  It is demonstrated that the magnetic interactions can be drastically
different for nano-sized systems compared to those of bulk or surfaces. Using a
real-space formalism we have developed a method to calculate non-collinear
magnetization structures and hence exchange interactions. Our results for
magnetic clusters supported on a Cu(111) surface show that the magnetic
ordering as a rule is non-collinear and can not always be described using a
simple Heisenberg Hamiltonian. We suggest that ab initio calculations allowing
for non-collinear coupling between atomic spins is the best tool for analyzing
nano-sized magnets.


  It is known that the ideals of a Leavitt path algebra $L_K(E)$ generated by
$\Pl(E)$, by $\Pc(E)$ or by $\Pec(E)$ are invariant under isomorphism. Though
the ideal generated by $\Pb(E)$ is not invariant we find its \lq\lq
natural\rq\rq\ replacement (which is indeed invariant): the one generated by
the vertices of $\Pbp$ (vertices with pure infinite bifurcations). We also give
some procedures to construct invariant ideals from previous known invariant
ideals. One of these procedures involves topology, so we introduce the $\tops$
topology and relate it to annihilators in the algebraic counterpart of the
work. To be more explicit: if $H$ is a hereditary saturated subset of vertices
providing an invariant ideal, its exterior $\ext(H)$ in the $\tops$ topology of
$E^0$ generates a new invariant ideal. The other constructor of invariant
ideals is more categorical in nature. Some hereditary sets can be seen as
functors from graphs to sets (for instance $\Pl$, etc). Thus a second method
emerges from the possibility of applying the induced functor to the quotient
graph. The easiest example is the known socle chain $\soc^{(1)}(\
)\subset\soc^{(2)}(\ )\subset\cdots$ all of which are proved to be invariant.
We generalize this idea to any hereditary and saturated invariant functor.
Finally we investigate a kind of composition of hereditary and saturated
functors which is associative.


  Magnetars are neutron stars with extremely high surface magnetic fields. They
show diverse X-ray pulse profiles in the quiescent state. We perform a
systematic Fourier analysis of their soft X-ray pulse profiles. We find that
most magnetars have a single-peaked profile and hence have low amplitudes of
the second Fourier harmonics (A2). On the other hand, the pulsed fraction (PF)
spreads over a wide range. We compared the results with theoretical profiles
assuming various surface hotspot asymmetries, viewing geometries, and beaming
functions. We found that a single value of the intensity ratio r between two
antipodal hotspots is unable to reproduce the observed distribution of A2 and
PF for all magnetars. The inferred r is probably anticorrelated with the
thermal luminosity, implying that high-luminosity magnetars tend to have two
symmetric hotspots. Our results are consistent with theoretical predictions,
for which the existence of an evolving toroidal magnetic field breaks the
symmetry of the surface temperature.


  Motion of vortices in two-dimensional superfluids in the classical limit is
studied by solving the Gross-Pitaevskii equation numerically on a uniform
lattice. We find that, in the presence of a superflow directed along one of the
main lattice periods, vortices move with the superflow on fine lattices but
perpendicular to it on coarse ones. We interpret this result as a transition
from the full Magnus force in the Galilean-invariant limit to vanishing
effective Magnus force in a discrete system, in agreement with the existing
experiments on vortex motion in Josephson junction arrays.


  With the rapid development of Internet of Things (IoT), massive devices are
deployed, which poses severe challenges on access networks due to limited
communication resources. When massive users contend for access, the information
freshness gets worse caused by increasing collisions. It could be fatal for
information freshness sensing scenarios, such as remote monitoring systems or
self-driving systems, in which information freshness plays a critical part. In
this paper, by taking the Age of Information (AoI) as the primary performance
indicator, the information freshness using AMP-based grant-free scheme is
investigated and compared with grant-based scheme. Base on the analysis, a user
scheduling strategy with sleep threshold and forcing active threshold is
proposed to further reduce average AoI (AAoI). Numerical results reveal that
the AMP-based grant-free scheme can provide sufficient access capability with
less pilot resources, and it is robust to the fluctuation of the number of
active users. That ensures that the AMP-based grant-free scheme can keep the
AAoI at a low level. It is also shown that the proposed threshold strategy can
effectively improve the information freshness.


  Given a set of obstacles and two points, is there a path between the two
points that does not cross more than $k$ different obstacles? This is a
fundamental problem that has undergone a tremendous amount of work. It is known
to be NP-hard, even when the obstacles are very simple geometric shapes (e.g.,
unit-length line segments). The problem can be generalized into the following
graph problem: Given a planar graph $G$ whose vertices are colored by color
sets, two designated vertices $s, t \in V(G)$, and $k \in \mathbb{N}$, is there
an $s$-$t$ path in $G$ that uses at most $k$ colors? If each obstacle is
connected, the resulting graph satisfies the color-connectivity property,
namely that each color induces a connected subgraph.
  We study the complexity and design algorithms for the above graph problem
with an eye on its geometric applications. We prove that without the
color-connectivity property, the problem is W[SAT]-hard parameterized by $k$. A
corollary of this result is that, unless W[2] $=$ FPT, the problem cannot be
approximated in FPT time to within a factor that is a function of $k$. By
describing a generic plane embedding of the graph instances, we show that our
hardness results translate to the geometric instances of the problem.
  We then focus on graphs satisfying the color-connectivity property. By
exploiting the planarity of the graph and the connectivity of the colors, we
develop topological results to "represent" the valid $s$-$t$ paths containing
subsets of colors from any vertex $v$. We employ these results to design an FPT
algorithm for the problem parameterized by both $k$ and the treewidth of the
graph, and extend this result to obtain an FPT algorithm for the
parameterization by both $k$ and the length of the path. The latter result
directly implies previous FPT results for various obstacle shapes, such as unit
disks and fat regions.


  We work the lattice fermions and non-Hermitian formulation in the 2D GNY
model and demonstrate the numerical implementation for two flavors by the
Hybrid Monte Carlo. Our approach has a notable advantage in dealing with chiral
symmetry on a lattice by avoiding the Nielsen-Ninomiya theorem, due to the
non-symmetrized finite-difference operator. We restore the hypercubic symmetry
by averaging over all possible orientations with the proper continuum limit.
Our study is the first simulation for the interacting fermion formulated in a
non-hermitian way. We compare the numerical solution with the one-loop
resummation. The resummation results matches with the numerical solution in
$\langle\phi\rangle$, $\langle\phi^2\rangle$,
$\langle\mathrm{Tr}(\bar{\psi}_1\psi_1+\bar{\psi}_2\psi_2)/2\rangle$, and
$\langle\mathrm{Tr}(\bar{\psi}_1\psi_1+\bar{\psi}_2\psi_2)\phi/2\rangle$. We
also used the one-loop resummation to provide the RG flow and asymptotic safety
in the 2D GNY model.


  The Ernst formulation of the Einstein equations is generalised to accommodate
$f(R)$ theories of gravity. It is shown that, as in general relativity, the
axisymmetric $f(R)$ field equations for a vacuum spacetime that is either
stationary or cylindrically symmetric reduce to a single, non-linear
differential equation for a complex-valued scalar function. As a worked
example, we apply the generalised Ernst equations to derive a $f(R)$
generalisation of the Zipoy-Voorhees metric, which may be used to describe the
gravitational field outside of an ellipsoidal neutron star. We also apply the
theory to investigate the phase speed of large-amplitude gravitational waves in
$f(R)$ gravity in the context of soliton-like solutions that display shock-wave
behaviour across the causal boundary.


  We characterize the range of the attenuated and non-attenuated $X$-ray
transform of compactly supported vector fields in the plane. The
characterization is in terms of a Hilbert transform associated with the
$A$-analytic functions \`{a} la Bukhgeim. As an application we determine
necessary and sufficient conditions for the attenuated Doppler and $X$-ray data
to be mistaken for each other.


  We selected 82 u-band variable objects based on the u-band photometry data
from SCUSS and SDSS, in the field of LAMOST Complete Spectroscopic Survey of
Pointing Area at Southern Galactic Cap. The magnitude variation of the targets
is restricted to larger than 0.2 mag and limiting magnitude down to 19.0 mag in
u-band. According to the spectra from LAMOST, there are 11 quasars with
red-shift between 0.4 and 1.8, 60 variable stars and 11 unidentified targets.
The variable stars include one active M-dwarf with a series of Balmer emission
lines, seven Horizontal Branch stars containing six RR Lyrae stars matching
with SIMBAD, and one giant, one AGB star and two RR Lyrae candidates by
different colour selections. All these variable stars mainly locate near the
main sequence in the g-r verse u-g diagram. The quasars are well distinguished
from stars by both u-g colour and variation in u-band.


  The almost sure rate of exponential-polynomial growth or decay of affine
stochastic Volterra and affine stochastic finite-delay equations is
investigated. These results are achieved under suitable smallness conditions on
the intensities of the deterministic and stochastic perturbations diffusion,
given that the asymptotic behaviour of the underlying deterministic resolvent
is determined by the zeros of its characteristic equation. The results rely
heavily upon a stochastic variant of the admissibility theory for linear
Volterra operators.


  Within the asymptotic safety scenario for gravity various conceptual issues
related to the scale dependence of the metric are analyzed. The running
effective field equations implied by the effective average action of Quantum
Einstein Gravity (QEG) and the resulting families of resolution dependent
metrics are discussed. The status of scale dependent vs. scale independent
diffeomorphisms is clarified, and the difference between isometries implemented
by scale dependent and independent Killing vectors is explained. A concept of
scale dependent causality is proposed and illustrated by various simple
examples. The possibility of assigning an "intrinsic length" to objects in a
QEG spacetime is also discussed.


  A SU(2) effective lagrangian is extended to a $SU_{L}(3)\otimes SU_{R}(3)$ by
including the vector and axial vector meson. With this effective lagrangian,
electromagnetic form factors of charged pion and kaon are calculated. The
pseudoscalar meson loops are taken into account. Good agreement with
experimental data is obtained for those form factors. Decay widths of $\rho\to
\pi\pi$ and $\phi\to K^{+}K^{-}$ are also calculated and shown to agree with
experimental data very well.


  We discuss Iitaka's theory of quasi-Albanese maps in details. We also give a
detailed proof of Kawamata's theorem on the quasi-Albanese maps for varieties
of the logarithmic Kodaira dimension zero. Note that Iitaka's theory is an
application of Deligne's mixed Hodge theory for smooth algebraic varieties.


