  The symmetry study of main differential equations of mechanics and
electrodynamics has shown, that differential equations, which are invariant
under transformations of groups, which are symmetry groups of mathematical
numbers (considered within the frames of the number theory) determine the
mathematical nature of the quantities, incoming in given equations. It allowed
to proof the main postulate of quantum mechanics, consisting in that, that to
any mechanical quantity can be set up into the correspondence the Hermitian
matrix by quantization.
  High symmetry of Maxwell equations allows to show, that to quantities,
incoming in given equations can be set up into the correspondence the
Quaternion (twice-Hermitian) matrix by their quantization.
  It is concluded, that the equations of the dynamics of mechanical systems are
not invariant under transformations of quaternion multiplicative group and,
consecuently, direct application of quaternions with usually used basis \{e, i,
j, k \} to build the new version of quantum mechanics, which was undertaken in
the number of modern publications, is incorrect. It is the consequence of
non-abelian character of given group. At the same time we have found the
correct ways for the creation of the new versions of quantum mechanics on the
quaternion base by means of choice of new bases in quaternion ring, from which
can be formed the bases for complex numbers under multiplicative groups of
which the equations of the dynamics of mechanical systems are invariant.


  A simulation model and design of Titanium Manganese Redox Flow Battery
(TMRFB) is proposed to study the distribution of dissociation rate,
overpotential, current density, and electrode potential. TMRFB is one of the
most promising new energy storages because of its high capacity and
eco-friendly characteristics in the current condition of energy scarcity and
environmental pollution. Moreover, Mn-based flow batteries are gaining
popularity due to their inexpensive cost and high energy density in lieu of all
vanadium redox flow batteries which are expensive. This research shows that the
surface dissociation rate of Ti4+/ Ti3+ and Mn3+/Mn2+ ions are higher at the
membrane and lower at the inlet where the velocity of the electrolyte flow is
higher; Furthermore, our work reveals that when the thickness of the electrode
is compressed from 4.5 mm to 3 mm, overpotential reduces whereas current
density and electrode potential increases. The COMSOL Multiphysics software is
used to solve the model's equations using the finite element approach. From the
dissociation rate it is concluded that less potential is required at the
membrane for the oxidation reduction reaction and with optimized electrolyte
flow rate battery performance can be improved. Thus, electrode compression
increases conductivity and battery performance.


  We consider a single-species diffusion-limited annihilation reaction with
reactants confined to a two-dimensional surface with one arbitrarily large
dimension and the other comparable in size to interparticle distances. This
situation could describe reactants which undergo both longitudinal and
transverse diffusion on long filamentous molecules (such as microtubules), or
molecules that undergo truly one-dimensional translational diffusion (e.g. a
transcription factor on DNA) but simultaneously exhibit diffusive behavior in a
second dimension corresponding to a rotational or conformational degree of
freedom. We combine simple analytical arguments and Monte Carlo simulations to
show that the reaction rate law exhibits a crossover from one-dimensional to
two-dimensional diffusion as a function of particle concentration and the size
of the smaller dimension. In the case of a reversible binding reaction, the
diffusion-limited reaction rate is given by the Smoluchowski expression, but
the crossover is revealed in the statistics of particle collision histories.
The results can also be applied to a particle-antiparticle annihilation
reaction.


  Graph convolution network based approaches have been recently used to model
region-wise relationships in region-level prediction problems in urban
computing. Each relationship represents a kind of spatial dependency, like
region-wise distance or functional similarity. To incorporate multiple
relationships into spatial feature extraction, we define the problem as a
multi-modal machine learning problem on multi-graph convolution networks.
Leveraging the advantage of multi-modal machine learning, we propose to develop
modality interaction mechanisms for this problem, in order to reduce
generalization error by reinforcing the learning of multimodal coordinated
representations. In this work, we propose two interaction techniques for
handling features in lower layers and higher layers respectively. In lower
layers, we propose grouped GCN to combine the graph connectivity from different
modalities for more complete spatial feature extraction. In higher layers, we
adapt multi-linear relationship networks to GCN by exploring the dimension
transformation and freezing part of the covariance structure. The adapted
approach, called multi-linear relationship GCN, learns more generalized
features to overcome the train-test divergence induced by time shifting. We
evaluated our model on ridehailing demand forecasting problem using two
real-world datasets. The proposed technique outperforms state-of-the art
baselines in terms of prediction accuracy, training efficiency,
interpretability and model robustness.


  We consider the control problem where, given an orthonormal tangent frame in
the hyperbolic plane or three dimensional hyperbolic space, one is allowed to
transport the frame a fixed distance $r > 0$ along the geodesic in direction of
the first vector, or rotate it in place a right angle. We characterize the
values of $r > 0$ for which the set of orthonormal frames accessible using
these transformations is discrete.
  In the hyperbolic plane this is equivalent to solving the discreteness
problem for a particular one parameter family of two-generator subgroups of
$PSL_2(\mathbb{R})$. In the three dimensional case we solve this problem for a
particular one parameter family of subgroups of the isometry group which have
four generators.


  Investigation of highly structured data sets to unveil statistical
regularities is of major importance in complex system research. The first step
is to choose the scale at which to observe the process, the most informative
scale being the one that includes the important features while disregarding
noisy details in the data. In the investigation of spatial patterns, the
optimal scale defines the optimal bin size of the histogram in which to
visualize the empirical density of the pattern. In this paper we investigate a
method proposed recently by K.~H.~Knuth to find the optimal bin size of an
histogram as a tool for statistical analysis of spatial point processes. We
test it through numerical simulations on various spatial processes which are of
interest in ecology. We show that Knuth optimal bin size rule reducing noisy
fluctuations performs better than standard kernel methods to infer the
intensity of the underlying process. Moreover it can be used to highlight
relevant spatial characteristics of the underlying distribution such as space
anisotropy and clusterization. We apply these findings to analyse cluster-like
structures in plants' arrangement of Barro Colorado Island rainforest.


  Guilt aversion induces experience of a utility loss in people if they believe
they have disappointed others, and this promotes cooperative behaviour in
human. In psychological game theory, guilt aversion necessitates modelling of
agents that have theory about what other agents think, also known as Theory of
Mind (ToM). We aim to build a new kind of affective reinforcement learning
agents, called Theory of Mind Agents with Guilt Aversion (ToMAGA), which are
equipped with an ability to think about the wellbeing of others instead of just
self-interest. To validate the agent design, we use a general-sum game known as
Stag Hunt as a test bed. As standard reinforcement learning agents could learn
suboptimal policies in social dilemmas like Stag Hunt, we propose to use
belief-based guilt aversion as a reward shaping mechanism. We show that our
belief-based guilt averse agents can efficiently learn cooperative behaviours
in Stag Hunt Games.


  This project develops a pseudo-random number generator (PRNG) using the
logistic map, implemented in Verilog HDL on an FPGA and processes its output
through a Central Limit Theorem (CLT) function to achieve a Gaussian
distribution. The system integrates additional FPGA modules for real-time
interaction and visualisation, including a clock generator, UART interface,
XADC, and a 7-segment display driver. These components facilitate the direct
display of PRNG values on the FPGA and the transmission of data to a laptop for
histogram analysis, verifying the Gaussian nature of the output. This approach
demonstrates the practical application of chaotic systems for generating
Gaussian-distributed pseudo-random numbers in digital hardware, highlighting
the logistic map's potential in PRNG design.


  We propose a new model within the ``Quark-nova'' scenario to interpret the
recent observations of early afterglows of long Gamma-Ray Bursts (GRB) with the
Swift satellite. This is a three-stage model within the context of a
core-collapse supernova. Stage 1 is an accreting (proto-) neutron star leading
to a possible delay between the core collapse and the GRB. Stage 2 is an
accreting quark-star, generating the prompt GRB. Stage 3, which occurs only if
the quark-star collapses to form a black-hole, consists of an accreting
black-hole. The jet launched in this accretion process interacts with the
ejecta from stage 2, and could generate the flaring activity frequently seen in
X-ray afterglows. This model may be able to account for both the energies and
the timescales of GRBs, in addition to the newly discovered early X-ray
afterglow features.


  Proximal policy optimization(PPO) has been proposed as a first-order
optimization method for reinforcement learning. We should notice that an
exterior penalty method is used in it. Often, the minimizers of the exterior
penalty functions approach feasibility only in the limits as the penalty
parameter grows increasingly large. Therefore, it may result in the low level
of sampling efficiency. This method, which we call proximal policy optimization
with barrier method (PPO-B), keeps almost all advantageous spheres of PPO such
as easy implementation and good generalization. Specifically, a new surrogate
objective with interior penalty method is proposed to avoid the defect arose
from exterior penalty method. Conclusions can be draw that PPO-B is able to
outperform PPO in terms of sampling efficiency since PPO-B achieved clearly
better performance on Atari and Mujoco environment than PPO.


  Recently, correlation filters have demonstrated the excellent performance in
visual tracking. However, the base training sample region is larger than the
object region,including the Interference Region(IR). The IRs in training
samples from cyclic shifts of the base training sample severely degrade the
quality of a tracking model. In this paper, we propose the novel
Region-filtering Correlation Tracking (RFCT) to address this problem. We
immediately filter training samples by introducing a spatial map into the
standard CF formulation. Compared with existing correlation filter trackers,
our proposed tracker has the following advantages: (1) The correlation filter
can be learned on a larger search region without the interference of the IR by
a spatial map. (2) Due to processing training samples by a spatial map, it is
more general way to control background information and target information in
training samples. The values of the spatial map are not restricted, then a
better spatial map can be explored. (3) The weight proportions of accurate
filters are increased to alleviate model corruption. Experiments are performed
on two benchmark datasets: OTB-2013 and OTB-2015. Quantitative evaluations on
these benchmarks demonstrate that the proposed RFCT algorithm performs
favorably against several state-of-the-art methods.


