  We have constructed the quasi-exactly-solvable two-mode bosonic realizations
of su(2) and su(1, 1) algebra. We derive the relations leading to the
conditions for quasi-exact solvability of two-boson Hamiltonians by determining
a general procedure which maps the Schwinger representations of the su(2) and
su(1, 1) algebras to the Gelfand-Dyson representations, respectively. This
mapping allows us to study nonlinear quantum-optical systems in the framework
of quasi-exact solvability. Our approach also leads to a simple construction of
special functions of two variables which are the most appropriate functions to
study quasi-probabilities in quantum optics.


  We propose a form of gravity-matter interaction given by $\omega RT$ in the
framework of $f(R,T)$ gravity and examine the effect of such interaction in
spherically symmetric compact stars. Treating the gravity-matter coupling as a
perturbative term on the background of Starobinsky gravity, we develop a
perturbation theory for equilibrium configurations. For illustration, we take
the case of quark stars and explore their various stellar properties. We find
that the gravity-matter coupling causes an increase in the stable maximal mass
which is relevant for recent observations on binary pulsars.


  All cubic couplings in type IIB supergravity on $AdS_5\times S^5$ that
involve two scalar fields $s^I$ that are mixtures of the five form field
strength on $S^5$ and the trace of the graviton on $S^5$ are derived by using
the covariant equations of motion and the quadratic action for type IIB
supergravity on $AdS_5\times S^5$. All corresponding three-point functions in
SYM$_4$ are calculated in the supergravity approximation. It is pointed out
that the scalars $s^I$ correspond not to the chiral primary operators in the
${\cal N}=4$ SYM but rather to a proper extension of the operators.


  We investigated the statistical properties of the weight distributions of
Japanese children who were born in 1996, from recent data. The weights of 16-
and 17-year-old male children have a lognormal distribution with a power-like
tail, which is best modeled by the double Pareto distribution. The emergence of
the power-like tail may be attributed to the low probability that an obese
person will attain a normal weight.


  Strong and weak (1, 3) homotopies are equivalence relations on knot
projections, defined by the first flat Reidemeister move and each of two
different types of the third flat Reidemeister moves. In this paper, we
introduce the cross chord number that is the minimal number of double points of
chords of a chord diagram. Cross chord numbers induce a strong (1, 3)
invariant. We show that Hanaki's trivializing number is a weak (1, 3)
invariant. We give a complete classification of knot projections having
trivializing number two up to the first flat Reidemeister moves using cross
chord numbers and the positive resolutions of double points. Two knot
projections with trivializing number two are both weak (1, 3) homotopy
equivalent and strong (1, 3) homotopy equivalent if and only if they can be
related by only the first flat Reidemeister moves. Finally, we determine the
strong (1, 3) homotopy equivalence class containing the trivial knot projection
and other classes of knot projections.


  We analyze the electronic properties of a simple stacking defect in Bernal
graphite. We show that a bound state forms, which disperses as $|\bfk-\bfK|^3$
in the vicinity of either of the two inequivalent zone corners $\bfK$. In the
presence of a strong c-axis magnetic field, this bound state develops a Landau
level structure which for low energies behaves as $E\nd_n\propto |n B|^{3/2}$.
We show that buried stacking faults have observable consequences for surface
spectroscopy, and we discuss the implications for the three-dimensional quantum
Hall effect (3DQHE). We also analyze the Landau level structure and chiral
surface states of rhombohedral graphite, and show that, when doped, it should
exhibit multiple 3DQHE plateaus at modest fields.


  Existential positive formulas form a fragment of first-order logic that
includes and is semantically equivalent to unions of conjunctive queries, one
of the most important and well-studied classes of queries in database theory.
We consider the complexity of counting the number of answers to existential
positive formulas on finite structures and give a trichotomy theorem on query
classes, in the setting of bounded arity. This theorem generalizes and unifies
several known results on the complexity of conjunctive queries and unions of
conjunctive queries.


  For equations $ x'(t) = -x(t) + \zeta f(x(t-h)), x \in \R, f'(0)= -1, \zeta >
0,$ with $C^3$-nonlinearity $f$ which has negative Schwarzian derivative and
satisfies $xf(x) < 0$ for $x\not=0$, we prove convergence of all solutions to
zero when both $\zeta -1 >0$ and $h(\zeta-1)^{1/8}$ are less than some constant
(independent on $h,\zeta$). This result gives additional insight to the
conjecture about the equivalence between local and global asymptotical
stabilities in the Mackey-Glass type delay differential equations.


  Non-local communication among position based qubits is described for the
system of the quantum electromagnetic resonator entangled to two semiconductor
electrostatic qubits via interaction between matter and radiation by
Jaynes-Cummings tight-binding Hamiltonian. Principle of quantum communication
between position dependent qubits is explained with usage of simplistic model.
All stages of derivation are presented. The case of two semiconductor
position-dependent qubits interacting with quantum electromagnetic cavity is
discussed and general form of tight-binding Hamiltonian is derived with
renormalized tight-binding coefficients. The obtained results bring foundation
for the construction of quantum networks and prospect of quantum internet. The
presented work brings the perspective of creation of quantum communication
networks between electrostatic position based qubits that are implementable in
semiconductor single electron devices and in particular in current CMOS
technologies. The case of two capacitively interacting qubits biased to quantum
electromagnetic cavity is also described.


  An equation of Monge-Amp\`ere type has, for the first time, been solved
numerically on the surface of the sphere in order to generate optimally
transported (OT) meshes, equidistributed with respect to a monitor function.
Optimal transport generates meshes that keep the same connectivity as the
original mesh, making them suitable for r-adaptive simulations, in which the
equations of motion can be solved in a moving frame of reference in order to
avoid mapping the solution between old and new meshes and to avoid load
balancing problems on parallel computers.
  The semi-implicit solution of the Monge-Amp\`ere type equation involves a new
linearisation of the Hessian term, and exponential maps are used to map from
old to new meshes on the sphere. The determinant of the Hessian is evaluated as
the change in volume between old and new mesh cells, rather than using
numerical approximations to the gradients.
  OT meshes are generated to compare with centroidal Voronoi tesselations on
the sphere and are found to have advantages and disadvantages; OT
equidistribution is more accurate, the number of iterations to convergence is
independent of the mesh size, face skewness is reduced and the connectivity
does not change. However anisotropy is higher and the OT meshes are
non-orthogonal.
  It is shown that optimal transport on the sphere leads to meshes that do not
tangle. However, tangling can be introduced by numerical errors in calculating
the gradient of the mesh potential. Methods for alleviating this problem are
explored.
  Finally, OT meshes are generated using observed precipitation as a monitor
function, in order to demonstrate the potential power of the technique.


  We introduce a model of interacting lattices at different resolutions driven
by the two-dimensional Ising dynamics with a nearest-neighbor interaction. We
study this model both with tools borrowed from equilibrium statistical
mechanics as well as non-equilibrium thermodynamics. Our findings show that
this model keeps the signature of the equilibrium phase transition. Moreover
the critical temperature of the equilibrium models correspond to the state
maximizing the entropy and delimits two out-of-equilibrium regimes, one
satisfying the Onsager relations for systems close to equilibrium and one
resembling convective turbulent states. Since the model preserves the entropy
and energy fluxes in the scale space, it seems a good candidate for parametric
studies of out-of-equilibrium turbulent systems.


  We study degree of irrationality of quasismooth anticanonically embedded
weighted Fano 3-fold hypersurfaces that have terminal singularities.


  This article introduces a set of distance education astronomy laboratory
exercises for use by college students and instructors and discuss first usage
results. This General Astronomy Education Source (GEAS) exercise set contains
eight two-week projects designed to guide students through both core content
and mathematical applications of general astronomy material. Projects are
divided between hands-on activities and computer-aided analyses of modern
astronomical data. The suite of online resources includes student and
instructor guides, laboratory report templates, learning objectives, video
tutorials, plotting tools, and web-based applications that allow students to
analyze both images and spectra of astronomical objects. A pilot usage study
indicates that distance learners using these materials perform as well or
better than a comparison cohort of on-campus students. We are actively seeking
collaborators to use these resources in astronomy courses and other educational
venues.


  J/psi suppression was proposed more than 25 years ago as an unambiguous
signature for the formation of the Quark Gluon Plasma in relativistic heavy ion
collisions. After intensive efforts, both experimental and theoretical, the
quarkonium saga remains exciting, producing surprising results and not fully
understood. This talk focuses on recent results on quarkonium production at
RHIC and the LHC.


  Based on some important properties of $dS$ space, we present a Beltrami model
${\cal B}_\Lambda$ that may shed light on the observable puzzle of $dS$ space
and the paradox between the special relativity principle and cosmological
principle. In ${\cal B}_\Lambda$, there are inertial-type coordinates and
inertial-type observers. Thus, the classical observables can be defined for
test particles and light signals. In addition, by choosing the definition of
simultaneity the Beltrami metric is transformed to the Robertson-Walker-like
metric. It is of positive spatial curvature of order $\Lambda$. This is more or
less indicated already by the CMB power spectrum from WMAP and should be
further confirmed by its data in large scale.


  Quasi-static transformations, or slow quenches, of many-body quantum systems
across quantum critical points create topological defects. The Kibble-Zurek
mechanism regulates the appearance of defects in a local quantum system through
a classical combinatorial process. However, long-range interactions disrupt the
conventional Kibble-Zurek scaling and lead to a density of defects that is
independent of the rate of the transformation. In this study, we analytically
determine the complete full counting statistics of defects generated by slow
annealing a strong long-range system across its quantum critical point. We
demonstrate that the mechanism of defect generation in long-range systems is a
purely quantum process with no classical equivalent. Furthermore, universality
is not only observed in the defect density but also in all the moments of the
distribution. Our findings can be tested on various experimental platforms,
including Rydberg gases and trapped ions.


  Automatic question generation can benefit many applications ranging from
dialogue systems to reading comprehension. While questions are often asked with
respect to long documents, there are many challenges with modeling such long
documents. Many existing techniques generate questions by effectively looking
at one sentence at a time, leading to questions that are easy and not
reflective of the human process of question generation. Our goal is to
incorporate interactions across multiple sentences to generate realistic
questions for long documents. In order to link a broad document context to the
target answer, we represent the relevant context via a multi-stage attention
mechanism, which forms the foundation of a sequence to sequence model. We
outperform state-of-the-art methods on question generation on three
question-answering datasets -- SQuAD, MS MARCO and NewsQA.