  We consider the dependence of the MgB_2 superconducting critical temperature
on the pressure. Our model exploits the influence of the large polarons on the
band structure of the layered MgB_2 superconductor. Namely, the hole
Pekar-Froehlich polarons form quasi two-dimensional potential wells in the
boron plane which shift the positions of the sigma- and pi-bands. This energy
shift depends on the pressure and the Cooper pairing of the correlated
sigma-electrons happens inside polaron wells. The results obtained are as
follows: dT_c/dp = -\alpha (5.2 \pm 0.9) K/GPa or dT_c/dp = -\alpha (6.9\pm
1.1) K/GPa for a different choice of the Grueneisen parameter. Being compared
with known experimental data they give us a resonable interval for the value of
the Froehlich electron-phonon coupling constant: \alpha = 0.15 - 0.45.


  Multi-class segmentation of cardiac magnetic resonance (CMR) images seeks a
separation of data into anatomical components with known structure and
configuration. The most popular CNN-based methods are optimised using pixel
wise loss functions, ignorant of the spatially extended features that
characterise anatomy. Therefore, whilst sharing a high spatial overlap with the
ground truth, inferred CNN-based segmentations can lack coherence, including
spurious connected components, holes and voids. Such results are implausible,
violating anticipated anatomical topology. In response, (single-class)
persistent homology-based loss functions have been proposed to capture global
anatomical features. Our work extends these approaches to the task of
multi-class segmentation. Building an enriched topological description of all
class labels and class label pairs, our loss functions make predictable and
statistically significant improvements in segmentation topology using a
CNN-based post-processing framework. We also present (and make available) a
highly efficient implementation based on cubical complexes and parallel
execution, enabling practical application within high resolution 3D data for
the first time. We demonstrate our approach on 2D short axis and 3D whole heart
CMR segmentation, advancing a detailed and faithful analysis of performance on
two publicly available datasets.


  In this paper, we present a method for instance ranking and retrieval at
fine-grained level based on the global features extracted from a
multi-attribute recognition model which is not dependent on landmarks
information or part-based annotations. Further, we make this architecture
suitable for mobile-device application by adopting the bilinear CNN to make the
multi-attribute recognition model smaller (in terms of the number of
parameters). The experiments run on the Dress category of DeepFashion In-Shop
Clothes Retrieval and CUB200 datasets show that the results of instance
retrieval at fine-grained level are promising for these datasets, specially in
terms of texture and color.


  The monodromy matrix, ${\hat{\cal M}}$, is constructed for two dimensional
tree level string effective action. The pole structure of ${\hat{\cal M}}$ is
derived using its factorizability property. It is found that the monodromy
matrix transforms non-trivially under the non-compact T-duality group, which
leaves the effective action invariant and this can be used to construct the
monodromy matrix for more complicated backgrounds starting from simpler ones.
We construct, explicitly, ${\hat{\cal M}}$ for the exactly solvable
Nappi-Witten model, both when B=0 and $B\neq 0$, where these ideas can be
directly checked. We consider well known charged black hole solutions in the
heterotic string theory which can be generated by T-duality transformations
from a spherically symmetric `seed' Schwarzschild solution. We construct the
monodromy matrix for the Schwarzschild black hole background of the heterotic
string theory.


  Minimization of internal degrees of freedom is an important step in the
cooling of atomic species to degeneracy temperature. Here, we report on the
loading of 6*10^5 thulium atoms optically polarized at maximum possible
magnetic quantum number mf=-4 state into dipole trap operating at 532 nm. The
purity of polarizations of the atoms was experimentally verified using a
Stern-Gerlach-type experiment. Experimental measured polarization of the state
is 3.91(26).


  We show that it is possible to have a topological phase in two-dimensional
quasicrystals without any magnetic field applied, but instead introducing an
artificial gauge field via dynamic modulation. This topological quasicrystal
exhibits scatter-free unidirectional edge states that are extended along the
system's perimeter, contrary to the states of an ordinary quasicrystal system,
which are characterized by power-law decay. We find that the spectrum of this
Floquet topological quasicrystal exhibits a rich fractal (self-similar)
structure of topological "minigaps," manifesting an entirely new phenomenon:
fractal topological systems. These topological minigaps form only when the
system size is sufficiently large because their gapless edge states penetrate
deep into the bulk. Hence, the topological structure emerges as a function of
the system size, contrary to periodic systems where the topological phase can
be completely characterized by the unit cell. We demonstrate the existence of
this topological phase both by using a topological index (Bott index) and by
studying the unidirectional transport of the gapless edge states and its
robustness in the presence of defects. Our specific model is a Penrose lattice
of helical optical waveguides - a photonic Floquet quasicrystal; however, we
expect this new topological quasicrystal phase to be universal.


  The usage of recommendation agents (RAs) in the online marketplace can help
consumers to locate their desired products. RAs can help consumers effectively
obtain comprehensive product information and compare their candidate target
products. As a result, RAs have affected consumers shopping behaviour. In this
study, we investigate the usage and the influence of RAs in the online
marketplace. Based on the Stimulus-Organism-Response (SOR) model, we propose
that the stimulus of using RAs (informativeness, product search effectiveness
and the lack of sociality stress) can affect consumers attitude (perceived
control and satisfaction), which further affects their behavioural outcomes
like impulsive purchase. We validate this research model with survey data from
157 users of RAs. The data largely support the proposed model and indicate that
the RAs can significantly contribute to impulsive purchase behaviour in online
marketplaces. Theoretical and practical contributions are discussed.


  We examine the hypothesis that mergers and close encounters between galaxies
can fuel AGNs by increasing the rate at which gas accretes towards the central
black hole. We compare the clustering of galaxies around radio-loud AGNs with
the clustering around a population of radio-quiet galaxies with similar masses,
colors and luminosities. Our catalog contains 2178 elliptical radio galaxies
with flux densities greater than 2.8 mJy at 1.4 GHz from the 6dFGS survey. We
find that radio AGNs with more than 200 times the median radio power have, on
average, more close (r<160 kpc) companions than their radio-quiet counterparts,
suggestive that mergers play a role in forming the most powerful radio
galaxies. For ellipticals of fixed stellar mass, the radio power is not a
function of large-scale environment nor halo mass, consistent with the radio
powers of ellipticals varying by orders of magnitude over billions of years.


  Classical Krylov subspace projection methods for the solution of linear
problem $Ax = b$ output an approximate solution $\widetilde{x}\simeq x$.
Recently, it has been recognized that projection methods can be understood from
a statistical perspective. These probabilistic projection methods return a
distribution $p(\widetilde{x})$ in place of a point estimate $\widetilde{x}$.
The resulting uncertainty, codified as a distribution, can, in theory, be
meaningfully combined with other uncertainties, can be propagated through
computational pipelines, and can be used in the framework of probabilistic
decision theory. The problem we address is that the current probabilistic
projection methods lead to the poorly calibrated posterior distribution. We
improve the covariance matrix from previous works in a way that it does not
contain such undesirable objects as $A^{-1}$ or $A^{-1}A^{-T}$, results in
nontrivial uncertainty, and reproduces an arbitrary projection method as a mean
of the posterior distribution. We also propose a variant that is numerically
inexpensive in the case the uncertainty is calibrated a priori. Since it
usually is not, we put forward a practical way to calibrate uncertainty that
performs reasonably well, albeit at the expense of roughly doubling the
numerical cost of the underlying projection method.


  We review classical properties of harmonic-oscillator coherent states. Then
we discuss which of these classical properties are preserved under the
group-theoretic generalization of coherent states. We prove that the
generalized coherent states of quantum systems with Lie-group symmetries are
the unique Bell states, i.e., the pure quantum states preserving the
fundamental classical property of satisfying Bell's inequality upon splitting.


  Exploiting robots for activities in human-shared environments, whether
warehouses, shopping centres or hospitals, calls for such robots to understand
the underlying physical interactions between nearby agents and objects. In
particular, modelling cause-and-effect relations between the latter can help to
predict unobserved human behaviours and anticipate the outcome of specific
robot interventions. In this paper, we propose an application of causal
discovery methods to model human-robot spatial interactions, trying to
understand human behaviours from real-world sensor data in two possible
scenarios: humans interacting with the environment, and humans interacting with
obstacles. New methods and practical solutions are discussed to exploit, for
the first time, a state-of-the-art causal discovery algorithm in some
challenging human environments, with potential application in many service
robotics scenarios. To demonstrate the utility of the causal models obtained
from real-world datasets, we present a comparison between causal and non-causal
prediction approaches. Our results show that the causal model correctly
captures the underlying interactions of the considered scenarios and improves
its prediction accuracy.


  Yang-Baxter (YB) map systems (or set-theoretic analoga of entwining YB
structures) are presented. They admit zero curvature representations with
spectral parameter depended Lax triples L1, L2, L3 derived from symplectic
leaves of 2 x 2 binomial matrices equipped with the Sklyanin bracket. A unique
factorization condition of the Lax triple implies a 3-dimensional compatibility
property of these maps. In case L1 = L2 = L3 this property yields the
se--theoretic quantum Yang-Baxter equation, i.e. the YB map property. By
considering periodic 'staircase' initial value problems on quadrilateral
lattices, these maps give rise to multidimensional integrable mappings which
preserve the spectrum of the corresponding monodromy matrix.


  Nowadays, Virtual Observatory standards, resources, and services became
powerful enough to help astronomers making real science on everyday basis. The
key to the VO success is its entire transparency for a scientific user. This
allows an astronomer to combine "online" VO-enabled parts with "offline"
research stages including dedicated data processing and analysis, observations,
numerical simulations; and helps to overpass one of the major issues that most
present-day VO studies do not go further than data mining. Here we will present
three VO-powered research projects combining VO and non-VO blocks, all of them
resulted in peer-reviewed publications.


  In general, homeowners refinance in response to a decrease in interest rates,
as their borrowing costs are lowered. However, it is worth investigating the
effects of refinancing after taking the underlying costs into consideration.
Here we develop a synthetic mortgage calculator that sufficiently accounts for
such costs and the implications on new monthly payments. To confirm the
accuracy of the calculator, we simulate the effects of refinancing over 15 and
30 year periods. We then model the effects of refinancing as risk to the issuer
of the mortgage, as there is negative duration associated with shifts in the
interest rate. Furthermore, we investigate the effects on the swap market as
well as the treasury bond market. We model stochastic interest rates using the
Vasicek model.