  Routing is a crucial component in the design of Flying Ad-Hoc Networks
(FANETs). State of the art routing solutions exploit the position of Unmanned
Aerial Vehicles (UAVs) and their mobility information to determine the
existence of links between them, but this information is often unreliable, as
the topology of FANETs can change quickly and unpredictably. In order to
improve the tracking performance, the uncertainty introduced by imperfect
measurements and tracking algorithms needs to be accounted for in the routing.
Another important element to consider is beamforming, which can reduce
interference, but requires accurate channel and position information to work.
In this work, we present the Beam Aware Stochastic Multihop Routing for FANETs
(BA-SMURF), a Software-Defined Networking (SDN) routing scheme that takes into
account the positioning uncertainty and beamforming design to find the most
reliable routes in a FANET. Our simulation results show that joint
consideration of the beamforming and routing can provide a 5% throughput
improvement with respect to the state of the art.


  With the rapid development of quantum computers the currently secure
cryptographic protocols may not stay that way. Quantum mechanics provides means
to create an inherently secure communication channel that is protected by the
laws of physics and not by the computational hardness of certain mathematical
problems. This paper is a non-technical overview of quantum key distribution,
one of the most well-known application of quantum cryptography, a type of
cryptography poised to exploit the laws of quantum mechanics directly.


  In this contributed presentation, we discuss and compare the mutually
opposite procedures of deformations and contractions of Lie algebras. We
suggest that with appropriate combinations of both procedures one may construct
new Lie algebras. We first discuss low-dimensional Lie algebras and illustrate
thereby that whereas for every contraction there exists a reverse deformation,
the converse is not true in general. Also we note that some Lie algebras
belonging to parameterized families are singled out by the irreversibility of
deformations and contractions. After reminding that global deformations of the
Witt, Virasoro, and affine Kac-Moody algebras allow one to retrieve Lie
algebras of Krichever-Novikov type, we contract the latter to find new infinite
dimensional Lie algebras.


  We prove a conjecture due to V.V. Shokurov on the boundedness of
$\epsilon$-log canonical complements on surfaces. As an application we give a
new proof to the boundedness of weak log Fano surfaces.


  In this paper, we consider dynamic precoder/decorrelator optimization for
multimedia streaming in MIMO interference networks. We propose a truly
cross-layer framework in the sense that the optimization objective is the
application level performance metrics for multimedia streaming, namely the
playback interruption and buffer overflow probabilities. The optimization
variables are the MIMO precoders/decorrelators at the transmitters and the
receivers, which are adaptive to both the instantaneous channel condition and
the playback queue length. The problem is a challenging multi-dimensional
stochastic optimization problem and brute-force solution has exponential
complexity. By exploiting the underlying timescale separation and special
structure in the problem, we derive a closed-form approximation of the value
function based on continuous time perturbation. Using this approximation, we
propose a low complexity dynamic MIMO precoder/decorrelator control algorithm
by solving an equivalent weighted MMSE problem. We also establish the technical
conditions for asymptotic optimality of the low complexity control algorithm.
Finally, the proposed scheme is compared with various baselines through
simulations and it is shown that significant performance gain can be achieved.


  The Australia Telescope Compact Array (ATCA) participated in a number of
survey programs to search for and image common class I methanol masers (at 36
and 44 GHz) with high angular resolution. In this paper, we discuss spatial and
velocity distributions revealed by these surveys. In particular, the number of
maser regions is found to fall off exponentially with the linear distance from
the associated young stellar object traced by the 6.7-GHz maser, and the scale
of this distribution is 263+/-15 milliparsecs. Although this relationship still
needs to be understood in the context of the broader field, it can be utilised
to estimate the distance using methanol masers only. This new technique has
been analysed to understand its limitations and future potential. It turned
out, it can be very successful to resolve the ambiguity in kinematic distances,
but, in the current form, is much less accurate (than the kinematic method) if
used on its own.


  In this paper, we propose a self-dependent two-way secure communication where
two sources exchange confidential messages via a wireless powered untrusted
amplify-and-forward (AF) relay and friendly jammer (FJ). By adopting the time
switching (TS) architecture at the relay, the data transmission is accomplished
in three phases: Phase I) Energy harvesting by the untrusted relay and the FJ
through non-information transmissions from the sources, Phase II) Information
transmission by the sources and jamming transmissions from the FJ to reduce
information leakage to the untrusted relay; and Phase III) Forwarding the
scaled version of the received signal from the untrusted relay to the sources.
For the proposed system, we derive a new closed-form lower bound expression for
the ergodic secrecy sum rate (ESSR). Numerical examples are provided to
demonstrate the impacts of different system parameters such as energy
harvesting time, transmit signal-to-noise ratio (SNR) and the relay/FJ location
on the secrecy performance. The numerical results illustrate that the proposed
network with friendly jamming (WFJ) outperforms traditional one-way
communication and the two-way without friendly jamming (WoFJ) policy.


  The annual modulation observed by DAMA/NaI and DAMA/Libra may be interpreted
in terms of elastic or inelastic scattering of dark matter particles. In this
paper we confront these two scenarios within the framework of a very simple
extension of the Standard Model, the Inert Doublet Model (IDM). In this model
the dark matter candidate is a scalar, the lightest component of an extra Higgs
doublet. We first revisit the case for the elastic scattering of a light scalar
WIMP, M_DM~10 GeV, a scenario which requires that a fraction of events in DAMA
are channelled. Second we consider the possibility of inelastic Dark Matter
(iDM). This option is technically natural in the IDM, in the sense that the
mass splitting between the lightest and next-to-lightest neutral scalars may be
protected by a Peccei-Quinn (PQ) symmetry. We show that candidates with a mass
M_DM between ~535 GeV and ~50 TeV may reproduce the DAMA data and have a cosmic
abundance in agreement with WMAP. This range may be extended to candidates as
light as ~50 GeV if we exploit the possibility that the approximate PQ symmetry
is effectively conserved and that a primordial asymmetry in the dark sector may
survive until freeze-out.


  Consider an algebraically closed field k and the Cremona group of all
birational transformations of the projective plane over k. We characterize
infinite order elements of this group having a non-zero power generating a
proper normal subgroup of the Cremona group.


  Deep neural networks based object detectors have shown great success in a
variety of domains like autonomous vehicles, biomedical imaging, etc. It is
known that their success depends on a large amount of data from the domain of
interest. While deep models often perform well in terms of overall accuracy,
they often struggle in performance on rare yet critical data slices. For
example, data slices like "motorcycle at night" or "bicycle at night" are often
rare but very critical slices for self-driving applications and false negatives
on such rare slices could result in ill-fated failures and accidents. Active
learning (AL) is a well-known paradigm to incrementally and adaptively build
training datasets with a human in the loop. However, current AL based
acquisition functions are not well-equipped to tackle real-world datasets with
rare slices, since they are based on uncertainty scores or global descriptors
of the image. We propose TALISMAN, a novel framework for Targeted Active
Learning or object detectIon with rare slices using Submodular MutuAl
iNformation. Our method uses the submodular mutual information functions
instantiated using features of the region of interest (RoI) to efficiently
target and acquire data points with rare slices. We evaluate our framework on
the standard PASCAL VOC07+12 and BDD100K, a real-world self-driving dataset. We
observe that TALISMAN outperforms other methods by in terms of average
precision on rare slices, and in terms of mAP.


  This research analyzes the effects of U.S. science and technology policy on
the technological performance of organizations in a global strategic alliance
network. During the mid-1980s the U.S. semiconductor industry appeared to be
collapsing. Industry leaders and policymakers moved to support and protect U.S.
firms by creating a program called Sematech. While many scholars regard
Sematech as a success, how the program succeeded remains unclear. This study
re-contextualizes Sematech as a network administrative organization which
lowered cooperation costs and enhanced resource combination for innovation at
the cutting edge. This study combines network analysis and longitudinal
regression techniques to test the effects of public policy on organizational
network position and technological performance in an unbalanced panel of
semiconductor firms between 1986 and 2001. This research suggests governments
might achieve policy through inter-organizational innovations aimed at the
development and administration of robust governance networks.


  Academic networks in the real world can usually be described by heterogeneous
information networks composed of multi-type nodes and relationships. Some
existing research on representation learning for homogeneous information
networks lacks the ability to explore heterogeneous information networks in
heterogeneous information networks. It cannot be applied to heterogeneous
information networks. Aiming at the practical needs of effectively identifying
and discovering scientific research teams from the academic heterogeneous
information network composed of massive and complex scientific and
technological big data, this paper proposes a scientific research team
identification method based on representation learning of academic
heterogeneous information networks. The attention mechanism at node level and
meta-path level learns low-dimensional, dense and real-valued vector
representations on the basis of retaining the rich topological information of
nodes in the network and the semantic information based on meta-paths, and
realizes effective identification and discovery of scientific research teams
and important team members in academic heterogeneous information networks based
on maximizing node influence. Experimental results show that our proposed
method outperforms the comparative methods.


  Objective. Covert aspects of ongoing user mental states provide key context
information for user-aware human computer interactions. In this paper, we focus
on the problem of estimating the vigilance of users using EEG and EOG signals.
Approach. To improve the feasibility and wearability of vigilance estimation
devices for real-world applications, we adopt a novel electrode placement for
forehead EOG and extract various eye movement features, which contain the
principal information of traditional EOG. We explore the effects of EEG from
different brain areas and combine EEG and forehead EOG to leverage their
complementary characteristics for vigilance estimation. Considering that the
vigilance of users is a dynamic changing process because the intrinsic mental
states of users involve temporal evolution, we introduce continuous conditional
neural field and continuous conditional random field models to capture dynamic
temporal dependency. Main results. We propose a multimodal approach to
estimating vigilance by combining EEG and forehead EOG and incorporating the
temporal dependency of vigilance into model training. The experimental results
demonstrate that modality fusion can improve the performance compared with a
single modality, EOG and EEG contain complementary information for vigilance
estimation, and the temporal dependency-based models can enhance the
performance of vigilance estimation. From the experimental results, we observe
that theta and alpha frequency activities are increased, while gamma frequency
activities are decreased in drowsy states in contrast to awake states.
Significance. The forehead setup allows for the simultaneous collection of EEG
and EOG and achieves comparative performance using only four shared electrodes
in comparison with the temporal and posterior sites.


