  We consider type IIA superstring theory on the background AdS4 x CP3, and the
classical solution describing a folded string spinning in AdS4 with angular
momentum in CP3. In the 't Hooft limit, it is the gravity dual of twist
operators in the ABJM superconformal theory. We quantize the classical solution
by algebraic curve methods and determine the first semiclassical correction to
the energy. We provide an integral representation for this quantity valid for
all values of the charges. We analyze its properties in the special regimes
associated with a short or long string providing various accurate analytical
expansions. Finally, we investigate various properties of the so-called slope,
the leading term of the energy for short strings, collecting information that
could be useful in attempts to generalize the exact results recently proposed
for the folded string in AdS5 x S5.


  The method of time delay interferometry (TDI) is proposed to cancel the laser
noise in space-borne gravitational-wave detectors. Among all different TDI
combinations, the most commonly used ones are the orthogonal channels A, E and
T, where A and E are signal-sensitive and T is signal-insensitive. Meanwhile,
for the detection of stochastic gravitational-wave background, one needs to
introduce the overlap reduction function to characterize the correlation
between channels. For the calculation of overlap reduction function, it is
often convenient to work in the low-frequency approximation, and assuming the
equal-arm Michelson channels. However, if one wishes to work on the overlap
reduction function of $\rm A/E$ channels, then the low-frequency approximation
fails. We derive the exact form of overlap reduction function for $\rm A/E$
channels. Based on the overlap reduction function, we calculate the sensitivity
curves of TianQin, TianQin I+II and TianQin + LISA. We conclude that the
detection sensitivity calculated with $\rm A/E$ channels is mostly consistent
with that obtained from the equal-arm Michelson channels.


  Block and G\"ottsche have defined a $q$-number refinement of counts of
tropical curves in $\mathbb{R}^2$. Under the change of variables $q=e^{iu}$, we
show that the result is a generating series of higher genus log Gromov-Witten
invariants with insertion of a lambda class. This gives a geometric
interpretation of the Block-G\"ottsche invariants and makes their deformation
invariance manifest.


  By analyzing the meson spectra obtained in the constituent quark model, we
find that the pseudoscalar mesons $\eta'(2^1S_0)$, $\eta(4^1S_0)$,
$\eta'(3^1S_0)$ and $\eta'(4^1S_0)$ are the possible candidates of
$\eta(1760)$, X(1835), X(2120) and X(2370). The strong decay widths of these
pseudoscalars to all the possible decay modes are calculated within the
framework of the $^3P_0$ model. Although the total width of $\eta'(2^1S_0)$ is
compatible with the experimental value of BES for $\eta(1760)$, the partial
decay width to $\omega\omega$ is too small, which is not consistent with the
result of BES. If the state X(1835) is interpreted as $\eta(4^1S_0)$, the total
decay width is compatible with the experimental data, and the main decay modes
will be $\pi a_0(980)$ and $\pi a_0(1450)$, which needs to be checked. The
assignment of X(2120) and X(2370) to $\eta'(3^1S_0)$ and $\eta'(4^1S_0)$ is
also disfavored in the present calculation because of the incompatibility of
the decay widths.


  In the construction of a cluster algebra on the homogeneous coordinate ring
of a partial flag variety by Gei{\ss}, Leclerc and Schr{\"{o}}er, they defined
a special map denoted by ``tilde". This map lifts each element $f$ of the
coordinate ring of a Schubert cell uniquely to an element $\widetilde{f}$ of
the (multi-homogeneous) coordinate ring of the corresponding partial flag
variety. The significance of this map appears from its essential role; it lifts
the cluster algebra of the coordinate ring of a cell to a cluster algebra
living in the coordinate ring of the corresponding partial flag variety. This
paper takes a closer look at this map and gives an explicit algorithm to
calculate it for the \textit{generalized minors}.


  We investigate a dense subgroup Gamma of the second Morava stabilizer group
given by a certain group of quasi-isogenies of a supersingular elliptic curve
in characteristic p. The group Gamma acts on the Bruhat-Tits building for
GL_2(Q_l) through its action on the l-adic Tate module. This action has finite
stabilizers, giving a small resolution for the homotopy fixed point spectrum
(E_2^hGamma)^hGal by spectra of topological modular forms. Here, E_2 is a
version of Morava E-theory and Gal = Gal(barF_p/F_p).


  Based on the Weierstrass representation of second variation we develop a
non-spectral theory of stability for isoperimetric problem with minimized and
constrained two-dimensional functionals of general type and free endpoints
allowed to move along two given planar curves. We apply this theory to the
axisymmetric pendular ring between two solid bodies without gravity to
determine the stability of menisci with free contact lines. For catenoid and
cylinder menisci and different solid shapes we determine the stability domain.
The other menisci (unduloid, nodoid and sphere) are considered in a simple
setup between two plates. We find the existence conditions of stable unduloid
menisci with and without inflection points.


  The vaccine adverse event reporting system (VAERS) is a vital resource for
post-licensure vaccine safety monitoring and has played a key role in assessing
the safety of COVID-19 vaccines. However it is difficult to properly identify
rare adverse events (AEs) associated with vaccines due to small or zero counts.
We propose a Bayesian model with a Dirichlet Process Mixture prior to improve
accuracy of the AE estimates with small counts by allowing data-guided
information sharing between AE estimates. We also propose a negative control
procedure embedded in our Bayesian model to mitigate the reporting bias due to
the heightened awareness of COVID-19 vaccines, and use it to identify
associated AEs as well as associated AE groups defined by the organ system in
the Medical Dictionary for Regulatory Activities (MedDRA) ontology. The
proposed model is evaluated using simulation studies, in which it outperforms
baseline models without information sharing and is applied to study the safety
of COVID-19 vaccines using VAERS data.


  High order actions proposed by Chin have been used for the first time in path
integral Monte Carlo simulations. Contrarily to the Takahashi-Imada action,
which is accurate to fourth order only for the trace, the Chin action is fully
fourth order, with the additional advantage that the leading fourth and sixth
order error coefficients are finely tunable. By optimizing two free parameters
entering in the new action we show that the time step error dependence achieved
is best fitted with a sixth order law. The computational effort per bead is
increased but the total number of beads is greatly reduced, and the efficiency
improvement with respect to the primitive approximation is approximately a
factor of ten. The Chin action is tested in a one-dimensional harmonic
oscillator, a H$_2$ drop, and bulk liquid $^4$He. In all cases a sixth-order
law is obtained with values of the number of beads that compare well with the
pair action approximation in the stringent test of superfluid $^4$He.


  We present a high-precision calculation of the recoil--finite-size correction
to the hyperfine splitting (HFS) in muonic and electronic hydrogen based on
nucleon electromagnetic form factors obtained from dispersion theory. This will
help guide the upcoming searches of the HFS transition in muonic hydrogen, and
will allow a precise determination of the polarizability and Zemach radius
contributions when this transition is found.


