  The phenomenon of coherent energetic pulse propagation in exciton-phonon
molecular chains such as $\alpha$-helix protein is studied using an ODE system
model of Davydov-Scott type, both with numerical studies using a new
unconditionally stable fourth order accurate energy-momentum conserving time
discretization, and with analytical explanation of the main numerical
observations.
  Physically natural impulsive initial data associated with the energy released
by ATP hydrolysis are used, and the best current estimates of physical
parameter values. In contrast to previous studies based on a proposed long wave
approximation by the nonlinear Schr\"odinger (NLS) equation and focusing on
initial data resembling the soliton solutions of that equation, the results
here instead lead to approximation by the third derivative nonlinear
Schr\"odinger equation, giving a far better fit to observed behavior. A good
part of the behavior is indeed explained well by the linear part of that
equation, the Airy PDE, while other significant features do not fit any PDE
approximation, but are instead explained well by a linearized analysis of the
ODE system.
  A convenient method is described for construction the highly stable, accurate
conservative time discretizations used, with proof of its desirable properties
for a large class of Hamiltonian systems, including a variety of molecular
models.


  We develop the nonadiabatic polaron theory of superconductivity of
$M_{x}C_{60}$ taking into account the polaron band narrowing and realistic
electron-phonon and Coulomb interactions. We argue that the crossover from the
BCS weak-coupling superconductivity to the strong-coupling polaronic and
bipolaronic superconductivity occurs at the BCS coupling constant $\lambda\sim
1$ independent of the adiabatic ratio, and there is nothing ``beyond'' Migdal's
theorem except small polarons for any realistic electron-phonon interaction. By
the use of the polaronic-type function and the ``exact'' diagonalization in the
truncated Hilbert space of vibrons (``phonons'') we calculate the ground state
energy and the electron spectral density of the $C_{60}^{-}$ molecule. This
allows us to describe the photoemission spectrum of $C_{60}^{-}$ in a wide
energy region and determine the electron-phonon interaction. The strongest
coupling is found with the high-frequency pinch $A_{g2}$ mode and with the
Frenkel exciton. We clarify the crucial role of high-frequency bosonic
excitations in doped fullerenes which reduce the bare bandwidth and the Coulomb
repulsion allowing the intermediate and low-frequency phonons to couple two
small polarons in a Cooper pair. The Eliashberg-type equations are solved for
low-frequency phonons. The value of the superconducting $T_{c}$, its pressure
dependence and the isotope effect are found to be in a remarkable agreement
with the available experimental data.


  In this paper we consider the question of when all Seshadri constants on a
product of two isogenous elliptic curves $E_1\times E_2$ without complex
multiplication are integers. By studying elliptic curves on $E_1\times E_2$ we
translate this question into a purely numerical problem expressed by quadratic
forms. By solving that problem, we show that all Seshadri constants on
$E_1\times E_2$ are integers if and only if the minimal degree of an isogeny
$E_1\to E_2$ equals 1 or 2. Furthermore, this method enables a characterization
of irreducible principal polarizations on $E_1\times E_2$.


  We present a new and complete numerical analysis of the decay of super-heavy
X particles, assumed to be the origin of cosmic rays with energy beyond the GZK
cut-off. The decay of X initiates a ``parton shower'', where we include all
degrees of freedom contained in the Minimal Supersymmetric Standard Model
(MSSM). Since at energies near $M_X$ all gauge couplings are of similar
magnitude, we include all of them, as well as third generation Yukawa
couplings. Technically the shower development is described through the DGLAP
evolution of the relevant fragmentation functions (FFs). We also carefully
treat the decay of the superparticles as well as heavy SM particles created in
the shower. Nonperturbative physics is parameterized through the input values
of the FFs, which we take from the literature. The final result is the the
complete spectrum of all stable particles at the very end of the shower :
protons, electrons, neutrinos, photons and neutralinos, for an energy range
from $10^{-7} M_X$ to $M_X$. In particular, the flux of high-energy neutralinos
is sizable ; it might serve as ``smoking gun'' signature for this kind of
scenario.


  Let ${\rm Z}(G)$ and ${\rm gp}(G)$ be the zero forcing number and the general
position number of a graph $G$, respectively. Known results imply that ${\rm
gp}(T)\ge {\rm Z}(T) + 1$ holds for every nontrivial tree $T$. It is proved
that the result extends to block graphs. For connected, unicyclic graphs $G$ it
is proved that ${\rm gp}(G) \ge {\rm Z}(G)$. The result extends neither to
bicyclic graphs nor to quasi-trees. Nevertheless, a large class of quasi-trees
is found for which ${\rm gp}(G) \ge {\rm Z}(G)$ holds.


  We analyze the instability of a vortex column in a dilute polymer solution at
large $\textit{Re}$ and $\textit{De}$ with $\textit{El} =
\textit{De}/\textit{Re}$, the elasticity number, being finite. Here,
$\textit{Re} = \Omega_0 a^2/\nu_s$ and $\textit{De} = \Omega_0 \tau$ are,
respectively, the Reynolds and Deborah numbers based on the core angular
velocity ($\Omega_0$), the radius of the column ($a$), the solvent-based
kinematic viscosity ($\nu_s = \mu_s/\rho$), and the polymeric relaxation time
($\tau$). The stability of small-amplitude perturbations in this distinguished
limit is governed by the elastic Rayleigh equation whose spectrum is
parameterized by $ \textrm{E} = \textit{El}(1-\beta)$, $\beta$ being the ratio
of the solvent to the solution viscosity. The neglect of the relaxation terms,
in the said limit, implies that the polymer solution supports undamped elastic
shear waves propagating relative to the base-state flow. The existence of these
shear waves leads to multiple (three) continuous spectra associated with the
elastic Rayleigh equation in contrast to just one for the original Rayleigh
equation. Further, unlike the neutrally stable inviscid case, an instability of
the vortex column arises for finite E due to a pair of elastic shear waves
being driven into a resonant interaction under the differential convection by
the irrotational shearing flow outside the core. An asymptotic analysis for the
Rankine profile shows the absence of an elastic threshold; although, for small
E, the growth rate of the unstable discrete mode is transcendentally small,
being O$(\textrm{E}^2e^{-1/\textrm{E}^{\frac{1}{2}}})$. An accompanying
numerical investigation shows that the instability persists for smooth
vorticity profiles, provided the radial extent of the transition region (from
the rotational core to the irrotational exterior) is less than a certain
$\textrm{E}$-dependent threshold.


  As a first goal, it is explained why Goodwillie-Weiss calculus of embeddings
offers new information about the Euclidean embedding dimension of P^m only for
m < 16. Concrete scenarios are described in these low-dimensional cases,
pinpointing where to look for potential, but critical, high-order obstructions
in the corresponding Taylor towers. For m > 15, the relation TC^S(P^m) > n-1 is
translated into the triviality of a certain cohomotopy Euler class which, in
turn, becomes the only Taylor obstruction to producing an n-dimensional
Euclidean embedding of P^m. A speculative bordism-type form of this primary
obstruction is proposed as an analogue of Davis' BP-approach to the immersion
problem of P^m. A form of the Euler class viewpoint is applied to show
TC^S(P^3) = 5, as well as to suggest a few higher dimensional projective spaces
for which the method could produce new information. As a second goal, the paper
extends Farber's work on the motion planning problem in order to develop the
notion of a symmetric motion planner for a mechanical system S. Following
Farber's lead, this concept is connected to the symmetric topological
complexity of the state space of S. The paper ends by sketching the
construction of a concrete 5-local-rules symmetric motion planner for P^3.


  A pervasive design issue of AI systems is their explainability--how to
provide appropriate information to help users understand the AI. The technical
field of explainable AI (XAI) has produced a rich toolbox of techniques.
Designers are now tasked with the challenges of how to select the most suitable
XAI techniques and translate them into UX solutions. Informed by our previous
work studying design challenges around XAI UX, this work proposes a design
process to tackle these challenges. We review our and related prior work to
identify requirements that the process should fulfill, and accordingly, propose
a Question-Driven Design Process that grounds the user needs, choices of XAI
techniques, design, and evaluation of XAI UX all in the user questions. We
provide a mapping guide between prototypical user questions and exemplars of
XAI techniques to reframe the technical space of XAI, also serving as boundary
objects to support collaboration between designers and AI engineers. We
demonstrate it with a use case of designing XAI for healthcare adverse events
prediction, and discuss lessons learned for tackling design challenges of AI
systems.


  We review an idea that uses details of the quasinormal mode spectrum of a
black hole to obtain the Bekenstein-Hawking entropy of $A/4$ in Loop Quantum
Gravity. We further comment on a recent proposal concerning the quasinormal
mode spectrum of rotating black holes. We conclude by remarking on a recent
proposal to include supersymmetry.


  We analyse the so-called small-world network model (originally devised by
Strogatz and Watts), treating it, among other things, as a case study of
non-linear coupled difference or differential equations. We derive a system of
evolution equations containing more of the previously neglected (possibly
relevant) non-linear terms. As an exact solution of this entangled system of
equations is out of question we develop a (as we think, promising) method of
enclosing the ``exact'' solutions for the expected quantities by upper and
lower bounds, which represent solutions of a slightly simpler system of
differential equation. Furthermore we discuss the relation between difference
and differential equations and scrutinize the limits of the spreading idea for
random graphs. We then show that there exists in fact a ``broad'' (with respect
to scaling exponents) crossover zone, smoothly interpolating between linear and
logarithmic scaling of the diameter or average distance. We are able to
corroborate earlier findings in certain regions of phase or parameter space (as
e.g. the finite size scaling ansatz) but find also deviations for other choices
of the parameters. Our analysis is supplemented by a variety of numerical
calculations, which, among other things, quantify the effect of various
approximations being made.
  With the help of our analytical results we manage to calculate another
important network characteristic, the (fractal) dimension, and provide
numerical values for the case of the small-world network.
  Catchwords: Small-World Networks, Non-linear Difference Equations


  A new scanning Fabry-Perot system will soon be available at the Nasmyth focus
of the 4,2m William Hershell Telescope (WHT). It has been designed by the
Laboratoire d'Astrophysique Experimentale (LAE) in Montreal and is being built
in collaboration with astronomers at the Instituto de Astrofisica de Canarias
(IAC). The instrument will see first light at the beginning of July 2007.