  Cross-spectral face recognition (CFR) refers to recognizing individuals using
face images stemming from different spectral bands, such as infrared vs.
visible. While CFR is inherently more challenging than classical face
recognition due to significant variation in facial appearance caused by the
modality gap, it is useful in many scenarios including night-vision biometrics
and detecting presentation attacks. Recent advances in convolutional neural
networks (CNNs) have resulted in significant improvement in the performance of
CFR systems. Given these developments, the contributions of this survey are
three-fold. First, we provide an overview of CFR, by formalizing the CFR
problem and presenting related applications. Secondly, we discuss the
appropriate spectral bands for face recognition and discuss recent CFR methods,
placing emphasis on deep neural networks. In particular we describe techniques
that have been proposed to extract and compare heterogeneous features emerging
from different spectral bands. We also discuss the datasets that have been used
for evaluating CFR methods. Finally, we discuss the challenges and future lines
of research on this topic.


  We propose a novel multi-scale message passing neural network algorithm for
learning the solutions of time-dependent PDEs. Our algorithm possesses both
temporal and spatial multi-scale resolution features by incorporating
multi-scale sequence models and graph gating modules in the encoder and
processor, respectively. Benchmark numerical experiments are presented to
demonstrate that the proposed algorithm outperforms baselines, particularly on
a PDE with a range of spatial and temporal scales.


  We present and summarize the results of recent studies on non-Euclidean
plates with imposed constant negative Gaussian curvature in both the F\"oppl -
von K\'arm\'an and Kirchhoff approximations. Motivated by experimental results
we focus on annuli with a periodic profile. We show that in the F\"oppl - von
K\'arm\'an approximation there are only two types of global minimizers -- flat
and saddle shaped deformations with localized regions of stretching near the
boundary of the annulus. We also show that there exists local minimizers with
$n$-waves that have regions of stretching near their lines of inflection. In
the Kirchhoff approximation we show that there exist exact isometric immersions
with periodic profiles. The number of waves in these configurations is set by
the condition that the bending energy remains finite and grows approximately
exponentially with the radius of the annulus. For large radii, these shape are
energetically favorable over saddle shapes and could explain why wavy shapes
are selected by crocheted models of the hyperbolic plane.


  We study the quantum mechanical states of electrons situated on a cylindrical
surface of finite axial length to model a semiconductor core-shell nanowire. We
calculate the conductance in the presence of a longitudinal magnetic field by
weakly coupling the cylinder to semi-infinite leads. Spin effects are accounted
for through Zeeman coupling and Rashba spin-orbit interaction (SOI). Emphasis
is on manifestations of flux-periodic (FP) oscillations and we show how factors
such as impurities, contact geometry and spin affect them. Oscillations survive
and remain periodic in the presence of impurities, noncircular contacts and
SOI, while Zeeman splitting results in aperiodicity, beating patterns and
additional background fluctuations. Our results are in qualitative agreement
with recent magnetotransport experiments performed on GaAs/InAs core-shell
nanowires. Lastly, we propose methods of data analysis for detecting the
presence of Rashba SOI in core-shell systems and for estimating the electron
g-factor in the shell.


  We present new HST optical and near-infrared (NIR) photometry of the rich
globular cluster (GC) system of NGC 4874, the cD galaxy in the core of the Coma
cluster (Abell 1656). NGC 4874 was observed with the HST Advanced Camera for
Surveys in the F475W (g) and F814W (I) passbands and the Wide Field Camera 3 IR
Channel in F160W (H). The GCs in this field exhibit a bimodal optical color
distribution with more than half of the GCs falling on the red side at g-I > 1.
Bimodality is also present, though less conspicuously, in the optical-NIR I-H
color. Consistent with past work, we find evidence for nonlinearity in the g-I
versus I-H color-color relation. Our results thus underscore the need for
understanding the detailed form of the color-metallicity relations in
interpreting observational data on GC bimodality. We also find a very strong
color-magnitude trend, or "blue tilt," for the blue component of the optical
color distribution of the NGC 4874 GC system. A similarly strong trend is
present for the overall mean I-H color as a function of magnitude; for M_814 <
-10 mag, these trends imply a steep mass-metallicity scaling with $Z\propto
M_{\rm GC}^{1.4\pm0.4}$, but the scaling is not a simple power law and becomes
much weaker at lower masses. As in other similar systems, the spatial
distribution of the blue GCs is more extended than that of the red GCs, partly
because of blue GCs associated with surrounding cluster galaxies. In addition,
the center of the GC system is displaced by 4+/-1 kpc towards the southwest
from the luminosity center of NGC 4874, in the direction of NGC 4872. Finally,
we remark on a dwarf elliptical galaxy with a noticeably asymmetrical GC
distribution. Interestingly, this dwarf has a velocity of nearly -3000 km/s
with respect to NGC 4874; we suggest it is on its first infall into the cluster
core and is undergoing stripping of its GC system by the cluster potential.


  This PhD research introduces three key contributions in the domain of object
motion detection:
  Multi-Hierarchical Spiking Neural Network (MHSNN): A specialized four-layer
Spiking Neural Network (SNN) architecture inspired by vertebrate retinas.
Trained on custom lab-generated images, it exhibited 6.75% detection error for
horizontal and vertical movements. While non-scalable, MHSNN laid the
foundation for further advancements. Hybrid Sensitive Motion Detector (HSMD):
Enhancing Dynamic Background Subtraction (DBS) using a tailored three-layer
SNN, stabilizing foreground data to enhance object motion detection. Evaluated
on standard datasets, HSMD outperformed OpenCV-based methods, excelling in four
categories across eight metrics. It maintained real-time processing
(13.82-13.92 fps) on a high-performance computer but showed room for hardware
optimisation. Neuromorphic Hybrid Sensitive Motion Detector (NeuroHSMD):
Building upon HSMD, this adaptation implemented the SNN component on dedicated
hardware (FPGA). OpenCL simplified FPGA design and enabled portability.
NeuroHSMD demonstrated an 82% speedup over HSMD, achieving 28.06-28.71 fps on
CDnet2012 and CDnet2014 datasets.
  These contributions collectively represent significant advancements in object
motion detection, from a biologically inspired neural network design to an
optimized hardware implementation that outperforms existing methods in accuracy
and processing speed.


  We train language models (LMs) with federated learning (FL) and differential
privacy (DP) in the Google Keyboard (Gboard). We apply the
DP-Follow-the-Regularized-Leader (DP-FTRL)~\citep{kairouz21b} algorithm to
achieve meaningfully formal DP guarantees without requiring uniform sampling of
client devices. To provide favorable privacy-utility trade-offs, we introduce a
new client participation criterion and discuss the implication of its
configuration in large scale systems. We show how quantile-based clip
estimation~\citep{andrew2019differentially} can be combined with DP-FTRL to
adaptively choose the clip norm during training or reduce the hyperparameter
tuning in preparation for training. With the help of pretraining on public
data, we train and deploy more than twenty Gboard LMs that achieve high utility
and $\rho-$zCDP privacy guarantees with $\rho \in (0.2, 2)$, with two models
additionally trained with secure aggregation~\citep{bonawitz2017practical}. We
are happy to announce that all the next word prediction neural network LMs in
Gboard now have DP guarantees, and all future launches of Gboard neural network
LMs will require DP guarantees. We summarize our experience and provide
concrete suggestions on DP training for practitioners.


  We study numerical methods for the generalized Langevin equation (GLE) with a
positive Prony series memory kernel, in which case the GLE can be written in an
extended variable Markovian formalism. We propose a new splitting method that
is easy to implement and is able to substantially improve the accuracy and
robustness of GLE simulations in a wide range of the parameters. An error
analysis is performed in the case of a one-dimensional harmonic oscillator,
revealing that several averages are exact for the newly proposed method.
Various numerical experiments in both equilibrium and nonequilibrium
simulations are also conducted to compare the method with popular alternatives
in interacting multi-particle systems.


  Gravitational waves induced by large primordial curvature fluctuations may
result in a sizable stochastic gravitational wave background. Interestingly,
curvature fluctuations are gradually generated by initial isocurvature
fluctuations, which in turn induce gravitational waves. Initial isocurvature
fluctuations commonly appear in multi-field models of inflation as well as in
the formation of scattered compact objects in the very early universe, such as
primordial black holes and solitons like oscillons and cosmic strings. Here we
provide a review on isocurvature induced gravitational waves and its
applications to dark matter and the primordial black hole dominated early
universe.


  We define multilevel codes on bipartite graphs that have properties analogous
to multilevel serial concatenations. A decoding algorithm is described that
corrects a proportion of errors equal to half the Blokh-Zyablov bound on the
minimum distance. The error probability of this algorithm has exponent similar
to that of serially concatenated multilevel codes.


  Chemical functionalization is a promising route to band gap engineering of
graphene. We chemically grafted nitrophenyl groups onto exfoliated single-layer
graphene sheets in the form of substrate-supported or free-standing films. Our
transport measurements demonstrate that non-suspended functionalized graphene
behaves as a granular metal, with variable range hopping transport and a
mobility gap ~ 0.1 eV at low temperature. For suspended graphene that allows
functionalization on both surfaces, we demonstrate tuning of its electronic
properties from a granular metal to a gapped semiconductor, in which charge
transport occurs via thermal activation over a gap ~ 80 meV. This non-invasive
and scalable functionalization technique paves the way for CMOS-compatible band
gap engineering of graphene electronic devices.


  Despite the impressive results of arbitrary image-guided style transfer
methods, text-driven image stylization has recently been proposed for
transferring a natural image into a stylized one according to textual
descriptions of the target style provided by the user. Unlike the previous
image-to-image transfer approaches, text-guided stylization progress provides
users with a more precise and intuitive way to express the desired style.
However, the huge discrepancy between cross-modal inputs/outputs makes it
challenging to conduct text-driven image stylization in a typical feed-forward
CNN pipeline. In this paper, we present DiffStyler, a dual diffusion processing
architecture to control the balance between the content and style of the
diffused results. The cross-modal style information can be easily integrated as
guidance during the diffusion process step-by-step. Furthermore, we propose a
content image-based learnable noise on which the reverse denoising process is
based, enabling the stylization results to better preserve the structure
information of the content image. We validate the proposed DiffStyler beyond
the baseline methods through extensive qualitative and quantitative
experiments. Code is available at
\url{https://github.com/haha-lisa/Diffstyler}.