  The objectives of this research were 1) to develop the application for
learning place value, 2) to determine the efficiency of developed application,
3) to compare academic achievement to compare academic achievement between
pre-lesson and post-lesson of students who learned with the developed
application about place value, 4) to compare academic achievement between
students who learned place value by the developed application and through
traditional method during post-lesson, 5) to compare retention of academic
achievement of application for learning place value after 2 weeks, and 6) to
find satisfactory of student who learned the application for learning place
value. The sample group selected through purposive sampling was 5 content
specialists and 400 pratomsuksa 1 students.


  Musculoskeletal disorder (MSD) is one of the major health problems in
physical work especially in manual handling jobs. In several literatures,
muscle fatigue is considered to be closely related to MSD, especially for
muscle related disorders. In addition to many existing analysis techniques for
muscle fatigue assessment and MSD risk analysis, in this paper, a new muscle
fatigue model was proposed. The new proposed model reflects the influence of
external load, workload history, and individual differences. This model is
simple in mathematics and can be easily applied in realtime calculation, such
as the application in realtime virtual work simulation and evaluation. The new
model was mathematically validated with 24 existing static models by comparing
the calculated METs, and qualitatively or quantitatively validated with 3
existing dynamic models. The proposed model shows high or moderate similarities
in predicting the METs with all the 24 static models. Validation results with
the three dynamic models were also promising. The main limitation of the model
is that it still lacks experimental validation for more dynamic situations.
Relevance to industry Muscle fatigue is one of the main reasons causing MSDs in
industry, especially for physical work. Correct evaluation of muscle fatigue is
necessary to determine work-rest regimens and reduce the risks of MSD.


  We consider an equation of the geodesic deviation appearing in the problem of
gravitational wave detection in an environment of gravitons. We investigate a
state-dependent graviton noise (as discussed in a recent paper of
Parikh,Wilczek and Zahariade) from the point of view of the Feynman integral
and stochastic differential equations. The evolution of the density matrix and
the transition probability in an environment of gravitons is obtained. We
express the time evolution by a solution of a stochastic geodesic deviation
equation with a noise dependent on the quantum state of the gravitational
field.


  We review recent results on the nonlinear development of thermal instability
in the context of the turbulent atomic interstellar medium (ISM). First, we
pre- sent a brief summary of the linear theory, remarking that, in the atomic
ISM, the wave mode is stable at small scales. Next, we revisit the growth of
isolated entropy perturbations in initially unstable gas, as a function of the
ratio $\eta$ of the cooling to the dynamical crossing times. Third, we consider
the evolution of {\it velocity} perturbations. These correspond to the wave
mode, and are stable at moderate amplitudes and small scales, as confirmed
numerically. Fourth, we consider the behavior of magnetic pressure in turbulent
regimes. We propose that recent findings of a poor B-rho correlation at low rho
are due to the different B-rho scalings for the slow and fast modes of non-
linear MHD waves. This implies that, in fully turbulent regimes, the magnetic
field may not be a very efficient source of pressure, and that polytropic de-
scriptions of magnetic pressure are probably not adequate. Finally, we discuss
simulations of the ISM (and resolution issues) concerned with the possibility
of significant amounts of gas being in the ``lukewarm'' temperature range be-
tween the warm and cold stable phases. The mass fraction in this range in-
creases, and the phase segregation decreases, as smaller scales are considered.
We attribute this to the enhanced stability of moderate, adiabatic-like veloc-
ity fluctuations with $\eta \gg 1$, to the recycling of gas from the dense to
the diffuse phase by stellar energy injection, and to the magnetic field not
being strongly turbulent there, possibly providing additional stability. Final-
ly, we suggest that the lukewarm gas can be observationally distinguished
through simultaneous determination of two of its thermodynamic variables.


  Topological superfluids are of technological relevance since they are
believed to host Majorana bound states, a powerful resource for quantum
computation and memory. Here we propose to realize topological superfluidity
with fermionic atoms in an optical lattice. We consider a situation where atoms
in two internal states experience different lattice potentials: one species is
localized and the other itinerant, and show how quantum fluctuations of the
localized fermions give rise to an attraction and strong spin-orbit coupling in
the itinerant band. At low temperature, these effects stabilize a topological
superfluid of mobile atoms even if their bare interactions are repulsive. This
emergent state can be engineered with ${}^{87}$Sr atoms in a superlattice with
a dimerized unit cell. To probe its unique properties we describe protocols
that use high spectral resolution and controllability of the Sr clock
transition, such as momentum-resolved spectroscopy and supercurrent response to
a synthetic (laser-induced) magnetic field.


  Volt/var control (VVC) of smart PV inverter is becoming one of the most
popular solutions to address the voltage challenges associated with high PV
penetration. This work focuses on the local droop VVC recommended by the grid
integration standards IEEE1547, rule21 and addresses their major challenges
i.e. appropriate parameters selection under changing conditions, and the
control being vulnerable to instability (or voltage oscillations) and
significant steady state error (SSE). This is achieved by proposing a two-layer
local real-time adaptive VVC that has two major features i.e. a) it is able to
ensure both low SSE and control stability simultaneously without compromising
either, and b) it dynamically adapts its parameters to ensure good performance
in a wide range of external disturbances such as sudden cloud cover, cloud
intermittency, and substation voltage changes. A theoretical analysis and
convergence proof of the proposed control is also discussed. The proposed
control is implementation friendly as it fits well within the integration
standard framework and depends only on the local bus information. The
performance is compared with the existing droop VVC methods in several
scenarios on a large unbalanced 3-phase feeder with detailed secondary side
modeling.


  We provide numerical evidence that the perturbative spectrum of anomalous
dimensions in maximally supersymmetric SU(N) Yang-Mills theory is chaotic at
finite values of N. We calculate the probability distribution of one-loop level
spacings for subsectors of the theory and show that for large N it is given by
the Poisson distribution of integrable models, while at finite values it is the
Wigner-Dyson distribution of the Gaussian orthogonal ensemble random matrix
theory. We extend these results to two-loop order and to a one-parameter family
of deformations. We further study the spectral rigidity for these models and
show that it is also well described by random matrix theory. Finally we
demonstrate that the finite-N eigenvectors possess properties of chaotic
states.


  Complete axiomatizations and exponential-time decision procedures are
provided for reasoning about knowledge and common knowledge when there are
infinitely many agents. The results show that reasoning about knowledge and
common knowledge with infinitely many agents is no harder than when there are
finitely many agents, provided that we can check the cardinality of certain set
differences G - G', where G and G' are sets of agents. Since our complexity
results are independent of the cardinality of the sets G involved, they
represent improvements over the previous results even with the sets of agents
involved are finite. Moreover, our results make clear the extent to which
issues of complexity and completeness depend on how the sets of agents involved
are represented.


  We analyze the performance of source-seeking dynamics involving either a
single vehicle or multiple flocking-vehicles embedded in an underlying strongly
convex scalar field with gradient based forcing terms. For multiple vehicles
under flocking dynamics embedded in quadratic fields, we show that the dynamics
of the center of mass are equivalent to the dynamics of a single agent. We
leverage the recently developed framework of $\alpha$-integral quadratic
constraints (IQCs) to obtain convergence rate estimates. We first present a
derivation of \textit{hard} Zames-Falb (ZF) $\alpha$-IQCs involving general
non-causal multipliers based on purely time-domain arguments and show that a
parameterization of the ZF multiplier, suggested in the literature for the
standard version of the ZF IQCs, can be adapted to the $\alpha$-IQCs setting to
obtain quasi-convex programs for estimating convergence rates. Owing to the
time-domain arguments, we can seamlessly extend these results to linear
parameter varying (LPV) vehicles possibly opening the doors to non-linear
vehicle models with quasi-LPV representations. We illustrate the theoretical
results on a linear time invariant (LTI) model of a quadrotor, a non-minimum
phase LTI plant and two LPV examples which show a clear benefit of using
general non-causal dynamic multipliers to drastically reduce conservatism.


  A key problem of eukaryotic cell motility is the signaling mechanism of
chemoattractant gradient sensing. Recent experiments have revealed the
molecular correlate of gradient sensing: Frontness molecules, such as PI3P and
Rac, localize at the front end of the cell, and backness molecules, such as Rho
and myosin II, accumulate at the back of the cell. Importantly, this
frontness-backness polarization occurs "spontaneously" even if the cells are
exposed to uniform chemoattractant profiles. The spontaneous polarization
suggests that the gradient sensing machinery undergoes a Turing bifurcation.
This has led to several classical activator-inhibitor and activator-substrate
models which identify the frontness molecules with the activator. Conspicuously
absent from these models is any accounting of the backness molecules. This
stands in sharp contrast to experiments which show that the backness pathways
inhibit the frontness pathways. Here, we formulate a model based on the
mutually inhibitory interaction between the frontness and backness pathways.
The model builds upon the mutual inhibition model proposed by Bourne and
coworkers (Xu et al, Cell, 114, 201--214, 2003). We show that mutual inhibition
alone, without the help of any positive feedback, can trigger spontaneous
polarization of the frontness and backness pathways. The spatial distribution
of the frontness and backness molecules in response to inhbition and activation
of the frontness and backness pathways are consistent with those observed in
experiments. Furthermore, depending on the parameter values, the model yields
spatial distributions corresponding to chemoattraction (frontness pathways
in-phase with the external gradient) and chemorepulsion (frontness pathways
out-of-phase with the external gradient).


  We construct infinitely many new 1-parameter families of simply connected
complete noncompact G_2-manifolds with controlled geometry at infinity. The
generic member of each family has so-called asymptotically locally conical
(ALC) geometry. However, the nature of the asymptotic geometry changes at two
special parameter values: at one special value we obtain a unique member of
each family with asymptotically conical (AC) geometry; on approach to the other
special parameter value the family of metrics collapses to an AC Calabi-Yau
3-fold. Our infinitely many new diffeomorphism types of AC G_2-manifolds are
particularly noteworthy: previously the three examples constructed by Bryant
and Salamon in 1989 furnished the only known simply connected AC G_2-manifolds.
  We also construct a closely related conically singular G_2 holonomy space:
away from a single isolated conical singularity, where the geometry becomes
asymptotic to the G_2-cone over the standard nearly K\"ahler structure on the
product of a pair of 3-spheres, the metric is smooth and it has ALC geometry at
infinity. We argue that this conically singular ALC G_2-space is the natural
G_2 analogue of the Taub-NUT metric in 4-dimensional hyperKaehler geometry and
that our new AC G_2-metrics are all analogues of the Eguchi-Hanson metric, the
simplest ALE hyperK\"ahler manifold. Like the Taub-NUT and Eguchi-Hanson
metrics, all our examples are cohomogeneity one, i.e. they admit an isometric
Lie group action whose generic orbit has codimension one.