  We determine the asymptotic relaxation rate of a Brownian particle in a
harmonic potential perturbed by quenched Gaussian disorder, a simplified model
for rugged energy landscapes in complex systems. Depending on the properties of
the disorder, we show that the mean and variance of the asymptotic relaxation
rate are non-monotonous functions of the parameters for a broad class of
disorders. In particular, the rate of relaxation may either increase or
decrease exponentially compared to the unperturbed case. In the limit of weak
disorder, we derive the probability distribution of the asymptotic relaxation
rate and show that it is Gaussian, with analytic expressions for the mean and
variance that feature universal limits. In comparison with other, well-studied
anomalous-relaxation effects that often lead to sub-exponential changes in the
relaxation rate, our results show that the effect of disorder is always
stronger in the long-time limit. These findings indicate that controlled
disorder may serve to tune the relaxation speed in complex systems.


  In this paper we present the design, manufacturing, characterization and
analysis of the coupling ratio spectral response for Multimode Interference
(MMI) couplers in Silicon-on-Insulator (SOI) technology. The couplers were
designed using a Si rib waveguide with SiO 2 cladding, on a regular 220 nm film
and 2 {\mu}m buried oxide SOI wafer. A set of eight different designs, three
canonical and five using a widened/narrowed coupler body, have been subject of
study, with coupling ratios 50:50, 85:15 and 72:28 for the former, and 95:05,
85:15, 75:25, 65:35 and 55:45 for the latter. Two wafers of devices were
fabricated, using two different etch depths for the rib waveguides. A set of
six dies, three per wafer, whose line metrology matched the design, were
retained for characterization. The coupling ratios obtained in the experimental
results match, with little deviations, the design targets for a wavelength
range between 1525 and 1575 nm, as inferred from spectral measurements and
statistical analyses. Excess loss for all the devices is conservatively
estimated to be less than approximately 2 dB. All the design parameters, body
width and length, input/output positions and widths, and tapers dimensions are
disclosed for reference.


  Many theories, from Supersymmetry to models of Strong Electroweak Symmetry
Breaking, look at the production of four top quarks as an interesting channel
to evidentiate signals of new physics beyond the Standard Model. The production
of four-top final states requires large partonic energies, above the 4mt
threshold, that are available at the CERN Large Hadron Collider and will become
more and more accessible with increasing energy and luminosity of the proton
beams. A good theoretical control on the Standard Model background is a
fundamental prerequisite for a correct interpretation of the possible signals
of new physics that may arise in this channel. In this paper we report on the
calculation of the next-to-leading order QCD corrections to the Standard Model
process pp -> tttt + X. As it is customary for such studies, we present results
for both integrated and differential cross sections. A judicious choice of a
dynamical scale allows us to obtain nearly constant K-factors in most
distributions.


  R 144 is the visually brightest WR star in the Large Magellanic Cloud (LMC).
R 144 was reported to be a binary, making it potentially the most massive
binary thus observed. We perform a comprehensive spectral, photometric,
orbital, and polarimetric analysis of R 144.
  R 144 is an eccentric (e=0.51) 74.2-d binary comprising two relatively
evolved (age~2 Myr), H-rich WR stars. The hotter primary (WN5/6h, T=50 kK) and
the cooler secondary (WN6/7h,T=45kK) have nearly equal masses. The combination
of low rotation and H-depletion observed in the system is well reproduced by
contemporary evolution models that include boosted mass-loss at the upper-mass
end. The systemic velocity of R 144 and its relative isolation suggest that it
was ejected as a runaway from the neighbouring R 136 cluster. The optical
light-curve shows a clear orbital modulation that can be well explained as a
combination of two processes: excess emission stemming from wind-wind
collisions and double wind eclipses. Our light-curve model implies an orbital
inclination of i=60.4+-1.5deg, resulting in accurately constrained dynamical
masses of 74+-4 and 69+-4 Msun. Assuming that both binary components are core
H-burning, these masses are difficult to reconcile with the derived
luminosities (logL1,2 = 6.44, 6.39 [Lsun]), which correspond to evolutionary
masses of the order of 110 and 100Msun, respectively. Taken at face value, our
results imply that both stars have high classical Eddington factors of Gamma_e
= 0.78+-0.1. If the stars are on the main sequence, their derived radii
(~25Rsun) suggest that they are only slightly inflated, even at this high
Eddington factor. Alternatively, the stars could be core-He burning, strongly
inflated from the regular size of classical Wolf-Rayet stars (~1Rsun), a
scenario that could help resolve the observed mass discrepancy.


  Loss of power and clear description of treatment differences are key issues
in designing and analyzing a clinical trial where non-proportional hazard is a
possibility. A log-rank test may be very inefficient and interpretation of the
hazard ratio estimated using Cox regression is potentially problematic. In this
case, the current ICH E9 (R1) addendum would suggest designing a trial with a
clinically relevant estimand, e.g., expected life gain. This approach considers
appropriate analysis methods for supporting the chosen estimand. However, such
an approach is case specific and may suffer lack of power for important choices
of the underlying alternate hypothesis distribution. On the other hand, there
may be a desire to have robust power under different deviations from
proportional hazards. Also, we would contend that no single number adequately
describes treatment effect under non-proportional hazards scenarios. The
cross-pharma working group has proposed a combination test to provide robust
power under a variety of alternative hypotheses. These can be specified for
primary analysis at the design stage and methods appropriately accounting for
combination test correlations are efficient for a variety of scenarios. We have
provided design and analysis considerations based on a combination test under
different non-proportional hazard types and present a straw man proposal for
practitioners. The proposals are illustrated with real life example and
simulation.


  We propose and test the Direct Waveform Inversion (DWI) scheme to
simultaneously invert for layered velocity and density profiles, using
reflection seismic waveforms recorded on the surface. The recorded data include
primary reflections and interbed multiples. DWI is implemented in the
time-space domain. By explicitly enforcing the wavefield time-space causality,
DWI can recursively determine the subsurface seismic structure in a local
fashion for both sharp interfaces as well as the properties of the layers, from
shallow to deep depths. DWI is different from the layer stripping methods in
the frequency domain. By not requiring a global initial model, DWI avoids many
nonlinear optimization problems, such as the local minima and the need for an
accurate initial model in most full waveform inversion schemes. Using two
numerical tests here, we demonstrate that the DWI scheme for multi-parameter
seismic inversion for velocity and density of layered media, using plane waves
of different incident angles. This represents a significant step comparing with
the previous DWI only inverting for the velocity.


  We use the Breit Pauli $R$-matrix method to calculate accurate energies and
radiative data for states in C I up to $n$=30 and with $l\le 3$. We provide the
full dataset of decays to the five 2s$^2$2p$^2$ ground configuration states
$^3$P$_{0,1,2}$, $^1$D$_2$, $^1$S$_0$. This is the first complete set of data
for transitions from $n\ge 5$. We compare oscillator strengths and transition
probabilities with the few previously calculated values for such transitions,
finding generally good agreement (within 10%) with the exception of values
recently recommended by NIST, where significant discrepancies are found. We
then calculate spectral line intensities originating from the Rydberg states
using typical chromospheric conditions and assuming LTE, and compare them with
well-calibrated SOHO SUMER UV spectra of the quiet Sun. The relative
intensities of the Rydberg series are in excellent agreement with observation,
which provides firm evidence for the identifications and blends of nearly 200
UV lines. Such comparison also resulted in a large number of new
identifications of C I lines in the spectra. We also estimate optical depth
effects and find that these can account for much of the absorption noted in the
observations. The atomic data can be applied to model a wide range of solar and
astrophysical observations.


  The set of linear structures of most known balanced Boolean functions is
nontrivial. In this paper, some balanced Boolean functions whose set of linear
structures is trivial are constructed. We show that any APN function in even
dimension must have a component whose set of linear structures is trivial. We
determine a general form for the number of bent components in quadratic APN
functions in even dimension and some bounds on the number are produced. We also
count bent components in any quadratic power functions.


  In underdoped cuprate superconductors, a rich competition occurs between
superconductivity and charge density wave (CDW) order. Whether rotational
symmetry breaking (nematicity) occurs intrinsically and generically or as a
consequence of other orders is under debate. Here we employ resonant x-ray
scattering in stripe-ordered (La,M)_2CuO_4 to probe the relationship between
electronic nematicity of the Cu 3d orbitals, structure of the (La,M)_2O_2
layers, and CDW order. We find distinct temperature dependences for the
structure of the (La,M)_2O_2 layers and the electronic nematicity of the CuO_2
planes, with only the latter being enhanced by the onset of CDW order. These
results identify electronic nematicity as an order parameter that is distinct
from a purely structural order parameter in underdoped striped cuprates.


  In the framework of the nonrelativistic QCD and a quark-diquark model of
baryons we have obtained the fragmentation functions for heavy quark to split
into spin-1/2 and spin-3/2 double heavy baryons. It was predicted the
production rates as well as the shape of the energy spectra for the $cc-$ and
$bc-$baryons in the region of $Z^o$ peak at LEP collider.


  Let $G = C_{n_1} \oplus ... \oplus C_{n_r}$ with $1 < n_1 \t ... \t n_r$ be a
finite abelian group, $\mathsf d^* (G) = n_1 + ... + n_r - r$, and let $\mathsf
d (G)$ denote the maximal length of a zero-sum free sequence over $G$. Then
$\mathsf d (G) \ge \mathsf d^* (G)$, and the standing conjecture is that
equality holds for $G = C_n^r$. We show that equality does not hold for $C_2
\oplus C_{2n}^r$, where $n \ge 3$ is odd and $r \ge 4$. This gives new
information on the structure of extremal zero-sum free sequences over
$C_{2n}^r$.


  Generalized Maxwell distribution is an extension of the classic Maxwell
distribution. In this paper, we concentrate on the joint distributional
asymptotics of normalized maxima and minima. Under optimal normalizing
constants, asymptotic expansions of joint distribution and density for
normalized partial maxima and minima are established. These expansions are used
to educe speeds of convergence of joint distribution and density of normalized
maxima and minima tending to its corresponding ultimate limits. Numerical
analysis are provided to support our results.


  There exist two different sorts of gaps in the nonsymmetric numerical
additive semigroups finitely generated by a minimal set of positive integers
{d_1,...,d_m}. The h-gaps are specific only for the nonsymmetric semigroups
while the g-gaps are possessed by both, symmetric and nonsymmetric semigroups.
We derive the generating functions for the corresponding sets of gaps,
Delta_H({\bf d}^m) and Delta_G({\bf d}^m), and prove several statements on the
minimal and maximal values of the h-gaps. Detailed description of both sorts of
gaps is given for three special kinds of nonsymmetric semigroups: semigroups
with maximal embedding dimension, semigroups of maximal and almost maximal
length, and pseudo--symmetric semigroups.