  Parts V, VI and VII of this study are dedicated to the computation of
paraxial rays and dynamic characteristics along the stationary rays obtained
numerically in Part III. In this part (Part V), we formulate the linear,
second-order, Jacobi dynamic ray tracing equation. In Part VI, we compare the
Lagrangian and Hamiltonian approaches to the dynamic ray tracing in
heterogeneous isotropic and anisotropic media; we demonstrate that the two
approaches are compatible and derive the relationships between the Lagrangian's
and Hamiltonian's Hessian matrices. In Part VII, we apply a similar
finite-element solver, as used for the kinematic ray tracing, to compute the
dynamic characteristics between the source and any point along the ray. The
dynamic characteristics in our study include the relative geometric spreading
and the phase correction factor due to caustics (i.e., the amplitude and the
phase of the Green's function of waves propagating in 3D heterogeneous
anisotropic media). The basic solution of the Jacobi equation is a shift vector
of a paraxial ray in the plane normal to the ray direction at each point along
the central ray. A general paraxial ray is defined by a linear combination of
up to four basic vector solutions, each corresponds to specific initial
conditions related to the ray coordinates at the source. We define the four
basic solutions with two pairs of initial condition sets: point-source and
plane-wave. For the proposed point-source ray coordinates and initial
conditions, we derive the ray Jacobian and relate it to the relative geometric
spreading for general anisotropy. Finally, we introduce a new dynamic
parameter, referred as the normalized geometrical spreading, considered a
measure of complexity of the propagated wave/ray phenomena, and hence, we
propose using a criterion based on this parameter as a qualifying factor
associated with the given ray solution.


  A problem of Erd\H{o}s (Amer. Math. Monthly 52: 494-498, 1945) and a theorem
of Fejes T\'oth and Fejes T\'oth (Acta Math. Acad. Sci. Hungar. 24: 229-232,
1973) initiated the study of non-separable arrangements of convex bodies and
the investigation of totally separable packings of convex bodies with both
topics analyzing the concept of separability from the point view of discrete
geometry. This article surveys the progress made on these and some closely
related problems and highlights the relevant questions that have been left
open.


  In this paper we propose new iterative algorithm of calculating the joint
distribution of the Parisian ruin time and the number of claims until Parisian
ruin for the classical risk model. Examples are provided when the generic claim
size is exponentially distributed.


  Quantum computational chemistry is a potential application of quantum
computers that is expected to effectively solve several quantum-chemistry
problems, particularly the electronic structure problem. Quantum computational
chemistry can be compared to the conventional computational devices. This
review comprehensively investigates the applications and overview of quantum
computational chemistry, including a review of the Hartree-Fock method for
quantum information scientists. Quantum algorithms, quantum phase estimation,
and variational quantum eigensolver, have been applied to the post-Hartree-Fock
method.


  We predict the phenomenon of antiferroelectric resonance (AFER), in which an
ac electric field causes magnetic ions located at noncentrosymmetric positions
in a multi-sublattice magnet to undergo magnetic transitions corresponding to
exchange collective excitations of the system. We construct a theory of such
resonances, and show that in magnets with collinear magnetic structures AFER is
caused by relativistic and exchange-relativistic magnetoelectric interactions,
while in the noncollinear magnets a significant contribution can also come from
the exchange magnetoelectric interaction. We predict an exchange enhancement of
the resonance by exchange modes, and discuss the role of AFER in causing
resonant enhancement of magnetooptical phenomena. The main results of our
theory are illustrated with the four-sublattice rhombohedral antiferromagnets
{\alpha}-Fe_2O_3 and Cr_2O_3, as examples.


  A crystal surface which is miscut with respect to a high symmetry plane
exhibits steps with a characteristic distance. It is argued that the continuum
description of growth on such a surface, when desorption can be neglected, is
given by the anisotropic version of the conserved KPZ equation (T. Sun, H. Guo,
and M. Grant, Phys. Rev. A 40, 6763 (1989)) with non-conserved noise. A
one--loop dynamical renormalization group calculation yields the values of the
dynamical exponent and the roughness exponent which are shown to be the same as
in the isotropic case. The results presented here should apply in particular to
growth under conditions which are typical for molecular beam epitaxy.


  This note aims to clarify what conditions on a connected Lie group G imply
that its maximal connected normal solvable subgroup R intersects each lattice
of G as a lattice in R.


  In this paper we study the interior transmission problem and transmission
eigenvalues for multiplicative perturbations of linear partial differential
operator of order $\ge 2$ with constant real coefficients. Under suitable
growth conditions on the symbol of the operator and the perturbation, we show
the discreteness of the set of transmission eigenvalues and derive sufficient
conditions on the existence of transmission eigenvalues. We apply these
techniques to the case of the biharmonic operator and the Dirac system. In the
hypoelliptic case we present a connection to scattering theory.


  Hiring robots for the workplaces is a challenging task as robots have to
cater to customer demands, follow organizational protocols and behave with
social etiquette. In this study, we propose to have a humanoid social robot,
Nadine, as a customer service agent in an open social work environment. The
objective of this study is to analyze the effects of humanoid robots on
customers at work environment, and see if it can handle social scenarios. We
propose to evaluate these objectives through two modes, namely, survey
questionnaire and customer feedback. We also propose a novel approach to
analyze customer feedback data (text) using sentic computing methods.
Specifically, we employ aspect extraction and sentiment analysis to analyze the
data. From our framework, we detect sentiment associated to the aspects that
mainly concerned the customers during their interaction. This allows us to
understand customers expectations and current limitations of robots as
employees.


  The dark matter in the universe can be in the form of a superheavy matter
species (WIMPZILLA). Several mechanisms have been proposed for the production
of WIMPZILLA particles during or immediately following the inflationary epoch.
Perhaps the most attractive mechanism is through gravitational particle
production, where particles are produced simply as a result of the expansion of
the universe. In this paper we present a detailed numerical calculation of
WIMPZILLA gravitational production in hybrid-inflation models and
natural-inflation models. Generalizing these findings, we also explore the
dependence of the gravitational production mechanism on various models of
inflation. We show that superheavy dark matter production seems to be robust,
with Omega_X h^2 ~ (M_X / (10^11 GeV))^2 (T_RH / (10^9 GeV)), so long as M_X <
H_I, where M_X is the WIMPZILLA mass, T_RH is the reheat temperature, and H_I
is the expansion rate of the universe during inflation.


  We present here the results of a deep survey in a 0.4 sq.deg. blank field in
Selected Area 57 conducted with the ISOPHOT instrument aboard ESAs Infrared
Space Observatory (ISO) at both 60 um and 90 um. The resulting sky maps have a
spatial resolution of 15 x 23 sq.arcsec. per pixel which is much higher than
the 90 x 90 sq.arcsec. pixels of the IRAS All Sky Survey. We describe the main
instrumental effects encountered in our data, outline our data reduction and
analysis scheme and present astrometry and photometry of the detected point
sources. With a formal signal to noise ratio of 6.75 we have source detection
limits of 90 mJy at 60 um and 50 mJy at 90 um. To these limits we find
cumulated number densities of 5+-3.5 per sq.deg. at 60 um and 14.8+-5.0 per
sq.deg.at 90 um. These number densities of sources are found to be lower than
previously reported results from ISO but the data do not allow us to
discriminate between no-evolution scenarios and various evolutionary models.


  A 2-D Riemann problem is designed to study the development and dynamics of
the slow shocks that are thought to form at the boundaries of reconnection
exhausts. Simulations are carried out for varying ratios of normal magnetic
field to the transverse upstream magnetic field (i.e., propagation angle with
respect to the upstream magnetic field). When the angle is sufficiently
oblique, the simulations reveal a large firehose-sense
(P_parallel>P_perpendicular) temperature anisotropy in the downstream region,
accompanied by a transition from a coplanar slow shock to a non-coplanar
rotational mode. In the downstream region the firehose stability parameter
epsilon=1-mu_0(P_parallel-P_perpendicular)/ B^2 tends to lock in to 0.25. This
balance arises from the competition between counterstreaming ions, which drives
epsilon down, and the scattering due to ion inertial scale waves, which are
driven unstable by the downstream rotational wave. At very oblique propagating
angles, 2-D turbulence also develops in the downstream region.


  We theoretically study the piezoelectric effects in moir\`e graphene systems.
Since the strain couples to the electrons in the system as a pseudo vector
potential, which has opposite signs for the $K$ and $K'$ valleys of graphene,
its effects on the two valleys with opposite Chern numbers do not cancel out,
but adds up. As a result, some components of the piezoelectric tensor in these
systems, which typically have non-trivial topology in their flat bands, are
nearly quantized in terms of the valley Chern numbers. Such a conclusion is
verified by numerical calculations of the in-plane piezoelectric response of
hBN-aligned twisted bilayer graphene, twisted bilayer-monolayer graphene, and
twisted double bilayer graphene systems using both continuum model and
atomistic tight-binding model. We find that by tuning the vertical displacement
field and/or twist angle, which may induce gap closures between the flat bands
and remote bands in these systems, plateau shapes of the piezoelectric response
are obtained, with abrupt jumps across the topological phase transitions. We
propose that such nearly quantized piezoelectric response may serve as a direct
experimental probe for the valley Chern numbers of the flat bands in moir\'e
graphene systems.


  In this paper, we use tensor models to analyze Covid-19 pandemic data. First,
we use tensor models, canonical polyadic and higher-order Tucker
decompositions, to extract patterns over multiple modes. Second, we implement a
tensor completion algorithm using canonical polyadic tensor decomposition to
predict spatiotemporal data from multiple spatial sources and to identify
Covid-19 hotspots. We apply a regularized iterative tensor completion technique
with a practical regularization parameter estimator to predict the spread of
Covid-19 cases and to find and identify hotspots. Our method can predict weekly
and quarterly Covid-19 spreads with high accuracy. Third, we analyze Covid-19
data in the US using a novel sampling method for alternating least-squares.
Moreover, we compare the algorithms with standard tensor decompositions in
terms of their interpretability, visualization and cost analysis. Finally, we
demonstrate the efficacy of the methods by applying the techniques to New
Jersey's Covid-19 data.


