  Pretrained Transformers (PT) have been shown to improve Out of Distribution
(OOD) robustness than traditional models such as Bag of Words (BOW), LSTMs,
Convolutional Neural Networks (CNN) powered by Word2Vec and Glove embeddings.
How does the robustness comparison hold in a real world setting where some part
of the dataset can be noisy? Do PT also provide more robust representation than
traditional models on exposure to noisy data? We perform a comparative study on
10 models and find an empirical evidence that PT provide less robust
representation than traditional models on exposure to noisy data. We
investigate further and augment PT with an adversarial filtering (AF) mechanism
that has been shown to improve OOD generalization. However, increase in
generalization does not necessarily increase robustness, as we find that noisy
data fools the AF method powered by PT.


  Let $A$ be a unital simple separable exact C$^*$-algebra which is
approximately divisible and of real rank zero. We prove that the set of
positive elements in $A$ with a fixed non-compact Cuntz class has vanishing
homotopy groups. Combined with work of S. Zhang for the case of compact
elements, this gives a complete calculation of the homotopy groups of Cuntz
classes for these algebras. Examples covered include approximately
finite-dimensional (AF) algebras and irrational noncommutative tori.


  We discuss the effect of certain types of static disorder, like that induced
by curvature or topological defects, on the quantum correction to the
conductivity in graphene. We find that when the intervalley scattering time is
long or comparable to $\tau_{\phi}$, these defects can induce an effective time
reversal symmetry breaking of the hamiltonian associated to each one of the two
valleys in graphene. The phenomenon suppresses the magnitude of the quantum
correction to the conductivity and may result in the complete absence of a low
field magnetoresistance, as recently found experimentally. Our work shows that
a quantitative description of weak localization in graphene must include the
analysis of new regimes, not present in conventional two dimensional electron
gases.


  We study the phase diagram of an imbalanced two-component Fermi gas in
optical lattices of 1-3 dimensions, considering the possibilities of the FFLO,
Sarma/breached pair, BCS and normal states as well as phase separation, at
finite and zero temperatures. In particular, phase diagrams with respect to
average chemical potential and the chemical potential difference of the two
components are considered, because this gives the essential information about
the shell structures of phases that will occur in presence of an additional
(harmonic) confinement. These phase diagrams in 1, 2 and 3 dimensions show in a
striking way the effect of Van Hove singularities on the FFLO state. Although
we focus on population imbalanced gases, the results are relevant also for the
(effective) mass imbalanced case. We demonstrate by LDA calculations that
various shell structures such as normal-FFLO-BCS-FFLO-normal, or FFLO-normal,
are possible in presence of a background harmonic trap. The phases are
reflected in noise correlations: especially in 1D the unpaired atoms leave a
clear signature of the FFLO state as a zero-correlation area (``breach'')
within the Fermi sea. This strong signature occurs both for a 1D lattice as
well as for a 1D continuum. We also discuss the effect of Hartree energies and
the Gorkov correction on the phase diagrams.


  We study the free boundary of the porous medium equation with nonlocal drifts
in dimension one. Under the assumption that the initial data has
super-quadratic growth at the free boundary, we show that the solution is
smooth in space and $C^{2,1}_{\loc}$ in time, and then the free boundary is
$C^{2,1}_{\loc}$. Moreover if the drift is local, both the solution and the
free boundary are smooth.


  Bringing a rigid object into contact with a soft elastic tube causes the tube
to conform to the surface of the object, resulting in contact lines. The
curvature of the tube walls near these contact lines is often large and is
typically regularized by the finite bending rigidity of the tube. Here, we show
using experiments and a F\"{o}ppl--von K\'{a}rm\'{a}n-like theory that a second
mechanism of curvature regularization occurs when the tube is axially
stretched. The radius of curvature obtained is unrelated to the bending
rigidity of the tube walls, increases with the applied stretching force and
decreases with sheet thickness, in contrast with the effects of finite bending
rigidity. %Moreover, the axial force decreases the contact area between the
tube and the intruding object, potentially reducing the drag necessary to
propel the object through the tube. We show that these features are due to an
interplay between geometry and mechanics specific to elastic tubes, but one
that is absent from both planar sheets and spherical shells.


  This work investigates the challenge of learning and reasoning for
Commonsense Question Answering given an external source of knowledge in the
form of a knowledge graph (KG). We propose a novel graph neural network
architecture, called Dynamic Relevance Graph Network (DRGN). DRGN operates on a
given KG subgraph based on the question and answers entities and uses the
relevance scores between the nodes to establish new edges dynamically for
learning node representations in the graph network. This explicit usage of
relevance as graph edges has the following advantages, a) the model can exploit
the existing relationships, re-scale the node weights, and influence the way
the neighborhood nodes' representations are aggregated in the KG subgraph, b)
It potentially recovers the missing edges in KG that are needed for reasoning.
Moreover, as a byproduct, our model improves handling the negative questions
due to considering the relevance between the question node and the graph
entities. Our proposed approach shows competitive performance on two QA
benchmarks, CommonsenseQA and OpenbookQA, compared to the state-of-the-art
published results.


  Nb-substituting Fe impurity in KNbO3 is studied in first-principles supercell
calculations by the linear muffin-tin orbital method. Possible ways to account
for the impurity charge compensation are discussed. Calculations are done in
the local density approximation (LDA) and, for better description of Coulomb
correlation effects within the localized impurity states, also in the LDA+U
scheme. The achievements and problems encountered in both approaches are
analyzed. It is found that the impurity possess either a low-spin configuration
(with 0 or 1 compensating electron), or a high-spin configuration (with 2 or 3
compensating electrons), the latter two apparently corresponding to practically
relevant rechargeable impurity states.


  Quasi-periodic oscillations, often present in the power density spectrum of
accretion disk around black holes, are useful probes for the understanding of
gravitational interaction in the near-horizon regime of black holes. Since the
presence of an extra spatial dimension modifies the near horizon geometry of
black holes, it is expected that the study of these quasi-periodic oscillations
may shed some light on the possible existence of these extra dimensions.
Intriguingly, most of the extra dimensional models, which are of significant
interest to the scientific community, predicts the existence of a tidal charge
parameter in black hole spacetimes. This tidal charge parameter can have an
overall negative sign and is a distinctive signature of the extra dimensions.
Motivated by this, we have studied the quasi-periodic oscillations for a
rotating braneworld black hole using the available theoretical models.
Subsequently, we have used the observations of the quasi-periodic oscillations
from available black hole sources, e.g., GRO J1655 -- 40, XTE J1550 -- 564, GRS
1915 + 105, H 1743 + 322 and Sgr A* and have compared them with the predictions
from the relevant theoretical models, in order to estimate the tidal charge
parameter. It turns out that among the 11 theoretical models considered here, 8
of them predict a negative value for the tidal charge parameter, while for the
others negative values of the tidal charge parameter are also well within the
1-$\sigma$ confidence interval.


  Spectral risk objectives - also called $L$-risks - allow for learning systems
to interpolate between optimizing average-case performance (as in empirical
risk minimization) and worst-case performance on a task. We develop stochastic
algorithms to optimize these quantities by characterizing their subdifferential
and addressing challenges such as biasedness of subgradient estimates and
non-smoothness of the objective. We show theoretically and experimentally that
out-of-the-box approaches such as stochastic subgradient and dual averaging are
hindered by bias and that our approach outperforms them.


  It is shown how an $SU(3)^{N}$ nonsupersymmetric quiver gauge theory can
accommodate the standard model with three chiral families and unify all of
$SU(3)_C$, $SU(2)_L$ and $U(1)_Y$ couplings with high accuracy at one unique
scale estimated as $M \simeq 4$ TeV.


  Using high resolution, two-dimensional hydrodynamical simulations, we
investigate the evolution of a self-gravitating multi-phase interstellar medium
in the central kiloparsec region of a galactic disk. We find that a
gravitationally and thermally unstable disk evolves, in a self-stabilizing
manner, into a globally quasi-stable disk that consists of cold (T < 100 K),
dense clumps and filaments surrounded by hot (T > 10^4 K), diffuse medium. The
quasi-stationary, filamentary structure of the cold gas is remarkable. The hot
gas, characterized by low-density holes and voids, is produced by shock
heating. The shocks derive their energy from differential rotation and
gravitational perturbations due to the formation of cold dense clumps. In the
quasi-stable phase where cold and dense clouds are formed, the effective
stability parameter, Q, has a value in the range 2-5. The dynamic range of our
multi-phase calculations is 10^6 - 10^7 in both density and temperature. Phase
diagrams for this turbulent medium are analyzed and discussed.


  We study local holomorphic maps between K\"ahler manifolds preserving
$(p,p)$-forms. In this direction, we prove that any such local holomorphic map
$F$ is a holomorphic isometry up to a scalar constant provided that $p$ is
strictly less than the complex dimension of the domain of $F$. We then study
local holomorphic maps between finite dimensional complex space forms
preserving invariant $(p,p)$-forms. It was proved by Calabi that there does not
exist a local holomorphic isometry between complex space forms $M$ and $N$
provided that $M$ and $N$ are of different types. In this article, we
generalize this result to local holomorphic maps between complex space forms
$M$ and $N$ preserving invariant $(p,p)$-forms whenever $M$ and $N$ are of
different types except for the case where the universal covers of $M, N$ are
biholomorphic to $\mathbb{C}^m, \mathbb{P}^n$, respectively and $2\le p=m<n$.
We also obtain some results in more general settings, including the study on
indefinite K\"ahler manifolds and relatives for K\"ahler manifolds.


  Previous work proposed a strong-disorder renormalization approach for the
Anderson model, using it to calculate the density of states and the inverse
participation ratio [Johri \& Bhatt, Phys.\ Rev.\ B {\bf 90} 060205(R) (2014)].
This is interesting because of the potential for expansion to higher dimensions
and to interacting systems. The original proposal used a non-standard
perturbation theory approach which avoided degeneracies. We implemented the
same structure but with standard Rayleigh-Schr\"odinger perturbation theory.
Here degeneracies do arise, and we consider two approaches, one in which
renormalization is suppressed if degeneracy is present and a second in which
the most common form of degeneracy is handled using standard degenerate
perturbation theory. The version in which degeneracies are not handled performs
similarly to the original proposal, and the addition of degeneracies provides
some improvement.


