  Let $P, Q$ be Heegaard surfaces of a closed orientable 3-manifold. In this
paper, we introduce a method for giving an upper bound of Hempel distance of
$P$ by using the Reeb graph derived from a certain horizontal arc in the
ambient space $[0,1]\times[0,1]$ of the Rubinstein-Scharlemann graphic derived
from $P$ and $Q$. This is a refinement of a part of Johnson's arguments used
for determining stable genera required for flipping high distance Heegaard
splittings.


  We employ the method of differential regularization to calculate explicitly
the one-loop effective action of a bosonized $U_L(3)\times U_R(3)$ extended
Nambu--Jona-Lasinio model consisting of scalar, pseudoscalar, vector and axial
vector fields.


  We describe a simple procedure for reducing ADC common noise in modular
detectors that does not require additional hardware. A method using detector
noise groups should work well for modular particle detectors such as segmented
electromagnetic calorimeters, plastic scintillator hodoscopes, cathode strip
wire chambers, segmented active targets, and the like. We demonstrate a
``second pedestal noise correction'' method by comparing representative ADC
pedestal spectra for various elements of the PIBETA detector before and after
the applied correction.


  The self-join finds all objects in a dataset within a threshold of each other
defined by a similarity metric. As such, the self-join is a building block for
the field of databases and data mining, and is employed in Big Data
applications. In this paper, we advance a GPU-efficient algorithm for the
similarity self-join that uses the Euclidean distance metric. The
search-and-refine strategy is an efficient approach for low dimensionality
datasets, as index searches degrade with increasing dimension (i.e., the curse
of dimensionality). Thus, we target the low dimensionality problem, and compare
our GPU self-join to a search-and-refine implementation, and a state-of-the-art
parallel algorithm. In low dimensionality, there are several unique challenges
associated with efficiently solving the self-join problem on the GPU. Low
dimensional data often results in higher data densities, causing a significant
number of distance calculations and a large result set. As dimensionality
increases, index searches become increasingly exhaustive, forming a performance
bottleneck. We advance several techniques to overcome these challenges using
the GPU. The techniques we propose include a GPU-efficient index that employs a
bounded search, a batching scheme to accommodate large result set sizes, and a
reduction in distance calculations through duplicate search removal. Our GPU
self-join outperforms both search-and-refine and state-of-the-art algorithms.


  We consider the location and order of capillary condensation transitions
occurring in deep grooves of width $L$ and depth $D$. For walls that are
completely wet by liquid (contact angle $\theta=0$) the transition is
continuous and its location is not sensitive to the depth of the groove.
However for walls which are partially wet by liquid, where the transition is
first-order, we show that the pressure at which it occurs is determined by a
modified Kelvin equation characterized by an edge contact angle $\theta_E$
describing the shape of the meniscus formed at the top of the groove. The
dependence of $\theta_E$ on the groove depth $D$ relies, in turn, on whether
corner menisci are formed at the bottom of the groove in the low density
gas-like phase. While for macroscopically wide grooves these are always present
when $\theta<45\degree$ we argue that their formation is inhibited in narrow
grooves. This has a number of implications including that the local pining of
the meniscus and location of the condensation transition is different depending
on whether the contact angle is greater or less than a universal value
$\theta^*\approx 31\degree$. Our arguments are supported by detailed
microscopic density functional theory calculations which show that the modified
Kelvin equation remains highly accurate even when $L$ and $D$ are of the order
of tens of molecular diameters.


  In this paper we present a general forward fitting method for multichannel
image restoration based on regularized chi2. We introduce separable
regularizations that account for the dynamic of the model and take advantage of
the continuities present in the data, leaving only two hyper-parameters to
tune. We illustrate a practical implementation of this method in the context of
host galaxy subtraction for the Nearby SuperNova factory. We show that the
image restoration obtained fulfills the stringent requirements on bias and
photometricity needed by this program. The reconstruction yields sub-percent
integrated residuals in all the synthetic filters considered both on real and
simulated data. Even though our implementation is tied to the SNfactory data,
the method translates to any hyper-spectral data. As such, it is of direct
relevance to several new generation instruments like MUSE. Also, this technique
could be applied to multi-band astronomical imaging for which image
reconstruction is important, for example to increase image resolution for weak
lensing surveys.


  We introduce non-linear Dirac operators in $\mathbb{R}^{n}$ associated to the
$p$-harmonic equation and we extend to other contexts including spin manifolds
and the sphere.


  Recent advances in random matrix theory have spurred the adoption of
eigenvalue-based detection techniques for cooperative spectrum sensing in
cognitive radio. Most of such techniques use the ratio between the largest and
the smallest eigenvalues of the received signal covariance matrix to infer the
presence or absence of the primary signal. The results derived so far in this
field are based on asymptotical assumptions, due to the difficulties in
characterizing the exact distribution of the eigenvalues ratio. By exploiting a
recent result on the limiting distribution of the smallest eigenvalue in
complex Wishart matrices, in this paper we derive an expression for the
limiting eigenvalue ratio distribution, which turns out to be much more
accurate than the previous approximations also in the non-asymptotical region.
This result is then straightforwardly applied to calculate the decision
threshold as a function of a target probability of false alarm. Numerical
simulations show that the proposed detection rule provides a substantial
performance improvement compared to the other eigenvalue-based algorithms.


  In this paper, we demonstrate that it is possible to create an adiabatic
quantum computing algorithm that solves the shortest path between any two
vertices on an undirected graph with at most 3V qubits, where V is the number
of vertices of the graph. We do so without relying on any classical algorithms,
aside from creating a (V x V) adjacency matrix. The objective of this paper is
to demonstrate the fact that it is possible to model large graphs on an
adiabatic quantum computer using the maximum number of qubits available and
random graph generators such as the Barabasi-Albert and the Erdos-Renyi methods
which can scale based on a power law.


  We present the phase diagram and associated fixed points for a wide class of
Gauge-Yukawa theories in $d=4+\epsilon$ dimensions. The theories we investigate
involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten
limit. The analysis is performed in steps, we start with QCD$_d$ and then we
add Yukawa interactions and scalars which we study at next-to- and
next-to-next-to-leading order. Interacting infrared fixed points naturally
emerge in dimensions lower than four while ultraviolet ones appear above four.
We also analyse the stability of the scalar potential for the discovered fixed
points. We argue for a very rich phase diagram in three dimensions while in
dimensions higher than four certain Gauge-Yukawa theories are ultraviolet
complete because of the emergence of an asymptotically safe fixed point.


  An essential problem in statistics and machine learning is the estimation of
expectations involving PDFs with intractable normalizing constants. The
self-normalized importance sampling (SNIS) estimator, which normalizes the IS
weights, has become the standard approach due to its simplicity. However, the
SNIS has been shown to exhibit high variance in challenging estimation
problems, e.g, involving rare events or posterior predictive distributions in
Bayesian statistics. Further, most of the state-of-the-art adaptive importance
sampling (AIS) methods adapt the proposal as if the weights had not been
normalized. In this paper, we propose a framework that considers the original
task as estimation of a ratio of two integrals. In our new formulation, we
obtain samples from a joint proposal distribution in an extended space, with
two of its marginals playing the role of proposals used to estimate each
integral. Importantly, the framework allows us to induce and control a
dependency between both estimators. We propose a construction of the joint
proposal that decomposes in two (multivariate) marginals and a coupling. This
leads to a two-stage framework suitable to be integrated with existing or new
AIS and/or variational inference (VI) algorithms. The marginals are adapted in
the first stage, while the coupling can be chosen and adapted in the second
stage. We show in several examples the benefits of the proposed methodology,
including an application to Bayesian prediction with misspecified models.


  We study twisted modules for (weak) quantum vertex algebras and we give a
conceptual construction of (weak) quantum vertex algebras and their twisted
modules. As an application we construct and classify irreducible twisted
modules for a certain family of quantum vertex algebras.


  We present a 2.5-dimensional magnetohydrodynamic simulation of a
systematically rotating prominence inside its coronal cavity using the
open-source \texttt{MPI-AMRVAC} code. Our simulation starts from a
non-adiabatic, gravitationally stratified corona, permeated with a sheared
arcade magnetic structure. The flux rope (FR) is formed through converging and
shearing footpoints driving, simultaneously applying randomized heating at the
bottom. The latter induces a left-right asymmetry of temperature and density
distributions with respect to the polarity-inversion line. This asymmetry
drives flows along the loops before the FR formation, which gets converted to
net rotational motions upon reconnection of the field lines. As the thermal
instability within the FR develops, angular momentum conservation about its
axis leads to a systematic rotation of both hot coronal and cold condensed
plasma. The initial rotational velocity exceeds $60\ \mathrm{km\ s^{-1}}$. The
synthesized images confirm the simultaneous rotations of the coronal plasma
seen in 211 and 193 \AA\ and condensations seen in 304 \AA. Furthermore, the
formation of the dark cavity is evident in 211 and 193 \AA\ images. Our
numerical experiment is inspired by observations of so-called giant solar
prominence tornadoes, and reveals that asymmetric FR formation can be crucial
in triggering rotational motions. We reproduce observed spinning motions inside
the coronal cavity, augmenting our understanding of the complex dynamics of
rotating prominences.


  The growth of misinformation technology necessitates the need to identify
fake videos. One approach to preventing the consumption of these fake videos is
provenance which allows the user to authenticate media content to its original
source. This research designs and investigates the use of provenance indicators
to help users identify fake videos. We first interview users regarding their
experiences with different misinformation modes (text, image, video) to guide
the design of indicators within users' existing perspectives. Then, we conduct
a participatory design study to develop and design fake video indicators.
Finally, we evaluate participant-designed indicators via both expert
evaluations and quantitative surveys with a large group of end-users. Our
results provide concrete design guidelines for the emerging issue of fake
videos. Our findings also raise concerns regarding users' tendency to
overgeneralize from misinformation warning messages, suggesting the need for
further research on warning design in the ongoing fight against misinformation.


  We discuss the conditions under which classically conformally invariant
models in four dimensions can arise out of non-conformal (Einstein) gravity. As
an `existence proof' that this is indeed possible we show how to derive N=4
super Yang Mills theory with any compact gauge group G from non-conformal
gauged N=4 supergravity as a special flat space limit. We stress the role that
the anticipated UV finiteness of the (so far unknown) underlying theory of
quantum gravity would have to play in such a scheme, as well as the fact that
the masses of elementary particles would have to arise via quantum
gravitational effects which mimic the conformal anomalies of standard (flat
space) UV divergent quantum field theory.