  The study explores cat state formation in the strong Rydberg dressing regime,
uncovering the emergence of cat states despite the presence of all orders of
nonlinearities. This unexplored regime demonstrates potential for rapid cat
state formation, particularly beneficial for operation in 2D lattices in
Rydberg labs. Additionally, the paper discusses the potential for creating a
superposition of m coherent spin states (m-SCSS), where the maximum m is
determined by the number of atoms within the blockade radius $m=\sqrt{N}$.


  The electronic properties of hydrogenated, spherical, Si/Ge and Ge/Si
core-shell nanocrystals with a diameter ranging from 1.8 to 4.0 nm are studied
within Density Functional Theory. Effects induced by quantum confinement and
strain on the near-band-edge states localization, as well as the band-offset
properties between Si and Ge regions, are investigated in detail. On the one
hand, we prove that Si(core)/Ge(shell) nanocrystals always show a type II
band-offset alignment, with the HOMO mainly localized on the Ge shell region
and the LUMO mainly localized on the Si core region. On the other hand, our
results point out that a type II offset cannot be observed in small (diameter
less than 3 nm) Ge(core)/Si(shell) nanocrystals. In these systems, quantum
confinement and strain drive the near-band-edge states to be mainly localized
on Ge atoms inducing a type I alignment. In larger Ge(core)/Si(shell)
nanocrystals, instead, the formation of a type II offset can be engineered by
playing with both core and shell thickness. The conditions that favor the
transition from a type I to a type II alignment for Ge(core)/Si(shell)
nanocrystals are discussed in detail.


  We study how a behavior (an idea, buying a product, having a disease,
adopting a cultural fad or a technology) spreads among agents in an a social
network that exhibits segregation or homophily (the tendency of agents to
associate with others similar to themselves). Individuals are distinguished by
their types (e.g., race, gender, age, wealth, religion, profession, etc.)
which, together with biased interaction patterns, induce heterogeneous rates of
adoption. We identify the conditions under which a behavior diffuses and
becomes persistent in the population. These conditions relate to the level of
homophily in a society, the underlying proclivities of various types for
adoption or infection, as well as how each type interacts with its own type. In
particular, we show that homophily can facilitate diffusion from a small
initial seed of adopters.


  It is shown, using sutured manifold theory, that if there are any 2-component
counterexamples to the Generalized Property R Conjecture, then any knot of
least genus among components of such counterexamples is not a fibered knot.
  The general question of what fibered knots might appear as a component of
such a counterexample is further considered; much can be said about the
monodromy of the fiber, particularly in the case in which the fiber is of genus
two.


  Motivated by recent proposals of correlation induced insensitivity of d-wave
superconductors to impurities, we develop a simple pairing theory for these
systems for up to a moderate strength of disorder. Our description implements
the key ideas of Anderson, originally proposed for disordered s-wave
superconductors, but in addition takes care of the inherent strong electronic
repulsion in these compounds, as well as disorder induced inhomogeneities. We
first obtain the self-consistent one-particle states, that capture the effects
of disorder exactly, and strong correlations using Gutzwiller approximation.
These `normal states', representing the interplay of strong correlations and
disorder, when coupled through pairing attractions following the path of
Bardeen-Cooper-Schrieffer (BCS), produce results nearly identical to those from
a more sophisticated Gutzwiller augmented Bogoliubov-de Gennes analysis.


  Due to the complexity of the natural world, a programmer cannot foresee all
possible situations, a connected and autonomous vehicle (CAV) will face during
its operation, and hence, CAVs will need to learn to make decisions
autonomously. Due to the sensing of its surroundings and information exchanged
with other vehicles and road infrastructure, a CAV will have access to large
amounts of useful data. While different control algorithms have been proposed
for CAVs, the benefits brought about by connectedness of autonomous vehicles to
other vehicles and to the infrastructure, and its implications on policy
learning has not been investigated in literature. This paper investigates a
data driven driving policy learning framework through an agent-based modelling
approaches. The contributions of the paper are two-fold. A dynamic programming
framework is proposed for in-vehicle policy learning with and without
connectivity to neighboring vehicles. The simulation results indicate that
while a CAV can learn to make autonomous decisions, vehicle-to-vehicle (V2V)
communication of information improves this capability. Furthermore, to overcome
the limitations of sensing in a CAV, the paper proposes a novel concept for
infrastructure-led policy learning and communication with autonomous vehicles.
In infrastructure-led policy learning, road-side infrastructure senses and
captures successful vehicle maneuvers and learns an optimal policy from those
temporal sequences, and when a vehicle approaches the road-side unit, the
policy is communicated to the CAV. Deep-imitation learning methodology is
proposed to develop such an infrastructure-led policy learning framework.


  The well-known notion of dimension for partial orders by Dushnik and Miller
allows to quantify the degree of incomparability and, thus, is regarded as a
measure of complexity for partial orders. However, despite its usefulness, its
definition is somewhat disconnected from the geometrical idea of dimension,
where, essentially, the number of dimensions indicates how many real lines are
required to represent the underlying partially ordered set.
  Here, we introduce a variation of the Dushnik-Miller notion of dimension that
is closer to geometry, the Debreu dimension, and show the following main
results: (i) how to construct its building blocks under some countability
restrictions, (ii) its relation to other notions of dimension in the
literature, and (iii), as an application of the above, we improve on the
classification of preordered spaces through real-valued monotones.


  The practice of uncertainty quantification (UQ) validation, notably in
machine learning for the physico-chemical sciences, rests on several graphical
methods (scattering plots, calibration curves, reliability diagrams and
confidence curves) which explore complementary aspects of calibration, without
covering all the desirable ones. For instance, none of these methods deals with
the reliability of UQ metrics across the range of input features (adaptivity).
Based on the complementary concepts of consistency and adaptivity, the toolbox
of common validation methods for variance- and intervals- based UQ metrics is
revisited with the aim to provide a better grasp on their capabilities. This
study is conceived as an introduction to UQ validation, and all methods are
derived from a few basic rules. The methods are illustrated and tested on
synthetic datasets and representative examples extracted from the recent
physico-chemical machine learning UQ literature.


  We investigate the form of the radiation emitted by an axion star-neutron
star binary using a $f(r)=\text{sech(r/R)}$ profile for the axion star. Our
analysis takes into account the co-rotating plasma of the neutron star. We find
that that there is significant enhancement to the radiated power if the neutron
star's spin is tilted towards the plane of the axion star-neutron star orbit,
compared to the case where it is perpendicular. We also examine whether the
neutron star's co-rotating plasma can play a role in the emitted power and we
find that even though dilute axion stars can in principle radiate more
efficiently than dense axion stars, they will be pulled apart by the tidal
forces of the neutron star


  The behavior of persistent current in a mesoscopic cylinder threaded by an
Aharonov-Bohm flux $\phi$ is carefully investigated within a Hartree-Fock mean
field approach. We examine the combined effect of second-neighbor hopping
integral and Hubbard correlation on the enhancement of persistent current in
presence of disorder. A significant change in current amplitude is observed
compared to the traditional nearest-neighbor hopping model and the current
amplitude becomes quite comparable to experimental realizations. Our analysis
is found to exhibit several interesting results which have so far remained
unaddressed.


  Generalized Disjunctive Programming (GDP) provides an alternative framework
to model optimization problems with both discrete and continuous variables. The
key idea behind GDP involves the use of logical disjunctions to represent
discrete decisions in the continuous space, and logical propositions to denote
algebraic constraints in the discrete space. Compared to traditional
mixed-integer programming (MIP), the inherent logic structure in GDP yields
tighter relaxations that are exploited by global branch and bound algorithms to
improve solution quality. In this paper, we present a general GDP model for
optimal control of hybrid systems that exhibit both discrete and continuous
dynamics. Specifically, we use GDP to formulate a model predictive control
(MPC) model for piecewise-affine systems with implicit switching logic. As an
example, the GDP-based MPC approach is used as a supervisory control to improve
energy efficiency in residential buildings with binary on/off, relay-based
thermostats. A simulation study is used to demonstrate the validity of the
proposed approach, and the improved solution quality compared to existing
MIP-based control approaches.


  Large language models (LLMs) often generate inaccurate or fabricated
information and generally fail to indicate their confidence, which limits their
broader applications. Previous work elicits confidence from LLMs by direct or
self-consistency prompting, or constructing specific datasets for supervised
finetuning. The prompting-based approaches have inferior performance, and the
training-based approaches are limited to binary or inaccurate group-level
confidence estimates. In this work, we present the advanced SaySelf, a training
framework that teaches LLMs to express more accurate fine-grained confidence
estimates. In addition, beyond the confidence scores, SaySelf initiates the
process of directing LLMs to produce self-reflective rationales that clearly
identify gaps in their parametric knowledge and explain their uncertainty. This
is achieved by using an LLM to automatically summarize the uncertainties in
specific knowledge via natural language. The summarization is based on the
analysis of the inconsistency in multiple sampled reasoning chains, and the
resulting data is utilized for supervised fine-tuning. Moreover, we utilize
reinforcement learning with a meticulously crafted reward function to calibrate
the confidence estimates, motivating LLMs to deliver accurate, high-confidence
predictions and to penalize overconfidence in erroneous outputs. Experimental
results in both in-distribution and out-of-distribution datasets demonstrate
the effectiveness of SaySelf in reducing the confidence calibration error and
maintaining the task performance. We show that the generated self-reflective
rationales are reasonable and can further contribute to the calibration. The
code is made public at https://github.com/xu1868/SaySelf.


  Some fixed point results of classical theory, such as Banach's Fixed Point
Theorem, have been previously extended by other authors to asymmetric spaces in
recent years. The aim of this paper is to extend to asymmetric spaces some
others fixed point results for contractions, shrinkage maps and non-expansive
maps. In fact, a version of Edelstein type theorem (Theorem 21), Schauder type
theorem (Theorem 22), and Kirk type theorem (Theorem 26) are stated and proved
in this new context. In order to do that, classical definitions and results
were adapted to this new context. Also, the normal structure in the asymmetric
case was considered.


  We consider an orienteering problem (OP) where an agent needs to visit a
series (possibly a subset) of depots, from which the maximal accumulated
profits are desired within given limited time budget. Different from most
existing works where the profits are assumed to be static, in this work we
investigate a variant that has arbitrary time-dependent profits. Specifically,
the profits to be collected change over time and they follow different (e.g.,
independent) time-varying functions. The problem is of inherent nonlinearity
and difficult to solve by existing methods. To tackle the challenge, we present
a simple and effective framework that incorporates time-variations into the
fundamental planning process. Specifically, we propose a deterministic
spatio-temporal representation where both spatial description and temporal
logic are unified into one routing topology. By employing existing basic
sorting and searching algorithms, the routing solutions can be computed in an
extremely efficient way. The proposed method is easy to implement and extensive
numerical results show that our approach is time efficient and generates
near-optimal solutions.