  We derive a non-Markovian theory for waiting time distributions of
consecutive single electron transfer events. The presented microscopic Pauli
rate equation formalism couples the open electrodes to the many-body system,
allowing to take finite bias and temperature into consideration. Numerical
results reveal transient oscillations of distinct system frequencies due to
memory in the waiting time distributions. Memory effects can be approximated by
an expansion in non-Markovian corrections. This method is employed to calculate
memory landscapes displaying preservation of memory over multiple consecutive
electron transfers.


  We investigate higher dimensional chain conditions, where the largeness
notion is given by Fubini products of a given ideal. From strong saturation
properties of an ideal, we derive abstractly versions of higher dimensional
$\Delta$-system lemma, which imply many posets, including any finite support
iteration of $\sigma$-centered posets and measure algebras, satisfy the higher
dimensional chain conditions. We then show that if a poset satisfies a
strengthening of the $\sigma$-finite chain condition by Horn and Tarski, then
it satisfies higher dimensional chain conditions. As an application, we derive
Ramsey-theoretic consequences, namely various partition hypotheses as studied
by Bannister, Bergfalk, Moore and Todorcevic, from the existence of ideals
satisfying strong chain conditions.


  Digital twins promise to revolutionize engineering by offering new avenues
for optimization, control, and predictive maintenance. We propose a novel
framework for simultaneously training the digital twin of an engineering system
and an associated control agent. The twin's training combines adjoint-based
data assimilation and system identification methods, while the control agent's
training merges model-based optimal control with model-free reinforcement
learning. The control agent evolves along two independent paths: one driven by
model-based optimal control and the other by reinforcement learning. The
digital twin serves as a virtual environment for confrontation and indirect
interaction, functioning as an "expert demonstrator." The best policy is
selected for real-world interaction and cloned to the other path if training
stagnates. We call this framework Reinforcement Twinning (RT). The framework is
tested on three diverse engineering systems and control tasks: (1) controlling
a wind turbine under varying wind speeds, (2) trajectory control of
flapping-wing micro air vehicles (FWMAVs) facing wind gusts, and (3) mitigating
thermal loads in managing cryogenic storage tanks. These test cases use
simplified models with known ground truth closure laws. Results show that the
adjoint-based digital twin training is highly sample-efficient, completing
within a few iterations. For the control agent training, both model-based and
model-free approaches benefit from their complementary learning experiences.
The promising results pave the way for implementing the RT framework on real
systems.


  In this paper, inspired from our previous algorithm, which was based on the
theory of Tsallis statistical mechanics, we develop a new evolving stochastic
learning algorithm for neural networks. The new algorithm combines
deterministic and stochastic search steps by employing a different adaptive
stepsize for each network weight, and applies a form of noise that is
characterized by the nonextensive entropic index q, regulated by a weight decay
term. The behavior of the learning algorithm can be made more stochastic or
deterministic depending on the trade off between the temperature T and the q
values. This is achieved by introducing a formula that defines a
time--dependent relationship between these two important learning parameters.
Our experimental study verifies that there are indeed improvements in the
convergence speed of this new evolving stochastic learning algorithm, which
makes learning faster than using the original Hybrid Learning Scheme (HLS). In
addition, experiments are conducted to explore the influence of the entropic
index q and temperature T on the convergence speed and stability of the
proposed method.


  We study quantum algorithms for several fundamental string problems,
including Longest Common Substring, Lexicographically Minimal String Rotation,
and Longest Square Substring. These problems have been widely studied in the
stringology literature since the 1970s, and are known to be solvable by
near-linear time classical algorithms. In this work, we give quantum algorithms
for these problems with near-optimal query complexities and time complexities.
Specifically, we show that:
  - Longest Common Substring can be solved by a quantum algorithm in $\tilde
O(n^{2/3})$ time, improving upon the recent $\tilde O(n^{5/6})$-time algorithm
by Le Gall and Seddighin (2020). Our algorithm uses the MNRS quantum walk
framework, together with a careful combination of string synchronizing sets
(Kempa and Kociumaka, 2019) and generalized difference covers.
  - Lexicographically Minimal String Rotation can be solved by a quantum
algorithm in $n^{1/2 + o(1)}$ time, improving upon the recent $\tilde
O(n^{3/4})$-time algorithm by Wang and Ying (2020). We design our algorithm by
first giving a new classical divide-and-conquer algorithm in near-linear time
based on exclusion rules, and then speeding it up quadratically using nested
Grover search and quantum minimum finding.
  - Longest Square Substring can be solved by a quantum algorithm in $\tilde
O(\sqrt{n})$ time. Our algorithm is an adaptation of the algorithm by Le Gall
and Seddighin (2020) for the Longest Palindromic Substring problem, but uses
additional techniques to overcome the difficulty that binary search no longer
applies.
  Our techniques naturally extend to other related string problems, such as
Longest Repeated Substring, Longest Lyndon Substring, and Minimal Suffix.


  Recently, a non-relativistic off-shell formulation of three dimensional
Newton-Cartan supergravity was proposed as the $c \rightarrow \infty$ limit of
three dimensional $\mathcal{N}=2$ supergravity in arXiv:1505.02095. In the
present paper we study supersymmetric backgrounds within this theory. Using
integrability constraints for the non-relativistic Killing spinor equations, we
explicitly construct all maximally supersymmetric solutions, which admit four
supercharges. In addition to these solutions, there are $\frac{1}{2}$-BPS
solutions with reduced supersymmetry. We give explicit examples of such
backgrounds and derive necessary conditions for backgrounds preserving two
supercharges. Finally, we address how supersymmetric backgrounds of
$\mathcal{N}=2$ supergravity are connected to the solutions found here in the
$c \rightarrow \infty$ limit.


  We report the generation of molecular hydrogen from water by laser
irradiation, without any electrodes and photocatalysts. A near infrared pulsed
nanosecond laser is used for exposure of colloidal solution of Au nanoparticles
suspended in water. Laser exposure of the colloidal solution results in
formation of plasma of laser breakdown of liquid and emission of H2. The rate
of H2 emission depends critically on the energy of laser pulses. There is a
certain threshold in laser fluence in liquid (around 50 J/cm2) below which
plasma disappears and H2 emission stops. H2 emission from colloidal solution of
Au nanoparticles in ethanol is higher than that from similar water colloid. It
is found that formation of plasma and emission of H2 or D2 can be induced by
laser exposure of pure liquids, either H2O or D2O, respectively. The results
are interpreted as water molecules splitting by direct electron impact from
breakdown plasma.


  In this paper, we study the thermodynamic features of a non-linear
magnetic-charged AdS black hole surrounded by quintessence, in the background
of perfect fluid dark matter(PFDM). After having constructed the corresponding
metric, we analyse the structure of the horizon. We find that the existence of
inner or outer horizon are constrained by the presence of dark matter.
Afterwards, we put out the mass and the temperature of the black hole, in order
to get its entropy. Subsequently, we find the expression of the pressure which
leads us to get the table of critical values and the isothermal diagram.
Especially, we find that the critical values of the temperature and the
pressure increase as the dark matter parameter increases. Also, analysing the
isothermal diagram, we observe a van der Waals-like behaviour remarked by the
presence of a first-order phase transition when we cross the critical
temperature. Additionally, we compute and plot the heat capacity and the
Hessian matrix of the black hole mass. For the heat capacity, we find that a
second-order phase transition occurs, leading the black hole to move from
stable phase to unstable one. Furthermore, it comes out that this phase
transition point is shifted towards higher values of the horizon radius, as we
decrease the dark matter density and increase the quintessence density.


  We present a new geometric approach to the flavour decomposition of an
arbitrary soft supersymmetry-breaking sector in the MSSM. Our approach is based
on the geometry that results from the quark and lepton Yukawa couplings, and
enables us to derive the necessary and sufficient conditions for a
linearly-independent basis of matrices related to the completeness of the
internal [SU(3) x U(1)]^5 flavour space. In a second step, we calculate the
effective Yukawa couplings that are enhanced at large values of tan(beta) for
general soft supersymmetry-breaking mass parameters. We highlight the
contributions due to non-universal terms in the flavour decompositions of the
sfermion mass matrices. We present numerical examples illustrating how such
terms are induced by renormalization-group evolution starting from universal
input boundary conditions, and demonstrate their importance for the
flavour-violating effective Yukawa couplings of quarks.


  In this paper we study the slope stratification on the good reduction of the
type C family Shimura varieties. We show that there is an open dense subset $U$
of the moduli space such that any point in $U$ can be deformed to a point with
a given lower {\it admissible} Newton polygon. For the Siegel moduli spaces,
this is obtained by F. Oort which plays an important role in his proof of the
strong Grothendieck conjecture concerning the slope stratification. We also
investigate the $p$-divisible groups and their isogeny classes arising from the
abelian varieties in question.


  To increase the flexibility and scalability of deep neural networks for image
reconstruction, a framework is proposed based on bandpass filtering. For many
applications, sensing measurements are performed indirectly. For example, in
magnetic resonance imaging, data are sampled in the frequency domain. The
introduction of bandpass filtering enables leveraging known imaging physics
while ensuring that the final reconstruction is consistent with actual
measurements to maintain reconstruction accuracy. We demonstrate this flexible
architecture for reconstructing subsampled datasets of MRI scans. The resulting
high subsampling rates increase the speed of MRI acquisitions and enable the
visualization rapid hemodynamics.


  We propose a microscopic state for the vortex phase of BSCO superconductors.
Around the vortex core or above H_{c2}, the d wave hole pairs form a
checkerboard localized in the commensurate antiferromagnetic background. We
discuss this theory in connection with recent STM experiments.