  We have studied a spectrum of Q0122+0338 (z = 1.202) obtained by the FOS on
board HST. We present the analysis of three associated absorption systems at z
= 1.207, 1.199 and 1.166. The most complex of these at z = 1.207 shows strong
absorption from the highly ionized transitions of Lyman alpha, Lyman beta, N V,
O VI, Si III, Si IV, and possibly P V. We derive minimal ionic column densities
and compare them with those predicted from numerical photoionization models. We
find that conditions in the absorbing gas are consistent with an absorber with
metallicity twice solar and a total absorbing column density of N(H) = 2*10^19
cm^2. The kinematics of the absorption lines in the z = 1.207 system suggest
that a correlation exists between the relative velocity and the creation
ionization potential energy for each transition. This is evidence that a
complex, multi-component absorber exists. Althought the location of the
absorber is uncertain, we consider the origin of this absorption system using
the available data and discuss how the high-ionization, and high-metallicity
indicate that the absorber may be intrinsic to Q0122+0338.


  We study the nonexpansivity of reflection mappings in geodesic spaces and
apply our findings to the averaged alternating reflection algorithm employed in
solving the convex feasibility problem for two sets in a nonlinear context. We
show that weak convergence results from Hilbert spaces find natural
counterparts in spaces of constant curvature. Moreover, in this particular
setting, one obtains strong convergence.


  Convolutional neural network (CNN) inference on mobile devices demands
efficient hardware acceleration of low-precision (INT8) general matrix
multiplication (GEMM). The systolic array (SA) is a pipelined 2D array of
processing elements (PEs), with very efficient local data movement, well suited
to accelerating GEMM, and widely deployed in industry. In this work, we
describe two significant improvements to the traditional SA architecture, to
specifically optimize for CNN inference. Firstly, we generalize the traditional
scalar PE, into a Tensor-PE, which gives rise to a family of new Systolic
Tensor Array (STA) microarchitectures. The STA family increases intra-PE
operand reuse and datapath efficiency, resulting in circuit area and power
dissipation reduction of as much as 2.08x and 1.36x respectively, compared to
the conventional SA at iso-throughput with INT8 operands. Secondly, we extend
this design to support a novel block-sparse data format called density-bound
block (DBB). This variant (STA-DBB) achieves a 3.14x and 1.97x improvement over
the SA baseline at iso-throughput in area and power respectively, when
processing specially-trained DBB-sparse models, while remaining fully backwards
compatible with dense models.


  Many assembly lines related optimization problems have been tackled by
researchers in the last decades due to its relevance for the decision makers
within manufacturing industry. Many of theses problems, more specifically
Assembly Lines Balancing and Sequencing problems, are known to be NP-Hard.
Therefore, Computational Intelligence solution approaches have been conceived
in order to provide practical use decision making tools. In this work, we
proposed a simultaneous solution approach in order to tackle both Balancing and
Sequencing problems utilizing an effective meta-heuristic algorithm referred as
Fish School Search. Three different test instances were solved with the
original and two modified versions of this algorithm and the results were
compared with Particle Swarm Optimization Algorithm.


  In this paper we solve a
  selection problem for multidimensional SDE
  $d X^\varepsilon(t)=a(X^\varepsilon(t)) d t+\varepsilon
\sigma(X^\varepsilon(t))\, d W(t)$, where the drift and diffusion are locally
Lipschitz continuous outside of a fixed hyperplane $H$.
  It is assumed that $X^\varepsilon(0)=x^0\in H$, the drift $a(x)$ has a
Hoelder asymptotics as $x$ approaches $H$, and the limit ODE $d X(t)=a(X(t))\,
d t$ does not have a unique solution.
  We show that if the drift pushes the solution away of $H$, then the limit
process with certain probabilities selects some extreme solutions to the limit
ODE. If the drift attracts the solution to $H$, then the limit process
satisfies an ODE with some averaged coefficients. To prove the last result we
formulate an averaging principle, which is quite general and new.


  The obstructive sleep apnea-hypopnea (OSAH) syndrome is a very common and
frequently undiagnosed sleep disorder. It is characterized by repeated events
of partial (hypopnea) or total (apnea) obstruction of the upper airway while
sleeping. This study makes use of a previously developed method called DAS-KSVD
for multiclass structured dictionary learning to automatically detect
individual events of apnea and hypopnea using only blood oxygen saturation
signals. The method uses a combined discriminant measure which is capable of
efficiently quantifying the degree of discriminability of each one of the atoms
in a dictionary. DAS-KSVD was applied to detect and classify apnea and hypopnea
events from signals obtained from the Sleep Heart Health Study database. For
moderate to severe OSAH screening, a receiver operating characteristic curve
analysis of the results shows an area under the curve of 0.957 and diagnostic
sensitivity and specificity of 87.56% and 88.32%, respectively. These results
represent improvements as compared to most state-of-the-art procedures. Hence,
the method could be used for screening OSAH syndrome more reliably and
conveniently, using only a pulse oximeter.


  Particle acceleration using ultraintense, ultrashort laser pulses is one of
the most attractive topics in relativistic laser-plasma research. We report
proton/ion acceleration in the intensity range of 5x1019 W/cm2 to 3.3x1020
W/cm2 by irradiating linearly polarized, 30-fs, 1-PW laser pulses on 10- to
100-nm-thick polymer targets. The proton energy scaling with respect to the
intensity and target thickness was examined. The experiments demonstrated, for
the first time with linearly polarized light, a transition from the target
normal sheath acceleration to radiation pressure acceleration and showed a
maximum proton energy of 45 MeV when a 10-nm-thick target was irradiated by a
laser intensity of 3.3x1020 W/cm2. The experimental results were further
supported by two- and three-dimensional particle-in-cell simulations. Based on
the deduced proton energy scaling, proton beams having an energy of ~ 200 MeV
should be feasible at a laser intensity of 1.5x1021 W/cm2.


  In a continuation of our previous work, we outline a theory which should lead
to the construction of a universal pre-building and versal building with a
$\phi$-harmonic map from a Riemann surface, in the case of two-dimensional
buildings for the group $SL_3$. This will provide a generalization of the space
of leaves of the foliation defined by a quadratic differential in the classical
theory for $SL_2$. Our conjectural construction would determine the exponents
for $SL_3$ WKB problems, and it can be put into practice on examples.


  Most of the architectural research on photonic implementations of
measurement-based quantum computing (MBQC) has focused on the quantum resources
involved in the problem with the implicit assumption that these will provide
the main constraints on system scaling. However, the `flying-qubit'
architecture of photonic MBQC requires specific timing constraints that need to
be met by the classical control system. This classical control includes, for
example: the amplification of the signals from single-photon detectors to
voltage levels compatible with digital systems; the implementation of a control
system which converts measurement outcomes into basis settings for measuring
subsequent cluster qubits, in accordance with the quantum algorithm being
implemented; and the digital-to-analog converter (DAC) and amplifier systems
required to set these measurement bases using a fast phase modulator. In this
paper, we analyze the digital system needed to implement arbitrary one-qubit
rotations and controlled-NOT (CNOT) gates in discrete-variable photonic MBQC,
in the presence of an ideal cluster state generator, with the main aim of
understanding the timing constraints imposed by the digital logic on the analog
system and quantum hardware. We use static timing analysis of a Xilinx FPGA (7
series) to provide a practical upper bound on the speed at which the adaptive
measurement processing can be performed, in turn constraining the photonic
clock rate of the system. Our work points to the importance of co-designing the
classical control system in tandem with the quantum system in order to meet the
challenging specifications of a photonic quantum computer.


  We propose a systematic methodology for defining tournament solutions as
extensions of maximality. The central concepts of this methodology are maximal
qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy
of tournament solutions, which encompasses the top cycle, the uncovered set,
the Banks set, the minimal covering set, the tournament equilibrium set, the
Copeland set, and the bipartisan set. Moreover, the hierarchy includes a new
tournament solution, the minimal extending set, which is conjectured to refine
both the minimal covering set and the Banks set.


  A Galois theory of differential fields with parameters is developed in a
manner that generalizes Kolchin's theory. It is shown that all connected
differential algebraic groups are Galois groups of some appropriate
differential field extension.


  We apply the instanton counting method to study a class of four-dimensional
$\mathcal{N}=2$ supersymmetric quiver gauge theories with alternating
$\mathrm{SO}$ and $\mathrm{USp}$ gauge groups. We compute the partition
function in the $\Omega$-background and express it as functional integrals over
density functions. Applying the saddle point method, we derive the limit shape
equations which determine the dominant instanton configurations in the flat
space limit. The solution to the limit shape equations gives the Seiberg-Witten
geometry of the low energy effective theory. As an illustrating example, we
work out explicitly the Seiberg-Witten geometry for linear quiver gauge
theories. Our result matches the Seiberg-Witten solution obtained previously
using the method of brane constructions in string theory.


  (abridged) Methods: We derive maps of submillimeter dust optical depth and
effective dust temperature from Herschel data that were calibrated against
Planck. After calibration, we then fit a modified blackbody to the
long-wavelength Herschel data, using the Planck-derived dust opacity spectral
index beta, derived on scales of 30' (or ~1 pc). We use this model to make
predictions of the submillimeter flux density at 850 micron, and we compare
these in turn with APEX-Laboca observations. Results: A comparison of the
submillimeter dust optical depth and near-infrared extinction data reveals
evidence for an increased submillimeter dust opacity at high column densities,
interpreted as an indication of grain growth in the inner parts of the core.
Additionally, a comparison of the Herschel dust model and the Laboca data
reveals that the frequency dependence of the submillimeter opacity, described
by the spectral index beta, does not change. A single beta that is only
slightly different from the Planck-derived value is sufficient to describe the
data, beta=1.53+/-0.07. We apply a similar analysis to Barnard 68, a core with
significantly lower column densities than FeSt 1-457, and we do not find
evidence for grain growth but also a single beta. Conclusions: While we find
evidence for grain growth from the dust opacity in FeSt 1-457, we find no
evidence for significant variations in the dust opacity spectral index beta on
scales 0.02<x<1 pc (or 36"<x<30'). The correction to the Planck-derived dust
beta that we find in both cases is on the order of the measurement error, not
including any systematic errors, and it would thus be reasonable to directly
apply the dust beta from the Planck all-sky dust model. As a corollary,
reliable effective temperature maps can be derived which would be otherwise
affected by beta variations.