  Machine Learning (ML) models have been shown to potentially leak sensitive
information, thus raising privacy concerns in ML-driven applications. This
inspired recent research on removing the influence of specific data samples
from a trained ML model. Such efficient removal would enable ML to comply with
the "right to be forgotten" in many legislation, and could also address
performance bottlenecks from low-quality or poisonous samples. In that context,
machine unlearning methods have been proposed to erase the contributions of
designated data samples on models, as an alternative to the often impracticable
approach of retraining models from scratch. This article presents a
comprehensive review of recent machine unlearning techniques, verification
mechanisms, and potential attacks. We further highlight emerging challenges and
prospective research directions (e.g. resilience and fairness concerns). We aim
for this paper to provide valuable resources for integrating privacy, equity,
andresilience into ML systems and help them "learn to unlearn".


  Inspired by the remarkable ability of the infant visual learning system, a
recent study collected first-person images from children to analyze the
`training data' that they receive. We conduct a follow-up study that
investigates two additional directions. First, given that infants can quickly
learn to recognize a new object without much supervision (i.e. few-shot
learning), we limit the number of training images. Second, we investigate how
children control the supervision signals they receive during learning based on
hand manipulation of objects. Our experimental results suggest that supervision
with hand manipulation is better than without hands, and the trend is
consistent even when a small number of images is available.


  The behaviour of fermions in the background of a double-step potential is
analyzed with a general mixing of scalar and vector couplings via continuous
chiral-conjugation transformation. Provided the vector coupling does not exceed
the scalar coupling, a Sturm-Liouville approaching for the double-step
potential shows that the transmission coefficient exhibits oscillations and
that a finite set of intrinsically relativistic bound-state solutions might
appear as poles of the transmission amplitude in a strong coupling regime. An
isolated bound-state solution resulting from coupled first-order equations
might also come into sight. It is also shown that all those possible bound
solutions disappear asymptotically as one approaches the conditions for the
realization of the so-called spin and pseudospin symmetries in a
four-dimensional space-time. Furthermore, we show that due to the additional
mass acquired by the fermion from the scalar background the high localization
of the fermion in an extreme relativistic regime does not violate the
Heisenberg uncertainty principle.


  Recent experimental results on hadronic tau decays into strange particles by
the OPAL collaboration are employed to determine V_us and m_s from moments of
the invariant mass distribution. Our results are V_us = 0.2208+-0.0034 and
m_s(2 GeV) = 81+-22 MeV. The error on V_us is dominated by experiment, and
should be improvable in the future. Nevertheless, already now our result is
competitive to the standard extraction of V_us from K_e3 decays, and it is
compatible with unitarity.


  An extension of the Wigner-Araki-Yanase theorem to multiplicative conserved
quantities is presented and approximate versions of the theorem are discussed.


  In this work we investigate the network MIMO techniques of interference
alignment (IA) and fully adaptive joint transmission coordinated multipoint
(CoMP) in an indoor very small cell environment. Our focus is on the overheads
in a system with quantized channel state feedback from the receiver to the
transmitter (based on the 802.11ac standard) and on the impact of non-ideal
hardware. The indoor office scenario should be the most favourable case in
terms of the required feedback rates due to the large coherence bandwidth and
coherence time of the channel. The evaluations are done using a real-world
wireless testbed with three BSs and three MSs all having two antennas. The
signal to noise ratio in the measurements is very high, 35-60dB, due to the
short transmission range. Under such conditions radio hardware impairments
becomes a major limitation on the performance. We quantify the impact of these
impairments. For a 23ms update interval the overhead is 2.5% and IA and CoMP
improves the sum throughput 27% and 47% in average (over the reference schemes
e.g. TDMA MIMO), under stationary conditions. When two people are walking in
the measurement area the throughput improvements drops to 16% and 45%,
respectively.


  Analytical solution for a thin hydrodynamic accretion disk shows that for
some values of the viscosity parameter part of the accretion flow in the disk
is not towards the star, but in the opposite direction. We study thin disks by
performing hydrodynamic simulations and compare the numerical with analytical
results. We confirm that for viscosity coefficient smaller than a critical
value, there is a backflow in simulations near the disk mid-plane. The distance
from the star to the starting point of backflow is increasing with viscosity,
as predicted by the analytical solution. When the viscosity coefficient is
larger than critical, there is no backflow in the disk.


  Using well-known facts on Jacobi polynomials, we derive some asymptotic
estimates for the maximum absolute value of generalized Gegenbauer polynomials.


  If $U$ is a unitary operator on a separable complex Hilbert space
$\mathcal{H}$, an application of the spectral theorem says there is a
conjugation $C$ on $\mathcal{H}$ (an antilinear, involutive, isometry on
$\mathcal{H}$) for which $ C U C = U^{*}.$ In this paper, we fix a unitary
operator $U$ and describe all of the conjugations $C$ which satisfy this
property. As a consequence of our results, we show that a subspace is
hyperinvariant for $U$ if and only if it is invariant for any conjugation $C$
for which $CUC = U^{*}$.


  Using transition-metal dichalcogenides as an example, we show that the
quantum interference arising in two- and three-photon absorption processes can
lead to controllable, highly localized carrier distributions in the Brillouin
zone. We contrast this with the previously studied one- and two-photon
absorption, and find qualitatively different features, including changes in the
relevance of interband and intraband processes according to the excitation
energy. Thus, the distribution of excitations arising under certain
circumstances in two- and three-photon absorption can facilitate the study of
far-from-equilibrium states that are initially well localized in crystal
momentum space.


  Extrasolar terrestrial planets with the potential to host life might have
large obliquities or be subject to strong obliquity variations. We revisit the
habitability of oblique planets with an energy balance climate model (EBM)
allowing for dynamical transitions to ice-covered snowball states as a result
of ice-albedo feedback. Despite the great simplicity of our EBM, it captures
reasonably well the seasonal cycle of global energetic fluxes at Earth's
surface. It also performs satisfactorily against a full-physics climate model
of a highly oblique Earth-like planet, in an unusual regime of circulation
dominated by heat transport from the poles to the equator. Climates on oblique
terrestrial planets can violate global radiative balance through much of their
seasonal cycle, which limits the usefulness of simple radiative equilibrium
arguments. High obliquity planets have severe climates, with large amplitude
seasonal variations, but they are not necessarily more prone to global snowball
transitions than low obliquity planets. We find that terrestrial planets with
massive CO2 atmospheres, typically expected in the outer regions of habitable
zones, can also be subject to such dynamical snowball transitions. Some of the
snowball climates investigated for CO2-rich atmospheres experience partial
atmospheric collapse. Since long-term CO2 atmospheric build-up acts as a
climatic thermostat for habitable planets, partial CO2 collapse could limit the
habitability of such planets. A terrestrial planet's habitability may thus
depend sensitively on its short-term climatic stability.


  Using radial velocity measurements from four instruments, we report the mass
and density of a $2.043\pm0.069 ~\rm{R}_{\oplus}$ sub-Neptune orbiting the
quiet K-dwarf Wolf 503 (HIP 67285). In addition, we present improved orbital
and transit parameters by analyzing previously unused short-cadence $K2$
campaign 17 photometry and conduct a joint radial velocity-transit fit to
constrain the eccentricity at $0.41\pm0.05$. The addition of a transit
observation by $Spitzer$ also allows us to refine the orbital ephemeris in
anticipation of further follow-up. Our mass determination,
$6.26^{+0.69}_{-0.70}~\rm{M}_{\odot}$, in combination with the updated radius
measurements, gives Wolf 503 b a bulk density of $\rho = 2.92\pm
^{+0.50}_{-0.44}$ $\rm{g}~\rm{cm}^{-3}$. Using interior composition models, we
find this density is consistent with an Earth-like core with either a
substantial $\rm{H}_2\rm{O}$ mass fraction ($45^{+19.12}_{-16.15}\%$) or a
modest H/He envelope ($0.5\pm0.28\%$). The low H/He mass fraction, along with
the old age of Wolf 503 ($11\pm2$ Gyrs), makes this sub-Neptune an opportune
subject for testing theories of XUV-driven mass loss while the brightness of
its host ($J=8.3$ mag) makes it an attractive target for transmission
spectroscopy.