  We propose a method for automatic local time-adaptation of the spectrogram of
audio signals: it is based on the decomposition of a signal within a Gabor
multi-frame through the STFT operator. The sparsity of the analysis in every
individual frame of the multi-frame is evaluated through the R\'enyi entropy
measures: the best local resolution is determined minimizing the entropy
values. The overall spectrogram of the signal we obtain thus provides local
optimal resolution adaptively evolving over time. We give examples of the
performance of our algorithm with an instrumental sound and a synthetic one,
showing the improvement in spectrogram displaying obtained with an automatic
adaptation of the resolution. The analysis operator is invertible, thus leading
to a perfect reconstruction of the original signal through the analysis
coefficients.


  Study on a rectified current induced by active particles has received a great
attention due to its possible application to a microscopic motor in biological
environments. Insertion of an {\em asymmetric} passive object amid many active
particles has been regarded as an essential ingredient for generating such a
rectified motion. Here, we report that the reverse situation is also possible,
where the motion of an active object can be rectified by its geometric
asymmetry amid many passive particles. This may describe an unidirectional
motion of polar biological agents with asymmetric shape. We also find a weak
but less diffusive rectified motion in a {\em passive} mode without energy
pump-in. This "moving by dissipation" mechanism could be used as a design
principle for developing more reliable microscopic motors.


  The spatially homogeneous Boltzmann equation with hard potentials is
considered for measure valued initial data having finite mass and energy. We
prove the existence of \emph{weak measure solutions}, with and without angular
cutoff on the collision kernel; the proof in particular makes use of an
approximation argument based on the Mehler transform. Moment production
estimates in the usual form and in the exponential form are obtained for these
solutions. Finally for the Grad angular cutoff, we also establish uniqueness
and strong stability estimate on these solutions.


  The supersymmetry transformation relating the Konishi operator to its lowest
descendant in the 10 of SU(4) is not manifest in the N=1 formulation of the
theory but rather uses an equation of motion. On the classical level one finds
one operator, the unintegrated chiral superpotential. In the quantum theory
this term receives an admixture by a second operator, the Yang-Mills part of
the Lagrangian. It has long been debated whether this "anomalous" contribution
is affected by higher loop corrections. We present a first principles
calculation at the second non-trivial order in perturbation theory using
supersymmetric dimensional reduction as a regulator and renormalisation by
Z-factors. Singular higher loop corrections to the renormalisation factor of
the Yang-Mills term are required if the conformal properties of two-point
functions are to be met. These singularities take the form determined in
preceding work on rather general grounds. Moreover, we also find non-vanishing
finite terms.
  The core part of the problem is the evaluation of a four-loop two-point
correlator which is accomplished by the Laporta algorithm. Apart from several
examples of the T1 topology with two lines of non-integer dimension we need the
first few orders in the epsilon expansion of three master integrals. The
approach is self-contained in that all the necessary information can be derived
from the power counting finiteness of some integrals.


  Using an octonionic formalism, we introduce a new mechanism for reducing 10
spacetime dimensions to 4 without compactification. Applying this mechanism to
the free, 10-dimensional, massless (momentum space) Dirac equation results in a
particle spectrum consisting of exactly 3 generations. Each generation contains
1 massive spin-1/2 particle with 2 spin states, 1 massless spin-1/2 particle
with only 1 helicity state, and their antiparticles --- precisely one
generation of leptons. There is also a single massless spin-1/2
particle/antiparticle pair with the opposite helicity and no generation
structure.
  We conclude with a discussion of some further consequences of this approach,
including those which could arise when using the formalism on a curved
spacetime background, as well as the implications for the nature of spacetime
itself.


  We present calculations of the prompt photon photoproduction at HERA collider
in the k_T-factorization approach. Both direct and resolved contributions are
taken into account. The conservative error analisys is performed. The
unintegrated parton densities in a proton and in a photon are determined using
the Kimber-Martin-Ryskin prescription. We investigate both inclusive and
associated with jet prompt photon photoproduction rates. In particular, we
study the angular correlations between produced photon and hadronic jet in the
transverse momentum plane which can provide a unique information about
non-collinear evolution dynamics. We compare our theoretical predictions with
recent experimental data taken by the H1 and ZEUS collaborations.


  Let $\mathbb{K}$ be a field of characteristic zero and $\mathbb{K}[x_1,
\dots, x_n]$ the corresponding multivariate polynomial ring. Given a sequence
of $s$ polynomials $\mathbf{f} = (f_1, \dots, f_s)$ and a polynomial $\phi$,
all in $\mathbb{K}[x_1, \dots, x_n]$ with $s<n$, we consider the problem of
computing the set $W(\phi, \mathbf{f})$ of points at which $\mathbf{f}$
vanishes and the Jacobian matrix of $\mathbf{f}, \phi$ with respect to $x_1,
\dots, x_n$ does not have full rank. This problem plays an essential role in
many application areas.
  In this paper we focus on a case where the polynomials are all invariant
under the action of the signed symmetric group $B_n$. We introduce a notion
called {\em hyperoctahedral representation} to describe $B_n$-invariant sets.
We study the invariance properties of the input polynomials to split $W(\phi,
\mathbf{f})$ according to the orbits of $B_n$ and then design an algorithm
whose output is a {hyperoctahedral representation} of $W(\phi, \mathbf{f})$.
The runtime of our algorithm is polynomial in the total number of points
described by the output.


  Large foundation models (LFMs) are claiming incredible performances. Yet
great concerns have been raised about their mythic and uninterpreted potentials
not only in machine learning, but also in various other disciplines. In this
position paper, we propose to identify a neglected issue deeply rooted in LFMs:
Catastrophic Inheritance, describing the weaknesses and limitations inherited
from biased large-scale pre-training data to behaviors of LFMs on the
downstream tasks, including samples that are corrupted, long-tailed, noisy,
out-of-distributed, to name a few. Such inheritance can potentially cause
catastrophes to downstream applications, such as bias, lack of generalization,
deteriorated performance, security vulnerability, privacy leakage, and value
misalignment. We discuss the challenges behind this issue and propose UIM, a
framework to Understand the catastrophic inheritance of LFMs from both
pre-training and downstream adaptation, Interpret the implications of
catastrophic inheritance on downstream tasks, and how to Mitigate it. UIM aims
to unite both the machine learning and social sciences communities for more
responsible and promising AI development and deployment.


  We propose a new technique of utilizing metamaterials-based sensor for rapid
diagnosis of covid-19 through electromagnetic-stimulated analysis of the blood
drawn from the patient. The sensor was inspired by a coronavirus in
plane-shaped design with presume that its circular structure might produce a
broader interaction of the electromagnetic waves with the blood sample. The
sensor was designed numerically and tested experimentally by evaluating
variations in the reflection coefficient (S11) and transmission coefficient
(S21) of the waves at resonant frequency. Results of covid-19 relevant blood
sample showed a pronounced shift in the main resonant frequency of about 740
MHz compared to that of the control blood sample. We believe that with the help
of the proposed sensor a significant breakthrough can be achieved for rapid
diagnosis of covid-19 within few seconds.


  High energy strong interaction physics is successfully described by the local
renormalizable gauge theory called Quantum-Chromo-Dynamics (QCD) with quarks
and gluons as ``elementary'' degrees of freedom, while intermediate energy
strong interaction physics shows up to be determined by a non-local,
non--renormalizable effective field theory (EFT) of ``effective'' degrees of
freedom like mesons, ground state baryons and resonances. Within the picture of
an effective field theory of strong interaction at intermediate energies I
present a ``toy-model'' in which fermionic and bosonic resonances are
considered to be ``particles'', i.e. they consistently are described by
(anti-)commuting effective field-operators (containing dynamics of infinitely
many quark-gluon or meson-nucleon diagrams) which are comfortably treated by
Wick's Theorem in a covariant framework and obey unitarity. Non-trivial
implications to couplings of non-local interactions are shown.


  We compute the magnetic susceptibility and specific heat of the spin-1/2
Heisenberg model on the kagome lattice with high-temperature expansions and
exact diagonalizations. We compare the results with the experimental data on
ZnCu3(OH)6Cl2 obtained by Helton et al. [Phys. Rev. Lett. 98, 107204 (2007)].
Down to k_BT/J~0.2, our calculations reproduce accurately the experimental
susceptibility, with an exchange interaction J~190K and a contribution of 3.7%
of weakly interacting impurity spins. The comparison between our calculations
of the specific heat and the experiments indicate that the low-temperature
entropy (below ~20K) is smaller in ZnCu3(OH)6Cl2 than in the kagome Heisenberg
model, a likely signature of other interactions in the system.


  We propose average Localisation-Recall-Precision (aLRP), a unified, bounded,
balanced and ranking-based loss function for both classification and
localisation tasks in object detection. aLRP extends the
Localisation-Recall-Precision (LRP) performance metric (Oksuz et al., 2018)
inspired from how Average Precision (AP) Loss extends precision to a
ranking-based loss function for classification (Chen et al., 2020). aLRP has
the following distinct advantages: (i) aLRP is the first ranking-based loss
function for both classification and localisation tasks. (ii) Thanks to using
ranking for both tasks, aLRP naturally enforces high-quality localisation for
high-precision classification. (iii) aLRP provides provable balance between
positives and negatives. (iv) Compared to on average $\sim$6 hyperparameters in
the loss functions of state-of-the-art detectors, aLRP Loss has only one
hyperparameter, which we did not tune in practice. On the COCO dataset, aLRP
Loss improves its ranking-based predecessor, AP Loss, up to around $5$ AP
points, achieves $48.9$ AP without test time augmentation and outperforms all
one-stage detectors. Code available at: https://github.com/kemaloksuz/aLRPLoss .


  This article examines differentiability properties of the value function of
positioning choice problems, a class of optimisation problems in
finite-dimensional Euclidean spaces. We show that positioning choice problems'
value function is always almost everywhere differentiable even when the
objective function is discontinuous. To obtain this result we first show that
the Dini superdifferential is always well-defined for the maxima of positioning
choice problems. This last property allows to state first-order necessary
conditions in terms of Dini supergradients. We then prove our main result,
which is an ad-hoc envelope theorem for positioning choice problems. Lastly,
after discussing necessity of some key assumptions, we conjecture that similar
theorems might hold in other spaces as well.