  In 2007, a very bright radio pulse was identified in the archival data of the
Parkes Telescope in Australia, marking the beginning of a new research branch
in astrophysics. In 2013, this kind of millisecond bursts with extremely high
brightness temperature takes a unified name, fast radio burst (FRB). Over the
first few years, FRBs seemed very mysterious because the sample of known events
was limited. With the improvement of instruments over the last five years,
hundreds of new FRBs have been discovered. The field is now undergoing a
revolution and understanding of FRB has rapidly increased as new observational
data increasingly accumulates. In this review, we will summarize the basic
physics of FRBs and discuss the current research progress in this area. We have
tried to cover a wide range of FRB topics, including the observational
property, propagation effect, population study, radiation mechanism, source
model, and application in cosmology. A framework based on the latest
observational facts is now under construction. In the near future, this
exciting field is expected to make significant breakthroughs.


  Upper and lower bounds are derived for the Gaussian mean width of the
intersection of a convex hull of $M$ points with an Euclidean ball of a given
radius. The upper bound holds for any collection of extreme point bounded in
Euclidean norm. The upper bound and the lower bound match up to a
multiplicative constant whenever the extreme points satisfy a one sided
Restricted Isometry Property.
  This bound is then applied to study the Lasso estimator in fixed-design
regression, the Empirical Risk Minimizer in the anisotropic persistence
problem, and the convex aggregation problem in density estimation.


  We propose a method for finding alternate features missing in the Lasso
optimal solution. In ordinary Lasso problem, one global optimum is obtained and
the resulting features are interpreted as task-relevant features. However, this
can overlook possibly relevant features not selected by the Lasso. With the
proposed method, we can provide not only the Lasso optimal solution but also
possible alternate features to the Lasso solution. We show that such alternate
features can be computed efficiently by avoiding redundant computations. We
also demonstrate how the proposed method works in the 20 newsgroup data, which
shows that reasonable features are found as alternate features.


  Projective measurements in random quantum circuits lead to a rich breadth of
entanglement phases and extend the realm of non-unitary quantum dynamics. Here
we explore the connection between measurement-only quantum circuits in one
spatial dimension and the statistical mechanics of loop models in two
dimensions. While Gaussian Majorana circuits admit a microscopic mapping to
loop models, for non-Gaussian, i.e., generic Clifford, circuits a corresponding
mapping may emerge only on a coarse grained scale. We then focus on a
fundamental symmetry of loop models: the orientability of world lines. We
discuss how orientability enters in the measurement framework, acting as a
separatrix for the universal long-wavelength behavior in a circuit. When
orientability is broken, the circuit falls into the universality class of
closely packed loops with crossings (CPLC) and features a Goldstone phase with
a peculiar, universal $\log^2(L)$-scaling of the entanglement entropy. In turn,
when orientability is preserved, the long-wavelength behavior of the circuit
mimics that of (coupled) two-dimensional Potts models. We demonstrate the
strength of the loop model approach by numerically simulating a variety of
measurement-only Clifford circuits. Upon varying the set of measured operators,
a rich circuit dynamics is observed, ranging from CPLC to the $1$-state Potts
model (percolation), the $2$-state Potts model (Ising) and coupled Potts models
(BKT) universality class. Loop models thus provide a handle to access a large
class of measurement-only circuits and yield a blueprint on how to realize
desired entanglement phases by measurement.


  We present the first results on the saturation of the f-mode instability in
neutron stars, due to nonlinear mode coupling. Emission of gravitational waves
drives the f-mode (fundamental mode) unstable in fast-rotating, newborn neutron
stars. The initial growth phase of the mode is followed by its saturation,
because of energy leaking to other modes of the star. The saturation point
determines the strain of the generated gravitational-wave signal, which can
then be used to extract information about the neutron star equation of state.
The parent (unstable) mode couples via parametric resonances with pairs of
daughter modes, with the triplets' evolution exhibiting a rich variety of
behaviors. We study both supernova- and merger-derived neutron stars, simply
modeled as polytropes in a Newtonian context, and show that the parent may
couple to many different daughter pairs during the star's evolution through the
instability window, with the saturation amplitude changing by orders of
magnitude.


  In the past five years, most of the paradigmatic concepts employed in
spintronics have been replicated substituting ferromagnets by antiferromagnets
in critical parts of the devices. The numerous research efforts directed to
manipulate and probe the magnetic moments in antiferromagnets have been
gradually established a new and independent field known as antiferromagnetic
spintronics. In this paper, we focus on the electrical control and detection of
antiferromagnetic moments at a constant temperature. We address separately the
experimental results concerning insulating and metallic thin films as they
correspond to voltage and electrical current controlled devices, respectively.
First, we present results on the voltage control of antiferromagnetic order in
insulating thin films. The experiments show that voltage pulses can switch the
chirality of a modulated antiferromagnetic structure. Second, we describe the
recent advances in metallic antiferromagnetic systems. We present results
obtained with the first USB-operated portable device able to perform the
non-volatile electrical current-induced switching of an antiferromagnet
combined with magnetoresistive readout at room temperature. We discuss on
potential applications that can be realized using antiferromagnetic memory
cells.


  When an image classifier outputs a wrong class label, it can be helpful to
see what changes in the image would lead to a correct classification. This is
the aim of algorithms generating counterfactual explanations. However, there is
no easily scalable method to generate such counterfactuals. We develop a new
algorithm providing counterfactual explanations for large image classifiers
trained with spectral normalisation at low computational cost. We empirically
compare this algorithm against baselines from the literature; our novel
algorithm consistently finds counterfactuals that are much closer to the
original inputs. At the same time, the realism of these counterfactuals is
comparable to the baselines. The code for all experiments is available at
https://github.com/benedikthoeltgen/DeDUCE.


  With the emerging connected-vehicle technologies and smart roads, the need
for intelligent adaptive traffic signal controls is more than ever before. This
paper proposes a novel Economic-driven Adaptive Traffic Signal Control (eATSC)
model with a hyper control variable - interest rate defined in economics for
traffic signal control at signalized intersections. The eATSC uses a continuous
compounding function that captures both the total number of vehicles and the
accumulated waiting time of each vehicle to compute penalties for different
directions. The computed penalties grow with waiting time and is used for
signal control decisions. Each intersection is assigned two intelligent agents
adjusting interest rate and signal length for different directions according to
the traffic patterns, respectively. The problem is formulated as a Markov
Decision Process (MDP) problem to reduce congestions, and a two-agent Double
Dueling Deep Q Network (DDDQN) is utilized to solve the problem. Under the
optimal policy, the agents can select the optimal interest rates and signal
time to minimize the likelihood of traffic congestion. To evaluate the
superiority of our method, a VISSIM simulation model with classic four-leg
signalized intersections is developed. The results indicate that the proposed
model is adequately able to maintain healthy traffic flow at the intersection.


  The cost of data annotation is a substantial impediment for multi-label image
classification: in every image, every category must be labeled as present or
absent. Single positive multi-label (SPML) learning is a cost-effective
solution, where models are trained on a single positive label per image. Thus,
SPML is a more challenging domain, since it requires dealing with missing
labels. In this work, we propose a method to turn single positive data into
fully-labeled data: Pseudo Multi-Labels. Basically, a teacher network is
trained on single positive labels. Then, we treat the teacher model's
predictions on the training data as ground-truth labels to train a student
network on fully-labeled images. With this simple approach, we show that the
performance achieved by the student model approaches that of a model trained on
the actual fully-labeled images.


  Facility location problems often permit facilities to be located at any
position. But what if this is not the case in practice? What if facilities can
only be located at particular locations like a highway exit or close to a bus
stop? We consider here the impact of such constraints on the location of
facilities on the performance of strategy proof mechanisms for locating
facilities.We study four different performance objectives: the total distance
agents must travel to their closest facility, the maximum distance any agent
must travel to their closest facility, and the utilitarian and egalitarian
welfare.We show that constraining facilities to a limited set of locations
makes all four objectives harder to approximate in general.


  We extract the individual contributions from u and d quarks to the Dirac and
Pauli form factors of the proton, after a critical examination of the available
measurements of electromagnetic nucleon form factors. From this data we
determine generalized parton distributions for valence quarks, assuming a
particular form for their functional dependence. The result allows us to study
various aspects of nucleon structure in the valence region. In particular, we
evaluate Ji's sum rule and estimate the total angular momentum carried by
valence quarks at the scale mu = 2 GeV to be J_v^u = 0.230 +0.009 -0.024 and
J_v^d = -0.004 +0.010 -0.016.


  The recent LIGO detection of gravitational waves (GW150914), likely
originating from the merger of two $\sim 30 M_\odot$ black holes suggests
progenitor stars of low metallicity ($[Z/Z_\odot] \lesssim 0.3$), constraining
when and where the progenitor of GW150914 may have formed. We combine estimates
of galaxy properties (metallicity, star formation rate and merger rate) across
cosmic time to predict the low redshift black hole - black hole merger rate as
a function of present day host galaxy mass, $M_\mathrm{gal}$, and the formation
redshift of the progenitor system $z_\mathrm{form}$ for different progenitor
metallicities $Z_\mathrm{c}$. At $Z_\mathrm{c}=0.1 Z_\odot$, the signal is
dominated by binaries in massive galaxies with $z_\mathrm{form}\simeq 2$, with
a small contribution from binaries formed around $z_\mathrm{form}\simeq 0.5$ in
dwarf galaxies. For $Z_\mathrm{c}=0.01Z_\odot$, fast mergers are possible and
very recent star formation in dwarfs likely dominates. Additional gravitational
wave detections from merging massive black holes will provide constraints on
the mass-metallicity relation and massive star formation at high redshifts.


