  From Oct. 2019 to Apr. 2020, LAMOST performs a time-domain spectroscopic
survey of four $K$2 plates with both low- and med-resolution observations. The
low-resolution spectroscopic survey gains 282 exposures ($\approx$46.6 hours)
over 25 nights, yielding a total of about 767,000 spectra, and the
med-resolution survey takes 177 exposures ($\approx$49.1 hours) over 27 nights,
collecting about 478,000 spectra. More than 70%/50% of
low-resolution/med-resolution spectra have signal-to-noise ratio higher than
10. We determine stellar parameters (e.g., $T_{\rm eff}$, log$g$, [Fe/H]) and
radial velocity (RV) with different methods, including LASP, DD-Payne, and
SLAM. In general, these parameter estimations from different methods show good
agreement, and the stellar parameter values are consistent with those of
APOGEE. We use the $Gaia$ DR2 RV data to calculate a median RV zero point
(RVZP) for each spectrograph exposure by exposure, and the RVZP-corrected RVs
agree well with the APOGEE data. The stellar evolutionary and spectroscopic
masses are estimated based on the stellar parameters, multi-band magnitudes,
distances and extinction values. Finally, we construct a binary catalog
including about 2700 candidates by analyzing their light curves, fitting the RV
data, calculating the binarity parameters from med-resolution spectra, and
cross-matching the spatially resolved binary catalog from $Gaia$ EDR3. The
LAMOST TD survey is expected to get breakthrough in various scientific topics,
such as binary system, stellar activity, and stellar pulsation, etc.


  We investigated six H II regions with infrared, bright rimmed bubble or
cometary morphology, in search of quantitative evidence for triggered star
formation, both collect and collapse and radiatively driven implosion. We
identified and classified 458 Young Stellar Objects (YSOs) in and around the H
II regions. YSOs were determined by fitting a collection of radiative transfer
model spectral energy distributions (SEDs) to infrared photometry for a large
sample of point sources. We determined areas where there exist enhanced
populations of relatively unevolved YSOs on the bright rims of these regions,
suggesting that star formation has been triggered there. We further
investigated the physical properties of the regions by using radio continuum
emission as a proxy for ionizing flux powering the H II regions, and 13CO (1-0)
observations to measure masses and gravitational stability of molecular clumps.
We used an analytical model of collect and collapse triggered star formation,
as well as a simulation of radiatively driven implosion, and thus we compare
the observed properties of the molecular gas with those predicted in the
triggering scenarios. Notably, those regions in our sample that show evidence
of cometary, or "blister," morphology are more likely to show evidence of
triggering.
  Keywords: HII regions -- ISM: bubbles -- Stars: formation -- Stars:
protostars


  We consider a Maxwell-$CP(2)$ model extended to include a magnetic impurity.
We focus our attention on the time-independent configurations with radial
symmetry, from which we minimize the corresponding energy by following the
Bogomol'nyi-Prasad-Sommerfield (BPS) prescription. We use the general
first-order expressions in order to introduce modified scenarios in which the
impurity plays a relevant role. We then solve the effective first-order
equations numerically by means of a finite-difference scheme, from which we
comment on the main changes on the shape of the final solutions caused by the
presence of a localised impurity. We also discuss the limit when the impurity
becomes a delta function.


  For continuous Mott metal-insulator transitions in layered two dimensional
systems, we demonstrate the phenomenon of dimensional decoupling: the system
behaves as a three-dimensional metal in the Fermi liquid side but as a stack of
decoupled two-dimensional layers in the Mott insulator. We show that the
dimensional decoupling happens at the Mott quantum critical point itself. We
derive the temperature dependence of the interlayer electric conductivity in
various crossover regimes near such a continuous Mott transition, and discuss
experimental implications.


  Bipartite quantum states are classified into three categories: separable
states, bound entangled states, and free entangled states. It is of great
importance to characterize these families of states for the development of
quantum information science. In this paper, I show that the separable states
and the bound entangled states have a common spectral property. More precisely,
I prove that for undistillable -- separable and bound entangled -- states, the
eigenvalue vector of the global system is majorized by that of the local
system. This result constitutes a new sufficient condition for distillability
of bipartite quantum states. This is achieved by proving that if a bipartite
quantum state satisfies the reduction criterion for distillability, then it
satisfies the majorization criterion for separability.


  Microarray studies, in order to identify genes associated with an outcome of
interest, usually produce noisy measurements for a large number of gene
expression features from a small number of subjects. One common approach to
analyzing such high-dimensional data is to use linear errors-in-variables
models; however, current methods for fitting such models are computationally
expensive. In this paper, we present two efficient screening procedures, namely
corrected penalized marginal screening and corrected sure independence
screening, to reduce the number of variables for final model building. Both
screening procedures are based on fitting corrected marginal regression models
relating the outcome to each contaminated covariate separately, which can be
computed efficiently even with a large number of features. Under mild
conditions, we show that these procedures achieve screening consistency and
reduce the number of features considerably, even when the number of covariates
grows exponentially with the sample size. Additionally, if the true covariates
are weakly correlated, corrected penalized marginal screening can achieve full
variable selection consistency. Through simulation studies and an analysis of
gene expression data for bone mineral density of Norwegian women, we
demonstrate that the two new screening procedures make estimation of linear
errors-in-variables models computationally scalable in high dimensional
settings, and improve finite sample estimation and selection performance
compared with estimators that do not employ a screening stage.


  Quantum anomalous Hall (QAH) phase is a two-dimensional bulk ferromagnetic
insulator with a nonzero Chern number in presence of spin-orbit coupling (SOC)
but absence of applied magnetic fields. Associated metallic chiral edge states
host dissipationless current transport in electronic devices. This intriguing
QAH phase has recently been observed in magnetic impurity-doped topological
insulators, {\it albeit}, at extremely low temperatures. Based on
first-principles density functional calculations, here we predict that layered
rhodium oxide K$_{0.5}$RhO$_2$ in noncoplanar chiral antiferromagnetic state is
an unconventional three-dimensional QAH insulator with a large band gap and a
Neel temperature of a few tens Kelvins. Furthermore, this unconventional QAH
phase is revealed to be the exotic quantum topological Hall effect caused by
nonzero scalar spin chirality due to the topological spin structure in the
system and without the need of net magnetization and SOC.


  In this work we clarify some properties of the one-loop IR divergences in
non-Abelian gauge field theories on non-commutative 4-dimensional Moyal space.
Additionally, we derive the tree-level Slavnov-Taylor identities relating the
two, three and four point functions, and verify their consistency with the
divergent one-loop level results. We also discuss the special case of two
dimensions.


  Within the past few years, we have witnessed the rising of quantum machine
learning (QML) models which infer electronic properties of molecules and
materials, rather than solving approximations to the electronic Schrodinger
equation. The increasing availability of large quantum mechanics reference data
sets have enabled these developments. We review the basic theories and key
ingredients of popular QML models such as choice of regressor, data of varying
trustworthiness, the role of the representation, and the effect of training set
selection. Throughout we emphasize the indispensable role of learning curves
when it comes to the comparative assessment of different QML models.


  As shown by S. Eilenberg and J.C. Moore (1965), for a monad $F$ with right
adjoint comonad $G$ on any catgeory $\mathbb{A}$, the category of unital
$F$-modules $\mathbb{A}_F$ is isomorphic to the category of counital
$G$-comodules $\mathbb{A}^G$. The monad $F$ is Frobenius provided we have $F=G$
and then $\mathbb{A}_F\simeq \mathbb{A}^F$. Here we investigate which kind of
equivalences can be obtained for non-unital monads (and non-counital comonads).


  Recently, the state-of-the-art models for image captioning have overtaken
human performance based on the most popular metrics, such as BLEU, METEOR,
ROUGE, and CIDEr. Does this mean we have solved the task of image captioning?
The above metrics only measure the similarity of the generated caption to the
human annotations, which reflects its accuracy. However, an image contains many
concepts and multiple levels of detail, and thus there is a variety of captions
that express different concepts and details that might be interesting for
different humans. Therefore only evaluating accuracy is not sufficient for
measuring the performance of captioning models --- the diversity of the
generated captions should also be considered. In this paper, we proposed a new
metric for measuring the diversity of image captions, which is derived from
latent semantic analysis and kernelized to use CIDEr similarity. We conduct
extensive experiments to re-evaluate recent captioning models in the context of
both diversity and accuracy. We find that there is still a large gap between
the model and human performance in terms of both accuracy and diversity and the
models that have optimized accuracy (CIDEr) have low diversity. We also show
that balancing the cross-entropy loss and CIDEr reward in reinforcement
learning during training can effectively control the tradeoff between diversity
and accuracy of the generated captions.


  We have undertaken a multiwavelength project to study the relatively unknown
properties of groups and poor clusters of galaxies at intermediate redshifts.
In this paper, we describe the XMM-Newton observations of six X-ray selected
groups with 0.2<z<0.6. The X-ray properties of these systems are generally in
good agreement with the properties of low-redshift groups. They appear to
follow the scaling relations between luminosity, temperature, and velocity
dispersion defined by low-redshift groups and clusters. The X-ray emission in
four of the six groups is also centered on a dominant early-type galaxy. The
lack of a bright elliptical galaxy at the peak of the group X-ray emission is
rare at low-redshifts, and the other two groups may be less dynamically
evolved. We find indications of excess entropy in these systems over
self-similar predictions out to large radii. We also confirm the presence of at
least one X-ray luminous AGN associated with a group member galaxy and find
several other potential group AGN.


  Modifications of CARLOMAT, a program for automatic computation of the lowest
order cross sections of multiparticle reactions, that include an abridgement of
the phase space integration routine, an interface to parton density functions,
improvement of the color matrix computation, supplementation of the
Cabibbo-Kobayashi-Maskawa mixing in the quark sector, implementation of
effective models such as scalar electrodynamics, the $Wtb$ interaction with
operators of dimension up to 5 and a general top--Higgs coupling, are
discussed. The modifications, together with recent developments concerning
mainly description of the $e^+e^-$ annihilation into hadrons at low energies,
broaden the spectrum of possible applications of the program.