  We study a one-parameter family of the fourth-order ordinary differential
equations obtained by similarity reduction of the modifed Sawada-Kotera
equation. We show that the birational transformations take this equation to the
polynomial Hamiltonian system in dimension four. We make this polynomial
Hamiltonian from the viewpoint of accessible singularity and local index. We
also give its symmetry and holomorphy conditions. These properties are new.
Moreover, we introduce a symmetric form in dimension five for this Hamiltonian
system by taking the two invariant divisors as the dependent variables. Thanks
to the symmetric form, we show that this system admits the affine Weyl group
symmetry of type $A_2^{(2)}$ as the group of its B{\"a}cklund transformations.


  The observational signatures of multi-field inflation will generally evolve
as the Universe reheats. We introduce a general analytic formalism for tracking
this evolution through perturbative reheating, applicable to two field models
with arbitrary separable potentials. The various transitions, including the
onset of scalar field oscillations and the reheating of each field, can happen
in different orders and on arbitrary hypersurfaces. The effective equations of
state of the oscillating fields are also arbitrary. Nevertheless, our results
are surprisingly simple. Our formalism encapsulates and generalises a huge
range of previous calculations including two-field inflation, spectator models,
the inhomogeneous end of inflation scenario and numerous generalised curvaton
scenarios.


  The purpose of this article is to classify the real hypersurfaces in complex
space forms of dimension 2 that are both Levi-flat and minimal. The main
results are as follows:
  When the curvature of the complex space form is nonzero, there is a
1-parameter family of such hypersurfaces. Specifically, for each one-parameter
subgroup of the isometry group of the complex space form, there is an
essentially unique example that is invariant under this one-parameter subgroup.
  On the other hand, when the curvature of the space form is zero, i.e., when
the space form is complex 2-space with its standard flat metric, there is an
additional `exceptional' example that has no continuous symmetries but is
invariant under a lattice of translations. Up to isometry and homothety, this
is the unique example with no continuous symmetries.


  In two-way channels, each user transmits and receives at the same time. This
allows each encoder to interactively adapt the current input to its own message
and all previously received signals. Such coding approach can introduce
correlation between inputs of different users, since all the users' outputs are
correlated by the nature of the channel. However, for some channels, such
adaptation in the coding scheme and its induced correlation among users are
useless in the sense that they do not help enlarge the capacity region with
respect to the standard coding method (where each user encodes only based on
its own message). In this paper, it is shown that adaptation is not helpful for
enlarging the capacity region of two classes of two-way discrete channels: the
modulo additive-noise channel with memory and the multiple access/degraded
broadcast channel.


  Context. The increased detection rate of Fast Radio Bursts (FRBs) makes it
likely to get samples of sizes $\mathcal{O}(10^2)$ to $\mathcal{O}(10^3)$ in
the near future. Because of their extragalactic origin can help us in
understanding the epoch of helium reionization.
  Aims. We try to identify the epoch of Helium II (HeII) reionization, via the
observations of early FRBs in range of $z=3$ to $4$.
  Methods. We build a model of FRB Dispersion Measure following the HeII
reionization model, density fluctuation in large scale structure, host galaxy
interstellar medium and local environment of FRB contribution. The model is fit
to the ideal intergalactic medium (IGM) dispersion measure model to check the
goodness of constraining the HeII reionization via FRB measurement statistics.
  Conclusion. We report our findings under two categories, accuracy in
detection of HeII reionization via FRBs assuming no uncertainty in the redshift
measurement and alternatively assuming a varied level of uncertainty in
redshift measurement of the FRBs. We show that under the first case, a
detection of $N\sim\mathcal{O} (10^2)$ FRBs give an uncertainty of $\sigma
(z_{r, fit})\sim0.5$ from the fit model, and a detection of $N\sim\mathcal{O}
(10^3)$ gives an uncertainty of $\sigma (z_{r, fit})\sim0.1$. While assuming a
redshift uncertainty of level $5-20\%$, changes the $\sigma (z_{r,
fit})\sim0.5$ to $0.6$ for $N\sim 100$ and $\sigma (z_{r, fit})\sim0.1$ to
$0.15$ for $N \sim 1000$ case.


  This is an English translation of Ostrowski's article "\"Uber Dirichletsche
Reihen und algebraische Differentialgleichungen" published German in Math.
Zeit. vol. 8, 1920, pp. 241-298. In this article, Ostrowski proves a conjecture
of Hilbert that the two variable function $\zeta(x,s)=\sum_{n\ge 1}
\frac{x^n}{n^s}$ cannot be written as a composition of analytic functions of
one variable and algebraic functions of any number of variables.


  Retrievability measures the influence a retrieval system has on the access to
information in a given collection of items. This measure can help in making an
evaluation of the search system based on which insights can be drawn. In this
paper, we investigate the retrievability in an integrated search system
consisting of items from various categories, particularly focussing on
datasets, publications \ijdl{and variables} in a real-life Digital Library
(DL). The traditional metrics, that is, the Lorenz curve and Gini coefficient,
are employed to visualize the diversity in retrievability scores of the
\ijdl{three} retrievable document types (specifically datasets, publications,
and variables). Our results show a significant popularity bias with certain
items being retrieved more often than others. Particularly, it has been shown
that certain datasets are more likely to be retrieved than other datasets in
the same category. In contrast, the retrievability scores of items from the
variable or publication category are more evenly distributed. We have observed
that the distribution of document retrievability is more diverse for datasets
as compared to publications and variables.


  Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are
modelled numerically, within the framework of the recently derived
2+1-dimensional cKdV-type equation. In a case study, we consider concentric
waves from a localised initial condition and waves in a 2D version of the
dam-break problem, as well as discussing the effect of a piecewise-constant
shear flow. The modelling shows, in particular, the formation of 2D dispersive
shock waves (DSWs) and oscillatory wave trains. The surface and interfacial
DSWs generated in our numerical experiments look distinctively different.


  Momentum feedback from super-Eddington accretion offers a simple explanation
for the observed M-sigma and M-M_{spheroid} relations between supermassive
black holes (SMBH) and the spheroids of their host galaxies. Recently Ferrarese
et al. and Wehner & Harris observed analogous relations between the masses of
central star clusters and their hosts. We show that stellar winds and
supernovae from such nuclear clusters (NC) give similar feedback explanations
for this case also, and we discuss the connection to the Faber-Jackson relation
for the spheroids themselves.


  We investigate shadowing corrections to the polarized deuteron structure
functions g_1^d and b_1. In the kinematic domain of current fixed target
experiments we observe that shadowing effects in g_1^d are approximately twice
as large as for the unpolarized structure function F_2^d. Furthermore, we find
that b_1 is surprisingly large at x < 0.1 and receives dominant contributions
from coherent double scattering.


  We study the transport properties of a quantum dot driven by either a
rotating magnetic field or an ac gate voltage using the Floquet master-equation
approach. Both types of ac driving lead to photon-assisted tunneling where
quantized amounts of energy are exchanged with the driving field. It is found
that the differential-conductance peak due to photon-assisted tunneling does
not survive in the Coulomb-blockade regime when the dot is driven by a rotating
magnetic field. Furthermore, we generalize the MacDonald formula to calculate
the time-averaged noise spectra of ac-driven quantum dots. Besides the peak at
zero frequency, the noise spectra show additional peaks or dips in the presence
of an ac field. For the case of an applied ac gate voltage, the peak or dip
position is fixed at the driving frequency, whereas the position changes with
increasing amplitude for the case of a rotating magnetic field. Additional
features appear in the noise spectra if a dc magnetic field is applied in
addition to a rotating field. In all cases, the peak or dip positions can be
understood from the energy differences of two available Floquet channels.


  We present a method to approximate Gaussian process regression models for
large datasets by considering only a subset of the data. Our approach is novel
in that the size of the subset is selected on the fly during exact inference
with little computational overhead. From an empirical observation that the
log-marginal likelihood often exhibits a linear trend once a sufficient subset
of a dataset has been observed, we conclude that many large datasets contain
redundant information that only slightly affects the posterior. Based on this,
we provide probabilistic bounds on the full model evidence that can identify
such subsets. Remarkably, these bounds are largely composed of terms that
appear in intermediate steps of the standard Cholesky decomposition, allowing
us to modify the algorithm to adaptively stop the decomposition once enough
data have been observed.


  We present the first computation of the cosmological perturbations generated
during inflation up to second order in deviations from the homogeneous
background solution. Our results, which fully account for the inflaton
self-interactions as well as for the second-order fluctuations of the
background metric, provide the exact expression for the gauge-invariant
curvature perturbation bispectrum produced during inflation in terms of the
slow-roll parameters or, alternatively, in terms of the scalar spectral $n_S$
and and the tensor to adiabatic scalar amplitude ratio $r$. The bispectrum
represents a specific non-Gaussian signature of fluctuations generated by
quantum oscillations during slow-roll inflation. However, our findings indicate
that detecting the non-Gaussianity in the cosmic microwave background
anisotropies emerging from the second-order calculation will be a challenge for
the forthcoming satellite experiments.


  Rational approximation appears in many contexts throughout science and
engineering, playing a central role in linear systems theory, special function
approximation, and many others. There are many existing methods for solving the
rational approximation problem, from fixed point methods like the
Sanathanan-Koerner iteration and Vector Fitting, to partial interpolation
methods like Adaptive Anderson Antoulas (AAA). While these methods can often
find rational approximations with a small residual norm, they are unable to
find optimizers with respect to a weighted l2 norm with a square dense
weighting matrix. Here we develop a nonlinear least squares approach
constructing rational approximations with respect to this norm. We explore this
approach using two parameterizations of rational functions: a ratio of two
polynomials and a partial fraction expansion. In both cases, we show how we can
use Variable Projection (VARPRO) to reduce the dimension of the optimization
problem. As many applications seek a real rational approximation that can be
described as a ratio of two real polynomials, we show how this constraint can
be enforced in both parameterizations. Although this nonlinear least squares
approach often converge to suboptimal local minimizers, we find this can be
largely mitigated by initializing the algorithm using the poles of the AAA
algorithm applied to the same data. This combination of initialization and
nonlinear least squares enables us to construct rational approximants using
dense and potentially ill-conditioned weight matrices such as those that appear
as a step in new H2 model reduction algorithm recently developed by the
authors.