  A unified thermodynamic formalism describing the efficiency of learning is
proposed. First, we derive an inequality, which is more strength than
Clausius's inequality, revealing the lower bound of the entropy-production rate
of a subsystem. Second, the inequality is transformed to determine the general
upper limit for the efficiency of learning. In particular, we exemplify the
bound of the efficiency in nonequilibrium quantum-dot systems and networks of
living cells. The framework provides a fundamental trade-off relationship
between energy and information inheriting in stochastic thermodynamic
processes.


  We show that when the propensity score is estimated using a suitable
covariate balancing procedure, the commonly used inverse probability weighting
(IPW) estimator, augmented inverse probability weighting (AIPW) with linear
conditional mean, and inverse probability weighted regression adjustment
(IPWRA) with linear conditional mean are all numerically the same for
estimating the average treatment effect (ATE) or the average treatment effect
on the treated (ATT). Further, suitably chosen covariate balancing weights are
automatically normalized, which means that normalized and unnormalized versions
of IPW and AIPW are identical. For estimating the ATE, the weights that achieve
the algebraic equivalence of IPW, AIPW, and IPWRA are based on propensity
scores estimated using the inverse probability tilting (IPT) method of Graham,
Pinto and Egel (2012). For the ATT, the weights are obtained using the
covariate balancing propensity score (CBPS) method developed in Imai and
Ratkovic (2014). These equivalences also make covariate balancing methods
attractive when the treatment is confounded and one is interested in the local
average treatment effect.


  We analyze the infrared (IR) spectral energy distributions (SEDs) for
10micron < lambda(rest) < 100micron for ~600 galaxies at z~0.7 in the extended
Chandra Deep Field South by stacking their Spitzer 24, 70 and 160micron images.
We place interesting constraints on the average IR SED shape in two bins: the
brightest 25% of z~0.7 galaxies detected at 24micron, and the remaining 75% of
individually-detected galaxies. Galaxies without individual detections at
24micron were not well-detected at 70micron and 160micron even through
stacking. We find that the average IR SEDs of z~0.7 star-forming galaxies fall
within the diversity of z~0 templates. While dust obscuration Lir/Luv seems to
be only a function of star formation rate (SFR; ~ Lir+Luv), not of redshift,
the dust temperature of star-forming galaxies (with SFR ~ 10 solar mass per
year) at a given IR luminosity was lower at z~0.7 than today. We suggest an
interpretation of this phenomenology in terms of dust geometry: intensely
star-forming galaxies at z~0 are typically interacting, and host dense
centrally-concentrated bursts of star formation and warm dust temperatures. At
z~0.7, the bulk of intensely star-forming galaxies are relatively undisturbed
spirals and irregulars, and we postulate that they have large amounts of
widespread lower-density star formation, yielding lower dust temperatures for a
given IR luminosity. We recommend what IR SEDs are most suitable for modeling
intermediate redshift galaxies with different SFRs.


  Since shape optimization methods have been proven useful for identifying
interfaces in models governed by partial differential equations, we show how
shape optimization techniques can also be applied to an interface
identification problem constrained by a nonlocal Dirichlet problem. Here, we
focus on deriving the second shape derivative of the corresponding reduced
functional and we further investigate a second order optimization algorithm.


  Characterizing materials with spatially varying thermal conductivities is
significant to unveil the structure-property relation for a wide range of
functional materials, such as chemical-vapor-deposited diamonds, ion-irradiated
materials, nuclear materials under radiation, and battery electrode materials.
Although the development of thermal conductivity microscopy based on
time/frequency-domain thermoreflectance (TDTR/FDTR) enabled in-plane scanning
of thermal conductivity profile, measuring depth-dependent thermal conductivity
remains challenging. This work proposed a machine-learning-based reconstruction
method for extracting depth-dependent thermal conductivity K(z) directly from
frequency-domain phase signals. We demonstrated that the simple
supervised-learning algorithm kernel ridge regression (KRR) can reconstruct
K(z) without requiring pre-knowledge about the functional form of the profile.
The reconstruction method can not only accurately reproduce typical K(z)
distributions such as the pre-assumed exponential profile of
chemical-vapor-deposited (CVD) diamonds and Gaussian profile of ion-irradiated
materials, but also complex profiles artificially constructed by superimposing
Gaussian, exponential, polynomial, and logarithmic functions. In addition to
FDTR, the method also shows excellent performances of reconstructing K(z) of
ion-irradiated semiconductors from TDTR signals. This work demonstrates that
combining machine learning with pump-probe thermoreflectance is an effective
way for depth-dependent thermal property mapping.


  The recognition, involvement, and description of main actors influences the
story line of the whole text. This is of higher importance as the text per se
represents a flow of words and expressions that once it is read it is lost. In
this respect, the understanding of a text and moreover on how the actor exactly
behaves is not only a major concern: as human beings try to store a given input
on short-term memory while associating diverse aspects and actors with
incidents, the following approach represents a virtual architecture, where
collocations are concerned and taken as the associative completion of the
actors' acting. Once that collocations are discovered, they become managed in
separated memory blocks broken down by the actors. As for human beings, the
memory blocks refer to associative mind-maps. We then present several priority
functions to represent the actual temporal situation inside a mind-map to
enable the user to reconstruct the recent events from the discovered temporal
results.


  The Gemini Planet Imager Exoplanet Survey (GPIES) is a multi-year direct
imaging survey of 600 stars to discover and characterize young Jovian
exoplanets and their environments. We have developed an automated data
architecture to process and index all data related to the survey uniformly. An
automated and flexible data processing framework, which we term the Data
Cruncher, combines multiple data reduction pipelines together to process all
spectroscopic, polarimetric, and calibration data taken with GPIES. With no
human intervention, fully reduced and calibrated data products are available
less than an hour after the data are taken to expedite follow-up on potential
objects of interest. The Data Cruncher can run on a supercomputer to reprocess
all GPIES data in a single day as improvements are made to our data reduction
pipelines. A backend MySQL database indexes all files, which are synced to the
cloud, and a front-end web server allows for easy browsing of all files
associated with GPIES. To help observers, quicklook displays show reduced data
as they are processed in real-time, and chatbots on Slack post observing
information as well as reduced data products. Together, the GPIES automated
data processing architecture reduces our workload, provides real-time data
reduction, optimizes our observing strategy, and maintains a homogeneously
reduced dataset to study planet occurrence and instrument performance.


  Among the geniuses of mankind, Einstein was probably one of those who made
more erroneous claims, and often changed his opinion during the years on
important scientific subjects. However, it is important to bear in mind that
his mistakes were always due to a misinterpretation of the results obtained
from his equations, since he was often biased by his own view of the universe.
Einstein's equations have always given the correct answer and, till now, there
is no evidence that they might not be correct.


  The Askaryan Radio Array (ARA) is an ultra-high energy ($>10^{17}$ eV) cosmic
neutrino detector in phased construction near the South Pole. ARA searches for
radio Cherenkov emission from particle cascades induced by neutrino
interactions in the ice using radio frequency antennas ($\sim150-800$ MHz)
deployed at a design depth of 200 m in the Antarctic ice. A prototype ARA
Testbed station was deployed at $\sim30$ m depth in the 2010-2011 season and
the first three full ARA stations were deployed in the 2011-2012 and 2012-2013
seasons. We present the first neutrino search with ARA using data taken in 2011
and 2012 with the ARA Testbed and the resulting constraints on the neutrino
flux from $10^{17}-10^{21}$ eV.


  We report on optical, near-infrared and centimeter radio observations of
GRB000418 which allow us to follow the evolution of the afterglow from 2 to 200
days after the gamma-ray burst. In modeling these broad-band data, we find that
an isotropic explosion in a constant density medium is unable to simultaneously
fit both the radio and optical data. However, a jet-like outflow with an
opening angle of 10-20 degress provides a good description of the data. The
evidence in favor of a jet interpretation is based on the behavior of the radio
light curves, since the expected jet break is masked at optical wavelengths by
the light of the host galaxy. We also find evidence for extinction, presumably
arising from within the host galaxy, with A(V)=0.4 mag, and host flux densities
of F_R=1.1 uJy and F_K=1.7 uJy. These values supercede previous work on this
burst due to the availability of a broad-band data set allowing a global
fitting approach. A model in which the GRB explodes into a wind-stratified
circumburst medium cannot be ruled out by these data. However, in examining a
sample of other bursts (e.g. GRB990510, GRB000301C) we favor the jet
interpretation for GRB000418.


  We present a measurement of the volumetric Type Ia supernova (SN Ia) rate out
to z ~ 1.6 from the Hubble Space Telescope Cluster Supernova Survey. In
observations spanning 189 orbits with the Advanced Camera for Surveys we
discovered 29 SNe, of which approximately 20 are SNe Ia. Twelve of these SNe Ia
are located in the foregrounds and backgrounds of the clusters targeted in the
survey. Using these new data, we derive the volumetric SN Ia rate in four broad
redshift bins, finding results consistent with previous measurements at z > 1
and strengthening the case for a SN Ia rate that is equal to or greater than
~0.6 x 10^-4/yr/Mpc^3 at z ~ 1 and flattening out at higher redshift. We
provide SN candidates and efficiency calculations in a form that makes it easy
to rebin and combine these results with other measurements for increased
statistics. Finally, we compare the assumptions about host-galaxy dust
extinction used in different high-redshift rate measurements, finding that
different assumptions may induce significant systematic differences between
measurements.


  Multimodal hate detection, which aims to identify harmful content online such
as memes, is crucial for building a wholesome internet environment. Previous
work has made enlightening exploration in detecting explicit hate remarks.
However, most of their approaches neglect the analysis of implicit harm, which
is particularly challenging as explicit text markers and demographic visual
cues are often twisted or missing. The leveraged cross-modal attention
mechanisms also suffer from the distributional modality gap and lack logical
interpretability. To address these semantic gaps issues, we propose TOT: a
topology-aware optimal transport framework to decipher the implicit harm in
memes scenario, which formulates the cross-modal aligning problem as solutions
for optimal transportation plans. Specifically, we leverage an optimal
transport kernel method to capture complementary information from multiple
modalities. The kernel embedding provides a non-linear transformation ability
to reproduce a kernel Hilbert space (RKHS), which reflects significance for
eliminating the distributional modality gap. Moreover, we perceive the topology
information based on aligned representations to conduct bipartite graph path
reasoning. The newly achieved state-of-the-art performance on two publicly
available benchmark datasets, together with further visual analysis,
demonstrate the superiority of TOT in capturing implicit cross-modal alignment.