  In many computer vision tasks, we expect a particular behavior of the output
with respect to rotations of the input image. If this relationship is
explicitly encoded, instead of treated as any other variation, the complexity
of the problem is decreased, leading to a reduction in the size of the required
model. In this paper, we propose the Rotation Equivariant Vector Field Networks
(RotEqNet), a Convolutional Neural Network (CNN) architecture encoding rotation
equivariance, invariance and covariance. Each convolutional filter is applied
at multiple orientations and returns a vector field representing magnitude and
angle of the highest scoring orientation at every spatial location. We develop
a modified convolution operator relying on this representation to obtain deep
architectures. We test RotEqNet on several problems requiring different
responses with respect to the inputs' rotation: image classification,
biomedical image segmentation, orientation estimation and patch matching. In
all cases, we show that RotEqNet offers extremely compact models in terms of
number of parameters and provides results in line to those of networks orders
of magnitude larger.


  When finding the nonzero eigenvalues for Hamiltonian eigenvalue problems it
is especially important to locate not only the unstable eigenvalues (i.e.,
those with positive real part), but also those which are purely imaginary but
have negative Krein signature. These latter eigenvalues have the property that
they can become unstable upon collision with other purely imaginary
eigenvalues, i.e., they are a necessary building block in the mechanism leading
to the so-called Hamiltonian-Hopf bifurcation. In this paper we review a
general theory for constructing a meromorphic matrix-valued function, the
so-called Krein matrix, which has the property of not only locating the
unstable eigenvalues, but also those with negative Krein signature. These
eigenvalues are realized as zeros of the determinant. The resulting finite
dimensional problem obtained by setting the determinant of the Krein matrix to
zero presents a valuable simplification. In this paper the usefulness of the
technique is illustrated through prototypical examples of spectral analysis of
states that have arisen in recent experimental and theoretical studies of
atomic Bose-Einstein condensates. In particular, we consider one-dimensional
settings (the cigar trap) possessing real-valued multi-dark-soliton solutions,
and two-dimensional settings (the pancake trap) admitting complex multi-vortex
stationary waveforms.


  The spread of the coronavirus disease 2019 (COVID-19) caused by severe acute
respiratory syndrome coronavirus-2 (SARS-CoV-2) has become a global health
crisis. The binding affinity of SARS-CoV-2 (in particular the receptor binding
domain, RBD) to its receptor angiotensin converting enzyme 2 (ACE2) and the
antibodies is of great importance in understanding the infectivity of COVID-19
and evaluating the candidate therapeutic for COVID-19. In this work, we propose
a new method based on molecular mechanics/Poisson-Boltzmann surface area
(MM/PBSA) to accurately calculate the free energy of SARS-CoV-2 RBD binding to
ACE2 and antibodies. The calculated binding free energy of SARS-CoV-2 RBD to
ACE2 is -13.3 kcal/mol, and that of SARS-CoV RBD to ACE2 is -11.4 kcal/mol,
which agrees well with experimental result (-11.3 kcal/mol and -10.1 kcal/mol,
respectively). Moreover, we take two recently reported antibodies as the
example, and calculate the free energy of antibodies binding to SARS-CoV-2 RBD,
which is also consistent with the experimental findings. Further, within the
framework of the modified MM/PBSA, we determine the key residues and the main
driving forces for the SARS-CoV-2 RBD/CB6 interaction by the computational
alanine scanning method. The present study offers a computationally efficient
and numerically reliable method to evaluate the free energy of SARS-CoV-2
binding to other proteins, which may stimulate the development of the
therapeutics against the COVID-19 disease in real applications.


  Recent studies on fully dielectric multilayered metamaterials have shown that
the negligibly small nonlocal effects (spatial dispersion) typically observed
in the limit of deeply subwavelength layers may be significantly enhanced by
peculiar boundary effects occurring in certain critical parameter regimes.
These phenomena, observed so far in periodic and randomly disordered
geometries, are manifested as strong differences between the exact optical
response of finite-size metamaterial samples and the prediction from
conventional effective-theory-medium models based on mixing formulae. Here,
with specific focus on the Thue-Morse geometry, we make a first step toward
extending the studies above to the middle-ground of aperiodically ordered
multilayers, lying in between perfect periodicity and disorder. We show that,
also for these geometries, there exist critical parameter ranges that favor the
buildup of boundary effects leading to strong enhancement of the (otherwise
negligibly weak) nonlocality. However, the underlying mechanisms are
fundamentally different from those observed in the periodic case, and exhibit
typical footprints (e.g., fractal gaps, quasi-localized states) that are
distinctive of aperiodic order. The outcomes of our study indicate that
aperiodic order plays a key role in the buildup of the aforementioned boundary
effects, and may also find potential applications to optical sensors, absorbers
and lasers.


  Zero-shot learning (ZSL) aims at understanding unseen categories with no
training examples from class-level descriptions. To improve the discriminative
power of zero-shot learning, we model the visual learning process of unseen
categories with inspiration from the psychology of human creativity for
producing novel art. We relate ZSL to human creativity by observing that
zero-shot learning is about recognizing the unseen and creativity is about
creating a likable unseen. We introduce a learning signal inspired by
creativity literature that explores the unseen space with hallucinated
class-descriptions and encourages careful deviation of their visual feature
generations from seen classes while allowing knowledge transfer from seen to
unseen classes. Empirically, we show consistent improvement over the state of
the art of several percents on the largest available benchmarks on the
challenging task or generalized ZSL from a noisy text that we focus on, using
the CUB and NABirds datasets. We also show the advantage of our approach on
Attribute-based ZSL on three additional datasets (AwA2, aPY, and SUN). Code is
available.


  We study the spectral properties of classical and quantum Markovian processes
that are reset at random times to a specific configuration or state with a
reset rate that is independent of the current state of the system. We
demonstrate that this simple reset dynamics causes a uniform shift in the
eigenvalues of the Markov generator, excluding the zero mode corresponding to
the stationary state, which has the effect of accelerating or even inducing
relaxation to a stationary state. Based on this result, we provide expressions
for the stationary state and probability current of the reset process in terms
of weighted sums over dynamical modes of the reset-free process. We also
discuss the effect of resets on processes that display metastability. We
illustrate our results with two classical stochastic processes, the totally
asymmetric random walk and the one-dimensional Brownian motion, as well as two
quantum models: a particle coherently hopping on a chain and the dissipative
transverse field Ising model, known to exhibit metastability.


  Intestinal parasites are responsible for several diseases in human beings. In
order to eliminate the error-prone visual analysis of optical microscopy
slides, we have investigated automated, fast, and low-cost systems for the
diagnosis of human intestinal parasites. In this work, we present a hybrid
approach that combines the opinion of two decision-making systems with
complementary properties: ($DS_1$) a simpler system based on very fast
handcrafted image feature extraction and support vector machine classification
and ($DS_2$) a more complex system based on a deep neural network, Vgg-16, for
image feature extraction and classification. $DS_1$ is much faster than $DS_2$,
but it is less accurate than $DS_2$. Fortunately, the errors of $DS_1$ are not
the same of $DS_2$. During training, we use a validation set to learn the
probabilities of misclassification by $DS_1$ on each class based on its
confidence values. When $DS_1$ quickly classifies all images from a microscopy
slide, the method selects a number of images with higher chances of
misclassification for characterization and reclassification by $DS_2$. Our
hybrid system can improve the overall effectiveness without compromising
efficiency, being suitable for the clinical routine -- a strategy that might be
suitable for other real applications. As demonstrated on large datasets, the
proposed system can achieve, on average, 94.9%, 87.8%, and 92.5% of Cohen's
Kappa on helminth eggs, helminth larvae, and protozoa cysts, respectively.


  Flat bands are of extreme interest in a broad spectrum of fields since given
by their high degeneracy, a small perturbation introduced in the system is able
to push the ground state in the direction of an ordered phase of interest.
Hence the flat band engineering in real materials attracts huge attention.
However, manufacturing a flat band represents a difficult task because its
appearance in a real system is connected to rigid mathematical conditions
relating a part of Hamiltonian parameters. Consequently, whenever a flat band
is desired to be manufactured, these Hamiltonian parameters must be tuned
exactly to the values fixed by these rigid mathematical conditions. Here we
demonstrate that taking the many-body spin-orbit interaction (SOI) into account
-- which can be continuously tuned e.g. by external electric fields --, these
rigid mathematical conditions can be substantially relaxed. On this line we
show that a $\sim 20-30 \%$ variation in the Hamiltonian parameters rigidly
fixed by the flat band conditions can also lead to flat bands in the same or in
a bit displaced position on the energy axis. This percentage can even increase
to $\sim 80 \%$ in the presence of an external magnetic field. The study is
made in the case of conducting polymers. These systems are relevant not only
because they have broad application possibilities, but also because they can be
used to present the mathematical background of the flat band conditions in full
generality, in a concise, clear and understandable manner applicable everywhere
in itinerant systems.


  Seamlessly interacting with humans or robots is hard because these agents are
non-stationary. They update their policy in response to the ego agent's
behavior, and the ego agent must anticipate these changes to co-adapt. Inspired
by humans, we recognize that robots do not need to explicitly model every
low-level action another agent will make; instead, we can capture the latent
strategy of other agents through high-level representations. We propose a
reinforcement learning-based framework for learning latent representations of
an agent's policy, where the ego agent identifies the relationship between its
behavior and the other agent's future strategy. The ego agent then leverages
these latent dynamics to influence the other agent, purposely guiding them
towards policies suitable for co-adaptation. Across several simulated domains
and a real-world air hockey game, our approach outperforms the alternatives and
learns to influence the other agent.


  We introduce a simple and intuitive framework that provides quantitative
explanations of statistical models through the probabilistic assessment of
input feature importance. The core idea comes from utilizing the Dirichlet
distribution to define the importance of input features and learning it via
approximate Bayesian inference. The learned importance has probabilistic
interpretation and provides the relative significance of each input feature to
a model's output, additionally assessing confidence about its importance
quantification. As a consequence of using the Dirichlet distribution over the
explanations, we can define a closed-form divergence to gauge the similarity
between learned importance under different models. We use this divergence to
study the feature importance explainability tradeoffs with essential notions in
modern machine learning, such as privacy and fairness. Furthermore, BIF can
work on two levels: global explanation (feature importance across all data
instances) and local explanation (individual feature importance for each data
instance). We show the effectiveness of our method on a variety of synthetic
and real datasets, taking into account both tabular and image datasets. The
code is available at https://github.com/kamadforge/featimp_dp.