  We describe a superconducting device capable of producing laser light in the
visible range at half the Josephson generation frequency, with the optical
phase of the light locked to the superconducting phase difference. An earlier
proposed device, the so called "half-Josephson laser" [Phys. Rev. Lett. 107,
073901 (2011)], cannot provide long coherence times, because of spontaneous
switchings between the emitter states. To circumvent this we consider N >> 1
emitters driving an optical resonator mode. We derive a general model that
captures essential physics of such devices while not depending on specific
microscopic details. We find the conditions under which the coherence times are
exponentially long, thus surpassing the fundamental limitation on the coherence
times of common lasers. For this we study the noise in the device. In
particular, we are interested in the rate of large fluctuations of the light
field in the limit where the typical fluctuations are small. The large
fluctuations are responsible for switching of the laser between stable states
of radiation and therefore determine the coherence time.


  The effective action induced by fermions in the chiral Schwinger model with
charges (3,4,5) is investigated. Pauli-Villars regularization is combined with
momentum cut-off for the evaluation of the fermion determinants on continuum
gauge fields interpolated between lattice points. The convergence and gauge
variance are studied numerically on gauge configurations taken from quenched
updating.


  We present a derivation of the holographic dual of logarithmic negativity in
AdS$_3$/CFT$_2$ that was recently conjectured in [Phys. Rev. D 99, 106014
(2019)]. This is given by the area of an extremal cosmic brane that terminates
on the boundary of the entanglement wedge. The derivation consists of relating
the recently introduced R\'enyi reflected entropy to the logarithmic negativity
in holographic conformal field theories. Furthermore, we clarify previously
mysterious aspects of negativity at large central charge seen in conformal
blocks and comment on generalizations to generic dimensions, dynamical
settings, and quantum corrections.


  We present Spitzer IRS spectra (R ~600, 10 - 38 micron) of 38 positions in
the Galactic Center (GC), all at the same Galactic longitude and spanning
plus/minus 0.3 degrees in latitude. Our positions include the Arches Cluster,
the Arched Filaments, regions near the Quintuplet Cluster, the ``Bubble'' lying
along the same line-of-sight as the molecular cloud G0.11-0.11, and the diffuse
interstellar gas along the line-of-sight at higher Galactic latitudes. From
measurements of the [O IV], [Ne II], [Ne III], [Si II], [S III], [S IV], [Fe
II], [Fe III], and H_2 S(0), S(1), and S(2) lines we determine the gas
excitation and ionic abundance ratios. The Ne/H and S/H abundance ratios are ~
1.6 times that of the Orion Nebula. The main source of excitation is
photoionization, with the Arches Cluster ionizing the Arched Filaments and the
Quintuplet Cluster ionizing the gas nearby and at lower Galactic latitudes
including the far side of the Bubble. In addition, strong shocks ionize gas to
O^{+3} and destroy dust grains, releasing iron into the gas phase (Fe/H ~ 1.3
times 10^{-6} in the Arched Filaments and Fe/H ~ 8.8 times 10^{-6} in the
Bubble). The shock effects are particularly noticeable in the center of the
Bubble, but O$^{+3}$ is present in all positions. We suggest that the shocks
are due to the winds from the Quintuplet Cluster Wolf-Rayet stars. On the other
hand, the H_2 line ratios can be explained with multi-component models of warm
molecular gas in photodissociation regions without the need for H_2 production
in shocks.


  Let $G$ be a finite $p$-group of nilpotency class 2. We find necessary and
sufficient conditions on $G$ such that each central automorphism of $G$ fixes
the center of $G$ element-wise.


  To allow non-designers' involvement in design projects new methods are
needed. Co-design gives the same opportunity to all the multidisciplinary
participants to co-create ideas simultaneously. Nevertheless, current co-design
processes involving such users tend to limit their contribution to the proposal
of basic design ideas only through brainstorming. The co-design approach needs
to be enhanced by a properly suited representational ecosystem supporting
active participation and by conscious use of structured verbal exchanges giving
awareness of the creative process. In this respect, we developed two social
virtual reality co-design systems, and a co-design verbal exchange methodology
to favour participants' awareness of the co-creative process. By using such
representations and verbal exchanges, participants could co-create with more
ease by benefiting from being informed of the process and from the collective
immersion, empowering their participation. This paper presents the rationale
behind this approach of using Social VR in co-design and the feedback of three
co-design workshops.


  Ethnic achievement gaps are often explained in terms of student and school
factors. The decomposition of these gaps into their within- and between-school
components has therefore been applied as a strategy to quantify the overall
influence of each set of factors. Three competing approaches have previously
been proposed, but each is limited to the study of student-school
decompositions of the gap between two ethnic groups (e.g., White and Black).
The authors show that these approaches can be reformulated as mediation models
facilitating new extensions to allow additional levels in the school system
(e.g., classrooms, school districts, geographic areas) and multiple ethnic
groups (e.g., White, Black, Hispanic, Asian). The authors illustrate these
extensions using administrative data for high school students in Colombia and
highlight the increased substantive insights and nuanced policy implications
they afford.


  Contrastive Language-Image Pre-training (CLIP) achieves remarkable
performance in various downstream tasks through the alignment of image and text
input embeddings and holds great promise for anomaly detection. However, our
empirical experiments show that the embeddings of text inputs unexpectedly
tightly cluster together, far away from image embeddings, contrary to the
model's contrastive training objective to align image-text input pairs. We show
that this phenomenon induces a `similarity bias' - in which false negative and
false positive errors occur due to bias in the similarities between images and
the normal label text embeddings. To address this bias, we propose a novel
methodology called BLISS which directly accounts for this similarity bias
through the use of an auxiliary, external set of text inputs. BLISS is simple,
it does not require strong inductive biases about anomalous behaviour nor an
expensive training process, and it significantly outperforms baseline methods
on benchmark image datasets, even when access to normal data is extremely
limited.


  Recent results on the QCD phase diagram are reviewed. We begin with a
detailed introduction of lattice techniques. Then results at vanishing chemical
potential are presented. The order of the phase transition, the transition
temperature and the equation of state are discussed. At non-vanishing chemical
potential we study the mu-T phase line, the critical point as well as the
equation of state.


  While the classification of $\alpha'$ corrections of string inspired
effective theories remains an unsolved problem, we show how to classify duality
invariant $\alpha'$ corrections for purely time-dependent (cosmological)
backgrounds. We determine the most general duality invariant theory to all
orders in $\alpha'$ for the metric, $b$-field, and dilaton. The resulting
Friedmann equations are studied when the spatial metric is a time-dependent
scale factor times the Euclidean metric and the $b$-field vanishes. These
equations can be integrated perturbatively to any order in $\alpha'$. We
construct non-perturbative solutions and display duality invariant theories
featuring string-frame de Sitter vacua.


  Generation-based fuzz testing can uncover various bugs and security
vulnerabilities. However, compared to mutation-based fuzz testing, it takes
much longer to develop a well-balanced generator that produces good test cases
and decides where to break the underlying structure to exercise new code paths.
We propose a novel approach to combine a trained test case generator deep
learning model with a double deep Q-network (DDQN) for the first time. The DDQN
guides test case creation based on a code coverage signal. Our approach
improves the code coverage performance of the underlying generator model by up
to 18.5\% for the Firefox HTML rendering engine compared to the baseline
grammar based fuzzer.


  Optical spectropolarimetry and broadband polarimetry in other wavebands has
been a key to understanding many diverse aspects of AGN. In some cases
polarization is due to synchrotron radiation, and in other cases it's due to
scattering. Recognition of relativistically beamed optical synchrotron emission
by polarization was vital for understanding blazars (BL Lacs and Optically
Violently Variable quasars), both physically and geometrically. Radio
polarimetry of quiescent AGN is equally important, again for both purposes.
Scattering polarization was central to the Unified Model for Seyferts, Radio
Galaxies and (high ionization) Ultraluminous Infrared Galaxies. It provides a
periscope for viewing AGN from other directions. Finally, if we could
understand its message, polarization would also provide major insights
regarding the nature of the AGN "Featureless Continuum" and Broad (emission)
Line Region. I point out that high ionization ULIRGs have all the exact right
properties to be called Quasar 2s. Mid-IR observations generally don't
penetrate to the nucleus, greatly reducing their ability to diagnose the energy
source. In particular, LINER ULIRGs aren't necessarily starburst-dominated, as
has been claimed.


  While there exist various candidates, the identification of dark matter
remains unresolved. Recently it was argued that the generalized uncertainty
principle (GUP) may prevent a black hole from evaporating completely, and as a
result there should exist a Planck-size BHR at the end of its evaporation. We
speculate that the stability of BHR may be further protected by supersymmetry
in the form of extremal black hole. If this is indeed the case and if a
sufficient amount of small black holes can be produced in the early universe,
then the resultant BHRs can be an interesting candidate for DM. We demonstrate
that this is the case in the hybrid inflation model. By assuming BHR as DM, our
notion imposes a constraint on the hybrid inflation potential. We show that
such a constraint is not fine-tuned. Possible observational signatures are
briefly discussed.


  Optical precision spectroscopy of isotope shifts can be used to test for new
forces beyond the Standard Model, and to determine basic properties of atomic
nuclei. We measure isotope shifts on the highly forbidden ${}^2S_{1/2}
\rightarrow {}^2F_{7/2}$ octupole transition of trapped
$^{168,170,172,174,176}$Yb ions. When combined with previous measurements in
Yb$^+$ and very recent measurements in Yb, the data reveal a King plot
nonlinearity of up to 240$\sigma$. The trends exhibited by experimental data
are explained by nuclear density functional theory calculations with the Fayans
functional. We also find, with 4.3$\sigma$ confidence, that there is a second
distinct source of nonlinearity, and discuss its possible origin.