  One of the most important invariants in singularity theory is the Hodge
spectrum. Calculating the Hodge spectrum is a difficult task and formulas exist
for only a few cases. In this article the main result is the formula for
reduced hyperplane arrangements in four variables.


  The Caltech Submillimeter Observatory has detected triply deuterated ammonia,
ND3, through its 10a-00s transition near 310 GHz. Emission is found in the NGC
1333 region, both towards IRAS 4A and a position to the South-East where DCO+
peaks. In both cases, the hyperfine ratio indicates that the emission is
optically thin. Column densities of ND3 are 3--6 x 10^11 cm^-2 for T_ex=10 K
and twice as high for T_ex=5 K. Using a Monte Carlo radiative transfer code and
a model of the structure of the IRAS source with temperature and density
gradients, the estimated ND3 abundance is 3.2 x 10^-12 if ND3/H2 is constant
throughout the envelope. In the more likely case that ND3/H2D+ is constant,
ND3/H2 peaks in the cold outer parts of the source at a value of 1.0 x 10^-11.
To reproduce the observed NH3/ND3 abundance ratio of ~1000, grain surface
chemistry requires an atomic D/H ratio of ~0.15 in the gas phase, >10 times
higher than in recent chemical models. More likely, the deuteration of NH3
occurs by ion-molecule reactions in the gas phase, in which case the data
indicate that deuteron transfer reactions are much faster than proton
transfers.


  We construct a simple example, surely known to Harry Kesten, of an
R-transient Markov chain on a countable state space S with cemetery state
delta. The transition matrix K on S is irreducible and strictly substochastic.
We determine the Yaglom limit, that is, the limiting conditional behavior given
non-absorption. Each starting state x in S results in a different Yaglom limit.
Each Yaglom limit is an rho-invariant quasi-stationary distribution where
rho=1/R and R is the convergence parameter of $K$. Yaglom limits that depend on
the starting state are related to a nontrivial rho-Martin entrance boundary.


  In the quasistatic regime, generic modifications to gravity can give rise to
novel scale-dependence of the gravitational field equations. Crucially, the
detectability of the new scale-dependent terms hinges upon the existence of an
effective mass scale or length scale at which corrections to General Relativity
become relevant. Starting from only a few basic principles, we derive the
general form of this scale-dependence. Our method recovers results previously
known in the specific case of Horndeski gravity, but also shows that they are
valid more generally, beyond the regime of scalar field theories. We forecast
the constraints that upcoming experiments will place on the existence of a new
fundamental mass scale or length scale in cosmology.


  An outburst of the X-ray transient source XTE J1806--246 (2S1803--245) has
been observed by Rossi X-ray Timing Explorer in April-July 1998. Strong
quasi-periodical oscillations (QPO) with a central peak frequency around 9 Hz
was detected in one observation of the series performed by PCA/RXTE experiment.
X-ray flux from the source during the observation with QPO was maximal. The
energy spectrum of XTE J1806--246 at this time was softer than for other
observations. A sufficient variability of the QPO parameters has been detected,
in short-term correlation with the flux variability. Fractional amplitudes of
Very Low frequency Noise and QPO component of power density spectrum
demonstrate strong energy dependence, while other parameters do not change
significantly.


  Recent work has shown that pairwise interactions may not be sufficient to
fully model ecological dynamics in the wild. In this letter, we consider a
replicator dynamic that takes both pairwise and triadic interactions into
consideration using a rank-three tensor. We study {these} new nonlinear
dynamics using a generalized rock-paper-scissors game whose dynamics are well
understood in the {standard} replicator sense. We show that the addition of
higher-order dynamics leads to the creation of a subcritical Hopf bifurcation
and consequently an unstable limit cycle. It is known that this kind of
behaviour cannot occur in the pairwise replicator in any three strategy games,
showing the effect higher-order interactions can have on the resulting dynamics
of the system. We numerically characterize parameter regimes in which limit
cycles exist and discuss possible ways to generalize this approach to studying
higher-order interactions.


  We introduce and study the game of "Selfish Cops and Active Robber" (SCAR)
which can be seen as an multiplayer variant of the "classic" two-player Cops
and Robbers (CR) game. In classic CR all cops are controlled by a single
player, who has no preference over which cop captures the robber. In SCAR, on
the other hand, each of N-1 cops is controlled by a separate player, and a
single robber is controlled by the N-th player; and the capturing cop player
receives a higher reward than the non-capturing ones. Consequently, SCAR is an
N-player pursuit game on graphs, in which each cop player has an increased
motive to be the one who captures the robber. The focus of our study is the
existence and properties of SCAR Nash Equilibria (NE). In particular, we prove
that SCAR always has one NE in deterministic positional strategies and (for N
greater than two) another in deterministic nonpositional strategies.
Furthermore, we study conditions which, at equilibrium, guarantee either
capture or escape of the robber and show that (because of the antagonism
between the "selfish" cop players) the robber may, in certain SCAR
configurations, be captured later than he would be in classic CR, or even not
captured at all. Finally we define the selfish cop number of a graph and study
its connection to the classic cop number.


  We investigate the finite-temperature and -density chiral Gross-Neveu model
with an axial U$_A$(1) symmetry in $1+1$ dimensions on the lattice. In the
limit where the number of flavors $N_\mathrm{f}$ tends to infinity the
continuum model has been solved analytically and shows two phases: a symmetric
high-temperature phase with a vanishing condensate and a low-temperature phase
in which the complex condensate forms a chiral spiral which breaks translation
invariance. In the lattice simulations we employ chiral SLAC fermions with
exact axial symmetry. Similarly to $N_\mathrm{f}\to\infty$, we find for $8$
flavors, where quantum and thermal fluctuations are suppressed, two distinct
regimes in the $(T,\mu)$ phase diagram, characterized by qualitatively
different behavior of the two-point functions of the condensate fields. More
surprisingly, at $N_\mathrm{f}=2$, where fluctuations are no longer suppressed,
the model still behaves similarly to the $N_\mathrm{f}\to\infty$ model and we
conclude that the chiral spiral leaves its footprints even on systems with a
small number of flavors. For example, at low temperature the two-point
functions are still dominated by chiral spirals with pitches proportional to
the inverse chemical potential, although in contrast to large-$N_\mathrm{f}$
their amplitudes decrease with distance. We argue that these results should not
be interpreted as the spontaneous breaking of a continuous symmetry, which is
forbidden in two dimensions. Finally, using Dyson-Schwinger equations we
calculate the decay of the U$_A$(1)-invariant fermion four-point function in
search for a BKT phase at zero temperature.


