
topics dear to logicians are less important than usually presented, and that
less-known ideas from logic may be more useful for the working computer
scientist.


  We provide a faithful translation of Hans Richter's important 1949 paper
"Verzerrungstensor, Verzerrungsdeviator und Spannungstensor bei endlichen
Form\"anderungen" from its original German version into English, complemented
by an introduction summarizing Richter's achievements.


  In the medium term, quantum computing must tackle two key challenges: fault
tolerance and security. Fault tolerance will be solved with sufficiently high
quality experiments on large numbers of qubits, but the scale and complexity of
these devices means that a cloud-based access model is likely to dominate. How
can we risk evaluating valuable computations on an untrusted server? Here we
detail a verifiable circuit-based model that only requires classical
communication between parties. The server is blind to the details of the
computation, which is computationally secure.


  The recent measurements of $R_{K^+}$, $R_{K_S^0}$, $R_{K^{*+}}$,
$B_s\to\mu^+\mu^-$, a set of CP-averaged angular observables for the $B^0\to
K^{*0}\mu^+\mu^-$ decay, and its isospin partner $B^+\to K^{*+}\mu^+\mu^-$ by
the LHCb Collaboration, consistently hint at lepton universality violation in
the $b\to s\ell\ell$ transitions. In this work, we first perform global fits to
the $b\to s\ell\ell$ data and show that five one-dimensional scenarios, i.e,
$\delta C_9^{\mu}$, $\delta C_{10}^{\mu}$, $\delta C_L^{\mu}$, $\delta
C_9^{\mu}=C_{10}^{\mu\prime}$, and $\delta C_9^{\mu}=-C_9^{\mu\prime}$ can best
explain the so-called B anamolies. Furthermore, we explore how these scenarios
can be distinguished from each other. For this purpose, we first study the
combinations of four angular asymmetries $A_i$~$(i=3,4,5,9)$ and find that they
cannot distinguish the five new physics scenarios. We then show that a newly
constructed ratio $R_{S}$ can uniquely discriminate the five new physics
scenarios in proper intervals of $q^2$ if it can be measured with a percent
level precision.


  Two short seminal papers of Margulis used Kazhdan's property $(T)$ to give,
on the one hand, explicit constructions of expander graphs, and to prove, on
the other hand, the uniqueness of some invariant means on compact simple Lie
groups. These papers opened a rich line of research on expansion and spectral
gap phenomena in finite and compact simple groups. In this paper we survey the
history of this area and point out a number of problems which are still open.


  Most current classifiers are vulnerable to adversarial examples, small input
perturbations that change the classification output. Many existing attack
algorithms cover various settings, from white-box to black-box classifiers, but
typically assume that the answers are deterministic and often fail when they
are not. We therefore propose a new adversarial decision-based attack
specifically designed for classifiers with probabilistic outputs. It is based
on the HopSkipJump attack by Chen et al. (2019, arXiv:1904.02144v5 ), a strong
and query efficient decision-based attack originally designed for deterministic
classifiers. Our P(robabilisticH)opSkipJump attack adapts its amount of queries
to maintain HopSkipJump's original output quality across various noise levels,
while converging to its query efficiency as the noise level decreases. We test
our attack on various noise models, including state-of-the-art off-the-shelf
randomized defenses, and show that they offer almost no extra robustness to
decision-based attacks. Code is available at
https://github.com/cjsg/PopSkipJump .


  We report the discovery of the sixth known eclipsing double white dwarf (WD)
system, SDSS J1152+0248, with a 2.3968 +/- 0.0003 h orbital period, in data
from the Kepler Mission's K2 continuation. Analysing and modelling the K2 data
together with ground-based fast photometry, spectroscopy, and radial-velocity
measurements, we determine that the primary is a DA-type WD with mass M1 = 0.47
+/- 0.11 Msun, radius R1 = 0.0197 +/- 0.0035 Rsun, and cooling age t1 = 52 +/-
36 Myr. No lines are detected, to within our sensitivity, from the secondary
WD, but it is likely also of type DA. Its central surface brightness, as
measured from the secondary eclipse, is 0.31 of the primary's surface
brightness. Its mass, radius, and cooling age, respectively, are M2 = 0.44 +/-
0.09 Msun, R2 = 0.0223 +0.0064 -0.0050 Rsun, and t2 = 230 +/- 100 Myr. SDSS
J1152+0248 is a near twin of the double-lined eclipsing WD system CSS 41177.


  A 4-regular planar graph $G$ is said to be circle representable if there
exists a collection of circles drawn on the plane such that the touching and
crossing points correspond to the vertices of $G$, and the circular arcs
between those points correspond to the edges of $G$. Lov\'asz (1970)
conjectured that every 4-regular planar graph has a circle representation, but
an infinite family of counterexamples was given by Bekos and Raftopoulou
(2015). We reduce the order of the smallest known counterexamples among simple
graphs from 822 to 68 based on a multigraph counterexample of order 12.


  The relativistic Langevin equation poses a number of technical and conceptual
problems related to its derivation and underlying physical assumptions.
Recently, a method has been proposed in [A. Petrosyan and A. Zaccone, J. Phys.
A: Math. Theor. 55 015001 (2022)] to derive the relativistic Langevin equation
from a first-principles particle-bath Lagrangian. As a result of the
particle-bath coupling, a new ``restoring force'' term appeared, which breaks
translation symmetry. Here we revisit this problem aiming at deriving a fully
translation-invariant relativistic Langevin equation. We successfully do this
by adopting the renormalization potential protocol originally suggested by
Caldeira and Leggett. The relativistic renormalization potential is derived
here and shown to reduce to Caldeira and Leggett's form in the non-relativistic
limit. The introduction of this renormalization potential successfully removes
the restoring force and a fully translation-invariant relativistic Langevin
equation is derived for the first time. The physically necessary character of
the renormalization potential is discussed in analogy with non-relativistic
systems, where it emerges due to the renormalization of the tagged particle
dynamics due to its interaction with the bath oscillators (a phenomenon akin to
level-repulsion or avoided-crossing in condensed matter). We discuss the
properties that the corresponding non-Markovian friction kernel has to satisfy,
with implications ranging from transport models of the quark-gluon plasma, to
relativistic viscous hydrodynamic simulations, and to electrons in graphene.


  We apply the Kubo-Anderson stochastic theory of molecular spectral lineshape
to the case of polaritons formed in the collective strong coupling regime. We
investigate both the fast and slow limits of the random frequency modulation of
the emitter as well as the intermediate regime and show how the interplay
between the characteristic timescales of the cavity and the molecular disorder
is expressed in the observed polaritons lineshapes. The analytical solution
obtained for the slow limit is valid for any ratio between the inhomogeneous
broadening of the molecules and the Rabi splitting, especially relevant for
molecular polaritons where these two quantities can be of the same order of
magnitude.


  The magnetic behaviour of nanoparticles of antiferromagnetic ferritin, with a
mean Fe loading of 410 atoms per core, has been investigated by 57Fe Mossbauer
absorption spectroscopy down to very low temperature (34mK). In previous
experi- ments of frequency dependent magnetic susceptibility and magnetic noise
performed at 25mK in similar samples, it was claimed that a resonance at a
frequency of about 10**8 Hz, due to a macroscopic coherent state, had been
observed. However, our search of incoherent tunnel fluctuations around 10**8 Hz
using 57Fe Mossbauer spectroscopy, whose "window" of measurement of fluctuation
frequencies lies in this frequency range, was unsuccessful. This casts a doubt
about the previous observa- tion of macroscopic quantum coherence in ferritin.


  The objective of few-shot named entity recognition is to identify named
entities with limited labeled instances. Previous works have primarily focused
on optimizing the traditional token-wise classification framework, while
neglecting the exploration of information based on NER data characteristics. To
address this issue, we propose a Multi-Task Semantic Decomposition Framework
via Joint Task-specific Pre-training (MSDP) for few-shot NER. Drawing
inspiration from demonstration-based and contrastive learning, we introduce two
novel pre-training tasks: Demonstration-based Masked Language Modeling (MLM)
and Class Contrastive Discrimination. These tasks effectively incorporate
entity boundary information and enhance entity representation in Pre-trained
Language Models (PLMs). In the downstream main task, we introduce a multi-task
joint optimization framework with the semantic decomposing method, which
facilitates the model to integrate two different semantic information for
entity classification. Experimental results of two few-shot NER benchmarks
demonstrate that MSDP consistently outperforms strong baselines by a large
margin. Extensive analyses validate the effectiveness and generalization of
MSDP.