  In this paper, we present the geometric Hardy inequality for the
sub-Laplacian in the half-spaces on the stratified groups. As a consequence, we
obtain the following geometric Hardy inequality in a half-space on the
Heisenberg group with a sharp constant
  \begin{equation*}
  \int_{\mathbb{H}^+} |\nabla_{H}u|^p d\xi \geq \left(\frac{p-1}{p}\right)^p
\int_{\mathbb{H}^+} \frac{\mathcal{W}(\xi)^p}{dist(\xi,\partial
\mathbb{H}^+)^p} |u|^p d\xi, \,\, p>1,
  \end{equation*}
  which solves the conjecture in the paper \cite{Larson}. Also, we obtain a
version of the Hardy-Sobolev inequality in a half-space on the Heisenberg group
  \begin{equation*}
  \left(\int_{\mathbb{H}^+} |\nabla_{H} u|^p d\xi -
\left(\frac{p-1}{p}\right)^p \int_{\mathbb{H}^+}
\frac{\mathcal{W}(\xi)^p}{dist(\xi,\partial \mathbb{H}^+)^p} |u|^p d\xi
\right)^{\frac{1}{p}} \geq C \left(\int_{\mathbb{H}^+} |u|^{p^*}
d\xi\right)^{\frac{1}{p^*}},
  \end{equation*}
  where $dist(\xi,\partial \mathbb{H}^+)$ is the Euclidean distance to the
boundary, $p^* := Qp/(Q-p)$, $2\leq p<Q$, and
  $$\mathcal{W}(\xi)=\left(\sum_{i=1}^{n}\langle X_i(\xi), \nu
\rangle^2+\langle Y_i(\xi), \nu \rangle^2\right)^{\frac{1}{2}},$$
  is the angle function. For $p=2$, this gives the Hardy-Sobolev-Maz'ya
inequality on the Heisenberg group.


  The olivine compound Mn2GeO4 is shown to feature both a ferroelectric
polarization and a ferromagnetic magnetization that are directly coupled and
point along the same direction. We show that a spin spiral generates
ferroelectricity (FE), and a canted commensurate order leads to weak
ferromagnetism (FM). Symmetry suggests that the direct coupling between the FM
and FE is mediated by Dzyaloshinskii-Moriya interactions that exist only in the
ferroelectric phase, controlling both the sense of the spiral rotation and the
canting of the commensurate structure. Our study demonstrates how
multi-component magnetic structures found in magnetically-frustrated materials
like Mn2GeO4 provide a new route towards functional materials that exhibit
coupled FM and FE.


  The collaborative filtering (CF) problem with only user-item interaction
information can be solved by graph signal processing (GSP), which uses low-pass
filters to smooth the observed interaction signals on the similarity graph to
obtain the prediction signals. However, the interaction signal may not be
sufficient to accurately characterize user interests and the low-pass filters
may ignore the useful information contained in the high-frequency component of
the observed signals, resulting in suboptimal accuracy. To this end, we propose
a personalized graph signal processing (PGSP) method for collaborative
filtering. Firstly, we design the personalized graph signal containing richer
user information and construct an augmented similarity graph containing more
graph topology information, to more effectively characterize user interests.
Secondly, we devise a mixed-frequency graph filter to introduce useful
information in the high-frequency components of the observed signals by
combining an ideal low-pass filter that smooths signals globally and a linear
low-pass filter that smooths signals locally. Finally, we combine the
personalized graph signal, the augmented similarity graph and the
mixed-frequency graph filter by proposing a pipeline consisting of three key
steps: pre-processing, graph convolution and post-processing. Extensive
experiments show that PGSP can achieve superior accuracy compared with
state-of-the-art CF methods and, as a nonparametric method, PGSP has very high
training efficiency.


In this paper we classify reflection subgroups of Euclidean Coxeter groups.


  This paper proposes an adaptive randomization procedure for two-stage
randomized controlled trials. The method uses data from a first-wave experiment
in order to determine how to stratify in a second wave of the experiment, where
the objective is to minimize the variance of an estimator for the average
treatment effect (ATE). We consider selection from a class of stratified
randomization procedures which we call stratification trees: these are
procedures whose strata can be represented as decision trees, with differing
treatment assignment probabilities across strata. By using the first wave to
estimate a stratification tree, we simultaneously select which covariates to
use for stratification, how to stratify over these covariates, as well as the
assignment probabilities within these strata. Our main result shows that using
this randomization procedure with an appropriate estimator results in an
asymptotic variance which is minimal in the class of stratification trees.
Moreover, the results we present are able to accommodate a large class of
assignment mechanisms within strata, including stratified block randomization.
In a simulation study, we find that our method, paired with an appropriate
cross-validation procedure ,can improve on ad-hoc choices of stratification. We
conclude by applying our method to the study in Karlan and Wood (2017), where
we estimate stratification trees using the first wave of their experiment.


  The current state-of-the-art model HiAGM for hierarchical text classification
has two limitations. First, it correlates each text sample with all labels in
the dataset which contains irrelevant information. Second, it does not consider
any statistical constraint on the label representations learned by the
structure encoder, while constraints for representation learning are proved to
be helpful in previous work. In this paper, we propose HTCInfoMax to address
these issues by introducing information maximization which includes two
modules: text-label mutual information maximization and label prior matching.
The first module can model the interaction between each text sample and its
ground truth labels explicitly which filters out irrelevant information. The
second one encourages the structure encoder to learn better representations
with desired characteristics for all labels which can better handle label
imbalance in hierarchical text classification. Experimental results on two
benchmark datasets demonstrate the effectiveness of the proposed HTCInfoMax.


  The conformal anomaly and the Virasoro algebra are fundamental aspects of 2D
conformal field theory and conformally covariant models in planar random
geometry. In this article, we explicitly derive the Virasoro algebra from an
axiomatization of the conformal anomaly in terms of real determinant lines,
one-dimensional vector spaces associated to Riemann surfaces with analytically
parametrized boundary components. Here, analytical orientation-preserving
diffeomorphisms and deformations of the circle naturally act on the boundary
components. We introduce a sewing operation on the real determinant lines over
the semigroup of annuli, which then induces central extensions of the
diffeomorphism group, as well as of the complex deformations.
  Our main theorem shows that on the one hand, the cocycle associated to the
central extension of diffeomorphisms is trivial, while on the other hand, the
Lie algebra cocycle associated to the central extension of complex deformations
is nontrivial, yielding the imaginary part of the Gel'fand-Fuks cocycle. We
thus answer a question, partly negatively and partly affirmatively, discussed
by Andre Henriques and Dylan Thurston in 2011. The proof uses concrete
computations, which we aim to be accessible to a wide audience.
  We also show an explicit relation to loop Loewner energy, anticipating the
real determinant lines to be pertinent to locally conformally covariant
(Malliavin-Kontsevich-Suhov) measures on curves and loops, as well as to
K\"ahler geometry and geometric quantization of moduli spaces of Riemann
surfaces. Inherently, the conformal anomaly and real determinant line bundles
are expected to be universal, following a classification of modular functors.


  This paper tries to justify the relevance of an introductory course in
Mathematical Logic in the Philosophy curriculum for analyzing philosophical
arguments in natural language. It is argued that the representation of the
structure of natural language arguments in Freeman's diagramming system can
provide an intuitive foundation for the inferential processes involved in the
use of First Order Logic natural deduction rules.


  An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$
is a permutation of $W$. We study anagram-free graph colouring and give bounds
on the chromatic number. Alon et al. (2002) asked whether anagram-free
chromatic number is bounded by a function of the maximum degree. We answer this
question in the negative by constructing graphs with maximum degree 3 and
unbounded anagram-free chromatic number. We also prove upper and lower bounds
on the anagram-free chromatic number of trees in terms of their radius and
pathwidth. Finally, we explore extensions to edge colouring and
$k$-anagram-free colouring.


  By adjusting the tunnelling couplings over longer than nearest neighbor
distances it is possible in discrete lattice models to reproduce the properties
of the lowest energy band of a real, continuous periodic potential. We propose
to include such terms in problems with interacting particles and we show that
they have significant consequences for scattering and bound states of atom
pairs in periodic potentials.


  We show that rotating black holes do not experience any tidal deformation
when they are perturbed by a weak and adiabatic gravitational field. The tidal
deformability of an object is quantified by the so-called "Love numbers", which
describe the object's linear response to its external tidal field. In this
work, we compute the Love numbers of Kerr black holes and find that they vanish
identically. We also compute the dissipative part of the black hole's tidal
response, which is non-vanishing due to the absorptive nature of the event
horizon. Our results hold for arbitrary values of black hole spin, for both the
electric-type and magnetic-type perturbations, and to all orders in the
multipole expansion of the tidal field. The boundary conditions at the event
horizon and at asymptotic infinity are incorporated in our study, as they are
crucial for understanding the way in which these tidal effects are mapped onto
gravitational-wave observables. In closing, we address the ambiguity issue of
Love numbers in General Relativity, which we argue is resolved when those
boundary conditions are taken into account. Our findings provide essential
inputs for current efforts to probe the nature of compact objects through the
gravitational waves emitted by binary systems.


  We derive photon counting statistics for an output field of a single-photon
wave packet interacting with a quantum system (e.g. a quantum harmonic
oscillator or a two-level atom). We determine the exclusive probability
densities for the output field by making use of quantum filtering theory. The
quantum trajectories for continuous in time measurements of the output field
(reflected and transmitted), are determined starting from a collision model and
difference filtering equations. We provide analytical formulae for quantum
trajectories associated with a two-dimensional stochastic counting process, we
describe their structure, and give a physical interpretation to them. Moreover,
we provide analytical expressions for probability densities for the times of
successive photon detections for a single-photon field scattered on a two-level
atom, for an arbitrary photon profile and any initial state of the atom.


  In this work we discuss the recent criticism by Zdziarski of the maximal jet
model derived in Falcke & Biermann (1995). We agree with Zdziarski that in
general a jet's internal energy is not bounded by its rest-mass energy density.
We describe the effects of the mistake on conclusions that have been made using
the maximal jet model and show when a maximal jet is an appropriate assumption.
The maximal jet model was used to derive a 1-D hydrodynamical model of jets in
agnjet, a model that does multiwavelength fitting of quiescent/hard state X-ray
binaries and low-luminosity active galactic nuclei. We correct algebraic
mistakes made in the derivation of the 1-D Euler equation and relax the maximal
jet assumption. We show that the corrections cause minor differences as long as
the jet has a small opening angle and a small terminal Lorentz factor. We find
that the major conclusion from the maximal jet model, the jet-disk symbiosis,
can be generally applied to astrophysical jets. We also show that isothermal
jets are required to match the flat radio spectra seen in low-luminosity X-ray
binaries and active galactic nuclei, in agreement with other works.