  Biopolymers serve as one-dimensional tracks on which motor proteins move to
perform their biological roles. Motor protein phenomena have inspired
theoretical models of one-dimensional transport, crowding, and jamming.
Experiments studying the motion of Xklp1 motors on reconstituted antiparallel
microtubule overlaps demonstrated that motors recruited to the overlap walk
toward the plus end of individual microtubules and frequently switch between
filaments. We study a model of this system that couples the totally asymmetric
simple exclusion process (TASEP) for motor motion with switches between
antiparallel filaments and binding kinetics. We determine steady-state motor
density profiles for fixed-length overlaps using exact and approximate
solutions of the continuum differential equations and compare to kinetic Monte
Carlo simulations. Overlap motor density profiles and motor trajectories
resemble experimental measurements. The phase diagram of the model is similar
to the single-filament case for low switching rate, while for high switching
rate we find a new low density-high density-low density-high density phase. The
overlap center region, far from the overlap ends, has a constant motor density
as one would naively expect. However, rather than following a simple binding
equilibrium, the center motor density depends on total overlap length, motor
speed, and motor switching rate. The size of the crowded boundary layer near
the overlap ends is also dependent on the overlap length and switching rate in
addition to the motor speed and bulk concentration. The antiparallel
microtubule overlap geometry may offer a previously unrecognized mechanism for
biological regulation of protein concentration and consequent activity.


  Existing exoplanet radial velocity surveys are complete in the planetary
mass-semimajor axis (Mp-a) plane over the range 0.1 AU < a < 2.0 AU where Mp >~
100 M_Earth. We marginalize over mass in this complete domain of parameter
space and demonstrate that the observed semimajor axis distribution is
inconsistent with models of planet formation that use the full Type I migration
rate derived from a linear theory and that do not include the effect of the ice
line on the disk surface density profile. However, the efficiency of Type I
migration can be suppressed by both nonlinear feedback and the barriers
introduced by local maxima in the disk pressure distribution, and we confirm
that the synthesized Mp-a distribution is compatible with the observed data if
we account for both retention of protoplanetary embryos near the ice line and
an order-of-magnitude reduction in the efficiency of Type I migration. The
validity of these assumption can be checked because they also predict a
population of short-period rocky planets with a range of masses comparable to
that of the Earth as well as a "desert" in the Mp-a distribution centered
around Mp ~ 30-50 M_Earth and a < 1 AU. We show that the expected "desert" in
the Mp-a plane will be discernible by a radial velocity survey with 1 m/s
precision and n ~ 700 radial velocity observations of program stars.


  We consider chiral fluids within the standard framework of a chiral-invariant
underlying field theory, anomalous in presence of electromagnetic fields. Apart
from the Noether axial current of the underlying theory, in the limit of ideal
fluid there exist extra conserved currents, corresponding to classical helical
motions. The extra conservation laws are known to break down once viscosity is
non-vanishing. Which looks puzzling, as if introduction of viscosity were
inconsistent with chiral invariance. As a resolution of the puzzle, we argue
that locally one can introduce an inertial frame where an extra conservation
law still holds. In other words, the extra currents are covariantly conserved.
The emergent gravitational field is determined by dynamics of the viscous
fluid. We turn then to instabilities of chiral plasma against decays into
helical magnetic or vortical configurations. We emphasise similarity between
the two cases in the far infrared region, responsible for the decays. This
similarity is not apparent within the standard counting of orders in derivative
expansion. The material was originally prepared for a review talk by the
author.


  RV6Sn6 (R=rare earth) compounds are appealing materials platforms for
exploring the interplay between R-site magnetism and nontrivial band topology
associated with the nonmagnetic vanadium-based kagome network. Here we present
the synthesis and characterization of the kagome metal TbV6Sn6 via
single-crystal x-ray diffraction, magnetization, transport, and heat capacity
measurements. Magnetization measurements reveal strong, uniaxial magnetic
anisotropy rooted in the alignment of Tb3{\AA} moments in the interplane
direction below 4.3(2) K. TbV6Sn6 exhibits multiband transport behavior with
high mobilities of charge carriers, and our measurements suggest TbV6Sn6 is a
promising candidate for hosting Chern gaps driven via the interplay between
Tb-site magnetic order and the band topology of the V-site kagome network.


  In this paper we study germs of holomorphic foliations, at the origin of the
complex plane, tangent to Pfaffian hypersurfaces - integral hypersurfaces of
real analytic 1-forms - satisfying the Rolle-Khovanskii condition. This
hypothesis leads us to conclude that such a foliation is defined by a closed
meromorphic 1-form, also allowing the classification of the simple models in
its reduction of singularities.


  The zero-phonon transition rate of a nitrogen-vacancy center is enhanced by a
factor of ~70 by coupling to a photonic crystal resonator fabricated in
monocrystalline diamond using standard semiconductor fabrication techniques.
Photon correlation measurements on the spectrally filtered zero-phonon line
show antibunching, a signature that the collected photoluminescence is emitted
primarily by a single nitrogen-vacancy center. The linewidth of the coupled
nitrogen-vacancy center and the spectral diffusion are characterized using
high-resolution photoluminescence and photoluminescence excitation
spectroscopy.


  Age of information (AoI) is one of the key performance metrics for Internet
of things (IoT) systems. Timely status updates are essential for many IoT
applications; however, they are subject to strict constraints related on the
available energy and unreliability of underlying information sources. Hence,
the scheduling of status updates must be carefully planned to preserve energy,
but at the same time, it may happen that when a status update is needed, there
is no reliable up-to-date information content to refresh. As a solution to
overcome these unpredictabilities, one can employ multiple sources that track
the same signal of interest, but with different energy costs and reliabilities,
which we call information source diversity. We consider an energy-harvesting
monitoring node equipped with a finite-size battery and collecting status
updates from multiple heterogeneous information sources. We investigate the
policies that minimize the average AoI, and evaluate the role of information
source diversity on the system performance. To do so, we formulate the problem
as a Markov decision process (MDP). The optimal policy represents the
scheduling of actions, such as an update from one of the sources or remaining
idle, based on the current energy level and the AoI at the monitoring node. We
analyze the structure of the optimal solution for different cost/AoI
distribution combinations, and compare the performance of the optimal policy
with an aggressive strategy that transmits whenever possible.


  Proximal operators are of particular interest in optimization problems
dealing with non-smooth objectives because in many practical cases they lead to
optimization algorithms whose updates can be computed in closed form or very
efficiently. A well-known example is the proximal operator of the vector
$\ell_1$ norm, which is given by the soft-thresholding operator. In this paper
we study the proximal operator of the mixed $\ell_{1,\infty}$ matrix norm and
show that it can be computed in closed form by applying the well-known
soft-thresholding operator to each column of the matrix. However, unlike the
vector $\ell_1$ norm case where the threshold is constant, in the mixed
$\ell_{1,\infty}$ norm case each column of the matrix might require a different
threshold and all thresholds depend on the given matrix. We propose a general
iterative algorithm for computing these thresholds, as well as two efficient
implementations that further exploit easy to compute lower bounds for the mixed
norm of the optimal solution. Experiments on large-scale synthetic and real
data indicate that the proposed methods can be orders of magnitude faster than
state-of-the-art methods.


  In this work we present a general theorem concerning chain rules for linear
openness of set-valued mappings acting between metric spaces. As particular
cases, we obtain classical and also some new results in this field of research,
including the celebrated Lyusternik-Graves Theorem. The applications deal with
the study of the well-posedness of the solution mappings associated to
parametric variational systems. Sharp estimates for the involved regularity
moduli are given.


  A key challenge in the practical application of Gaussian processes (GPs) is
selecting a proper covariance function. The moving average, or process
convolutions, construction of GPs allows some additional flexibility, but still
requires choosing a proper smoothing kernel, which is non-trivial. Previous
approaches have built covariance functions by using GP priors over the
smoothing kernel, and by extension the covariance, as a way to bypass the need
to specify it in advance. However, such models have been limited in several
ways: they are restricted to single dimensional inputs, e.g. time; they only
allow modelling of single outputs and they do not scale to large datasets since
inference is not straightforward. In this paper, we introduce a nonparametric
process convolution formulation for GPs that alleviates these weaknesses by
using a functional sampling approach based on Matheron's rule to perform fast
sampling using interdomain inducing variables. Furthermore, we propose a
composition of these nonparametric convolutions that serves as an alternative
to classic deep GP models, and allows the covariance functions of the
intermediate layers to be inferred from the data. We test the performance of
our model on benchmarks for single output GPs, multiple output GPs and deep GPs
and find that our approach can provide improvements over standard GP models,
particularly for larger datasets.


  In this paper, we set up a "dictionary" between discrete Schr\"odinger
operators and the holomorphic dynamics on certain affine cubic surfaces,
building on previous work by Cantat, Damanik and Gorodetski.
  Paragraphs 3.2.2 and 3.2.3 were written by Serge Cantat as an appendix.


  This paper focused on showing that the fully differential cross section of
ionization during a collision of a proton and an antiproton with a hydrogen
atom is directly expressed by the time-dependent wave function. For the
projectile, wave function corresponding to the specific scattering angle was
converted by two-dimensional Fourier transform from the wave functions of
corresponding to impact parameters. This wave function shows how the ejected
electron probability density distribution varies with time. We are shown that
the calculation of the fully differential cross section of ionization can be
directly determined by the local value of the wave function without the need to
calculate the spatial integral for calculating the transition amplitude. It has
been shown that the direct determination of the fully differential cross
section by this time-dependent wave function is in good agreement with the
results of determined the traditional method is by the transition amplitude.