  Postulating the existence of a fnite-mass mediator of T,P-odd coupling
between atomic electrons and nucleons we consider its effect on permanent
electric dipole moment (EDM) of diamagnetic atoms. We present both numerical
and analytical analysis for such mediator-induced EDMs and compare it with EDM
results for the conventional contact interaction. Based on this analysis we
derive limits on coupling strengths and carrier masses from experimental limits
on EDM of 199Hg atom.


  We show how to achieve full spectral characterization of general multiaxis
additive noise. Our pulsed spectral estimation technique is based on sequence
repetition and frequency-comb sampling and is applicable even to models where a
large qubit energy-splitting is present (as is typically the case for spin
qubits in semiconductors, for example), as long as the noise is stationary and
a second-order (Gaussian) approximation to the controlled reduced dynamics is
viable. Our new result is crucial to extending the applicability of these
protocols, now standard in dephasing-dominated platforms such as silicon-based
qubits, to experimental platforms where both $T_1$ and $T_2$ processes are
significant, such as superconducting qubits.


  We investigate the impact of dust-induced gas fragmentation on the formation
of the first low-mass, metal-poor stars (< 1Msun) in the early universe.
Previous work has shown the existence of a critical dust-to-gas ratio, below
which dust thermal cooling cannot cause gas fragmentation. Assuming the first
dust is silicon-based, we compute critical dust-to-gas ratios and associated
critical silicon abundances ([Si/H]crit). At the density and temperature
associated with protostellar disks, we find that a standard Milky Way grain
size distribution gives [Si/H]crit = -4.5 +/- 0.1, while smaller grain sizes
created in a supernova reverse shock give [Si/H]crit = -5.3 +/- 0.1. Other
environments are not dense enough to be influenced by dust cooling. We test the
silicate dust cooling theory by comparing to silicon abundances observed in the
most iron-poor stars ([Fe/H] < -4.0). Several stars have silicon abundances low
enough to rule out dust-induced gas fragmentation with a standard grain size
distribution. Moreover, two of these stars have such low silicon abundances
that even dust with a shocked grain size distribution cannot explain their
formation. Adding small amounts of carbon dust does not significantly change
these conclusions. Additionally, we find that these stars exhibit either high
carbon with low silicon abundances or the reverse. A silicate dust scenario
thus suggests that the earliest low-mass star formation in the most metal-poor
regime may have proceeded through two distinct cooling pathways: fine structure
line cooling and dust cooling. This naturally explains both the carbon-rich and
carbon-normal stars at extremely low [Fe/H].


  The Sun is located close to the Galactic mid-plane, meaning that we observe
the Galaxy through significant quantities of dust. Moreover, the vast majority
of the Galaxy's stars also lie in the disc, meaning that dust has an enormous
impact on the massive astrometric, photometric and spectroscopic surveys of the
Galaxy that are currently underway. To exploit the data from these surveys we
require good three-dimensional maps of the Galaxy's dust. We present a new
method for making such maps in which we form the best linear unbiased predictor
of the extinction at an arbitrary point based on the extinctions for a set of
observed stars. This method allows us to avoid the artificial inhomogeneities
(so-called 'fingers of God') and resolution limits that are characteristic of
many published dust maps. Moreover, it requires minimal assumptions about the
statistical properties of the interstellar medium. In fact, we require only a
model of the first and second moments of the dust density field. The method is
suitable for use with directly measured extinctions, such as those provided by
the Rayleigh-Jeans colour excess method, and inferred extinctions, such as
those provided by hierarchical Bayesian models like StarHorse. We test our
method by mapping dust in the region of the giant molecular cloud Orion A. Our
results indicate a foreground dust cloud at a distance of 350 pc, which has
been identified in work by another author.


  We present a new approach to interpreting IRR that is empirical and
contextualized. It is based upon benchmarking IRR against baseline measures in
a replication, one of which is a novel cross-replication reliability (xRR)
measure based on Cohen's kappa. We call this approach the xRR framework. We
opensource a replication dataset of 4 million human judgements of facial
expressions and analyze it with the proposed framework. We argue this framework
can be used to measure the quality of crowdsourced datasets.


  We report the discovery of excess broad band absorption near 2250 A (EBBA) in
the spectra of seven broad absorption line (BAL) quasars. By comparing with the
statistical results from the control quasar sample, the significance for the
detections are all above the > 4{\sigma} level, with five above > 5{\sigma}.
The detections have also been verified by several other independent methods.
The EBBAs present broader and weaker bumps at smaller wavenumbers than the
Milky Way, and similar to the Large Magellanic Cloud. The EBBA bump may be
related to the 2175 A bump seen in the Local Group and may be a counterpart of
the 2175 A bump under different conditions in the early Universe. Furthermore,
five objects in this sample show low-ionization broad absorption lines
(LoBALs), such as Mg II and Al III, in addition to the high-ionization broad
absorption lines (HiBALs) of C IV and Si IV. The fraction of LoBALs in our
sample, ~70%, is surprisingly high compared to that of general BAL quasars,
~10%. Although the origin of the bump is still not clear, the coexistence of
both BALs and bumps and the significantly high fraction of LoBALs may indicate
the bump carriers is closely related to the early evolution phase of quasars.


  In order to investigate the origin of the until now unaccounted excess noise
and to minimize the uncontrollable phenomena at the transition in X-ray
microcalorimeters we have developed superconducting transition-edge sensors
into an edgeless geometry, the so-called Corbino disk (CorTES), with
superconducting contacts in the centre and at the outer perimeter. The measured
rms current noise and its spectral density can be modeled as resistance noise
resulting from fluctuations near the equilibrium superconductor-normal metal
boundary


  We calculate the resistivity associated with an Ising-nematic quantum
critical point in the presence of disorder and acoustic phonons in the lattice
model. We use the memory-matrix transport theory, which has a crucial advantage
compared to other methods of not relying on the existence of well-defined
quasiparticles in the low-energy effective theory. As a result, we obtain that
by including an inevitable interaction between the nematic fluctuations and the
elastic degrees of freedom of the lattice (parametrized by the nemato-elastic
coupling $\kappa_{\text{latt}}$), the resistivity $\rho(T)$ of the system as a
function of temperature obeys a universal scaling form described by
$\rho(T)\sim T\ln (1/T)$ at high temperatures, reminiscent of the paradigmatic
strange metal regime observed in many strongly correlated compounds. For a
window of temperatures comparable with
$\kappa^{3/2}_{\text{latt}}\varepsilon_F$ (where $\varepsilon_F$ is the Fermi
energy of the microscopic model), the system displays another regime in which
the resistivity is consistent with a description in terms of $\rho(T)\sim
T^{\alpha}$, where the effective exponent roughly satisfies the inequality
$1\lesssim\alpha\lesssim 2$. However, in the low-temperature limit (i.e.,
$T\ll\kappa^{3/2}_{\text{latt}}\varepsilon_F$), the properties of the quantum
critical state change in an important way depending on the types of disorder
present in the system: It can either recover a conventional Fermi liquid
described by $\rho(T)\sim T^2$ or it could exhibit yet another non-Fermi liquid
regime characterized by the scaling form $\rho(T)-\rho_0\sim T^2\ln T$. Our
results emphasize the key role played by both phonon and disorder effects in
the scenario of nematic quantum criticality and might be fundamental for
addressing recent transport experiments in some iron-based superconductors.


  Active galactic nuclei (AGNs) have been one of the most widely discussed
sources of ultrahigh-energy cosmic rays (UHECRs). The recent results of Pierre
Auger observatory (PAO) have indicated a possible composition change of UHECRs
above ~10^{18.5} eV towards heavy nuclei. We show here that if indeed UHECRs
are largely heavy nuclei, then nearby radio quiet AGNs can also be viable
sources of UHECRs. We derive constraints on the acceleration sites which enable
acceleration of UHECRs to 10^{20} eV without suffering losses. We show that the
acceleration of UHECRs and the survival of energetic heavy nuclei are possible
in the parsec scale weak jets that are typically observed in these objects, the
main energy loss channel being photodisintegration. On this scale, energy
dissipation by shock waves resulting from interactions inside a jet or of the
jet with surrounding material are expected, which may accelerate the particles
up to very high energies. We discuss the possible contribution of radio-quiet
AGNs to the observed UHECR flux, and show that the required energy production
rate in UHECRs by a single object could be as low as ~ 3*10^{39} erg/s, which
is less than a percent of the bolometric luminosity, and thus energetically
consistent. We discuss consequences of this model, the main one being the
difficulty in detecting energetic secondaries (\gamma-rays and neutrinos) from
the same sources.


  Influence of a spiral spin structure on the superconducting (SC) pairing in
the most probable active $\gamma$ band of $Sr_2RuO_4$ is studied in the mean
field approximation. Such structure with "incommensurate" vector
$Q=2\pi(1/3,1/3)$ has been proposed as that which removes the nesting
instability in $\alfa, \betta$ bands. The model pairing interaction of adjacent
centres is adopted. The mixed singlet and triplet SC order is revealed. The
d-wave singlet pairing is accompanied by formation of the p-wave triplet pairs
with large total momentum Q and spin projections $\pm 1$ onto axis normal to
the spin rotation plane of the spiral structure. Both the superconducting and
normal states have a broken time reversal symmetry which might be detected by
polarised photoemission.


  We characterize those $k$-automatic sets $S$ of natural numbers that form an
additive basis for the natural numbers, and we show that this characterization
is effective. In addition, we give an algorithm to determine the smallest $j$
such that $S$ forms an additive basis of order $j$, if it exists.


  Neural network methods exhibit strong performance only in a few resource-rich
domains. Practitioners, therefore, employ domain adaptation from resource-rich
domains that are, in most cases, distant from the target domain. Domain
adaptation between distant domains (e.g., movie subtitles and research papers),
however, cannot be performed effectively due to mismatches in vocabulary; it
will encounter many domain-specific words (e.g., "angstrom") and words whose
meanings shift across domains(e.g., "conductor"). In this study, aiming to
solve these vocabulary mismatches in domain adaptation for neural machine
translation (NMT), we propose vocabulary adaptation, a simple method for
effective fine-tuning that adapts embedding layers in a given pre-trained NMT
model to the target domain. Prior to fine-tuning, our method replaces the
embedding layers of the NMT model by projecting general word embeddings induced
from monolingual data in a target domain onto a source-domain embedding space.
Experimental results indicate that our method improves the performance of
conventional fine-tuning by 3.86 and 3.28 BLEU points in En-Ja and De-En
translation, respectively.