  We provide the most accurate results for the QCD transition line so far. We
optimize the definition of the crossover temperature $T_c$, allowing for its
very precise determination, and extrapolate from imaginary chemical potential
up to real $\mu_B \approx 300$ MeV. The definition of $T_c$ adopted in this
work is based on the observation that the chiral susceptibility as a function
of the condensate is an almost universal curve at zero and imaganiary $\mu_B$.
We obtain the parameters $\kappa_2=0.0153(18)$ and $\kappa_4=0.00032(67)$ as a
continuum extrapolation based on $N_t=10,12$ and $16$ lattices with physical
quark masses. We also extrapolate the peak value of the chiral susceptibility
and the width of the chiral transition along the crossover line. In fact, both
of these are consistent with a constant function of $\mu_B$. We see no sign of
criticality in the explored range.


  This paper presents a high-order method for solving an interface problem for
the Poisson equation on embedded meshes through a coupled finite element and
integral equation approach. The method is capable of handling homogeneous or
inhomogeneous jump conditions without modification and retains high-order
convergence close to the embedded interface. We present finite element-integral
equation (FE-IE) formulations for interior, exterior, and interface problems.
The treatments of the exterior and interface problems are new. The resulting
linear systems are solved through an iterative approach exploiting the
second-kind nature of the IE operator combined with algebraic multigrid
preconditioning for the FE part. Assuming smooth continuations of coefficients
and right-hand-side data, we show error analysis supporting high-order
accuracy. Numerical evidence further supports our claims of efficiency and
high-order accuracy for smooth data.


  In clinical research and clinical decision-making, it is important to know if
a study changes or only supports the current standards of care for specific
disease management. We define such a change as transformative and a support as
incremental research. It usually requires a huge amount of domain expertise and
time for humans to finish such tasks. Faculty Opinions provides us with a
well-annotated corpus on whether a research challenges or only confirms
established research. In this study, a machine learning approach is proposed to
distinguishing transformative from incremental clinical evidence. The texts
from both abstract and a 2-year window of citing sentences are collected for a
training set of clinical studies recommended and labeled by Faculty Opinions
experts. We achieve the best performance with an average AUC of 0.755
(0.705-0.875) using Random Forest as the classifier and citing sentences as the
feature. The results showed that transformative research has typical language
patterns in citing sentences unlike abstract sentences. We provide an efficient
tool for identifying those clinical evidence challenging or only confirming
established claims for clinicians and researchers.


  A boson mapping of pair field operators is presented. The mapping preserves
all hermiticity properties and the Poisson bracket relations between fields and
momenta. The most practical application of the boson mapping is to field
theories which exhibit bound states of pairs of fields. As a concrete
application we consider, in the low energy limit, the Wick-Cutkosky model with
equal mass for the charged fields.


  It is shown how to construct a basis in which two arbitrary complex
antisymmetric matrices C and C' acquire simultaneously canonical forms. The
present construction is not restricted by any conditions on properties of the
C^+C' matrix. Canonical bases pertaining to the generator-coordinate-method
treatment of many-fermion systems are discussed.


  We report a comparative study of the dynamics of Cu2O, Ag2O and Au2O (i.e.
M2O with M = Au, Ag and Cu) using first principle calculations based on the
density functional theory. Here for the first time we show that the nature of
chemical bonding and open space in the unit cell are directly related to the
magnitude of thermal expansion coefficient. A good match between the calculated
phonon density of states and that derived from inelastic neutron scattering
measurements is obtained for Cu2O and Ag2O. The calculated thermal expansions
of Ag2O and Cu2O are negative, in agreement with available experimental data,
while it is found to be positive for Au2O. We identify the low energy phonon
modes responsible for this anomalous thermal expansion. We further calculate
the charge density in the three compounds and find that the magnitude of the
ionic character of the Ag2O, Cu2O, and Au2O crystals is in decreasing order,
with an Au-O bond of covalent nature strongly rigidifying the Au4O tetrahedral
units. The nature of the chemical bonding is also found to be an important
ingredient to understand the large shift of the phonon frequencies of these
solids with pressure and temperature. In particular, the quartic component of
the anharmonic term in the crystal potential is able to account for the
temperature dependence of the phonon modes.


  On-shell kinematics for gluon scattering can be parametrized with points on
the celestial sphere; in the limit where these points collide, it is known that
tree-level gluon scattering amplitudes exhibit an operator product expansion
(OPE)-like structure. While it is possible to obtain singular contributions to
this celestial OPE, getting regular contributions from both holomorphic and
anti-holomorphic sectors is more difficult. In this paper, we use twistor
string theory to describe the maximal helicity violating (MHV) sector of
tree-level, four-dimensional gluon scattering as an effective 2d conformal
field theory on the celestial sphere. By organizing the OPE between vertex
operators in this theory in terms of soft gluon descendants, we obtain
all-order expressions for the celestial OPE which include all regular
contributions in the collinear expansion. This gives new, all-order formulae
for the collinear splitting function (in momentum space) and celestial OPE
coefficients (in the conformal primary basis) of tree-level MHV gluon
scattering. We obtain these results for both positive and negative helicity
gluons, and for any incoming/outgoing kinematic configuration within the MHV
sector.


  Direct comparison is made of the steady-sates and coarsening dynamics in a
local system and its nonlocal generalization. The example system is the surface
of a solid film in a strong electric field; the morphological evolution of the
surface is described, in the long-wavelength approximation, by the amplitude
PDE for the film height function. It is shown that the amplitude of the
steady-state and the coarsening rate of the surface structure are very
sensitive to the radius of the long-range interaction, and that both quantities
increase as the radius decreases.


  Sequential ionization of fullerene cluster ions (C$_{60}$)$_{n}^{+}$ within
multiply-charged helium nanodroplets leads to the intriguing phenomenon of
forming and stabilizing doubly- and triply-charged fullerene oligomers.
Surprisingly, we have detected (C$_{60}$)$_{2}^{2+}$ and (C$_{60}$)$_{2}^{3+}$,
indicating that dimers, rather than the previously established pentamers and
dodecamers, are the smallest fullerene cluster sizes capable of stabilizing two
and even three charges. This remarkable resilience against Coulomb explosion is
achieved through efficient cooling within the superfluid environment of helium
nanodroplets, and a sequential ionization scheme that populates covalently
bound or physisorbed fullerene dimers. Calculations support the stability of
four differently bonded (C$_{60}$)$_{2}^{2+}$ and (C$_{60}$)$_{2}^{3+}$ isomers
and predict a low Coulomb barrier (<0.4 eV) preventing even dissociation of
cold van der Waals complexes.


  In this paper, we present a possible theoretical explanation for benford's
law. We develop a recursive relation between the probabilities, using simple
intuitive ideas. We first use numerical solutions of this recursion and verify
that the solutions converge to the benford's law. Finally we solve the
recursion analytically to yeild the benford's law for base 2.


  A brief summary of the main properties of the unidentified gamma-ray sources
detected by EGRET is presented, with particular emphasis on the different
populations and their phenomenological characteristics.


  One of the most popular clustering algorithms is the celebrated $D^\alpha$
seeding algorithm (also know as $k$-means++ when $\alpha=2$) by Arthur and
Vassilvitskii (2007), who showed that it guarantees in expectation an
$O(2^{2\alpha}\cdot \log k)$-approximate solution to the ($k$,$\alpha$)-means
cost (where euclidean distances are raised to the power $\alpha$) for any
$\alpha\ge 1$. More recently, Balcan, Dick, and White (2018) observed
experimentally that using $D^\alpha$ seeding with $\alpha>2$ can lead to a
better solution with respect to the standard $k$-means objective (i.e. the
$(k,2)$-means cost).
  In this paper, we provide a rigorous understanding of this phenomenon. For
any $\alpha>2$, we show that $D^\alpha$ seeding guarantees in expectation an
approximation factor of $$ O_\alpha \left((g_\alpha)^{2/\alpha}\cdot
\left(\frac{\sigma_{\mathrm{max}}}{\sigma_{\mathrm{min}}}\right)^{2-4/\alpha}\cdot
(\min\{\ell,\log k\})^{2/\alpha}\right)$$ with respect to the standard
$k$-means cost of any underlying clustering; where $g_\alpha$ is a parameter
capturing the concentration of the points in each cluster,
$\sigma_{\mathrm{max}}$ and $\sigma_{\mathrm{min}}$ are the maximum and minimum
standard deviation of the clusters around their means, and $\ell$ is the number
of distinct mixing weights in the underlying clustering (after rounding them to
the nearest power of $2$). We complement these results by some lower bounds
showing that the dependency on $g_\alpha$ and
$\sigma_{\mathrm{max}}/\sigma_{\mathrm{min}}$ is tight.
  Finally, we provide an experimental confirmation of the effects of the
aforementioned parameters when using $D^\alpha$ seeding. Further, we
corroborate the observation that $\alpha>2$ can indeed improve the $k$-means
cost compared to $D^2$ seeding, and that this advantage remains even if we run
Lloyd's algorithm after the seeding.


  In economic systems, the mix of products that countries make or export has
been shown to be a strong leading indicator of economic growth. Hence, methods
to characterize and predict the structure of the network connecting countries
to the products that they export are relevant for understanding the dynamics of
economic development. Here we study the presence and absence of industries at
the global and national levels and show that these networks are significantly
nested. This means that the less filled rows and columns of these networks'
adjacency matrices tend to be subsets of the fuller rows and columns. Moreover,
we show that nestedness remains relatively stable as the matrices become more
filled over time and that this occurs because of a bias for industries that
deviate from the networks' nestedness to disappear, and a bias for the missing
industries that reduce nestedness to appear. This makes the appearance and
disappearance of individual industries in each location predictable. We
interpret the high level of nestedness observed in these networks in the
context of the neutral model of development introduced by Hidalgo and Hausmann
(2009). We show that, for the observed fills, the model can reproduce the high
level of nestedness observed in these networks only when we assume a high level
of heterogeneity in the distribution of capabilities available in countries and
required by products. In the context of the neutral model, this implies that
the high level of nestedness observed in these economic networks emerges as a
combination of both, the complementarity of inputs and heterogeneity in the
number of capabilities available in countries and required by products. The
stability of nestedness in industrial ecosystems, and the predictability
implied by it, demonstrates the importance of the study of network properties
in the evolution of economic networks.