  Complex applications such as big data analytics involve different forms of
coupling relationships that reflect interactions between factors related to
technical, business (domain-specific) and environmental (including
socio-cultural and economic) aspects. There are diverse forms of couplings
embedded in poor-structured and ill-structured data. Such couplings are
ubiquitous, implicit and/or explicit, objective and/or subjective,
heterogeneous and/or homogeneous, presenting complexities to existing learning
systems in statistics, mathematics and computer sciences, such as typical
dependency, association and correlation relationships. Modeling and learning
such couplings thus is fundamental but challenging. This paper discusses the
concept of coupling learning, focusing on the involvement of coupling
relationships in learning systems. Coupling learning has great potential for
building a deep understanding of the essence of business problems and handling
challenges that have not been addressed well by existing learning theories and
tools. This argument is verified by several case studies on coupling learning,
including handling coupling in recommender systems, incorporating couplings
into coupled clustering, coupling document clustering, coupled recommender
algorithms and coupled behavior analysis for groups.


  Using a macroscopic analysis, we show that time-dependent noncollinear spin
transport possesses a wavelike character. This leads to modifications of pure
spin-diffusion dynamics and allows one to extract a finite spin-signal
propagation velocity. We numerically study the dynamics of a pure spin current
pumped into a nonmagnetic layer for precession frequencies ranging from GHz to
THz.


  Hybrid volumetric medical image segmentation models, combining the advantages
of local convolution and global attention, have recently received considerable
attention. While mainly focusing on architectural modifications, most existing
hybrid approaches still use conventional data-independent weight initialization
schemes which restrict their performance due to ignoring the inherent
volumetric nature of the medical data. To address this issue, we propose a
learnable weight initialization approach that utilizes the available medical
training data to effectively learn the contextual and structural cues via the
proposed self-supervised objectives. Our approach is easy to integrate into any
hybrid model and requires no external training data. Experiments on multi-organ
and lung cancer segmentation tasks demonstrate the effectiveness of our
approach, leading to state-of-the-art segmentation performance. Our proposed
data-dependent initialization approach performs favorably as compared to the
Swin-UNETR model pretrained using large-scale datasets on multi-organ
segmentation task. Our source code and models are available at:
https://github.com/ShahinaKK/LWI-VMS.


  In this paper we calculate the vacuum expectation values of the stress-energy
bitensor of a massive quantum scalar field with general coupling to
N-dimensional Euclidean spaces and hyperbolic spaces which are Euclidean
sections of the anti-de Sitter (AdS) spaces. These correlators, also known as
the noise kernel, act as sources in the Einstein-Langevin equations of
stochastic gravity [1,2] which govern the induced metric fluctuations beyond
the mean-field dynamics described by the semiclassical Einstein equations of
semiclassical gravity. Because these spaces are maximally symmetric the
eigenmodes have analytic expressions which facilitate the computation of the
zeta-function [3,4]. Upon taking the second functional variation of the
generalized zeta function introduced in [5] we obtain the correlators of the
stress tensor for these two classes of spacetimes. Both the short and the large
geodesic distance limits of the correlators are presented for dimensions up to
11. We mention current research problems in early universe cosmology, black
hole physics and gravity-fluid duality where these results can be usefully
applied to.


  Since late 2019, the global spread of COVID-19 has affected people's daily
life. Temperature is an early and common symptom of Covid. Therefore, a
convenient and remote temperature detection method is needed. In this paper, a
non-contact method for detecting body temperature is proposed. Our developed
algorithm based on blackbody radiation calculates the body temperature of a
user-selected area from an obtained image. The findings were confirmed using a
FLIR Thermal Camera with an accuracy of 97%.


  We point out basic misunderstandings about quantum field theory, general
relativity and partial derivatives in the above Comments. In reply to a second
comment on our first reply by the same author, we also identify precisely where
the author's original calculation goes wrong and correct it, yielding the same
local Hawking temperature as obtained by the Hamilton-Jacobi method.


  Sabotage modal logic (SML) is a kind of dynamic logics. It extends static
modal logic with a dynamic modality which is interpreted as "after deleting an
arrow in the frame, the formula is true". In the present paper, we are aiming
at solving an open problem, namely giving a Sahlqvist-type correspondence
theorem for sabotage modal logic. In this paper, we define sabotage Sahlqvist
formulas and give an algorithm to compute the first-order correspondents of
sabotage Sahlqvist formulas. We give some remarks and future directions at the
end of the paper.


  Face aging has received continuous research attention over the past two
decades. Although previous works on this topic have achieved impressive
success, two longstanding problems remain unsettled: 1) generating diverse and
plausible facial aging patterns at the target age stage; 2) measuring the
rationality of identity variation between the original portrait and its
syntheses with age progression or regression. In this paper, we introduce
${\rm{DLAT}}^{\boldsymbol{+}}$ to realize Diverse and Lifespan Age
Transformation on human faces, where the diversity jointly manifests in the
transformation of facial textures and shapes. Apart from the diversity
mechanism embedded in the model, multiple consistency restrictions are
leveraged to keep it away from counterfactual aging syntheses. Moreover, we
propose a new metric to assess the rationality of Identity Deviation under Age
Gaps (IDAG) between the input face and its series of age-transformed
generations, which is based on statistical laws summarized from plenty of
genuine face-aging data. Extensive experimental results demonstrate the
uniqueness and effectiveness of our method in synthesizing diverse and
perceptually reasonable faces across the whole lifetime.


  We perform an exact diagonalization study of the spin-$1/2$ XXZ Heisenberg
antiferromagnet on the kagome lattice at finite magnetization $m = \frac{2}{3}$
with an emphasis on the XY point ($J_z = 0$), and in the presence of a small
chiral term. Recent analytic work by Kumar, Sun and Fradkin [Phys. Rev. B 90,
174409 (2014)] on the same model, using a newly developed flux attachment
transformation, predicts a plateau at this value of the magnetization described
by a chiral spin liquid (CSL) with a spin Hall conductance of $\sigma_{xy} =
\frac{1}{2}$. Such a state is topological in nature, has a ground state
degeneracy and exhibits fractional excitations. We analyze the degeneracy
structure in the low energy manifold, identify the candidate topological states
and use them to compute the modular matrices and Chern numbers all of which
strongly agree with expected theoretical behavior for the $\sigma_{xy} =
\frac{1}{2}$ CSL. We argue that the evidence suggests the CSL is robust even in
the limit of zero external chirality.


  Understanding the underlying factors responsible for higher-than-anticipated
local field enhancements that trigger vacuum breakdown on pristine metal
surfaces is crucial for the development of devices capable of withstanding
intense operational fields. In this study, we investigate the behavior of
nominally flat copper electrode surfaces exposed to electric fields of hundreds
of MV/m. Our novel approach considers curvature-driven diffusion processes to
elucidate the formation of sharp breakdown precursors. To do so, we develop a
mesoscale finite element model that accounts for driving forces arising from
both electrostatic and surface-tension-induced contributions to the free
energy. Our findings reveal a dual influence: surface tension tends to mitigate
local curvature, while the electric field drives mass transport toward regions
of high local field density. This phenomenon triggers the growth of sharper
protrusions, ultimately leading to a rapid enhancement of local fields and,
consequently, system instability. Furthermore, we delineate supercritical and
subcritical regimes across a range of initial surface roughness. Our numerical
results align closely with experimentally reported data, predicting critical
precursor formation fields in the range of 200 MV/m to 500 MV/m.


  The X$^{1}\Sigma ^{+}$ state of NaRb was studied by Fourier transform
spectroscopy. An accurate potential energy curve was derived from more than
8800 transitions in isotopomers $^{23}$Na$^{85}$Rb and $^{23}$Na$^{87}$Rb. This
potential reproduces the experimental observations within their uncertainties
of 0.003 \rcm to 0.007 \rcm. The outer classical turning point of the last
observed energy level ($v''=76$, $J''=27$) lies at $\approx 12.4$ \AA, leading
to a energy of 4.5 \rcm below the ground state asymptote.


  In this paper, we provide an easy proof of the Four-colour Theorem in a
special case indeed.


  The cross section for the reaction $dd\rightarrow \,^4\!H\!e\,\eta$ close to
threshold is estimated in a two-step model, similar to that which successfully
describes near-threshold $pd\rightarrow \,^3\!H\!e\,\eta$ production. A
$\pi$-meson, created in a $dp\rightarrow \,^3\!H\!e\,\pi^o$ process on one
nucleon in the target deuteron, is converted into an $\eta$-meson by a
secondary $\pi^o n \to n\,\eta$ reaction on the other nucleon. The kinematics
are such that both processes are nearly physical so that only small Fermi
momenta are required. The predictions of the model are in good agreement with
recent Saclay experimental data.
  An analogous model, when applied to the near-threshold
$n\,^3\!H\!e\rightarrow \,^4\!H\!e\,\eta$ reaction, predicts a cross section of
a rather similar size, but experimental difficulties render this a doubtful
means of studying the $\eta\, ^4\!H\!e$ interaction.


  The crystalline or liquid character of the downward cusp states in N-electron
parabolic quantum dots (QD's) at high magnetic fields is investigated using
conditional probability distributions obtained from exact diagonalization.
These states are of crystalline character for fractional fillings covering both
low and high values, unlike the liquid Jastrow-Laughlin wave functions, but in
remarkable agreement with the rotating-Wigner-molecule ones [Phys. Rev. B 66,
115315 (2002)]. The crystalline arrangement consists of concentric polygonal
rings that rotate independently of each other, with the electrons on each ring
rotating coherently. We show that the rotation stabilizes the Wigner molecule
relative to the static one defined by the broken-symmetry
unrestricted-Hartree-Fock solution. We discuss the non-rigid behavior of the
rotating Wigner molecule and pertinent features of the excitation spectrum,
including the occurrence of a gap between the ground and first excited states
that underlies the incompressibility of the system. This leads us to conjecture
that the rotating crystal (and not the static one) remains the relevant ground
state for low fractional fillings even at the thermodynamic limit.