  Let $a_n$ be the random increasing sequence of natural numbers which takes
each value independently with decreasing probability of order $n^{-\alpha}$, $0
< \alpha < 1/2$. We prove that, almost surely, for every measure-preserving
system $(X,T)$ and every $f \in L^1(X)$ orthogonal to the invariant factor, the
modulated, random averages \[ \sup_{b} \Big| \frac{1}{N} \sum_{n = 1}^N b(n)
T^{a_{n}} f \Big| \] converge to $0$ pointwise almost everywhere, where the
supremum is taken over a set of bounded functions with certain uniform
approximation properties.


  We show that if G is a Chevalley group of rank n and F_q[t,t^{-1}] is the
ring of Laurent polynomials over a finite field, then G(F_q[t,t^{-1}]) is of
type F_{2n-1}. This bound is optimal because it is known -- and we show again
-- that the group is not of type F_{2n}.


  Electrical transport of a polar heterointerface between two insulating
perovskites, KTaO3 and SrTiO3, is studied. It is formed between a thin KTaO3
film deposited on a top of TiO2- terminated (100) SrTiO3 substrate. The
resulting (KO)1-(TiO2)0 heterointerface is expected to be hole-doped according
to formal valences of K (1+) and Ti (4+). We observed electrical conductivity
and mobility in the KTaO3/SrTiO3 similar to values measured earlier in
electron-doped LaAlO3/SrTiO3 heterointerfaces. However, the sign of the charge
carriers in KTaO3/SrTiO3 obtained from the Hall measurements is negative. The
result is an important clue to the true origin of the doping at perovskite
oxide hetero-interfaces.


  A quantum spin Hall (QSH) insulator is a novel two-dimensional quantum state
of matter that features quantized Hall conductance in the absence of magnetic
field, resulting from topologically protected dissipationless edge states that
bridge the energy gap opened by band inversion and strong spin-orbit coupling.
By investigating electronic structure of epitaxially grown monolayer 1T'-WTe2
using angle-resolved photoemission (ARPES) and first principle calculations, we
observe clear signatures of the topological band inversion and the band gap
opening, which are the hallmarks of a QSH state. Scanning tunneling microscopy
measurements further confirm the correct crystal structure and the existence of
a bulk band gap, and provide evidence for a modified electronic structure near
the edge that is consistent with the expectations for a QSH insulator. Our
results establish monolayer 1T'-WTe2 as a new class of QSH insulator with large
band gap in a robust two-dimensional materials family of transition metal
dichalcogenides (TMDCs).


  In this paper, we study a safe control design for dynamical systems in the
presence of uncertainty in a dynamical environment. The worst-case error
approach is considered to formulate robust Control Barrier Functions (CBFs) in
an optimization-based control synthesis framework. It is first shown that
environmentally robust CBF formulations result in second-order cone programs
(SOCPs). Then, a novel scheme is presented to formulate robust CBFs which takes
the nominally safe control as its desired control input in optimization-based
control design and then tries to minimally modify it whenever the robust CBF
constraint is violated. This proposed scheme leads to quadratic programs (QPs)
which can be easily solved. Finally, the effectiveness of the proposed approach
is demonstrated on an adaptive cruise control example.


  We recall the basic physical principles governing the evolution of stars with
some emphasis on the role played by the nuclear reactions. We argue that in
general it is not possible from observations of stars to deduce constraints on
the nuclear reaction rates. This is the reason why precise measurements of
nuclear reaction rates are a necessity in order to make progresses in stellar
physics, nucleosynthesis and chemical evolution of galaxies. There are however
some stars which provides useful constraint on nuclear processes. The
Wolf-Rayet stars of the WN type present at their surface CNO equilibrium
patterns. There is also the particular case of the abundance of $^{22}$Ne at
the surface of WC stars. The abundance of this element is a measure of the
initial CNO content. Very interestingly, recent determinations of its abundance
at the surface of WC stars tend to confirm that massive stars in the solar
neighborhood have initial metallicities in agreement with the Asplund et al.
(2005) solar abundances.


  A composite system of Majorana-hosted semiconductor nanowire and
superconducting flux qubit is inves- tigated. It is found that the coupling
between these two subsystems can be controlled electrically, supplying a
convenient method to implement {\pi}/8 phase gate of a Majorana-based
topological qubit. We also present a scheme to transfer information from the
flux qubit to the topological qubit using Landau-Zener transition. In addition,
a structure named top-flux-flux is proposed to retrieve the information stored
in the topological qubit. With the demonstration of the entanglement of two
topological qubits, it is very promising to do quantum information process with
this hybrid system.


  We have determined the dispersion relation of a neutrino test particle
propagating in the cosmic neutrino background. Describing the relic neutrinos
and antineutrinos from the hot big bang as a dense medium, a matter potential
or refractive index is obtained. The vacuum neutrino mixing angles are
unchanged, but the energy of each mass state is modified. Using a matrix in the
space of neutrino species, the induced potential is decomposed into a part
which produces signatures in beta-decay experiments and another part which
modifies neutrino oscillations. The low temperature of the relic neutrinos
makes a direct detection extremely challenging. From a different point of view,
the identified refractive effects of the cosmic neutrino background constitute
an ultralow background for future experimental studies of nonvanishing Lorentz
violation in the neutrino sector.


  We measure the magnetic damping parameter a in thin film CoFeB and permalloy
(Py) nanomagnets at room temperature using ferromagnetic resonance driven by
microwave frequency spin-transfer torque. We obtain $\alpha_{CoFeB} = 0.014 \pm
0.003$ and $\alpha_{Py}=0.010 \pm 0.002$, values comparable to measurements for
extended thin films, but significantly less than the effective damping
determined previously for similar nanomagnets by fits to time-domain studies of
large-angle magnetic excitations and magnetic reversal. The greater damping
found for the large amplitude nanomagnet dynamics is attributed to the
nonlinear excitation of non-uniform magnetic modes.


  An efficient discrete time and space Markov chain approximation employing a
Brownian bridge correction for computing curvilinear boundary crossing
probabilities for general diffusion processes was recently proposed in Liang
and Borovkov (2021). One of the advantages of that method over alternative
approaches is that it can be readily extended to computing expectations of
path-dependent functionals over the event of the process trajectory staying
between two curvilinear boundaries. In the present paper, we extend the scheme
to compute expectations of the Feynman--Kac type that frequently appear in
option pricing. To illustrate our approximation scheme, we apply it in three
special cases. For sufficiently smooth integrands, numerical experiments
suggest that the proposed approximation converges at the rate $O(n^{-2})$,
where $n$ is the number of steps on the uniform time grid used


  Many beloved programming systems are image-based: self-contained worlds that
persist both code and data in a single file. Examples include Smalltalk, LISP,
HyperCard, Flash, and spreadsheets. Image-based programming avoids much of the
complexity of modern programming technology stacks and encourages more casual
and exploratory programming. However conventional file-based programming has
better support for collaboration and deployment. These problems have been
blamed for the limited commercial success of Smalltalk. We propose to enable
collaboration in image-based programming via types and structure editing.
  We focus on the problem of schema change on persistent data. We turn to
static types, which paradoxically require more schema change but also provide a
mechanism to express and execute those changes. To determine those changes we
turn to structure editing, so that we can capture changes in type definitions
with sufficient fidelity to automatically adapt the data to suit. We conjecture
that typical schema changes can be handled through structure editing of static
types.
  That positions us to tackle collaboration with what could be called version
control for structure editing. We present a theory realizing this idea, which
is our main technical contribution. While we focus here on editing types, if we
can extend the approach to cover the entire programming experience then it
would offer a new way to collaborate in image-based programming.


  Efficiently measuring nonlinear properties, like the entanglement spectrum,
is a significant yet challenging task from quantum information processing to
many-body physics. Current methodologies often suffer from an exponential
scaling of the sampling cost or require auxiliary qubits and deep quantum
circuits. To address these limitations, we propose an efficient auxiliary-free
replica shadow (AFRS) framework, which leverages the power of the joint
entangling operation on a few input replicas while integrating the mindset of
shadow estimation. We rigorously prove that AFRS can offer exponential
improvements in estimation accuracy compared with the conventional shadow
method, and facilitate the simultaneous estimation of various nonlinear
properties, unlike the destructive swap test. Additionally, we introduce an
advanced local-AFRS variant tailored to estimating local observables with even
constant-depth local quantum circuits, which significantly simplifies the
experimental realization compared with the general swap test. Our work paves
the way for the application of AFRS on near-term quantum hardware, opening new
avenues for efficient and practical quantum measurements.