  Increasing practical interest has been shown in regression problems where the
errors, or disturbances, are centred in a way that reflects particular
characteristics of the mechanism that generated the data. In economics this
occurs in problems involving data on markets, productivity and auctions, where
it can be natural to centre at an end-point of the error distribution rather
than at the distribution's mean. Often these cases have an extreme-value
character, and in that broader context, examples involving meteorological,
record-value and production-frontier data have been discussed in the
literature. We shall discuss nonparametric methods for estimating regression
curves in these settings, showing that they have features that contrast so
starkly with those in better understood problems that they lead to apparent
contradictions. For example, merely by centring errors at their end-points
rather than their means the problem can change from one with a familiar
nonparametric character, where the optimal convergence rate is slower than
$n^{-1/2}$, to one in the super-efficient class, where the optimal rate is
faster than $n^{-1/2}$. Moreover, when the errors are centred in a non-standard
way there is greater intrinsic interest in estimating characteristics of the
error distribution, as well as of the regression mean itself. The paper will
also address this aspect of the problem.


  In recent years, there has been significant research focusing on addressing
security concerns in single-modal person re-identification (ReID) systems that
are based on RGB images. However, the safety of cross-modality scenarios, which
are more commonly encountered in practical applications involving images
captured by infrared cameras, has not received adequate attention. The main
challenge in cross-modality ReID lies in effectively dealing with visual
differences between different modalities. For instance, infrared images are
typically grayscale, unlike visible images that contain color information.
Existing attack methods have primarily focused on the characteristics of the
visible image modality, overlooking the features of other modalities and the
variations in data distribution among different modalities. This oversight can
potentially undermine the effectiveness of these methods in image retrieval
across diverse modalities. This study represents the first exploration into the
security of cross-modality ReID models and proposes a universal perturbation
attack specifically designed for cross-modality ReID. This attack optimizes
perturbations by leveraging gradients from diverse modality data, thereby
disrupting the discriminator and reinforcing the differences between
modalities. We conducted experiments on two widely used cross-modality
datasets, namely RegDB and SYSU, which not only demonstrated the effectiveness
of our method but also provided insights for future enhancements in the
robustness of cross-modality ReID systems.


  Sensitive Arecibo observations provide an unprecedented ability to detect
nulls for an accurate pulse-modulation quelling (PMQ) analysis. We demonstrate
that a number of conal pulsars show "periodic nulling" similar to the
phenomenon found earlier in pulsar B1133+16.


  We study analytic and Borel subsets defined similarily to the old example of
analytic complete set given by Luzin. Luzin's example, which is essentially a
subset of the Baire space, is based on the natural partial order on naturals,
i.e. division. It consists of sequences which contain increasing subsequence in
given order. We consider a variety of sets defined in a similar way. Some of
them occurs to be Borel subsets of the Baire space, while others are analytic
complete, hence not Borel. In particular, we show that an analogon of Luzin
example based on the natural linear order on rationals is analytic complete. We
also characterise all countable linear orders having such property.


  We reconsider the problem of calculating the vacuum free energy (density) of
QCD and the shift of the quark condensates in the presence of a uniform
background magnetic field using two-and-three-flavor chiral perturbation theory
($\chi$PT). Using the free energy, we calculate the degenerate, light quark
condensates in the two-flavor case and the up, down and strange quark
condensates in the three-flavor case. We also use the vacuum free energy to
calculate the (renormalized) magnetization of the QCD vacuum, which shows that
it is paramagnetic. We find that the three-flavor light-quark condensates and
(renormalized) magnetization are improvements on the two-flavor results. We
also find that the average light quark condensate is in agreement with the
lattice up to $eB=0.2 {\rm\ GeV^{2}}$, and the (renormalized) magnetization is
in agreement up to $eB=0.3 {\rm\ GeV^{2}}$, while three-flavor $\chi$PT, which
gives a non-zero shift in the difference between the light quark condensates
unlike two-flavor $\chi$PT, underestimates the difference compared to lattice
QCD.


  A concise guide to very basic bicategory theory, from the definition of a
bicategory to the coherence theorem.


  Exploration is essential for solving complex Reinforcement Learning (RL)
tasks. Maximum State-Visitation Entropy (MSVE) formulates the exploration
problem as a well-defined policy optimization problem whose solution aims at
visiting all states as uniformly as possible. This is in contrast to standard
uncertainty-based approaches where exploration is transient and eventually
vanishes. However, existing approaches to MSVE are theoretically justified only
for discrete state-spaces as they are oblivious to the geometry of continuous
domains. We address this challenge by introducing Geometric Entropy
Maximisation (GEM), a new algorithm that maximises the geometry-aware Shannon
entropy of state-visits in both discrete and continuous domains. Our key
theoretical contribution is casting geometry-aware MSVE exploration as a
tractable problem of optimising a simple and novel noise-contrastive objective
function. In our experiments, we show the efficiency of GEM in solving several
RL problems with sparse rewards, compared against other deep RL exploration
approaches.


  An algorithm based on Artificial Neural Networks is proposed in this paper to
improve the accuracy of Inertial Navigation System (INS)/ Global Navigation
Satellite System (GNSS) integrated navigation during the absence of GNSS
signals. The INS which can be used to continuously position autonomous vehicles
during GNSS signal losses around urban canyons, bridges, tunnels and trees,
suffers from unbounded exponential error drifts cascaded over time during the
integration of the gyroscope and double integration of the accelerometer to
displacement. More so, the error drift is characterised by a pattern dependent
on time. The Input Delay Neural Network (IDNN) has the ability to learn the
error drift over time [1] and possesses the quality of being more
computationally efficient than the Recurrent Neural Network (RNN), Long
Short-Term Memory, and the Gated Recurrent Unit Network. Furthermore published
literatures focus on travel routes which do not take complex driving scenarios
into consideration, we therefore investigate in this paper the performance of
the proposed algorithm on challenging scenarios, such as hard brake,
roundabouts, sharp cornering, successive left and right turns and quick changes
in vehicular acceleration across numerous test sequences. The results obtained
show that the Neural Network-based approaches are able to provide up to 89.55 %
improvement on the INS displacement estimation and 93.35 % on the INS
orientation rate estimation.


  We present a powerful method for exploring various processes in the presence
of strong external fields and matter. The method implies utilization of the
exact solutions of the modified Dirac equations which contain the effective
potentials accounting for the influences of external electromagnetic fields and
matter on particles. We briefly discuss the basics of the method and its
applications to studies of different processes, including a recently proposed
new mechanism of radiation by neutrinos and electrons moving in matter (the
spin light of the neutrino and electron). In view of a recent "prediction" of
an order-of-magnitude change of the muon lifetime under the influence of an
electromagnetic field of a CO$_2$ laser, we revisit the issue and show that
such claims are nonrealistic.


  Many of the experiments proposed to look for interference CP violation in
neutral B mesons concentrate on tagged decay into CP eigenstates. Aleksan,
Dunietz, Kayser and Le Diberder have shown that one can also look for
interference CP violation using tagged decays into non-CP eigenstates. In all
these methods, one must trace the time dependence of the decays. In this
article we discuss a new method to search for interference CP violation by
using only time integrated rates into non-CP eigenstates. The method hinges on
the comparison between the decays of $\Upsilon(4S)$ into $f f$, $\bar{f}
\bar{f}$, and $f \bar{f}$, and also uses the rates for $l^+ f$ and $l^- f$.
This method does not depend on how the $\Upsilon(4S)$ is produced; provided
enough statistics, one can use both symmetric and asymmetric colliders.


  Inspired by recent breakthroughs with topological quantum materials, which
pave the way to novel, high-efficiency, low-energy magnetoelectric devices and
fault-tolerant quantum information processing, inter alia, topological quantum
walks have emerged as an exciting topic in its own right, especially due to the
theoretical and experimental simplifications this approach offers. Motivated by
impressive progress in topological quantum walks, we provide a perspective on
theoretical studies and experimental investigations of topological quantum
walks focusing on current explorations of topological properties arising for
single-walker quantum walks.


  Analysing the cubic sectors of a real polynomial of degree n, a modification
of the Newton Rule is Signs is proposed with which stricter upper bound on the
number of real roots can be found. A new necessary condition for reality of the
roots of a polynomial is also proposed. Relationship among the quadratic
elements of the polynomial is established through its roots and those of its
derivatives. Some aspects of polynomial discriminants are also discussed - the
relationship between the discriminants of real polynomials, the discriminants
of their derivatives, and the quadratic elements - following a discriminant of
the discriminant approach.


  High-speed solar wind streams (HSSs) interact with the preceding ambient
solar wind to form Stream Interaction Regions (SIRs), which are a primary
source of recurrent geomagnetic storms. However, HSSs may also encounter and
subsequently interact with Interplanetary Coronal Mass Ejections (ICMEs). In
particular, the impact of the interaction between slower ICMEs and faster HSSs,
represents an unexplored area that requires further in-depth investigation.
This specific interaction can give rise to unexpected geomagnetic storm
signatures, diverging from the conventional expectations of individual SIR
events sharing similar HSS properties. Our study presents a comprehensive
analysis of solar wind data spanning from 1996 to 2020, capturing 23 instances
where such encounters led to geomagnetic storms ($SymH$ $< -30$ nT). We
determined that interaction events between preceding slower ICMEs and faster
HSSs possess the potential to induce substantial storm activity, statistically
nearly doubling the geoeffective impact in comparison to SIR storm events. The
increase in the amplitude of the $SymH$ index appears to result from heightened
dynamic pressure, often coupled with the concurrent amplification of the CMEs
rearward $|B|$ and/or $B_z$ components.


  Given two $n_i$-dimensional Alexandrov spaces $X_i$ of curvature $\ge 1$, the
join of $X_1$ and $X_2$ is an $(n_1+n_2+1)$-dimensional Alexandrov space $X$ of
curvature $\ge 1$, which contains $X_i$ as convex subsets such that their
points are $\frac \pi2$ apart. If a group acts isometrically on a join that
preserves $X_i$, then the orbit space is called quotient of join. We show that
an $n$-dimensional Alexandrov space $X$ with curvature $\ge 1$ is isometric to
a finite quotient of join, if $X$ contains two compact convex subsets $X_i$
without boundary such that $X_1$ and $X_2$ are at least $\frac \pi2$ apart and
$\dim(X_1)+\dim(X_2)=n-1$.