  We introduce generalization of famous Macdonald polynomials for the case of
super-Young diagrams that contain half-boxes on the equal footing with full
boxes. These super-Macdonald polynomials are polynomials of extended set of
variables: usual $p_k$ variables are accompanied by anti-commuting Grassmann
variables $\theta_k$. Starting from recently defined super-Schur polynomials
and exploiting orthogonality relations with triangular decompositions we are
able to fully determine super-Macdonald polynomials. These new polynomials have
similar properties to canonical Macdonald polynomials -- they respect two
different orderings in the set of (super)-Young diagrams simultaneously.


  In this paper, we view matrix frames as representations of quivers and study
them within the general framework of quiver invariant theory. We are thus led
to consider the large class of semi-stable matrix frames. Within this class, we
are particularly interested in radial isotropic and Parseval matrix frames.
  Using methods from quiver invariant theory [CD19], we first prove a far
reaching generalization of Barthe's Radial Isotropy Theorem [Bar98] to matrix
frames (see Theorems 1(3) and 29). With this tool at our disposal, we provide a
quiver invariant theoretic approach to the Paulsen problem for matrix frames.
We show in Theorem 2 that for any given $\varepsilon$-nearly equal-norm
Parseval frame $\mathcal{F}$ of $n$ matrices with $d$ rows there exists an
equal-norm Parseval frame $\mathcal{W}$ of $n$ matrices with $d$ rows such that
$\mathsf{dist}^2(\mathcal{F},\mathcal{W})\leq 46 \epsilon d^2$.


  We give a direct geometric interpretation of the path model using galleries
in the $1-$skeleton of the Bruhat-Tits building associated to a semi-simple
algebraic group. This interpretation allows us to compute the coefficients of
the expansion of the Hall-Littlewood polynomials in the monomial basis. The
formula we obtain is a "geometric compression" of the one proved by Schwer, its
specialization to the case ${\tt A}_n$ turns out to be equivalent to
Macdonald's formula.


  We describe our experiment with an alternate approach to presenting cosmic
ray research. The goal was to more widely promote cosmic ray research and
attract diverse audiences, especially those from groups that are
underrepresented in science or that do not have experience attending science
outreach events. The IceCube Neutrino Observatory education and outreach team
brought together local teenagers, internationally accomplished artists, science
communicators, and scientists to produce an interactive gallery exhibit,
Messages, that explores the cosmic ray community and science. The artists
collaborated with the scientists and students to create two original
installations that will be displayed at the UW-Madison Memorial Union Gallery
for six weeks, from mid-June, 2019, through the end of the International Cosmic
Ray Conference 2019. Event Horizon by Abdu'Allah with Ladoni features portraits
of cosmic ray researchers and high school students who are learning more about
the field. This installation will examine the science community as it is and as
it could be. Messages from the Horizon by Hosale with Madsen is inspired by
previous immersive works. It combines sound and light to explore what we know
and how we know it.


  We compare model results from a semi-analytic (merger-tree based) framework
for high-redshift (z ~ 5-20) galaxy formation against reionization indicators,
including the Planck electron scattering optical depth and the ionizing photon
emissivity, to shed light on the reionization history and sources in Cold (CDM)
and Warm Dark Matter (WDM; particle masses of $m_x = 1.5,3$ and 5 keV)
cosmologies. This model includes all the key processes of star formation,
supernova feedback, the merger/accretion/ejection driven evolution of gas and
stellar mass and the effect of the ultra-violet background (UVB) in
photo-evaporating the gas content of low-mass galaxies. We find that the delay
in the start of reionization in light (1.5 keV) WDM models can be compensated
by a steeper redshift evolution of the ionizing photon escape fraction and a
faster mass assembly, resulting in reionization ending at comparable redshifts
(z~5.5) in all the DM models considered. We find the bulk of the reionization
photons come from galaxies with a halo mass $M_h < 10^9 M_\odot$ and a UV
magnitude $ -15 < M_{UV} < -10$ in CDM. The progressive suppression of low-mass
halos with decreasing $m_x$ leads to a shift in the reionization population to
larger halo masses of $M_h > 10^9 M_\odot$ and $ -17 < M_{UV} < -13$ for 1.5
keV WDM. We find that current observations of the electron scattering optical
depth and the Ultra-violet luminosity function are equally compatible with all
the (cold and warm) DM models considered in this work. We propose that global
indicators including the redshift evolution of the stellar mass density and the
stellar mass-halo mass relation, observable with the James Webb Space
Telescope, can be used to distinguish between CDM and WDM (1.5 keV)
cosmologies.


  A wide-frequency radio study of Active Galactic Nuclei (AGN) is crucial to
evaluate the intervening radiative mechanisms responsible for the observed
emission and relate them with the underlying accretion physics. We present wide
frequency (5-45 GHz), high-sensitivity (few microJy/beam), (sub)-kpc JVLA
observations of a sample of 30 nearby (0.003 < z < 0.3) AGN detected by
INTEGRAL/IBIS at hard-X-ray. We find a high detection fraction of radio
emission at all frequencies, i.e. > 95 per cent at 5, 10 and 15 GHz and > 80
per cent at 22 and 45 GHz. Two sources out of 30 remain undetected at our high
sensitivities. The nuclear radio morphology is predominantly compact, sometimes
accompanied by extended jet-like structures, or more complex features. The
radio Spectral Energy Distributions (SEDs) of the radio cores appear either as
a single or as a broken power-law, a minority of them exhibits a peaked
component. The spectral slopes are either flat/inverted or steep, up to a
break/peak or over the whole range. The sample mean SED shows a flat slope up
to 15 GHz which steepens between 15 and 22 GHz and becomes again flat above 22
GHz. Significant radio-X-ray correlations are observed at all frequencies.
About half of the sample features extended emission, clearly resolved by the
JVLA, indicating low-power jets or large scale outflows. The unresolved cores,
which often dominate the radio power, may be of jet, outflow, and/or coronal
origin, depending on the observed frequency.


  We present our investigations of the physical and dynamical properties of
selected Earth co-orbital asteroids. The photometric optical light curves as
well as rotation periods and pole solutions for a sample of four Earth
co-orbital asteroids, namely (138175) 2000 EE104 (P=13.9476+/-0.0051 hrs),
(418849) 2008 WM64 (P=2.4077+/-0.0001 hrs), 2016 CA138 (P=5.3137+/-0.0016 hrs)
and 2017 SL16 (P=0.3188+/-0.0053 hrs), are determined or improved and presented
in this work. For this investigation, we combine observations carried out at
the Bulgarian National Astronomical Observatory - Rozhen using the FoReRo2
instrument attached to the 2mRCC telescope as well as sparse data from AstDys2
database. Parallel to the rotational properties we did numerical dynamical
simulations to investigate the orbital stability of those objects and to find
out if there is a relation with their rotational properties. Our results show
that the orbit stability is affected by the orbit itself and mainly its
eccentricity and inclination, which are responsible for the close encounters
with other Solar system planets. We cannot make a definitive conclusion about
the relation between orbit stability and the rotational state of the asteroids,
so we need further investigations and observations in order to prove or
disprove it.


  This paper proposes using ChatGPT, an innovative technology with various
applications, as an assistant for psychotherapy. ChatGPT can serve as a patient
information collector, a companion for patients in between therapy sessions,
and an organizer of gathered information for therapists to facilitate treatment
processes. The research identifies five research questions and discovers useful
prompts for fine-tuning the assistant, which shows that ChatGPT can participate
in positive conversations, listen attentively, offer validation and potential
coping strategies without providing explicit medical advice, and help
therapists discover new insights from multiple conversations with the same
patient. Using ChatGPT as an assistant for psychotherapy poses several
challenges that need to be addressed, including technical as well as
human-centric challenges which are discussed.


  The development of energy conversion techniques enhances the coupling between
the gas network and power system. However, challenges remain in the joint
optimal dispatch of electricity-gas systems. The dynamic model of the gas
network, described by partial differential equations, is complex and
computationally demanding for power system operators. Furthermore, information
privacy concerns and limited accessibility to detailed gas network models by
power system operators necessitate quantifying the equivalent energy storage
capacity of gas networks. This paper proposes a multi-port energy storage model
with time-varying capacity to represent the dynamic gas state transformation
and operational constraints in a compact and intuitive form. The model can be
easily integrated into the optimal dispatch problem of the power system. Test
cases demonstrate that the proposed model ensures feasible control strategies
and significantly reduces the computational burden while maintaining high
accuracy in the joint optimal dispatch of electricity-gas systems. In contrast,
the existing static equivalent model fails to capture the full flexibility of
the gas network and may yield infeasible results.


  Deploying language models (LMs) necessitates outputs to be both high-quality
and compliant with safety guidelines. Although Inference-Time Guardrails (ITG)
offer solutions that shift model output distributions towards compliance, we
find that current methods struggle in balancing safety with helpfulness. ITG
Methods that safely address non-compliant queries exhibit lower helpfulness
while those that prioritize helpfulness compromise on safety. We refer to this
trade-off as the guardrail tax, analogous to the alignment tax. To address
this, we propose PrimeGuard, a novel ITG method that utilizes structured
control flow.
  PrimeGuard routes requests to different self-instantiations of the LM with
varying instructions, leveraging its inherent instruction-following
capabilities and in-context learning. Our tuning-free approach dynamically
compiles system-designer guidelines for each query. We construct and release
safe-eval, a diverse red-team safety benchmark. Extensive evaluations
demonstrate that PrimeGuard, without fine-tuning, overcomes the guardrail tax
by (1) significantly increasing resistance to iterative jailbreak attacks and
(2) achieving state-of-the-art results in safety guardrailing while (3)
matching helpfulness scores of alignment-tuned models. Extensive evaluations
demonstrate that PrimeGuard, without fine-tuning, outperforms all competing
baselines and overcomes the guardrail tax by improving the fraction of safe
responses from 61% to 97% and increasing average helpfulness scores from 4.17
to 4.29 on the largest models, while reducing attack success rate from 100% to
8%.
  PrimeGuard implementation is available at
https://github.com/dynamofl/PrimeGuard and safe-eval dataset is available at
https://huggingface.co/datasets/dynamoai/safe_eval.


  The problem of finding upper bounds for minimal vertex number of graphs with
a given automorphism group is addressed in this article for the case of cyclic
$2$-groups. We show that for any natural $n\ge 2$ there is an undirected graph
having $2^n+6$ vertices and automorphism group cyclic of order $2^n$. This
confirms an upper bound claimed by other authors for minimal number of vertices
of undirected graphs having automorphism group $\mathbb{Z}/2^n\mathbb{Z}$.