  Digital contact tracing has been deployed as a public health intervention to
help suppress the spread of COVID-19 in many jurisdictions. However, most
governments have struggled with low uptake and participation rates, limiting
the effectiveness of the tool. This paper characterises a number of systems
developed around the world, comparing the uptake rates for systems with
different technology, data architectures, and mandates. The paper then
introduces the MAST framework (motivation, access, skills, and trust), adapted
from the digital inclusion literature, to explore the drivers and barriers that
influence people's decisions to participate or not in digital contact tracing
systems. Finally, the paper discusses some suggestions for policymakers on how
to influence those drivers and barriers in order to improve uptake rates.
Examples from existing digital contact tracing systems are presented
throughout, although more empirical experimentation is required to support more
concrete conclusions on what works.


  We introduce a methodology to extend the Fisher matrix forecasts to mildly
non-linear scales without the need of selecting a cosmological model. We make
use of standard non-linear perturbation theory for biased tracers complemented
by counterterms, and assume that the cosmological distances can be measured
accurately with standard candles. Instead of choosing a specific model, we
parametrize the linear power spectrum and the growth rate in several $k$ and
$z$ bins. We show that one can then obtain model-independent constraints of the
expansion rate $E(z)=H(z)/H_0$ and the growth rate $f(k,z)$, besides the bias
functions. We apply the technique to both Euclid and DESI public specifications
in the range $0.6\le z \le 1.8$ and show that the gain in precision when going
from $k_{\rm max} = 0.1$ to $0.2\,h$/Mpc is around two- to threefold, while it
reaches four- to ninefold when extending to $k_{\rm max} = 0.3\,h$/Mpc. In
absolute terms, with $k_{\rm max}=0.2\,h/$Mpc, one can reach high precision on
$E(z)$ at each $z$-shell: 8-10% for DESI with $\Delta z=0.1$, 5-6% for Euclid
with $\Delta z=0.2-0.3$. This improves to 1-2% if the growth rate $f$ is taken
to be $k$-independent. The growth rate itself has in general much weaker
constraints, unless assumed to be $k$-independent, in which case the gain is
similar to the one for $E(z)$ and uncertainties around 5-15% can be reached at
each $z$-bin. We also discuss how neglecting the non-linear corrections can
have a large effect on the constraints even for $k_{\rm max}=0.1\,h/$Mpc,
unless one has independent strong prior information on the non-linear
parameters.


  In quantum computation, information is processed by gates that must
coherently couple separate qubits. In many systems the qubits are naturally
coupled, but such an always-on interaction limits the algorithms that may be
implemented. Coupling interactions may also be directed in devices and circuits
that are provided with additional control wiring. This can be achieved by
adjusting the gate voltage in a semiconductor device or an additional flux in a
superconducting device. Such control signals must be applied adiabatically
(limiting the speed) and the additional wiring provides pathways for noise,
which leads to decoherence. Here we demonstrate an alternative approach to
coupling by exploiting the nonlinear behaviour of a degenerately doped silicon
transistor. A single transistor can exhibit a large number of individual
resonances, which are seen as changes in the source-drain current of a
dc-biased device. These resonances may be addressed in frequency space due to
their high quality factors. Two widely separated resonances are addressed and
coupled in three-frequency spectroscopy by ensuring that the third frequency
corresponds to the difference between the two individual resonances. The
nonlinearity causes the generation of additional driving signals with
appropriate frequency and phase relationships to ensure coupling, resulting in
additional spectroscopic features that could be exploited for rapid state
manipulation and gate operations.


  A qubit memory is the building block for quantum information. Cavity-enhanced
spin-wave-photon entanglement has been achieved by applying dual-control modes.
However, owing to cross readouts between the modes, the qubit retrieval
efficiency is about one quarter lower than that for a single spin-wave mode at
all storage times. Here, we overcome cross readouts using a multiplexed ring
cavity. The cavity is embedded with a polarization interferometer, and we
create a write-out photonic qubit entangled with a magnetic-field-insensitive
spin-wave qubit by applying a single-mode write-laser beam to cold atoms. The
spin-wave qubit is retrieved with a single-mode read-laser beam, and the
quarter retrieval-efficiency loss is avoided at all storage times. Our
experiment demonstrates 50% intrinsic retrieval efficiency for 540 microsecond
storage time, which is 13.5 times longer than the best reported result.
Importantly, our multiplexed-cavity scheme paves one road to generate
perfect-cavity-enhanced and large-scale multiplexed spin-wave-photon
entanglement with a long lifetime.


  This paper explores the process calculus $\text{CLL}_R$ furtherly.
  First, we prove that for any equation $X=_{RS} t_X$ such that $X$ is strongly
guarded in $t_X$, $\langle X|X=t_X \rangle$ is the largest solution w.r.t
$\sqsubseteq_{RS}$.
  Second, we encode a fragment of action-based CTL in $\text{CLL}_R$.


  Estimating frequencies of items over data streams is a common building block
in streaming data measurement and analysis. Misra and Gries introduced their
seminal algorithm for the problem in 1982, and the problem has since been
revisited many times due its practicality and applicability. We describe a
highly optimized version of Misra and Gries' algorithm that is suitable for
deployment in industrial settings. Our code is made public via an open source
library called DataSketches that is already used by several companies and
production systems.
  Our algorithm improves on two theoretical and practical aspects of prior
work. First, it handles weighted updates in amortized constant time, a common
requirement in practice. Second, it uses a simple and fast method for merging
summaries that asymptotically improves on prior work even for unweighted
streams. We describe experiments confirming that our algorithms are more
efficient than prior proposals.


  We study partition function of four-dimensional $\mathcal{N}=1$
supersymmetric field theory on $T^2 \times S^2$. By applying supersymmetry
localization, we show that the $T^2 \times S^2$ partition function is given by
elliptic genus of certain two-dimensional $\mathcal{N}=(0,2)$ theory. As an
application, we discuss a relation between 4d Seiberg duality duality and 2d
$(0,2)$ triality, proposed by Gadde, Gukov and Putrov. In other examples, we
identify 4d theories giving elliptic genera of K3, M-strings and E-strings. In
the example of K3, we find that there are two 4d theories giving the elliptic
genus of K3. This would imply new four-dimensional duality.


  We study the critical behavior of a noisy kinetic opinion model subject to
resilience to change depending on aging, defined as the time spent on the
current opinion state. In this model, the opinion of each agent can take the
three discrete values, the extreme ones $\pm 1$, and also the intermediate
value 0, and it can evolve through kinetic exchange when interacting with
another agent, or independently, by stochastic choice (noise). The probability
of change by pairwise interactions depends on the age that the agent has
remained in the same state, according to a given kernel. We particularly
develop the cases where the probability decays either algebraically or
exponentially with the age, and we also consider the anti-aging scenario where
the probability increases with the age, meaning that it is more likely to
change mind the longer the persistence in the current state. For the opinion
dynamics in a complete graph, we obtain analytical predictions for the critical
curves of the order parameters, in perfect agreement with agent-based
simulations. We observe that sufficiently weak aging (slow change of the kernel
with the age) favors partial consensus with respect to the aging-insensitive
scenario, while for sufficiently strong aging, as well as for anti-aging, the
opposite trend is observed.


  Although van der Waals (vdW) layered MoS2 shows the phase transformation from
the semiconducting 2H-phase to the metallic 1T-phase through chemical lithium
intercalation, vdW MoTe2 is thermodynamically reversible between the 2H- and
1T'-phases, and can be further transformed by energetics, laser irradiation,
strain or pressure, and electrical doping. Here, thickness- and
temperature-dependent optical properties of 1T'-MoTe2 thin films grown by
chemical vapor depsition are investigated via Fourier-transformed infrared
spectroscopy. An optical gap of 28 +/- 2 meV in a 3-layer (or 2 nm) thick
1T'-MoTe2 is clearly observed at a low temperature region below 50K. No
discernible optical bandgap is observed in samples thicker than ~4 nm. The
observed thickness-dependent bandgap results agree with the measured dc
resistivity data; the thickness-dependent 1T'-MoTe2 clearly demonstrates the
metal-semiconductor transition at a crossover below the 2 nm-thick sample.


  We propose a new method of extracting $V_{bu}$ from measurements of
Semi-leptonic B decay which has much less theoretical uncertainties than
conventional methods.


