  The physics of active super massive black holes (BHs) is governed by their
mass (M_BH), spin (a*) and accretion rate ($\dot{M}$). This work is the first
in a series of papers with the aim of testing how these parameters determine
the observable attributes of active galactic nuclei (AGN). We have selected a
sample in a narrow redshift range, centered on z~1.55, that covers a wide range
in M_BH and $\dot{M}$, and are observing them with X-shooter, covering rest
wavelengths ~1200-9800 \AA. The current work covers 30 such objects and focuses
on the origin of the AGN spectral energy distribution (SED). After estimating
M_BH and $\dot{M}$ based on each observed SED, we use thin AD models and a
Bayesian analysis to fit the observed SEDs in our sample. We are able to fit
22/30 of the SEDs. Out of the remaining 8 SEDs, 3 can be fit by the thin AD
model by correcting the observed SED for reddening within the host galaxy and 4
can be fit by adding a disc wind to the model. In four of these 8 sources,
Milky Way-type extinction, with the strong 2175\AA\ feature, provides the best
reddening correction. The distribution in spin parameter covers the entire
range, from -1 to 0.998, and the most massive BHs have spin parameters greater
than 0.7. This is consistent with the "spin-up" model of BH evolution.
Altogether, these results indicate that thin ADs are indeed the main power
houses of AGN, and earlier claims to the contrary are likely affected by
variability and a limited observed wavelength range.


  In the Earth-field range, the nonlinear Zeeman (NLZ) effect has been a
bottleneck limiting the sensitivity and accuracy of atomic magnetometry from
physical mechanism. To break this bottleneck, various techniques are introduced
to suppress the NLZ effect. Here we revisit the spin dynamics in the
Earth-field-range magnetometry and identify the existence of the intrinsic spin
squeezed state (SSS) generated from the geomagnetically induced NLZ effect with
the oscillating squeezing degree and squeezing axis. Such oscillating features
of the SSS prevent its direct observation and as well, accessibility to
magnetic sensing. To exploit quantum advantage of the intrinsic SSS in the
Earth-field-range magnetometry, it's essential to lock the oscillating SSS to a
persistent one. Hence, we develop a quantum locking technique to achieve a
persistent SSS, benefiting from which the sensitivity of the Earth-field-range
magnetometer is quantum-enhanced. This work presents an innovative way turning
the drawback of NLZ effect into the quantum advantage and opens a new access to
quantum-enhanced magnetometry in the Earth-field range.


  We report one-pot chemical vapor deposition (CVD) growth of large-area Janus
SeMoS monolayers, with the asymmetric top (Se) and bottom (S) chalcogen atomic
planes with respect to the central transition metal (Mo) atoms. The formation
of these two-dimensional semiconductor monolayers takes place upon the
thermodynamic equilibrium-driven exchange of the bottom Se atoms of the
initially grown MoSe2 single crystals on gold foils with S atoms. The growth
process is characterized by complementary experimental techniques including
Raman and X-ray photoelectron spectroscopy and the growth mechanisms are
rationalized by first principle calculations. The remarkably high optical
quality of the synthesized Janus monolayers is demonstrated by optical and
magneto-optical measurements which reveal the strong exciton-phonon coupling
and enable to obtain the exciton g-factor of -3.3.


  This research aims to estimate three parameters in a stochastic generalized
logistic differential equation. We assume the intrinsic growth rate and shape
parameters are constant but unknown. To estimate these two parameters, we use
the maximum likelihood method and establish that the estimators for these two
parameters are strongly consistent. We estimate the diffusion parameter by
using the quadratic variation processes. To test our results, we evaluate two
data scenarios, complete and incomplete, with fixed values assigned to the
three parameters. In the incomplete data scenario, we apply an Expectation
Maximization algorithm.


  Study of the primary anisotropies of the Cosmic Microwave Background (CMB)
can be used to determine the cosmological parameters to a very high precision.
The power spectrum of the secondary CMB anisotropies due to the thermal
Sunyaev-Zel'dovich Effect (SZE) by clusters of galaxies, can then be studied,
to constrain more cluster specific properties (like gas mass). We show the SZE
power spectrum from clusters to be a sensitive probe of any possible evolution
(or constancy) of the gas mass fraction. The position of the peak of the SZE
power spectrum is a strong discriminatory signature of different gas mass
fraction evolution models. For example, for a flat universe, there can be a
difference in the $l$ values (of the peak) of {\it as much as 3000} between a
constant gas mass fraction model and an evolutionary one. Moreover,
observational determination of power spectrum, from blank sky surveys, is
devoid of any selection effects that can possibly affect targeted X-ray or
radio studies of gas mass fractions in galaxy clusters.


  The interaction of an $E/A$=57.6-MeV $^{17}$Ne beam with a Be target was used
to populate levels in $^{16}$Ne following neutron knockout reactions. The decay
of $^{16}$Ne states into the three-body $^{14}$O+$p$+$p$ continuum was observed
in the High Resolution Array (HiRA). For the first time for a 2p emitter,
correlations between the momenta of the three decay products were measured with
sufficient resolution and statistics to allow for an unambiguous demonstration
of their dependence on the long-range nature of the Coulomb interaction.
Contrary to previous experiments, the intrinsic decay width of the $^{16}$Ne
ground state was found to be narrow ($\Gamma<60$~keV), consistent with
theoretical estimates.


  It is shown that Einstein-Yang-Mills-dilaton theory has a countable family of
static globally regular solutions which are purely magnetic but uncharged. The
discrete spectrum of masses of these solutions is bounded from above by the
mass of extremal Gibbons-Maeda solution. As follows from linear stability
analysis all solutions are unstable.


  In this paper, we propose an efficient NAS algorithm for generating
task-specific models that are competitive under multiple competing objectives.
It comprises of two surrogates, one at the architecture level to improve sample
efficiency and one at the weights level, through a supernet, to improve
gradient descent training efficiency. On standard benchmark datasets (C10,
C100, ImageNet), the resulting models, dubbed NSGANetV2, either match or
outperform models from existing approaches with the search being orders of
magnitude more sample efficient. Furthermore, we demonstrate the effectiveness
and versatility of the proposed method on six diverse non-standard datasets,
e.g. STL-10, Flowers102, Oxford Pets, FGVC Aircrafts etc. In all cases,
NSGANetV2s improve the state-of-the-art (under mobile setting), suggesting that
NAS can be a viable alternative to conventional transfer learning approaches in
handling diverse scenarios such as small-scale or fine-grained datasets. Code
is available at https://github.com/mikelzc1990/nsganetv2


  Background: A relative biological effectiveness (RBE) of 1.1 is used for
proton therapy though clinical evidence of varying RBE was raised. Clinical
studies on RBE variability have been conducted for decades for carbon
radiation, which could advance the understanding of the clinical proton RBE
given an ion-independent RBE model. In this work, such a model, linear and
simple, using the beam quantity Q = Z^2/E (Z = ion charge, E = kinetic energy
per nucleon) was tested and compared to the commonly used, proton-specific and
linear energy transfer (LET) based Wedenberg RBE model. Material and methods:
The Wedenberg and Q models, both predicting RBEmax and RBEmin (i.e., RBE at
vanishing and very high dose, respectively), are compared in terms of
ion-dependence and prediction power. An experimental in-vitro data ensemble
covering 115 publications for various ions was used as dataset. Results: The
model parameter of the Q model was observed to be similar for different ions
(in contrast to LET). The Q model was trained without any prior knowledge of
proton data. For proton RBE, the differences between experimental data and
corresponding predictions of the Wedenberg or the Q model were highly
comparable. Conclusions: A simple linear RBE model using Q instead of LET was
proposed and tested to be able to predict proton RBE using model parameter
trained based on only RBE data of other particles in a clinical proton energy
range for a large in-vitro dataset. Adding (pre)clinical knowledge from carbon
ion therapy may, therefore, reduce the dominating biological uncertainty in
proton RBE modelling. This would translate in reduced RBE related uncertainty
in proton therapy treatment planning.


  Understanding the set of conditions that allow rocky planets to have liquid
water on their surface -- in the form of lakes, seas or oceans -- is a major
scientific step to determine the fraction of planets potentially suitable for
the emergence and development of life as we know it on Earth. This effort is
also necessary to define and refine the so-called "Habitable Zone" (HZ) in
order to guide the search for exoplanets likely to harbor remotely detectable
life forms. Until now, most numerical climate studies on this topic have
focused on the conditions necessary to maintain oceans, but not to form them in
the first place. Here we use the three-dimensional Generic Planetary Climate
Model (PCM), historically known as the LMD Generic Global Climate Model (GCM),
to simulate water-dominated planetary atmospheres around different types of
Main-Sequence stars. The simulations are designed to reproduce the conditions
of early ocean formation on rocky planets due to the condensation of the
primordial water reservoir at the end of the magma ocean phase. We show that
the incoming stellar radiation (ISR) required to form oceans by condensation is
always drastically lower than that required to vaporize oceans. We introduce a
Water Condensation Limit, which lies at significantly lower ISR than the inner
edge of the HZ calculated with three-dimensional numerical climate simulations.
This difference is due to a behavior change of water clouds, from low-altitude
dayside convective clouds to high-altitude nightside stratospheric clouds.
Finally, we calculated transit spectra, emission spectra and thermal phase
curves of TRAPPIST-1b, c and d with H2O-rich atmospheres, and compared them to
CO2 atmospheres and bare rock simulations. We show using these observables that
JWST has the capability to probe steam atmospheres on low-mass planets, and
could possibly test the existence of nightside water clouds.


  Let $\Omega$ be a strongly Lipschitz domain of $\reel^n$. Consider an
elliptic second order divergence operator $L$ (including a boundary condition
on $\partial\Omega$) and define a Hardy space by imposing the non-tangential
maximal function of the extension of a function $f$ via the Poisson semigroup
for $L$ to be in$L^1$. Under suitable assumptions on $L$, we identify this
maximal Hardy space with atomic Hardy spaces, namely with $H^1(\reel^n)$ if
$\Omega=\reel^n$, $H^{1}_{r}(\Omega)$ under the Dirichlet boundary condition,
and $H^{1}_{z}(\Omega)$ under the Neumann boundary condition. In particular, we
obtain a new proof of the atomic decomposition for $H^{1}_{z}(\Omega)$. A
version for local Hardy spaces is also given. We also present an overview of
the theory of Hardy spaces and BMO spaces on Lipschitz domains with proofs.