  Solving the Traveling Salesperson Problem (TSP) remains a persistent
challenge, despite its fundamental role in numerous generalized applications in
modern contexts. Heuristic solvers address the demand for finding high-quality
solutions efficiently. Among these solvers, the Lin-Kernighan-Helsgaun (LKH)
heuristic stands out, as it complements the performance of genetic algorithms
across a diverse range of problem instances. However, frequent timeouts on
challenging instances hinder the practical applicability of the solver.
  Within this work, we investigate a previously overlooked factor contributing
to many timeouts: The use of a fixed candidate set based on a tree structure.
Our investigations reveal that candidate sets based on Hamiltonian circuits
contain more optimal edges. We thus propose to integrate this promising
initialization strategy, in the form of POPMUSIC, within an efficient restart
version of LKH. As confirmed by our experimental studies, this refined TSP
heuristic is much more efficient - causing fewer timeouts and improving the
performance (in terms of penalized average runtime) by an order of magnitude -
and thereby challenges the state of the art in TSP solving.


  Stellar coronae have been invoked to explain the apparently extragalactic
dispersion measures observed in fast radio bursts. This paper demonstrates that
the suggested plasma densities would lead to deviations from the standard
dispersion curve that are inconsistent with the data. The problem is then
turned around and higher-order dispersion terms are connected to the moments of
the density distribution along the line of sight. The deviations quantified in
three observed bursts are analysed and a lower limit on the maximum electron
density is obtained in one case, although with considerable uncertainty.
Selection effects are then discussed and shown to be non-restrictive in
relation to plasma density, except at the lowest frequencies and highest
temperatures.


  In this paper we continue our analysis of intertwining relations for both
self-adjoint and not self-adjoint operators. In particular, in this last
situation, we discuss the connection with pseudo-hermitian quantum mechanics
and the role of Riesz bases.


  We propose a novel strategy for multivariate extreme value index estimation.
In applications such as finance, volatility and risk present in the components
of a multivariate time series are often driven by the same underlying factors,
such as the subprime crisis in the US. To estimate the latent risk, we apply a
two-stage procedure. First, a set of independent latent series is estimated
using a method of latent variable analysis. Then, univariate risk measures are
estimated individually for the latent series to assess their contribution to
the overall risk. As our main theoretical contribution, we derive conditions
under which the effect of the first step to the asymptotic behavior of the risk
estimators is negligible. Simulations demonstrate the theory under both i.i.d.
and dependent data, and an application into financial data illustrates the
usefulness of the method in extracting joint sources of risk in practice.


  In recent work by Dani and Mainkar, a family of finite simple graphs was used
to construct nilmanifolds admitting Anosov diffeomorphisms. Our main object of
study is this particular set of graphs, which we call Anosov graphs. Moreover,
Dani and Mainkar give a lower bound on the number of Anosov graphs in terms of
the number of vertices and number of edges. In this work, we improve this lower
bound in terms of vertices and edges, and we give lower and upper bounds solely
in terms of the number of vertices.


  Coronavirus (COVID-19) creates fear and uncertainty, hitting the global
economy and amplifying the financial markets volatility. The oil price reaction
to COVID-19 was gradually accommodated until March 09, 2020, when, 49 days
after the release of the first coronavirus monitoring report by the World
Health Organization (WHO), Saudi Arabia floods the market with oil. As a
result, international prices drop with more than 20% in one single day. Against
this background, the purpose of this paper is to investigate the impact of
COVID-19 numbers on crude oil prices, while controlling for the impact of
financial volatility and the United States (US) economic policy uncertainty.
Our ARDL estimation shows that the COVID-19 daily reported cases of new
infections have a marginal negative impact on the crude oil prices in the long
run. Nevertheless, by amplifying the financial markets volatility, COVID-19
also has an indirect effect on the recent dynamics of crude oil prices.


  The progenitors of many Type II supernovae have been observationally
identified but the search for Type Ibc supernova (SN Ibc) progenitors has thus
far been unsuccessful, despite the expectation that they are luminous
Wolf-Rayet (WR) stars. We investigate how the evolution of massive helium stars
affects their visual appearances, and discuss the implications for the
detectability of SN Ibc progenitors. Massive WR stars that rapidly lose their
helium envelopes through stellar-wind mass-loss end their lives when their
effective temperatures -- related to their hydrostatic surfaces -- exceed about
150kK.At their pre-supernova stage, their surface properties resemble those of
hot Galactic WR stars of WO sub-type. These are visually faint with narrow-band
visual magnitudes Mv = -1.5 ~ -2.5, despite their high bolometric luminosities
(log L/Lsun = 5.6 ~ 5.7), compared to the bulk of Galactic WR stars (Mv < -4).
In contrast, relatively low-mass helium stars that retain a thick helium
envelope appear fairly bright in optical bands, depending on the final masses
and the history of the envelope expansion during the late evolutionary stages.
We conclude that SNe Ibc observations have so far not provided strong
constraints on progenitor bolometric luminosities and masses, even with the
deepest searches. We also argue that Ic progenitors are more challenging to
identify than Ib progenitors in any optical images.


  We study the ODE/IM correspondence for ODE associated to $\hat{\mathfrak
g}$-valued connections, for a simply-laced Lie algebra $\mathfrak g$. We prove
that subdominant solutions to the ODE defined in different fundamental
representations satisfy a set of quadratic equations called $\Psi$-system. This
allows us to show that the generalized spectral determinants satisfy the Bethe
Ansatz equations.


  This is a translation into English from the original Latin of Leonhard
Euler's Exercitatio analytica, Nova Acta Academiae Scientarum Imperialis
Petropolitinae 8 (1794), 69-72; E664 in the Enestrom index. In it Euler uses
the infinite product identity for sin to prove some properties of the series
for the Riemann zeta function for even n.


  The locality conditions for the vanishing of local anomalies in field theory
are shown to admit a geometrical interpretation in terms of local equivariant
cohomology, thus providing a method to deal with the problem of locality in the
geometrical approaches to the study of local anomalies based on the
Atiyah-Singer index theorem. The local cohomology is shown to be related to the
cohomology of jet bundles by means of the variational bicomplex theory. Using
these results and the techniques for the computation of the cohomology of
invariant variational bicomplexes in terms of relative Gel'fand-Fuks cohomology
introduced in [6], we obtain necessary and sufficient conditions for the
cancellation of local gravitational and mixed anomalies.


  We develop a new rank-based approach for univariate two-sample testing in the
presence of missing data which makes no assumptions about the missingness
mechanism. This approach is a theoretical extension of the
Wilcoxon-Mann-Whitney test that controls the Type I error by providing exact
bounds for the test statistic after accounting for the number of missing
values. Greater statistical power is shown when the method is extended to
account for a bounded domain. Furthermore, exact bounds are provided on the
proportions of data that can be missing in the two samples while yielding a
significant result. Simulations demonstrate that our method has good power,
typically for cases of $10\%$ to $20\%$ missing data, while standard imputation
approaches fail to control the Type I error. We illustrate our method on
complex clinical trial data in which patients' withdrawal from the trial lead
to missing values.


  We calculate the two-body nonleptonic B decays using the factorization
method. The recent measured decays by CLEO Collaboration can be explained in
the factorization approach. We propose a number of ratios of branching ratios
to determine the effective coefficients and the form factors.


  Inverse problems, where in broad sense the task is to learn from the noisy
response about some unknown function, usually represented as the argument of
some known functional form, has received wide attention in the general
scientific disciplines. How- ever, in mainstream statistics such inverse
problem paradigm does not seem to be as popular. In this article we provide a
brief overview of such problems from a statistical, particularly Bayesian,
perspective.
  We also compare and contrast the above class of problems with the perhaps
more statistically familiar inverse regression problems, arguing that this
class of problems contains the traditional class of inverse problems. In course
of our review we point out that the statistical literature is very scarce with
respect to both the inverse paradigms, and substantial research work is still
necessary to develop the fields.


  We give a short review of gamma-ray burst (GRB) observations with the
Konus-WIND (KW) experiment, which has been providing a continuous all-sky
coverage in the 20 keV-15 MeV band during the period from 1994 to present. The
recent results include a systematic study of GRBs with known redshifts and a
search for ultra-long GRBs in the KW archival data. We also discuss the KW
capabilities for multi-messenger astronomy.


  To provide a better streaming experience, video clients today select their
video rates by observing and estimating the available capacity. Recent work has
shown that capacity estimation is fraught with difficulties because of complex
interactions between the ABR control loop, HTTP server performance and TCP
congestion control. Estimation-based rate selection algorithms can lead to
unnecessary rebuffering events and suboptimal video quality. This paper argues
that we should do away with estimating network capacity, and instead directly
observe and control the playback buffer--which is the state variable we are
most interested in controlling. We present a class of "buffer-based" rate
selection algorithms that reduce the rebuffering rate while allowing us to
control the delivered video quality. We implemented our algorithms inside the
Netflix video client and ran a series of experiments spanning millions of
Netflix users around the world. Our results show that by doing away with
estimating network capacity and instead focusing on buffer occupancy, we can
reduce rebuffer rates by 20% while holding video rate constant.


  The profusion of spectral bands generated by the acquisition process of
hyperspectral images generally leads to high computational costs. Such
difficulties arise in particular with nonlinear unmixing methods, which are
naturally more complex than linear ones. This complexity, associated with the
high redundancy of information within the complete set of bands, make the
search of band selection algorithms relevant. With this work, we propose a band
selection strategy in reproducing kernel Hilbert spaces that allows to
drastically reduce the processing time required by nonlinear unmixing
techniques. Simulation results show a complexity reduction of two orders of
magnitude without compromising unmixing performance.


  Commutator-based entropic uncertainty relations in multidimensional position
and momentum spaces are derived, twofold generalizing previous entropic
uncertainty relations for one-mode states. They provide optimal lower bounds
and imply the multidimensional variance-based uncertainty principle. The
article concludes with an open conjecture.