  The study of semantics in Genetic Program (GP) deals with the behaviour of a
program given a set of inputs and has been widely reported in helping to
promote diversity in GP for a range of complex problems ultimately improving
evolutionary search. The vast majority of these studies have focused their
attention in single-objective GP, with just a few exceptions where Pareto-based
dominance algorithms such as NSGA-II and SPEA2 have been used as frameworks to
test whether highly popular semantics-based methods, such as Semantic
Similarity-based Crossover (SSC), helps or hinders evolutionary search.
Surprisingly it has been reported that the benefits exhibited by SSC in SOGP
are not seen in Pareto-based dominance Multi-objective GP. In this work, we are
interested in studying if the same carries out in Multi-objective Evolutionary
Algorithms based on Decomposition (MOEA/D). By using the MNIST dataset, a
well-known dataset used in the machine learning community, we show how SSC in
MOEA/D promotes semantic diversity yielding better results compared to when
this is not present in canonical MOEA/D.


  The idea of rough statistical convergence for double sequences was studied by
Ozcan and Or[29] in a intuitionistic fuzzy normed space. Recently the same has
been generalized in the ideal context by Hossain and Banerjee[15] for
sequences. Here in this paper we have discussed the idea of rough ideal
convergence of double sequences in intuitionistic fuzzy normed spaces
generalizing the idea of rough statistical convergence of double sequences.
Also we have defined rough I2-cluster points for a double sequence and also
investigated some of the basic properties associated with rough I2-limit set of
a double sequence in a intuitionistic fuzzy normed space.


  In this paper, we discuss the educational value of a few mid-size and one
large applied research projects at the Computer Science Department of Okanagan
College (OC) and at the Universities of Paris East Creteil (LACL) and Orleans
(LIFO) in France. We found, that some freshmen students are very active and
eager to be involved in applied research projects starting from the second
semester. They are actively participating in programming competitions and want
to be involved in applied research projects to compete with sophomore and older
students. Our observation is based on five NSERC Engage College and Applied
Research and Development (ARD) grants, and several small applied projects.
Student involvement in applied research is a key motivation and success factor
in our activities, but we are also involved in transferring some results of
applied research, namely programming techniques, into the parallel programming
courses for beginners at the senior- and first-year MSc levels. We illustrate
this feedback process with programming notions for beginners, practical tools
to acquire them and the overall success/failure of students as experienced for
more than 10 years in our French University courses.


  We consider viscous, heat conducting mixtures of molecularly miscible
chemical species forming a fluid in which the constituents can undergo chemical
reactions. Assuming a common temperature for all components, we derive a closed
system of partial mass and partial momentum balances plus a mixture balance of
internal energy. This is achieved by careful exploitation of the entropy
principle and requires appropriate definitions of absolute temperature and
chemical potentials, based on an adequate definition of thermal energy
excluding diffusive contributions. The resulting interaction forces split into
a thermo-mechanical and a chemical part, where the former turns out to be
symmetric in case of binary interactions. For chemically reacting systems and
as a new result, the chemical interaction force is a contribution being
non-symmetric outside of chemical equilibrium. The theory also provides a
rigorous derivation of the so-called generalized thermodynamic driving forces,
avoiding the use of approximate solutions to the Boltzmann equations. Moreover,
using an appropriately extended version of the entropy principle and
introducing cross-effects already before closure as entropy invariant couplings
between principal dissipative mechanisms, the Onsager symmetry relations become
a strict consequence. With a classification of the factors in the binary
products of the entropy production according to their parity--instead of the
classical partition into so-called fluxes and driving forces--the apparent
anti-symmetry of certain couplings is thereby also revealed. If the diffusion
velocities are small compared to the speed of sound, the Maxwell-Stefan
equations follow in the case without chemistry, thereby neglecting wave
phenomena in the diffusive motion. This results in a reduced model with only
mass being balanced individually. In the reactive case ...


  We demonstrate high optical quality factors in aluminum nitride (AlN)
photonic crystal nanobeam cavities. Suspended AlN photonic crystal nanobeams
are fabricated in sputter-deposited AlN-on-insulator substrates using a
self-protecting release process. Employing one-dimensional photonic crystal
cavities coupled to integrated optical circuits we measure quality factors up
to 146,000. By varying the waveguide-cavity coupling gap, extinction ratios in
excess of 15 dB are obtained. Our results open the door for integrated photonic
bandgap structures made from a low loss, wide-transparency, nonlinear optical
material system.


  A set of Maplev R.3 software routines, for plotting 2D/3D projections of
Poincar\'e surfaces-of-section of Hamiltonian dynamical systems, is presented.
The package consists of a plotting-command plus a set of facility-commands for
a quick setup of the Hamilton equations of motion, initial conditions for
numerical experiments, and for the zooming of plots.


  We present a model for price dynamics in the Automated Market Makers (AMM)
setting. Within this framework, we propose a reference market price following a
geometric Brownian motion. The AMM price is constrained by upper and lower
bounds, determined by constant multiplications of the reference price. Through
the utilization of local times and excursion-theoretic approaches, we derive
several analytical results, including its time-changed representation and
limiting behavior.


  We describe the measurement and modeling of amplitude noise and phase noise
in ultra-high Q nanomechanical resonators made from stoichiometric silicon
nitride. With quality factors exceeding 2 million, the resonators' noise
performance is studied with high precision. We find that the amplitude noise
can be well described by the thermomechanical model, however, the resonators
exhibit sizable extra phase noise due to their intrinsic frequency
fluctuations. We develop a method to extract the resonator frequency
fluctuation of a driven resonator and obtain a noise spectrum with dependence,
which could be attributed to defect motion with broadly distributed relaxation
times.


  The Adaptive Multiple Importance Sampling (AMIS) algorithm is aimed at an
optimal recycling of past simulations in an iterated importance sampling
scheme. The difference with earlier adaptive importance sampling
implementations like Population Monte Carlo is that the importance weights of
all simulated values, past as well as present, are recomputed at each
iteration, following the technique of the deterministic multiple mixture
estimator of Owen and Zhou (2000). Although the convergence properties of the
algorithm cannot be fully investigated, we demonstrate through a challenging
banana shape target distribution and a population genetics example that the
improvement brought by this technique is substantial.


  We study a 1D Fermi gas with attractive short range-interactions in a
disordered potential by the density matrix renormalization group (DMRG)
technique. This setting can be implemented experimentally by using cold atom
techniques. We identify a region of parameters for which disorder enhances the
superfluid state. As disorder is further increased, global superfluidity
eventually breaks down. However this transition occurs before the transition to
the insulator state takes place. This suggests the existence of an intermediate
metallic `pseudogap' phase characterized by strong pairing but no quasi
long-range order.


  In this project, we created a database with two types of annotations used in
the emotion recognition domain : Action Units and Valence Arousal to try to
achieve better results than with only one model. The originality of the
approach is also based on the type of architecture used to perform the
prediction of the emotions : a categorical Generative Adversarial Network. This
kind of dual network can generate images based on the pictures from the new
dataset thanks to its generative network and decide if an image is fake or real
thanks to its discriminative network as well as help to predict the annotations
for Action Units and Valence Arousal due to its categorical nature. GANs were
trained on the Action Units model only, then the Valence Arousal model only and
then on both the Action Units model and Valence Arousal model in order to test
different parameters and understand their influence. The generative and
discriminative aspects of the GANs have performed interesting results.


  This paper is devoted to the study of the random displacement model on
$\R^d$. We prove that, in the weak displacement regime, Anderson and dynamical
localization holds near the bottom of the spectrum under a generic assumption
on the single site potential and a fairly general assumption on the support of
the possible displacements. This result follows from the proof of the existence
of Lifshitz tail and of a Wegner estimate for the model under scrutiny.


  We study classical M5 brane solutions in the probe limit in the $AdS_7 \times
S^4$ spacetime geometry with worldvolume 3-form flux. These solutions describe
the holography of codimension-4 defects in the 6d boundary dual
$\mathcal{N}=(0,2)$ supersymmetric gauge theories. Starting from some half-BPS
solutions which follow stricter BPS conditions, we find a general
$\frac{1}{16}$-BPS solution. We show how some of the \textit{giant-like} M5
brane solutions here may be related to the codimension-2 surface operators in
the 4d gauge theory.