  Recently the matcher game was introduced. In this game, two players create a
maximal matching by one player repeatedly choosing a vertex and the other
player choosing a $K_2$ containing that vertex. One player tries to minimize
the result and the other to maximize the result.In this paper we propose a
generalization of this game where $K_2$ is replaced by a general graph $F$. We
focus here on the case of $F=P_3$. We provide some general results and lower
bounds for the game, investigate the graphs where the game ends with all
vertices taken, and calculate the value for some specific families of graphs.


  Modification of the renormalization-group approach, invoking Stratonovich
transformation at each step, is proposed to describe phase transitions in 3D
Ising-class systems. The proposed method is closely related to the mean-field
approximation. The low-order scheme works well for a wide thermal range, is
consistent with a scaling hypothesis and predicts very reasonable values of
critical indices.


  Many machine learning systems are vulnerable to small perturbations made to
inputs either at test time or at training time. This has received much recent
interest on the empirical front due to applications where reliability and
security are critical. However, theoretical understanding of algorithms that
are robust to adversarial perturbations is limited.
  In this work we focus on Principal Component Analysis (PCA), a ubiquitous
algorithmic primitive in machine learning. We formulate a natural robust
variant of PCA where the goal is to find a low dimensional subspace to
represent the given data with minimum projection error, that is in addition
robust to small perturbations measured in $\ell_q$ norm (say $q=\infty$).
Unlike PCA which is solvable in polynomial time, our formulation is
computationally intractable to optimize as it captures a variant of the
well-studied sparse PCA objective as a special case. We show the following
results:
  -Polynomial time algorithm that is constant factor competitive in the
worst-case with respect to the best subspace, in terms of the projection error
and the robustness criterion.
  -We show that our algorithmic techniques can also be made robust to
adversarial training-time perturbations, in addition to yielding
representations that are robust to adversarial perturbations at test time.
Specifically, we design algorithms for a strong notion of training-time
perturbations, where every point is adversarially perturbed up to a specified
amount.
  -We illustrate the broad applicability of our algorithmic techniques in
addressing robustness to adversarial perturbations, both at training time and
test time. In particular, our adversarially robust PCA primitive leads to
computationally efficient and robust algorithms for both unsupervised and
supervised learning problems such as clustering and learning adversarially
robust classifiers.


  We have studied the kinematics of the ionized gas and stellar component in
Mrk334 using methods of panoramic (3D) spectroscopy. The observations were
performed at the prime focus of the SAO RAS 6-m telescope with the
integral-field spectrograph MPFS (Afanasiev et al. 2001) and with a scanning
Fabry-Perot interferometer (FPI), installed on the multimode device SCORPIO
(Afanasiev & Moiseev 2005). Based on these data, the monochromatic maps and
velocity fields in different emission lines of the ionized gas were
constructed. The diagnostic diagrams have been made based on the emission lines
ratios.


  We present an instrument to perform frequency-domain electron spin resonance
(ESR) experiments that is based on coplanar waveguides and field modulation. A
large parameter space in frequency (up to 25 GHz), magnetic field (up to 8 T),
and temperature (down to 1.6 K) is accessible. We performed experiments on DPPH
(2,2-diphenyl-1-picrylhydrazyl) as a standard to calibrate the field modulation
as well as on a carbon fibre sample to estimate the overall sensitivity of the
instruments. Spectra of a ruby sample in a broad frequency- and field range at
cryogenic temperatures are recorded with and without field modulation. The
comparison reveals the improved signal-to-noise ratio achieved by field
modulation.


  We analyze optimal strategies for the allocation of a finite budget that can
be invested in different advertising channels over time with the objective of
influencing social opinions in a network of individuals. In our analysis, we
consider both exogenous influence mechanisms, such as advertising campaigns, as
well as endogenous mechanisms of social influence, such as word-of-mouth and
peer-pressure, which are modeled using diffusion dynamics.
  We show that for a broad family of objective functions, the optimal influence
strategy at every time uses all channels at either their maximum rate or not at
all, i.e., a bang-bang strategy. Furthermore, we prove that the number of
switches between these extremes is bounded above by a term that is typically
much smaller than the number of agents. This means that the optimal influence
strategy is to exert maximum effort in waves for every channel, and then cease
effort and let the effects propagate. We also show that, at the beginning of
the campaign, the total cost-adjusted reach of an exogenous advertising channel
determines its relative value. In contrast, as we approach our investment
horizon (e.g., election day), the optimal strategy is to invest in channels
able to target individuals instead of broad-reaching channels. We demonstrate
that the optimal influence strategies are easily computable in several
practical cases, and explicitly characterize the optimal controls for the case
of linear objective functions in closed form. Finally, we see that, in the
canonical example of designing an election campaign, identifying late-deciders
is a critical component in the optimal design.


  The Crab Nebula emits bright non-thermal radiation from radio to the most
energetic photons. The underlying physical model of a relativistic wind from
the pulsar terminating in a hydrodynamic standing shock remains unchanged since
the early 1970s. In this model, an increase of the toroidal magnetic field
downstream from the shock is expected. We introduce a detailed radiative model
to calculate non-thermal synchrotron and inverse Compton as well as thermal
dust emission self-consistently to compare quantitatively with observational
data. Special care is given to the radial dependence of electron and seed field
density. The radiative model is used to estimate the parameters of electrons
and dust in the nebula. A combined fit based upon a $\chi^2$ minimisation
reproduces successfully the complete data set used. For the best-fitting model,
the energy density of the magnetic field dominates over the particle energy
density up to a distance of $\approx 1.3~r_s$ ($r_s$: distance of the
termination shock from the pulsar). The very high energy (VHE: $E>100$ GeV)
gamma-ray spectra set the strongest constraints on the radial dependence of the
magnetic field: $B(r)=(264\pm9)~\mu\mathrm{G} (r/r_s)^{-0.51\pm0.03}$. The
reconstructed magnetic field and its radial dependence indicates a ratio of
Poynting to kinetic energy flux $\sigma\approx 0.1$ at the termination shock,
$\approx 30$ times larger than estimated up to now. Consequently, the
confinement of the nebula would require additional mechanisms to slow down the
flow through e.g. excitation of small-scale turbulence with possible
dissipation of magnetic field.


  Off-grid systems have emerged as a sustainable and cost-effective solution
for rural electrification. In sub-Sarahan Africa (SSA), a great number of
solar-hybrid microgrids have been installed or planned, operating stand-alone
or grid-tied to a weak grid. Presence of intermittent energy sources
necessitates the provision of energy storage for system balancing. Reliability
and economic performance of those rural microgrids strongly depend on specific
control strategies. This work develops a predictive control framework dedicated
to rural microgrids incorporating a temperature-dependent battery degradation
model. Based on a scalable DC PV-battery microgrid, the realistic simulation
shows its superior performance in the reliability improvement and cost
reduction. Compared with the day-ahead control without the
temperature-dependent battery degradation model, this control strategy can
improve the reliability by 5.5% and extend the lead-acid battery life time by
26%, equivalent to lowering the levelised cost of electricity (LCOE) by 13%.


  We assume that the Stefan problem with undercooling has a classical solution
until the moment of contact of free boundaries and the free boundaries have
continuous velocities until the moment of contact. Under these assumptions, we
construct a smooth approximation of the global solution of the Stefan problem
with undercooling, which, until the contact, gives the classical solution
mentioned above and, after the contact, gives a solution which is the solution
of the heat equation.


  We show that the locus of stable rank four vector bundles without theta
divisor over a smooth projective curve of genus two is in canonical bijection
with the set of theta-characteristics. We give several descriptions of these
bundles and compute the degree of the rational theta map.


  We study a variation of the Trotter-Suzuki decomposition, in which a
Hamiltonian exponential is approximated by an ordered product of two-qubit
operator exponentials such that the Trotter step size is enhanced for a small
number of terms. Such decomposition directly reflects hardware constraints of
distributed quantum computers, where operations on monolithic quantum devices
are fast compared to entanglement distribution across separate nodes using
interconnects. We simulate non-equilibrium dynamics of transverse-field Ising
and XY spin chain models and investigate the impact of locally increased
Trotter step sizes that are associated with an increasingly sparse use of the
quantum interconnect. We find that the overall quality of the approximation
depends smoothly on the local sparsity and that the proliferation of local
errors is slow. As a consequence, we show that fast local operations on
monolithic devices can be leveraged to obtain an overall improved result
fidelity even on distributed quantum computers where the use of interconnects
is costly.


  The rapid development of telecommunication networks is driven by user demands
for new applications and advances in technologies. The explosive growth of the
internet traffic is due to its use for collecting the information,
communication, multimedia application, entertainment, etc. These applications
are imposing a tremendous demand for bandwidth capacity on telecommunication
network. The introduction of fiber optics had proved to meet the huge demand of
bandwidth. These requirement can be meet by all optical network which is
capable of transmitting enormous data at very high speed, around 50 Tera bits
per seconds (Tbps) A wavelength conversion technique is addressed in this paper
to reduced the blocking probability in wavelength routed networks. It is seen
that the blocking probability of traffic requests decreases as the wavelength
conversion factor increases. We explode the possibility for network with
different size with variation in wavelength per link. In this work the
evaluation of wavelength routed optical network with varying number of
wavelength converters, different traffic types are carried out and results are
shown that the blocking probability is minimum with 50% to 60% wavelength
convertible nodes. Wavelength convertible nodes more than 60% are not showing
much effect on reduction in blocking probability rather it results in increase
in overall cost of network.


  Following the reasoning of Claudson and Halpern, it is shown that
"fifth-time" stabilized quantum gravity is equivalent to Langevin evolution
(i.e. stochastic quantization) between fixed non-singular, but otherwise
arbitrary, initial and final states. The simple restriction to a fixed final
state at $t_5 \rightarrow \infty$ is sufficient to stabilize the theory. This
equivalence fixes the integration measure, and suggests a particular
operator-ordering, for the fifth-time action of quantum gravity. Results of a
numerical simulation of stabilized, latticized Einstein-Cartan theory on some
small lattices are reported. In the range of cosmological constant $\l$
investigated, it is found that: 1) the system is always in the broken phase
$<det(e)> \ne 0$; and 2) the negative free energy is large, possibly singular,
in the vincinity of $\l = 0$. The second finding may be relevant to the
cosmological constant problem.