  We investigate nonlinear stability of two classes of cosmological solutions
in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW)
solutions and anisotropic FLRW solutions. For this purpose we construct the
linear cosmological perturbation theory around axisymmetric Bianchi type--I
backgrounds. We then expand the background around the two classes of solutions,
which are fixed points of the background evolution equation, and analyze linear
perturbations on top of it. This provides a consistent truncation of nonlinear
perturbations around these fixed point solutions and allows us to analyze
nonlinear stability in a simple way. In particular, it is shown that isotropic
FLRW solutions exhibit nonlinear ghost instability. On the other hand,
anisotropic FLRW solutions are shown to be ghost-free for a range of parameters
and initial conditions.


  We present a market-based approach to the Air Traffic Flow Management (ATFM)
problem. The goods in our market are delays and buyers are airline companies;
the latter pay money to the FAA to buy away the desired amount of delay on a
per flight basis. We give a notion of equilibrium for this market and an LP
whose solution gives an equilibrium allocation of flights to landing slots as
well as equilibrium prices for the landing slots. Via a reduction to matching,
we show that this equilibrium can be computed combinatorially in strongly
polynomial time. Moreover, there is a special set of equilibrium prices, which
can be computed easily, that is identical to the VCG solution, and therefore
the market is incentive compatible in dominant strategy.


  In this note we study Kloosterman sums twisted by a multiplicative characters
modulo a prime power. We show, by an elementary calculation, that these sums
become equidistributed on the real line with respect to a suitable measure.


  For finite sequence $\underbar{\em d}$ of positive integers, we consider
graphs that have $\underbar{\em d}$ as their list of vertex degrees, and
bipartite graphs for which each part has $\underbar{\em d}$ as its list of
vertex degrees. In particular, we make a connection between a result for
bipartite graphs by Alon, Ben-Shimon and Krivelevich and a result of Zverovich
and Zverovich for graphs, and we give an improvement of a result of Zverovich
and Zverovich. We show that the bipartite graphs with vertex degree sequences
$(\underbar{\em d},\underbar{\em d}\,)$ are in one to one correspondence with
graphs with loops with reduced degree sequence $\underbar{\em d}$, where the
reduced degree of a vertex is defined to be the number of edges incident to the
vertex, with loops counted only once. We also give two Erd\H{o}s--Gallai type
theorems for graphs with loops.


  The magnetic field plays a key role in producing solar flares, so that the
investigation on the relationship between the magnetic field properties and
flares is significant. In this paper, based on the magnetic field extrapolated
from the photospheric vector magnetograms of the active region NOAA 9077
obtained at Huairou Solar Observing Station, the magnetic field parameters
including the height of field lines, force-free factor, free magnetic energy
and inclination angle were studied with respect to an X-class flare in this
region. We found that the magnetic field lines became lower and the ratio of
number of closed field lines to those of open field lines increased after the
flare. The force-free factor ($\alpha$) attained a large value before the flare
and then decreased after the flare for the closed field lines, while the open
field lines showed the opposite tendency. Free energy reach to maximum before
flare, then decrease after flare. The magnetic inclination angles showed
opposite change trends after the flare for closed and open field lines.
Therefore, we may conclude that non-potential energy released by flare mostly
contained in the closed magnetic field lines.


  We study multi-qubit quantum gates intrinsic to an array of semiconductor
quantum dots and investigate how they can be implemented in a scalable way. The
intrinsic quantum gates refer to the class of natural-forming transformations
in the qubit rotating-frame under direct exchange coupling, and can be
recognized as an instruction set of spin-qubit chips. Adopting perturbative
treatment, we can model the intrinsic gates by first-order dynamics in the
coupling strength and develop a general formalism for identifying the
multi-qubit intrinsic gates under arbitrary array connectivity. The
advantageous applications of the intrinsic gates in quantum computing and
quantum error correction are explored. Factors influencing the fidelities of
the multi-qubit intrinsic gates are also discussed. To overcome the problem of
inhomogeneous coupling, we propose a theoretical scheme in which single-qubit
pulses are applied to dynamically calibrate the connecting bonds. This scheme
can be further combined with periodic dynamical decoupling for robust
implementations of multi-qubit gates in large-scale quantum computers.


  We present a new kinematic model for the Small Magellanic Cloud (SMC), using
data from the \gaia\ Data Release 2 catalog. We identify a sample of
astrometrically well-behaved red giant (RG) stars belonging to the SMC and
cross-match with publicly available radial velocity (RV) catalogs. We create a
3D spatial model for the RGs, using RR Lyrae for distance distributions, and
apply kinematic models with varying rotation properties and a novel tidal
expansion prescription to generate mock proper motion (PM) catalogs. When we
compare this series of mock catalogs to the observed RG data, we find a
combination of moderate rotation (with a magnitude of $\sim10-20$ km s$^{-1}$
at 1 kpc from the SMC center, inclination between $\sim50-80$ degrees, and a
predominantly north-to-south line of nodes position angle of $\sim180$ degrees)
and tidal expansion (with a scaling of $\sim10$ km s$^{-1}$ kpc$^{-1}$) is
required to explain the PM signatures. The exact best-fit parameters depend
somewhat on whether we assess only the PMs or include the RVs as a qualitative
check, leaving some small tension remaining between the PM and RV conclusions.
In either case, the parameter space preferred by our model is different both
from previously inferred rotational geometries, including from the SMC H{\small
I} gas and from the RG RV-only analyses, and new SMC PM analyses which conclude
that a rotation signature is not detectable. Taken together this underscores
the need to treat the SMC as a series of different populations with distinct
kinematics.


  We introduce a new approach in distributed deep learning, utilizing Geoffrey
Hinton's Forward-Forward (FF) algorithm to speed up the training of neural
networks in distributed computing environments. Unlike traditional methods that
rely on forward and backward passes, the FF algorithm employs a dual forward
pass strategy, significantly diverging from the conventional backpropagation
process. This novel method aligns more closely with the human brain's
processing mechanisms, potentially offering a more efficient and biologically
plausible approach to neural network training. Our research explores different
implementations of the FF algorithm in distributed settings, to explore its
capacity for parallelization. While the original FF algorithm focused on its
ability to match the performance of the backpropagation algorithm, the
parallelism aims to reduce training times and resource consumption, thereby
addressing the long training times associated with the training of deep neural
networks. Our evaluation shows a 3.75 times speed up on MNIST dataset without
compromising accuracy when training a four-layer network with four compute
nodes. The integration of the FF algorithm into distributed deep learning
represents a significant step forward in the field, potentially revolutionizing
the way neural networks are trained in distributed environments.


  In semiconductors, spin-orbit effective magnetic fields, i.e., the Rashba and
Dresselhaus fields, are used to control electron-spin polarization. This
operation, however, destroys the electron-spin coherence, and the spin
polarization is limited to the vicinity of a ferromagnetic source electrode. In
this paper, we propose the use of dilute magnetic semiconductors to improve the
coherence of spatially oscillating electron-spin polarization. In dilute
magnetic semiconductors, the electron-spin polarization near the source
electrode dynamically induces the local spin polarization of magnetic
impurities through s-d spin-flip scattering. This impurity-spin polarization
improves, in turn, the coherence of the electron-spin polarization, and this
improved electron-spin polarization induces impurity-spin polarization farther
in the adjacent region. Because of this positive feedback, the coherent and
synchronized spatial oscillations of electron- and impurity-spin polarizations
grow cooperatively. A numerical calculation for a CdMnTe quantum well
demonstrates the validity of this mechanism.


  We derive oscillatory signals in correlation functions in two-field open
inflation by means of the in-in formalism; such signatures are caused by
resonances between oscillations in the tunnelling field and fluctuations in the
inflaton during the curvature dominated, intermediate and subsequent
inflationary regime. While amplitudes are model-dependent, we find distinct
oscillations in the power and bi-spectrum that can act as a direct probe of the
curvature dominated phase and thus, indirectly, strengthen the claim of the
string landscape if they were observed. We comment on the prospects of
detecting these tell-tale signs in current experiments, which is challenging,
but not impossible.
  At the technical level, we pay special attention to the applicability
conditions for truncation fluctuations to the light (inflaton) field and derive
upper limits on the oscillation amplitude of the heavy field. A violation of
these bounds requires a multi-field analysis at the perturbed level.


  Let $\mu(\varepsilon)$ be the minimum number of cubes of side $\varepsilon$
needed to cover the unit three-torus $[\mathbb{R}/\mathbb{Z}]^3$. We prove new
lower and upper bounds for $\mu(\varepsilon)$ and find the exact value for all
$\varepsilon\geq\frac{7}{15}$ and all
$\varepsilon\in\left[\frac{1}{r+1/(r^2+r+1)},\frac{1}{r-1/(r^2-1)}\right)$ for
any integer $r\geq 2$.


  Apps' pervasive role in our society led to the definition of test automation
approaches to ensure their dependability. However, state-of-the-art approaches
tend to generate large numbers of test inputs and are unlikely to achieve more
than 50% method coverage. In this paper, we propose a strategy to achieve
significantly higher coverage of the code affected by updates with a much
smaller number of test inputs, thus alleviating the test oracle problem. More
specifically, we present ATUA, a model-based approach that synthesizes App
models with static analysis, integrates a dynamically-refined state abstraction
function and combines complementary testing strategies, including (1) coverage
of the model structure, (2) coverage of the App code, (3) random exploration,
and (4) coverage of dependencies identified through information retrieval. Its
model-based strategy enables ATUA to generate a small set of inputs that
exercise only the code affected by the updates. In turn, this makes common test
oracle solutions more cost-effective as they tend to involve human effort. A
large empirical evaluation, conducted with 72 App versions belonging to nine
popular Android Apps, has shown that ATUA is more effective and less effort
intensive than state-of-the-art approaches when testing App updates.


  This paper presents a new Vision Transformer (ViT) architecture Multi-Scale
Vision Longformer, which significantly enhances the ViT of
\cite{dosovitskiy2020image} for encoding high-resolution images using two
techniques. The first is the multi-scale model structure, which provides image
encodings at multiple scales with manageable computational cost. The second is
the attention mechanism of vision Longformer, which is a variant of Longformer
\cite{beltagy2020longformer}, originally developed for natural language
processing, and achieves a linear complexity w.r.t. the number of input tokens.
A comprehensive empirical study shows that the new ViT significantly
outperforms several strong baselines, including the existing ViT models and
their ResNet counterparts, and the Pyramid Vision Transformer from a concurrent
work \cite{wang2021pyramid}, on a range of vision tasks, including image
classification, object detection, and segmentation. The models and source code
are released at \url{https://github.com/microsoft/vision-longformer}.