  This paper shows how maximum possible configuration efficiency of an
indefinitely large software system is constrained by chosing a fixed upper
limit to the number of program units per subsystem. It is then shown how the
configuration efficiency of an indefinitely large software system depends on
the ratio of the total number of informaiton hiding violational software units
divided by the total number of program units.


  The Kepler planet candidates are an interesting testbed for planet formation
scenarios. We present results from N-body simulations of multi-planetary
systems that resemble those observed by Kepler. We add both smooth (Type I/II)
and stochastic migration forces. The observed period ratio distribution is
inconsistent with either of those two scenarios on its own.
  However, applying both stochastic and smooth migration forces to the planets
simultaneously results in a period ratio distribution that is similar to the
observed one. This is a natural scenario if planets form in a turbulent
proto-planetary disk where these forces are always present. We show how the
observed period ratio and eccentricity distribution can constrain the relative
strength of these forces, a parameter which has been notoriously hard to
predict for decades.
  We make the source code of our simulations and the initial conditions freely
available to enable the community to expand this study and include effect other
than planetary migration.


  In this paper, we investigate the algebraic and geometric properties of the
hyperbolic Toda equations $u_{xy}=\exp(Ku)$ associated with nondegenerate
symmetrizable matrices $K$. A hierarchy of analogs to the potential modified
Korteweg-de Vries equation $u_t=u_{xxx}+u_x^3$ is constructed, and its relation
with the hierarchy for the Korteweg-de Vries equation $T_t=T_{xxx}+TT_x$ is
established. Group-theoretic structures for the dispersionless
(2+1)-dimensional Toda equation $u_{xy}=\exp(-u_{zz})$ are obtained. Geometric
properties of the multi-component nonlinear Schr\"odinger equation type systems
$\Psi_t = i\Psi_{xx} + i f(|\Psi|) \Psi$ (multi-soliton complexes) are
described.


  Compilation of papers presented by the VERITAS Collaboration at the 35th
International Cosmic Ray Conference (ICRC), held July 12 through July 20, 2017
in Busan, South Korea.


  This paper presents the results of a laboratory study involving Mailvelope, a
modern PGP client that integrates tightly with existing webmail providers. In
our study, we brought in pairs of participants and had them attempt to use
Mailvelope to communicate with each other. Our results shown that more than a
decade and a half after \textit{Why Johnny Can't Encrypt}, modern PGP tools are
still unusable for the masses. We finish with a discussion of pain points
encountered using Mailvelope, and discuss what might be done to address them in
future PGP systems.


  We prove Cherlin's conjecture, concerning binary primitive permutation
groups, for those groups with socle isomorphic to a sporadic simple group.


  We study an electron distribution under a quasiperiodic potential in light of
hyperuniformity, aiming to establish a classification and analysis method for
aperiodic but orderly density distributions realized in, e.g., quasicrystals.
Using the Aubry-Andre-Harper model, we first reveal that the electron-charge
distribution changes its character as the increased quasiperiodic potential
alters the eigenstates from extended to localized ones. While these changes of
the charge distribution are characterized by neither multifractality nor
translational-symmetry breaking, they are characterized by hyperuniformity
class and its order metric. We find a nontrivial relationship between the
density of states at the Fermi level, a charge-distribution histogram, and the
hyperuniformity class. The change to a different hyperuniformity class occurs
as a first-order phase transition except for an electron-hole symmetric point,
where the transition is of the third order. Moreover, we generalize the
hyperuniformity order metric to a function, to capture more detailed features
of the density distribution, in some analogy with a generalization of the
fractal dimension to a multifractal one.


  Under the condition of partial surface wettability, thin liquid films can be
destabilized by small perturbations and rupture into droplets. As successfully
predicted by the thin film equation (TFE), the rupture dynamics are dictated by
the liquid-solid interaction. The theory describes the latter using the
disjoining pressure or, equivalently, the contact angle. The introduction of a
secondary fluid can lead to a richer phenomenology thanks to the presence of
different fluid/surface interaction energies but has so far not been
investigated. In this work, we study the rupture of liquid films with different
heights immersed in a secondary fluid using a multi-component lattice Boltzmann
(LB) approach. We investigate a wide range of surface interaction energies,
equilibrium contact angles, and film thicknesses. We found that the rupture
time can differ by about one order of magnitude for identical equilibrium
contact angles but different surface free energies. Interestingly, the TFE
describes the observed breakup dynamics qualitatively well, up to equilibrium
contact angles as large as 130$^\circ$. A small film thickness is a much
stricter requirement for the validity of the TFE, and agreement with LB results
is found only for ratios $\epsilon=h/L$ of the film height $h$ and lateral
system size $L$ such as $\epsilon\lesssim\times10^{-3}$.


  Predicting performance-related behavior of the underlying network structure
becomes more and more indispensable in terms of the aspired application outcome
quality. However, the reliable forecast of QoS metrics like packet transfer
delay in wireless network systems is still a challenging task. Even though
existing approaches are technically capable of determining such network
properties under certain assumptions, they mostly abstract away from primal
aspects that inherently have an essential impact on temporal network
performance dynamics. Also, they usually require auxiliary resources to be
implemented and deployed along with the actual network components. In the
course of developing a lightweight measurement-based alternative for the
self-inspection and prediction of volatile performance characteristics in
environments of any kind, we selectively investigate the duration of message
delivery and packet loss rate against various parameters peculiar to common
radio network technologies like Wireless Sensor Networks (WSNs). Our hands-on
experiments reveal the relations between the oftentimes underestimated medium
access delay and a variety of main influencing factors including packet size,
backoff period, and number of neighbor nodes contending for the communication
medium. A closed formulation of selected weighted drivers facilitates the
average-case prediction of inter-node packet transfer delays for arbitrary
configurations of given network parameters even on resource-scarce WSN devices.
We validate our prediction method against basic multi-hop networking scenarios.
Yield field test results proof the basic feasibility and high precision of our
approach to network property estimation in virtue of self-governed local
measurements and regression-based calculations paving the way for a prospective
self-management of network properties based upon autonomous distributed
coordination.


  We theoretically investigate the optical rotational Doppler Effect using
modal expansion method. We find that the frequency shift content is only
determined by the surface of spinning object and the reduced Doppler shift is
linear to the change of mode index. The theoretical model makes us better
understand the physical processes of rotational Doppler Effect. It can provide
theoretical guidance for many related applications, such as detection of
rotating bodies, detection of OAM and frequency shift.


  It is known that solutions of nonlocal dispersal evolution equations do not
become smoother in space as time elapses. This lack of space regularity would
cause a lot of difficulties in studying transition fronts in nonlocal
equations. In the present paper, we establish some general criteria concerning
space regularity of transition fronts in nonlocal dispersal evolution equations
with a large class of nonlinearities, which allows the applicability of various
techniques for reaction-diffusion equations to nonlocal equation, and hence
serves as an initial and fundamental step for further studying various
qualitative properties of transition fronts such as stability and uniqueness.
We also prove the existence of continuously differentiable and increasing
interface location functions, which give a better characterization of the
propagation of transition fronts and are of great technical importance.


  Two single parameter families of polyhedra $P(\psi)$ are constructed in three
dimensional spaces of constant curvature $C(\psi)$. Identification of the faces
of the polyhedra via isometries results in cone manifolds $M(\psi)$ which are
topologically $S^1\timesS^2$, $S^3$ or singular $S^2$. The singular set of
$M(\psi)$ can have self intersections for some values of $\psi$ and can also be
the Whitehead link or form other configurations. Curvature varies continuously
with $\psi$. At $\psi=0$ spontaneous surgery occurs and the topological type of
$M(\psi)$ changes. This phenomenon is described.


  A revision of the recursive method proposed by S.A. Shakir [Am. J.Phys.
\textbf{52}, 845 (1984)] to solve bound eigenvalues of the Schr\"odinger
equation is presented. Equations are further simplified and generalized for
computing wave functions of any given one-dimensional potential, providing
accurate solutions not only for bound states but also for scattering and
resonant states, as demonstrated here for a few examples.


  We report on a discrete-time quantum walk that uses the momentum of
ultra-cold rubidium-87 atoms as the walk space and two internal atomic states
as the coin degree of freedom. Each step of the walk consists of a coin toss (a
microwave pulse) followed by a unitary shift operator (a resonant ratchet
pulse). We carry out a comprehensive experimental study on the effects of
various parameters, including the strength of the shift operation, coin
parameters, noise, and initialization of the system on the behavior of the
walk. The walk dynamics can be well controlled in our experiment; potential
applications include atom interferometry and engineering asymmetric walks.


  We introduce a random matrix model where the entries are dependent across
both rows and columns. More precisely, we investigate matrices of the form
$\X=(X_{(i-1)n+t})_{it}\in\R^{p\times n}$ derived from a linear process
$X_t=\sum_j c_j Z_{t-j}$, where the $\{Z_t\}$ are independent random variables
with bounded fourth moments. We show that, when both $p$ and $n$ tend to
infinity such that the ratio $p/n$ converges to a finite positive limit $y$,
the empirical spectral distribution of $p^{-1}\X\X^{\T}$ converges almost
surely to a deterministic measure. This limiting measure, which depends on $y$
and the spectral density of the linear process $X_t$, is characterized by an
integral equation for its Stieltjes transform. The matrix $p^{-1}\X\X^{\T}$ can
be interpreted as an approximation to the sample covariance matrix of a
high-dimensional process whose components are independent copies of $X_t$.


  Video object detection targets to simultaneously localize the bounding boxes
of the objects and identify their classes in a given video. One challenge for
video object detection is to consistently detect all objects across the whole
video. As the appearance of objects may deteriorate in some frames, features or
detections from the other frames are commonly used to enhance the prediction.
In this paper, we propose a Plug & Play scale-adaptive convolutional regression
tracker for the video object detection task, which could be easily and
compatibly implanted into the current state-of-the-art detection networks. As
the tracker reuses the features from the detector, it is a very light-weighted
increment to the detection network. The whole network performs at the speed
close to a standard object detector. With our new video object detection
pipeline design, image object detectors can be easily turned into efficient
video object detectors without modifying any parameters. The performance is
evaluated on the large-scale ImageNet VID dataset. Our Plug & Play design
improves mAP score for the image detector by around 5% with only little speed
drop.