  We use the background field method to systematically derive CFT data for the
critical $\phi^6$ vector model in three dimensions, and the Gross-Neveu model
in dimensions $2\leq d \leq 4$. Specifically, we calculate the OPE coefficients
and anomalous dimensions of various operators, up to next-to-leading order in
the $1/N$ expansion.


  We provide a general program for finding nice arrangements of points in real
or complex projective space from transitive actions of finite groups. In many
cases, these arrangements are optimal in the sense of maximizing the minimum
distance. We introduce our program in terms of general Schurian association
schemes before focusing on the special case of Gelfand pairs. Notably, our
program unifies a variety of existing packings with heretofore disparate
constructions. In addition, we leverage our program to construct the first
known infinite family of equiangular lines with Heisenberg symmetry.


  With malware detection techniques increasingly adopting machine learning
approaches, the creation of precise training sets becomes more and more
important. Large data sets of realistic web traffic, correctly classified as
benign or malicious are needed, not only to train classic and deep learning
algorithms, but also to serve as evaluation benchmarks for existing malware
detection products. Interestingly, despite the vast number and versatility of
threats a user may encounter when browsing the web, actual malicious content is
often hard to come by, since prerequisites such as browser and operating system
type and version must be met in order to receive the payload from a malware
distributing server. In combination with privacy constraints on data sets of
actual user traffic, it is difficult for researchers and product developers to
evaluate anti-malware solutions against large-scale data sets of realistic web
traffic. In this paper we present WebEye, a framework that autonomously creates
realistic HTTP traffic, enriches recorded traffic with additional information,
and classifies records as malicious or benign, using different classifiers. We
are using WebEye to collect malicious HTML and JavaScript and show how datasets
created with WebEye can be used to train machine learning based malware
detection algorithms. We regard WebEye and the data sets it creates as a tool
for researchers and product developers to evaluate and improve their AI-based
anti-malware solutions against large-scale benchmarks.


  Dual AdS/CFT correlators can be computed in two ways: differentiate the bulk
partition function with respect to boundary conditions, or extrapolate bulk
correlation functions to the boundary. These dictionaries were conjectured to
be equivalent by Banks, Douglas, Horowitz, and Martinec. We revisit this
question at the level of bulk path integrals, showing that agreement in the
presence of interactions requires careful treatment of the renormalization of
bulk composite operators. By contrast, we emphasize that proposed dS/CFT
analogues of the two dictionaries are inequivalent. Next, we show quite
generally that the wave function for Euclidean AdS analytically continues to
the dS wave function with Euclidean initial conditions. Most of our arguments
consider interacting fields on a fixed background, but in a final section we
discuss the inclusion of bulk dynamical gravity.


  We consider waves travelling in two different mediums each endowed with a
different constant speed of propagation. At the interface between the two
mediums, the refraction of the rays of the optic geometry is described by the
Snell-Descartes law. We provide sufficient conditions on the geometry of the
mediums and on the speed of propagation for the boundary controllability.


  Recent solar spectroscopic observations have shown that coronal spectral
lines can exhibit asymmetric profiles, with enhanced emissions at their blue
wings. These asymmetries correspond to rapidly upflowing plasmas at speeds
exceeding ~ 50 km/s. Here, we perform a study of the density of the rapidly
upflowing material and compare it to that of the line core which corresponds to
the bulk of the plasma. For this task we use spectroscopic observations of
several active regions taken by the Extreme Ultraviolet Imaging Spectrometer of
the Hinode mission. The density sensitive ratio of the Fe XIV lines at 264.78
and 274.20 A is used to determine wing and core densities. We compute the ratio
of the blue wing density to the core density and find that most values are of
order unity. This is consistent with the predictions for coronal nanoflares if
most of the observed coronal mass is supplied by chromospheric evaporation
driven by the nanoflares. However, much larger blue wing-to-core density ratios
are predicted if most of the coronal mass is supplied by heated material
ejected with type II spicules. Our measurements do not rule out a spicule
origin for the blue wing emission, but they argue against spicules being a
primary source of the hot plasma in the corona. We note that only about 40% of
the pixels where line blends could be safely ignored have blue wing asymmetries
in both Fe XIV lines. Anticipated sub-arcsecond spatial resolution
spectroscopic observations in future missions could shed more light on the
origin of blue, red, and mixed asymmetries.


  We prove a kind of integral expressions for finite multiple harmonic sums and
multiple zeta-star values. Moreover, we introduce a class of multiple
integrals, associated with some combinatorial data (called 2-labeled posets).
This class includes both multiple zeta and zeta-star values of Euler-Zagier
type, and also several other types of multiple zeta values. We show that these
integrals can be used to obtain some relations among such zeta values quite
transparently.


  Native defects in semiconductors play an important role in their
optoelectronic properties. Nickel oxide (NiO) is one of the few wide-gap p-type
oxide semiconductors and its conductivity is believed to be controlled
primarily by Ni-vacancy acceptors. Herein, we present a systematic study
comparing the optoelectronic properties of stoichiometric NiO, oxygen-rich NiO
with Ni vacancies (NiO:VNi), and Ni-rich NiO with O vacancies (NiO:VO). The
optical properties were obtained by spectroscopic ellipsometry, while valence
band spectra were probed by high-resolution x-ray photoelectron spectroscopy.
The experimental results are directly compared to first-principles density
functional theory + U calculations. Computational results confirm that gap
states are present in both NiO systems with vacancies. Gap states in NiO:Vo are
predominantly Ni 3d states, while those in NiO:VNi are composed of both Ni 3d
and O 2p states. The absorption spectra of the NiO:VNi sample show significant
defect-induced features below 3.0 eV compared to NiO and NiO:VO samples. The
increase in sub-gap absorptions in NiO:VNi can be attributed to gap states
observed in the electronic density of states. The relation between native
vacancy defects and electronic and optical properties of NiO are demonstrated,
showing that at similar vacancy concentration, the optical constants of NiO:VNi
deviate significantly from those of NiO:VO. Our experimental and computational
results reveal that although VNi are effective acceptors in NiO, they also
degrade the visible transparency of the material. Hence, for transparent
optoelectronic device applications, an optimization of native VNi defects with
extrinsic doping is required to simultaneously enhance p-type conductivity and
transparency.


  Context. Recently, for the first time the abundance of P has been measured in
disk stars. This provides the opportunity of comparing the observed abundances
with predictions from theoretical models. Aims. We aim at predicting the
chemical evolution of P in the Milky Way and compare our results with the
observed P abundances in disk stars in order to put constraints on the P
nucleosynthesis. Methods. To do that we adopt the two-infall model of galactic
chemical evolution, which is a good model for the Milky Way, and compute the
evolution of the abundances of P and Fe. We adopt stellar yields for these
elements from different sources. The element P should have been formed mainly
in Type II supernovae. Finally, Fe is mainly produced by Type Ia supernovae.
Results. Our results confirm that to reproduce the observed trend of [P/Fe] vs.
[Fe/H] in disk stars, P is formed mainly in massive stars. However, none of the
available yields for P can reproduce the solar abundance of this element. In
other words, to reproduce the data one should assume that massive stars produce
more P than predicted by a factor of ~ 3. Conclusions. We conclude that all the
available yields of P from massive stars are largely underestimated and that
nucleosynthesis calculations should be revised. We also predict the [P/Fe]
expected in halo stars.


  We consider a Landau theory of coupled charge and spin-density wave order
parameters as a simple model for the ordering that has been observed
experimentally in the La_2NiO_4 and La_2CuO_4 families of doped
antiferromagnets. The period of the charge-density wave is generically half
that of the spin-density wave, or equivalently the charges form antiphase
domain walls in the antiferromagnetic order. A sharp distinction exists between
the case in which the ordering is primarily charge driven (which produces a
sequence of transitions in qualitative agreement with experiment) or spin
driven (which does not). We also find that stripes with non-collinear spin
order (i.e. spiral phases) are possible in a region of the phase diagram where
the transition is spin driven; the spiral is circular only when there is no
charge order, and is otherwise elliptical with an eccentricity proportional to
the magnitude of the charge order.


  Large language models (LLMs) have become a significant workload since their
appearance. However, they are also computationally expensive as they have
billions of parameters and are trained with massive amounts of data. Thus,
recent works have developed dedicated CUDA kernels for LLM training and
inference instead of relying on compilergenerated ones, so that hardware
resources are as fully utilized as possible. In this work, we explore the
possibility of GPU native instruction optimization to further push the CUDA
kernels to extreme performance. Contrary to prior works, we adopt an automatic
optimization approach by defining a search space of possible GPU native
instruction schedules, and then we apply stochastic search to perform
optimization. Experiments show that SIP can further improve CUDA kernel
throughput by automatically discovering better GPU native instruction schedules
and the optimized schedules are tested by 10 million test samples.


  We present the Spectroscopic Time-Resolving Observatory for Broadband Energy
X-rays (STROBE-X), a probe-class mission concept selected for study by NASA. It
combines huge collecting area, high throughput, broad energy coverage, and
excellent spectral and temporal resolution in a single facility. STROBE-X
offers an enormous increase in sensitivity for X-ray spectral timing, extending
these techniques to extragalactic targets for the first time. It is also an
agile mission capable of rapid response to transient events, making it an
essential X-ray partner facility in the era of time-domain, multi-wavelength,
and multi-messenger astronomy. Optimized for study of the most extreme
conditions found in the Universe, its key science objectives include: (1)
Robustly measuring mass and spin and mapping inner accretion flows across the
black hole mass spectrum, from compact stars to intermediate-mass objects to
active galactic nuclei. (2) Mapping out the full mass-radius relation of
neutron stars using an ensemble of nearly two dozen rotation-powered pulsars
and accreting neutron stars, and hence measuring the equation of state for
ultradense matter over a much wider range of densities than explored by NICER.
(3) Identifying and studying X-ray counterparts (in the post-Swift era) for
multiwavelength and multi-messenger transients in the dynamic sky through
cross-correlation with gravitational wave interferometers, neutrino
observatories, and high-cadence time-domain surveys in other electromagnetic
bands. (4) Continuously surveying the dynamic X-ray sky with a large duty cycle
and high time resolution to characterize the behavior of X-ray sources over an
unprecedentedly vast range of time scales. STROBE-X's formidable capabilities
will also enable a broad portfolio of additional science.