  We construct certain eigenfunctions of the Calogero-Sutherland hamiltonian
for particles on a circle, with mixed boundary conditions. That is, the
behavior of the eigenfunction, as neighbouring particles collide, depend on the
pair of colliding particles. This behavior is generically a linear combination
of two types of power laws, depending on the statistics of the particles
involved. For fixed ratio of each type at each pair of neighboring particles,
there is an eigenfunction, the ground state, with lowest energy, and there is a
discrete set of eigenstates and eigenvalues, the excited states and the
energies above this ground state. We find the ground state and special excited
states along with their energies in a certain class of mixed boundary
conditions, interpreted as having pairs of neighboring bosons and other
particles being fermions. These particular eigenfunctions are characterised by
the fact that they are in direct correspondence with correlation functions in
boundary conformal field theory. We expect that they have applications to
measures on certain configurations of curves in the statistical O(n) loop
model. The derivation, although completely independent from results of
conformal field theory, uses ideas from the "Coulomb gas" formulation.


  Precise and efficient automated identification of Gastrointestinal (GI) tract
diseases can help doctors treat more patients and improve the rate of disease
detection and identification. Currently, automatic analysis of diseases in the
GI tract is a hot topic in both computer science and medical-related journals.
Nevertheless, the evaluation of such an automatic analysis is often incomplete
or simply wrong. Algorithms are often only tested on small and biased datasets,
and cross-dataset evaluations are rarely performed. A clear understanding of
evaluation metrics and machine learning models with cross datasets is crucial
to bring research in the field to a new quality level. Towards this goal, we
present comprehensive evaluations of five distinct machine learning models
using Global Features and Deep Neural Networks that can classify 16 different
key types of GI tract conditions, including pathological findings, anatomical
landmarks, polyp removal conditions, and normal findings from images captured
by common GI tract examination instruments. In our evaluation, we introduce
performance hexagons using six performance metrics such as recall, precision,
specificity, accuracy, F1-score, and Matthews Correlation Coefficient to
demonstrate how to determine the real capabilities of models rather than
evaluating them shallowly. Furthermore, we perform cross-dataset evaluations
using different datasets for training and testing. With these cross-dataset
evaluations, we demonstrate the challenge of actually building a generalizable
model that could be used across different hospitals. Our experiments clearly
show that more sophisticated performance metrics and evaluation methods need to
be applied to get reliable models rather than depending on evaluations of the
splits of the same dataset, i.e., the performance metrics should always be
interpreted together rather than relying on a single metric.


  Nowadays, there are many applications of text mining over corpora from
different languages. However, most of them are based on texts in prose, lacking
applications that work with poetry texts. An example of an application of text
mining in poetry is the usage of features derived from their individual words
in order to capture the lexical, sublexical and interlexical meaning, and infer
the General Affective Meaning (GAM) of the text. However, even though this
proposal has been proved as useful for poetry in some languages, there is a
lack of studies for both Spanish poetry and for highly-structured poetic
compositions such as sonnets. This article presents a study over an annotated
corpus of Spanish sonnets, in order to analyse if it is possible to build
features from their individual words for predicting their GAM. The purpose of
this is to model sonnets at an affective level. The article also analyses the
relationship between the GAM of the sonnets and the content itself. For this,
we consider the content from a psychological perspective, identifying with tags
when a sonnet is related to a specific term. Then, we study how GAM changes
according to each of those psychological terms.
  The corpus used contains 274 Spanish sonnets from authors of different
centuries, from 15th to 19th. This corpus was annotated by different domain
experts. The experts annotated the poems with affective and lexico-semantic
features, as well as with domain concepts that belong to psychology. Thanks to
this, the corpus of sonnets can be used in different applications, such as
poetry recommender systems, personality text mining studies of the authors, or
the usage of poetry for therapeutic purposes.


  The honeycomb Kitaev spin model provides a quantum spin liquid in the ground
state, where the spin excitations are fractionalized into itinerant and
localized Majorana fermions; the former spectrum has a broad continuum ranging
up to a high energy, while the latter has a sharp peak at a low energy. Despite
tremendous efforts, it remains elusive to clearly identify these distinct
Majorana excitations in experiments. Here we show their manifestation in the
time evolution after quenching the magnetic field, by using the time-dependent
Majorana mean-field theory for both the ferromagnetic and antiferromagnetic
Kitaev models. We find that the transient spin dynamics from the quantum spin
liquid states is qualitatively different from the conventional spin precessions
by the quench from the high-field forced-ferromagnetic state. We obtain
peculiar time evolutions with distinct time scales, i.e., short-time decay of
high-energy components associated with the itinerant Majorana excitations, and
long-lived excitations at a low energy by the localized ones. These peculiar
behaviors are caused by the energy transfer between the two Majorana
quasiparticles after the field quench. Moreover, we find that the Majorana
semimetal with the point nodes in equilibrium turns into a Majorana metal with
the transient "Fermi surfaces" by the energy transfer. In particular, for the
quench from the intermediate-field quantum spin liquid in the antiferromagnetic
Kitaev model, the Fermi surfaces change their topology in the time evolution,
which is regarded as a dynamical version of the Majorana "Lifshitz transition".
Our results unveil that the real-time dynamics provides another route to not
only the identification of the fractional Majorana excitations in candidate
materials of Kitaev magnets but also unprecedented quantum phases that cannot
be stabilized as the equilibrium states.


  Strongly squeezed light at telecommunication wavelengths is the necessary
resource for one-sided device-independent quantum key distribution via fibre
networks. Reducing the optical pump power that is required for its generation
will advance this quantum technology towards efficient out-of-laboratory
operation. Here, we investigate the second-harmonic pump power requirement for
parametric generation of continuous-wave squeezed vacuum states at 1550nm in a
state-of-the-art doubly-resonant standing-wave PPKTP cavity setup. We use
coarse adjustment of the Gouy phase via the cavity length together with
temperature fine-tuning for simultaneously achieving double resonance and
(quasi) phase matching, and observe a squeeze factor of 13dB at 1550nm from
just 12mW external pump power at 775nm. We anticipate that optimizing the
cavity coupler reflectivity will reduce the external pump power to 3mW, without
reducing the squeeze factor.


  The magnetic fields in heavy-ion collisions are important ingredients for
many interesting phenomena, such as the Chiral Magnetic Effect, Chiral Magnetic
Wave, the directed flow $v_1$ of $D^0$ mesons and the splitting of the spin
polarization of the $\Lambda$/$\bar{\Lambda}$. Quantitative studies of these
phenomena however suffer from limited understanding on the dynamical evolution
of these fields in the medium created by the collisions, which remains a
critical and challenging problem. The initial magnetic fields from the
colliding nuclei decay very fast in the vacuum but their lifetime could be
extended through medium response due to electrically conducting quarks and
antiquarks. Here we perform a detailed analysis of such medium effect on the
dynamical magnetic fields by numerically solving the Maxwell's equations
concurrently with the expanding medium described by viscous hydrodynamics,
under the assumption of negligible back reaction of the fields on the fluid
evolution. Our results suggest a considerable enhancement of late time magnetic
fields, the magnitude of which depends sensitively on the fireball expansion as
well as the medium electric conductivity both before and during hydrodynamic
stage.


  We propose a scenario which can explain large lepton asymmetry and small
baryon asymmetry simultaneously. Large lepton asymmetry is generated through
Affleck-Dine (AD) mechanism and almost all the produced lepton numbers are
absorbed into Q-balls (L-balls). If the lifetime of the L-balls is longer than
the onset of electroweak phase transition but shorter than the epoch of big
bang nucleosynthesis (BBN), the large lepton asymmetry in the L-balls is
protected from sphaleron effects. On the other hand, small (negative) lepton
numbers are evaporated from the L-balls due to thermal effects, which are
converted into the observed small baryon asymmetry by virtue of sphaleron
effects. Large and positive lepton asymmetry of electron type is often
requested from BBN. In our scenario, choosing an appropriate flat direction in
the minimal supersymmetric standard model (MSSM), we can produce positive
lepton asymmetry of electron type but totally negative lepton asymmetry.


  We study the role of ensemble averaging in holography by exploring the
relation between the universal late time behavior of the spectral form factor
and the second Renyi entropy of a thermal mixed state of the doubled system.
Both quantities receive contributions from wormhole saddle-points: in the
former case they lead to non-factorization while in the latter context they
quantify decoherence due to the interaction with an environment. Our reasoning
indicates that the space-time continuity responsible for non-factorization and
space-time continuity through entanglement are in direct competition with each
other. In an accompanying paper, we examine this dual relationship in a general
class of 1D quantum systems with the help of a simple geometric path integral
prescription.


  A perturbative approach to quantum field theory involves the computation of
loop integrals, as soon as one goes beyond the leading term in the perturbative
expansion. First I review standard techniques for the computation of loop
integrals. In a second part I discuss more advanced algorithms. For these
algorithms algebraic methods play an important role. A special section is
devoted to multiple polylogarithms.
  I tried to make these notes self-contained and accessible both to physicists
and mathematicians.


  Feza G\"ursey was a brilliant physicist who loved symmetries and beautiful
mathematical structures such as group theory and division algebras. In this
centenary year, I give a brief review of some of his contributions and then
zero-in on group theory and discuss how it can give us a new perspective on a
centuries-old topic, namely, fluid dynamics, including new facets such as the
chiral magnetic effect. \vskip .1in \noindent This is a slightly edited and
enhanced version of a colloquium at the Middle East Technical University on
December 9, 2021, which was organized in celebration of the centenary of Feza
G\"ursey. The video of the presentation can be accessed by following the link
given at http://www.physics.metu.edu.tr/Department/FezaGursey2021 or by
clicking https://www.youtube.com/watch?v=DstVVuOlqGk for direct access.