  We give an exact solution to the Kolmogorov equation describing genetic drift
for an arbitrary number of alleles at a given locus. This is achieved by
finding a change of variable which makes the equation separable, and therefore
reduces the problem with an arbitrary number of alleles to the solution of a
set of equations that are essentially no more complicated than that found in
the two-allele case. The same change of variable also renders the Kolmogorov
equation with the effect of mutations added separable, as long as the mutation
matrix has equal entries in each row. Thus this case can also be solved exactly
for an arbitrary number of alleles. The general solution, which is in the form
of a probability distribution, is in agreement with the previously known
results--which were for the cases of two and three alleles only. Results are
also given for a wide range of other quantities of interest, such as the
probabilities of extinction of various numbers of alleles, mean times to these
extinctions, and the means and variances of the allele frequencies. To aid
dissemination, these results are presented in two stages: first of all they are
given without derivations and too much mathematical detail, and then
subsequently derivations and a more technical discussion are provided.


  Exact solutions of the perturbations equations in the magnetized LambdaCDM
scenario are presented. They apply during the dark ages and, more specifically,
after the baryons are freed from the drag of the photons. The magnetized growth
rate of matter perturbations is compared with the growth index obtained in the
concordance paradigm and under the assumption that dark energy does not cluster
for a redshift window ranging from the epoch of reionization to the stage of
dark-energy dominance. The constraints derived from this analysis are shown to
be qualitatively complementary and quantitatively competitive with the bounds
stemming from the analysis of the distortion patterns induced by the magnetized
adiabatic mode on the temperature and polarization anisotropies of the Cosmic
Microwave Background.


  We present a detailed analysis of the surface brightness distribution of the
brightest cluster galaxy (BCG) in each of 24 galaxy clusters at 0.03<z<0.13. We
use two-dimensional profile fitting to model the surface brightness out to
r=300 kpc for each BCG, comparing r^{1/4}, r^{1/n}, and double r^{1/4} models.
We obtain statistically superior fits using a two component model consisting of
a pair of r^{1/4} profiles with independent scale lengths, ellipticities, and
orientations. The two component model can simply reproduce the observed
position angle and ellipticity gradients, which cannot generally be explained
purely by triaxiality. The inner component of our two component model has
properties similar to a typical massive elliptical galaxy and is clearly
associated with the BCG. The outer component is 10-40 times larger in scale,
has ~10 times the total luminosity of the inner component, and exhibits a
steeper <\mu>-r_e relation than that of the elliptical fundamental plane. We
interpret this outer component as a population of intracluster stars tracing
the cluster potential. The two components are strongly aligned
(|\Delta\theta|<10\degr) in roughly 40% of the clusters. When they are not
aligned, the components tend toward high degrees of misalignment, suggesting
that accretion of infalling material may change the orientation of some BCGs
for a time. The extent of the outer component and its similar elongation to
published cluster galaxy distributions indicates that the evolution of the
intracluster light is tied to the cluster as a whole rather than to the BCG.


  In the conventional theory of density wave ordering in metals, the onset of
spin density wave (SDW) order co-incides with the reconstruction of the Fermi
surfaces into small 'pockets'. We present models which display this transition,
while also displaying an alternative route between these phases via an
intermediate phase with topological order, no broken symmetry, and pocket Fermi
surfaces. The models involve coupling emergent gauge fields to a fractionalized
SDW order, but retain the canonical electron operator in the underlying
Hamiltonian. We establish an intimate connection between the suppression of
certain defects in the SDW order, and the presence of Fermi surface sizes
distinct from the Luttinger value in Fermi liquids. We discuss the relevance of
such models to the physics of the hole-doped cuprates near optimal doping.


  We construct frames adapted to a given cover of the time-frequency or
time-scale plane. The main feature is that we allow for quite general and
possibly irregular covers. The frame members are obtained by maximizing their
concentration in the respective regions of phase-space. We present applications
in time-frequency, wavelet and Gabor analysis.


  We use an elliptic system of equations with complex coefficients for a set of
complex-valued tensor fields as a tool to construct infinite-dimensional
families of non-singular stationary black holes, real-valued Lorentzian
solutions of the Einstein-Maxwell-dilaton-scalar
fields-Yang-Mills-Higgs-Chern-Simons-$f(R)$ equations with a negative
cosmological constant. The families include an infinite-dimensional family of
solutions with the usual AdS conformal structure at conformal infinity.


  The kinematic dynamo (KD) describes the growth of magnetic fields generated
by the flow of a conducting medium in the limit of vanishing backaction of the
fields onto the flow. The KD is therefore an important model system for
understanding astrophysical magnetism. Here, the mathematical correspondence
between the KD and a specific stochastic differential equation (SDE) viewed
from the perspective of the supersymmetric theory of stochastics (STS) is
discussed. The STS is a novel, approximation-free framework to investigate
SDEs. The correspondence reported here permits insights from the STS to be
applied to the theory of KD and vice versa. It was previously known that the
fast KD in the idealistic limit of no magnetic diffusion requires chaotic
flows. The KD-STS correspondence shows that this is also true for the diffusive
KD. From the STS perspective, the KD possesses a topological supersymmetry and
the dynamo effect can be viewed as its spontaneous breakdown. This
supersymmetry breaking can be regarded as the stochastic generalization of the
concept of dynamical chaos. As this supersymmetry breaking happens in both the
diffusive and the non-diffusive case, the necessity of the underlying SDE being
chaotic is given in either case. The observed exponentially growing and
oscillating KD modes prove physically that dynamical spectra of the STS
evolution operator that break the topological supersymmetry exist with both,
real and complex ground state eigenvalues. Finally, we comment on the
non-existence of dynamos for scalar quantities.


  We propose a scheme for generating multipartite entangled coherent states via
entanglement swapping, with an example of a physical realization in ion traps.
Bipartite entanglement of these multipartite states is quantified by the
concurrence. We also use the $N$--tangle to compute multipartite entanglement
for certain systems. Finally we establish that these results for entanglement
can be applied to more general multipartite entangled nonorthogonal states.


  We present the results of numerical analysis of Gauss-Bessel beam reflection
from a dielectric film under different angles of incidence. A transverse shift
of the beam under the orbital momentum sign change is observed. The value of
the shift is independent of the polarization state of the incident beam.


  We consider a stochastic volatility model where the dynamics of the
volatility are described by a linear function of the (time extended) signature
of a primary process which is supposed to be a polynomial diffusion. We obtain
closed form expressions for the VIX squared, exploiting the fact that the
truncated signature of a polynomial diffusion is again a polynomial diffusion.
Adding to such a primary process the Brownian motion driving the stock price,
allows then to express both the log-price and the VIX squared as linear
functions of the signature of the corresponding augmented process. This feature
can then be efficiently used for pricing and calibration purposes. Indeed, as
the signature samples can be easily precomputed, the calibration task can be
split into an offline sampling and a standard optimization. We also propose a
Fourier pricing approach for both VIX and SPX options exploiting that the
signature of the augmented primary process is an infinite dimensional affine
process. For both the SPX and VIX options we obtain highly accurate calibration
results, showing that this model class allows to solve the joint calibration
problem without adding jumps or rough volatility.


  We have observed the central 45' region of the Galaxy at 620 MHz band of the
Giant Metrewave Radio Telescope (GMRT) in radio continuum, and measured the
polarisation properties of 64 small diameter background extragalactic sources
seen through the -6 deg < l < 6 deg, -2 deg < b < 2 deg region with the
Australia Telescope Compact Array (ATCA) and the Very Large Array (VLA). Our
620 MHz observations show that Sgr A* is located behind the HII region Sgr A
West. Using the ATCA and the VLA observations, we measured the Faraday rotation
measure (RM) of the polarised sources. The measured RMs are mostly positive,
and show no reversal of sign across the rotation axis of the Galaxy. This rules
out any circularly symmetric model of magnetic field in the region. We estimate
the magnetic field strength in the region to be ~10 microGauss, which raises
doubts against an all pervasive milliGauss field in the central few hundred pc
of the Galaxy.


  In order to establish a correspondence between the reformulation of quantum
mechanics without potential function and the conventional quantum mechanics; we
obtained the potential function of the New Wilson - Racah quantum system in [3]
using any of the proposed formulas in [4]. To achieve this, we used the matrix
elements of the potential function and the basis element of the configuration
space.


  We study a modified non-linear Schroedinger equation on a 2 dimensional
sphere with radius R aiming to describe electron-phonon interactions on
fullerenes and fullerides. These electron-phonon interactions are known to be
important for the explanation of the high transition temperature of
superconducting fullerides. Like in the $R\to \infty$ limit, we are able to
construct non-spinning as well as spinning solutions which are characterised by
the number of nodes of the wave function. These solutions are closely related
to the spherical harmonic functions. For small R, we discover specific branches
of the solutions. Some of the branches survive in the $R\to\infty$ limit and
the solutions obtained on the plane ($R=\infty$) are recovered.


  In this paper, we implement exponential integrators, specifically Integrating
Factor (IF) and Exponential Time Differencing (ETD) methods, using
pseudo-spectral techniques to solve phase-field equations within a Python
framework. These exponential integrators have showcased robust performance and
accuracy when addressing stiff nonlinear partial differential equations. We
compare these integrators to the well-known implicit-explicit (IMEX) Euler
integrators used in phase-field modeling. The synergy between pseudo-spectral
techniques and exponential integrators yields significant benefits for modeling
intricate systems governed by phase-field dynamics, such as solidification
processes and pattern formation. Our comprehensive Python implementation
illustrates the effectiveness of this combined approach in solving phase-field
model equations. The results obtained from this implementation highlight the
accuracy and computational advantages of the ETD method compared to other
numerical techniques.


  The connectivity of a graph is an important parameter to measure its
reliability. Structure and substructure connectivity, component connectivity
and $k$-restricted connectivity are well-known generalizations of the concept
of connectivity, which have been extensively studied from the combinatorial
point of view. Very little result is known about their complexity other than
the recently obtained computational complexity of $k$-restricted
edge-connectivity. In this paper, we zero in on characterizing the complexity
of structure and substructure connectivity, component connectivity and
$k$-restricted connectivity of graphs, showing that they are all NP-complete.