  Studied is the deformation of super Virasoro algebra proposed by Belov and
Chaltikhian. Starting from abstract realizations in terms of the FFZ type
generators, various connections of them to other realizations are shown,
especially to deformed field representations, whose bosonic part generator is
recently reported as a deformed string theory on a noncommutative world-sheet.
The deformed Virasoro generators can also be expressed in terms of ordinary
free fields in a highly nontrivial way.


  We continue the study of the effective action for low $x$ physics based on a
Wilson renormalization group approach. We express the full nonlinear
renormalization group equation in terms of the average value and the average
fluctuation of extra color charge density generated by integrating out gluons
with intermediate values of $x$. This form clearly exhibits the nature of the
phenomena driving the evolution and should serve as the basis of the analysis
of saturation effects at high gluon density at small $x$.


  The under integration of the volume terms in the discontinuous Galerkin
spectral element approximation introduces errors at non-conforming element
faces that do not cancel and lead to free-stream preservation errors. We derive
volume and face conditions on the geometry under which a constant state is
preserved. From those, we catalog six special cases on the geometry that
preserve a constant state, the most general being to approximate the geometry
sub-parametrically to one half the order of the solution. Numerical examples
are presented to illustrate the results.


  A network of three or more gravitational wave detectors simultaneously taking
data is required to generate a well-localized sky map for gravitational wave
sources, such as GW170817. Local seismic disturbances often cause the LIGO and
Virgo detectors to lose light resonance in one or more of their component optic
cavities, and the affected detector is unable to take data until resonance is
recovered. In this paper, we use machine learning techniques to gain insight
into the predictive behavior of the LIGO detector optic cavities during the
second LIGO-Virgo observing run. We identify a minimal set of optic cavity
control signals and data features which capture interferometer behavior leading
to a loss of light resonance, or lockloss. We use these channels to accurately
distinguish between lockloss events and quiet interferometer operating times
via both supervised and unsupervised machine learning methods. This analysis
yields new insights into how components of the LIGO detectors contribute to
lockloss events, which could inform detector commissioning efforts to mitigate
the associated loss of uptime. Particularly, we find that the state of the
component optical cavities is a better predictor of loss of lock than ground
motion trends. We report prediction accuracies of 98% for times just prior to
lock loss, and 90% for times up to 30 seconds prior to lockloss, which shows
promise for this method to be applied in near-real time to trigger preventative
detector state changes. This method can be extended to target other auxiliary
subsystems or times of interest, such as transient noise or loss in detector
sensitivity. Application of these techniques during the third LIGO-Virgo
observing run and beyond would maximize the potential of the global detector
network for multi-messenger astronomy with gravitational waves.


  At air-water interfaces, the Lifshitz interaction by itself does not promote
ice growth. On the contrary, we find that the Lifshitz force promotes the
growth of an ice film, up to 1-8 nm thickness, near silica-water interfaces at
the triple point of water. This is achieved in a system where the combined
effect of the retardation and the zero frequency mode influences the
short-range interactions at low temperatures, contrary to common understanding.
Cancellation between the positive and negative contributions in the Lifshitz
spectral function is reversed in silica with high porosity. Our results provide
a model for how water freezes on glass and other surfaces.


  Let $G$ be a finite abelian group, and let $f: G \to \C$ be a complex
function on $G$. The uncertainty principle asserts that the support $\supp(f)
:= \{x \in G: f(x) \neq 0\}$ is related to the support of the Fourier transform
$\hat f: G \to \C$ by the formula $$ |\supp(f)| |\supp(\hat f)| \geq |G|$$
where $|X|$ denotes the cardinality of $X$. In this note we show that when $G$
is the cyclic group $\Z/p\Z$ of prime order $p$, then we may improve this to $$
|\supp(f)| + |\supp(\hat f)| \geq p+1$$ and show that this is absolutely sharp.
As one consequence, we see that a sparse polynomial in $\Z/p\Z$ consisting of
$k+1$ monomials can have at most $k$ zeroes. Another consequence is a short
proof of the well-known Cauchy-Davenport inequality.


  We propose a discontinuous finite element approximation for a model of
quasi-static growth of brittle fractures in linearly elastic bodies formulated
by Francfort and Marigo, and based on the classical Griffith's criterion. We
restrict our analysis to the case of anti-planar shear and we consider
discontinuous displacements which are piecewise affine with respect to a
regular triangulation.


  Topological Data Analysis (TDA) offers a suite of computational tools that
provide quantified shape features in high dimensional data that can be used by
modern statistical and predictive machine learning (ML) models. In particular,
persistent homology (PH) takes in data (e.g., point clouds, images, time
series) and derives compact representations of latent topological structures,
known as persistence diagrams (PDs). Because PDs enjoy inherent noise
tolerance, are interpretable and provide a solid basis for data analysis, and
can be made compatible with the expansive set of well-established ML model
architectures, PH has been widely adopted for model development including on
sensitive data, such as genomic, cancer, sensor network, and financial data.
Thus, TDA should be incorporated into secure end-to-end data analysis
pipelines. In this paper, we take the first step to address this challenge and
develop a version of the fundamental algorithm to compute PH on encrypted data
using homomorphic encryption (HE).


  If a quantum mechanical particle is scattered by a potential well, the wave
function of the particle can propagate with negative phase time. Due to the
analogy of the Schr\"odinger and the Helmholtz equation this phenomenon is
expected to be observable for electromagnetic wave propagation. Experimental
data of electromagnetic wells realized by wave guides filled with different
dielectrics confirm this conjecture now.


  In this paper, we report our detailed analysis of the new strong-coupling
regime between Alfv\'en and fast modes in Poynting-dominated plasma turbulence,
reported in our previous work Takamoto & Lazarian (2016), which is an important
effect for many relativistic plasma phenomena, and calls for new theories of
Poynting-dominated MHD turbulence. We performed numerical simulations of
relativistic MHD turbulence in isothermal plasmas, and analyzed the ratio of
fast to Alfv\'en mode energy. We found that the increase of the fast mode with
the background $\sigma$-parameter can be observed even in isothermal plasma,
showing that such a phenomena is universal in trans-Alfv\'enic turbulence in
Poynting-dominated plasmas. To study the detailed energy conversion process, we
also performed a series of simulations of decaying turbulence injecting pure
Alfv\'en, fast, and slow modes, respectively, and investigated the development
of the mode conversion from the each mode. We also found that the mode
conversion between Alfv\'en and fast modes is nearly insensitive to the
background temperature. Finally, we report a result of a simulation with
initially fast mode dominated turbulence. It developed into a temporally
strong-coupling regime, which is a strong evidence for the existence of our
suggesting strong-coupling regime of fast and Alfv\'en modes. Our result
suggests that the strong turbulence in Poynting-dominated plasma is very
different from that in the non-relativistic plasma. It will also give an
important guidance to studies of particle acceleration and non-thermal photon
emission from Poynting-dominated plasma.


  We report the detection, for the first time, of HCO+ (J=1-0) emission as well
as marginal CO (J=1-0) emission toward the planetary nebula (PN) K3-35 as a
result of a molecular survey carried out toward this source. We also report new
observations of the previously detected CO (J=2-1) and water maser emission, as
well as upper limits for the emission of the SiO, H13CO+, HNC, HCN, HC3OH,
HC5N, CS, HC3N, 13CO, CN, and NH3 molecules. From the ratio of CO (J=2-1) to CO
(J=1-0) emission we have estimated the kinetic temperature of the molecular
gas, obtaining a value of ~20 K. Using this result, we have estimated a
molecular mass for the envelope of ~ 0.017 M_Sun, and an HCO+ abundance
relative to H_2 of 6 X 10^-7, similar to the abundances found in other PNe.
K~3-35 is remarkable because it is one of the two PNe reported to exhibit water
maser emission, which is present in the central region as well as at a distance
of $\simeq$ 5000 AU away from the center. The presence of molecular emission
provides some clues that could help to understand the persistence of water
molecules in the envelope of K 3-35. The HCO$^{+}$ emission could be arising in
dense molecular clumps, that may provide the shielding mechanism which protects
water molecules in this source.


  We report optical spectroscopic observations of RX J0018.8+1602, a ROSAT
X-ray source proposed to be an intermediate redshift cluster of galaxies. Our
observations confirm the identification of RX J0018.8+1602 and provide
measurements of its mean radial velocity (z=0.5406 +/- 0.0006) and velocity
dispersion (sigma_p = 200 [+110, -80] km/s). This is the second poor cluster
that has been found to be a companion to CL 0016+16 (z=0.5455), the other one
being RX J0018.3+1618 (z=0.5506). The 0.2-2 keV band source-frame X-ray
luminosity summed over both companion clusters is 5E44 ergs/s, which is a
significant fraction, ~23%, of the X-ray luminosity of the main cluster. The
companions are located at angular distances of 10 arcmin to 25 arcmin (minimum
physical scales of 5 Mpc to 12 Mpc) from CL 0016+16 and we propose that they
represent a new large-scale component of the X-ray emission from clusters of
galaxies. Similar low X-ray luminosity poor clusters surrounding nearby Abell
clusters can explain the excess power observed in the angular cross-correlation
function between Abell clusters and the X-ray background on inferred physical
scales of 14--20 Mpc (Soltan et al. 1996).


  Accommodating all the weights on-chip for large-scale NNs remains a great
challenge for SRAM based computing-in-memory (SRAM-CIM) with limited on-chip
capacity. Previous non-volatile SRAM-CIM (nvSRAM-CIM) addresses this issue by
integrating high-density single-level ReRAMs on the top of high-efficiency
SRAM-CIM for weight storage to eliminate the off-chip memory access. However,
previous SL-nvSRAM-CIM suffers from poor scalability for an increased number of
SL-ReRAMs and limited computing efficiency. To overcome these challenges, this
work proposes an ultra-high-density three-level ReRAMs-assisted
computing-in-nonvolatile-SRAM (TL-nvSRAM-CIM) scheme for large NN models. The
clustered n-selector-n-ReRAM (cluster-nSnRs) is employed for reliable
weight-restore with eliminated DC power. Furthermore, a ternary SRAM-CIM
mechanism with differential computing scheme is proposed for energy-efficient
ternary MAC operations while preserving high NN accuracy. The proposed
TL-nvSRAM-CIM achieves 7.8x higher storage density, compared with the
state-of-art works. Moreover, TL-nvSRAM-CIM shows up to 2.9x and 1.9x enhanced
energy-efficiency, respectively, compared to the baseline designs of SRAM-CIM
and ReRAM-CIM, respectively.