  We construct gradient K\"ahler-Ricci solitons on Ricci-flat K\"ahler cone
manifolds and on line bundles over toric Fano manifolds. Certain shrinking and
expanding solitons are pasted together to form eternal solutions of the Ricci
flow. The method we employ is the Calabi ansatz over Sasaki-Einstein manifolds,
and the results generalize constructions of Cao and Feldman-Ilmanen-Knopf.


  It is an outstanding problem whether a pipe-flow system on a star-shaped
network is stabilisable by a feedback control on the common vertex. In the
present paper we deal with this problem. In particular, we study the equation
governing the small vibrations of a stretched elastic pipe conveying fluid in a
star-shaped network and examine the question of vertex feedback stabilisability
of such a system via control moments. Finding an answer to the question is not
straightforward, for the system operator associated with the corresponding
closed-loop system is unbounded and nonselfadjoint. An approach to the study of
the stabilisation problem for the closed-loop system is presented based on the
spectral approach previously introduced by the authors for star graphs of
stretched elastic beams. When the tension in the pipes is greater than the
square of the fluid-flow velocity, we establish a positive result that in fact
gives the strong property of uniform exponential stability of the closed-loop
system.


  The unity of mathematics has its power to compactify experiences in a form
capable of being transferred and modified or adapted to new mathematical
situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a
dream, an ideal that doesn't exist. We shall point to diachronic and cross
cultural disunities, to semantic, semiotic and philosophic ambiguities and to
the non-acceptance of certain mathematical texts by some practitioners of the
subject.


  The popular, stable, robust and computationally inexpensive cubic spline
interpolation algorithm is adopted and used for finite temperature Green's
function calculations of realistic systems. We demonstrate that with
appropriate modifications the temperature dependence can be preserved while the
Green's function grid size can be reduced by about two orders of magnitude by
replacing the standard Matsubara frequency grid with a sparser grid and a set
of interpolation coefficients. We benchmarked the accuracy of our algorithm as
a function of a single parameter sensitive to the shape of the Green's
function. Through numerous examples, we confirmed that our algorithm can be
utilized in a systematically improvable, controlled, and black-box manner and
highly accurate one- and two-body energies and one-particle density matrices
can be obtained using only around 5% of the original grid points. Additionally,
we established that to improve accuracy by an order of magnitude, the number of
grid points needs to be doubled, whereas for the Matsubara frequency grid an
order of magnitude more grid points must be used. This suggests that realistic
calculations with large basis sets that were previously out of reach because
they required enormous grid sizes may now become feasible.


  We calculate some ${\cal O}(\alpha_s^2)$ corrections to the JIMWLK kernel in
the framework of the light-cone wave function approach to the high energy limit
of QCD. The contributions that we consider originate from higher order
corrections in the strong coupling and in the density of the projectile to the
solution of the classical Yang-Mills equations of motion that determine the
Weizs\"acker-Williams fields of the projectile. We study the structure of these
corrections in the dipole limit, showing that they are subleading in the limit
of large number of colours $N$, and that they cannot be fully recast in the
form of dipole degrees of freedom.


  We study the linearized Bogoliubov excitation spectrum of infinitely long
anharmonically trapped Bose-Einstein condensates, with the aim of overcoming
inhomogeneous broadening. We compare the Bogoliubov spectrum of a harmonic trap
with that of a theoretical flat-bottom trap and find a dramatic reduction in
the inhomogeneous broadening of the lineshape of Bogoliubov excitations. While
the Bragg excitation spectrum for a condensate in a harmonic trap supports a
number of radial modes, the flat trap is found to significantly support just
one mode. We also study the excitation spectrum of realistic anharmonic traps
with potentials of finite power dependence on the radial coordinate. We observe
a correlation between the number of radial modes and the number of bound states
in the effective potential of the quasi-particles. Finally we compare a full
numerical Gross-Pitaevskii simulation of a finite-length condensate to our
model of infinite, linearized Gross-Pitaevskii excitations. We conclude that
our model captures the essential physics.


  The theory of quantum jump trajectories provides a new framework for
understanding dynamical phase transitions in open systems. A candidate for such
transitions is the atom maser, which for certain parameters exhibits strong
intermittency in the atom detection counts, and has a bistable stationary
state. Although previous numerical results suggested that the "free energy" may
not be a smooth function, we show that the atom detection counts satisfy a
large deviations principle, and therefore we deal with a phase cross-over
rather than a genuine phase transition. We argue however that the latter occurs
in the limit of infinite pumping rate. As a corollary, we obtain the Central
Limit Theorem for the counting process.
  The proof relies on the analysis of a certain deformed generator whose
spectral bound is the limiting cumulant generating function. The latter is
shown to be smooth, so that a large deviations principle holds by the
Gartner-Ellis Theorem. One of the main ingredients is the Krein-Rutman theory
which extends the Perron-Frobenius theorem to a general class of positive
compact semigroups.


  The lasso has been studied extensively as a tool for estimating the
coefficient vector in the high-dimensional linear model; however, considerably
less is known about estimating the error variance in this context. In this
paper, we propose the natural lasso estimator for the error variance, which
maximizes a penalized likelihood objective. A key aspect of the natural lasso
is that the likelihood is expressed in terms of the natural parameterization of
the multiparameter exponential family of a Gaussian with unknown mean and
variance. The result is a remarkably simple estimator of the error variance
with provably good performance in terms of mean squared error. These
theoretical results do not require placing any assumptions on the design matrix
or the true regression coefficients. We also propose a companion estimator,
called the organic lasso, which theoretically does not require tuning of the
regularization parameter. Both estimators do well empirically compared to
preexisting methods, especially in settings where successful recovery of the
true support of the coefficient vector is hard. Finally, we show that existing
methods can do well under fewer assumptions than previously known, thus
providing a fuller story about the problem of estimating the error variance in
high-dimensional linear models.


  It is known that if a nonlinear control affine system without drift is
bracket generating, then its associated sub-Laplacian is invertible under some
conditions on the domain. In this note, we investigate the converse. We show
how invertibility of the sub-Laplacian operator implies a weaker form of
controllability, where the reachable sets of a neighborhood of a point have
full measure. From a computational point of view, one can then use the spectral
gap of the (infinite-dimensional) self-adjoint operator to define a notion of
degree of controllability.
  An essential tool to establish the converse result is to use the relation
between invertibility of the sub-Laplacian to the the controllability of the
corresponding continuity equation using possibly non-smooth controls. Then
using Ambrosio-Gigli-Savare's superposition principle from optimal transport
theory we relate it to controllability properties of the control system. While
the proof can be considered of the Perron-Frobenius type, we also provide a
second dual Koopman point of view.


  Research on innovation and sustainability is prolific but fragmented. This
study integrates the research on innovation in management and business and STEM
fields for sustainability in a unified framework for the case of developing
countries (i.e., the Global South). It presents and discusses the output,
impact, and structure of such research based on a sample of 14,000+ articles
and conference proceedings extracted from the bibliographic database Scopus.
The findings reveal research output inflections after global announcements such
as UN-Earth Summits. The study also reveals the indisputable leadership of
China in overall output and research agenda-setting. Nonetheless, countries
such as India, Mexico, and Nigeria are either more efficient or impactful. GS
research published in highly reputable journals is still scarce but increasing
modestly. Central topic clusters (e.g., knowledge management) remain peripheral
to the global Sustainable Development Goals (SDGs) research landscape. Finally,
academic-corporate collaboration is in its infancy and limited to particular
economic sectors: energy, pharmaceuticals, and high-tech.