  Fractional repetition (FR) codes are a class of repair efficient erasure
codes that can recover a failed storage node with both optimal repair bandwidth
and complexity. In this paper, we study the minimum distance of FR codes, which
is the smallest number of nodes whose failure leads to the unrecoverable loss
of the stored file. We consider upper bounds on the minimum distance and
present several families of explicit FR codes attaining these bounds. The
optimal constructions are derived from regular graphs and combinatorial
designs, respectively.


  On the triangular lattice, for $J_2/J_1$ between $1/8$ and $1$, the classical
Heisenberg model with first and second neighbor interactions presents
four-sublattice ordered ground-states. Spin-wave calculations of Chubukov and
Jolicoeur\cite{cj92} and Korshunov\cite{k93} suggest that quantum fluctuations
select amongst these states a colinear two-sublattice order. From theoretical
requirements, we develop the full symmetry analysis of the low lying levels of
the spin-1/2 Hamiltonian in the hypotheses of either a four or a two-sublattice
order. We show on the exact spectra of periodic samples ($N=12,16$ and $28$)
how quantum fluctuations select the colinear order from the four-sublattice
order.


  In the first part of this paper, we extend the result of Li-Wang on the
linearized embedding problem to a compact manifold of arbitrary dimension.
Using this, we then show that any metric perturbation of a embedded $n$-sphere
is also isometrically embedded up to a solution of the homogenous Codazzi
equation, irrespective of the ambient geometry. In the second part we
specialize to dimension two, and study these results within an ambient Null
Cone. Specifically, given a path of metrics on the 2-sphere and an initial
isometric embedding, we develop a small parameter existence and uniqueness
theorem for paths of isometric embeddings. In the final part, after imposing
asymptotic decay conditions on the Null Cone, we show that any metric on the
2-sphere can be isometrically embedded up to a scaling factor. We then prove
the existence of a foliation in a neighborhood of infinity.


  By restricting the spatial energy transmission of an electromagnetic wave,
dielectric waveguides transmit light over long distances at sustained
intensity. Waveguides have been used in the microwave and optical range to
maintain strong signal intensities in connection with lasers, but guiding of
intense short-wavelength radiation such as x-rays has proven more cumbersome.
Here we investigate theoretically how tapered x-ray waveguides can focus and
guide radiation from x-ray free electron lasers. Elliptical waveguides using a
cladding material with high atomic number such as platinum can maintain an
x-ray intensity up to three orders of magnitude larger than in free space. This
feature can be used to significantly enhance resonant interactions of x-rays,
for instance driving nuclear transitions up to transient nuclear population
inversion. This could be the first breakthrough in nuclear state population
control. Our results anticipate the important role of tapered x-ray waveguides
in the emerging field of x-ray quantum optics with nuclear transitions.


  We investigate the average bipartite entanglement, over all possible
divisions of a multipartite system, as a useful measure of multipartite
entanglement. We expose a connection between such measures and
quantum-error-correcting codes by deriving a formula relating the weight
distribution of the code to the average entanglement of encoded states.
Multipartite entangling power of quantum evolutions is also investigated.


  Bipartite networks are a well known strategy to study a variety of phenomena.
The commonly used method to deal with this type of network is to project the
bipartite data into a unipartite weighted graph and then using a backboning
technique to extract only the meaningful edges. Despite the wide availability
of different methods both for projection and backboning, we believe that there
has been little attention to the effect that the combination of these two
processes has on the data and on the resulting network topology. In this paper
we study the effect that the possible combinations of projection and backboning
techniques have on a bipartite network. We show that the 12 methods group into
two clusters producing unipartite networks with very different topologies. We
also show that the resulting level of network centralization is highly affected
by the combination of projection and backboning applied.


  We discuss the Hirota bilinear equation for the CKP hierarchy introduced by
Date, Jimbo, Kashiwara and Miwa in J. Phys. Soc. Japan. 50(11), 3813-3818
(1981), and its algebraic properties. We review in parallel the two
bosonizations of the CKP hierarchy: one arising from a twisted Heisenberg
algebra (van de Leur, Orlov and Shiota, SIGMA 8, 28 (2012)), and the second
from an untwisted Heisenberg algebra (Anguelova, J. Math. Phys. 58(7), 071707
(2017)). In particular, we recount the decompositions into irreducible
Heisenberg modules and the (twisted) fermionic structures of the spaces spanned
by the highest weight vectors under the two Heisenberg actions. We show that
the two bosonizations give rise to four different diagonalizable grading
operators on the CKP Fock space, not all of them commuting among each other. We
compute the various graded dimensions related to these four grading operators.
We prove a sum-vs-product identity relating the bosonic vs fermionic
descriptions under the untwisted Heisenberg action, utilizing the charge and
the degree grading operators. As a corollary, the resulting identities relate
the CKP hierarchy, the Dyson crank of a partition and the Hammond-Lewis birank
of a distinct integer bipartition.


  Given a bipartite quantum system represented by a tensor product of two
Hilbert spaces, we give an elementary argument showing that if either component
space is infinite-dimensional, then the set of nonseparable density operators
is trace-norm dense in the set of all density operators (and the separable
density operators nowhere dense). This result complements recent detailed
investigations of separability, which show that when both component Hilbert
spaces are finite-dimensional, there is a separable neighborhood (perhaps very
small for large dimensions) of the maximally mixed state.


  This is the fourth installment of a series. The main point of the entire
series is the following: given a triangulated category T, it is possible to
attach to it a K-theory space.


  We extend the argument presented by Benincasa, Boucher-Veronneau, and Cachazo
to show that graviton tree amplitudes are well behaved under large complex
deformations of the momenta of a pair of like-helicity gravitons. This shows
that BCFW recursion relations for gravity amplitudes can be constructed using
such shifts, providing an alternative proof to the recent one by Arkani-Hamed
and Kaplan. By using auxiliary recursion relations the cancellations which are
hidden when using covariant Feynman diagrams become manifest.


  We study the security of a specific authentication procedure of interest in
the context of Quantum Key Distribution (QKD). It works as follows: use a
secret but fixed Strongly Universal$_2$ (SU$_2$) hash function and encrypt the
output tag with a one-time pad (OTP). If the OTP is completely secret, the
expected time for an adversary to create a tag for a chosen message is
exponential in the tag length. If, however, the OTP is partially known in each
authentication round, as is the case in practical QKD protocols, then the
picture is different; the adversary's partial knowledge of the OTP in each
authentication round gives partial information on the secret hash function, and
this weakens the authentication in later rounds. The effect of this is that the
lifetime of the system is linear in the length of the fixed key. This is
supported by the composability theorem for QKD, that in this setting provides
an upper bound to the security loss on the secret hash function, which is
exponential in the number of authentication rounds. This needs to be taken into
account when using the protocol, since the authentication gets weakened at each
subsequent round and thus the QKD generated is key is not as strong as when the
authentication is strong. Some countermeasures are discussed at the end of this
paper.


  We present a hybrid asymptotic/numerical method for the accurate computation
of single and double layer heat potentials in two dimensions. It has been shown
in previous work that simple quadrature schemes suffer from a phenomenon called
"geometrically-induced stiffness," meaning that formally high-order accurate
methods require excessively small time steps before the rapid convergence rate
is observed. This can be overcome by analytic integration in time, requiring
the evaluation of a collection of spatial boundary integral operators with
non-physical, weakly singular kernels. In our hybrid scheme, we combine a local
asymptotic approximation with the evaluation of a few boundary integral
operators involving only Gaussian kernels, which are easily accelerated by a
new version of the fast Gauss transform. This new scheme is robust, avoids
geometrically-induced stiffness, and is easy to use in the presence of moving
geometries. Its extension to three dimensions is natural and straightforward,
and should permit layer heat potentials to become flexible and powerful tools
for modeling diffusion processes.


  There have been several reports of exotic nuclear fragments, with highly
unusual charge to mass ratio, in cosmic ray experiments. Although there exist
experimental uncertainties which make them, at best, only candidate "exotic"
events, it is important to understand what they could be, if they are
eventually confirmed. Among other possible explanations, some authors have
interpreted them to be lumps of strange quark matter (strangelets). A major
problem with such an interpretation is that to reach the earth's surface, they
must possess an unusually high penetrability through the terrestrial
atmosphere. We show that a recently proposed mechanism for the propagation of
strangelets through the earth's atmosphere, together with a proper account of
charge capture and ionisation loss, would solve this problem. We also argue
that this could lead to viable strategies for definitive detection of strange
quark matter in cosmic ray flux using a ground based large area array of
passive detectors.