  We study compactness properties of the set of conformally flat singular
metrics with constant, positive sixth order Q-curvature on a finitely punctured
sphere. Based on a recent classification of the local asymptotic behavior near
isolated singularities, we introduce a notion of necksize for these metrics in
our moduli space, which we use to characterize compactness. More precisely, we
prove that if the punctures remain separated and the necksize at each puncture
is bounded away from zero along a sequence of metrics, then a subsequence
converges with respect to the Gromov--Hausdorff metric. Our proof relies on an
upper bound estimate which is proved using moving planes and a blow-up
argument. This is combined with a lower bound estimate which is a consequence
of a removable singularity theorem. We also introduce a homological invariant
which may be of independent interest for upcoming research.


  We present a study of the digitized Quantum Annealing protocol proposed by R.
Barends et al., Nature 534, 222 (2016). Our analysis, performed on the
benchmark case of a transverse Ising chain problem, shows that the algorithm
has a well defined optimal working point for the annealing time
$\tau^{\mathrm{opt}}_\mathrm{P}$ --- scaling as
$\tau^{\mathrm{opt}}_\mathrm{P}\sim \mathrm{P}$, where $\mathrm{P}$ is the
number of digital Trotter steps --- beyond which, the residual energy error
shoots-up towards the value characteristic of the maximally disordered state.
We present an analytical analysis for the translationally invariant transverse
Ising chain case, but our numerical evidence suggests that this scenario is
more general, surviving, for instance, the presence of disorder.


  In gaussian theories of structure formation, the galaxy cluster abundance is
an extremely sensitive probe of the density fluctuation power spectrum and of
the density parameter, $\Omega$. We develop this theme by deriving and studying
in detail the mass function of collapsed objects and its relation to these
quantities. Application to current data yields constraints which are degenerate
between the amplitude of the perturbations and the density parameter; we
nevertheless obtain an important limit on the present day mass perturbation
amplitude as a function of $\Omega$ and can rule-out the `standard' cold dark
matter (CDM) model. Future observations of the evolution of the cluster
abundance will break the degeneracy and provide important constraints on both
the power spectrum and the density parameter, individually. We focus primarily
on X-ray clusters in the discussion, and finish with a presentation of the
promising new field of Sunyaev-Zel'dovich observations of cluster evolution.


  The X-ray emission from active galactic nuclei (AGN) is believed to come from
a combination of inverse Compton scattering of photons from the accretion disk
and reprocessing of the direct X-ray emission by reflection. We present hard
(10-80 keV) and soft (0.5-8 keV) X-ray monitoring of a gravitationally lensed
quasar RX J1131-1231 with NuSTAR, Swift, and XMM-Newton between 10 June 2016
and 30 November 2020. Comparing the amplitude of quasar microlensing
variability at the hard and soft bands allows a size comparison, where larger
sources lead to smaller microlensing variability. During the period between 6
June 2018 and 30 November 2020, where both the hard and soft light curves are
available, the hard and soft bands varied by factors of 3.7 and 5.5,
respectively, with rms variability of $0.40\pm0.05$ and $0.57\pm0.02$. Both the
variability amplitude and rms are moderately smaller for the hard X-ray
emission, indicating that the hard X-ray emission is moderately larger than the
soft X-ray emission region. We found the reflection fraction from seven joint
hard and soft X-ray monitoring epochs is effectively consistent with a constant
with low significance variability. After decomposing the total X-ray flux into
direct and reprocessed components, we find a smaller variability amplitude for
the reprocessed flux compared to the direct emission. The power-law cutoff
energy is constrained at 96$^{+47}_{-24}$ keV, which position the system in the
allowable parameter space due to the pair production limit.


  Let ${\cal A}$ be a von Neumann algebra and ${\cal P}_{\cal A}$ the manifold
of projections in ${\cal A}$. There is a natural linear connection in ${\cal
P}_{\cal A}$, which in the finite dimensional case coincides with the the
Levi-Civita connection of the Grassmann manifold of $\mathbb{C}^n$. In this
paper we show that two projections $p,q$ can be joined by a geodesic, which has
minimal length (with respect to the metric given by the usual norm of ${\cal
A}$), if and only if $$ p\wedge q^\perp\sim p^\perp\wedge q, $$ where $\sim$
stands for the Murray-von Neumann equivalence of projections. It is shown that
the minimal geodesic is unique if and only if $p\wedge q^\perp= p^\perp\wedge
q=0$. If ${\cal A}$ is a finite factor, any pair of projections in the same
connected component of ${\cal P}_{\cal A}$ (i.e., with the same trace) can be
joined by a minimal geodesic.
  We explore certain relations with Jones' index theory for subfactors. For
instance, it is shown that if ${\cal N}\subset{\cal M}$ are {\bf II}$_1$
factors with finite index $[{\cal M}:{\cal N}]=t^{-1}$, then the geodesic
distance $d(e_{\cal N},e_{\cal M})$ between the induced projections $e_{\cal
N}$ and $e_{\cal M}$ is $d(e_{\cal N},e_{\cal M})=\arccos(t^{1/2})$.


  Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution
to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is
explicitly found. This allows the derivation of the equation of state for the
fluid taking both the virial and the compressibility routes. An analysis of the
virial coefficients and the determination of the radius of convergence of the
virial series are carried out. Molecular dynamics simulations of the same
system are also performed and a comparison between the simulation results for
the compressibility factor and theoretical expressions for the same quantity is
presented.


  This paper presents a simple yet effective two-stage framework for
semi-supervised medical image segmentation. Unlike prior state-of-the-art
semi-supervised segmentation methods that predominantly rely on pseudo
supervision directly on predictions, such as consistency regularization and
pseudo labeling, our key insight is to explore the feature representation
learning with labeled and unlabeled (i.e., pseudo labeled) images to regularize
a more compact and better-separated feature space, which paves the way for
low-density decision boundary learning and therefore enhances the segmentation
performance. A stage-adaptive contrastive learning method is proposed,
containing a boundary-aware contrastive loss that takes advantage of the
labeled images in the first stage, as well as a prototype-aware contrastive
loss to optimize both labeled and pseudo labeled images in the second stage. To
obtain more accurate prototype estimation, which plays a critical role in
prototype-aware contrastive learning, we present an aleatoric uncertainty-aware
method, namely AUA, to generate higher-quality pseudo labels. AUA adaptively
regularizes prediction consistency by taking advantage of image ambiguity,
which, given its significance, is under-explored by existing works. Our method
achieves the best results on three public medical image segmentation
benchmarks.


  In A- and late B-type stars, strong magnetic fields are always associated
with Ap and Bp chemical peculiarities. However, it is not clear at what point
in a star's evolution those peculiarities develop. Strong magnetic fields have
been observed in pre-main sequence A and B stars (Herbig Ae and Be stars), and
these objects have been proposed to be the progenitors of Ap and Bp stars.
However, the photospheric chemical abundances of these magnetic Herbig stars
have not been studied carefully, and furthermore the chemical abundances of
'normal' non-magnetic Herbig stars remain poorly characterized. To investigate
this issue, we have studied the photospheric compositions of 23 Herbig stars,
four of which have confirmed magnetic fields. Surprisingly, we found that half
the non-magnetic stars in our sample show lambda Bootis chemical peculiarities
to varying degrees. For the stars with detected magnetic fields, we find one
chemically normal star, one star with lambda Boo peculiarities, one star
displaying weak Ap/Bp peculiarities, and one somewhat more evolved star with
somewhat stronger Ap/Bp peculiarities. These results suggests that Ap/Bp
peculiarities are preceded by magnetic fields, and that these peculiarities
develop over the pre-main sequence lives of A and B stars. The incidence of
lambda Boo stars we find is much higher than that seen on the main sequence. We
argue that a selective accretion model for the formation of lambda Boo
peculiarities is a natural explanation for this remarkably large incidence.


  We present Mi{\dh}eind's submission for the English$\to$Icelandic and
Icelandic$\to$English subsets of the 2021 WMT news translation task.
Transformer-base models are trained for translation on parallel data to
generate backtranslations iteratively. A pretrained mBART-25 model is then
adapted for translation using parallel data as well as the last backtranslation
iteration. This adapted pretrained model is then used to re-generate
backtranslations, and the training of the adapted model is continued.


  The objective of this paper is to derive some interesting properties of
Genocchi, Euler and Bernstein polynomials by means of the orthogonality of
Hermite polynomials.


  We present here the first detailed study of a giant radio galaxy of the
Fat-Double type. The lobes of the double radio galaxy SGRS J0515-8100 have
transverse widths that are 1.3 times their extent from the center, their
surface brightness is the lowest among known giant radio sources and the lobes
have relatively steep radio spectra. We infer that these wide lobes were
created as a result of a highly variable and intermittent jet whose axis
direction also varied significantly: the Fat-Double lobes in this giant radio
source are a result of the ejection and deposition of synchrotron plasma over a
wide range of angles over time rather than the expansion of relic lobes.
Additionally, the optical host shows evidence for an ongoing galaxy-galaxy
interaction. SGRS J0515-8100 supports the hypothesis that interactions with
companions might perturb the inner accretion disk that produces and sustains
the jets at the centers of active galactic nuclei. As a result, it appears
unnecessary to invoke black-hole coalescence to explain such morphologies,
implying that the corresponding event rates predicted for gravitational wave
detectors may be overestimates.


  We present a geometric construction of central S^1-extensions of the
quantomorphism group of a prequantizable, compact, symplectic manifold, and
explicitly describe the corresponding lattice of integrable cocycles on the
Poisson Lie algebra. We use this to find nontrivial central S^1-extensions of
the universal cover of the group of Hamiltonian diffeomorphisms. In the
process, we obtain central S^1-extensions of Lie groups that act by exact
strict contact transformations.


  Cousin's lemma is a compactness principle that naturally arises when studying
the gauge integral, a generalisation of the Lebesgue integral. We study the
axiomatic strength of Cousin's lemma for various classes of functions, using
Friedman and Simpson's reverse mathematics in second-order arithmetic. We prove
that, over $\mathsf{RCA}_0$:
  (i) Cousin's lemma for continuous functions is equivalent to the system
$\mathsf{WKL}_0$;
  (ii) Cousin's lemma for Baire 1 functions is at least as strong as
$\mathsf{ACA}_0$;
  (iii) Cousin's lemma for Baire 2 functions is at least as strong as
$\mathsf{ATR}_0$.