  In this paper, we investigate the Painlev\'e asymptotics in a transition zone
for the solutions to the Cauchy problem of the Novikov equation under a nonzero
background \begin{align}
  &u_{t}-u_{txx}+4 u_{x}=3uu_xu_{xx}+u^2u_{xxx}, \nonumber
  &u(x, 0)=u_{0}(x),\nonumber \end{align} where $u_0(x)\rightarrow \kappa>0, \
x\rightarrow \pm \infty$ and $u_0(x)-\kappa$ is assumed in the Schwarz space.
This result is established by performing the $\overline\partial$-steepest
descent analysis to a Riemann-Hilbert problem associated with the the Cauchy
problem in a new spatial scale
  \begin{equation*} y = x - \int_{x}^{\infty}
\left((u-u_{xx}+1)^{2/3}-1\right)ds,
  \end{equation*}
  for large times in the transition zone $y/t \approx -1/8 $. It is shown that
the leading order term of the asymptotic approximation comes from the
contribution of solitons, while the sub-leading term is related to the solution
of the Painlev\'e \uppercase\expandafter{\romannumeral2} equation.n.


  Shear-induced turbulence could play a significant role in mixing momentum and
chemical species in stellar radiation zones, as discussed by Zahn (1974). In
this paper we analyze the results of direct numerical simulations of stratified
plane Couette flows, in the limit of rapid thermal diffusion, to measure the
turbulent diffusivity and turbulent viscosity as a function of the local shear
and the local stratification. We find that the stability criterion proposed by
Zahn (1974), namely that the product of the gradient Richardson number and the
Prandtl number must be smaller than a critical values $(J\Pr)_c$ for
instability, adequately accounts for the transition to turbulence in the flow,
with $(J\Pr)_c \simeq 0.007$. This result recovers and confirms the prior
findings of Prat et al. (2016). Zahn's model for the turbulent diffusivity and
viscosity (Zahn 1992), namely that the mixing coefficient should be
proportional to the ratio of the thermal diffusivity to the gradient Richardson
number, does not satisfactorily match our numerical data when applied as is. It
fails (as expected) in the limit of large stratification where the Richardson
number exceeds the aforementioned threshold for instability, but it also fails
in the limit of low stratification where the turbulent eddy scale becomes
limited by the computational domain size. We propose a revised model for
turbulent mixing by diffusive stratified shear instabilities, that now properly
accounts for both limits, fits our data satisfactorily, and recovers Zahn's
1992 model in the limit of large Reynolds numbers.


  The wide acceptance of large language models (LLMs) has unlocked new
applications and social risks. Popular countermeasures aim at detecting
misinformation, usually involve domain specific models trained to recognize the
relevance of any information. Instead of evaluating the validity of the
information, we propose to investigate LLM generated text from the perspective
of trust. In this study, we define trust as the ability to know if an input
text was generated by a LLM or a human. To do so, we design SPOT, an efficient
method, that classifies the source of any, standalone, text input based on
originality score. This score is derived from the prediction of a given LLM to
detect other LLMs. We empirically demonstrate the robustness of the method to
the architecture, training data, evaluation data, task and compression of
modern LLMs.


  We present near-infrared (NIR; J & Ks) survey of the Great Observatories
Origins Deep Survey-North (GOODS-N) field. The publicly available imaging data
were obtained using the MOIRCS instrument on the 8.2m Subaru and the WIRCam
instrument on the 3.6m Canada-France-Hawaii Telescope (CFHT). These
observations fulfill a serious wavelength gap in the GOODS-N data - i.e., lack
of deep NIR observations. We combine the Subaru/MOIRCS and CFHT/WIRCam archival
data to generate deep J and Ks band images, covering the full GOODS-N field
(~169 sq. arcmin) to an AB magnitude limit of ~25 mag (3sigma). We applied
z'-band dropout color selection criteria, using the NIR data generated here. We
have identified two possible Lyman Break Galaxy (LBG) candidates at z\gtrsim6.5
with J\lesssim24.5. The first candidate is a likely LBG at z\sim6.5 based on a
weak spectral feature tentatively identified as Lyalpha line in the deep
Keck/DEIMOS spectrum, while the second candidate is a possible LBG at z\sim7
based on its photometric redshift. These z'-dropout objects, if confirmed, are
among the brightest such candidates found so far. At z\gtrsim6.5, their star
formation rate is estimated as 100-200 solar mass per year. If they continue to
form stars at this rate, they assemble a stellar mass of ~5x10^10 solar mass
after about 400 million years, becoming the progenitors of massive galaxies
observed at z\sim5. We study the implication of the z'-band dropout candidates
discovered here, in constraining the bright-end of the luminosity function and
understanding the nature of high redshift galaxies.


  We study spin squeezing under non-Markovian channels, and consider an
ensemble of $N$ independent spin-1/2 particles with exchange symmetry. Each
spin interacts with its own bath, and the baths are independent and identical.
For this kind of open system, the spin squeezing under decoherence can be
investigated from the dynamics of the local expectations, and the multi-qubit
dynamics can be reduced into the two-qubit one. The reduced dynamics is
obtained by the hierarchy equation method, which is a exact without
rotating-wave and Born-Markov approximation. The numerical results show that
the spin squeezing displays multiple sudden vanishing and revival with lower
bath temperature, and it can also vanish asymptotically.


  Let $L$ be a slim, planar, semimodular lattice (slim means that it does not
contain ${\mathsf M}_3$-sublattices). We call the interval $I = [o, i]$ of $L$
\emph{rectangular}, if there are $u_l, u_r \in [o, i] - \{o,i\}$ such that $i =
u_l \vee u_r$ and $o = u_l \wedge u_r$ where $u_l$ is to the left of $u_r$.
  \emph{The first result}: a rectangular interval of a rectangular lattice is a
rectangular lattice. As an application, we get a recent result of G. Cz\'edli.
  In a 2017 paper, G. Cz\'edli introduced a very powerful diagram type for
slim, planar, semimodular lattices, the \emph{$\mathcal{C}_1$-diagrams}.
  We revisit the concept of \emph{natural diagrams} I introduced with E.~Knapp
about a dozen years ago. Given a slim rectangular lattice $L$, we construct its
natural diagram in one simple step. \emph{The second result} shows that for a
slim rectangular lattice, a~natural diagram is the same as a
$\mathcal{C}_1$-diagram. Therefore, natural diagrams have all the nice
properties of $\mathcal{C}_1$-diagrams.


  We investigate the phase diagram and the BCS-BEC crossover of a homogeneous
three-component ultracold Fermi gas with a U(3) invariant attractive
interaction. We show that the system at sufficiently low temperatures exhibits
population imbalance, as well as fermionic pairing. We describe the crossover
in this system, connecting the weakly interacting BCS regime of the partially
population-imbalanced fermion pairing state and the BEC limit with three weakly
interacting species of molecules, including pairing fluctuations within a
t-matrix calculation of the particle self-energies.


  We will prove that, for any abelian group $G$, the canonical (surjective and
continuous) mapping $\boldsymbol{\beta}G \to {\frak b}G$ from the
Stone-\v{C}ech compactification $\boldsymbol{\beta}G$ of $G$ to its Bohr
compactfication ${\frak b}G$ is a homomorphism with respect to the semigroup
operation on $\boldsymbol{\beta}G$, extending the multiplication on $G$, and
the group operation on ${\frak b}G$. Moreover, the Bohr compactification
${\frak b}G$ is canonically isomorphic (both in algebraic and topological
sense) to the quotient of $\boldsymbol{\beta}G$ with respect to the least
closed congruence relation on $\boldsymbol{\beta}G$ merging all the Schur
ultrafilters on $G$ into the unit of $G$.


  Electrical impedance tomography is an imaging modality for extracting
information on the conductivity distribution inside a physical body from
boundary measurements of current and voltage. In many practical applications,
it is a priori known that the conductivity consists of embedded inhomogeneities
in an approximately constant background. This work introduces an iterative
reconstruction algorithm that aims at finding the maximum a posteriori estimate
for the conductivity assuming an edge-preferring prior. The method is based on
applying (a single step of) priorconditioned lagged diffusivity iteration to
sequential linearizations of the forward model. The algorithm is capable of
producing reconstructions on dense unstructured three-dimensional finite
element meshes and with a high number of measurement electrodes. The
functionality of the proposed technique is demonstrated with both simulated and
experimental data in the framework of the complete electrode model, which is
the most accurate model for practical impedance tomography.


  The time-dependent $CP$ asymmetry in $B_s^0 \to J/\psi K^+K^-$ decays is
measured using $pp$ collision data, corresponding to an integrated luminosity
of $3.0$fb$^{-1}$, collected with the LHCb detector at centre-of-mass energies
of $7$ and $8$TeV. In a sample of 96 000 $B_s^0 \to J/\psi K^+K^-$ decays, the
$CP$-violating phase $\phi_s$ is measured, as well as the decay widths
$\Gamma_{L}$ and $\Gamma_{H}$ of the light and heavy mass eigenstates of the
$B_s^0-\bar{B}_s^0$ system. The values obtained are $\phi_s = -0.058 \pm 0.049
\pm 0.006$ rad, $\Gamma_s \equiv (\Gamma_{L}+\Gamma_{H})/2 = 0.6603 \pm 0.0027
\pm 0.0015$ps$^{-1}$, and$\Delta\Gamma_s \equiv \Gamma_{L} - \Gamma_{H} =
0.0805 \pm 0.0091 \pm 0.0032$ps$^{-1}$, where the first uncertainty is
statistical and the second systematic. These are the most precise single
measurements of those quantities to date. A combined analysis with $B_s^{0} \to
J/\psi \pi^+\pi^-$ decays gives $\phi_s = -0.010 \pm 0.039 $rad. All
measurements are in agreement with the Standard Model predictions. For the
first time the phase $\phi_s$ is measured independently for each polarisation
state of the $K^+K^- $ system and shows no evidence for polarisation
dependence.


  We use a direct numerical integration of the Vlasov equation in spherical
symmetry with a background gravitational potential to determine the evolution
of a collection of particles in different models of a galactic halo. Such a
collection is assumed to represent a dark matter inhomogeneity which reaches a
stationary state determined by the virialization of the system. We describe
some features of the stationary states and, by using several halo models,
obtain distinctive signatures for the evolution of the inhomogeneities in each
of the models.


  We study the relationship between foreign debt and GDP growth using a panel
dataset of 50 countries from 1997 to 2015. We find that economic growth
correlates positively with foreign debt and that the relationship is causal in
nature by using the sovereign credit default swap spread as an instrumental
variable. Furthermore, we find that foreign debt increases investment and then
GDP growth in subsequent years. Our findings suggest that lower sovereign
default risks lead to higher foreign debt contributing to GDP growth more in
OECD than non-OECD countries.