  Since the start of the still ongoing COVID-19 pandemic, there have been many
modeling efforts to assess several issues of importance to public health. In
this work, we review the theory behind some important mathematical models that
have been used to answer questions raised by the development of the pandemic.
We start revisiting the basic properties of simple Kermack-McKendrick type
models. Then, we discuss extensions of such models and important
epidemiological quantities applied to investigate the role of heterogeneity in
disease transmission e.g. mixing functions and superspreading events, the
impact of non-pharmaceutical interventions in the control of the pandemic,
vaccine deployment, herd-immunity, viral evolution and the possibility of
vaccine escape. From the perspective of mathematical epidemiology, we highlight
the important properties, findings, and, of course, deficiencies, that all
these models have.


  Deep networks, composed of multiple layers of hierarchical distributed
representations, tend to learn low-level features in initial layers and
transition to high-level features towards final layers. Paradigms such as
transfer learning, multi-task learning, and continual learning leverage this
notion of generic hierarchical distributed representations to share knowledge
across datasets and tasks. Herein, we study the layer-wise transferability of
representations in deep networks across a few datasets and tasks and note some
interesting empirical observations.


  The principle of orthogonal time-frequency-space (OTFS) signaling is firstly
analyzed, followed by explaining that OTFS embeds another signaling scheme
referred to as orthogonal short-time Fourier (OSTF). Then, the relationship
among OTFS, OSTF, orthogonal frequency-division multiplexing (OFDM) and
single-carrier frequency-division multiple-access (SC-FDMA) is explored,
demonstrating that OSTF/OTFS are fundamentally the extensions of OFDM/SC-FDMA
from one-dimensional (1D) signaling to two-dimensional (2D) signaling. Hence,
the characteristics and performance of OSTF/OTFS schemes can be perceived from
the well-understood OFDM/SC-FDMA schemes. Accordingly, the advantages and
disadvantages of OSTF/OTFS are discussed. Furthermore, from the principles of
OFDM/SC-FDMA, the multiuser multiplexing in OSTF/OTFS systems is analyzed with
respect to uplink and downlink, respectively. Added on this, a range of
generalized multiplexing schemes are presented, whose characteristics are
briefly analyzed.


  We evaluate the doping dependence of the quasiparticle current and low
temperature superfluid density in two slave-particle theories of the tt't''J
model -- the slave-boson theory and doped-carrier theory. In the slave-boson
theory, the nodal quasiparticle current renormalization factor $\alpha$
vanishes proportionally to the zero temperature superfluid density $\rho_S(0)$;
however, we find that away from the $\rho_S(0) \to 0$ limit $\alpha$ displays a
much weaker doping dependence than $\rho_S(0)$. A similar conclusion applies to
the doped-carrier theory, which differentiates the nodal and antinodal regions
of momentum space. Due to its momentum space anisotropy, the doped-carrier
theory enhances the value of $\alpha$ in the hole doped regime, bringing it to
quantitative agreement with experiments, and reproduces the asymmetry between
hole and electron doped cuprate superconductors. Finally, we use the
doped-carrier theory to predict a specific experimental signature of local
staggered spin correlations in doped Mott insulator superconductors which, we
propose, should be observed in STM measurements of underdoped high-Tc
compounds. This experimental signature distinguishes the doped-carrier theory
from other candidate mean-field theories of high-Tc superconductors, like the
slave-boson theory and the conventional BCS theory.


  It is proposed that the mathematical formalism that is most appropriate for
the study of spatially non-integrable cosmological models is the transverse
geometry of a one-dimensional foliation (congruence) defined by a physical
observer. By that means, one can discuss the geometry of space, as viewed by
that observer, without the necessity of introducing a complementary sub-bundle
to the line bundle of the observer or a codimension-one foliation transverse to
the foliation of the observer. The concept of groups of transverse isometries
acting on such a spacetime and the relationship of transverse geometry to
spacetime threadings (1+3 decompositions) is also discussed.


  In hep-ph/0404212 Diakonov, Petrov, and Polyakov respond to my recent
comments on their 1997 paper, ``Exotic anti-decuplet of baryons: prediction
from chiral solitons''. Their responses do not address the basic issues or
alter the conclusions in my paper.


  Mobile applications (a.k.a., apps), which facilitate a large variety of tasks
on mobile devices, have become indispensable in our everyday lives.
Accomplishing a task may require the user to navigate among various apps.
Unlike Web pages that are inherently interconnected through hyperlinks, mobile
apps are usually isolated building blocks, and the lack of direct links between
apps has largely compromised the efficiency of task completion. In this paper,
we present the first in-depth empirical study of inter-app navigation behaviors
of smartphone users based on a comprehensive dataset collected through a
sizable user study over three months. We propose a model to distinguish
informational pages and transitional pages, based on which a large number of
inter-app navigation are identified. We reveal that developing 'tunnels'
between of isolated apps has a huge potential to reduce the cost of navigation.
Our analysis provides various practical implications on how to improve
app-navigation experiences from both the operating system's perspective and the
developer's perspective.


  Many-electron systems confined to a quasi-1D geometry by a cylindrical
distribution of positive charge have been investigated by density functional
computations in the unrestricted local spin density approximation. Our
investigations have been focused on the low density regime, in which electrons
are localised. The results reveal a wide variety of different charge and spin
configurations, including linear and zig-zag chains, single and double-strand
helices, and twisted chains of dimers. The spin-spin coupling turns from weakly
anti-ferromagnetic at relatively high density, to weakly ferromagnetic at the
lowest densities considered in our computations. The stability of linear chains
of localised charge has been investigated by analysing the radial dependence of
the self-consistent potential and by computing the dispersion relation of
low-energy harmonic excitations.


  When the ion mean free path much exceeds the Larmor radius in a plasma, the
viscous stress tensor is altered dramatically, and depends only upon quantities
measured along the field lines. This regime corresponds to typical interstellar
medium conditions in galaxies and protogalaxies, even if the magnetic field is
extremely weak, with a negligible Lorentz force on all scales of interest. In
this work, the only role of the magnetic field is to channel angular momentum
transport along its lines of force. We show that differential rotation in such
a gas is highly unstable, with a maximum growth rate exceeding that of the
magnetorotational instability. The regime of interest has been treated
previously by plasma kinetic methods. Where there is overlap, our work appears
to be in agreement with the kinetic results. The nonlinear outcome of this
instability is likely to be a turbulent process, significantly augmenting the
magnetorotational instability, and important to the initial phases of the
amplification of small galactic magnetic fields.


  Distribution systems hold a very significant position in the power system
since it is the main point of link between bulk power and consumers. A planned
and effective distribution network is the key to cope up with the ever
increasing demand for domestic, industrial and commercial load. The load-flow
study of radial distribution network is of prime importance for effective
planning of load transfers. Power companies are interested in finding the most
efficient configuration for minimization of real power loses and load balancing
among distribution feeders to save energy and enhance the over all performance
of distribution system.
  This thesis presents a fast and efficient method for load-flow analysis of
radial distribution networks. The proposed method is based on linear data
structure. The order of time and space complexity is reported here. There is
significant saving in no. of steps execution. Using graph theory concept and
exploiting multi-cores architecture, the proposed method for load flow can be
further investigated for obtaining more optimized solutions.


  Neurological diseases are observed in approximately one billion people
worldwide. A further increase is foreseen at the global level as a result of
population growth and aging. Individuals with neurological disorders often
experience cognitive, motor, sensory, and lower extremity dysfunctions. Thus,
the possibility of falling and balance problems arise due to the postural
control deficiencies that occur as a result of the deterioration in the
integration of multi-sensory information. We propose a novel rehabilitation
framework, Integrated Balance Rehabilitation (I-BaR), to improve the
effectiveness of the rehabilitation with objective assessment, individualized
therapy, convenience with different disability levels and adoption of an
assist-as-needed paradigm and, with an integrated rehabilitation process as a
whole, i.e., ankle-foot preparation, balance, and stepping phases,
respectively. Integrated Balance Rehabilitation allows patients to improve
their balance ability by providing multi-modal feedback: visual via utilization
of Virtual Reality; vestibular via anteroposterior and mediolateral
perturbations with the robotic platform; proprioceptive via haptic feedback.


  This is the second of a series of papers in which we present a new solution
to reconcile the prediction of single stellar population (SSP) models with the
observed stellar mass-to-light ($M/L$) ratios of globular clusters (GCs) in M31
and its trend with respect to $\mathrm{[Fe/H]}$. In the present work our focus
is on the empirical relation between age and metallicity for GCs and its effect
on the $M/L$ ratio. Assuming that there is an anti-correlation between the age
of M31 GCs and their metallicity, we evolve dynamical SSP models of GCs to
establish a relation between the $M/L$ ratio (in the $V$ and $K$ band) and
metallicity. We then demonstrate that the established $M/L-\mathrm{[Fe/H]}$
relation is in perfect agreement with that of M31 GCs. In our models we
consider both the canonical initial mass function (IMF) and the top-heavy IMF
depending on cluster birth density and metallicity as derived independently
from Galactic GCs and ultra-compact dwarf galaxies by Marks et al. Our results
signify that the combination of the density- and metallicity-dependent
top-heavy IMF, the anti-correlation between age and metallicity, stellar
evolution and standard dynamical evolution yields the best possible agreement
with the observed trend of $M/L-\mathrm{[Fe/H]}$ for M31 GCs.


  We study incommensurate fractional variational problems in terms of a
generalized fractional integral with Lagrangians depending on classical
derivatives and generalized fractional integrals and derivatives. We obtain
necessary optimality conditions for the basic and isoperimetric problems,
transversality conditions for free boundary value problems, and a generalized
Noether type theorem.