  We propose a new architecture for implementing electronic interferometry in
quantum Hall bars. It exploits scattering among parallel edge channels. In
contrast to previous developments, this one employs a simply-connected mesa
admitting serial concatenation of building elements closer to optical
analogues. Implementations of Mach-Zehnder and Hambury-Brown-Twiss
interferometers are discussed together with new structures yet unexplored in
quantum electronics.


  While gravitational wave (GW) standard sirens from neutron star (NS) mergers
have been proposed to offer good measurements of the Hubble constant, we show
in this paper how a variation of the expanding photosphere method (EPM) or
spectral-fitting expanding atmosphere method, applied to the kilonovae (KNe)
associated with the mergers, can provide an independent distance measurement to
individual mergers that is potentially accurate to within a few percent. There
are four reasons why the KN-EPM overcomes the major uncertainties commonly
associated with this method in supernovae: 1) the early continuum is very
well-reproduced by a blackbody spectrum, 2) the dilution effect from electron
scattering opacity is likely negligible, 3) the explosion times are exactly
known due to the GW detection, and 4) the ejecta geometry is, at least in some
cases, highly spherical and can be constrained from line-shape analysis. We
provide an analysis of the early VLT/X-shooter spectra AT2017gfo showing how
the luminosity distance can be determined, and find a luminosity distance of
$D_L = 44.5\pm0.8$ Mpc in agreement with, but more precise than, previous
methods. We investigate the dominant systematic uncertainties, but our simple
framework, which assumes a blackbody photosphere, does not account for the full
time-dependent three-dimensional radiative transfer effects, so this distance
should be treated as preliminary. The luminosity distance corresponds to an
estimated Hubble constant of $H_0 = 67.0\pm 3.6$ km s$^{-1}$ Mpc$^{-1}$, where
the dominant uncertainty is due to the modelling of the host peculiar velocity.
We also estimate the expected constraints on $H_0$ from future KN-EPM-analysis
with the upcoming O4 and O5 runs of the LIGO collaboration GW-detectors, where
five to ten similar KNe would yield 1\% precision cosmological constraints.


  We show that conjecture 15 in the article by Rabern et al. is wrong, comment
on theorem 24 there, and conclude with some remarks on structures similar to
the Yablo construction.


  Understanding the physical processes that drive star formation is a key
challenge for galaxy formation models. In this article we study the tight
correlation between the star formation rate (SFR) and stellar mass of galaxies
at a given redshift, how halo growth influences star formation, and star
formation histories of individual galaxies. We study these topics using
Illustris, a state-of-the-art cosmological hydrodynamical simulation of galaxy
formation. Illustris reproduces the observed relation (the star formation main
sequence; SFMS) between SFR and stellar mass at redshifts z=0 and z=4, but at
intermediate redshifts of z~2, the simulated SFMS has a significantly lower
normalisation than reported by observations. The scatter in the relation is
consistent with the observed scatter. However, the fraction of outliers above
the SFR-stellar mass relation in Illustris is less than that observed. Galaxies
with halo masses of ~10^{12} solar masses dominate the SFR density of the
Universe, in agreement with the results of abundance matching. Furthermore,
more-massive galaxies tend to form the bulk of their stars at high redshift,
which indicates that `downsizing' occurs in Illustris. We also studied the star
formation histories of individual galaxies, including the use of a principal
component analysis decomposition. We find that for fixed stellar mass, galaxies
that form earlier have more-massive black holes at z=0, indicating that star
formation and black hole growth are tightly linked processes in Illustris.
While many of the properties of normal star-forming galaxies are
well-reproduced in the Illustris simulation, forming a realistic population of
starbursts will likely require higher resolution and probably a more
sophisticated treatment of star formation and feedback from stars and black
holes.


  It is well established that MgII absorption lines detected in background
quasar spectra arise from gas structures associated with foreground galaxies.
The degree to which galaxy evolution is driven by the gas cycling through halos
is highly uncertain because their gas mass density is poorly constrained.
Fitting the MgII equivalent width (W) distribution with a Schechter function
and applying the N(HI)-W correlation of Menard & Chelouche, we computed
Omega(HI)_MgII ~ Omega(HI)_halo =(1.41 +0.75 -0.44)x10^-4 for 0.4<z<1.4. We
exclude DLAs from our calculations so that Omega(HI)_halo comprises accreting
and/or outflowing halo gas not locked up in cold neutral clouds. We deduce the
cosmic HI gas mass density fraction in galactic halos traced by MgII absorption
is Omega(HI)_halo/Omega(HI)_DLA=15% and Omega(HI)_halo/Omega_b=0.3%. Citing
several lines of evidence, we propose infall/accretion material is sampled by
small W whereas outflow/winds are sampled by large W, and find Omega(HI)_infall
is consistent with Omega(HI)_outflow for bifurcation at
W=1.23^{+0.15}_{-0.28}\AA; cold accretion would then comprise no more than ~7%
of of the total HI mass density. We discuss evidence that (1) the total HI mass
cycling through halos remains fairly constant with cosmic time and that the
accretion of HI gas sustains galaxy winds, and (2) evolution in the cosmic star
formation rate depends primarily on the rate at which cool HI gas cycles
through halos.


  This paper retraces the historical development of wireless LAN technology in
the context of the pursuit of ever higher data rate, describes the significant
technical breakthroughs that are now occurring, and speculates on future
directions that the technology may take over the remainder of the decade. The
challenges that these developments have created for low power operation are
considered, as well as some of the opportunities that are presented to mitigate
them. The importance of MIMO as an emerging technology for 802.11 is
specifically highlighted, both in terms of the significant increase in data
rate and range that it enables as well as the considerable challenge that it
presents for the development of low power wireless LAN products.


  Partitioning and transport of water and small solutes into and through
nanopores is important to a variety of chemical and biological processes and
applications. Here we study the partitioning of positive ions of increasing
size into the pore interior using extensive molecular dynamics simulations.
Despite the simplicity of the simulation system, the results provide new and
useful insights on both the pore hydration and ion partitioning. For low
negative charge densities on the pore, the driving force for partitioning of
positive ions into the pore is weak, and no partitioning is observed.
Increasing the pore charge gradually leads to partitioning of positive ions
into the pore. Interestingly, over a range of intermediate negative charge
densities, nanopores display both thermodynamic as well as kinetic selectivity
toward partitioning of the larger K+ and Cs+ ions into their interior over the
smaller Na+ ions. The variation of thermodynamic driving force and the average
partitioning time with the pore charge density together suggest the presence of
free energy barriers in the partitioning process. We discuss the role of ion
hydration in the bulk and in the pore interior as well as of the pore hydration
in determining the barrier heights for ion partitioning and the observed
thermodynamic and kinetic selectivity.


  We assess which Kahler potentials in supergravity lead to viable single-field
inflationary models that are consistent with Planck. We highlight the role of
symmetries, such as shift, Heisenberg and supersymmetry, in these
constructions. Also the connections to string theory are pointed out. Finally,
we discuss a supergravity model for arbitrary inflationary potentials that is
suitable for open string inflation and generalize it to the case of closed
string inflation. Our model includes the recently discussed supergravity
reformulation of the Starobinsky model of inflation as well as an interesting
alternative with comparable predictions.


  We derive formulas for the Coulomb matrix within the full-potential
linearized augmented-plane-wave (FLAPW) method. The Coulomb matrix is a central
ingredient in implementations of many-body perturbation theory, such as the
Hartree-Fock and GW approximations for the electronic self-energy or the
random-phase approximation for the dielectric function. It is represented in
the mixed product basis, which combines numerical muffin-tin functions and
interstitial plane waves that are here expanded with the Rayleigh formula. The
resulting algorithm is very efficient in terms of both computational cost and
accuracy and is superior to an implementation with the Fourier transform of the
step function. In order to allow an analytic treatment of the divergence at k=0
in reciprocal space, we expand the Coulomb matrix analytically around this
point without resorting to a projection onto plane waves. We then apply a basis
transformation that diagonalizes the Coulomb matrix and confines the divergence
to a single eigenvalue. At the same time, response matrices like the dielectric
function separate into head, wings, and body with the same mathematical
properties as in a plane-wave basis. As an illustration we apply the formulas
to electron-energy-loss spectra for nickel at different k vectors including
k=0. The convergence of the spectra towards the result at k=0 is clearly seen.
Our treatment also allows to include transitions from core states that give
rise to a shallow peak at high energies and lead to good agreement with
experiment.


  The Chandra image of the central region of the Coma cluster reveals that both
its dominant galaxies, NGC4874 and NGC4889, retain the central parts of their
X-ray gas coronae. The interstellar gas with a temperature of 1-2 keV is
confined by the hot intergalactic medium of the Coma cluster into compact
clouds (only 3 kpc in radius) containing 10^8 M_sun of gas. The physical state
of the gas in these clouds appears to be determined by a delicate balance
between radiative cooling and suppressed (by a factor of 30-100) heat
conduction through the interface between these clouds and the hot cluster gas.


  Hybrid photonic nanostructures allow the engineering of novel interesting
states of light. One recent example is topological photonic crystals where a
nontrivial Berry phase of the photonic band structure gives rise to
topologically protected unidirectionally-propagating (chiral) edge states of
photons. Here we demonstrate that by coupling an array of emitters to the
chiral photonic edge state one can create strongly correlated states of photons
in a highly controllable way. These are topologically protected and have a
number of remarkable universal properties: The outcome of scattering does not
depend on the positions of emitters and is given only by universal numbers, the
zeroes of Laguerre polynomials; two-photon correlation functions manifest a
well-pronounced even-odd effect with respect to the number of emitters, and the
result of scattering is robust with respect to fluctuations in the emitters'
transition frequencies.