  We study the last-passage growth model on the planar integer lattice with
exponential weights. With boundary conditions that represent the equilibrium
exclusion process as seen from a particle right after its jump we prove that
the variance of the last-passage time in a characteristic direction is of order
t^{2/3}. With more general boundary conditions that include the rarefaction fan
case we show that the last-passage time fluctuations are still of order
t^{1/3}, and also that the transversal fluctuations of the maximal path have
order t^{2/3}. We adapt and then build on a recent study of Hammersley's
process by Cator and Groeneboom, and also utilize the competition interface
introduced by Ferrari, Martin and Pimentel. The arguments are entirely
probabilistic, and no use is made of the combinatorics of Young tableaux or
methods of asymptotic analysis.


  In this paper we design non-uniform bit-wise puncturing distributions for
irregular non-binary LDPC (NB-LDPC) codes. The puncturing distributions are
optimized by minimizing the decoding threshold of the punctured LDPC code, the
threshold being computed with a Monte-Carlo implementation of Density
Evolution. First, we show that Density Evolution computed with Monte-Carlo
simulations provides accurate (very close) and precise (small variance)
estimates of NB-LDPC code ensemble thresholds. Based on the proposed method, we
analyze several puncturing distributions for regular and semi-regular codes,
obtained either by clustering punctured bits, or spreading them over the
symbol-nodes of the Tanner graph. Finally, optimized puncturing distributions
for non-binary LDPC codes with small maximum degree are presented, which
exhibit a gap between 0.2 and 0.5 dB to the channel capacity, for punctured
rates varying from 0.5 to 0.9.


  We review the impact of tetrahedral order on the macroscopic dynamics of
bent-core liquid crystals. We discuss tetrahedral order comparing with other
types of orientational order, like nematic, polar nematic, polar smectic, and
active polar order. In particular, we present hydrodynamic equations for
phases, where only tetrahedral order exists or tetrahedral order is combined
with nematic order. Among the latter we discriminate between three cases, where
the nematic director (a) orients along a 4-fold, or (b) along a 3-fold symmetry
axis of the tetrahedral structure. For the optically isotropic T_d phase, which
only has tetrahedral order, we focus on the coupling of flow with e.g.
temperature gradients and on the specific orientation behavior in external
electric fields. For the transition to the nematic phase, electric fields lead
to a temperature shift that is linear in the field strength. Electric fields
induce nematic order, again linear in the field strength. If strong enough,
electric fields can change the tetrahedral structure and symmetry leading to a
polar phase. We briefly deal with the T phase that arises when tetrahedral
order occurs in a system of chiral molecules. To case (a) belong (i) the
non-polar, achiral, optically uniaxial D2d phase with ambidextrous helicity and
with orientational frustration in external fields, (ii) the non-polar
tetragonal S4 phase, (iii) the non-polar, orthorhombic D2 phase that is
structurally chiral featuring ambidextrous chirality, (iv) the polar
orthorhombic C2v phase, and (v) the polar monoclinic C2 phase. Case (b) results
in a trigonal C3v phase that behaves like a biaxial polar nematic phase.
Finally we discuss some experiments that show typical effects related to the
existence of tetrahedral order.


  We develop the basic formalism of complex $q$-analysis to study the solutions
of second order $q$-difference equations which reduce, in the $q\rightarrow 1$
limit, to the ordinary Laplace equation in Euclidean and Minkowski space. After
defining an inner product on the function space we construct and study the
properties of the solutions, and then apply this formalism to the
Schr\"{o}dinger equation and two-dimensional scalar field theory.


  We carry out a systematic study of the electronic and magnetic structure of
the ambient-pressure bilayer La$_3$Ni$_2$O$_7$. Employing the hybrid
exchange-correlation functional, we show that the exchange-correlation pushes
the antibonding $d_{z^2}$ bands below the Fermi level to be fully occupied. The
calculated Fermi surfaces and the correlation normalized band structure match
well with the experimental findings at ambient pressure. Moreover, the
electronic susceptibility calculated for this new band structure features
nesting-induced peaks near the wave vector $Q=(\pi/2, \pi/2)$, suggesting a
possible density wave instability in agreement with recent experiments. Through
a mean field study and DFT+U calculation, we confirm the spin-charge
intertwined double stripe order is the magnetic ground state. Our results
provide a faithful description for the low-pressure La$_3$Ni$_2$O$_7$
electronic structure.


  We study specific features of resonant mode conversion in nonlinear
waveguides stimulated by the bi-harmonic longitudinal modulation of its
parameters, which includes changes of the waveguide depth as well as its
bending (in the one-dimensional case) or spiraling (in the two-dimensional
case). We demonstrate the possibility of simultaneous excitation of
higher-order modes of different parities and topologies with controllable
energy weights. The output mode composition is highly sensitive to the
variation in the input power and detuning from the resonant modulation
frequency.


  We study the effective field theory for fermions in the color-flavor locked
(CFL) phase of high density QCD. The effective theory contains a flavor nonet
of baryons interacting with a nonet of pseudoscalar Goldstone bosons as well as
a singlet scalar Goldstone boson. The theory is similar to chiral perturbation
theory in the one-baryon sector. We explain how to incorporate quark mass terms
and study the spectrum as a function of the strange quark mass. Without meson
condensation gapless baryon modes appears if the strange quark mass exceeds a
critical value m_s^2/(2p_F)=Delta, where p_F is the Fermi momentum and Delta is
the gap in the chiral limit. We show that kaon condensation leads to a
rearrangement of the baryon spectrum and shifts the critical strange quark mass
for the appearance of a gapless mode to higher values.


  A model for off-resonant microscopic cascading of (hyper)polarizabilities is
developed using a self-consistent field approach to study mesoscopic systems of
nonlinear polarizable atoms and molecules. We find enhancements in the
higher-order susceptibilities resulting from geometrical and boundary
orientation effects. We include an example of the dependence on excitation beam
cross sectional structure and a simplified derivation of the microscopic
cascading of the nonlinear optical response in guest-host systems.


  We compare and contrast two approaches to the structure theory for Lie
pseudo-groups, the first due to Cartan, and the second due to the first two
authors. We argue that the latter approach offers certain advantages from both
a theoretical and practical standpoint.


  We discuss an improved theoretical description of the semi-inclusive B meson
decays $B\to K(K^*)X$. The decay distributions are calculated. Their branching
ratios are found to be appreciable. The CP asymmetries in the neutral B modes
$\bar{B^0}\to K^-(K^{*-})X$ are sizable. An observation of direct CP violation
and a measurement of $\gamma$ may come from these neutral B modes.


  Social media content routinely incorporates multi-modal design to covey
information and shape meanings, and sway interpretations toward desirable
implications, but the choices and outcomes of using both texts and visual
images have not been sufficiently studied. This work proposes a computational
approach to analyze the outcome of persuasive information in multi-modal
content, focusing on two aspects, popularity and reliability, in
COVID-19-related news articles shared on Twitter. The two aspects are
intertwined in the spread of misinformation: for example, an unreliable article
that aims to misinform has to attain some popularity. This work has several
contributions. First, we propose a multi-modal (image and text) approach to
effectively identify popularity and reliability of information sources
simultaneously. Second, we identify textual and visual elements that are
predictive to information popularity and reliability. Third, by modeling
cross-modal relations and similarity, we are able to uncover how unreliable
articles construct multi-modal meaning in a distorted, biased fashion. Our work
demonstrates how to use multi-modal analysis for understanding influential
content and has implications to social media literacy and engagement.


  In this paper, we give a resolution of the generalized Fermat equations $$x^5
+ y^5 = 3 z^n \text{ and } x^{13} + y^{13} = 3 z^n,$$ for all integers $n \ge
2$, and all integers $n \ge 2$ which are not a multiple of $7$, respectively,
using the modular method with Frey elliptic curves over totally real fields.
The results require a refined application of the multi-Frey technique, which we
show to be effective in new ways to reduce the bounds on the exponents $n$.
  We also give a number of results for the equations $x^5 + y^5 = d z^n$, where
$d = 1, 2$, under additional local conditions on the solutions. This includes a
result which is reminiscent of the second case of Fermat's Last Theorem, and
which uses a new application of level raising at $p$ modulo $p$.


  For a coherent filtered D-module we show that the dual of each graded piece
over the structure sheaf is isomorphic to a certain graded piece of the
ring-theoretic local cohomology complex of the graded quotient of the dual of
the filtered D-module along the zero-section of the cotangent bundle. This
follows from a similar assertion for coherent graded modules over a polynomial
algebra over the structure sheaf. We also prove that the local cohomology
sheaves can be calculated by using the higher direct images of the twists of
the associated sheaf complex on the projective cotangent bundle. These are
closely related to local duality, essentially due to Grothendieck.


  Detector developments are currently enabling new capabilities in the field of
transmission electron microscopy (TEM). We have investigated the limits of a
hybrid pixel detector, Medipix3, to record dynamic, time varying, electron
signals. Operating with an energy of 60keV, we have utilised electrostatic
deflection to oscillate electron beam position on the detector. Adopting a
pump-probe imaging strategy we have demonstrated that temporal resolutions
three orders of magnitude smaller than are available for typically used TEM
imaging detectors are possible. Our experiments have shown that energy
deposition of the primary electrons in the hybrid pixel detector limits the
overall temporal resolution. Through adjustment of user specifiable thresholds
or the use of charge summing mode, we have obtained images composed from
summing 10,000s frames containing single electron events to achieve temporal
resolution less than 100ns. We propose that this capability can be directly
applied to studying repeatable material dynamic processes but also to implement
low-dose imaging schemes in scanning transmission electron microscopy.


  We report on the fabrication and characterization of a few-electron quantum
dot controlled by a single gate electrode. Our device has a double-quantum-well
design, in which the doping controls the occupancy of the lower well while the
upper well remains empty under the free surface. A small air-bridged gate
contacts the surface, and is positively biased to draw laterally confined
electrons into the upper well. Electrons tunneling between this
accumulation-mode dot and the lower well are detected using a quantum point
contact (QPC), located slightly offset from the dot gate. The charge state of
the dot is measured by monitoring the differential transconductance of the QPC
near pinch-off. Addition spectra starting with N=0 were observed as a function
of gate voltage. DC sensitivity to single electrons was determined to be as
high as 8.6%, resulting in a signal-to-noise ratio of ~9:1 with an equivalent
noise bandwidth of 12.1 kHz. Analysis of random telegraph signals associated
with the zero to one electron transition allowed a measurement of the lifetimes
for the filled and empty states of the one-electron dot: 0.38 ms and 0.22 ms,
respectively, for a device with a 10 nm AlInAs tunnel barrier between the two
wells.