  Multimode fibres (MMFs) are attracting interest for complex spatiotemporal
dynamics, and for ultrafast fibre sources, imaging and telecommunications. This
new interest is based on three key properties: their high spatiotemporal
complexity (information capacity), the important role of disorder, and complex
intermodal interactions. To date, phenomena in MMFs have been studied only in
limiting cases where one or more of these properties can be neglected. Here we
study MMFs in a regime in which all these elements are integral. We observe a
spatial beam-cleaning process preceding spatiotemporal modulation instability.
We show that the origin of these processes is a universal unstable attractor in
graded-index MMFs. Both the self-organization of the attractor, as well as its
instability, are caused by intermodal interactions characterized by cooperating
disorder, nonlinearity and dissipation. The demonstration of a
disorder-enhanced nonlinear process in MMF has important implications for
telecommunications, and the multifaceted complexity of the dynamics showcases
MM waveguides as ideal laboratories for many topics and applications in
complexity science.


  We study Andreev reflection in a one-dimensional square-well pair-potential.
We discuss the history of the model. The current-phase relation is presented as
a sum over Matsubara frequencies. How the current arises from bound and
continuum levels is found by analytic continuation. We discuss two limiting
cases of the square-well potential, the zero-length well and the infinite well.
The model is quantitatively valid in some cases but forms the basis for
understanding a wide range of problems in inhomogeneous superconductivity and
superfluidity.


  Recent studies have demonstrated the emerging capabilities of foundation
models like ChatGPT in several fields, including affective computing. However,
accessing these emerging capabilities is facilitated through prompt
engineering. Despite the existence of some prompting techniques, the field is
still rapidly evolving and many prompting ideas still require investigation. In
this work, we introduce a method to evaluate and investigate the sensitivity of
the performance of foundation models based on different prompts or generation
parameters. We perform our evaluation on ChatGPT within the scope of affective
computing on three major problems, namely sentiment analysis, toxicity
detection, and sarcasm detection. First, we carry out a sensitivity analysis on
pivotal parameters in auto-regressive text generation, specifically the
temperature parameter $T$ and the top-$p$ parameter in Nucleus sampling,
dictating how conservative or creative the model should be during generation.
Furthermore, we explore the efficacy of several prompting ideas, where we
explore how giving different incentives or structures affect the performance.
Our evaluation takes into consideration performance measures on the affective
computing tasks, and the effectiveness of the model to follow the stated
instructions, hence generating easy-to-parse responses to be smoothly used in
downstream applications.


  The formation of supermassive stars has generally been studied under the
assumption of rapid accretion of pristine metal-free gas. Recently it was
found, however, that gas enriched to metallicities up to $Z \sim 10^{-3}$
Z$_{\odot}$ can also facilitate supermassive star formation, as long as the
total mass infall rate onto the protostar remains sufficiently high. We extend
the analysis further by examining how the abundance of supermassive star
candidate haloes would be affected if all haloes with super-critical infall
rates, regardless of metallicity were included. We investigate this scenario by
identifying all atomic cooling haloes in the Renaissance simulations with
central mass infall rates exceeding a fixed threshold. We find that among these
haloes with central mass infall rates above 0.1 M$_{\odot}$ yr$^{-1}$
approximately two-thirds of these haloes have metallicities of $Z > 10^{-3}$
Z$_{\odot}$. If metal mixing within these haloes is inefficient early in their
assembly and pockets of metal-poor gas can remain then the number of haloes
hosting supermassive stars can be increased by at least a factor of four.
Additionally the centres of these high infall-rate haloes provide ideal
environments in which to grow pre-existing black holes. Further research into
the (supermassive) star formation dynamics of rapidly collapsing haloes, with
inhomogeneous metal distributions, is required to gain more insight into both
supermassive star formation in early galaxies as well as early black hole
growth.


  This paper is devoted to the study of tilt stability in finite dimensional
optimization via the approach of using the subgradient graphical derivative. We
establish a new characterization of tilt-stable local minimizers for a broad
class of unconstrained optimization problems in terms of a uniform positive
definiteness of the subgradient graphical derivative of the objective function
around the point in question. By applying this result to nonlinear programming
under the metric subregularity constraint qualification, we derive a
second-order characterization and several new sufficient conditions for tilt
stability. In particular, we show that each stationary point of a nonlinear
programming problem satisfying the metric subregularity constraint
qualification is a tilt-stable local minimizer if the classical strong
second-order sufficient condition holds.


  The two main theorems of this paper provide a characterization of hyperbolic
affine iterated function systems defined on Rm. Atsushi Kameyama (Distances on
Topological Self-Similar Sets, Proceedings of Symposia in Pure Mathematics,
Volume 72.1, 2004) asked the following fundamental question: given a
topological self-similar set, does there exist an associated system of
contraction mappings? Our theorems imply an affirmative answer to Kameyama's
question for self-similar sets derived from affine transformations on Rm.


  Face recognition based on the deep convolutional neural networks (CNN) shows
superior accuracy performance attributed to the high discriminative features
extracted. Yet, the security and privacy of the extracted features from deep
learning models (deep features) have been often overlooked. This paper proposes
the reconstruction of face images from deep features without accessing the CNN
network configurations as a constrained optimization problem. Such optimization
minimizes the distance between the features extracted from the original face
image and the reconstructed face image. Instead of directly solving the
optimization problem in the image space, we innovatively reformulate the
problem by looking for a latent vector of a GAN generator, then use it to
generate the face image. The GAN generator serves as a dual role in this novel
framework, i.e., face distribution constraint of the optimization goal and a
face generator. On top of the novel optimization task, we also propose an
attack pipeline to impersonate the target user based on the generated face
image. Our results show that the generated face images can achieve a
state-of-the-art successful attack rate of 98.0\% on LFW under type-I attack @
FAR of 0.1\%. Our work sheds light on the biometric deployment to meet the
privacy-preserving and security policies.


  The tilt pattern of the CuO_6 octahedra in the LTT phase of the cuprate
superconductors leads to planar anisotropies for the exchange coupling and
hopping integrals. Here, we show that these anisotropies provide a possible
structural mechanism for the orientation of stripes. A t_x-t_y-J_x-J_y model
thus serves as an effective Hamiltonian to describe stripe formation and
orientation in LTT-phase cuprates.


  We provide an elementary proof of a lemma that plays an important role in the
classification of parallel mean curvature surfaces in two-dimensional complex
space forms.


  The KdV hierarchy is a paradigmatic example of the rich mathematical
structure underlying integrable systems and has far-reaching connections in
several areas of theoretical physics. While the positive part of the KdV
hierarchy is well known, in this paper we consider an affine Lie algebraic
construction for its negative part. We show that the original Miura
transformation can be extended to a gauge transformation that implies several
new types of relations among the negative flows of the KdV and mKdV
hierarchies. Contrary to the positive flows, such a ``gauge-Miura''
correspondence becomes degenerate whereby more than one negative mKdV model is
mapped into a single negative KdV model. For instance, the sine-Gordon and
another negative mKdV flow are mapped into a single negative KdV flow which
inherits solutions of both former models. The gauge-Miura correspondence
implies a rich degeneracy regarding solutions of these hierarchies. We obtain
similar results for the generalized KdV and mKdV hierachies constructed with
the affine Lie algebra $\widehat{s\ell}(r+1)$. In this case the first negative
mKdV flow corresponds to an affine Toda field theory and the gauge-Miura
correspondence yields its KdV counterpart. In particular, we show explicitly a
KdV analog of the Tzitz\'{e}ica-Bullough-Dodd model. In short, we uncover a
rich mathematical structure for the negative flows of integrable hierarchies
obtaining novel relations and integrable systems.


  Oxygen abundances for a large sample of dwarf and giant stars kinematically
selected to be part of the Galactic thin and thick disks have been determined
from a non-LTE analysis of the O I triplet lines at 777 nm. The abundance
analysis was performed using the infrared flux method temperature scale,
trigonometric surface gravities, and accurate atomic data. Within this
framework, the ionization balance of iron lines could not be satisfied and so
we adopted the iron abundances from Fe II lines only given that they are
relatively less sensitive to changes in the atmospheric parameters. We show the
resulting [O/Fe] vs. [Fe/H] relationship and briefly discuss its implications.