  We investigate the possibility to measure the nonforward gluon distribution
function by means of diffractively produced \pi^+\pi^- and K^+K^- pairs in
polarized lepton nucleon scattering. The resulting cross sections are small and
are dominated by the gluonic contribution. We find relatively large spin
asymmetries, both for \pi^+\pi^- and for K^+K^- pairs.


  We study dynamical behavior of the Chinese stock markets by investigating the
statistical properties of daily ensemble returns and varieties defined
respectively as the mean and the standard deviation of the ensemble daily price
returns of a portfolio of stocks traded in China's stock markets on a given
day. The distribution of the daily ensemble returns has an exponential form in
the center and power-law tails, while the variety distribution is log-Gaussian
in the bulk followed by a power-law tail for large varieties. Based on
detrended fluctuation analysis, R/S analysis and modified R/S analysis, we find
evidence of long memory in the ensemble returns and strong evidence of long
memory in the evolution of variety.


  In this paper we consider the relationship between the Assouad and
box-counting dimension and how both behave under the operation of taking
products. We introduce the notion of `equi-homogeneity' of a set, which
requires a uniformity in the size of local covers at all lengths and at all
points. We prove that the Assouad and box-counting dimensions coincide for sets
that have equal upper and lower box-counting dimensions provided that the set
`attains' these dimensions (analogous to `s-sets' when considering the
Hausdorff dimension), and the set is equi-homogeneous. Using this fact we show
that for any $\alpha\in(0,1)$ and any $\beta,\gamma\in(0,1)$ such that $\beta +
\gamma\geq 1$ we can construct two generalised Cantor sets $C$ and $D$ such
that $\text{dim}_{B}C=\alpha\beta$, $\text{dim}_{B}D=\alpha\gamma$, and
$\text{dim}_{A}C=\text{dim}_{A}D=\text{dim}_{A}(C\times
D)=\text{dim}_{B}(C\times D)=\alpha$.


  Dineutrino modes offer promising searches for new physics. The potential
aspects of these modes are reviewed in detail. Performing a proper combination
of them, novel tests of the SM symmetries are derived. Different
phenomenological applications are worked out, including charm, beauty and
kaons, which result in novel tests of lepton universality and charged lepton
flavour conservation with flavour-summed dineutrino observables, in addition to
improved bounds on $\tau\,\ell$ couplings with $\ell=e,\mu,\tau$.


  We investigated the temperature dependence of the density-of-states in the
iron-based superconductor SmO_1-xF_xFeAs (x=0, 0.12, 0.15, 0.2) with high
resolution angle-integrated photoemission spectroscopy. The density-of-states
suppression is observed with decreasing temperature in all samples, revealing
two characteristic energy scales (10meV and 80meV). However, no obvious doping
dependence is observed. We argue that the 10meV suppression is due to an
anomalously doping-independent normal state pseudogap, which becomes the
superconducting gap once in the superconducting state; and alert the
possibility that the 80meV-scale suppression might be an artifact of the
polycrystalline samples.


  A function is strongly non-recursive (SNR) if it is eventually different from
each recursive function. We obtain hierarchy results for the mass problems
associated with computing such functions with varying growth bounds. In
particular, there is no least and no greatest Muchnik degree among those of the
form SNR$_f$ consisting of SNR functions bounded by varying recursive bounds
$f$.
  We show that the connection between SNR functions and canonically immune sets
is, in a sense, as strong as that between DNR (diagonally non-recursive)
functions and effectively immune sets. Finally, we introduce pandemic
numberings, a set-theoretic dual to immunity.


  Designing digital artifacts is not a linear, straightforward process. This is
particularly true when applying a user-centered design approach, or co-design,
with users who are unable to participate in the design process. Although the
reduced participation of a particular user group may harm the end result, the
literature on solving this issue is sparse. In this article, proxy design is
outlined as a method for involving a user group as proxy users to speak on
behalf of a group that is difficult to reach. We present a design ethnography
spanning three years at a cancer rehabilitation clinic, where digital artifacts
were designed to be used collaboratively by nurses and patients. The empirical
data were analyzed using content analysis and consisted of 20 observation days
at the clinic, six proxy design workshops, 21 telephone consultations between
patients and nurses, and log data from the digital artifact. We show that
simulated consultations, with nurses roleplaying as proxies for patients
ignited and initiated the design process and enabled an efficient in-depth
understanding of patients. Moreover, we reveal how proxy design as a method
further expanded the design. We illustrate: (1) proxy design as a method for
initiating design, (2) proxy design as an embedded element in co-design and (3)
six design guidelines that should be considered when engaging in proxy design.
The main contribution is the conceptualization of proxy design as a method that
can ignite and initiate the co-design process when important users are
unreachable, vulnerable or unable to represent themselves in the co-design
process. Based on the empirical findings from a design ethnography that
involved nurses as proxy users speaking on behalf of patients, the article
shows that roleplaying in proxy design is a fitting way of initiating the
design process, outlining proxy design as an embedded element of co-design.


  We associate a cohomological invariant to each outer action of a group on a
factor, and classify them by the invariant in the case that the group is a
countable discrete amenable group and the factor is appoximately finite
dimensional. The invariant defined for the group Out(M)=Aut(M)/Int(M) is called
the intrinsic modular obstruction. The invariant for an outer action alpha is
given as the pull back of the intrinsic modular obstruction, which is called
the modular obstruction of alpha and denoted by Ob_m(alpha). This is the first
part of the theory and presents general theory. In the case that the factor is
not of type III_0, the invariant is substantially simplified. These cases and
examples will be discussed in forthcoming paper.


  In this paper, we establish Anderson localization for the quantum kicked
rotor model. More precisely, we proved that
  \begin{equation*} H=\tan\pi\left(x_0+my_0+\frac{m(m-1)}{2}\omega\right)
\delta_{mn}+\epsilon S_\phi \end{equation*} has pure point spectrum with
exponentially decaying eigenfunctions for almost all $\omega \in DC$
(diophantine condition).


  In this paper we obtain three results concerning the geometry of complete
noncompact positively curved K\"{a}hler manifolds at infinity. The first one
states that the order of volume growth of a complete noncompact K\"{a}hler
manifold with positive bisectional curvature is at least half of the real
dimension (i.e., the complex dimension). The second one states that the
curvature of a complete noncompact K\"{a}hler manifold with positive
bisectional curvature decays at least linearly in the average sense. The third
result is concerned with the relation between the volume growth and the
curvature decay. We prove that the curvature decay of a complete noncompact
K\"{a}hler manifold with nonnegative curvature operator and with the maximal
volume growth is precisely quadratic in certain average sense.


  To alleviate the burdens on the fronthaul and reduce the transmit latency,
the device-to-device (D2D) communication is presented in cloud radio access
networks (C-RANs). Considering dynamic traffic arrivals and time-varying
channel conditions, the resource allocation in C-RANs with D2D is formulated
into a stochastic optimization problem, which is aimed at maximizing the
overall throughput subject to network stability, interference, and fronthaul
capacity constraints. Leveraging on the Lyapunov optimization technique, the
stochastic optimization problem is transformed into a delay-aware optimization
problem, which is a mixed-integer nonlinear programming problem and can be
decomposed into three subproblems: mode selection, uplink beamforming design,
and power control. An optimization solution that consists of a modified branch
and bound method as well as a weighted minimum mean square error approach has
been developed to obtain the close-to-optimal solution. Simulation results
validate that the D2D can improve throughput, decrease latency, and alleviate
the burdens of the constrained fronthaul in C-RANs. Furthermore, an average
throughput-delay tradeoff can be achieved by the proposed solution.


  The Predictive Information is the mutual information between the past and the
future, I(X_past; X_future). We hypothesize that capturing the predictive
information is useful in RL, since the ability to model what will happen next
is necessary for success on many tasks. To test our hypothesis, we train Soft
Actor-Critic (SAC) agents from pixels with an auxiliary task that learns a
compressed representation of the predictive information of the RL environment
dynamics using a contrastive version of the Conditional Entropy Bottleneck
(CEB) objective. We refer to these as Predictive Information SAC (PI-SAC)
agents. We show that PI-SAC agents can substantially improve sample efficiency
over challenging baselines on tasks from the DM Control suite of continuous
control environments. We evaluate PI-SAC agents by comparing against
uncompressed PI-SAC agents, other compressed and uncompressed agents, and SAC
agents directly trained from pixels. Our implementation is given on GitHub.


  The WMAP and Planck observations show that the quadrupole and octopole
orientations of the CMB might align with each other. We reveal that the
quadrupole--octopole alignment is a natural implication of the primordial power
spectrum in an anisotropic spacetime. The primordial power spectrum is
presented with a dipolar modulation. We obtain the privileged plane by
employing the ``power tensor'' technique. At this plane, there is the maximum
correlation between quadrupole and octopole. The probability for the alignment
is much larger than what in the isotropic universe. We find that this model
would lead to deviations from the statistical isotropy only for low--\(\ell\)
multipoles.


  Difference-in-differences is one of the most used identification strategies
in empirical work in economics. This chapter reviews a number of important,
recent developments related to difference-in-differences. First, this chapter
reviews recent work pointing out limitations of two way fixed effects
regressions (these are panel data regressions that have been the dominant
approach to implementing difference-in-differences identification strategies)
that arise in empirically relevant settings where there are more than two time
periods, variation in treatment timing across units, and treatment effect
heterogeneity. Second, this chapter reviews recently proposed alternative
approaches that are able to circumvent these issues without being substantially
more complicated to implement. Third, this chapter covers a number of
extensions to these results, paying particular attention to (i) parallel trends
assumptions that hold only after conditioning on observed covariates and (ii)
strategies to partially identify causal effect parameters in
difference-in-differences applications in cases where the parallel trends
assumption may be violated.