  Data labeling is often the most challenging task when developing
computational pathology models. Pathologist participation is necessary to
generate accurate labels, and the limitations on pathologist time and demand
for large, labeled datasets has led to research in areas including weakly
supervised learning using patient-level labels, machine assisted annotation and
active learning. In this paper we explore self-supervised learning to reduce
labeling burdens in computational pathology. We explore this in the context of
classification of breast cancer tissue using the Barlow Twins approach, and we
compare self-supervision with alternatives like pre-trained networks in
low-data scenarios. For the task explored in this paper, we find that ImageNet
pre-trained networks largely outperform the self-supervised representations
obtained using Barlow Twins.


  Excitement about the promise of quantum computers is tempered by the reality
that the hardware remains exceptionally fragile and error-prone, forming a
bottleneck in the development of novel applications. In this manuscript, we
describe and experimentally test a fully autonomous workflow designed to
deterministically suppress errors in quantum algorithms from the gate level
through to circuit execution and measurement. We introduce the key elements of
this workflow, delivered as a software package called Fire Opal, and survey the
underlying physical concepts: error-aware compilation, automated system-wide
gate optimization, automated dynamical decoupling embedding for circuit-level
error cancellation, and calibration-efficient measurement-error mitigation. We
then present a comprehensive suite of performance benchmarks executed on IBM
hardware, demonstrating up to > 1000X improvement over the best alternative
expert-configured techniques available in the open literature. Benchmarking
includes experiments using up to 16 qubit systems executing: Bernstein
Vazirani, Quantum Fourier Transform, Grover's Search, QAOA, VQE, Syndrome
extraction on a five-qubit Quantum Error Correction code, and Quantum Volume.
Experiments reveal a strong contribution of Non-Markovian errors to baseline
algorithmic performance; in all cases the deterministic error-suppression
workflow delivers the highest performance and approaches incoherent error
bounds without the need for any additional sampling or randomization overhead,
while maintaining compatibility with all additional probabilistic error
suppression techniques.


  We expand on the previously published Gr{\o}nbech-Jensen Farago (GJF)
thermostat, which is a thermodynamically sound variation on the
St{\o}rmer-Verlet algorithm for simulating discrete-time Langevin equations.
The GJF method has been demonstrated to give robust and accurate
configurational sampling of the phase space, and its applications to, e.g.,
Molecular Dynamics is well established. A new definition of the discrete-time
velocity variable is proposed based on analytical calculations of the kinetic
response of a harmonic oscillator subjected to friction and noise. The new
companion velocity to the GJF method is demonstrated to yield correct and
time-step-independent kinetic responses for, e.g., kinetic energy, its
fluctuations, and Green-Kubo diffusion based on velocity autocorrelations. This
observation allows for a new and convenient Leap-Frog algorithm, which
efficiently and precisely represents statistical measures of both kinetic and
configurational properties at any time step within the stability limit for the
harmonic oscillator. We outline the simplicity of the algorithm and demonstrate
its attractive time-step-independent features for nonlinear and complex systems
through applications to a one-dimensional nonlinear oscillator and
three-dimensional Molecular Dynamics.


  A novel simulation strategy is proposed to search for semiconductor quantum
devices which are optimized with respect to required performances. Based on
evolutionary programming, a tecnique implementing the paradigm of genetic
algorithms to more complex data structures than strings of bits, the proposed
algorithm is able to deal with quantum devices with preset non-trivial
constraints (transition energies, geometrical requirements, etc.). Therefore,
our approach allows for automatic design, thus avoiding costly by-hand
optimizations. We demonstrate the advantages of the proposed algorithm by a
relevant and non-trivial application, the optimization of a
second-harmonic-generation device working under resonance conditions.


  We consider the localization properties of a lattice of coupled masses and
springs with random mass and spring constant values. We establish the full
phase diagrams of the system for pure mass and pure spring disorder. The phase
diagrams exhibit regions of stable as well as unstable wave modes. The latter
are of interest for the instantaneous-normal-mode spectra of liquids and the
nascent field of acoustic metamaterials. We show the existence of
delocalization-localization transitions throughout the phase diagram and
establish, by high-precision numerical studies, that the universality of these
transitions is of the Anderson type.


  0-brane of type IIA string theory can be interpreted as a dimensional
reduction of a gravitational wave in 11 dimensions. We observe that a similar
interpretation applies also to the D-instanton background of type IIB theory:
it can be viewed as a reduction (along one spatial and one time-like direction)
of a wave in a 12-dimensional theory. The instanton charge is thus related to a
linear momentum in 12 dimensions. This suggests that the instanton should play
as important role in type IIB theory as the 0-brane is supposed to play in type
IIA theory.


  We study the higher-order corrections to structure functions in inclusive
deep-inelastic scattering (DIS) in massless perturbative QCD, in the context of
the conjectured absence of even-n values of the Riemann zeta-function zeta_n,
i.e., of powers of pi^2, in Euclidean physical quantities. We provide
substantial additional support for this conjecture by demonstrating that it
holds, as far as it can be tested by the results of diagram computations, for
the physical anomalous dimensions of structure functions at the fourth and
fifth order in the strong coupling constant alpha_s. The conjecture is then
employed to predict hitherto unknown zeta_4 and zeta_6 contributions to the
anomalous dimensions for parton distributions and to the coefficient functions
for the longitudinal structure function F_L.


  This note continues the theoretical development of deterministic integer
factorization algorithms based on systems of polynomials equations. The main
result establishes a new deterministic time complexity bench mark in integer
factorization.


  The increasing installation of controllable Distributed Energy Resources
(DERs) in Distribution Networks (DNs) opens up new opportunities for the
provision of ancillary services to the Transmission Network (TN) level. As the
penetration of smart meter devices and communication infrastructure in DNs
increases, they become more observable and controllable with centralized
optimization-based control schemes becoming efficient and practical. In this
paper, we propose a centralized tractable Optimal Power Flow (OPF)-based
control scheme that optimizes the real-time operation of active DNs, while also
considering the provision of voltage support as an ancillary service to the TN.
We embed in the form of various constraints the current voltage support
requirements of Switzerland and investigate the potential benefit of ancillary
services provision assuming different operational modes of the DER inverters.
We demonstrate the performance of the proposed scheme using a combined HV-MV-LV
test system.


  We consider a L\'evy process in the plane and we use it to construct a family
of complex-valued random fields that we show to converge in law, in the space
of continuous functions, to a complex Brownian sheet. We apply this result to
obtain weak approximations of the random field solution to a semilinear
one-dimensional stochastic heat equation driven by the space-time white noise.


  Wirelessly streaming high quality 360 degree videos is still a challenging
problem. When there are many users watching different 360 degree videos and
competing for the computing and communication resources, the streaming
algorithm at hand should maximize the average quality of experience (QoE) while
guaranteeing a minimum rate for each user. In this paper, we propose a
\emph{cross layer} optimization approach that maximizes the available rate to
each user and efficiently uses it to maximize users' QoE. Particularly, we
consider a tile based 360 degree video streaming, and we optimize a QoE metric
that balances the tradeoff between maximizing each user's QoE and ensuring
fairness among users. We show that the problem can be decoupled into two
interrelated subproblems: (i) a physical layer subproblem whose objective is to
find the download rate for each user, and (ii) an application layer subproblem
whose objective is to use that rate to find a quality decision per tile such
that the user's QoE is maximized. We prove that the physical layer subproblem
can be solved optimally with low complexity and an actor-critic deep
reinforcement learning (DRL) is proposed to leverage the parallel training of
multiple independent agents and solve the application layer subproblem.
Extensive experiments reveal the robustness of our scheme and demonstrate its
significant performance improvement compared to several baseline algorithms.


  Discovering dark matter at high energy colliders continues to be a compelling
and well-motivated possibility. Weakly interacting massive particles are a
particularly interesting class in which the dark matter particles interact with
the standard model weak gauge bosons. Neutralinos are a prototypical example
that arise in supersymmetric models. In the limit where all other superpartners
are decoupled, it is known that for relic density motivated masses, the rates
for neutralinos are too small to be discovered at the Large Hadron Collider
(LHC), but that they may be large enough for a 100 TeV collider to observe. In
this work we perform a careful study in the vector boson fusion channel for
pure winos and pure higgsinos. We find that given a systematic uncertainty of
1% (5%), with 3000 fb$^{-1}$, the LHC is sensitive to winos of 240 GeV (125
GeV) and higgsinos of 125 GeV (55 GeV). A future 100 TeV collider would be
sensitive to winos of 1.1 TeV (750 GeV) and higgsinos of 530 GeV (180 GeV) with
a 1% (5%) uncertainty, also with 3000 fb$^{-1}$.


  Let x and y be points chosen uniformly at random from $\Z_n^4$, the
four-dimensional discrete torus with side length n. We show that the length of
the loop-erased random walk from x to y is of order $n^2 (\log n)^{1/6}$,
resolving a conjecture of Benjamini and Kozma. We also show that the scaling
limit of the uniform spanning tree on $\Z_n^4$ is the Brownian continuum random
tree of Aldous. Our proofs use the techniques developed by Peres and Revelle,
who studied the scaling limits of the uniform spanning tree on a large class of
finite graphs that includes the d-dimensional discrete torus for $d \geq 5$, in
combination with results of Lawler concerning intersections of four-dimensional
random walks.


  In this work we performed a numerical study of an epidemic model that mimics
the endemic state of whooping cough in the pre-vaccine era. We considered a
stochastic SIR model on dynamical networks that involve local and global
contacts among individuals and analyzed the influence of the network properties
on the characterization of the quasi-stationary state. We computed probability
density functions (PDF) for infected fraction of individuals and found that
they are well fitted by gamma functions, excepted the tails of the
distributions that are q-exponentials. We also computed the fluctuation power
spectra of infective time series for different networks. We found that network
effects can be partially absorbed by rescaling the rate of infective contacts
of the model. An explicit relation between the effective transmission rate of
the disease and the correlation of susceptible individuals with their infective
nearest neighbours was obtained. This relation quantifies the known screening
of infective individuals observed in these networks. We finally discuss the
goodness and limitations of the SIR model with homogeneous mixing and
parameters taken from epidemiological data to describe the dynamic behaviour
observed in the networks studied.