  The statistical approach is used to calculate the parton distribution
functions (PDFs) of the nucleon. At first it is assumed that the partons are
free particles and the light-front kinematic variables are employed to extract
the Bjorken $x$-dependence of the PDFs. These PDFs are used to evaluate the
combinations of the sea quarks such as $\bar d-\bar u$. As our first attempt to
improve the result, we make the statistical parameters to depend on $Q^2$,
using different values of Gottfried sum rule. The related results are
indicating better behavior by accessing to the PDFs while they contain the
$Q^2$ dependence parameters. As a further task and in order to have more
improvement in the calculations, a linear potential is considered to describe
the quark interactions. The solution of the related Dirac equation yields the
Airy function and is considered as a wave function in spatial space. Using the
fourier transformation the wave functions are obtained in momentum space. Based
on the light-front kinematic variables and using a special method which we call
it "k method", these functions can be written in terms of the Bjorken
$x$-variable. Following that the statistical features are accompanied with
these functions. Considering an effective approach which is used in this
article, we do not need to resort to any extra effects as were assumed in some
articles to get a proper results for PDFs. The obtained results for $\bar
d-\bar u$ and the $\frac{\bar d}{\bar u}$ ratio, using our effective approach,
are in good agreement with the available experimental data and some theoretical
results.


  As an essential resource management problem in network virtualization,
virtual network embedding (VNE) aims to allocate the finite resources of
physical network to sequentially arriving virtual network requests (VNRs) with
different resource demands. Since this is an NP-hard combinatorial optimization
problem, many efforts have been made to provide viable solutions. However, most
existing approaches have either ignored the admission control of VNRs, which
has a potential impact on long-term performances, or not fully exploited the
temporal and topological features of the physical network and VNRs. In this
paper, we propose a deep Hierarchical Reinforcement Learning approach to learn
a joint Admission Control and Resource Allocation policy for VNE, named
HRL-ACRA. Specifically, the whole VNE process is decomposed into an upper-level
policy for deciding whether to admit the arriving VNR or not and a lower-level
policy for allocating resources of the physical network to meet the requirement
of VNR through the HRL approach. Considering the proximal policy optimization
as the basic training algorithm, we also adopt the average reward method to
address the infinite horizon problem of the upper-level agent and design a
customized multi-objective intrinsic reward to alleviate the sparse reward
issue of the lower-level agent. Moreover, we develop a deep feature-aware graph
neural network to capture the features of VNR and physical network and exploit
a sequence-to-sequence model to generate embedding actions iteratively.
Finally, extensive experiments are conducted in various settings, and show that
HRL-ACRA outperforms state-of-the-art baselines in terms of both the acceptance
ratio and long-term average revenue. Our code is available at
\url{https://github.com/GeminiLight/hrl-acra}.


  A model with flat FRW symmetries and G and Lambda variable,is considered in
such a way that the momentum-energy tensor that describes the model is
characterized by a bulk viscosity parameter. In this paper it is showed how to
apply the dimensional method in order to solve the outlined equations in a
trivial way.


  We propose a novel embedding model that represents relationships among
several elements in bibliographic information with high representation ability
and flexibility. Based on this model, we present a novel search system that
shows the relationships among the elements in the ACL Anthology Reference
Corpus. The evaluation results show that our model can achieve a high
prediction ability and produce reasonable search results.


  The intensive synchrotron radiation resulting from quarks interacting with
the collective confining color field in relativistic heavy ion collisions is
discussed. The spectrum of photons with large transverse momentum is calculated
and compared with the experimental data to demonstrate the feasibility of this
type of radiation. A study of the earlier predicted azimuthal anisotropy in the
angular distribution of dileptons with respect to the three-momentum of the
pair is performed as well. This boundary-induced mechanism of lepton pair
production is shown to possess the features that are distinctly different from
the standard mechanisms and can potentially provide an efficient probe of
quark-gluon plasma formation.


  We report the discovery of 59 globular clusters (GCs) and two candidate GCs
in a search of the halo of M31, primarily via visual inspection of CHFT/MegaCam
imagery from the Pan-Andromeda Archaeological Survey (PAndAS). The superior
quality of these data also allow us to check the classification of remote
objects in the Revised Bologna Catalogue (RBC), plus a subset of GC candidates
drawn from SDSS imaging. We identify three additional new GCs from the RBC, and
confirm the GC nature of 11 SDSS objects (8 of which appear independently in
our remote halo catalogue); the remaining 188 candidates across both lists are
either foreground stars or background galaxies. Our new catalogue represents
the first uniform census of GCs across the M31 halo - we find clusters to the
limit of the PAndAS survey area at projected radii of up to R_proj ~ 150 kpc.
Tests using artificial clusters reveal that detection incompleteness cuts in at
luminosities below M_V = -6.0; our 50% completeness limit is M_V ~ -4.1. We
construct a uniform set of PAndAS photometric measurements for all known GCs
outside R_proj = 25$ kpc, and any new GCs within this radius. With these data
we update results from Huxor et al. (2011), investigating the luminosity
function (LF), colours and effective radii of M31 GCs with a particular focus
on the remote halo. We find that the GCLF is clearly bimodal in the outer halo
(R_proj > 30 kpc), with the secondary peak at M_V ~ -5.5. We argue that the GCs
in this peak have most likely been accreted along with their host dwarf
galaxies. Notwithstanding, we also find, as in previous surveys, a substantial
number of GCs with above-average luminosity in the outer M31 halo - a
population with no clear counterpart in the Milky Way.


  If the cyclic sequences of {face types} {at} all vertices in a map are the
same, then the map is said to be a semi-equivelar map. In particular, a
semi-equivelar map is equivelar if the faces are the same type. Homological
quantum codes represent a subclass of topological quantum codes. In this
article, we introduce {thirteen} new classes of quantum codes. These codes are
associated with the following: (i) equivelar maps of type $ [k^k]$, (ii)
equivelar maps on the double torus along with the covering of the maps, and
(iii) semi-equivelar maps on the surface of \Echar{-1}, along with {their}
covering maps. The encoding rate of the class of codes associated with the maps
in (i) is such that $ \frac{k}{n}\rightarrow 1 $ as $ n\rightarrow\infty $, and
for the remaining classes of codes, the encoding rate is $
\frac{k}{n}\rightarrow \alpha $ as $ n\rightarrow \infty $ with $ \alpha< 1 $.


  The magnetothermodynamics of skyrmion type matter described by the gauged BPS
baby Skyrme model at zero temperature is investigated. We prove that the BPS
property of the model is preserved also for boundary conditions corresponding
to an asymptotically constant magnetic field. The BPS bound and the
corresponding BPS equations saturating the bound are found. Further, we show
that one may introduce pressure in the gauged model by a redefinition of the
superpotential. Interestingly, this is related to non-extremal type solutions
in the so-called fake supersymmetry method. Finally, we compute the equation of
state of magnetized BSP baby skyrmions inserted into an external constant
magnetic field $H$ and under external pressure $P$, i.e., $V=V(P,H)$, where $V$
is the "volume" (area) occupied by the skyrmions. We show that the BPS baby
skyrmions form a ferromagnetic medium.


  We prove that if x^m + c*x^n permutes the prime field GF(p), where m>n>0 and
c is in GF(p)^*, then gcd(m-n,p-1) > sqrt{p} - 1. Conversely, we prove that if
q>=4 and m>n>0 are fixed and satisfy gcd(m-n,q-1) > 2q*(log log q)/(log q),
then there exist permutation binomials over GF(q) of the form x^m + c*x^n if
and only if gcd(m,n,q-1) = 1.


  The Anderson metal-insulator transition is a fundamental phenomenon in
condensed matter physics, describing the transition from a conducting
(metallic) to a non-conducting (insulating) state driven by disorder in a
material. At the critical point of the Anderson transition, wave functions
exhibit multifractal behavior, and energy levels display a universal
distribution, indicating non-trivial correlations in the eigenstates. Recent
studies have shown that proteins, traditionally considered as insulators,
exhibit much higher conductivity than previously assumed. In this paper, we
investigate several proteins known for their efficient electron transport
properties. We compare their energy level statistics, eigenfunction
correlation, and electron return probability to those expected in metallic,
insulating, or critical states. Remarkably, these proteins exhibit properties
of critically disordered metals in their natural state without any parameter
adjustment. Their composition and geometry are self-organized into the critical
state of the Anderson transition, and their fractal properties are universal
and unique among critical systems. Our findings suggest that proteins' wave
functions fulfill "holographic" area laws, and the correlation fractal
dimension is precisely $d_2=2$.