  Rare events play a key role in many applications and numerous algorithms have
been proposed for estimating the probability of a rare event. However,
relatively little is known on how to quantify the sensitivity of the
probability with respect to model parameters. In this paper, instead of the
direct statistical estimation of rare event sensitivities, we develop novel and
general uncertainty quantification and sensitivity bounds which are not tied to
specific rare event simulation methods and which apply to families of rare
events. Our method is based on a recently derived variational representation
for the family of R\'enyi divergences in terms of risk sensitive functionals
associated with the rare events under consideration. Based on the derived
bounds, we propose new sensitivity indices for rare events and relate them to
the moment generating function of the score function. The bounds scale in such
a way that we additionally develop sensitivity indices for large deviation rate
functions.


  We investigate the non-Gaussianity of primordial curvature perturbation in
the modulated reheating scenario where the primordial perturbation is generated
due to the spacial fluctuation of the inflaton decay rate to radiation. We use
the $\delta N$ formalism to evaluate the trispectrum of curvature perturbation
as well as its bispectrum. We give expressions for three non-linear parameters
$f_{NL}, \tau_{NL}$ and $g_{NL}$ in the modulated reheating scenario. If the
intrinsic non-Gaussianity of scalar field fluctuations and third derivative of
the decay rate with respect to scalar fields are negligibly small, $g_{NL}$ has
at least the same order of magnitude as $f_{NL}$. We also give general
inequality between $f_{NL}$ and $\tau_{NL}$ which is true for other
inflationary scenarios as long as primordial non-Gaussianity comes from
super-horizon evolution.


  Real-world applications often require a large gallery of 3D assets that share
a consistent theme. While remarkable advances have been made in general 3D
content creation from text or image, synthesizing customized 3D assets
following the shared theme of input 3D exemplars remains an open and
challenging problem. In this work, we present ThemeStation, a novel approach
for theme-aware 3D-to-3D generation. ThemeStation synthesizes customized 3D
assets based on given few exemplars with two goals: 1) unity for generating 3D
assets that thematically align with the given exemplars and 2) diversity for
generating 3D assets with a high degree of variations. To this end, we design a
two-stage framework that draws a concept image first, followed by a
reference-informed 3D modeling stage. We propose a novel dual score
distillation (DSD) loss to jointly leverage priors from both the input
exemplars and the synthesized concept image. Extensive experiments and user
studies confirm that ThemeStation surpasses prior works in producing diverse
theme-aware 3D models with impressive quality. ThemeStation also enables
various applications such as controllable 3D-to-3D generation.


  We present our experiences using cloud computing to support data-intensive
analytics on satellite imagery for commercial applications. Drawing from our
background in high-performance computing, we draw parallels between the early
days of clustered computing systems and the current state of cloud computing
and its potential to disrupt the HPC market. Using our own virtual file system
layer on top of cloud remote object storage, we demonstrate aggregate read
bandwidth of 230 gigabytes per second using 512 Google Compute Engine (GCE)
nodes accessing a USA multi-region standard storage bucket. This figure is
comparable to the best HPC storage systems in existence. We also present
several of our application results, including the identification of field
boundaries in Ukraine, and the generation of a global cloud-free base layer
from Landsat imagery.


  We test the recently proposed (Mediavilla et al. 2018) black hole mass
scaling relationship based on the redshift {with respect to the quasar's rest
frame} of the Fe III$\lambda\lambda$2039-2113 line blend. To this end, we fit
this feature in the spectra of a well suited sample of quasars, observed with
X-shooter at the Very Large Telescope (VLT), whose masses have been
independently estimated using the virial theorem. For the quasars of this
sample we consistently confirm the redshift of the Fe
III$\lambda\lambda$2039-2113 blend and find that it correlates with the squared
widths of H$\beta$, H$\alpha$ and Mg II, which are commonly used as a measure
of $M_{BH}/R$ to determine masses from the virial theorem. The average
differences between virial and Fe III$\lambda\lambda$2039-2113 redshift based
masses are 0.18$\pm 0.21$ dex, 0.18$\pm 0.22$ dex and 0.14$\pm 0.21$ dex, when
the full widths at half maximum (FWHM) of the H$\beta$, H$\alpha$ and MgII
lines are, respectively, used. The difference is reduced to 0.10$\pm 0.16$ dex
when the standard deviation, $\sigma$, of {the} MgII line is used, instead. We
also study the high S/N composite quasar spectra of the Baryon Oscillation
Spectroscopic Survey (BOSS), finding that the Fe III$\lambda\lambda$2039-2113
redshifts and Mg II squared widths, $FWHM_{MgII}^2$, match very well the
correlation found for the individual quasar spectra observed with X-shooter.
This correlation is expected if the redshift is gravitational.


  We show how important phenomena in social networks like coordination, trust
and the communication of unsubstantiated information (gossip) can be modelled
and understood using epistemic networks or epinets: directed graphs comprising
networked agents and the key facts, statements or other kinds of propositional
beliefs relevant to their actions. We use epinets to sharpen the explanatory
and reach of social network analysis to situations problematic to both
network-structural approaches and epistemic game theory.


  Order-disorder transitions of a vortex lattice transfer type-II
superconductors from a low critical current state to a high one. The similar
transition between different current states can be caused by electromagnetic
granularity. A sigmoid curve is proposed to describe the corresponding peak in
a field dependence of the macroscopic critical density. Using the extended
critical state model, analytic expressions are obtained for the field
dependencies of the local critical current density, the depth of equilibrium
surface region, and the macroscopic critical current density. The expressions
are well fit to published data.


  We treat the problem of finding transitive subgroups G of S_n containing
normal subgroups N_1 and N_2, with N_1 transitive and N_2 not transitive, such
that G/N_1 is isomorphic G/N_2. We show that such G exist whenever n has a
prime factor that also divides the Euler-phi function of n. We show that no
such G exist when n = pq for p < q with p not dividing q-1.


  We derive lower bounds on the Bayes risk in decentralized estimation, where
the estimator does not have direct access to the random samples generated
conditionally on the random parameter of interest, but only to the data
received from local processors that observe the samples. The received data are
subject to communication constraints, due to quantization and the noise in the
communication channels from the processors to the estimator. We first derive
general lower bounds on the Bayes risk using information-theoretic quantities,
such as mutual information, information density, small ball probability, and
differential entropy. We then apply these lower bounds to the decentralized
case, using strong data processing inequalities to quantify the contraction of
information due to communication constraints. We treat the cases of a single
processor and of multiple processors, where the samples observed by different
processors may be conditionally dependent given the parameter, for
noninteractive and interactive communication protocols. Our results recover and
improve recent lower bounds on the Bayes risk and the minimax risk for certain
decentralized estimation problems, where previously only conditionally
independent sample sets and noiseless channels have been considered. Moreover,
our results provide a general way to quantify the degradation of estimation
performance caused by distributing resources to multiple processors, which is
only discussed for specific examples in existing works.


  In a previous paper we investigate a Lagrangian field theory for the
gravitational field (which is there represented by a section g^a of the
orthonormal coframe bundle over Minkowski spacetime. Such theory, under
appropriate conditions, has been proved to be equivalent to a Lorentzian
spacetime structure, where the metric tensor satisfies Einstein field
equations. Here, we first recall that according to quantum field theory ideas
gravitation is described by a Lagrangian theory of a possible massive graviton
field (generated by matter fields and coupling also to itself) living in
Minkowski spacetime. The graviton field is moreover supposed to be represented
by a symmetric tensor field h carrying the representations of spin two and zero
of the Lorentz group. Such a field, then (as it is well known), must
necessarily satisfy the gauge condition given by Eq.(3) below. Next, we
introduce an ansatz relating h to the 1-form fields g^a. Then, using the
Clifford bundle formalism we derive, from our Lagrangian theory, the exact wave
equation for the graviton and investigate the role of the gauge condition given
by Eq.(3) in obtaining a reliable conservation law for the energy-momentum
tensor of the gravitational plus the matter fields in Minkowski spacetime.
Finally we ask the question: does Eq.(3) fix any gauge condition for the field
g of the effective Lorentzian spacetime structure that represents the field h
in our theory? We show that no gauge condition is fixed a priory, as is the
case in General Relativity. Moreover we investigate under which conditions we
may fix Logunov gauge condition.


  Recently, a novel 4D Einstein-Gauss-Bonnet gravity has been proposed by
Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] by rescaling the coupling
$\alpha \rightarrow \alpha/(D-4)$ and taking the limit $D\rightarrow 4$ at the
level of equations of motion. This prescription, though was shown to bring
non-trivial effects for some spacetimes with particular symmetries, remains
mysterious and calls for scrutiny. Indeed, there is no continuous way to take
the limit $D\rightarrow 4$ in the higher $D$-dimensional equations of motion
because the tensor indices depend on the spacetime dimension and behave
discretely. On the other hand, if one works with four-dimensional spacetime
indices the contribution corresponding to the Gauss-Bonnet term vanishes
identically in the equations of motion. A necessary condition (but may not be
sufficient) for this procedure to work is that there is an embedding of the
four-dimensional spacetime into the higher $D$-dimensional spacetime so that
the equations in the latter can be properly interpreted after taking the limit.
In this note, working with 2D Einstein gravity, we show several subtleties when
applying the method used in [Phys. Rev. Lett. 124, 081301 (2020)].


  Eigenstate-preserving multi-qubit parity measurements lie at the heart of
stabilizer quantum error correction, which is a promising approach to mitigate
the problem of decoherence in quantum computers. In this work we explore a
high-fidelity, eigenstate-preserving parity readout for superconducting qubits
dispersively coupled to a microwave resonator, where the parity bit is encoded
in the amplitude of a coherent state of the resonator. Detecting photons
emitted by the resonator via a current biased Josephson junction yields
information about the parity bit. We analyse theoretically the measurement
back-action in the limit of a strongly coupled fast detector and show that in
general such a parity measurement, while approximately Quantum Non-Demolition
(QND) is not eigenstate-preserving. To remediate this shortcoming we propose a
simple dynamical decoupling technique during photon detection, which greatly
reduces decoherence within a given parity subspace. Furthermore, by applying a
sequence of fast displacement operations interleaved with the dynamical
decoupling pulses, the natural bias of this binary detector can be efficiently
suppressed. Finally, we introduce the concept of a heralded parity measurement,
where a detector click guarantees successful multi-qubit parity detection even
for finite detection efficiency.