  Progress of experimental techniques at nanoscale in the last decade made
optical measurements in current-carrying nanojunctions a reality thus
indicating emergence of a new field of research coined as optoelectronics.
Optical spectroscopy of open nonequilibrium systems is a natural meeting point
for (at least) two research areas: nonlinear optical spectroscopy and quantum
transport, each with its own theoretical toolbox. We review recent progress in
the field comparing theoretical treatments of optical response in nanojunctions
as is accepted in nonlinear spectroscopy and quantum transport communities. A
unified theoretical description of spectroscopy in nanojunctions is presented.
We argue that theoretical approaches of the quantum transport community (and in
particular, the Green function based considerations) yield a convenient tool
for optoelectronics when radiation field is treated classically, and that
differences between the toolboxes may become critical when studying quantum
radiation field in junctions.


  Many unsupervised domain adaptation (UDA) methods have been proposed to
bridge the domain gap by utilizing domain invariant information. Most
approaches have chosen depth as such information and achieved remarkable
success. Despite their effectiveness, using depth as domain invariant
information in UDA tasks may lead to multiple issues, such as excessively high
extraction costs and difficulties in achieving a reliable prediction quality.
As a result, we introduce Edge Learning based Domain Adaptation (ELDA), a
framework which incorporates edge information into its training process to
serve as a type of domain invariant information. In our experiments, we
quantitatively and qualitatively demonstrate that the incorporation of edge
information is indeed beneficial and effective and enables ELDA to outperform
the contemporary state-of-the-art methods on two commonly adopted benchmarks
for semantic segmentation based UDA tasks. In addition, we show that ELDA is
able to better separate the feature distributions of different classes. We
further provide an ablation analysis to justify our design decisions.


  We provide a non-renormalization theorem for the coefficients of the
conformal anomaly associated with operators with vanishing anomalous
dimensions. Such operators include conserved currents and chiral operators in
superconformal field theories. We illustrate the theorem by computing the
conformal anomaly of 2-point functions both by a computation in the conformal
field theory and via the adS/CFT correspondence. Our results imply that 2- and
3-point functions of chiral primary operators in N=4 SU(N) SYM will not
renormalize provided that a ``generalized Adler-Bardeen theorem'' holds. We
further show that recent arguments connecting the non-renormalizability of the
above mentioned correlation functions to a bonus U(1)_Y symmetry are incomplete
due to possible U(1)_Y violating contact terms. The tree level contribution to
the contact terms may be set to zero by considering appropriately normalized
operators. Non-renormalizability of the above mentioned correlation functions,
however, will follow only if these contact terms saturate by free fields.


  Two major momentum-based techniques that have achieved tremendous success in
optimization are Polyak's heavy ball method and Nesterov's accelerated
gradient. A crucial step in all momentum-based methods is the choice of the
momentum parameter $m$ which is always suggested to be set to less than $1$.
Although the choice of $m < 1$ is justified only under very strong theoretical
assumptions, it works well in practice even when the assumptions do not
necessarily hold. In this paper, we propose a new momentum based method
$\textit{ADINE}$, which relaxes the constraint of $m < 1$ and allows the
learning algorithm to use adaptive higher momentum. We motivate our hypothesis
on $m$ by experimentally verifying that a higher momentum ($\ge 1$) can help
escape saddles much faster. Using this motivation, we propose our method
$\textit{ADINE}$ that helps weigh the previous updates more (by setting the
momentum parameter $> 1$), evaluate our proposed algorithm on deep neural
networks and show that $\textit{ADINE}$ helps the learning algorithm to
converge much faster without compromising on the generalization error.


  We review practical challenges in building and deploying ethical AI at the
scale of contemporary industrial and societal uses. Apart from the purely
technical concerns that are the usual focus of academic research, the
operational challenges of inconsistent regulatory pressures, conflicting
business goals, data quality issues, development processes, systems integration
practices, and the scale of deployment all conspire to create new ethical
risks. Such ethical concerns arising from these practical considerations are
not adequately addressed by existing research results. We argue that a holistic
consideration of ethics in the development and deployment of AI systems is
necessary for building ethical AI in practice, and exhort researchers to
consider the full operational contexts of AI systems when assessing ethical
risks.


  Retinal fundus photographs have been used in the diagnosis of many ocular
diseases such as glaucoma, pathological myopia, age-related macular
degeneration and diabetic retinopathy. With the development of computer
science, computer aided diagnosis has been developed to process and analyse the
retinal images automatically. One of the challenges in the analysis is that the
quality of the retinal image is often degraded. For example, a cataract in
human lens will attenuate the retinal image, just as a cloudy camera lens which
reduces the quality of a photograph. It often obscures the details in the
retinal images and posts challenges in retinal image processing and analysing
tasks. In this paper, we approximate the degradation of the retinal images as a
combination of human-lens attenuation and scattering. A novel
structure-preserving guided retinal image filtering (SGRIF) is then proposed to
restore images based on the attenuation and scattering model. The proposed
SGRIF consists of a step of global structure transferring and a step of global
edge-preserving smoothing. Our results show that the proposed SGRIF method is
able to improve the contrast of retinal images, measured by histogram flatness
measure, histogram spread and variability of local luminosity. In addition, we
further explored the benefits of SGRIF for subsequent retinal image processing
and analysing tasks. In the two applications of deep learning based optic cup
segmentation and sparse learning based cup-to-disc ratio (CDR) computation, our
results show that we are able to achieve more accurate optic cup segmentation
and CDR measurements from images processed by SGRIF.


  Evidence is provided that the global distribution of tropical hurricanes is
principally determined by a universal function H of a single variable z that in
turn is expressible in terms of the local sea surface temperature and latitude.
The data-driven model presented here carries stark implications for the large
increased numbers of hurricanes which it predicts for a warmer world. Moreover,
the rise in recent decades in the numbers of hurricanes in the Atlantic, but
not the Pacific basin, is shown to have a simple explanation in terms of the
specific form of H(z), which yields larger percentage increases when a fixed
increase in sea surface temperature occurs at higher latitudes and lower
temperatures.


  Transport in metals with strongly anisotropic single-particle spectrum is
studied. Coherent band transport in all directions, described by the standard
Boltzmann equation, is shown to withstand both elastic and inelastic scattering
as long as $E_F\tau\gg 1$. A model of phonon-assisted tunneling via resonant
states located in between the layers is suggested to explain a non-monotonic
temperature dependence of the c-axis resistivity observed in experiments.


  We study the photon generation from vacuum via the Dynamical Casimir Effect
in a cavity containing a N-level detector in equally-spaced resonant ladder
configuration or N-1 identical resonant two-level atoms. If the modulation
frequency equals exactly twice the unperturbed cavity frequency, the photon
growth goes on steadily for odd N, while for even N at most N-2 photons can be
generated. This finding is corroborated by numerical calculations. In the limit
$N\to\infty$ we obtain the harmonic oscillator model of the detector, which
admits analytical results.


  In an earlier paper, we discuss the ``popcorn'' model for baryon production
in quark and gluon jets, and present an improved model (which we call Modified
Popcorn Scenarium, MOPS). In this paper we give a manual to the MC program
based on MOPS, and also discuss the application of the model to baryon
fragmentation, i.e. fragmentation of strings originally contaning a diquark.
Model predictions for baryon production in DIS are compared with data.


  We present the results of a study of a statistically significant sample of
galaxies which clearly demonstrate that supermassive black holes are
generically present in all morphological types. Our analysis is based on the
quantitative morphological classification of 1.12 million galaxies in the SDSS
DR7 and on the detection of black hole activity via two different methods, the
first one based on their X-ray/radio emission and the second one based on their
mid-infrared colors. The results of the first analysis confirm the correlation
between black hole and total stellar mass for 8 galaxies and includes one
galaxy classified as bulgeless. The results of our second analysis, consisting
of 15,991 galaxies, show that galaxies hosting a supermassive black hole follow
the same morphological distribution as the general population of galaxies in
the same redshift range. In particular, the fraction of bulgeless galaxies,
1,450 galaxies or 9 percent, is found to be the same as in the general
population. We also present the correlation between black hole and total
stellar mass for 6,247 of these galaxies. Importantly, whereas previous studies
were limited to primarily bulge-dominated systems, our study confirms this
relationship to all morphological types, in particular, to 530 bulgeless
galaxies. Our results indicate that the true correlation that exists for
supermassive black holes and their host galaxies is between the black hole mass
and the total stellar mass of the galaxy and hence, we conclude that the
previous assumption that the black hole mass is correlated with the bulge mass
is only approximately correct.


  We study the nonlinearity (NL) in the conversion from charge to voltage in
infrared detectors (HXRG) for use in precision astronomy. We present laboratory
measurements of the NL function of a H2RG detector and discuss the accuracy to
which it would need to be calibrated in future space missions to perform
cosmological measurements through the weak gravitational lensing technique. In
addition, we present an analysis of archival data from the infrared H1RG
detector of the Wide Field Camera 3 in the Hubble Space Telescope that provides
evidence consistent with the existence of a sensor effect analogous to the
brighter-fatter effect found in Charge-Coupled Devices. We propose a model in
which this effect could be understood as shifts in the effective pixel
boundaries, and discuss prospects of laboratory measurements to fully
characterize this effect.


  A Jantzen type filtration for generalised Varma modules of Lie superalgebras
is introduced. In the case of type I Lie superalgebras, it is shown that the
generalised Jantzen filtration for any Kac module is the unique Loewy
filtration, and the decomposition numbers of the layers of the filtration are
determined by the coefficients of inverse Kazhdan-Lusztig polynomials.
Furthermore, the length of the Jantzen filtration for any Kac module is
determined explicitly in terms of the degree of atypicality of the highest
weight. These results are applied to obtain a detailed description of the
submodule lattices of Kac modules.