  Both null and timelike rays experience trajectory bending in a gravitational
field. In this work, we systematically develop a perturbative method to compute
the deflection angle of rays with general velocity $v$ in arbitrary static and
spherically symmetric spacetimes and in equatorial plane of arbitrary static
and axisymmetric spacetimes. We show that the expansion in the large closest
approach $x_0$ limit depends on the asymptotic behavior of the metric functions
only, and the generated integrand is always integrable, resulting in a
deflection angle in a series form of either $x_0$ or $b$, the impact parameter.
Using this method, the deflection angles as series of both $x_0$ and $b$ are
found in Schwarzschild, Reissner-Nordstr\"{o}m and Kerr-Newman spacetimes to
17-th, 15-th and 6-th orders respectively, for both lightrays and particles
with general velocity. The effects of the impact parameter, velocity and other
parameters of the spacatimes are briefly analyzed. Moreover, we show that for
spacetimes whose metric functions are only asymptotically known, the deflection
angle in the weak field limit can also be calculated. Furthermore, it is shown
that the deflection angle in general static and spherically symmetric spacetime
and equatorial plane of static and axisymmetric spacetime to the lowest
non-trivial order, depends only on the impact parameter, velocity of the
particle, and the effective ADM mass of the spacetime but not on other
parameters such as charge or angular momentum. These deflection angles are used
in an exact gravitational lensing equation and the corresponding apparent
angles of the images of the source are also solved perturbatively.


  The properties of a dilute Ising magnet are studied using a two-dimensional
spin-pseudospin model with charged impurities and a frustration caused by the
competition of the charge and magnetic orderings. Based on the classical Monte
Carlo method, the ground state phase diagram has been obtained and also unusual
phase states appeared at finite temperatures have been studied. The regions in
which order-order phase transitions and also reentrant phase transition are
observed have been found.


  This paper optimizes motion planning when there is a known risk that the road
choice suggested by a Satnav (GPS) is not on a shortest path. At every branch
node of a network Q, a Satnav (GPS) points to the arc leading to the
destination, or home node, H - but only with a high known probability p. Always
trusting the Satnav's suggestion may lead to an infinite cycle. If one wishes
to reach H in least expected time, with what probability q=q(Q,p) should one
trust the pointer (if not, one chooses randomly among the other arcs)? We call
this the Faulty Satnav (GPS) Problem. We also consider versions where the trust
probability q can depend on the degree of the current node and a `treasure
hunt' where two searchers try to reach H first. The agent searching for H need
not be a car, that is just a familiar example -- it could equally be a UAV
receiving unreliable GPS information. This problem has its origin not in driver
frustration but in the work of Fonio et al (2017) on ant navigation, where the
pointers correspond to pheromone markers pointing to the nest. Neither the
driver or ant will know the exact process by which a choice (arc) is suggested,
which puts the problem into the domain of how much to trust an option suggested
by AI.


  The magic nature of the $^{54}$Ca nucleus is investigated in the light of the
recent experimental results. We employ both HFB and HF+BCS methods using
Skyrme-type SLy5, SLy5+T and T44 interactions. The evolution of the
single-particle spectra is studied for the N=34 isotones: $^{60}$Fe, $^{58}$Cr,
$^{56}$Ti and $^{54}$Ca. An increase is obtained in the neutron spin-orbit
splittings of $p$ and $f$ states due to the effect of the tensor force which
also makes $^{54}$Ca a magic nucleus candidate. QRPA calculations on top of
HF+BCS are performed to investigate the first $J^{\pi}$=$2^{+}$ states of the
calcium isotopic chain. A good agreement for excitation energies is obtained
when we include the tensor force in the mean-field part of the calculations.
The first $2^{+}$ states indicate a subshell closure for both $^{52}$Ca and
$^{54}$Ca nuclei. We confirm that the tensor part of the interaction is quite
essential in explaining the neutron subshell closure in $^{52}$Ca and $^{54}$Ca
nuclei.


  Fermionic functional renormalization group (FRG) is applied to describe the
superfluid phase transition of the two-component fermionic system with
attractive contact interaction. Connection between the fermionic FRG approach
and the Bardeen-Cooper-Schrieffer (BCS) theory with its Gorkov and
Melik-Barkhudarov (GMB) correction is made clear, and the FRG flow of the
fermion self-energy is also studied to go beyond the BCS+GMB theory. The
superfluid transition temperature and the associated chemical potential are
calculated in the region of the negative scattering length using fermionic FRG.


  In this paper, we present an algorithm for optimizing synchronizability of
complex dynamical networks. Based on some network properties, rewirings, i.e.
eliminating an edge and creating a new edge elsewhere, are performed
iteratively avoiding always self-loops and multiple edges between the same
nodes. We show that the method is able to enhance the synchronizability of
networks of any size and topological properties in a small number of steps that
scales with the network size.Although we take the eigenratio of the Laplacian
as the target function for optimization, we will show that it is also possible
to choose other appropriate target functions exhibiting almost the same
performance. The optimized networks are Ramanujan graphs, and thus, this
rewiring algorithm could be used to produce Ramanujan graphs of any size and
average degree.


  Using Blackwell's definition of comparing two experiments, a comparison is
made with \textit{generalized AG - divergence} measure having one and two
scalar parameters. Connection of \textit{generalized AG - divergence} measure
with \textit{Fisher measure of information} is also presented. A unified
\textit{generalization of AG - divergence}and\textit{Jensen-Shannon divergence
measures} is also presented.


  There are many programming languages in the world today.Each language has
their advantage and disavantage. In this paper, we will discuss ten programming
languages: C++, C#, Java, Groovy, JavaScript, PHP, Schalar, Scheme, Haskell and
AspectJ. We summarize and compare these ten languages on ten different
criterion. For example, Default more secure programming practices, Web
applications development, OO-based abstraction and etc. At the end, we will
give our conclusion that which languages are suitable and which are not for
using in some cases. We will also provide evidence and our analysis on why some
language are better than other or have advantages over the other on some
criterion.


  We construct an equivalence of $E_{2}$ algebras between two models for the
Thom spectrum of the free loop space that are related by derived Koszul
duality. To do this, we describe the functoriality and invariance properties of
topological Hochschild cohomology.


  In this work, we develop a mathematical framework to model a quantum system
whose Hamiltonian may depend on the state of changing environment, that evolves
according to a Markovian process. When the environment changes its state, the
quantum system may suffer a shock that produces an instantaneous transition
among its states. The model that we propose can be readily adapted to more
general settings.\\ To avoid collateral analytical issues, we consider the case
of quantum systems with finite dimensional state space, in which case the
observables are described by Hermitian matrices. We show how to average over
the environment to predict the expected values of observables.


  Einstein's theory of General Relativity is the benchmark example for
empirical success and mathematical elegance in theoretical physics. However, in
spite of being the most successfully tested theory in physics, there are strong
theoretical and observational arguments for why General Relativity should fail.
It is not a question of if, but rather a question of where and when! I start by
recounting the tremendous success in observational cosmology over the past
three decades, that has led to the era of precision cosmology. I will then
summarize the pathologies in Einstein's theory of gravity, as the cornerstone
of standard cosmological model. Attempts to address these pathologies are
either inspired by mathematical elegance, or empirical falsifiability. Here, I
provide different arguments for why a falsifiable solution should violate
Lorentz symmetry, or revive "gravitational aether". Deviations from Einstein's
gravity are then expected in: 1) cosmological matter-radiation transition, 2)
neutron stars, 3) gravitomagnetic effect, 4) astrophysical black holes, and
their potential connection to dark energy, and 5) early Universe, where the
predictions are ranked by their degree of robustness and falsifiability.