  We investigate the collider phenomenology of gluino-bino co-annihilation
scenario both at the Tevatron and 7 TeV LHC. This scenario can be realized, for
example, in a class of realistic supersymmetric models with non-universal
gaugino masses and t-b-\tau Yukawa unification. The NLSP gluino and LSP bino
should be nearly degenerate in mass, so that the typical gluino search channels
involving leptons or hard jets are not available. Consequently, the gluino can
be lighter than various bounds on its mass from direct searches. We propose a
new search for NLSP gluino involving multi-b final states, arising from the
three-body decay \tilde{g}-> b\bar{b}\tilde{\chi}_1^0. We identify two
realistic models with gluino mass of around 300 GeV for which the three-body
decay is dominant, and show that a 4.5 \sigma observation sensitivity can be
achieved at the Tevatron with an integrated luminosity of 10 fb^{-1}. For the 7
TeV LHC with 50 pb^{-1} of integrated luminosity, the number of signal events
for the two models is O(10), to be compared with negligible SM background
event.


  We extend and review our analysis of the nucleon \to \Delta(1232) transition
electroweak form factors from Ref. [1]. New fit of the \Delta(1232) vector form
factors to electron-proton scattering F_2 structure function is introduced as
well, leading to results different from the popular parametrization of Ref.
[2]. A clear model dependence of the extracted parameters emerges. Fit to
neutrino scattering data is performed in all available isospin channels. The
resulting axial mass is M_{A\Delta}=0.85^{+0.09}_{-0.08} (GeV) and $C_5^A(0) =
1.10^{+0.15}_{-0.14}. The latter value is in accordance with Goldberger-Treiman
relation as long as the deuteron effects are included.


  We show that ''almost all'' exceptional modules over wild canonical algebra
$\Lambda$ can be described by matrices having coefficients
$\lambda_i-\lambda_j$, where $\lambda_i, \lambda_j$ are elements from the
parameter sequence. The proof is based on Schofield induction for sheaves in
the associated categories of weighted projective lines and an extended version
of C. M. Ringel's proof for the $''0, \,1''$ matrix property for exceptional
representations for finite acyclic quivers.


  The applicability of the quasi-static approximation for calculating the
two-photon annihilation rate of the scalar f_0(980) meson envisaged as a K\bar
K molecule is critically re-examined. It is shown that the validity of this
approximation depends on the detailed interplay between the momentum dependence
of the annihilation amplitude and the momentum transform of the bound state
wave function of the annihilating pair. The approximation becomes invalid when
these two scales of variation are similar. An improved method of calculation
based on the inclusion of electromagnetic corrections to the kernel of the
Bethe-Salpeter equation for the interacting K\bar K pair is outlined to cover
this case and applied to re-evaluate the two-photon decay width for f_0(980) in
a one boson exchange model for the interkaon interaction. The corrections are
significant and result in a much better agreement with experiment.


  Post-selection inference (PoSI) is a statistical technique for obtaining
valid confidence intervals and p-values when hypothesis generation and testing
use the same source of data. PoSI can be used on a range of popular algorithms
including the Lasso. Data carving is a variant of PoSI in which a portion of
held out data is combined with the hypothesis generating data at inference
time. While data carving has attractive theoretical and empirical properties,
existing approaches rely on computationally expensive MCMC methods to carry out
inference. This paper's key contribution is to show that pivotal quantities can
be constructed for the data carving procedure based on a known parametric
distribution. Specifically, when the selection event is characterized by a set
of polyhedral constraints on a Gaussian response, data carving will follow the
sum of a normal and a truncated normal (SNTN), which is a variant of the
truncated bivariate normal distribution. The main impact of this insight is
that obtaining exact inference for data carving can be made computationally
trivial, since the CDF of the SNTN distribution can be found using the CDF of a
standard bivariate normal. A python package sntn has been released to further
facilitate the adoption of data carving with PoSI.


  Deterministic control of coherent random light is highly important for
information transmission through complex media. However, only a few simple
speckle transformations can be achieved through diffusers without prior
characterization. As recently shown, spiral wavefront modulation of the
impinging beam allows permuting intensity maxima and intrinsic $\pm 1$-charged
optical vortices. Here, we study this cyclic-group algebra when combining
spiral phase transforms of charge $n$, with $D_3$- and $D_4$-point-group
symmetry star-like amplitude modulations. This combination allows statistical
strengthening of permutations and controlling the period to be 3 and 4,
respectively. Phase saddle-points are shown to complete the cycle. These
results offer new tools to manipulate critical points in speckles.


  Phage lambda is one of the most studied biological models in modern molecular
biology. Over the past 50 years quantitative experimental knowledge on this
biological model has been accumulated at all levels: physics, chemistry,
genomics, proteomics, functions, and more. All its components have been known
to a great detail. The theoretical task has been to integrate its components to
make the organism working quantitatively in a harmonic manner. This would test
our biological understanding and would lay a solid fundamental for further
explorations and applications, an obvious goal of systems biology. One of the
outstanding challenges in doing so has been the so-called stability puzzle of
lambda switch: the biologically observed robustness and its difficult
mathematical reconstruction based on known experimental values. In this chapter
we review the recent theoretical and experimental efforts on tackling this
problem. An emphasis is put on the minimum quantitative modeling where a
successful numerical agreement between experiments and modeling has been
achieved. A novel method tentatively named stochastic dynamical structure
analysis emerged from such study is also discussed within a broad modeling
perspective.


  Intel OptaneTM DC Persistent Memory resides on the memory bus and approaches
DRAM in access latency. One avenue for its adoption is to employ it in place of
persistent storage; another is to use it as a cheaper and denser extension of
DRAM. In pursuit of the latter goal, we present the design of a volatile Optane
NVRAM cache as a component in a storage engine underlying MongoDB. The primary
innovation in our design is a new cache admission policy. We discover that on
Optane NVRAM, known for its limited write throughput, the presence of writes
disproportionately affects the throughput of reads, much more so than on DRAM.
Therefore, an admission policy that indiscriminately admits new data (and thus
generates writes), severely limits the rate of data retrieval and results in
exceedingly poor performance for the cache overall. We design an admission
policy that balances the rate of admission with the rate of lookups using
dynamically observed characteristics of the workload. Our implementation
outperforms OpenCAS (an off-the-shelf Optane-based block cache) in all cases,
and Intel Memory Mode in cases where the database size exceeds the available
NVRAM. Our cache is decoupled from the rest of the storage engine and uses
generic metrics to guide its admission policy; therefore our design can be
easily adopted in other systems.


  The recent experimental results on leptonic $D^+_{(s)}$ decays, semileptonic
$D$ decays, determinations of decay constants and form factors, as well as
extractions of $|V_{cd}|$ and $|V_{cs}|$ are briefly reviewed. Global analysis
of all existing measurements of leptonic $D^+_{(s)}$ decays and semileptonic
$D$ decays yields $|V_{cd}|=0.2157\pm 0.0045$ and $|V_{cs}|=0.983\pm 0.011$,
which are the most precision determinations of these two CKM matrix elements up
to date.


  This paper proposes a novel weakly-supervised semantic segmentation method
using image-level label only. The class-specific activation maps from the
well-trained classifiers are used as cues to train a segmentation network. The
well-known defects of these cues are coarseness and incompleteness. We use
super-pixel to refine them, and fuse the cues extracted from both a color image
trained classifier and a gray image trained classifier to compensate for their
incompleteness. The conditional random field is adapted to regulate the
training process and to refine the outputs further. Besides initializing the
segmentation network, the previously trained classifier is also used in the
testing phase to suppress the non-existing classes. Experimental results on the
PASCAL VOC 2012 dataset illustrate the effectiveness of our method.


  The article `Global regularity for the 3D Navier-Stokes and the 3D Euler
equations'(arXiv:0711.2453) is withdrawn due to a serious error in the proof.


  We study optical metrics via null geodesics as a central force system, deduce
the related Binet equation and apply the analysis to certain solutions of
Einstein's equations with and without spherical symmetry. A general formula for
the deflection angle in the weak lensing regime for the
Schwarzschild-Tangherlini (ST) metric is derived. In addition, we obtain a new
weak lensing formula for the deflection angle on the equatorial plane of a Kerr
black hole (BH). We also explore the bending of light by considering the
gravitational objects described by the Tomimatsu-Sato (TS) metric.


  In complex tasks where the reward function is not straightforward and
consists of a set of objectives, multiple reinforcement learning (RL) policies
that perform task adequately, but employ different strategies can be trained by
adjusting the impact of individual objectives on reward function. Understanding
the differences in strategies between policies is necessary to enable users to
choose between offered policies, and can help developers understand different
behaviors that emerge from various reward functions and training
hyperparameters in RL systems. In this work we compare behavior of two policies
trained on the same task, but with different preferences in objectives. We
propose a method for distinguishing between differences in behavior that stem
from different abilities from those that are a consequence of opposing
preferences of two RL agents. Furthermore, we use only data on preference-based
differences in order to generate contrasting explanations about agents'
preferences. Finally, we test and evaluate our approach on an autonomous
driving task and compare the behavior of a safety-oriented policy and one that
prefers speed.


  We explore training Binary Neural Networks (BNNs) as a discrete variable
inference problem over a factor graph. We study the behaviour of this
conversion in an under-parameterized BNN setting and propose stochastic
versions of Belief Propagation (BP) and Survey Propagation (SP) message passing
algorithms to overcome the intractability of their current formulation.
Compared to traditional gradient methods for BNNs, our results indicate that
both stochastic BP and SP find better configurations of the parameters in the
BNN.


  We prove that, in the optimal transportation problem with general costs and
positive continuous densities, the potential function is always of class
$W^{2,p}_{loc}$ for any $p \geq 1$ outside of a closed singular set of measure
zero. We also establish global $W^{2,p}$ estimates when the cost is a small
perturbation of the quadratic cost. The latter result is new even when the cost
is exactly the quadratic cost.


  Gradual typing is an approach to integrating static and dynamic typing within
the same language, and puts the programmer in control of which regions of code
are type checked at compile-time and which are type checked at run-time.
  In this paper, we focus on the pi-calculus equipped with types for the
modeling of input-output capabilities of channels. We present our preliminary
work towards a gradually typed version of this calculus. We present a type
system, a cast insertion procedure that automatically inserts run-time checks,
and an operational semantics of a pi-calculus that handles casts on channels.
Although we do not claim any theoretical results on our formulations, we
demonstrate our calculus with an example and discuss our future plans.