  We present a tight-binding parametrization for penta-graphene that correctly
describes its electronic band structure and linear optical response. The set of
parameters is validated by comparing to ab-initio density functional theory
calculations for single-layer penta-graphene, showing a very good global
agreement. We apply this parameterization to penta-graphene nanoribbons,
achieving an adequate description of quantum-size effects. Additionally, a
symmetry-based analysis of the energy band structure and the optical
transitions involved in the absorption spectra is introduced, allowing for the
interpretation of the optoelectronic features of these systems.


  Time series are presented for the class II methanol maser source G12.89+0.49,
which has been monitored for nine years at the Hartebeesthoek Radio Astronomy
Observatory. The 12.2 and 6.7 GHz methanol masers were seen to exhibit rapid,
correlated variations on timescales of less than a month. Daily monitoring has
revealed that the variations have a periodic component with a period of 29.5
days. The period seems to be stable over the 110 cycles spanned by the time
series. There are variations from cycle to cycle, with the peak of the flare
occurring anywhere within an eleven day window but the minima occur at the same
phase of the cycle. Time delays of up to 5.7 days are seen between spectral
features at 6.7 GHz and a delay of 1.1 day is seen between the dominant 12.2
GHz spectral feature and its 6.7 GHz counterpart.


  In this work we study the de Haas van Alfhen (dHvA) effect for neutral atoms
with a nonvanishing magnetic moment interacting with an electric field.
Considering the particles confined in a two dimensional (2D) atomic cloud and
using the Landau-Aharonov-Casher (LAC) theory, we obtain the effective magnetic
field as well as the energy eigenfunctions and eigenvalues of the system.
Assuming the neutral atoms as being $ ^{87}\mathrm{Rb} $ ultracold Rydberg
atoms we calculate the degeneracy of the energy levels. Under a strong
effective magnetic field regime we present the quantum oscillations in the
energy and effective magnetization of the atomic gas. From the dHvA period we
determine the area of the Fermi circle of the atomic cloud.


  In this article we provide simple and provable bounds on the size and shape
of the quasiconformal deformation space of the groups $\IZ_p*\IZ_q$, the free
product of cyclic groups of order $p$ and $q$, in $\PSL(2,\IC)$ for $3\leq p,q
\leq \infty$. Though simple, these bounds are sharp, meeting the highly fractal
boundary of the deformation space in four cusp groups. Such bounds have great
utility in computer assisted searches for extremal Kleinian groups so as to
identify universal constraints (volume, length spectra, etc) on the geometry
and topology of hyperbolic $3$-orbifolds. As an application, we prove a
strengthened version of a conjecture by Morier-Genoud, Ovsienko, and Veselov on
the faithfulness of the specialised Burau representation.


  In 1976, Leon Simon showed that if a compact subset of the boundary of a
domain is smooth and has negative mean curvature, then the non-parametric least
area problem with Lipschitz continuous Dirichlet boundary data has a
generalized solution which is continuous on the union of the domain and this
compact subset of the boundary, even if the generalized solution does not take
on the prescribed boundary data. Simon's result has been extended to boundary
value problems for prescribed mean curvature equations by other authors. In
this note, we construct Dirichlet problems in domains with corners and
demonstrate that the variational solutions of these Dirichlet problems are
discontinuous at the corner, showing that Simon's assumption of regularity of
the boundary of the domain is essential.


  Hubbard chains with periodically modulated coupling constants in a magnetic
field exhibit gaps at zero temperature in their magnetic and charge excitations
in a variety of situations. In addition to fully gapped situations (plateau in
the magnetization curve and charge gap), we have shown [cond-mat/9908398] that
plateaux also appear in the presence of massless modes, leading to a plateau
with a magnetization m whose value depends continuously on the filling n. Here
we detail and extend the arguments leading to such doping-dependent
magnetization plateaux. First we analyze the low-lying excitations using
Abelian bosonization. We compute the susceptibility and show that due to the
constraint of fixed n, it vanishes at low temperatures (thus leading to a
magnetization plateau) even in the presence of one massless mode. Next we study
correlation functions and show that one component of the superconducting order
parameter develops quasi-long-range order on a doping-dependent magnetization
plateau. We then use perturbation theory in the on-site repulsion U to compute
the width of these plateaux up to first order in U. Finally, we compute
groundstate phase diagrams and correlation functions by Lanczos diagonalization
of finite clusters, confirming the presence of doping-dependent plateaux and
their special properties.


  Field localization boosts nonlinear optical processes at the hot spots of
metal nanostructures. Fano resonances can further enhance these "local"
processes taking place at the hot spots. However, in conventional nonlinear
materials, the frequency conversion takes place along the entire crystal body.
That is, the conversion process is "unlocalized". The path interference (Fano
resonance) schemes developed for localized processes become useless in such
materials. Here, we develop Fano enhancement schemes for unlocalized nonlinear
optical processes. We show that 3 orders of magnitude Fano enhancement multiply
the enhancements achieved via field trapping techniques, e.g., in
epsilon-near-zero~(ENZ) materials. We demonstrate the phenomenon both
analytically and by numerical solutions of Maxwell's equations. The match
between the two solutions is impressive. We observe that the interference
scheme for unlocalized processes is richer than the one for the local
processes. The method can be employed for any kind of nonlinear optical
conversion. Moreover, the Fano enhancement can be continuously controlled by an
applied voltage.


  To the best of our knowledge, we first present a live system that generates
personalized photorealistic talking-head animation only driven by audio signals
at over 30 fps. Our system contains three stages. The first stage is a deep
neural network that extracts deep audio features along with a manifold
projection to project the features to the target person's speech space. In the
second stage, we learn facial dynamics and motions from the projected audio
features. The predicted motions include head poses and upper body motions,
where the former is generated by an autoregressive probabilistic model which
models the head pose distribution of the target person. Upper body motions are
deduced from head poses. In the final stage, we generate conditional feature
maps from previous predictions and send them with a candidate image set to an
image-to-image translation network to synthesize photorealistic renderings. Our
method generalizes well to wild audio and successfully synthesizes
high-fidelity personalized facial details, e.g., wrinkles, teeth. Our method
also allows explicit control of head poses. Extensive qualitative and
quantitative evaluations, along with user studies, demonstrate the superiority
of our method over state-of-the-art techniques.


  We demonstrate that a lightly-strained germanium channel ($\varepsilon_{//}$
= -0.41%) in an undoped Ge/Si$_{0.1}$Ge$_{0.9}$ heterostructure field effect
transistor supports a 2D hole gas with mobility in excess of 1$\times$10$^{6}$
cm$^{2}$/Vs and percolation density less than 5$\times$10$^{10}$ cm$^{-2}$.
This low disorder 2D hole system shows tunable fractional quantum Hall effect
at low density and low magnetic field. The low-disorder and small effective
mass (0.068$m_e$) defines lightly-strained germanium as a basis to tune the
strength of the spin-orbit coupling for fast and coherent quantum hardware.


  The emergence of a classical spacetime from any quantum gravity model is
still a subtle and only partially understood issue. If indeed spacetime is
arising as some sort of large scale condensate of more fundamental objects then
it is natural to expect that matter, being a collective excitations of the
spacetime constituents, will present modified kinematics at sufficiently high
energies. We consider here the phenomenology of the dissipative effects
necessarily arising in such a picture. Adopting dissipative hydrodynamics as a
general framework for the description of the energy exchange between collective
excitations and the spacetime fundamental degrees of freedom, we discuss how
rates of energy loss for elementary particles can be derived from dispersion
relations and used to provide strong constraints on the base of current
astrophysical observations of high energy particles.


  In this paper, we address a method that integrates reinforcement learning
into the Monte Carlo tree search to boost online path planning under fully
observable environments for automated parking tasks. Sampling-based planning
methods under high-dimensional space can be computationally expensive and
time-consuming. State evaluation methods are useful by leveraging the prior
knowledge into the search steps, making the process faster in a real-time
system. Given the fact that automated parking tasks are often executed under
complex environments, a solid but lightweight heuristic guidance is challenging
to compose in a traditional analytical way. To overcome this limitation, we
propose a reinforcement learning pipeline with a Monte Carlo tree search under
the path planning framework. By iteratively learning the value of a state and
the best action among samples from its previous cycle's outcomes, we are able
to model a value estimator and a policy generator for given states. By doing
that, we build up a balancing mechanism between exploration and exploitation,
speeding up the path planning process while maintaining its quality without
using human expert driver data.


  Motivated by Altshuler's famous characterization of the unit vector basis of
$c_0$ or $\ell_p$ among symmetric bases, we obtain similar characterizations
among democratic bases and among bidemocratic bases. We also prove a separate
characterization of the unit vector basis of $\ell_1$.