  A keyframe summary, or "static storyboard", is a collection of frames from a
video designed to summarise its semantic content. Many algorithms have been
proposed to extract such summaries automatically. How best to evaluate these
outputs is an important but little-discussed question. We review the current
methods for matching frames between two summaries in the formalism of graph
theory. Our analysis revealed different behaviours of these methods, which we
illustrate with a number of case studies. Based on the results, we recommend a
greedy matching algorithm due to Kannappan et al.


  An equation of motion for relativistic compact binaries is derived through
the third post-Newtonian (3 PN) approximation of general relativity. The strong
field point particle limit and multipole expansion of the stars are used to
solve iteratively the harmonically relaxed Einstein equations. We take into
account the Lorentz contraction on the multipole moments defined in our
previous works. We then derive a 3 PN acceleration of the binary orbital motion
of the two spherical compact stars based on a surface integral approach which
is a direct consequence of local energy momentum conservation. Our resulting
equation of motion admits a conserved energy (neglecting the 2.5 PN radiation
reaction effect), is Lorentz invariant and is unambiguous: there exist no
undetermined parameter reported in the previous works. We shall show that our 3
PN equation of motion agrees physically with the Blanchet and Faye 3 PN
equation of motion if $\lambda = - 1987/3080$, where $\lambda$ is the parameter
which is undetermined within their framework. This value of $\lambda$ is
consistent with the result of Damour, Jaranowski, and Sch\"afer who first
completed a 3 PN iteration of the ADM Hamiltonian in the ADMTT gauge using the
dimensional regularization.


  Lavrik and the author gave uniform bounds of the error term in the
approximate functional equation for the derivatives of the Hardy's Z-function.
We obtain a new bound of this error term which is much better for high order
derivatives.


  Despite significant progress, controlled generation of complex images with
interacting people remains difficult. Existing layout generation methods fall
short of synthesizing realistic person instances; while pose-guided generation
approaches focus on a single person and assume simple or known backgrounds. To
tackle these limitations, we propose a new problem, \textbf{Persons in Context
Synthesis}, which aims to synthesize diverse person instance(s) in consistent
contexts, with user control over both. The context is specified by the bounding
box object layout which lacks shape information, while pose of the person(s) by
keypoints which are sparsely annotated. To handle the stark difference in input
structures, we proposed two separate neural branches to attentively composite
the respective (context/person) inputs into shared ``compositional structural
space'', which encodes shape, location and appearance information for both
context and person structures in a disentangled manner. This structural space
is then decoded to the image space using multi-level feature modulation
strategy, and learned in a self supervised manner from image collections and
their corresponding inputs. Extensive experiments on two large-scale datasets
(COCO-Stuff \cite{caesar2018cvpr} and Visual Genome \cite{krishna2017visual})
demonstrate that our framework outperforms state-of-the-art methods w.r.t.
synthesis quality.


  The Carminati and McLenaghan (CM) curvature invariants are powerful tools for
probing spacetimes. Henry et al. formulated a method of plotting the CM
curvature invariants to study black holes. The CM curvature invariants are
scalar functions of the underlying spacetime. Consequently, they are
independent of the chosen coordinates and characterize the spacetime. For Class
B1 spacetimes, there are four independent CM curvature invariants: R, r1, r2,
and w2. Lorentzian traversable wormholes and warp drives are two theoretical
solutions to Einstein's field equations, which allow faster-than-light (FTL)
transport. The CM curvature invariants are plotted and analyzed for these
specific FTL spacetimes: (i) the Thin-Shell Flat-Face wormhole, (ii) the
Morris-Thorne wormhole, (iii) the Thin-Shell Schwarzschild wormhole, (iv) the
exponential metric, (v) the Alcubierre metric at constant velocity, (vi) the
Nat\'ario metric at constant velocity, and (vii) the Nat\'ario metric at an
accelerating velocity. Plots of the wormhole CM invariants confirm their
traversability and show how to distinguish the wormholes. The warp drive CM
invariants reveal key features such as a flat harbor in the center of each warp
bubble, a dynamic wake for each warp bubble, and rich internal structure(s) of
each warp bubble.


  Basaltic V-type asteroids are leftovers from the formation and evolution of
differentiated planetesimals. They are thought to originate from mantles and
crusts of multiple different parent bodies. Identifying the links between
individual V-type asteroids and multiple planetesimals is challenging,
especially in the inner part of the main asteroid belt, where the majority of
V-type asteroids are expected to have originated from a single planetesimal,
namely, (4) Vesta.
  In this work, we aim to trace the origin of a number of individual V-type
asteroids from the inner part of the main asteroid belt. The main goal is to
identify asteroids that may not be traced back to (4) Vesta and may therefore
originate from other differentiated planetesimals.
  We performed a 2 Gy backward numerical integration of the orbits of the
selected V-type asteroids. For each asteroid, we used 1001 clones to map the
effect of orbital uncertainties. In the integration, we use information on
physical properties of the considered V-type asteroids such as pole
orientation, rotational period, and thermal parameters.
  The majority of V-types in the inner main belt outside the Vesta family are
clearly Vesta fugitives. Two objects, namely, (3307) Athabasca and (17028) 1999
FJ$_{5}$, show no clear dynamical link to (4) Vesta. Together with (809) Lundia
(from our previous work), these objects could represent the parent bodies of
anomalous HED meteorites such as the Banbura Rockhole. Furthermore, some
objects of the low-inclination population cannot be traced back to (4) Vesta
within the 2 Gy integration.


  In this paper, an interference cancellation based neural receiver for
superimposed pilot (SIP) in multi-layer transmission is proposed, where the
data and pilot are non-orthogonally superimposed in the same time-frequency
resource. Specifically, to deal with the intra-layer and inter-layer
interference of SIP under multi-layer transmission, the interference
cancellation with superimposed symbol aided channel estimation is leveraged in
the neural receiver, accompanied by the pre-design of pilot code-division
orthogonal mechanism at transmitter. In addition, to address the complexity
issue for inter-vendor collaboration and the generalization problem in
practical deployments, respectively, this paper also provides a fixed SIP
(F-SIP) design based on constant pilot power ratio and scalable mechanisms for
different modulation and coding schemes (MCSs) and transmission layers.
Simulation results demonstrate the superiority of the proposed schemes on the
performance of block error rate and throughput compared with existing
counterparts.