  The emerging dynamic Virtual Reality (VR) applications are the best candidate
applications in high bandwidth indoor Terahertz (THz) wireless networks, with
the Reconfigurable Intelligent Surface (RIS) devices presenting a breakthrough
solution in extending the typically short THz communication range and
alleviating line-of-sight link blockages. In future smart factories, it is
envisioned that factory workers will use VR devices via VR application data
with high quality resolution, while transmitting over THz links and RIS
devices, enabled by the Mobile Edge Computing (MEC) capabilities. Since indoor
RIS placement is static, whereas VR users move and send multiple VR data
download requests simultaneously, there is a challenge of proper network load
balancing, which if unaddressed can result in poor resource utilization and low
throughput. To address this challenge, we propose a parallel downlink data
distribution system and develop multi-criteria optimization solutions that can
improve throughput, while transmitting each downlink data flow over a set of
possible paths between source and destination devices. The results show that
the proposed system can enhance the performance in terms of throughput benefit,
as compared to the system using one serial download link distribution.


  We have conducted a search for artificial radio emission associated with the
Kepler-160 system following the report of the discovery of the Earth-like
planet candidate KOI-456.04 on 2020 June 4 (arXiv:1905.09038v2). Our search
targeted both narrowband (2.97 Hz) drifting ($\pm 4$ Hz s$^{-1})$ and wideband
pulsed (5 ms at all bandwidths) artificially-dispersed technosignatures using
the turboSETI (arXiv:1709.03491v2) and SPANDAK pipelines, respectively, from
1-8 GHz. No candidates were identified above an upper limit Equivalent
Isotropic Radiated Power (EIRP) of $5.9 \times 10^{14}$ W for narrowband
emission and $7.3 \times 10^{12}$ W for wideband emission. Here we briefly
describe our observations and data reduction procedure.


  We calculate the four-loop massless QCD corrections with two closed quark
lines to quark and gluon form factors. The results for the gluon form factor
and the singlet part of the quark form factor are given for the first time.
From our analytic expressions for the form factors, we determine the
corresponding cusp anomalous dimensions. The relevant Feynman integrals are
obtained with novel integral reduction techniques and direct integration
methods.


  The current status of flavored dark matter is reviewed. We discuss the main
experimental constraints on models of flavored dark matter and survey some
possible considerations which are relevant for the constructions of models. We
then review the application of existing flavor principles to dark matter, with
an emphasis on minimal flavor violation, and discuss implications of flavored
dark matter on collider phenomenology.


  In this paper, we have presented an algorithm to generate various black hole
solutions in general relativity and alternative theories of gravity. The
algorithm involves few dimensional parameters that are assigned suitable values
to specify the required black hole.


  We present the guarded lambda-calculus, an extension of the simply typed
lambda-calculus with guarded recursive and coinductive types. The use of
guarded recursive types ensures the productivity of well-typed programs.
Guarded recursive types may be transformed into coinductive types by a
type-former inspired by modal logic and Atkey-McBride clock quantification,
allowing the typing of acausal functions. We give a call-by-name operational
semantics for the calculus, and define adequate denotational semantics in the
topos of trees. The adequacy proof entails that the evaluation of a program
always terminates. We introduce a program logic with L\"ob induction for
reasoning about the contextual equivalence of programs. We demonstrate the
expressiveness of the calculus by showing the definability of solutions to
Rutten's behavioural differential equations.


  Variant calling, the problem of estimating whether a position in a DNA
sequence differs from a reference sequence, given noisy, redundant, overlapping
short sequences that cover that position, is fundamental to genomics. We
propose a deep averaging network designed specifically for variant calling. Our
model takes into account the independence of each short input read sequence by
transforming individual reads through a series of convolutional layers,
limiting the communication between individual reads to averaging and
concatenating operations. Training and testing on the precisionFDA Truth
Challenge (pFDA), we match state of the art overall 99.89 F1 score. Genome
datasets exhibit extreme skew between easy examples and those on the decision
boundary. We take advantage of this property to converge models at 5x the speed
of standard epoch-based training by skipping easy examples during training. To
facilitate future work, we release our code, trained models and pre-processed
public domain datasets.


  In this paper we introduce and discuss numerical schemes for the
approximation of kinetic equations for flocking behavior with phase transitions
that incorporate uncertain quantities. This class of schemes here considered
make use of a Monte Carlo approach in the phase space coupled with a stochastic
Galerkin expansion in the random space. The proposed methods naturally preserve
the positivity of the statistical moments of the solution and are capable to
achieve high accuracy in the random space. Several tests on a kinetic alignment
model with self propulsion validate the proposed methods both in the
homogeneous and inhomogeneous setting, shading light on the influence of
uncertainties in phase transition phenomena driven by noise such as their
smoothing and confidence band.


  Two recent experimental observations pose a challenge to many cortical
models. First, the activity in the auditory cortex is sparse, and firing rates
can be described by a lognormal distribution. Second, the distribution of
non-zero synaptic strengths between nearby cortical neurons can also be
described by a lognormal distribution. Here we use a simple model of cortical
activity to reconcile these observations. The model makes the experimentally
testable prediction that synaptic efficacies onto a given cortical neuron are
statistically correlated, i.e. it predicts that some neurons receive many more
strong connections than other neurons. We propose a simple Hebb-like learning
rule which gives rise to both lognormal firing rates and synaptic efficacies.
Our results represent a first step toward reconciling sparse activity and
sparse connectivity in cortical networks.


  We present a novel high-fidelity real-time neural vocoder called VocGAN. A
recently developed GAN-based vocoder, MelGAN, produces speech waveforms in
real-time. However, it often produces a waveform that is insufficient in
quality or inconsistent with acoustic characteristics of the input mel
spectrogram. VocGAN is nearly as fast as MelGAN, but it significantly improves
the quality and consistency of the output waveform. VocGAN applies a
multi-scale waveform generator and a hierarchically-nested discriminator to
learn multiple levels of acoustic properties in a balanced way. It also applies
the joint conditional and unconditional objective, which has shown successful
results in high-resolution image synthesis. In experiments, VocGAN synthesizes
speech waveforms 416.7x faster on a GTX 1080Ti GPU and 3.24x faster on a CPU
than real-time. Compared with MelGAN, it also exhibits significantly improved
quality in multiple evaluation metrics including mean opinion score (MOS) with
minimal additional overhead. Additionally, compared with Parallel WaveGAN,
another recently developed high-fidelity vocoder, VocGAN is 6.98x faster on a
CPU and exhibits higher MOS.


  A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering
system, is investigated with classical, semiclassical, and quantum mechanical
methods at various center-to-center separations of the spheres. The efficiency
and scaling properties of the computations are discussed by comparisons to the
two-dimensional 3-disk system. While in systems with few degrees of freedom
modern quantum calculations are, in general, numerically more efficient than
semiclassical methods, this situation can be reversed with increasing dimension
of the problem. For the 4-sphere system with large separations between the
spheres, we demonstrate the superiority of semiclassical versus quantum
calculations, i.e., semiclassical resonances can easily be obtained even in
energy regions which are unattainable with the currently available quantum
techniques. The 4-sphere system with touching spheres is a challenging problem
for both quantum and semiclassical techniques. Here, semiclassical resonances
are obtained via harmonic inversion of a cross-correlated periodic orbit
signal.


  The Fr\'echet distance is a commonly used similarity measure between curves.
It is known how to compute the continuous Fr\'echet distance between two
polylines with $m$ and $n$ vertices in $\mathbb{R}^d$ in $O(mn (\log \log
n)^2)$ time; doing so in strongly subquadratic time is a longstanding open
problem. Recent conditional lower bounds suggest that it is unlikely that a
strongly subquadratic algorithm exists. Moreover, it is unlikely that we can
approximate the Fr\'echet distance to within a factor $3$ in strongly
subquadratic time, even if $d=1$. The best current results establish a tradeoff
between approximation quality and running time. Specifically, Colombe and Fox
(SoCG, 2021) give an $O(\alpha)$-approximate algorithm that runs in $O((n^3 /
\alpha^2) \log n)$ time for any $\alpha \in [\sqrt{n}, n]$, assuming $m = n$.
In this paper, we improve this result with an $O(\alpha)$-approximate algorithm
that runs in $O((n + mn / \alpha) \log^3 n)$ time for any $\alpha \in [1, n]$,
assuming $m \leq n$ and constant dimension $d$.


  The stationary distribution of a fully chaotic system typically exhibits a
fractal structure, which dramatically changes if the dynamical equations are
even slightly modified. Perturbative techniques are not expected to work in
this situation. In contrast, the presence of additive noise smooths out the
stationary distribution, and perturbation theory becomes applicable. We show
that a perturbation expansion for the Fokker-Planck evolution operator yields
surprisingly accurate estimates of long-time averages in an otherwise unlikely
scenario.


  We present an empirical approach for interpreting gravitational wave signals
of binary black hole mergers under the assumption that the underlying black
hole population is sourced by remnants of stellar evolution. Using the observed
relationship between galaxy mass and stellar metallicity, we predict the black
hole count as a function of galaxy stellar mass. We show, for example, that a
galaxy like the Milky Way should host millions of $\sim 30~M_\odot$ black holes
and dwarf satellite galaxies like Draco should host $\sim 100$ such remnants,
with weak dependence on the assumed IMF and stellar evolution model. Most
low-mass black holes ($\sim10 M_\odot$) typically reside within massive
galaxies ($M_\star \simeq 10^{11} M_\odot$) while massive black holes ($\sim
50~M_\odot$) typically reside within dwarf galaxies ($M_\odot \simeq 10^9
M_\odot$) today. If roughly $1\%$ of black holes are involved in a binary black
hole merger, then the reported merger rate densities from Advanced LIGO can be
accommodated for a range of merger timescales, and the detection of mergers
with $> 50~M_\odot$ black holes should be expected within the next decade.
Identifying the host galaxy population of the mergers provides a way to
constrain both the binary neutron star or black hole formation efficiencies and
the merger timescale distributions; these events would be primarily localized
in dwarf galaxies if the merger timescale is short compared to the age of the
universe and in massive galaxies otherwise. As more mergers are detected, the
prospect of identifying the host galaxy population, either directly through the
detection of electromagnetic counterparts of binary neutron star mergers or
indirectly through the anisotropy of the events, will become a realistic
possibility.