  We define the theta group associated to a simple coherent sheaf $\cal F$ on a
hyperk\"ahler manifold $X$ of Kummer type or OG6 type, provided $g^{*}({\cal
F})$ is isomorphic to $\cal F$ for every automorphism $g$ of $X$ acting
trivially on $H^2(X)$. Note that this condition is satisfied if $\cal F$ is
invertible, if $\cal F$ is one of the rank $4$ stable vector bundles on general
polarized HK fourfolds with certain discrete invariants constructed in
arXiv:2203.03987, or if $\cal F$ is the tangent bundle. We compute the
commutator pairings of theta groups of line bundles and the rank $4$ modular
vector bundles of arXiv:2203.03987 (the commutator pairing of the tangent
bundle is trivial). We have been motivated by the quest for an explicit
description of locally complete families of polarized varieties of Kummer (or
OG6) type.


  We study topological strings on local toric del Pezzo surfaces by a method
called remodeling the B-model which was recently proposed by Bouchard, Klemm,
Marino and Pasquetti. For a large class of local toric del Pezzo surfaces we
prove a functional formula of the Bergman kernel which is the basic constituent
of the topological string amplitudes by the topological recursion relation of
Eynard and Orantin. Because this formula is written as a functional of the
period, we can obtain the topological string amplitudes at any point of the
moduli space by a simple change of variables of the Picard-Fuchs equations for
the period. By this formula and mirror symmetry we compute the A-model
amplitudes on K_{F_2}, and predict the open orbifold Gromov-Witten invariants
of C^3/Z_4.


  We have found a NLS1 nucleus in the extensively studied eruptive BL Lac,
0846+51W1, out of a large sample of NLS1 compiled from the spectroscopic
dataset of SDSS DR1. Its optical spectrum can be well decomposed into three
components, a power law component from the relativistic jet, a stellar
component from the host galaxy, and a component from a typical NLS1 nucleus.
The emission line properties of 0846+51W1, FWHM(Hbeta) ~ 1710 km s^-1 and
[OIII]5007/Hbeta ~ 0.32 when it was in faint state, fulfil the conventional
definition of NLS1. Strong FeII emission is detected in the SDSS spectrum,
which is also typical of NLS1s. We try to estimate its central black hole mass
using various techniques and find that 0846+51W1 is very likely emitting at a
few times 10% L_Edd. We speculate that Seyfert-like nuclei, including NLS1s,
might be concealed in a significant fraction of BL Lacs but have not been
sufficiently explored due to the fact that, by definition, the optical-UV
continuum of such kind of objects are often overwhelmed by the synchrotron
emission.


  We survey some recent work on topological quantum computation with gapped
boundaries and boundary defects and list some open problems.


  Results of a new two-particle correlation analysis of central Pb+Au collision
data at 158 GeV per nucleon are presented. The emphasis is put on pion-proton
correlations and on the dependence of the two-pion correlation radii on the
azimuthal emission angle with respect to the reaction plane.


  The cophenetic metrics $d_{\varphi,p}$, for $p\in {0}\cup[1,\infty[$, are a
recent addition to the kit of available distances for the comparison of
phylogenetic trees. Based on a fifty years old idea of Sokal and Rohlf, these
metrics compare phylogenetic trees on a same set of taxa by encoding them by
means of their vectors of cophenetic values of pairs of taxa and depths of
single taxa, and then computing the $L^p$ norm of the difference of the
corresponding vectors. In this paper we compute the expected value of the
square of $d_{\varphi,2}$ on the space of fully resolved rooted phylogenetic
trees with $n$ leaves, under the Yule and the uniform probability
distributions.


  In recent advancements in novel view synthesis, generalizable Neural Radiance
Fields (NeRF) based methods applied to human subjects have shown remarkable
results in generating novel views from few images. However, this generalization
ability cannot capture the underlying structural features of the skeleton
shared across all instances. Building upon this, we introduce HFNeRF: a novel
generalizable human feature NeRF aimed at generating human biomechanic features
using a pre-trained image encoder. While previous human NeRF methods have shown
promising results in the generation of photorealistic virtual avatars, such
methods lack underlying human structure or biomechanic features such as
skeleton or joint information that are crucial for downstream applications
including Augmented Reality (AR)/Virtual Reality (VR). HFNeRF leverages 2D
pre-trained foundation models toward learning human features in 3D using neural
rendering, and then volume rendering towards generating 2D feature maps. We
evaluate HFNeRF in the skeleton estimation task by predicting heatmaps as
features. The proposed method is fully differentiable, allowing to successfully
learn color, geometry, and human skeleton in a simultaneous manner. This paper
presents preliminary results of HFNeRF, illustrating its potential in
generating realistic virtual avatars with biomechanic features using NeRF.


  Individual decision-makers consume information revealed by the previous
decision makers, and produce information that may help in future decisions.
This phenomenon is common in a wide range of scenarios in the Internet economy,
as well as in other domains such as medical decisions. Each decision-maker
would individually prefer to "exploit": select an action with the highest
expected reward given her current information. At the same time, each
decision-maker would prefer previous decision-makers to "explore", producing
information about the rewards of various actions. A social planner, by means of
carefully designed information disclosure, can incentivize the agents to
balance the exploration and exploitation so as to maximize social welfare.
  We formulate this problem as a multi-armed bandit problem (and various
generalizations thereof) under incentive-compatibility constraints induced by
the agents' Bayesian priors. We design an incentive-compatible bandit algorithm
for the social planner whose regret is asymptotically optimal among all bandit
algorithms (incentive-compatible or not). Further, we provide a black-box
reduction from an arbitrary multi-arm bandit algorithm to an
incentive-compatible one, with only a constant multiplicative increase in
regret. This reduction works for very general bandit setting that incorporate
contexts and arbitrary auxiliary feedback.


  Devices equipped with accelerometer sensors such as today's mobile devices
can make use of motion to exchange information. A typical example for shared
motion is shaking of two devices which are held together in one hand. Deriving
a shared secret (key) from shared motion, e.g. for device pairing, is an
obvious application for this. Only the keys need to be exchanged between the
peers and neither the motion data nor the features extracted from it. This
makes the pairing fast and easy. For this, each device generates an information
signal (key) independently of each other and, in order to pair, they should be
identical. The key is essentially derived by quantizing certain well
discriminative features extracted from the accelerometer data after an implicit
synchronization. In this paper, we aim at finding a small set of effective
features which enable a significantly simpler quantization procedure than the
prior art. Our tentative results with authentic accelerometer data show that
this is possible with a competent accuracy ($76$%) and key strength (entropy
approximately $15$ bits).


  Atomic basis sets are widely employed within quantum mechanics based
simulations of matter. We introduce a machine learning model that adapts the
basis set to the local chemical environment of each atom, prior to the start of
self consistent field (SCF) calculations. In particular, as a proof of
principle and because of their historic popularity, we have studied the
Gaussian type orbitals from the Pople basis set, i.e. the STO-3G, 3-21G, 6-31G
and 6-31G*. We adapt the basis by scaling the variance of the radial Gaussian
functions leading to contraction or expansion of the atomic orbitals.A data set
of optimal scaling factors for C, H, O, N and F were obtained by variational
minimization of the Hartree-Fock (HF) energy of the smallest 2500 organic
molecules from the QM9 database. Kernel ridge regression based machine learning
(ML) prediction errors of the change in scaling decay rapidly with training set
size, typically reaching less than 1 % for training set size 2000. Overall, we
find systematically lower variance, and consequently the larger training
efficiencies, when going from hydrogen to carbon to nitrogen to oxygen. Using
the scaled basis functions obtained from the ML model, we conducted HF
calculations for the subsequent 30'000 molecules in QM9. In comparison to the
corresponding default Pople basis set results we observed improved energetics
in up to 99 % of all cases. With respect to the larger basis set
6-311G(2df,2pd), atomization energy errors are lowered on average by ~31, 107,
11, and 11 kcal/mol for STO-3G, 3-21G, 6-31G and 6-31G*, respectively -- with
negligible computational overhead. We illustrate the high transferability of
adaptive basis sets for larger out-of-domain molecules relevant to addiction,
diabetes, pain, aging.


  We evaluate the evolution operator Z_Reg(R_2,R_1) introduced by Diakonov and
Petrov for the definition of the Wilson loop in terms of a path integral over
gauge degrees of freedom. We use the procedure suggested by Diakonov and Petrov
(Phys. Lett. B224 (1989) 131) and show that the evolution operator vanishes.


  Data on functional disability are of widespread policy interest in the United
States, especially with respect to planning for Medicare and Social Security
for a growing population of elderly adults. We consider an extract of
functional disability data from the National Long Term Care Survey (NLTCS) and
attempt to develop disability profiles using variations of the Grade of
Membership (GoM) model. We first describe GoM as an individual-level mixture
model that allows individuals to have partial membership in several mixture
components simultaneously. We then prove the equivalence between
individual-level and population-level mixture models, and use this property to
develop a Markov Chain Monte Carlo algorithm for Bayesian estimation of the
model. We use our approach to analyze functional disability data from the
NLTCS.


  Machine learning models are prone to making incorrect predictions on inputs
that are far from the training distribution. This hinders their deployment in
safety-critical applications such as autonomous vehicles and healthcare. The
detection of a shift from the training distribution of individual datapoints
has gained attention. A number of techniques have been proposed for such
out-of-distribution (OOD) detection. But in many applications, the inputs to a
machine learning model form a temporal sequence. Existing techniques for OOD
detection in time-series data either do not exploit temporal relationships in
the sequence or do not provide any guarantees on detection. We propose using
deviation from the in-distribution temporal equivariance as the non-conformity
measure in conformal anomaly detection framework for OOD detection in
time-series data.Computing independent predictions from multiple conformal
detectors based on the proposed measure and combining these predictions by
Fisher's method leads to the proposed detector CODiT with guarantees on false
detection in time-series data. We illustrate the efficacy of CODiT by achieving
state-of-the-art results on computer vision datasets in autonomous driving. We
also show that CODiT can be used for OOD detection in non-vision datasets by
performing experiments on the physiological GAIT sensory dataset. Code, data,
and trained models are available at
https://github.com/kaustubhsridhar/time-series-OOD.