  A new determination of the orbit of the Hyades double-lined spectroscopic
binary HD 27149 is presented. The well-defined orbit provides the spectroscopic
basis for an extremely accurate orbital parallax for the system -- in
particular, the size of the relative orbit ($a\sin i = (a_1 + a_2)\sin i =
(67.075 \pm 0.045) \times 10^6$ km) is accurate to $\pm 0.07$ %. The minimum
masses for the primary and secondary -- $m_1\sin ^3i = 1.096 \pm 0.002 M_\odot$
and $m_2\sin ^3i = 1.010 \pm 0.002 M_\odot$ -- are unexpectedly large for the
spectral types thus suggesting the possibility of eclipses. Although the
probability of eclipses is not large, the system being composed of G3V and G6V
stars in a 75-day orbit, the possibility is of great interest. A rediscussion
of a search for eclipses made by J{\o}rgensen & Olsen$^1$ in 1972 shows that
central eclipses can be excluded, but that shorter duration off-centre eclipses
cannot be ruled out. Ephemerides for possible primary and secondary eclipses
are given.


  We review the results on the cycle classes of the strata defined by the
height and the Artin invariant on the moduli of K3 surfaces in positive
characteristic obtained in joint work with Katsura and Ekedahl. In addition we
prove a new irreducibility result for these strata.


  The Tully-Fisher relation (TFR) expresses the connection between rotating
galaxies and the dark matter haloes they inhabit, and therefore contains a
wealth of information about galaxy formation. We construct a general framework
to investigate whether models based on halo abundance matching are able to
reproduce the observed stellar mass TFR and mass-size relation (MSR), and use
the data to constrain galaxy formation parameters. Our model tests a range of
plausible scenarios, differing in the response of haloes to disc formation, the
relative angular momentum of baryons and dark matter, the impact of selection
effects, and the abundance matching parameters. We show that agreement with the
observed TFR puts an upper limit on the scatter between galaxy and halo
properties, requires weak or reversed halo contraction, and favours selection
effects that preferentially eliminate fast-rotating galaxies. The MSR
constrains the ratio of the disc to halo specific angular momentum to be
approximately in the range 0.6-1.2. We identify and quantify two problems that
models of this nature face. (1) They predict too large an intrinsic scatter for
the MSR, and (2) they predict too strong an anticorrelation between the TFR and
MSR residuals. We argue that resolving these problems requires introducing a
correlation between stellar surface density and enclosed dark matter mass.
Finally, we explore the expected difference between the TFRs of central and
satellite galaxies, finding that in the favoured models this difference should
be detectable in a sample of ~700 galaxies.


  For I a proper, countably complete ideal on P(X) for some set X, can the
quotient Boolean algebra P(X)/I be complete? This question was raised by
Sikorski in 1949. By a simple projection argument as for measurable cardinals,
it can be assumed that X is an uncountable cardinal kappa, and that I is a
kappa-complete ideal on P(kappa) containing all singletons. In this paper we
provide consequences from and consistency results about completeness.


  Highly energetic particles in the medium of a quark gluon plasma undergo
processes of coherent medium induced radiation and scatterings off medium
particles. We solved the evolution equations for particle fragmentation
functions that describe in-medium evolution via these two in-medium processes
numerically via Monte-Carlo algorithms. We study the in-medium broadening of
the distribution over momentum components transverse to the jet-axis for
different cases of jet-medium interactions and different values of average
transverse momentum transfer.


  We demonstrate background-free quantum frequency conversion of single photons
from an epitaxially-grown InAs quantum dot. Single photons at \approx 980 nm
are combined with a pump laser near 1550 nm inside a periodically-poled lithium
niobate (PPLN) waveguide, generating single photons at \approx 600 nm. The
large red-detuning between the pump and signal wavelengths ensures nearly
background-free conversion, avoiding processes such as upconversion of
anti-Stokes Raman scattered pump photons in the PPLN crystal. Second-order
correlation measurements on the single photon stream are performed both before
and after conversion, confirming the preservation of photon statistics during
the frequency conversion process.


  We investigate the emergence of isotropic linear elasticity in amorphous and
polycrystalline solids, via extensive numerical simulations. We show that the
elastic properties are correlated over a finite length scale $\xi_E$, so that
the central limit theorem dictates the emergence of continuum linear isotropic
elasticity on increasing the specimen size. The stiffness matrix of systems of
finite size $L > \xi_E$ is obtained adding to that predicted by linear
isotropic elasticity a random one of spectral norm $(L/\xi_E)^{-3/2}$, in three
spatial dimensions. We further demonstrate that the elastic length scale
corresponds to that of structural correlations, which in polycrystals reflect
the typical size of the grain boundaries and length scales characterizing
correlations in the stress field. We finally demonstrate that the elastic
length scale affects the decay of the anisotropic long-ranged correlations of
locally defined shear modulus and shear stress.


  Transitional disks, protoplanetary disks with deep and wide central gaps, may
be the result of planetary sculpting. By comparing numerical planet-opening-gap
models with observed gaps, we find systems of 3-6 giant planets are needed in
order to open gaps with the observed depths and widths. We explore the
dynamical stability of such multi-planet systems using N-body simulations that
incorporate prescriptions for gas effects. We find they can be stable over a
typical disk lifetime, with the help of eccentricity damping from the residual
gap gas that facilitates planets locking into mean motion resonances. However,
in order to account for the occurrence rate of transitional disks, the planet
sculpting scenario demands gap-opening-friendly disk conditions, in particular,
a disk viscosity $\alpha\lesssim0.001$. In addition, the demography of giant
planets at $\sim 3-30$ AU separations, poorly constrained by current data, has
to largely follow occurrence rates extrapolated outward from radial velocity
surveys, not the lower occurrence rates extrapolated inward from direct imaging
surveys. Even with the most optimistic occurrence rates, transitional disks
cannot be a common phase that most gas disks experience at the end of their
life, as popularly assumed, simply because there are not enough planets to open
these gaps. Finally, as consequences of demanding almost all giant planets at
large separations participate in transitional disk sculpting, the majority of
such planets must form early and end up in a chain of mean motion resonances at
the end of disk lifetime.


  Complex assemblies of light-emitting polymer nanofibers with molecular
materials exhibiting optical gain can lead to important advance to amorphous
photonics and to random laser science and devices. In disordered mats of
nanofibers, multiple scattering and waveguiding might interplay to determine
localization or spreading of optical modes as well as correlation effects. Here
we study electrospun fibers embedding a lasing fluorene-carbazole-fluorene
molecule and doped with titania nanoparticles, which exhibit random lasing with
sub-nm spectral width and threshold of about 9 mJ cm^-2 for the absorbed
excitation fluence. We focus on the spatial and spectral behavior of optical
modes in the disordered and non-woven networks, finding evidence for the
presence of modes with very large spatial extent, up to the 100
micrometer-scale. These findings suggest emission coupling into integrated
nanofiber transmission channels as effective mechanism for enhancing spectral
selectivity in random lasers and correlations of light modes in the complex and
disordered material.


  This paper considers linear panel data models where the dependence of the
regressors and the unobservables is modelled through a factor structure. The
asymptotic setting is such that the number of time periods and the sample size
both go to infinity. Non-strong factors are allowed and the number of factors
can grow to infinity with the sample size. We study a class of two-step
estimators of the regression coefficients. In the first step, factors and
factor loadings are estimated. Then, the second step corresponds to the panel
regression of the outcome on the regressors and the estimates of the factors
and the factor loadings from the first step. Different methods can be used in
the first step while the second step is unique. We derive sufficient conditions
on the first-step estimator and the data generating process under which the
two-step estimator is asymptotically normal. Assumptions under which using an
approach based on principal components analysis in the first step yields an
asymptotically normal estimator are also given. The two-step procedure exhibits
good finite sample properties in simulations.