  We consider the Rudin-Osher-Fatemi variational denoising model with general
regularizing term in one-dimensional, vector-valued setting. We obtain local
estimates on the singular part of the variation measure of the minimizer in
terms of the singular part of the variation measure of the datum. In the case
of homogeneous regularizer, we prove local estimates on the whole variation
measure of the minimizer and deduce an analogous result for the gradient flow
of the regularizer.


  We investigate quasiparticle states associated with an isolated vortex in a
d-wave superconductor using a self-consistent Bogoliubov-de Gennes formalism.
For a pure $d_{x^2-y^2}$ superconductor we find that there exist no bound
states in the core; all the states are extended with continuous energy
spectrum. This result is inconsistent with the existing experimental data on
cuprates. We propose an explanation for this data in terms of a
magnetic-field-induced $d_{x^2-y^2}+id_{xy}$ state recently invoked in
connection with the thermal conductivity measurements on
Bi$_2$Sr$_2$CaCu$_2$O$_8$.


  On 3D imaging, light field cameras typically are of single shot, and however,
they heavily suffer from low spatial resolution and depth accuracy. In this
paper, by employing an optical projector to project a group of single
high-frequency phase-shifted sinusoid patterns, we propose a phase guided light
field algorithm to significantly improve both the spatial and depth resolutions
for off-the-shelf light field cameras. First, for correcting the axial
aberrations caused by the main lens of our light field camera, we propose a
deformed cone model to calibrate our structured light field system. Second,
over wrapped phases computed from patterned images, we propose a stereo
matching algorithm, i.e. phase guided sum of absolute difference, to robustly
obtain the correspondence for each pair of neighbored two lenslets. Finally, by
introducing a virtual camera according to the basic geometrical optics of light
field imaging, we propose a reorganization strategy to reconstruct 3D point
clouds with spatial-depth high resolution. Experimental results show that,
compared with the state-of-the-art active light field methods, the proposed
reconstructs 3D point clouds with a spatial resolution of 1280$\times$720 with
factors 10$\times$ increased, while maintaining the same high depth resolution
and needing merely a single group of high-frequency patterns.


  In this semi-expository note, we give a new proof of a structure theorem due
to Shimura for nearly holomorphic modular forms on the complex upper half
plane. Roughly speaking, the theorem says that the space of all nearly
holomorphic modular forms is the direct sum of the subspaces obtained by
applying appropriate weight-raising operators on the spaces of holomorphic
modular forms and on the one-dimensional space spanned by the weight 2 nearly
holomorphic Eisenstein series.
  While Shimura's proof was classical, ours is representation-theoretic. We
deduce the structure theorem from a decomposition for the space of n-finite
automorphic forms on SL_2(R). To prove this decomposition, we use the mechanism
of category O and a careful analysis of the various possible indecomposable
submodules. It is possible to achieve the same end by more direct methods, but
we prefer this approach as it generalizes to other groups.
  This note may be viewed as the toy case of our paper ["Lowest weight modules
of Sp_4(R) and nearly holomorphic Siegel modular forms"], where we prove an
analogous structure theorem for vector-valued nearly holomorphic Siegel modular
forms of degree two.


  We show that the dynamic magnetization at the edges of a thin magnetic
element with finite lateral size can be described by new effective boundary
conditions that take into account inhomogeneous demagnetizing fields near the
element edges. These fields play a dominant role in the effective pinning of
the dynamic magnetization at the boundaries of mesoscopic and nano-sized
magnetic elements. The derived effective boundary conditions generalize
well-known Rado-Weertman boundary conditions and are reduced to them in the
limiting case of a very thin magnetic element.


  We consider the possibility that neutrinos are coupled very weakly to an
extremely light scalar boson. We first analyze the simple problem of one
generation of neutrino and show that, for ranges of parameters that are allowed
by existing data, such a system can have serious consequences for the evolution
of stars and could impact precision laboratory measurements. We discuss the
extension to more generations and show that the general conclusion remains
viable. Finally, we note that, should such a scalar field be present,
experiments give information about effective masses, not the masses that arise
in unified field theories.


  We consider the degree-Rips construction from topological data analysis,
which provides a density-sensitive, multiparameter hierarchical clustering
algorithm. We analyze its stability to perturbations of the input data using
the correspondence-interleaving distance, a metric for hierarchical clusterings
that we introduce. Taking certain one-parameter slices of degree-Rips recovers
well-known methods for density-based clustering, but we show that these methods
are unstable. However, we prove that degree-Rips, as a multiparameter object,
is stable, and we propose an alternative approach for taking slices of
degree-Rips, which yields a one-parameter hierarchical clustering algorithm
with better stability properties. We prove that this algorithm is consistent,
using the correspondence-interleaving distance. We provide an algorithm for
extracting a single clustering from one-parameter hierarchical clusterings,
which is stable with respect to the correspondence-interleaving distance. And,
we integrate these methods into a pipeline for density-based clustering, which
we call Persistable. Adapting tools from multiparameter persistent homology, we
propose visualization tools that guide the selection of all parameters of the
pipeline. We demonstrate Persistable on benchmark datasets, showing that it
identifies multi-scale cluster structure in data.


  For real power series whose non-zero coefficients satisfy $|a_m|^{1/m}\to~1$
we prove a stronger version of Fabry theorem relating the frequency of sign
changes in the coefficients and analytic continuation of the sum of the power
series.


  Cancer stem cells have been shown to be critical to the development of a
variety of solid cancers. The precise interplay mechanisms between cancer stem
cells and the rest of a tissue are still not elucidated. To shed light on the
interactions between stem and non-stem cancer cell populations we develop a
two-population mathematical model, which is suitable to describe tumorsphere
growth. Both interspecific and intraspecific interactions, mediated by the
microenvironment, are included. We show that there is a tipping point,
characterized by a transcritical bifurcation, where a purely non-stem cell
attractor is replaced by a new attractor that contains both stem and
differentiated cancer cells. The model is then applied to describe the outcome
of a recent experiment. This description reveals that, while the intraspecific
interactions are inhibitory, the interspecific interactions stimulate growth.
This can be understood in terms of stem cells needing differentiated cells to
reinforce their niches, and phenotypic plasticity favoring the
de-differentiation of differentiated cells into cancer stem cells. We posit
that this is a consequence of the deregulation of the quorum sensing that
maintains homeostasis in healthy tissues.


  Molecular dynamics simulations in simplified models allow one to study the
scaling properties of folding times for many proteins together under a
controlled setting. We consider three variants of the Go models with different
contact potentials and demonstrate scaling described by power laws and no
correlation with the relative contact order parameter. We demonstrate existence
of at least three kinetic universality classes which are correlated with the
types of structure: the alpha-, alpha--beta-, and beta- proteins have the
scaling exponents of about 1.7, 2.5, and 3.2 respectively. The three classes
merge into one when the contact range is truncated at a 'reasonable' value. We
elucidate the role of the potential associated with the chirality of a protein.


  The magnetic state of low temperature martensite phase in Co-substituted
Ni-Mn-Sn-based ferromagnetic shape memory alloys (FSMAs) has been investigated,
in view of numerous conflicting reports of occurrences of spin glass (SG),
superparamagnetism (SPM) or long range anti-ferromagnetic (AF) ordering.
Combination of dc magnetization, ac susceptibility and small angle neutron
scattering (SANS) studies provide a clear evidence for AF order in martensitic
phase of Ni45Co5Mn38Sn12 alloy and rule out SPM and SG orders. Identical
studies on another alloy of close composition of Ni44Co6Mn40Sn10 point to
presence of SG order in martensitic phase and absence of SPM behavior, contrary
to earlier report. SANS results do show presence of nanometre-sized clusters
but they are found to grow in size from 3 nm at 30 K to 11 nm at 300 K, and do
not correlate with magnetism in these alloys.


  The validity of some rules in the classical theory of spin, which are
followed by the Bargmann--Michel--Telegdi formula for a relativistic particle
spin rotation in a constant homogeneous magnetic field, is analyzed. In the
framework of the quantum theory, we give examples where these rules are
violated. Consequences for polarization experiments are discussed.


  A geometric graph in the plane is angle-monotone of width $\gamma$ if every
pair of vertices is connected by an angle-monotone path of width $\gamma$, a
path such that the angles of any two edges in the path differ by at most
$\gamma$. Angle-monotone graphs have good spanning properties.
  We prove that every point set in the plane admits an angle-monotone graph of
width $90^\circ$, hence with spanning ratio $\sqrt 2$, and a subquadratic
number of edges. This answers an open question posed by Dehkordi, Frati and
Gudmundsson.
  We show how to construct, for any point set of size $n$ and any angle
$\alpha$, $0 < \alpha < 45^\circ$, an angle-monotone graph of width
$(90^\circ+\alpha)$ with $O(\frac{n}{\alpha})$ edges. Furthermore, we give a
local routing algorithm to find angle-monotone paths of width
$(90^\circ+\alpha)$ in these graphs. The routing ratio, which is the ratio of
path length to Euclidean distance, is at most $1/\cos(45^\circ +
\frac{\alpha}{2})$, i.e., ranging from $\sqrt 2 \approx 1.414$ to $2.613$. For
the special case $\alpha = 30^\circ$, we obtain the $\Theta_6$-graph and our
routing algorithm achieves the known routing ratio 2 while finding
angle-monotone paths of width $120^\circ$.


  We study numerically quantum diffusion of a particle on small-world networks
by integrating the time-dependent Schr\"odinger equation with a localized
initial state. The participation ratio, which corresponds to the number of
visited sites in the case of classical diffusion, as a function of time is
measured and the corresponding diffusion time $\tau$ is computed. In a local
regular network, i.e., in the network with the rewiring probability $p=0$, the
diffusion time depends on the network size $N$ as $\tau \sim N$, while the
behavior $\tau \sim \log N$ is observed as $p$ becomes finite. Such fast
diffusion of a particle on a complex network suggests that the small-world
transition is also the fast-world transition from a dynamic point of view. The
classical diffusion behavior is also studied and compared with the quantum
behavior.