  We present a multi-task learning framework to enable the training of one
universal incremental dialogue processing model with four tasks of disfluency
detection, language modelling, part-of-speech tagging, and utterance
segmentation in a simple deep recurrent setting. We show that these tasks
provide positive inductive biases to each other with the optimal contribution
of each one relying on the severity of the noise from the task. Our live
multi-task model outperforms similar individual tasks, delivers competitive
performance, and is beneficial for future use in conversational agents in
psychiatric treatment.


  In this paper, we combine the techniques of enlargement of filtrations and
stochastic control theory to establish an extension of the verification
theorem, where the coefficients of the stochastic controlled equation are
adapted to the underlying filtration and the controls are adapted to a bigger
filtration $\mathbf{G}$ than the one generated by the corresponding Brownian
motion $B$. Using the forward integral defined by Russo and Vallois
\cite{RV1993}, we show that there is a $\mathbf{G}$-adapted optimal control
with respect to a certain cost functional if and only if the Brownian motion
$B$ is a $\mathbf{G}$-semimartingale. The extended verification theorem allows
us to study a financial market with an insider in order to take advantage of
the extra information that the insider has from the beginning. Finally, we
consider two examples throughout the extended verification theorem. These
problems appear in financial markets with an insider.


  The general principles of Bayesian data analysis imply that models for survey
responses should be constructed conditional on all variables that affect the
probability of inclusion and nonresponse, which are also the variables used in
survey weighting and clustering. However, such models can quickly become very
complicated, with potentially thousands of poststratification cells. It is then
a challenge to develop general families of multilevel probability models that
yield reasonable Bayesian inferences. We discuss in the context of several
ongoing public health and social surveys. This work is currently open-ended,
and we conclude with thoughts on how research could proceed to solve these
problems.


  Let \sigma(n) be the sum of divisors of a positive integer n. Robin's theorem
states that the Riemann hypothesis is equivalent to the inequality
\sigma(n)<e^\gamma n\log\log n for all n>5040 (\gamma is Euler's constant). It
is a natural question in this direction to find a first integer, if exists,
which violates this inequality. Following this process, we introduce a new
sequence of numbers and call it as extremely abundant numbers. In this paper we
show that the Riemann hypothesis is true, if and only if, there are infinitely
many of these numbers. Moreover, we investigate some of their properties
together with superabundant and colossally abundant numbers.


  We report two novel fabrication techniques, as well as spectral transmission
and propagation loss measurements of the subwavelength plastic wires with
highly porous (up to 86%) and non-porous transverse geometries. The two
fabrication techniques we describe are based on the microstructured molding
approach. In one technique the mold is made completely from silica by stacking
and fusing silica capillaries to the bottom of a silica ampoule. The melted
material is then poured into the silica mold to cast the microstructured
preform. Another approach uses microstructured mold made of plastic which is
co-drawn with a cast preform. Material of the mold is then dissolved after
fiber drawing. We also describe a novel THz-TDS setup with an easily adjustable
optical path length, designed to perform cutback measurements using THz fibers
of up to 50 cm in length. We find that while both porous and non-porous
subwavelength fibers of the same outside diameter have low propagation losses
(\alpha \leg 0.02cm-1), however, the porous fibers exhibit a much wider
spectral transmission window and enable transmission at higher frequencies
compared to the non-porous fibers. We then show that the typical bell-shaped
transmission spectra of the subwavelengths fibers can be very well explained by
the onset of material absorption loss at higher frequencies due to strong
confinement of the modal fields in the material region of the fiber, as well as
strong coupling loss at lower frequencies due to mismatch of the modal field
diameter and a size of the gaussian-like beam of a THz source.


  Let $K$ be a global field of characteristic $p>0$. We study the cohomology of
arithmetic subgroups $\Gamma $ of $SL_{n+1}(K)$ (with respect to a fixed place
of $K$), under the hypothesis that these groups have no $p'$-torsion (any
arithmetic group possesses a normal subgroup of finite index without
$p'$-torsion). We define the cohomology of $\Gamma $ with compact supports and
values in ${\Bbb Z}[1/p]$, and we relate it to spaces of harmonic cocycles,
also with compact supports (\S 3). We give a description of the locus of these
supports, in particular by introducing a notion of cusp in dimension $n\geq 1$
(\S 4) and we calculate "geometrically" the Euler-Poincar\'e characteristic of
this cohomology, up to torsion (\S 5).


  We consider field theories that exhibit a supersymmetric Lifshitz scaling
with two real supercharges. The theories can be formulated in the language of
stochastic quantization. We construct the free field supersymmetry algebra with
rotation singlet fermions for an even dynamical exponent $z=2k$ in an arbitrary
dimension. We analyze the classical and quantum $z=2$ supersymmetric
interactions in $2+1$ and $3+1$ spacetime dimensions and reveal a supersymmetry
preserving quantum diagrammatic cancellation. Stochastic quantization indicates
that Lifshitz scale invariance is broken in the $(3+1)$-dimensional quantum
theory.


  The formation of planets is directly linked to the evolution of the
circumstellar (CS) disk from which they are born. The dissipation timescales of
CS disks are, therefore, of direct astrophysical importance in evaluating the
time available for planet formation. We employ Spitzer Space Telescope spectra
to complete the CS disk census for the late-type members of the ~8 Myr-old eta
Chamaeleontis star cluster. Of the 15 K- and M-type members, eight show excess
emission. We find that the presence of a CS disk is anti-correlated with
binarity, with all but one disk associated with single stars. With nine single
stars in total, about 80% retain a CS disk. Of the six known or suspected close
binaries the only CS disk is associated with the primary of RECX 9. No
circumbinary disks have been detected. We also find that stars with disks are
slow rotators with surface values of specific angular momentum j = 2-15 j_sun.
All high specific angular momentum systems with j = 20-30 j_sun are confined to
the primary stars of binaries. This provides novel empirical evidence for
rotational disk locking and again demonstrates the much shorter disk lifetimes
in close binary systems compared to single star systems. We estimate the
characteristic mean disk dissipation timescale to be ~5 Myr and ~9 Myr for the
binary and single star systems, respectively.


  We study hairy black holes in Einstein-Maxwell-complex scalar theory in
four-dimensional asymptotically global anti-de Sitter (AdS) spacetime when the
Robin boundary conditions are imposed on the scalar field. This setup is dual
to the double trace deformation of strongly interacting field theory on $R
\times S^2$ by charged scalar operators. We identify the instability of the
Reissner-Nordstr\"{o}m-AdS (RNAdS) black holes under the Robin boundary
conditions and construct backreacted geometries branching at the onset of the
instability. Also considering associated horizonless geometries called boson
stars, we obtain phase diagrams with fairly rich structure in the grand
canonical ensemble depending on the boundary condition parameter or the
deformation parameter, where phase transition occurs between thermal AdS,
RNAdS, charged boson stars, and hairy black holes.


  This survey describes some useful properties of the local homology of
abstract simplicial complexes. Although the existing literature on local
homology is somewhat dispersed, it is largely dedicated to the study of
manifolds, submanifolds, or samplings thereof. While this is a vital
perspective, the focus of this survey is squarely on the local homology of
abstract simplicial complexes. Our motivation comes from the needs of the
analysis of hypergraphs and graphs. In addition to presenting many classical
facts in a unified way, this survey presents a few new results about how local
homology generalizes useful tools from graph theory. The survey ends with a
statistical comparison of graph invariants with local homology.


  Quantum embedding theories are powerful tools for approximately solving
large-scale strongly correlated quantum many-body problems. The main idea of
quantum embedding is to glue together a highly accurate quantum theory at the
local scale and a less accurate quantum theory at the global scale. We
introduce the first quantum embedding theory that is also variational, in that
it is guaranteed to provide a one-sided bound for the exact ground-state
energy. Our method, which we call the variational embedding method, provides a
lower bound for this quantity. The method relaxes the representability
conditions for quantum marginals to a set of linear and semidefinite
constraints that operate at both local and global scales, resulting in a
semidefinite program (SDP) to be solved numerically. The accuracy of the method
can be systematically improved. The method is versatile and can be applied, in
particular, to quantum many-body problems for both quantum spin systems and
fermionic systems, such as those arising from electronic structure
calculations. We describe how the proper notion of quantum marginal,
sufficiently general to accommodate both of these settings, should be phrased
in terms of certain algebras of operators. We also investigate the duality
theory for our SDPs, which offers valuable perspective on our method as an
embedding theory. As a byproduct of this investigation, we describe a
formulation for efficiently implementing the variational embedding method via a
partial dualization procedure and the solution of quantum analogs of the
Kantorovich problem from optimal transport theory.


  The Holomorphic Embedding Load flow Method (HELM) employs complex analysis to
solve the load flow problem. It guarantees finding the correct solution when it
exists, and identifying when a solution does not exist. The method, however, is
usually computationally less efficient than the traditional Newton-Raphson
algorithm, which is generally considered to be a slow method in distribution
networks. In this paper, we present two HELM modifications that exploit the
radial and weakly meshed topology of distribution networks and significantly
reduce computation time relative to the original HELM implementation. We also
present comparisons with several popular load flow algorithms applied to
various test distribution networks.


  We discuss reductions of general N=1 four dimensional gauge theories on S^2.
The effective two dimensional theory one obtains depends on the details of the
coupling of the theory to background fields, which can be translated to a
choice of R-symmetry. We argue that, for special choices of R-symmetry, the
resulting two dimensional theory has a natural interpretation as an N=(0,2)
gauge theory. As an application of our general observations, we discuss
reductions of N=1 and N=2 dualities and argue that they imply certain two
dimensional dualities.


  We investigate thermal regime of the baryons behind shock waves arising in
the process of virialization of dark matter halos. We find a fraction of the
shocked gas cooled by radiation of HD molecules down to the temperature of the
cosmic microwave background (CMB): this fraction increases sharply from about
$f_{\rm c}\sim 10^{-3}$ for dark halos of $M=5\times 10^7\msun$ to $\sim 0.1$
for halos with $M=10^8\msun$ at $z=10$. We show, however, that further increase
of the mass does not lead to a significant growth of $f_{\rm c}$ -- the
assymptotic value for $M\gg 10^8\msun$ is of 0.2. We estimate star formation
rate associated with such shock waves, and show that it can be a small but not
negligible fraction of the star formation connected with cooling by HI and
H$_2$. We argue that extremely metal-poor low-mass stars in the Milky Way may
have been formed from primordial gas behind such shocks.