  We investigate the linear stability of a flat interface that separates a
liquid layer from a fully-developed turbulent gas flow. In this context,
linear-stability analysis involves the study of the dynamics of a
small-amplitude wave on the interface, and we develop a model that describes
wave-induced perturbation turbulent stresses (PTS). We demonstrate the effect
of the PTS on the stability properties of the system in two cases: for a
laminar thin film, and for deep-water waves. In the first case, we find that
the PTS have little effect on the growth rate of the waves, although they do
affect the structure of the perturbation velocities. In the second case, the
PTS enhance the maximum growth rate, although the overall shape of the
dispersion curve is unchanged. Again, the PTS modify the structure of the
velocity field, especially at longer wavelengths. Finally, we demonstrate a
kind of parameter tuning that enables the production of the thin-film (slow)
waves in a deep-water setting.


  We study the nonclassical properties and algebraic characteristics of the
negative binomial states introduced by Barnett recently. The ladder operator
formalism and displacement operator formalism of the negative binomial states
are found and the algebra involved turns out to be the SU(1,1) Lie algebra via
the generalized Holstein-Primarkoff realization. These states are essentially
Peremolov's SU(1,1) coherent states. We reveal their connection with the
geometric states and find that they are excited geometric states. As
intermediate states, they interpolate between the number states and geometric
states. We also point out that they can be recognized as the nonlinear coherent
states. Their nonclassical properties, such as sub-Poissonian distribution and
squeezing effect are discussed. The quasiprobability distributions in phase
space, namely the Q and Wigner functions, are studied in detail. We also
propose two methods of generation of the negative binomial states.


  We present a superconducting metamaterial saturable absorber at terahertz
frequencies. The absorber consists of an array of split ring resonators (SRRs)
etched from a 100nm YBaCu3O7 (YBCO) film. A polyimide spacer layer and gold
ground plane are deposited above the SRRs, creating a reflecting perfect
absorber. Increasing either the temperature or incident electric field (E)
decreases the superconducting condensate density and corresponding kinetic
inductance of the SRRs. This alters the impedance matching in the metamaterial,
reducing the peak absorption. At low electric fields, the absorption was
optimized near 80% at T=10K and decreased to 20% at T=70K. For E=40kV/cm and
T=10K, the peak absorption was 70% decreasing to 40% at 200kV/cm, corresponding
to a modulation of 43%.


  The present work is the second part of a pair of papers, considering Hybrid
Discontinuous Galerkin methods with relaxed H(div)-conformity. The first part
mainly dealt with presenting a robust analysis with respect to the mesh size
$h$ and the introduction of a reconstruction operator to restore
divergence-conformity and pressure robustness using a non conforming right hand
side. The aim of this part is the presentation of a high order polynomial
robust analysis for the relaxed $H(\operatorname{div})$-conforming Hybrid
Discontinuous Galerkin discretization of the two dimensional Stokes problem. It
is based on the recently proven polynomial robust LBB-condition for BDM
elements [P. L. Lederer, J. Sch\"oberl, IMA Journal of Numerical Analysis,
2017] and is derived by a direct approach instead of using a best approximation
C\'{e}a like result. We further treat the impact of the reconstruction operator
on the $hp$ analysis and present a numerical investigation considering
polynomial robustness. We conclude the paper presenting an efficient operator
splitting time integration scheme for the Navier--Stokes equations which is
based on the methods recently presented in [C. Lehrenfeld, J. Sch\"oberl,
\emph{Comp. Meth. Appl. Mech. Eng.}, 361 (2016)] and includes the ideas of the
reconstruction operator.


  In order to bridge the gap between heliospheric and solar observations of
coronal mass ejections (CMEs), one of the key steps is to improve the
understanding of their corresponding magnetic structures like the magnetic flux
ropes (MFRs). But it remains a challenge to confirm the existence of a coherent
MFR before or upon the CME eruption on the Sun and to quantitatively
characterize the CME-MFR due to the lack of direct magnetic field measurement
in the corona. In this study, we investigate the MFR structures, originating
from two active regions (ARs), AR 11719 and AR 12158, and estimate their
magnetic properties quantitatively. We perform the nonlinear force-free field
extrapolations with preprocessed photospheric vector magnetograms. In addition,
remote-sensing observations are employed to find indirect evidence of MFRs on
the Sun and to analyze the time evolution of magnetic reconnection flux
associated with the flare ribbons during the eruption. A coherent
"pre-existing" MFR structure prior to the flare eruption is identified
quantitatively for one event from the combined analysis of the extrapolation
and observation. Then the characteristics of MFRs for two events on the Sun
before and during the eruption, forming the CME-MFR, including the axial
magnetic flux, field-line twist, and reconnection flux, are estimated and
compared with the corresponding in situ modeling results. We find that the
magnetic reconnection associated with the accompanying flares for both events
injects significant amount of flux into the erupted CME-MFRs.


  Partitions of the set of primes are introduced based on the Chebyshev
polynomials at rationals. The prime densities of all such partitions are
established. Euler's Criterion for $SL(2,\mathbb Q)$ is formulated, which is
the bridge between the algebra of Chebyshev polynomials and number-theoretic
properties of the partitions. It is shown how to obtain in this way some of the
classical theory of Lucas sequences. A hidden symmetry of the problem is
revealed by the new language. As an application number-theoretic properties of
simple dynamical systems (rotations and certain interval maps) are discussed.


  Let $A$ be a simple abelian surface over an algebraically closed field $k$.
Let $S\subset A(k)$ be the set of torsion points $x$ of $A$ such that there
exists a genus $2$ curve $C$ and a map $f: C\to A$ such that $x$ is in the
image of $f$, and $f$ sends a Weierstrass point of $C$ to the origin of $A$.
The purpose of this note is to show that if $k$ has characteristic zero, then
$S$ is finite -- this is in contrast to the situation where $k$ is the
algebraic closure of a finite field, where $S=A(k)$, as shown by Bogomolov and
Tschinkel. We deduce that if $k=\bar{\mathbb{Q}}$, the Kummer surface
associated to $A$ has infinitely many $k$-points not contained in a rational
curve arising from a genus $2$ curve in $A$, again in contrast to the situation
over the algebraic closure of a finite field.


  In the present paper we describe new heuristic technique, which can be
applied to the optimization of pseudo-Boolean functions including Black-Box
functions. This technique is based on a simple procedure which consists in
transition from the optimization problem over Boolean hypercube to the
optimization problem of auxiliary function in a specially constructed metric
space. It is shown that there is a natural connection between the points of the
original Boolean hypercube and points from the new metric space. For the
Boolean hypercube with fixed dimension it is possible to construct a number of
such metric spaces. The proposed technique can be considered as a special case
of Variable Neighborhood Search, which is focused on pseudo-Boolean
optimization. Preliminary computational results show high efficiency of the
proposed technique on some reasonably hard problems. Also it is shown that the
described technique in combination with the well-known (1+1)-Evolutionary
Algorithm allows to decrease the upper bound on the runtime of this algorithm
for arbitrary pseudo-Boolean functions.


  Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on
$m$-columns of half-densities on a closed manifold $M$, whose principal symbol
is assumed to have simple eigenvalues. We show that the spectrum of $A$
decomposes, up to an error with superpolynomial decay, into $m$ distinct
series, each associated with one of the eigenvalues of the principal symbol of
$A$. These spectral results are then applied to the study of propagation of
singularities in hyperbolic systems. The key technical ingredient is the use of
the carefully devised pseudodifferential projections introduced in the first
part of this work, which decompose $L^2(M)$ into almost-orthogonal
almost-invariant subspaces under the action of both $A$ and the hyperbolic
evolution.


  The concept of broken symmetry is used to study bifurcations of equilibria
and dynamical instabilities in dynamic model of one-mode laser (nonresonant
complex Lorenz model) on the basis of modified Hopf theory. It is shown that an
invariant set of stationary points bifurcates into an invariant torus
(doubly-periodic branching solution). Influence of the symmetry breaking on
stability of branching solutions is investigated as a function of detuning. The
invariant torus is found to be stable under the detuning exceeds its critical
value, so that dynamically broken symmetry results in the apprearance of
low-frequency Goldstone-type mode. If the detuning then goes downward and
pumping is kept above the threshold, numerical analysis reveals that after a
cascade of period-doublings the strange Lorenz attractor is formed at small
values of detuning. It is found that there are three types of the system
behavior as pumping increases depending on the detuning. Quantum counterpart of
the complex Lorenz model is discussed.


  In this paper we propose an efficient stochastic optimization algorithm to
search for Bayesian experimental designs such that the expected information
gain is maximized. The gradient of the expected information gain with respect
to experimental design parameters is given by a nested expectation, for which
the standard Monte Carlo method using a fixed number of inner samples yields a
biased estimator. In this paper, applying the idea of randomized multilevel
Monte Carlo (MLMC) methods, we introduce an unbiased Monte Carlo estimator for
the gradient of the expected information gain with finite expected squared
$\ell_2$-norm and finite expected computational cost per sample. Our unbiased
estimator can be combined well with stochastic gradient descent algorithms,
which results in our proposal of an optimization algorithm to search for an
optimal Bayesian experimental design. Numerical experiments confirm that our
proposed algorithm works well not only for a simple test problem but also for a
more realistic pharmacokinetic problem.


  We discuss the current and prospective limits that can be placed on
supersymmetric contributions to $b\to s$ transitions in the Minimal
Supersymmetric Standard Model with general flavour mixing amongst the squarks.
We consider three processes: $\bar{B}\to X_s\gamma$, $\bar{B}_s\mu^+\mu^-$ and
$\bar{B}_s-B_s$ mixing, and pay particular attention to the large $\tan\beta$
regime and beyond leading order contributions where the difference between our
analysis and previous analyses is most pronounced. We find that even present
limits on BR$(\bar{B}_s\mu^+\mu^-)$ and $\Delta m_{B_s}$ often provide
additional constraints on the amount of flavour violation still allowed by
BR$(\bar{B}\to X_s\gamma)$. Limits on supersymmetric and Higgs mass parameters
can also be strongly dependent on the flavour violation. In particular, the
case $\mu<0$ can still be allowed, even for light sparticle masses. We discuss
how future measurements at the Tevatron, the LHC and elsewhere can improve
present limits but also provide unique signatures for the existence of flavour
violation.