  Systems subject to high-frequency driving exhibit Floquet prethermalization,
that is, they heat exponentially slowly on a time scale that is large in the
drive frequency, $\tau_{\rm h} \sim \exp(\omega)$. Nonetheless, local
observables can decay much faster via energy conserving processes, which are
expected to cause a rapid decay in the fidelity of an initial state. Here we
show instead that the fidelities of eigenstates of the time-averaged
Hamiltonian, $H_0$, display an exponentially long lifetime over a wide range of
frequencies -- even as generic initial states decay rapidly. When $H_0$ has
quantum scars, or highly excited-eigenstates of low entanglement, this leads to
long-lived non-thermal behavior of local observables in certain initial states.
We present a two-channel theory describing the fidelity decay time $\tau_{\rm
f}$: the interzone channel causes fidelity decay through energy absorption i.e.
coupling across Floquet zones, and ties $\tau_{\rm f}$ to the slow heating time
scale, while the intrazone channel causes hybridization between states in the
same Floquet zone. Our work informs the robustness of experimental approaches
for using Floquet engineering to generate interesting many-body Hamiltonians,
with and without scars.


  We recently developed an analytic theory of cumulative multibunch beam
breakup that includes a linear variation of transverse focusing across the
bunch train. The focusing variation saturates the exponential growth of the
beam breakup and establishes an algebraic decay of the transverse bunch
displacement versus bunch number. In this paper we illustrate how the focusing
variation works to suppress multibunch beam breakup, as well as how the
mechanism scales with accelerator and beam parameters.


  The Graph Isomorphism (GI) problem is a theoretically interesting problem
because it has not been proven to be in P nor to be NP-complete. Babai made a
breakthrough in 2015 when announcing a quasipolynomial time algorithm for GI
problem. Babai's work gives the most theoretically efficient algorithm for GI,
as well as a strong evidence favoring the idea that class GI $\ne$ NP and thus
P $\ne$ NP. Based on Babai's algorithm, we prove that GI can further be solved
by a parallel algorithm that runs in polynomial time using a quasipolynomial
number of processors. We achieve that result by identifying the bottlenecks in
Babai's algorithms and parallelizing them. In particular, we prove that color
refinement can be computed in parallel logarithmic time using a polynomial
number of processors, and the $k$-dimensional WL refinement can be computed in
parallel polynomial time using a quasipolynomial number of processors. Our work
suggests that Graph Isomorphism and GI-complete problems can be computed
efficiently in a parallel computer, and provides insights on speeding up
parallel GI programs in practice.


  Wind-fed models offer a unique way to form predictive models of the accretion
flow surrounding Sagittarius A*. We present 3D, wind-fed MHD and GRMHD
simulations spanning the entire dynamic range of accretion from parsec scales
to the event horizon. We expand on previous work by including nonzero black
hole spin and dynamically evolved electron thermodynamics. Initial conditions
for these simulations are generated from simulations of the observed Wolf-Rayet
stellar winds in the Galactic Centre. The resulting flow tends to be highly
magnetized ($\beta \approx 2$) with an $\sim$ $r^{-1}$ density profile
independent of the strength of magnetic fields in the winds. Our simulations
reach the MAD state for some, but not all cases. In tilted flows, SANE jets
tend to align with the angular momentum of the gas at large scales, even if
that direction is perpendicular to the black hole spin axis. Conversely, MAD
jets tend to align with the black hole spin axis. The gas angular momentum
shows similar behavior: SANE flows tend to only partially align while MAD flows
tend to fully align. With a limited number of dynamical free parameters, our
models can produce accretion rates, 230 GHz flux, and unresolved linear
polarization fractions roughly consistent with observations for several choices
of electron heating fraction. Absent another source of large-scale magnetic
field, winds with a higher degree of magnetization (e.g., where the magnetic
pressure is 1/100 of the ram pressure in the winds) may be required to get a
sufficiently large RM with consistent sign.


  A four-dimensional asymptotic expansion scheme is used to study the next
order effects of the nonlinearity near a spinning dynamical black hole. The
angular momentum flux and energy flux formula are then obtained by constructing
the reference frame in terms of the compatible constant spinors and the
compatibility of the coupling leading order Newman-Penrose equations. By using
the slow rotation and small-tide approximation for a spinning black hole, we
chose the horizon cross-section is spherical symmetric. It turns out the flux
formula is rather simple and can be compared with the known results. Directly
from the energy flux formula of the slow rotating dynamical horizon, we find
that the physically reasonable condition on the positivity of the gravitational
energy flux yields that the shear will monotonically decrease with time. Thus a
slow rotating dynamical horizon will asymptotically approaches an isolated
horizon during late time.


  This study investigates the representations and understandings of electric
fields expressed by Chinese high school students 15 to 16 years old who have
not received high school level physics instruction. The physics education
research literature has reported students conceptions of electric fields
post-instruction as indicated by students performance on textbook-style
questions. It has, however, inadequately captured student ideas expressed in
other situations yet informative to educational research. In this study, we
explore students ideas of electric fields pre-instruction as shown by students
representations produced in open-ended activities. 92 participant students
completed a worksheet that involved drawing comic strips about electric charges
as characters of a cartoon series. Three students who had spontaneously
produced arrow diagrams were interviewed individually after class. We
identified nine ideas related to electric fields that these three students
spontaneously leveraged in the comic strip activity. In this paper, we describe
in detail each idea and its situated context. As most research in the
literature has understood students as having relatively fixed conceptions and
mostly identified divergences in those conceptions from canonical targets, this
study shows students reasoning to be more variable in particular moments, and
that variability includes common sense resources that can be productive for
learning about electric fields.


  Given a complex polynomial $P$ with zeroes $z_1,\dotsc,z_d$, we show that the
asymptotic zero-counting measure of the iterated derivatives $Q^{(n)}, \
n=1,2,\dotsc$, where $Q=R/P$ is any irreducible rational function, converges to
an explicitly constructed probability measure supported by the Voronoi diagram
associated with $z_1,\dotsc,z_d$. This refines P\'olya's Shire theorem for
these functions. In addition, we prove a similar result, using currents, for
Voronoi diagrams associated with generic hyperplane configurations in $\mathbb
C^m$.


  We present the discovery and characterization of two warm mini-Neptunes
transiting the K3V star TOI-815 in a K-M binary system. Analysis of the spectra
and rotation period reveal it to be a young star with an age of
$200^{+400}_{-200}$Myr. TOI-815b has a 11.2-day period and a radius of
2.94$\pm$0.05$\it{R_{\rm\mathrm{\oplus}}}$ with transits observed by TESS,
CHEOPS, ASTEP, and LCOGT. The outer planet, TOI-815c, has a radius of
2.62$\pm$0.10$\it{R_{\rm\mathrm{\oplus}}}$, based on observations of three
non-consecutive transits with TESS, while targeted CHEOPS photometry and radial
velocity follow-up with ESPRESSO were required to confirm the 35-day period.
ESPRESSO confirmed the planetary nature of both planets and measured masses of
7.6$\pm$1.5 $\it{M_{\rm \mathrm{\oplus}}}$
($\rho_\mathrm{P}$=1.64$^{+0.33}_{-0.31}$gcm$^{-3}$) and
23.5$\pm$2.4$\it{M_{\rm\mathrm{\oplus}}}$
($\rho_\mathrm{P}$=7.2$^{+1.1}_{-1.0}$gcm$^{-3}$) respectively. Thus, the
planets have very different masses, unlike the usual similarity of masses in
compact multi-planet systems. Moreover, our statistical analysis of
mini-Neptunes orbiting FGK stars suggests that weakly irradiated planets tend
to have higher bulk densities compared to those suffering strong irradiation.
This could be ascribed to their cooler atmospheres, which are more compressed
and denser. Internal structure modeling of TOI-815b suggests it likely has a
H-He atmosphere constituting a few percent of the total planet mass, or higher
if the planet is assumed to have no water. In contrast, the measured mass and
radius of TOI-815c can be explained without invoking any atmosphere,
challenging planetary formation theories. Finally, we infer from our
measurements that the star is viewed close to pole-on, which implies a
spin-orbit misalignment at the 3$\sigma$ level.


  Using mid-infrared (MIR) images of four photometric bands of the Infrared
Camera (IRC) onboard the AKARI satellite, S7 (7 um), S11 (11 um), L15 (15 um),
and L24 (24 um), we investigate the interstellar dust properties of the nearby
pair of galaxies M51 with respect to its spiral arm structure. The arm and
interarm regions being defined based on a spatially filtered stellar component
model image, we measure the arm-to-interarm contrast for each band. The
contrast is lowest in the S11 image, which is interpreted as that among the
four AKARI MIR bands the S11 image best correlates with the spatial
distribution of dust grains including colder components, while the L24 image
with the highest contrast traces warmer dust heated by star forming activities.
The surface brightness ratio between the bands, i.e. color, is measured over
the disk of the main galaxy, M51a, at 300 pc resolution. We find that the
distribution of S7/S11 is smooth and well traces the global spiral arm pattern
while L15/S11 and L24/S11 peak at individual HII regions. This result indicates
that the ionization state of PAHs is related to the spiral structure.
Comparison with observational data and dust models also supports the importance
of the variation in the PAH ionization state within the M51a disk. However, the
mechanism driving this variation is not yet clear from currently available data
sets. Another suggestion from the comparison with the models is that the PAH
fraction to the total dust mass is higher than previously estimated.


  Bistability, a universal phenomenon found in diverse fields such as biology,
chemistry, and physics, describes a scenario in which a system has two stable
equilibrium states and resets to one of the two states. The ability to switch
between these two states is the basis for a wide range of applications,
particularly in memory and logic operations. Here, we present a universal
approach to achieve bistable switching in magnonics, the field processing data
using spin waves. As an exemplary application, we use magnonic bistability to
experimentally demonstrate the still missing magnonic repeater. A pronounced
bistable window is observed in a 1um wide magnonic conduit under an external rf
drive characterized by two magnonic stable states defined as low and high
spin-wave amplitudes. The switching between these two states is realized by
another propagating spin wave sent into the rf driven region. This magnonic
bistable switching is used to design the magnonic repeater, which receives the
original decayed and distorted spin wave and regenerates a new spin wave with
amplified amplitude and normalized phase. Our magnonic repeater is proposed to
be installed at the inputs of each magnonic logic gate to overcome the
spin-wave amplitude degradation and phase distortion during previous
propagation and achieve integrated magnonic circuits or magnonic neuromorphic
networks.