  Due to the constraints of the imaging device and high cost in operation time,
computer tomography (CT) scans are usually acquired with low intra-slice
resolution. Improving the intra-slice resolution is beneficial to the disease
diagnosis for both human experts and computer-aided systems. To this end, this
paper builds a novel medical slice synthesis to increase the between-slice
resolution. Considering that the ground-truth intermediate medical slices are
always absent in clinical practice, we introduce the incremental cross-view
mutual distillation strategy to accomplish this task in the self-supervised
learning manner. Specifically, we model this problem from three different
views: slice-wise interpolation from axial view and pixel-wise interpolation
from coronal and sagittal views. Under this circumstance, the models learned
from different views can distill valuable knowledge to guide the learning
processes of each other. We can repeat this process to make the models
synthesize intermediate slice data with increasing inter-slice resolution. To
demonstrate the effectiveness of the proposed approach, we conduct
comprehensive experiments on a large-scale CT dataset. Quantitative and
qualitative comparison results show that our method outperforms
state-of-the-art algorithms by clear margins.


  In most stochastic models of molecular sequence evolution the probability of
each possible pattern of homologous characters at a site is estimated
numerically. However in the case of Kimura's three-substitution-types (K3ST)
model, these probabilities can be expressed analytically by Hadamard
conjugation as a function of the phylogeny T and the substitution probabilities
on each edge of T, together with an analytic inverse function. In this paper we
produce a direct proof of these results, using pathset distances which
generalise pairwise distances between sequences. This interpretation allows us
to apply Hadamard conjugation to a number of topical problems in the
mathematical analysis of sequence evolution.


  The QCD equation of state at finite baryon density is studied in the
framework of a Cluster Expansion Model (CEM), which is based on the fugacity
expansion of the net baryon density. The CEM uses the two leading Fourier
coefficients, obtained from lattice simulations at imaginary $\mu_B$, as the
only model input and permits a closed analytic form. Excellent description of
the available lattice data at both $\mu_B = 0$ and at imaginary $\mu_B$ is
obtained. We also demonstrate how the Fourier coefficients can be reconstructed
from baryon number susceptibilities.


  This is the first paper in a series of work we have accomplished over the
past three years. In this paper, we have constructed a consistent formal plane
geometry system. This will serve as a crucial bridge between IMO-level plane
geometry challenges and readable AI automated reasoning. Within this formal
framework, we have been able to seamlessly integrate modern AI models with our
formal system. AI is now capable of providing deductive reasoning solutions to
IMO-level plane geometry problems, just like handling other natural languages,
and these proofs are readable, traceable, and verifiable. We propose the
geometry formalization theory (GFT) to guide the development of the geometry
formal system. Based on the GFT, we have established the FormalGeo, which
consists of 88 geometric predicates and 196 theorems. It can represent,
validate, and solve IMO-level geometry problems. we also have crafted the FGPS
(formal geometry problem solver) in Python. It serves as both an interactive
assistant for verifying problem-solving processes and an automated problem
solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former
contains 6,981 (expand to 133,818 through data augmentation) geometry problems,
while the latter includes 18 (expand to 2,627 and continuously increasing)
IMO-level challenging geometry problems. All annotated problems include
detailed formal language descriptions and solutions. Implementation of the
formal system and experiments validate the correctness and utility of the GFT.
The backward depth-first search method only yields a 2.42% problem-solving
failure rate, and we can incorporate deep learning techniques to achieve lower
one. The source code of FGPS and datasets are available at
https://github.com/BitSecret/FGPS.


  In this text, we recall some basics and results about complex geometry and
currents in the complex scenario. Most of the results are classic and their
evidence is not given here. On the other hand, we describe in detail some
notions to help the reader who is unfamiliar with complex geometry or currents.
The main references for abstract current theory are [Che03] [dR84] [Fed69]
[Sch66] [War71]. The reader will find in [JP] [Gun90] [Hor83] [Lel68] [Nar66]
the basics of chains in complex varieties. We also refer to [JP] [PA78] [Huy05]
[Voi02] for K\"ahler's compact variety theory


  We present a numerical method to determine the complex acoustic impedance at
the open surface of an arbitrarily shaped cavity, associated to an impinging
planar acoustic wave with a given wavenumber vector and frequency. We have
achieved this by developing the first inverse Helmholtz Solver (iHS), which
implicitly reconstructs the complex acoustic waveform--at a given frequency--up
to the unknown impedance boundary, hereby providing the spatial distribution of
impedance as a result of the calculation for that given frequency. We show that
the algebraic closure conditions required by the inverse Helmholtz problem are
physically related to the assignment of the spatial distribution of the
pressure phase over the unknown impedance boundary. The iHS is embarrassingly
parallelizable over the frequency domain allowing for the straightforward
determination of the full broadband impedance at every point of the target
boundary. In this paper, we restrict our analysis to two-dimensions only. We
first validate our results against Rott's quasi one-dimensional thermoacoustic
theory for viscid and inviscid constant-area rectangular ducts, test our iHS in
a fully unstructured fashion with a geometrically complex cavity, and finally,
present a simplified, two-dimensional analysis of a sample of carbon-carbon
ultrasonically absorptive coatings (C/C UACs) manufactured in DLR-Stuttgart,
and used in the hypersonic transition delay experiments by Wagner et al. in
AIAA 2012-5865. The final goal is to model C/C UACs with multi-oscillator Time
Domain Impedance Boundary Conditions (TDIBC) developed by Lin et al. in JFM
(2016) to be applied in direct numerical simulations (DNS) focused on the
overlying boundary layer, eliminating the need to simultaneously resolve the
microscopic porous structure of the C/C UACs.


  The current winning recipe for automatic summarization is using proprietary
large-scale language models (LLMs) such as ChatGPT as is, or imitation learning
from them as teacher models. While increasingly ubiquitous dependence on such
large-scale language models is convenient, there remains an important question
of whether small-scale models could have achieved competitive results, if we
were to seek an alternative learning method -- that allows for a more
cost-efficient, controllable, yet powerful summarizer. We present InfoSumm, a
novel framework to distill a powerful summarizer based on the
information-theoretic objective for summarization, without relying on either
the LLM's capability or human-written references. To achieve this, we first
propose a novel formulation of the desiderata of summarization (saliency,
faithfulness and brevity) through the lens of mutual information between the
original document and the summary. Based on this formulation, we start off from
Pythia-2.8B as the teacher model, which is not yet capable of summarization,
then self-train the model to optimize for the information-centric measures of
ideal summaries. Distilling from the improved teacher, we arrive at a compact
but powerful summarizer with only 568M parameters that performs competitively
against ChatGPT, without ever relying on ChatGPT's capabilities. Extensive
analysis demonstrates that our approach outperforms in-domain supervised models
in human evaluation, let alone state-of-the-art unsupervised methods, and wins
over ChatGPT in controllable summarization.


  We aim at contributing to the resolution of three of the fundamental puzzles
related to the still unsolved problem of the structure of the dense core of
compact stars (CS): (i) the hyperon puzzle: how to reconcile pulsar masses of
$2\,$M$_\odot$ with the hyperon softening of the equation of state (EoS); (ii)
the masquerade problem: modern EoS for cold, high density hadronic and quark
matter are almost identical; and (iii) the reconfinement puzzle: what to do
when after a deconfinement transition the hadronic EoS becomes favorable again?
We show that taking into account the compositeness of baryons (by excluded
volume and/or quark Pauli blocking) on the hadronic side and confining and
stiffening effects on the quark matter side results in an early phase
transition to quark matter with sufficient stiffening at high densities which
removes all three present-day puzzles of CS interiors. Moreover, in this new
class of EoS for hybrid CS falls the interesting case of a strong first order
phase transition which results in the observable high mass twin star
phenomenon, an astrophysical observation of a critical endpoint in the QCD
phase diagram.


  In this work, we investigate if the learned encoder of the end-to-end
convolutional time domain audio separation network (Conv-TasNet) is the key to
its recent success, or if the encoder can just as well be replaced by a
deterministic hand-crafted filterbank. Motivated by the resemblance of the
trained encoder of Conv-TasNet to auditory filterbanks, we propose to employ a
deterministic gammatone filterbank. In contrast to a common gammatone
filterbank, our filters are restricted to 2 ms length to allow for low-latency
processing. Inspired by the encoder learned by Conv-TasNet, in addition to the
logarithmically spaced filters, the proposed filterbank holds multiple
gammatone filters at the same center frequency with varying phase shifts. We
show that replacing the learned encoder with our proposed multi-phase gammatone
filterbank (MP-GTF) even leads to a scale-invariant source-to-noise ratio
(SI-SNR) improvement of 0.7 dB. Furthermore, in contrast to using the learned
encoder we show that the number of filters can be reduced from 512 to 128
without loss of performance.


  It is shown that a recent critique (arXiv:1210.1130 and arXiv:1211.4639)
concerning the analytical solution of the Rabi model is unfounded.


  In this paper we describe an approach to constraint-based syntactic theories
in terms of finite tree automata. The solutions to constraints expressed in
weak monadic second order (MSO) logic are represented by tree automata
recognizing the assignments which make the formulas true. We show that this
allows an efficient representation of knowledge about the content of
constraints which can be used as a practical tool for grammatical theory
verification. We achieve this by using the intertranslatability of formulas of
MSO logic and tree automata and the embedding of MSO logic into a constraint
logic programming scheme. The usefulness of the approach is discussed with
examples from the realm of Principles-and-Parameters based parsing.


  We present the HERA CO-Line Extragalactic Survey (HERACLES), an atlas of CO
emission from 18 nearby galaxies that are also part of The HI Nearby Galaxy
Survey (THINGS) and the Spitzer Infrared Nearby Galaxies Survey (SINGS). We
used the HERA multi-pixel receiver on the IRAM 30-m telescope to map the CO
J=2-1 line over the full optical disk (defined by the isophotal radius r_25) of
each target, at 13" angular resolution and 2.6 km/s velocity resolution. Here
we describe the observations and reduction of the data and show channel maps,
azimuthally averaged profiles, integrated intensity maps, and peak intensity
maps. The implied H2 masses range from 7 \times 10^6 to 6 \times 10^9 M_sun,
with four low metallicity dwarf irregular galaxies yielding only upper limits.
In the cases where CO is detected, the integrated H2-to-HI ratios range from
0.02 - 1.13 and H2-to-stellar mass ratios from 0.01 to 0.25. Exponential scale
lengths of the CO emission for our targets are in the range 0.8 - 3.2 kpc, or
0.2 \pm 0.05 r_25. The intensity-weighted mean velocity of CO matches that of
HI very well, with a 1\sigma scatter of only 6 km/s. The CO J=2-1 / J=1-0 line
ratio varies over a range similar to that found in the Milky Way and other
nearby galaxies, \sim 0.6 - 1.0, with higher values found in the centers of
galaxies. The typical line ratio, \sim 0.8, could be produced by optically
thick gas with an excitation temperature of \sim 10 K.