  Although all superconducting cuprates display charge-ordering tendencies,
their low-temperature properties are distinct, impeding efforts to understand
the phenomena within a single conceptual framework. While some systems exhibit
stripes of charge and spin, with a locked periodicity, others host charge
density waves (CDWs) without any obviously related spin order. Here we use
resonant inelastic x-ray scattering (RIXS) to follow the evolution of charge
correlations in the canonical stripe ordered cuprate
La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ (LBCO~$1/8$) across its ordering transition.
We find that high-temperature charge correlations are unlocked from the
wavevector of the spin correlations, signaling analogies to CDW phases in
various other cuprates. This indicates that stripe order at low temperatures is
stabilized by the coupling of otherwise independent charge and spin density
waves, with important implications for the relation between charge and spin
correlations in the cuprates.


  Instrumental variables have been widely used to estimate the causal effect of
a treatment on an outcome. Existing confidence intervals for causal effects
based on instrumental variables assume that all of the putative instrumental
variables are valid; a valid instrumental variable is a variable that affects
the outcome only by affecting the treatment and is not related to unmeasured
confounders. However, in practice, some of the putative instrumental variables
are likely to be invalid. This paper presents a simple and general approach to
construct a confidence interval that is robust to possibly invalid instruments.
The robust confidence interval has theoretical guarantees on having the correct
coverage and can also be used to assess the sensitivity of inference when
instrumental variables assumptions are violated. The paper also shows that the
robust confidence interval outperforms traditional confidence intervals popular
in instrumental variables literature when invalid instruments are present. The
new approach is applied to a developmental economics study of the causal effect
of income on food expenditures.


  We analyse six classes of t-channel dark matter simplified models in which
the Standard Model field content is extended by a coloured mediator and a dark
matter state. The two new states are enforced to be odd under a new parity,
while all Standard Model fields are taken even so that dark matter stability is
guaranteed. We study several possibilities for the spin of the new particles
and the self-conjugate property of the dark matter, and we focus on model
configurations in which the dark matter couples to the right-handed up quark
for simplicity. We investigate how the parameter spaces of the six models can
be constrained by current and future cosmological, astrophysical and collider
searches, and we highlight the strong complementary between those probes. Our
results demonstrate that scenarios featuring a complex (non self-conjugate)
dark matter field are excluded by cosmology and astrophysics alone, the only
possibility to avoid these bounds being to invoke very weak couplings and
mechanisms such as conversion-driven freeze-out. For models with self-conjugate
dark matter, mediator and dark matter masses are pushed deep into the TeV
regime, with the lower limits on the mediator mass reaching 3 to 4 TeV and
those on the dark matter mass 1 to 2 TeV. In large parts of the parameter space
these strong bounds are driven by same-sign mediator pair production, a channel
so far not considered in the experimental analyses embedding t-channel dark
matter model interpretations.


  IR spectroscopy has been widely used for chemical identification and
quantitative analysis of reactions occurring in a specific time and space
domains by measuring an average signal of the entire system1. Achieving IR
measurements with nanometer-scale spatial resolution is highly desirable to
obtain a detailed understanding of the composition, structure and function of
interfaces2-5. The challenges in IR nanoscopy yet exist owing to the small
molecular cross section and pristine optical diffraction limit. Although atomic
force microscopy (AFM) based techniques, such as scattering-type scanning
near-field optical microscopy and photothermal-induced resonance microscopy
(PTIR), can acquire IR spectroscopy in a few tens of nanometer scale
resolution6-9, IR measurements with monolayer level sensitivity remains elusive
and can only be realized under critical conditions10,11. Herein, we demonstrate
sub-10 nm spatial resolution sampling a volume of ~360 molecules with a strong
field enhancement at the sample-tip junction by implementing noble metal
substrates (Au, Ag, Pt) in photo-induced force microscopy (PiFM). This
technique shows versatility and robustness of PiFM, and is promising for
application in interfacial studies with hypersensitivity and super spatial
resolution.


  The mass matrix for Gauss-Lobatto grid points is usually approximated by
Gauss-Lobatto quadrature because this leads to a diagonal matrix that is easy
to invert. The exact mass matrix and its inverse are full. We show that the
exact mass matrix \emph{and} its inverse differ from the approximate diagonal
ones by a simple rank-1 update (outer product). They can thus be applied to an
arbitrary vector in $O(N)$ operations instead of $O(N^2)$.


  We report a development of a new fast surface-based method for numerical
calculations of solvation energy of biomolecules with a large number of charged
groups. The procedure scales linearly with the system size both in time and
memory requirements, is only a few percent wrong for any molecular
configurations of arbitrary sizes, gives explicit value for the reaction field
potential at any point, provides both the solvation energy and its derivatives
suitable for Molecular Dynamics simulations. The method works well both for
large and small molecules and thus gives stable energy differences for
quantities such as solvation energies of molecular complex formation.


  We analyze thermodynamic behavior of general $n$-component mean-field spin
glass models in order to identify origin of the hierarchical structure of the
order parameters from the replica-symmetry breaking solution. We derive a
configurationally dependent free energy with local magnetizations and averaged
local susceptibilities as order parameters. On an example of the replicated
Ising spin glass we demonstrate that the hierarchy of order parameters in
mean-field models results from the structure of inter-replica susceptibilities.
These susceptibilities serve for lifting the degeneracy due to the existence of
many metastable states and for recovering thermodynamic homogeneity of the free
energy.


  The so-called fast polar decoding schedules are meant to improve the decoding
speed of the sequential-natured successive cancellation list decoders. The
decoding speedup is achieved by replacing various parts of the serial decoding
process with efficient special-purpose decoder nodes. This work incorporates
the fast decoding schedules for polar codes into their quantized finite
alphabet decoding. In a finite alphabet successive cancellation list decoder,
the log-likelihood ratio computations are replaced with lookup operations on
low-resolution integer messages. The lookup tables are designed using the
information bottleneck method. It is shown that the finite alphabet decoders
can also leverage the special decoder nodes found in the literature. Besides
their inherent decoding speed improvement, the use of these special decoder
nodes drastically reduces the number of lookup tables required to perform the
finite alphabet decoding. In order to perform quantized decoding using lookup
operations, the proposed decoders require up to 93% less unique lookup tables
as compared to the ones that use the conventional successive cancellation
schedule. Moreover, the proposed decoders exhibit negligible loss in error
correction performance without necessitating alterations to the lookup table
design process.


  We measure the low lying eigenmodes of an overlap Dirac operator on 2--flavor
staggered configurations. By comparing the eigenmode distribution to the
predictions of Random Matrix Theory we test to what accuracy staggered
configurations describe continuum QCD. The agreement between the numerical data
and RMT implies that at our quark mass values the lattice artifacts of the
staggered configurations are comparable to overlap configurations. We identify
the overlap valence mass that best matches the staggered sea quarks and predict
the value of the infinite volume 2-flavor chiral condensate.


  Sulfur-bearing molecules play an important role in prebiotic chemistry and
planet habitability. They are also proposed probes of chemical ages, elemental
C/O ratio, and grain chemistry processing. Commonly detected in diverse
astrophysical objects, including the Solar System, their distribution and
chemistry remain, however, largely unknown in planet-forming disks. We present
CS ($2-1$) observations at $\sim0."3$ resolution performed within the ALMA-MAPS
Large Program toward the five disks around IM Lup, GM Aur, AS 209, HD 163296,
and MWC 480. CS is detected in all five disks, displaying a variety of radial
intensity profiles and spatial distributions across the sample, including
intriguing apparent azimuthal asymmetries. Transitions of C$_2$S and SO were
also serendipitously covered but only upper limits are found. For MWC 480, we
present complementary ALMA observations at $\sim0."5$, of CS, $^{13}$CS,
C$^{34}$S, H$_2$CS, OCS, and SO$_2$. We find a column density ratio
N(H$_{2}$CS)/N(CS)$\sim2/3$, suggesting that a substantial part of the sulfur
reservoir in disks is in organic form (i.e., C$_x$H$_y$S$_z$). Using
astrochemical disk modeling tuned to MWC 480, we demonstrate that
$N$(CS)/$N$(SO) is a promising probe for the elemental C/O ratio. The
comparison with the observations provides a super-solar C/O. We also find a
depleted gas-phase S/H ratio, suggesting either that part of the sulfur
reservoir is locked in solid phase or that it remains in an unidentified
gas-phase reservoir. This paper is part of the MAPS special issue of the
Astrophysical Journal Supplement.


  We investigate the variability of Cygnus X-1 in the context of shot moise
models, and employ a peak detection algorithm to select individual shots. For a
long observation of the low, hard state, the distribution of time intervals
between shots is found to be consistent with a purely random process, contrary
to previous claims in the literature. The detected shots are fit to several
model templates and found to have a broad range of shapes. The fitted shots
have a distribution of timescales from below 10 milliseconds to above 1 second.
The coherence of the cross spectrum of light curves of these data in different
energy bands is also studied. The observed high coherence implies that the
transfer function between low and high energy variability is uniform. The
uniformity of the tranfer function implies that the observed distribution of
shot widths cannot have been acquired through Compton scattering. Our results
in combination with other results in the literature suggest that shot
luminosities are correlated with one another. We discuss how our experimental
methodology relates to non-linear models of variability.


  We present spectroscopy of stars in the immediate vicinity of the dwarf nova
(DN) KZ Gem to confirm its identification, which had been ambiguous in the
literature. Analysis of 73 radial velocities spanning from 2014 to 2019
provides a high-precision orbital period of 0.2224628(2)\,d ($\sim5.34$\,hr)
and shows KZ\,Gem to be a double-lined DN. Time series photometry taken from
2016 to 2018 shows a variable double-hump modulation with a full amplitude of
$\sim0.3$\,mag, along with five Gaussian-like transient events lasting
$\sim30$\,min or more. Using the light curve code XRBinary and nonlinear
fitting code NMfit, we obtain an optimized binary model of the dwarf nova (DN)
KZ Gem, from time series photometry, consisting of a Roche-lobe-filling K type
dwarf with a mass transfer rate of $2.7\,-\,7.9\times10^{-10}\,{\rm
M}_{\odot}\,{\rm yr}^{-1}$ to a large, cool and thick disk surrounding a white
dwarf, in an orbit with an inclination of $51^{\circ}.6(\pm1^{\circ}.4)$. Two
hotspots on the disk are demonstrated to cause the observed variations in the
ellipsoidal modulations from the secondary star. This physical model is
compatible with the Gaia distance of KZ\,Gem.