  In sports betting it is easier to predict the winner of a game match than the
team that covers the bet. Since, a winner team might not cover a bet.
  This study focuses on the relation of the variable win to the betting
variable cover the point spread. The study is performed with data from
professional basketball (betting lines and scores) and tries to answer the
question: Does the winning team always covers the point spread?. In order to
answer this question, a regression analysis is performed taking into account
the most and less winning teams, together with their betting variables since
the 1990-1991 NBA season. The regression results are inserted in the SPXS
expert system revealing an indirect factor analysis that correlates betting
variables with teams winning percentages.


  We present the current status of the search for new physics effects in the
mixing quantities $\Delta M_s$, $\Delta \Gamma_s$ and $\phi_s$ of the neutral
$B_s$-system.


  "F-free" CeOBiS$_2$ single crystals have successfully grown, thoroughly
eliminating a concern about F-contamination by using a high-purity CsCl flux.
The obtained crystals have a plate-like shape with a size of 1.0-3.0 mm in the
well-developed plane. Single crystal X-ray structural analysis clearly revealed
that the CeOBiS$_2$ crystallizes with a space group $P4/nmm$ (with lattice
parameters of $a$ = 4.0189(6) {\AA}, $c$ = 13.573(2) {\AA}). The bond valence
sum estimation and X-ray photoelectron spectroscopy analysis showed that the
chemical state of Ce was in the mixed valence of Ce$^{3+}$ and Ce$^{4+}$. The
single crystals show superconductivity with zero resistivity at $\sim$1.3 K.
This is the first conclusive evidence of superconductivity driven by Ce valence
fluctuation in surely non-doped CeOBiS$_2$. The superconducting transition
temperature was enhanced up to $\sim$3.8 K by applying hydrostatic pressure.


  In recent years, a plethora of high spectral resolution observations of
sub-mm and FIR transitions of methylidene (CH), have demonstrated this radical
to be a valuable proxy for H2, that can be used for characterising molecular
gas within the interstellar medium (ISM) on a Galactic scale, including the
CO-dark component. Here we report the discovery of the 13CH isotopologue in the
ISM using the upGREAT receiver on board SOFIA. We have detected the three
hyperfine structure components of the 2THz frequency transition from its
ground-state toward four high-mass star-forming regions and determine 13CH
column densities. The ubiquity of molecules containing carbon in the ISM has
turned the determination of the ratio between the abundances of carbon's two
stable isotopes, 12C/13C, into a cornerstone for Galactic chemical evolution
studies. Whilst displaying a rising gradient with Galactocentric distance, this
ratio, when measured using observations of different molecules (CO, H2CO, and
others) shows systematic variations depending on the tracer used. These
observed inconsistencies may arise from optical depth effects, chemical
fractionation or isotope-selective photo-dissociation. Formed from C+ either
via UV-driven or turbulence-driven chemistry, CH reflects the fractionation of
C+, and does not show any significant fractionation effects unlike other
molecules previously used to determine the 12C/13C isotopic ratio which make it
an ideal tracer for the 12C/13C ratio throughout the Galaxy. Therefore, by
comparing the derived column densities of 13CH with previously obtained SOFIA
data of the corresponding transitions of the main isotopologue 12CH, we derive
12C/13C isotopic ratios toward Sgr B2(M), G34.26+0.15, W49(N) and W51E. Adding
our values derived from 12/13CH to previous calculations of the Galactic
isotopic gradient we derive a revised value of 12C/13C = 5.85(0.50)R_GC +
15.03(3.40).


  We employ a coarse-graining approach to analyze nonlinear cascades in
Boussinesq flows using high-resolution simulation data. We derive budgets which
resolve the evolution of energy and potential enstrophy simultaneously in space
and in scale. We then use numerical simulations of Boussinesq flows, with
forcing in the large-scales, and fixed rotation and stable stratification along
the vertical axis, to study the inter-scale flux of energy and potential
enstrophy in three different regimes of stratification and rotation: (i) strong
rotation and moderate stratification, (ii) moderate rotation and strong
stratification, and (iii) equally strong stratification and rotation. In all
three cases, we observe constant fluxes of both global invariants, the mean
energy and mean potential enstrophy, from large to small scales. The existence
of constant potential enstrophy flux ranges provides the first direct empirical
evidence in support of the notion of a cascade of potential enstrophy. The
persistent forward cascade of the two invariants reflects a marked departure of
these flows from two-dimensional turbulence.


  It has been recently argued that the depletion attraction may play an
important role in different aspects of the cellular organization, ranging from
the organization of transcriptional activity in transcription factories to the
formation of the nuclear bodies. In this paper we suggest a new application of
these ideas in the context of the splicing process, a crucial step of messanger
RNA maturation in Eukaryotes. We shall show that entropy effects and the
resulting depletion attraction may explain the relevance of the aspecific
intron length variable in the choice of the splice-site recognition modality.
On top of that, some qualitative features of the genome architecture of higher
Eukaryotes can find an evolutionary realistic motivation in the light of our
model.


  Let $A=\oplus_{i\in \nn}A_i$ be an excellent homogeneous Noetherian graded
ring and let $M=\oplus_{n\in \zz}M_n$ be a finitely generated graded
$A$-module. We consider $M$ as a module over $A_0$ and show that the
$(S_k)$-loci of $M$ are open in $\Spec(A_0)$. In particular, the Cohen-Macaulay
locus $U^0_{CM}=\{\p\in \Spec(A_0) \mid M_\p {is Cohen-Macaulay}\}$ is an open
subset of $\Spec(A_0)$. We also show that the $(S_k)$-loci on the homogeneous
parts $M_n$ of $M$ are eventually stable. As an application we obtain that for
a finitely generated Cohen-Macaulay module $M$ over an excellent ring $A$ and
for an ideal $I\subseteq A$ which is not contained in any minimal prime of $M$
the $(S_k)$-loci for the modules $M/I^nM$ are eventually stable.


  We study the computational complexity and variance of multilevel best linear
unbiased estimators introduced in [D. Schaden and E. Ullmann, SIAM/ASA J.
Uncert. Quantif., (2020)]. We specialize the results in this work to PDE-based
models that are parameterized by a discretization quantity, e.g., the finite
element mesh size. In particular, we investigate the asymptotic complexity of
the so-called sample allocation optimal best linear unbiased estimators
(SAOBs). These estimators have the smallest variance given a fixed
computational budget. However, SAOBs are defined implicitly by solving an
optimization problem and are difficult to analyze. Alternatively, we study a
class of auxiliary estimators based on the Richardson extrapolation of the
parametric model family. This allows us to provide an upper bound for the
complexity of the SAOBs, showing that their complexity is optimal within a
certain class of linear unbiased estimators. Moreover, the complexity of the
SAOBs is not larger than the complexity of Multilevel Monte Carlo. The
theoretical results are illustrated by numerical experiments with an elliptic
PDE.


  We construct eigenspectra from the DR1 quasars in the SDSS using the
Karhunen-Lo\`eve (KL) transform (or Principal Component Analysis, PCA) in
different redshift and luminosity bins. We find that the quasar spectra can be
classified, by the first two eigenspectra, into a continuous sequence in the
variation of the spectral slope. We also find a dependence on redshift and
luminosity in the eigencoefficients. The dominant redshift effect is the
evolution of the blended Fe~II emission (optical) and the Balmer continuum (the
``small-bump'', $\lambda_{rest} \approx 2000-4000$\AA), while the luminosity
effect is related to the Baldwin effect. Correlations among several major broad
emission lines are found, including the well-known ``Eigenvector-1''.


  Visual prediction models are a promising solution for visual-based robotic
grasping of cluttered, unknown soft objects. Previous models from the
literature are computationally greedy, which limits reproducibility; although
some consider stochasticity in the prediction model, it is often too weak to
catch the reality of robotics experiments involving grasping such objects.
Furthermore, previous work focused on elementary movements that are not
efficient to reason in terms of more complex semantic actions. To address these
limitations, we propose VP-GO, a ``light'' stochastic action-conditioned visual
prediction model. We propose a hierarchical decomposition of semantic grasping
and manipulation actions into elementary end-effector movements, to ensure
compatibility with existing models and datasets for visual prediction of
robotic actions such as RoboNet. We also record and release a new open dataset
for visual prediction of object grasping, called PandaGrasp. Our model can be
pre-trained on RoboNet and fine-tuned on PandaGrasp, and performs similarly to
more complex models in terms of signal prediction metrics. Qualitatively, it
outperforms when predicting the outcome of complex grasps performed by our
robot.


  We study the thermodynamic properties of a dirty ferromagnetic
S$\mid$F$\mid$S Josephson junction with s-wave superconducting leads in the
low-temperature regime. We employ a full numerical solution with a set of
realistic parameters and boundary conditions, considering both a uniform and
non-uniform exchange field in the form of a Bloch domain wall ferromagnetic
layer. The influence of spin-active interfaces is incorporated via a
microscopic approach. We mainly focus on how the electronic specific heat and
density of states (DOS) of such a system is affected by the \textit{proximity
effect}, which may be tuned via the superconducting phase difference. Our main
result is that it is possible to \textit{strongly modify the electronic
specific heat} of the system by changing the phase difference between the two
superconducting leads from 0 up to nearly $\pi$ at low temperatures. An
enhancement of the specific heat will occur for small values $h\simeq\Delta$ of
the exchange field, while for large values of $h$ the specific heat is
suppressed by increasing the phase difference between the superconducting
leads. These results are all explained in terms of the proximity-altered DOS in
the ferromagnetic region, and we discuss possible methods for experimental
detection of the predicted effect.


  Multi-modality image fusion involves integrating complementary information
from different modalities into a single image. Current methods primarily focus
on enhancing image fusion with a single advanced task such as incorporating
semantic or object-related information into the fusion process. This method
creates challenges in achieving multiple objectives simultaneously. We
introduce a target and semantic awareness joint-driven fusion network called
TSJNet. TSJNet comprises fusion, detection, and segmentation subnetworks
arranged in a series structure. It leverages object and semantically relevant
information derived from dual high-level tasks to guide the fusion network.
Additionally, We propose a local significant feature extraction module with a
double parallel branch structure to fully capture the fine-grained features of
cross-modal images and foster interaction among modalities, targets, and
segmentation information. We conducted extensive experiments on four publicly
available datasets (MSRS, M3FD, RoadScene, and LLVIP). The results demonstrate
that TSJNet can generate visually pleasing fused results, achieving an average
increase of 2.84% and 7.47% in object detection and segmentation mAP @0.5 and
mIoU, respectively, compared to the state-of-the-art methods.