  The linear coupling method was introduced recently by Allen-Zhu and Orecchia
for solving convex optimization problems with first order methods, and it
provides a conceptually simple way to integrate a gradient descent step and
mirror descent step in each iteration. The high-level approach of the linear
coupling method is very flexible, and it has shown initial promise by providing
improved algorithms for packing and covering linear programs. Somewhat
surprisingly, however, while the dependence of the convergence rate on the
error parameter $\epsilon$ for packing problems was improved to
$O(1/\epsilon)$, which corresponds to what accelerated gradient methods are
designed to achieve, the dependence for covering problems was only improved to
$O(1/\epsilon^{1.5})$, and even that required a different more complicated
algorithm. Given the close connections between packing and covering problems
and since previous algorithms for these very related problems have led to the
same $\epsilon$ dependence, this discrepancy is surprising, and it leaves open
the question of the exact role that the linear coupling is playing in
coordinating the complementary gradient and mirror descent step of the
algorithm. In this paper, we clarify these issues for linear coupling
algorithms for packing and covering linear programs, illustrating that the
linear coupling method can lead to improved $O(1/\epsilon)$ dependence for both
packing and covering problems in a unified manner, i.e., with the same
algorithm and almost identical analysis. Our main technical result is a novel
diameter reduction method for covering problems that is of independent interest
and that may be useful in applying the accelerated linear coupling method to
other combinatorial problems.


  This paper introduces a new Monte Carlo algorithm to invert large matrices.
It is based on simultaneous coupled draws from two random vectors whose
covariance is the required inverse. It can be considered a generalization of a
previously reported algorithm for hermitian matrices inversion based in only
one draw. The use of two draws allows the inversion on non-hermitian matrices.
Both the conditions for convergence and the rate of convergence are similar to
the Gauss-Seidel algorithm. Results on two examples are presented, a real
non-symmetric matrix related to quantitative genetics and a complex
non-hermitian matrix relevant for physicists. Compared with other Monte Carlo
algorithms it reveals a large reduction of the processing time showing eight
times faster processing in the examples studied.


  We present the first direct-numerical-simulation study of the statistical
properties of two-dimensional superfluid turbulence in the
Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both
normal-fluid and superfluid energy spectra can exhibit two power-law regimes,
the first associated with an inverse cascade of energy and the second with the
forward cascade of enstrophy. We quantify the mutual-friction-induced alignment
of normal and superfluid velocities by obtaining probability distribution
functions of the angle between them and the ratio of their moduli. Our study
leads to specific suggestions for experiments.


  The real-world data is often susceptible to label noise, which might
constrict the effectiveness of the existing state of the art algorithms for
ordinal regression. Existing works on ordinal regression do not take label
noise into account. We propose a theoretically grounded approach for class
conditional label noise in ordinal regression problems. We present a deep
learning implementation of two commonly used loss functions for ordinal
regression that is both - 1) robust to label noise, and 2) rank consistent for
a good ranking rule. We verify these properties of the algorithm empirically
and show robustness to label noise on real data and rank consistency. To the
best of our knowledge, this is the first approach for robust ordinal regression
models.


  Reconstructing the room transfer functions needed to calculate the complex
sound field in a room has several important real-world applications. However,
an unpractical number of microphones is often required. Recently, in addition
to classical signal processing methods, deep learning techniques have been
applied to reconstruct the room transfer function starting from a very limited
set of measurements at scattered points in the room. In this paper, we employ
complex-valued neural networks to estimate room transfer functions in the
frequency range of the first room resonances, using a few irregularly
distributed microphones. To the best of our knowledge, this is the first time
that complex-valued neural networks are used to estimate room transfer
functions. To analyze the benefits of applying complex-valued optimization to
the considered task, we compare the proposed technique with a state-of-the-art
kernel-based signal processing approach for sound field reconstruction, showing
that the proposed technique exhibits relevant advantages in terms of phase
accuracy and overall quality of the reconstructed sound field. For informative
purposes, we also compare the model with a similarly-structured data-driven
approach that, however, applies a real-valued neural network to reconstruct
only the magnitude of the sound field.


  Using the white noise space framework, we define a class of stochastic
processes which include as a particular case the fractional Brownian motion and
its derivative. The covariance functions of these processes are of a special
form, studied by Schoenberg, von Neumann and Krein.


  Beurling density plays a key role in the study of frame-spectrality of
normalized Lebesgue measure restricted to a set. Accordingly, in this paper,
the authors study the $s$-Beurling densities of regular maximal orthogonal sets
of a class of self-similar spectral measures, where $s$ is the Hausdorff
dimension of its support and obtain their exact upper bound of the densities.


  We determine the complete NLL running of the static potential associated with
the locally 1/2 BPS Wilson loop in N=4 supersymmetric Yang-Mills theory. We
present results for the SU(N_c) singlet as well as for the adjoint
configuration and arbitrary N_c at weak coupling. In order to derive the
respective anomalous dimensions we perform a two-loop calculation in the N=4
supersymmetric version of the effective field theory pNRQCD. In addition we
confirm the recently obtained fixed-order result for the singlet static
potential generated exclusively by ladder diagrams to the third order in the
t`Hooft coupling. We also give an explicit expression for the logarithmic
contribution of all non-ladder diagrams at this order.


  We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC)
algorithm to address the issue of field size in random network coding. ARCNC
operates as a convolutional code, with the coefficients of local encoding
kernels chosen randomly over a small finite field. The lengths of local
encoding kernels increase with time until the global encoding kernel matrices
at related sink nodes all have full rank. Instead of estimating the necessary
field size a priori, ARCNC operates in a small finite field. It adapts to
unknown network topologies without prior knowledge, by locally incrementing the
dimensionality of the convolutional code. Because convolutional codes of
different constraint lengths can coexist in different portions of the network,
reductions in decoding delay and memory overheads can be achieved with ARCNC.
We show through analysis that this method performs no worse than random linear
network codes in general networks, and can provide significant gains in terms
of average decoding delay in combination networks.


  In arXiv:1409.6313 we proposed a formula for the 3-point structure constants
of Toda field theory, derived using topological strings and the AGT-W
correspondence from the partition functions of the non-Lagrangian $T_N$
theories on $S^4$. In this article, we show how the semi-degeneration of one of
the three primary fields on the Toda side corresponds to a particular Higgsing
of the $T_N$ theories and derive the well-known formula by Fateev and Litvinov.


  Bundle adjustment (BA) is a technique for refining sensor orientations of
satellite images, while adjustment accuracy is correlated with feature matching
results. Feature match-ing often contains high uncertainties in weak/repeat
textures, while BA results are helpful in reducing these uncertainties. To
compute more accurate orientations, this article incorpo-rates BA and feature
matching in a unified framework and formulates the union as the optimization of
a global energy function so that the solutions of the BA and feature matching
are constrained with each other. To avoid a degeneracy in the optimization, we
propose a comprised solution by breaking the optimization of the global energy
function into two-step suboptimizations and compute the local minimums of each
suboptimization in an incremental manner. Experiments on multi-view
high-resolution satellite images show that our proposed method outperforms
state-of-the-art orientation techniques with or without accurate least-squares
matching.


  Mass perturbations of the twisted N=4 supersymmetric gauge theory considered
by Vafa and Witten to test S-duality are studied for the case of Kahler
four-manifolds. It is shown that the resulting mass-perturbed theory can be
regarded as an equivariant extension associated to a U(1) symmetry of the
twisted theory, which is only present for Kahler manifolds. In addition, it is
shown that the partition function, the only topological invariant of the
theory, remains invariant under the perturbation.


  Performing linear operations using optical devices is a crucial building
block in many fields ranging from telecommunication to optical analogue
computation and machine learning. For many of these applications, key
requirements are robustness to fabrication inaccuracies and reconfigurability.
Current designs of custom-tailored photonic devices or coherent photonic
circuits only partially satisfy these needs. Here, we propose a way to perform
linear operations by using complex optical media such as multimode fibers or
thin scattering layers as a computational platform driven by wavefront shaping.
Given a large random transmission matrix (TM) representing light propagation in
such a medium, we can extract a desired smaller linear operator by finding
suitable input and output projectors. We discuss fundamental upper bounds on
the size of the linear transformations our approach can achieve and provide an
experimental demonstration. For the latter, first we retrieve the complex
medium's TM with a non-interferometric phase retrieval method. Then, we take
advantage of the large number of degrees of freedom to find input wavefronts
using a Spatial Light Modulator (SLM) that cause the system, composed of the
SLM and the complex medium, to act as a desired complex-valued linear operator
on the optical field. We experimentally build several $16\times16$
complex-valued operators, and are able to switch from one to another at will.
Our technique offers the prospect of reconfigurable, robust and
easy-to-fabricate linear optical analogue computation units.


  Simultaneous modeling of the spatio-temporal variation patterns of brain
functional network from 4D fMRI data has been an important yet challenging
problem for the field of cognitive neuroscience and medical image analysis.
Inspired by the recent success in applying deep learning for functional brain
decoding and encoding, in this work we propose a spatio-temporal convolutional
neural network (ST-CNN)to jointly learn the spatial and temporal patterns of
targeted network from the training data and perform automatic, pin-pointing
functional network identification. The proposed ST-CNN is evaluated by the task
of identifying the Default Mode Network (DMN) from fMRI data. Results show that
while the framework is only trained on one fMRI dataset,it has the sufficient
generalizability to identify the DMN from different populations of data as well
as different cognitive tasks. Further investigation into the results show that
the superior performance of ST-CNN is driven by the jointly-learning scheme,
which capture the intrinsic relationship between the spatial and temporal
characteristic of DMN and ensures the accurate identification.