  Dielectric elastomers (DEs) are a type of multifunctional materials with
salient features that are very attractive in developing soft, lightweight, and
small-scale transducers and robotics. This paper reviews the mechanics of soft
DE structures, focusing on their dynamic responses, including vibrations and
waves in typical structures. The basic formulations of nonlinear
electroelasticity are briefly summarized by following the descriptions of
Dorfmann and Ogden. The recent advances in the study on linearized dynamic
problems of DE plates and shells are then outlined according to the geometric
configurations as well as the coordinates thereof adopted. Some interesting
observations from the numerical results are highlighted, and the underlying
physics is discussed. For completeness, an account of the nonlinear dynamic
characteristics of DE structures is also given. For DE structures with a
periodic arrangement, i.e., DE phononic crystals (PCs) or metamaterials, this
paper reviews the designs, solutions, and results to illustrate the wide-range
tunability of band structure that is realized by large reversible deformation
and electromechanical coupling. The present literature survey could be a useful
guide for future studies on the dynamic topics of DE structures.


  Lithium borosilicate (LBS) glass is a prototypical lithium-ion conducting
oxide glasses available for an all-solid state buttery. Nevertheless, the
atomistic modeling of LBS glass using $ab$ $initio$ (AIMD) and classical
molecular dynamics (CMD) simulations have critical limitations due to
computational cost and inaccuracy in reproducing the glass microstructures,
respectively. To overcome these difficulties, a machine-learning potential
(MLP) was examined in this work for modeling LBS glasses using DeepMD. The
glass structures obtained by this MLP possessed fourhold-coordinated boron
($^4$B) confirmed well with the experimental data and abundance of
three-membered rings. The models were energetically more stable compared with
those constructed with a functional force-field even though both the models
included reasonable $^4$B. The results confirmed MLP to be superior to model
the boron-containing glasses and address the inherent shortcomings of the AIMD
and CMD. This study also discusses some limitations of MLP for modeling
glasses.


  Breakthroughs extending nanostructure engineering beyond what is possible
with current fabrication techniques will be crucial for enabling
next-generation nanotechnologies. Nanoepitaxy of strain-engineered bent
nanowire heterostructures presents a promising platform for realizing bottom-up
and scalable fabrication of nanowire devices. The synthesis of these structures
requires the selective asymmetric deposition of lattice-mismatched shells-a
complex growth process which is not well understood. We present the
nanoepitaxial growth of GaAs-InP core-shell bent nanowires and connecting
nanowire pairs to form nano-arches. Compositional analysis of nanowire
cross-sections reveals the critical role of adatom diffusion in the
nanoepitaxial growth process, which leads to two distinct growth regimes:
indium-diffusion limited growth and phosphorous-limited growth. The highly
controllable phosphorous-limited growth mode is employed to synthesize
connected nanowire pairs and quantify the role of flux shadowing on the shell
growth process. These results provide important insight into three-dimensional
nanoepitaxy and enable new possibilities for nanowire device fabrication.


  We consider the setting of iterative learning control, or model-based policy
learning in the presence of uncertain, time-varying dynamics. In this setting,
we propose a new performance metric, planning regret, which replaces the
standard stochastic uncertainty assumptions with worst case regret. Based on
recent advances in non-stochastic control, we design a new iterative algorithm
for minimizing planning regret that is more robust to model mismatch and
uncertainty. We provide theoretical and empirical evidence that the proposed
algorithm outperforms existing methods on several benchmarks.


  We propose ProtLLM, a versatile cross-modal large language model (LLM) for
both protein-centric and protein-language tasks. ProtLLM features a unique
dynamic protein mounting mechanism, enabling it to handle complex inputs where
the natural language text is interspersed with an arbitrary number of proteins.
Besides, we propose the protein-as-word language modeling approach to train
ProtLLM. By developing a specialized protein vocabulary, we equip the model
with the capability to predict not just natural language but also proteins from
a vast pool of candidates. Additionally, we construct a large-scale interleaved
protein-text dataset, named InterPT, for pre-training. This dataset
comprehensively encompasses both (1) structured data sources like protein
annotations and (2) unstructured data sources like biological research papers,
thereby endowing ProtLLM with crucial knowledge for understanding proteins. We
evaluate ProtLLM on classic supervised protein-centric tasks and explore its
novel protein-language applications. Experimental results demonstrate that
ProtLLM not only achieves superior performance against protein-specialized
baselines on protein-centric tasks but also induces zero-shot and in-context
learning capabilities on protein-language tasks.


  Neural models, with their ability to provide novel representations, have
shown promising results in prediction tasks in healthcare. However, patient
demographics, medical technology, and quality of care change over time. This
often leads to drop in the performance of neural models for prospective
patients, especially in terms of their calibration. The deep kernel learning
(DKL) framework may be robust to such changes as it combines neural models with
Gaussian processes, which are aware of prediction uncertainty. Our hypothesis
is that out-of-distribution test points will result in probabilities closer to
the global mean and hence prevent overconfident predictions. This in turn, we
hypothesise, will result in better calibration on prospective data.
  This paper investigates DKL's behaviour when facing a temporal shift, which
was naturally introduced when an information system that feeds a cohort
database was changed. We compare DKL's performance to that of a neural baseline
based on recurrent neural networks. We show that DKL indeed produced superior
calibrated predictions. We also confirm that the DKL's predictions were indeed
less sharp. In addition, DKL's discrimination ability was even improved: its
AUC was 0.746 (+- 0.014 std), compared to 0.739 (+- 0.028 std) for the
baseline. The paper demonstrated the importance of including uncertainty in
neural computing, especially for their prospective use.


  Matter-wave interferometry with nanoparticles will enable the development of
quantum sensors capable of probing ultraweak fields with unprecedented
applications for fundamental physics. The high sensitivity of such devices
however makes them susceptible to a number of noise and decoherence sources and
as such can only operate when sufficient isolation from the environment is
achieved. It is thus imperative to model and characterize the interaction of
nanoparticles with the environment and to estimate its deleterious effects. The
aim of this paper will be to study the decoherence of the matter-wave
interferometer due to dipole-dipole interactions which is one of the
unavoidable channels for decoherence even for a neutral micro-crystal. We will
start the analysis from QED and show that it reduces to the scattering model
characterized by the differential cross-section. We will then obtain simple
expressions for the decoherence rate in the short and long wavelength limits
that can be readily applied to estimate the available coherence time. We will
conclude by applying the obtained formulae to estimate the dipole-dipole
decoherence rate for the Quantum Gravity-induced Entanglement of Masses (QGEM)
protocol and discuss if the effects should be mitigated.


  The quality of non-default ranking on e-commerce platforms, such as based on
ascending item price or descending historical sales volume, often suffers from
acute relevance problems, since the irrelevant items are much easier to be
exposed at the top of the ranking results. In this work, we propose a two-stage
ranking scheme, which first recalls wide range of candidate items through
refined query/title keyword matching, and then classifies the recalled items
using BERT-Large fine-tuned on human label data. We also implemented parallel
prediction on multiple GPU hosts and a C++ tokenization custom op of
Tensorflow. In this data challenge, our model won the 1st place in the
supervised phase (based on overall F1 score) and 2nd place in the final phase
(based on average per query F1 score).


  We derive expressions for the leading-order far-field flows generated by
externally driven and active (swimming) colloids at planar fluid-fluid
interfaces. We consider colloids adjacent to the interface or adhered to the
interface with a pinned contact line. The Reynolds and capillary numbers are
assumed much less than unity, in line with typical micron-scale colloids
involving air- or alkane-aqueous interfaces. For driven colloids, the
leading-order flow is given by the point-force (and/or torque) response of this
system. For active colloids, the force-dipole (stresslet) response occurs at
leading order. At clean (surfactant-free) interfaces, these hydrodynamic modes
are essentially a restricted set of the usual Stokes multipoles in a bulk
fluid. To leading order, driven colloids exert Stokeslets parallel to the
interface, while active colloids drive differently oriented stresslets
depending on the colloid's orientation. We then consider how these modes are
altered by the presence of an incompressible interface, a typical circumstance
for colloidal systems at small capillary numbers in the presence of surfactant.
The leading-order modes for driven and active colloids are restructured
dramatically. For driven colloids, interfacial incompressibility substantially
weakens the far-field flow normal to the interface; the point-force response
drives flow only parallel to the interface. However, Marangoni stresses induce
a new dipolar mode, which lacks an analogue on a clean interface.
Surface-viscous stresses, if present, potentially generate very long-ranged
flow on the interface and the surrounding fluids. Our results have important
implications for colloid assembly and advective mass transport enhancement near
fluid boundaries.


  This paper presents a new topology for photonic crystals to replace the
monochromator, introducing them with a new alignment (the so-called extended
Trinitron) to guide the chromatic pattern producing a spatial distribution
similar to that of conventional diffraction gratings. The spectrophotometer
uses a LED white light as light source instead of chambers with halogen lamps
and mirrors. The system was designed using actual data from the manufacturer of
photonic crystals and the total system response is compared against that one of
a conventional spectrophotometer with a LED white light or tungsten bulb as a
light source. It is shown that the spectral responses are similar in photonic
panels containing more than twenty elements.


  A Mellin transform representation is derived for the associated Legendre
functions of the first kind on the cut


  We report an inter-comparison of some popular algorithms within the
artificial neural network domain (viz., Local search algorithms, global search
algorithms, higher order algorithms and the hybrid algorithms) by applying them
to the standard benchmarking problems like the IRIS data, XOR/N-Bit parity and
Two Spiral. Apart from giving a brief description of these algorithms, the
results obtained for the above benchmark problems are presented in the paper.
The results suggest that while Levenberg-Marquardt algorithm yields the lowest
RMS error for the N-bit Parity and the Two Spiral problems, Higher Order
Neurons algorithm gives the best results for the IRIS data problem. The best
results for the XOR problem are obtained with the Neuro Fuzzy algorithm. The
above algorithms were also applied for solving several regression problems such
as cos(x) and a few special functions like the Gamma function, the
complimentary Error function and the upper tail cumulative
$\chi^2$-distribution function. The results of these regression problems
indicate that, among all the ANN algorithms used in the present study,
Levenberg-Marquardt algorithm yields the best results. Keeping in view the
highly non-linear behaviour and the wide dynamic range of these functions, it
is suggested that these functions can be also considered as standard benchmark
problems for function approximation using artificial neural networks.