  Recently, a new class of supernovae Ia was discovered: the supernovae Iax;
the increasing sample of these objects share common features as lower
maximum-light velocities and typically lower peak magnitudes. In our scenario,
the progenitors of the SNe Iax are very massive white dwarfs, possibly hybrid
C+O+Ne white dwarfs; due to the accretion from a binary companion, they reach
the Chandrasekhar mass and undergo a central carbon deflagration, but the
deflagration is quenched when it reaches the outer O +Ne layer. This class of
SNe Ia are expected to be rarer than standard SNe Ia and do not affect the
chemical evolution in the solar neighbourhood; however, they have a short delay
time and they could influence the evolution of metal-poor systems. Therefore,
we have included in a stochastic chemical evolution model for the dwarf
spheroidal galaxy Ursa minor the contribution of SNe Iax. The model predicts a
spread in [Mn/Fe] in the ISM medium at low metallicity and - at the same time -
a decrease of the [alpha/Fe] elements, as in the classical time delay model.
This is in surprising agreement with the observed abundances in stars of Ursa
minor and provide a strong indication to the origin of this new classes of
SNIa.


  Unusual emission of light, called the unconventional Smith-Purcell radiation
(uSPR) in this paper, was demonstrated from an electron traveling near a finite
photonic crystal (PhC) at an ultra-relativistic velocity. This phenomenon is
not related to the accepted mechanism of the conventional SPR and arises
because the evanescent light from the electron has such a small decay constant
in the ultra-relativistic regime that it works practically as a plane-wave
probe entering the PhC from one end. We analyze the dependence of the SPR
spectrum on the velocity of electron and on the parity of excited photonic
bands and show, for PhCs made up of a finite number of cylinders, that uSPR
probes the photonic band structure very faithfully.


  Matrix factorization has found incredible success and widespread application
as a collaborative filtering based approach to recommendations. Unfortunately,
incorporating additional sources of evidence, especially ones that are
incomplete and noisy, is quite difficult to achieve in such models, however, is
often crucial for obtaining further gains in accuracy. For example, additional
information about businesses from reviews, categories, and attributes should be
leveraged for predicting user preferences, even though this information is
often inaccurate and partially-observed. Instead of creating customized methods
that are specific to each type of evidences, in this paper we present a generic
approach to factorization of relational data that collectively models all the
relations in the database. By learning a set of embeddings that are shared
across all the relations, the model is able to incorporate observed information
from all the relations, while also predicting all the relations of interest.
Our evaluation on multiple Amazon and Yelp datasets demonstrates effective
utilization of additional information for held-out preference prediction, but
further, we present accurate models even for the cold-starting businesses and
products for which we do not observe any ratings or reviews. We also illustrate
the capability of the model in imputing missing information and jointly
visualizing words, categories, and attribute factors.


  Stable ring vortex solitons, featuring a bright-shape, appear to be very rare
in nature. However, here we show that they exist and can be made dynamically
stable in defocusing cubic nonlinear media with an imprinted Bessel optical
lattice. We find the families of vortex lattice solitons and reveal their
salient properties, including the conditions required for their stability. We
show that the higher the soliton topological charge, the deeper the lattice
modulation necessary for stabilization.


We study integral geometric properties of non-compact harmonic spaces.


  Theoretical foundations of the problem of quantum spin tunneling in magnetic
nanostructures are presented. Several model problems are considered in detail,
including recent new results on tunneling in antiferromagnetic nanoparticles
and topologically nontrivial magnetic structures in systems with reduced
dimension.


  The natural indirect effect (NIE) and mediation proportion (MP) are two
measures of primary interest in mediation analysis. The standard approach for
estimating NIE and MP is through the product method, which involves a model for
the outcome conditional on the mediator and exposure and another model
describing the exposure-mediator relationship. The purpose of this article is
to comprehensively develop and investigate the finite-sample performance of NIE
and MP estimators via the product method. With four common data types, we
propose closed-form interval estimators via the theory of estimating equations
and multivariate delta method, and evaluate its empirical performance relative
to the bootstrap approach. In addition, we have observed that the rare outcome
assumption is frequently invoked to approximate the NIE and MP with a binary
outcome, although this approximation may lead to non-negligible bias when the
outcome is common. We therefore introduce the exact expressions for NIE and MP
with a binary outcome without the rare outcome assumption and compare its
performance with the approximate estimators. Based upon these theoretical
developments and empirical studies, we offer several practical recommendations
to inform practice. An R package mediateP is developed to implement the methods
for point and variance estimation discussed in this paper.


  Adversarial attack of CNN aims at deceiving models to misbehave by adding
imperceptible perturbations to images. This feature facilitates to understand
neural networks deeply and to improve the robustness of deep learning models.
Although several works have focused on attacking image classifiers and object
detectors, an effective and efficient method for attacking single object
trackers of any target in a model-free way remains lacking. In this paper, a
cooling-shrinking attack method is proposed to deceive state-of-the-art
SiameseRPN-based trackers. An effective and efficient perturbation generator is
trained with a carefully designed adversarial loss, which can simultaneously
cool hot regions where the target exists on the heatmaps and force the
predicted bounding box to shrink, making the tracked target invisible to
trackers. Numerous experiments on OTB100, VOT2018, and LaSOT datasets show that
our method can effectively fool the state-of-the-art SiameseRPN++ tracker by
adding small perturbations to the template or the search regions. Besides, our
method has good transferability and is able to deceive other top-performance
trackers such as DaSiamRPN, DaSiamRPN-UpdateNet, and DiMP. The source codes are
available at https://github.com/MasterBin-IIAU/CSA.


  We show that nonlinear phase shifts and third-order dispersion can compensate
each other in short-pulse fiber amplifiers. In particular, we consider
chirped-pulse fiber amplifiers at wavelengths for which the fiber dispersion is
normal. The nonlinear phase shift accumulated in the amplifier can be
compensated by the third-order dispersion of the combination of a fiber
stretcher and grating compressor. A numerical model is used to predict the
compensation, and initial experimental results that exhibit the main features
of the calculations are presented. In the presence of third-order dispersion,
an optimal nonlinear phase shift reduces the pulse duration, and enhances the
peak power and pulse contrast compared to the pulse produced in linear
propagation. Contrary to common belief, fiber stretchers can perform as well or
better than grating stretchers in fiber amplifiers, while offering the major
practical advantages of a waveguide medium. The relative benefits of a fiber
stretcher increase with increasing pulse energy, so the results presented here
will be relevant to fiber amplifiers designed for the highest pulse energies.


  A generalized Bailey pair, which contains several special cases considered by
Bailey (\emph{Proc. London Math. Soc. (2)}, 50 (1949), 421--435), is derived
and used to find a number of new Rogers-Ramanujan type identities.
Consideration of associated $q$-difference equations points to a connection
with a mild extension of Gordon's combinatorial generalization of the
Rogers-Ramanujan identities (\emph{Amer. J. Math.}, 83 (1961), 393--399). This,
in turn, allows the formulation of natural combinatorial interpretations of
many of the identities in Slater's list (\emph{Proc. London Math. Soc. (2)} 54
(1952), 147--167), as well as the new identities presented here. A list of 26
new double sum--product Rogers-Ramanujan type identities are included as an
appendix.


  In this work we characterise the properties of the object SDSS
J020536.84-081424.7, an extended nebular region with projected extension of $14
\times 14$ kpc$^{2}$ in the line of sight of the ETG Mrk 1172, using
unprecedented spectroscopic data from MUSE. We perform a spatially resolved
stellar population synthesis and estimate the stellar mass for both Mrk 1172
($1 \times 10^{11} M_{\odot}$) and our object of study ($3 \times 10^{9}
M_{\odot}$). While the stellar content of Mrk 1172 is dominated by an old
($\sim 10$ Gyr) stellar population, the extended nebular emission has its light
dominated by young to intermediate age populations (from $\sim 100$ Myr to
$\sim 1$ Gyr) and presents strong emission lines such as: H${\beta}$, [O III]
${\lambda}{\lambda}$4959,5007, H${\alpha}$, [N II]
${\lambda}{\lambda}$6549,6585 and [S II] ${\lambda}{\lambda}$6717,6732. Using
these emission lines we find that it is metal-poor (with $Z \sim$ 1/3
$Z_{\odot}$, comparable to the LMC) and is actively forming stars ($0.70$
M$_{\odot}$ yr$^{-1}$), especially in a few bright clumpy knots that are
readily visible in H${\alpha}$. The object has an ionised gas mass $\geq 3.8
\times 10^{5}$ M$_{\odot}$. Moreover, the motion of the gas is well described
by a gas in circular orbit in the plane of a disk and is being affected by
interaction with Mrk 1172. We conclude that SDSS J020536.84-081424.7 is most
likely a dwarf irregular galaxy (dIGal).


  An operator that generates an approximate symmetry of long-range Rydberg
molecules (LRRMs) formed by two alkali atoms, one in a Rydberg state and the
other in the ground state, is identified. This is first done by evaluating the
natural orbitals associated to a variational calculation of the binding wave
function within the Born-Oppenheimer description of the molecule including $s-$
and $p-$ Fermi pseudopotential and the hyperfine structure energy terms. The
resulting orbitals with highest occupation number are shown to be identical to
those obtained by a perturbative model for high angular momentum -- trilobite
and butterfly -- LRRMs. Whenever the slight dependence of the quantum defects
of the Rydberg electron on its total momentum $\vec j = \vec \ell +\vec s_1$
can be neglected, the symmetry operator of the high angular momentum LRRMs
orbitals is identified as the sum of the spin of the Rydberg electron $\vec
s_1$, spin of the valence electron $\vec s_2$ and the spin of nucleus $\vec i$
of the ground state atom, $\vec {N} =\vec {s_1} + \vec {s_2} + \vec {i}$. The
spin-orbitals that diagonize $\vec{N}$ define compact basis sets for the
description of LRRMs beyond the aforementioned approximations. The matrix
elements of the Hamitonian in these basis sets have simple expressions, so that
the relevance of triplet and singlet contributions can be directly estimated.
The expected consequences of this approximate spin-symmetry on the spectra of
LRRMs are briefly described.


  A special class of type Ia supernovae that is not subject to ordinary and
additional intragalactic gray absorption and chemical evolution has been
identified. Analysis of the Hubble diagrams constructed for these supernovae
confirms the accelerated expansion of the Universe irrespective of the chemical
evolution and possible gray absorption in galaxies.


  We describe how the strings, which are classical solutions of the continuum
three-dimensional U(1)+Higgs theory, can be studied on the lattice. The effect
of an external magnetic field is also discussed and the first results on the
string free energy are presented. It is shown that the string free energy can
be used as an order parameter when the scalar self-coupling is large and the
transition is continuous.