  Reinforcement Learning (RL) has been used to finetune Large Language Models
(LLMs) using a reward model trained from preference data, to better align with
human judgment. The recently introduced direct alignment methods, which are
often simpler, more stable, and computationally lighter, can more directly
achieve this. However, these approaches cannot optimize arbitrary rewards, and
the preference-based ones are not the only rewards of interest for LLMs (eg.,
unit tests for code generation or textual entailment for summarization, among
others). RL-finetuning is usually done with a variation of policy gradient,
which calls for on-policy or near-on-policy samples, requiring costly
generations. We introduce Contrastive Policy Gradient, or CoPG, a simple and
mathematically principled new RL algorithm that can estimate the optimal policy
even from off-policy data. It can be seen as an off-policy policy gradient
approach that does not rely on important sampling techniques and highlights the
importance of using (the right) state baseline. We show this approach to
generalize the direct alignment method IPO (identity preference optimization)
and classic policy gradient. We experiment with the proposed CoPG on a toy
bandit problem to illustrate its properties, as well as for finetuning LLMs on
a summarization task, using a learned reward function considered as ground
truth for the purpose of the experiments.


  We present measurements of the spatial clustering of ultraluminous infrared
galaxies in two redshift intervals, 1.5<z<2.0 and 2<z<3. Both samples cluster
strongly, with r_0=14.40+/-1.99 h^-1 Mpc for the 2<z<3 sample, and
r_0=9.40+/-2.24 h^-1 Mpc for the 1.5<z<2.0 sample, making them among the most
biased galaxies at these epochs. These clustering amplitudes are consistent
with both populations residing in dark matter haloes with masses of ~6x10^13
solar masses. We infer that a minimum dark matter halo mass is an important
factor for all forms of luminous, obscured activity in galaxies at z>1.
Adopting plausible models for the growth of DM haloes with redshift, then the
haloes hosting the 2<z<3 sample will likely host the richest clusters of
galaxies at z=0, whereas the haloes hosting the 1.5<z<2.0 sample will likely
host poor to rich clusters at z=0.


  We re-examine the age-velocity dispersion relation in the solar neighborhood
using improved stellar age estimates that are based on Hipparcos parallaxes and
recent stellar evolution calculations. The resulting relation shows that the
Milky Way stellar disk was relatively quiescent, suffering little heating or
dispersion increase between 3 and 9 Gyrs. However, at an age of 9 Gyrs there is
an abrupt increase in the stellar velocity dispersions. To explain the abrupt
increase (by almost a factor of 2) in dispersions we propose that the Milky Way
suffered a minor merger 9 Gyrs ago that created the thick disk. The quiescent
phase is consistent with inefficient heating caused by scattering from tightly
wound transient spiral structure. It is possible that many galaxy disks have
radial velocity dispersions at the point where heating from spiral structure
becomes inefficient. Surface brightness profiles and dispersion measurements
can be used to predict spiral arm winding numbers at this saturation point. A
comparison between the observed and predicted winding numbers could test this
hypothesis and also search for evidence of merger induced disk heating in
nearby galaxies.


  We posit that autoregressive flow models are well-suited to performing a
range of causal inference tasks - ranging from causal discovery to making
interventional and counterfactual predictions. In particular, we exploit the
fact that autoregressive architectures define an ordering over variables,
analogous to a causal ordering, in order to propose a single flow architecture
to perform all three aforementioned tasks. We first leverage the fact that flow
models estimate normalized log-densities of data to derive a bivariate measure
of causal direction based on likelihood ratios. Whilst traditional measures of
causal direction often require restrictive assumptions on the nature of causal
relationships (e.g., linearity),the flexibility of flow models allows for
arbitrary causal dependencies. Our approach compares favourably against
alternative methods on synthetic data as well as on the Cause-Effect Pairs
bench-mark dataset. Subsequently, we demonstrate that the invertible nature of
flows naturally allows for direct evaluation of both interventional and
counterfactual predictions, which require marginalization and conditioning over
latent variables respectively. We present examples over synthetic data where
autoregressive flows, when trained under the correct causal ordering, are able
to make accurate interventional and counterfactual predictions


  A set of two-dimensional semi-riemannian submanifolds of flat semi-riemannian
manifolds is associated to each Toda theory. The method and an example are
given to Toda theories associated to real finite dimensional Lie algebras.


  Background: Biological data often originate from samples containing mixtures
of subpopulations, corresponding e.g. to distinct cellular phenotypes. However,
identification of distinct subpopulations may be difficult if biological
measurements yield distributions that are not easily separable. Results: We
present Multiresolution Correlation Analysis (MCA), a method for visually
identifying subpopulations based on the local pairwise correlation between
covariates, without needing to define an a priori interaction scale. We
demonstrate that MCA facilitates the identification of differentially regulated
subpopulations in simulated data from a small gene regulatory network, followed
by application to previously published single-cell qPCR data from mouse
embryonic stem cells. We show that MCA recovers previously identified
subpopulations, provides additional insight into the underlying correlation
structure, reveals potentially spurious compartmentalizations, and provides
insight into novel subpopulations. Conclusions: MCA is a useful method for the
identification of subpopulations in low-dimensional expression data, as
emerging from qPCR or FACS measurements. With MCA it is possible to investigate
the robustness of covariate correlations with respect subpopulations,
graphically identify outliers, and identify factors contributing to
differential regulation between pairs of covariates. MCA thus provides a
framework for investigation of expression correlations for genes of interests
and biological hypothesis generation.


  A qualitative analysis is given to the data on the full magnetic and velocity
vector fields in a growing sunspot group, recorded nearly simultaneously with
the Solar Optical Telescope on the Hinode satellite. Observations of a young
bipolar subregion developing within AR 11313 were carried out on 9-10 October
2011. Our aim was to form am idea about the consistency of the observed pattern
with the well-known rising-tube model of the formation of bipolar acrive
regions and sunspot groups. We find from our magnetograms that the
distributions of the vertical [B_v] and the horizontal [B_h] component of the
magnetic field over the area of the magnetic subregion are spatially well
correlated; in contrast, the rise of a flux-tube loop would result in a
qualitatively different pattern, with the maxima of the two magnetic-field
components spatially separated: the vertical field would be the strongest where
either spot emerges, while the maximum horizontal-field strengths would be
reached in between them. A specific feature, which we call the bordering
effect, is revealed: some local extrema of B_v are bordered with areas of
locally enhanced B_h. This effect suggests a fountainlike spatial structure of
the magnetic field near the B_v extrema, which is also hardly compatible with
the emergence of a flux-tube loop. The vertical-velocity field in the area of
the developing active subregion does not exhibit any upflow on the scale of the
whole subregion, which should be related to the rising-tube process. Thus, our
observational data can hardly be interpreted in the framework of the
rising-tube model.


  In this paper, a unified gas-kinetic scheme (UGKS) with simplified
multi-scale numerical flux is proposed for the thermodynamic non-equilibrium
flow simulation involving the excitation of molecular vibrational degrees of
freedom in all flow regimes. The present UGKS keep the basic conservation laws
of the macroscopic flow variables and the microscopic gas distribution function
in a discretized space. In order to improve the efficiency of the UGKS, a
simplify multi-scale numerical flux is directly constructed from the
characteristic difference solution of the kinetic model equation. In addition,
a new BGK-type kinetic model for diatomic gases is proposed to describe the
high-temperature thermodynamic non-equilibrium effect, which is a
phenomenological relaxation model with the continuous distribution modes of
rotational and vibrational energies. In present model, the equilibrium
distribution functions is constructed by using a multi-dimensional Hermitian
expansion around the Maxwellian distribution to achieve the correct Prandtl
number and proper relaxation rate of heat fluxes. Furthermore, the application
of the unstructured discrete velocity space (DVS) and a simple integration
error correction reduce the number of velocity mesh significantly and make the
present method be a efficient tool for simulations of flows in all flow
regimes. The new scheme are examined in a series of cases, such as Sod's shock
tube, high non-equilibrium shock structure, hypersonic flow around a circular
cylinder with Knudsen (Kn) number Kn = 0.01, and the rarefied hypersonic flow
over a flat plate with a sharp leading edge. The present UGKS results agree
well with the benchmark data of DSMC and the other validated methods.


  Automatic Dependent Surveillance - Broadcast (ADS-B) is the next generation
communication technology selected for allowing commercial and military aircraft
to deliver flight information to both ground base stations and other airplanes.
Today, it is already on-board of 80% of commercial aircraft, and it will become
mandatory by the 2020 in the US and the EU. ADS-B has been designed without any
security consideration --- messages are delivered wirelessly in clear text and
they are not authenticated. In this paper we propose Securing Open Skies (SOS),
a lightweight and standard-compliant framework for securing ADS-B technology
wireless communications. SOS leverages the well-known \muTESLA protocol, and
includes some modifications necessary to deal with the severe bandwidth
constraints of the ADS-B communication technology. In addition, SOS is
resilient against message injection attacks, by recurring to majority voting
techniques applied on central community servers. Overall, SOS emerges as a
lightweight security solution, with a limited bandwidth overhead, that does not
require any modification to the hardware already deployed. Further, SOS is
standard compliant and able to reject active adversaries aiming at disrupting
the correct functioning of the communication system. Finally, comparisons
against state-of-the-art solutions do show the superior quality and viability
of our solution.


  Out-of-time-order correlators (OTOC), recently being the center of discussion
on quantum chaos, are a tool to understand the information scrambling in
different phases of quantum many-body systems. We propose a disordered ladder
spin model, XX-ladder, which can be designed in a scalable cold atom setup to
detect OTOC with a novel sign reversal protocol for the evolution backward in
time. We study both the clean and disordered limits of XX-ladder and
characterize different phases (ergodic-MBL) of the model based on the decay
properties of OTOCs. Emergent effective lightcone shows sublinear behaviour,
while the butterfly cones drastically differ from the lightcone via
demonstrating superlinear behaviour. Based on our results, one can observe how
the information scrambling changes in the transition from well-studied 1D spin
models to unexplored 2D spin models in a local setting.


  Imitation learning (IL) is a simple and powerful way to use high-quality
human driving data, which can be collected at scale, to produce human-like
behavior. However, policies based on imitation learning alone often fail to
sufficiently account for safety and reliability concerns. In this paper, we
show how imitation learning combined with reinforcement learning using simple
rewards can substantially improve the safety and reliability of driving
policies over those learned from imitation alone. In particular, we train a
policy on over 100k miles of urban driving data, and measure its effectiveness
in test scenarios grouped by different levels of collision likelihood. Our
analysis shows that while imitation can perform well in low-difficulty
scenarios that are well-covered by the demonstration data, our proposed
approach significantly improves robustness on the most challenging scenarios
(over 38% reduction in failures). To our knowledge, this is the first
application of a combined imitation and reinforcement learning approach in
autonomous driving that utilizes large amounts of real-world human driving
data.