  This work gives a Lie operator derivation of various Boris solvers via a
detailed study of trajectory errors in a constant magnetic field. These errors
in the gyrocenter location and the gyroradius are the foundational basis for
why Boris solvers existed, independent of any finite-difference schemes. This
work shows that there are two distinct ways of eliminating these errors so that
the trajectory of a charged particle in a constant magnetic field is exactly on
the cyclotron orbit. One way reproduces the known second-order symmetric Boris
solver. The other yields a previously unknown, but also on-orbit solver, not
derivable from finite-difference schemes. By revisiting some historical
calculations, it is found that many publications do not distinguish the poorly
behaved leap-frog Boris solver from the symmetric second-order Boris algorithm.
This symmetric second-order Boris solver's trajectory is much more accurate and
remains close to the exact orbit in a combined $nonuniform$ electric and
magnetic field at time-steps greater than the cyclotron period. Finally, this
operator formalism showed that Buneman's cycloid fitting scheme is
mathematically identical to Boris' on-orbit solver and that Boris' E-B
splitting is unnecessary.


  We discuss procedures for error-tolerant spin control in environments that
permit transient, large-angle reorientation of magnetic bias field. Short
sequences of pulsed, non-resonant magnetic field pulses in a laboratory-frame
meridional plane are derived. These are shown to have band-pass excitation
properties comparable to established amplitude-modulated, resonant pulses used
in high, static-field magnetic resonance. Using these meridional pulses, we
demonstrate robust $z$ inversion in proton ($^{1}$H) nuclear magnetic resonance
near earth's field.


  Layered van der Waals (vdW) magnets can maintain a magnetic order even down
to the single-layer regime and hold promise for integrated spintronic devices.
While the magnetic ground state of vdW magnets was extensively studied, key
parameters of spin dynamics, like the Gilbert damping, crucial for designing
ultra-fast spintronic devices, remains largely unexplored. Despite recent
studies by optical excitation and detection, achieving spin wave control with
microwaves is highly desirable, as modern integrated information technologies
predominantly are operated with these. The intrinsically small numbers of
spins, however, poses a major challenge to this.
  Here, we present a hybrid approach to detect spin dynamics mediated by
photon-magnon coupling between high-Q superconducting resonators and ultra-thin
flakes of Cr$_2$Ge$_2$Te$_6$ (CGT) as thin as 11\,nm. We test and benchmark our
technique with 23 individual CGT flakes and extract an upper limit for the
Gilbert damping parameter. These results are crucial in designing on-chip
integrated circuits using vdW magnets and offer prospects for probing spin
dynamics of monolayer vdW magnets.


  We perform the twistor (half-Fourier) transform of all tree n-particle
superamplitudes in N=4 SYM and show that it has a transparent geometric
interpretation. We find that the N^kMHV amplitude is supported on a set of
(2k+1) intersecting lines in twistor space and demonstrate that the
corresponding line moduli form a lightlike (2k+1)-gon in moduli space. This
polygon is triangulated into two kinds of lightlike triangles lying in
different planes. We formulate simple graphical rules for constructing the
triangulated polygons, from which the analytic expressions of the N^kMHV
amplitudes follow directly, both in twistor and in momentum space. We also
discuss the ordinary and dual conformal properties and the cancellation of
spurious singularities in twistor space.


  Federated bilevel optimization (FBO) has shown great potential recently in
machine learning and edge computing due to the emerging nested optimization
structure in meta-learning, fine-tuning, hyperparameter tuning, etc. However,
existing FBO algorithms often involve complicated computations and require
multiple sub-loops per iteration, each of which contains a number of
communication rounds. In this paper, we propose a simple and flexible FBO
framework named SimFBO, which is easy to implement without sub-loops, and
includes a generalized server-side aggregation and update for improving
communication efficiency. We further propose System-level heterogeneity robust
FBO (ShroFBO) as a variant of SimFBO with stronger resilience to heterogeneous
local computation. We show that SimFBO and ShroFBO provably achieve a linear
convergence speedup with partial client participation and client sampling
without replacement, as well as improved sample and communication complexities.
Experiments demonstrate the effectiveness of the proposed methods over existing
FBO algorithms.


  Natural language inference (NLI) aims to determine the logical relationship
between two sentences, such as Entailment, Contradiction, and Neutral. In
recent years, deep learning models have become a prevailing approach to NLI,
but they lack interpretability and explainability. In this work, we address the
explainability of NLI by weakly supervised logical reasoning, and propose an
Explainable Phrasal Reasoning (EPR) approach. Our model first detects phrases
as the semantic unit and aligns corresponding phrases in the two sentences.
Then, the model predicts the NLI label for the aligned phrases, and induces the
sentence label by fuzzy logic formulas. Our EPR is almost everywhere
differentiable and thus the system can be trained end to end. In this way, we
are able to provide explicit explanations of phrasal logical relationships in a
weakly supervised manner. We further show that such reasoning results help
textual explanation generation.


  Since 2014, the NIH funded iDASH (integrating Data for Analysis,
Anonymization, SHaring) National Center for Biomedical Computing has hosted
yearly competitions on the topic of private computing for genomic data. For one
track of the 2020 iteration of this competition, participants were challenged
to produce an approach to federated learning (FL) training of genomic cancer
prediction models using differential privacy (DP), with submissions ranked
according to held-out test accuracy for a given set of DP budgets. More
precisely, in this track, we are tasked with training a supervised model for
the prediction of breast cancer occurrence from genomic data split between two
virtual centers while ensuring data privacy with respect to model transfer via
DP. In this article, we present our 3rd place submission to this competition.
During the competition, we encountered two main challenges discussed in this
article: i) ensuring correctness of the privacy budget evaluation and ii)
achieving an acceptable trade-off between prediction performance and privacy
budget.


  The small-world transition is a first-order transition at zero density $p$ of
shortcuts, whereby the normalized shortest-path distance undergoes a
discontinuity in the thermodynamic limit. On finite systems the apparent
transition is shifted by $\Delta p \sim L^{-d}$. Equivalently a ``persistence
size'' $L^* \sim p^{-1/d}$ can be defined in connection with finite-size
effects. Assuming $L^* \sim p^{-\tau}$, simple rescaling arguments imply that
$\tau=1/d$. We confirm this result by extensive numerical simulation in one to
four dimensions, and argue that $\tau=1/d$ implies that this transition is
first-order.


  A fundamental challenge for quantum information processing is reducing the
impact of environmentally-induced errors. Quantum error detection (QED)
provides one approach to handling such errors, in which errors are rejected
when they are detected. Here we demonstrate a QED protocol based on the idea of
quantum un-collapsing, using this protocol to suppress energy relaxation due to
the environment in a three-qubit superconducting circuit. We encode quantum
information in a target qubit, and use the other two qubits to detect and
reject errors caused by energy relaxation. This protocol improves the storage
time of a quantum state by a factor of roughly three, at the cost of a reduced
probability of success. This constitutes the first experimental demonstration
of an algorithm-based improvement in the lifetime of a quantum state stored in
a qubit.


  Scanning tunneling and atomic force microscopies (STM/nc-AFM) are rapidly
progressing to offer unprecedented spatial resolution of a diverse array of
chemical species. In particular, they are employed to characterize on-surface
chemical reactions by directly examining precursors and products. Chiral
effects and self-assembled structures can also be investigated. This open
source, modular, python based scheme automates the categorization of a variety
of molecules present in medium sized (10$\times$10 to 100$\times$100 nm)
scanned probe images.


  Multimodal learning has been lacking principled ways of combining information
from different modalities and learning a low-dimensional manifold of meaningful
representations. We study multimodal learning and sensor fusion from a latent
variable perspective. We first present a regularized recurrent attention filter
for sensor fusion. This algorithm can dynamically combine information from
different types of sensors in a sequential decision making task. Each sensor is
bonded with a modular neural network to maximize utility of its own
information. A gating modular neural network dynamically generates a set of
mixing weights for outputs from sensor networks by balancing utility of all
sensors' information. We design a co-learning mechanism to encourage
co-adaption and independent learning of each sensor at the same time, and
propose a regularization based co-learning method. In the second part, we focus
on recovering the manifold of latent representation. We propose a co-learning
approach using probabilistic graphical model which imposes a structural prior
on the generative model: multimodal variational RNN (MVRNN) model, and derive a
variational lower bound for its objective functions. In the third part, we
extend the siamese structure to sensor fusion for robust acoustic event
detection. We perform experiments to investigate the latent representations
that are extracted; works will be done in the following months. Our experiments
show that the recurrent attention filter can dynamically combine different
sensor inputs according to the information carried in the inputs. We consider
MVRNN can identify latent representations that are useful for many downstream
tasks such as speech synthesis, activity recognition, and control and planning.
Both algorithms are general frameworks which can be applied to other tasks
where different types of sensors are jointly used for decision making.


  Recent studies indicate that some Galactic open clusters (OCs) exhibit
extended main-sequence turnoff (eMSTO) in their colour-magnitude diagrams
(CMDs). However, the number of Galactic OCs with eMSTO structures detected so
far is limited, and the reasons for their formation are still unclear. This
work identifies 26 Galactic OCs with undiscovered eMSTOs and investigates the
causes of these features. Stellar population types and fundamental parameters
of cluster samples are acquired using CMD fitting methods. Among them, the
results of 11 OCs are reliable as the observed CMDs are well-reproduced. We
propose the crucial role of stellar binarity and confirm the importance of
stellar rotation in reproducing eMSTO morphologies. The results also show that
the impact of age spread is important, as it can adequately explain the
structure of young OCs and fit the observed CMDs of intermediate-age OCs
better.


  The Hamiltonian cycle problem (HCP) is an important combinatorial problem
with applications in many areas. It is among the first problems used for
studying intrinsic properties, including phase transitions, of combinatorial
problems. While thorough theoretical and experimental analyses have been made
on the HCP in undirected graphs, a limited amount of work has been done for the
HCP in directed graphs (DHCP). The main contribution of this work is an
effective algorithm for the DHCP. Our algorithm explores and exploits the close
relationship between the DHCP and the Assignment Problem (AP) and utilizes a
technique based on Boolean satisfiability (SAT). By combining effective
algorithms for the AP and SAT, our algorithm significantly outperforms previous
exact DHCP algorithms, including an algorithm based on the award-winning
Concorde TSP algorithm. The second result of the current study is an
experimental analysis of phase transitions of the DHCP, verifying and refining
a known phase transition of the DHCP.