  Supermassive black holes (SMBHs) are nowadays believed to reside in most
local galaxies, and the available data show an empirical correlation between
bulge luminosity - or stellar velocity dispersion - and black hole mass,
suggesting a single mechanism for assembling black holes and forming spheroids
in galaxy halos. The evidence is therefore in favour of a co-evolution between
galaxies, black holes and quasars. In cold dark matter cosmogonies, small-mass
subgalactic systems form first to merge later into larger and larger
structures. In this paradigm galaxy halos experience multiple mergers during
their lifetime. If every galaxy with a bulge hosts a SMBH in its center, and a
local galaxy has been made up by multiple mergers, then a black hole binary is
a natural evolutionary stage. The evolution of the supermassive black hole
population clearly has to be investigated taking into account both the
cosmological framework and the dynamical evolution of SMBHs and their hosts.
The seeds of SMBHs have to be looked for in the early Universe, as very
luminous quasars are detected up to redshift higher than z=6. These black holes
evolve then in a hierarchical fashion, following the merger hierarchy of their
host halos. Accretion of gas, traced by quasar activity, plays a fundamental
role in determining the two parameters defining a black hole: mass and spin. A
particularly intriguing epoch is the initial phase of SMBH growth. It is very
challenging to meet the observational constraints at z=6 if BHs are not fed at
very high rates in their infancy.


  We provide a dispersion-theoretical representation of the reaction amplitudes
$\gamma K\to K \pi$ in all charge channels, based on modern pion-kaon $P$-wave
phase shift input. Crossed-channel singularities are fixed from phenomenology
as far as possible. We demonstrate how the subtraction constants can be matched
to a low-energy theorem and radiative couplings of the $K^*(892)$ resonances,
thereby providing a model-independent framework for future analyses of
high-precision kaon Primakoff data.


  We analyze the experimental observation of metastable anisotropy resistance
orientation at half filled quantum Hall fluids by means of a model of a quantum
nematic liquid in an explicit symmetry breaking potential. We interpret the
observed ``rotation'' of the anisotropy axis as a process of nucleation of
nematic domains and compute the nucleation rate within this model. By comparing
with experiment, we are able to predict the critical radius of nematic bubbles,
$R_c\sim 2.6 \mu m $. Each domain contains about $10^4$ electrons.


  Learning-based depth estimation has witnessed recent progress in multiple
directions; from self-supervision using monocular video to supervised methods
offering highest accuracy. Complementary to supervision, further boosts to
performance and robustness are gained by combining information from multiple
signals. In this paper we systematically investigate key trade-offs associated
with sensor and modality design choices as well as related model training
strategies. Our study leads us to a new method, capable of connecting
modality-specific advantages from polarisation, Time-of-Flight and
structured-light inputs. We propose a novel pipeline capable of estimating
depth from monocular polarisation for which we evaluate various training
signals. The inversion of differentiable analytic models thereby connects scene
geometry with polarisation and ToF signals and enables self-supervised and
cross-modal learning. In the absence of existing multimodal datasets, we
examine our approach with a custom-made multi-modal camera rig and collect
CroMo; the first dataset to consist of synchronized stereo polarisation,
indirect ToF and structured-light depth, captured at video rates. Extensive
experiments on challenging video scenes confirm both qualitative and
quantitative pipeline advantages where we are able to outperform competitive
monocular depth estimation method.


  There is currently a significant need for robust and efficient methods for
characterizing quantum devices. While there has been significant progress in
this direction, there remains a crucial need to precisely determine the
strength and type of errors on individual gate operations, in order to assess
and improve control as well as reliably bound the total error in a quantum
circuit given some partial information about the errors on the components. In
this work, we first provide an optimal bound on the total fidelity of a circuit
in terms of component fidelities, which can be efficiently experimentally
estimated via randomized benchmarking. We then derive a tighter bound that
applies under additional information about the coherence of the error, namely,
the unitarity, which can also be efficiently estimated via a related
experimental protocol. This improved bound smoothly interpolates between the
worst-case quadratic and best-case linear scalings for composite error
channels. As an application we show how our analysis substantially improves the
achievable precision on estimates of the error rates of individual gates under
interleaved randomized benchmarking, enabling greater precision for current
experimental methods to assess and tune-up control over quantum gate
operations.


  Attractors of cooperative dynamical systems are particularly simple; for
example, a nontrivial periodic orbit cannot be an attractor. This paper
provides characterizations of attractors for the wider class of coherent
systems, defined by the property that no directed feedback loops are negative.
Several new results for cooperative systems are obtained in the process.


  We investigate the non-perturbative renormalization group flow of the scalar
Galileon model in flat space. We discuss different expansion schemes of the
Galileon truncation, including a heat-kernel based derivative expansion, a
vertex expansion in momentum space and a curvature expansion in terms of a
covariant geometric formulation. We find that the Galileon symmetry prevents a
quantum induced renormalization group running of the Galileon couplings.
Consequently, the Galileon truncation only features a trivial Gaussian fixed
point.


  A one-relator group with lower central series of length \omega^2 is
constructed. This answers a problem of G. Baumslag.


  We establish the existence of loop type subcontinua of nonnegative solutions
for a class of concave-convex type elliptic equations with indefinite weights,
under Dirichlet and Neumann boundary conditions. Our approach depends on local
and global bifurcation analysis from the zero solution in a non-regular
setting, since the nonlinearities considered are not differentiable at zero, so
that the standard bifurcation theory does not apply. To overcome this
difficulty, we combine a regularization scheme with a priori bounds, and
Whyburn's topological method. Furthermore, via a continuity argument we prove a
positivity property for subcontinua of nonnegative solutions. These results are
based on a positivity theorem for the associated concave problem proved in
[15], and extend previous results established in the powerlike case.


  Consider a directed network where each node is either red (using the red
product), blue (using the blue product), or uncolored (undecided). Then in each
round, an uncolored node chooses red (resp. blue) with some probability
proportional to the number of its red (resp. blue) out-neighbors. What is the
best strategy to maximize the expected final number of red nodes given the
budget to select $k$ red seed nodes? After proving that this problem is
computationally hard, we provide a polynomial time approximation algorithm with
the best possible approximation guarantee, building on the monotonicity and
submodularity of the objective function and exploiting the Monte Carlo method.
Furthermore, our experiments on various real-world and synthetic networks
demonstrate that our proposed algorithm outperforms other algorithms.
Additionally, we investigate the convergence time of the aforementioned process
both theoretically and experimentally. In particular, we prove several tight
bounds on the convergence time in terms of different graph parameters, such as
the number of nodes/edges, maximum out-degree and diameter, by developing novel
proof techniques.


  Hybridization of semiconducting and magnetic materials into a single
heterostructure is believed to be potentially applicable to the design of novel
functional spintronic devices. In the present work we report epitaxial
stabilization of four magnetically ordered iron oxide phases (Fe3O4,
{\gamma}-Fe2O3, {\alpha}-Fe2O3 and most exotic metastable {\epsilon}-Fe2O3) in
the form of nanometer sized single crystalline films on GaN(0001) surface. The
epitaxial growth of as many as four distinctly different iron oxide phases is
demonstrated within the same single-target Laser MBE technological process on a
GaN semiconductor substrate widely used for electronic device fabrication. The
discussed iron oxides belong to a family of simple formula magnetic materials
exhibiting a rich variety of outstanding physical properties including peculiar
Verwey and Morin phase transitions in Fe3O4 and {\alpha}-Fe2O3 and multiferroic
behavior in metastable magnetically hard {\epsilon}-Fe2O3 ferrite. The physical
reasons standing behind the nucleation of a particular phase in an epitaxial
growth process deserve interest from the fundamental point of view. The
practical side of the presented study is to exploit the tunable polymorphism of
iron oxides for creation of ferroic-on-semiconductor heterostructures usable in
novel spintronic devices. By application of a wide range of experimental
techniques the surface morphology, crystalline structure, electronic and
magnetic properties of the single phase iron oxide epitaxial films on GaN have
been studied. A comprehensive comparison has been made to the properties of the
same ferrite materials in the bulk and nanostructured form reported by other
research groups.


  We introduce a ring of noncommutative shifted symmetric functions based on an
integer-indexed sequence of shift parameters. Using generating series and
quasideterminants, this multiparameter approach produces deformations of the
ring of noncommutative symmetric functions. Shifted versions of ribbon Schur
functions are defined and form a basis for the ring. Further, we produce
analogues of Jacobi-Trudi and N\"agelsbach-Kostka formulas, a duality
anti-algebra isomorphism, shifted quasi-Schur functions, and Giambelli's
formula in this setup. In addition, an analogue of power sums is provided,
satisfying versions of Wronski and Newton formulas. Finally, a realization of
these noncommutative shifted symmetric functions as rational functions in
noncommuting variables is given. These realizations have a shifted symmetry
under exchange of the variables and are well-behaved under extension of the
list of variables.


  The focus of this investigation is to quantify the conversion of magnetic to
thermal energy initiated by a quiet Sun cancellation event and to explore the
resulting dynamics from the interaction of the opposite polarity magnetic
features. We used imaging spectroscopy in the H$\alpha$ line, along with
spectropolarimetry in the \ion{Fe}{I} 6173~{\AA} and \ion{Ca}{II} 8542~{\AA}
lines from the Swedish Solar Telescope (SST) to study a reconnection-related
cancellation and the appearance of a quiet Sun Ellerman bomb (QSEB). We
observed, for the first time, QSEB signature in both the wings and core of the
\ion{Fe}{I} 6173~{\AA} line. We also found that, at times, the \ion{Fe}{I}
line-core intensity reaches higher values than the quiet Sun continuum
intensity. From FIRTEZ-dz inversions of the Stokes profiles in \ion{Fe}{I} and
\ion{Ca}{II} lines, we found enhanced temperature, with respect to the quiet
Sun values, at the photospheric ($\log\tau_c$ = -1.5; $\sim$1000 K) and lower
chromospheric heights ($\log\tau_c$ = -4.5; $\sim$360 K). From the calculation
of total magnetic energy and thermal energy within these two layers it was
confirmed that the magnetic energy released during the flux cancellation can
support heating in the aforesaid height range. Further, the temperature
stratification maps enabled us to identify cumulative effects of successive
reconnection on temperature pattern, including recurring temperature
enhancements. Similarly, Doppler velocity stratification maps revealed impacts
on plasma flow pattern, such as a sudden change in the flow direction.