  Novel data acquisition schemes have been an emerging need for scanning
microscopy based imaging techniques to reduce the time in data acquisition and
to minimize probing radiation in sample exposure. Varies sparse sampling
schemes have been studied and are ideally suited for such applications where
the images can be reconstructed from a sparse set of measurements. Dynamic
sparse sampling methods, particularly supervised learning based iterative
sampling algorithms, have shown promising results for sampling pixel locations
on the edges or boundaries during imaging. However, dynamic sampling for
imaging skeleton-like objects such as metal dendrites remains difficult. Here,
we address a new unsupervised learning approach using Hierarchical Gaussian
Mixture Mod- els (HGMM) to dynamically sample metal dendrites. This technique
is very useful if the users are interested in fast imaging the primary and
secondary arms of metal dendrites in solidification process in materials
science.


  The polarization properties of macroscopic Bell states are characterized
using three-dimensional quantum polarization tomography. This method utilizes
three-dimensional inverse Radon transform to reconstruct the polarization
quasiprobability distribution function of a state from the probability
distributions measured for various Stokes observables. The reconstructed 3D
distributions obtained for the macroscopic Bell states are compared with those
obtained for a coherent state with the same mean photon number. The results
demonstrate squeezing in one or more Stokes observables.


  Globular clusters are dense stellar systems whose core slowly contracts under
the effect of self-gravity. The rate of this process was recently found to be
directly linked to the initial amount of velocity anisotropy: tangentially
anisotropic clusters contract faster than radially anisotropic ones.
Furthermore, initially anisotropic clusters are found to generically tend
towards more isotropic distributions during the onset of contraction.
Chandrasekhar's "non-resonant" (NR) theory of diffusion describes this
relaxation as being driven by a sequence of local two-body deflections along
each star's orbit. We explicitly tailor this NR prediction to anisotropic
clusters, and compare it with $N$-body realisations of Plummer spheres with
varying degrees of anisotropy. The NR theory is shown to recover remarkably
well the detailed shape of the orbital diffusion and the associated initial
isotropisation, up to a global multiplicative prefactor which increases with
anisotropy. Strikingly, a simple effective isotropic prescription provides
almost as good a fit, as long as the cluster's anisotropy is not too strong.
For these more extreme clusters, accounting for long-range resonant relaxation
may be necessary to capture these clusters' long-term evolution.


  We study the three-dimensional atomic Bose gas using renormalization group
techniques. Using our knowledge of the microscopic details of the interatomic
interaction, we determine the correct initial values of our renormalization
group equations and thus obtain also information on nonuniversal properties. As
a result, we can predict for instance the critical temperature of the gas and
the superfluid and condensate density of the Bose-Einstein condensed phase in
the regime $na\Lambda_{th}^2\ll 1$.


  Privacy is a major issue in learning from distributed data. Recently the
cryptographic literature has provided several tools for this task. However,
these tools either reduce the quality/accuracy of the learning
algorithm---e.g., by adding noise---or they incur a high performance penalty
and/or involve trusting external authorities.
  We propose a methodology for {\sl private distributed machine learning from
light-weight cryptography} (in short, PD-ML-Lite). We apply our methodology to
two major ML algorithms, namely non-negative matrix factorization (NMF) and
singular value decomposition (SVD). Our resulting protocols are communication
optimal, achieve the same accuracy as their non-private counterparts, and
satisfy a notion of privacy---which we define---that is both intuitive and
measurable. Our approach is to use lightweight cryptographic protocols (secure
sum and normalized secure sum) to build learning algorithms rather than wrap
complex learning algorithms in a heavy-cost MPC framework.
  We showcase our algorithms' utility and privacy on several applications: for
NMF we consider topic modeling and recommender systems, and for SVD, principal
component regression, and low rank approximation.


  In the present work we show that the correct determination of surface
morphology using Scanning Force Microscopy (SFM) imaging and Power Spectral
Density (PSD) analysis of the surface roughness is an extremely demanding task
that is easily affected by experimental parameters such as scan speed and
feedback parameters. We present examples were the measured topography data is
significantly influenced by the feedback response of the SFM system and the PSD
curves calculated from this experimental data do not correspond to that of the
true topography. Instead, either features are "lost" due to low pass filtering
or features are "created" due to oscillation of the feedback loop. In order to
overcome these serious problems we show that the interaction signal (error
signal) can be used not only to quantitatively control but also to
significantly improve the quality of the topography raw data used for the PSD
analysis. In particular, the calibrated error signal image can be used in
combination with the topography image in order to obtain a correct
representation of surface morphology ("true" topographic image). From this
"true" topographic image a faithful determination of the PSD of surface
morphology is possible. The corresponding PSD curve is not affected by the
fine-tuning of feedback parameters, and allows for much faster image
acquisition speeds without loss information in the PSD curve.


  PLAnetary Transits and Oscillations of stars (PLATO) is the ESA M3 space
mission dedicated to detect and characterise transiting exoplanets including
information from the asteroseismic properties of their stellar hosts. The
uninterrupted and high-precision photometry provided by space-borne instruments
such as PLATO require long preparatory phases. An exhaustive list of tests are
paramount to design a mission that meets the performance requirements, and as
such, simulations are an indispensable tool in the mission preparation. To
accommodate PLATO's need of versatile simulations prior to mission launch -
that at the same time describe accurately the innovative but complex
multi-telescope design - we here present the end-to-end PLATO simulator
specifically developed for the purpose, namely PlatoSim. We show step-by-step
the algorithms embedded into the software architecture of PlatoSim that allow
the user to simulate photometric time series of CCD images and light curves in
accordance to the expected observations of PLATO. In the context of the PLATO
payload, a general formalism of modelling, end-to-end, incoming photons from
the sky to the final measurement in digital units is discussed. We show the
strong predictive power of PlatoSim through its diverse applicability and
contribution to numerous working groups within the PLATO Mission Consortium.
This involves the on-going mechanical integration and alignment, performance
studies of the payload, the pipeline development and assessments of the
scientific goals. PlatoSim is a state-of-the-art simulator that is able to
produce the expected photometric observations of PLATO to a high level of
accuracy. We demonstrate that PlatoSim is a key software tool for the PLATO
mission in the preparatory phases until mission launch and prospectively
beyond.


  Aims: ARCiS, a novel code for the analysis of exoplanet transmission and
emission spectra is presented. The aim of the modelling framework is to provide
a tool able to link observations to physical models of exoplanet atmospheres.
Methods: The modelling philosophy chosen in this paper is to use physical and
chemical models to constrain certain parameters while keeping free the parts
where our physical understanding is still more limited. This approach, in
between full physical modelling and full parameterisation, allows us to use the
processes we understand well and parameterise those less understood. A Bayesian
retrieval framework is implemented and applied to the transit spectra of a set
of 10 hot Jupiters. The code contains chemistry and cloud formation and has the
option for self consistent temperature structure computations. Results: The
code presented is fast and flexible enough to be used for retrieval and for
target list simulations for e.g. JWST or the ESA Ariel missions. We present
results for the retrieval of elemental abundance ratios using the physical
retrieval framework and compare this to results obtained using a parameterised
retrieval setup. Conclusions: We conclude that for most of the targets
considered the current dataset is not constraining enough to reliably pin down
the elemental abundance ratios. We find no significant correlations between
different physical parameters. We confirm that planets in our sample with a
strong slope in the optical transmission spectrum are the planets where we find
cloud formation to be most active. Finally, we conclude that with ARCiS we have
a computationally efficient tool to analyse exoplanet observations in the
context of physical and chemical models.


  Motivated by recent works on ``Higgsless theories,'' I discuss an
$SU(2)_0\times SU(2)^{N}\times U(1)$ gauge theory with arbitrary bifundamental
(or custodial SU(2) preserving) symmetry breaking between the gauge subgroups
and with ordinary matter transforming only under the U(1) and $SU(2)_0$. When
the couplings, $g_j$, of the other SU(2)s are very large, this reproduces the
standard model at the tree level. I calculate the $W$ and $Z$ masses and other
electroweak parameters in a perturbative expansion in $1/g_j^2$, and give
physical interpretations of the results in a mechanical analog built out of
masses and springs. In the mechanical analog, it is clear that even for
arbitrary patterns of symmetry breaking, it is not possible (in the
perturbative regime) to raise the Higgs mass by a large factor while keeping
the $S$ parameter small.


  We consider the astrophysical implications of the diffusion equation solution
for Ultra-High Energy Cosmic Rays (UHECR) in the expanding universe, obtained
in paper I (V.Berezinsky & A.Gazizov, ApJ 643 (2006) 8). The UHECR spectra are
calculated in a model with sources located in vertices of the cubic grid with a
linear constant (source separation) d. The calculations are performed for
various magnetic field configurations (B_c,l_c), where l_c is the basic scale
of the turbulence and B_c is the coherent magnetic field on this scale. The
main purpose of these calculations is to demonstrate the validity of the
solution obtained in paper I and to compare this solution with the Syrovatsky
solution used in previous works. The Syrovatsky solution must be necessarily
embedded in the static cosmological model. The formal comparison of the two
solutions with all parameters being fixed identically reveals the appreciable
discrepancies between two spectra. These discrepancies are less if in both
models the different sets of the best-fit parameters are used.


  In this paper, we present a multimodal approach to simultaneously analyze
facial movements and several peripheral physiological signals to decode
individualized affective experiences under positive and negative emotional
contexts, while considering their personalized resting dynamics. We propose a
person-specific recurrence network to quantify the dynamics present in the
person's facial movements and physiological data. Facial movement is
represented using a robust head vs. 3D face landmark localization and tracking
approach, and physiological data are processed by extracting known attributes
related to the underlying affective experience. The dynamical coupling between
different input modalities is then assessed through the extraction of several
complex recurrent network metrics. Inference models are then trained using
these metrics as features to predict individual's affective experience in a
given context, after their resting dynamics are excluded from their response.
We validated our approach using a multimodal dataset consists of (i) facial
videos and (ii) several peripheral physiological signals, synchronously
recorded from 12 participants while watching 4 emotion-eliciting video-based
stimuli. The affective experience prediction results signified that our
multimodal fusion method improves the prediction accuracy up to 19% when
compared to the prediction using only one or a subset of the input modalities.
Furthermore, we gained prediction improvement for affective experience by
considering the effect of individualized resting dynamics.