  Using Lefschetz numbers of certain involutions, we provide lower bounds for
the cuspidal cohomology of principal congruence subgroups of Bianchi groups.
The asymptotic lower bounds that follow from our results complement recent
results of Calegari-Emerton, Marshall and Finis-Grunewald-Tirao. Moreover, we
discuss the relationship between these involutions and the base change classes
in the cohomology.


  Construction of future electron-positron colliders (or dedicated electron
linac) and muon colliders close to Future Circular Collider will give
opportunity to utilize highest energy proton and nucleus beams for
lepton-hadron and photon-hadron collisions. In this paper we estimate main
parameters of the FCC based ep and \mu p colliders.


  A classification technique for identifying focal mechanism type and fault
plane orientation based on the polarity of P-wave "first motion" data is
derived. A support vector machine is used to classify the polarity data in the
space of spherical harmonic functions. The classification is non-parametric in
the sense that there is no requirement to make a priori assumptions source
mechanism. A metric of similarity potentially able to distinguish shear versus
tensile dislocation without requiring estimation of the fault plane orientation
is a natural consequence of this procedure. Going further, correlation
functions between template source mechanism is derived, gives an estimate of
fault plane orientation assuming a particular source mechanism.


  Recently, the use of millimeter wave (mmW) frequencies has emerged as a
promising solution for wirelessly connecting unmanned aerial vehicles (UAVs) to
ground users. However, employing UAVassisted directional mmW links is
challenging due to the random fluctuations of hovering UAVs. In this paper, the
performance of UAV-based mmW links is investigated when UAVs are equipped with
square array antennas. The 3GPP antenna propagation patterns are used to model
the square array antenna. It is shown that the square array antenna is
sensitive to both horizontal and vertical angular vibrations of UAVs. In order
to explore the relationship between the vibrations of UAVs and their antenna
pattern, the UAV-based mmW channels are characterized by considering the large
scale path loss, small scale fading along with antenna patterns as well as the
random effect of UAVs' angular vibrations. To enable effective performance
analysis, tractable and closed-form statistical channel models are derived for
aerial-to-aerial (A2A), ground-to-aerial (G2A), and aerial-to-ground (A2G)
channels. The accuracy of analytical models is verified by employing Monte
Carlo simulations. Analytical results are then used to study the effect of
antenna pattern gain under different conditions for the UAVs' angular
vibrations for establishing reliable UAV-assisted mmW links in terms of
achieving minimum outage probability.


  Using techniques from integrable systems, we obtain a number of exact results
for random partitions. In particular, we prove a simple formula for correlation
functions of what we call the Schur measure on partitions (which is a far
reaching generalization of the Plancherel measure, see math.CO/9905032) and
also show that these correlations functions are tau-functions for the Toda
lattice hierarchy. Also we give a new proof of the formula due to Bloch and the
author, see alg-geom/9712009, for the so called n-point functions of the
uniform measure on partitions and comment on the local structure of a typical
partition.


  Based on dynamical cluster approximation (DCA) quantum Monte Carlo
simulations, we study the interaction-driven Mott metal-insulator transition
(MIT) in the half-filled Hubbard model on the anisotropic two-dimensional
triangular lattice, where the degree of frustration is varied between the
unfrustrated case and the fully frustrated, isotropic triangular lattice. Upon
increasing the DCA cluster size, we analyze the evolution of the MIT phase
boundary as a function of frustration in the phase diagram spanned by the
interaction strength and temperature, and provide a quantitative description of
the MIT phase boundary in the triangular lattice Hubbard model. Qualitative
differences in the phase boundary between the unfrustrated and fully frustrated
cases are exhibited. In particular, a change in the sign of the phase boundary
slope is observed, which via an impurity cluster eigenstate analysis, may be
related to a change in the nature of the insulating state. We discuss our
findings within the scenario that the triangular lattice electron system might
exhibit a quantum critical Mott MIT with a possible quantum spin liquid
insulating state, such as considered for the organic charge transfer salts
$\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$ and
EtMe$_{3}$Sb[Pd(dmit)$_{2}$]$_{2}$.


  The Rasnik 3-point alignment system, now widely applied in particle physics
experiments and in the instrumentation of gravitational wave experiments, can
be used as N-point alignment system by daisy chain N individual 3-point
systems. The conceptual implementation of Rasnik chains in C3 is presented. The
proper operation of a laser diode and a CMOS image sensor in liquid nitrogen
has been verified. Next plans for testing a small but complete system, immersed
in liquid nitrogen, are presented.


  Recent work has identified that the primary differences between quenched and
dynamical spectroscopy can be described by chiral loop effects. Here we
highlight the features of this study.


  We consider here a particular quadratic equation linking two elements of a
C-Algebra. By analysing powers of the unknowns, it appears a double sequence of
polynomials related to classical Bernoulli polynomials. We get the generating
functions, integral forms and explicit formulas for the coefficients involving
cosecant and tangent numbers. We also study the use of these polynomials for
the calculation of some integral transforms.


  We investigate the prospects of searching dark sector models via exotic
Z-boson decay at future $e^+ e^-$ colliders with Giga Z and Tera Z options.
Four general categories of dark sector models: Higgs portal dark matter, vector
portal dark matter, inelastic dark matter and axion-like particles, are
considered. Focusing on channels motivated by the dark sector models, we carry
out a model independent study of the sensitivities of Z-factories in probing
exotic decays. The limits on branching ratios of the exotic Z decay are
typically $\mathcal{O} (10^{-6} - 10^{-8.5}) $ for the Giga Z and $\mathcal{O}
(10^{-7.5} - 10^{-11})$ for the Tera Z, and they are compared with the
projection for the high luminosity LHC. We demonstrate that future Z-factories
can provide its unique and leading sensitivity, and highlight the
complementarity with other experiments, including the indirect and direct dark
matter search limits, and the existing collider limits. Future Z factories will
play a leading role to uncover the hidden sector of the universe in the future.


  Described in this paper is a new method for determining the non-diffractive
part of the inelastic proton-proton cross section, at the LHC centre of mass
energy of 14TeV. The method is based on counting the number of inelastic
proton-proton interactions in the collision regions. According to preliminary
investigation, this measurement will be best suited for the initial low
luminosity phase of the LHC. The dominant uncertainty on this measurement comes
from knowledge of the proton-proton luminosity.


  We analyze an optimal control problem for systems of integral equations of
Volterra type with two independent variables. These systems generalize both,
the hyperbolic control problems for systems of Goursat-Darboux type, and the
optimal control of ordinary (i.e. with one independent variable) Volterra
integral equations. We prove extremal principles akin to Pontryagin's maximum
principle.


  We derive valuations of a portfolio of financial instruments from a
securities lending perspective, under different assumptions, and show a
weighting scheme that converges to the true valuation. We illustrate conditions
under which our alternative weighting scheme converges faster to the true
valuation when compared to the minimum variance weighting. This weighting
scheme is applicable in any situation where multiple forecasts are made and we
need a methodology to combine them. Our valuations can be useful either to
derive a bidding strategy for an exclusive auction or to design an appropriate
auction mechanism, depending on which side of the fence a participant sits
(whether the interest is to procure the rights to use a portfolio for making
stock loans such as for a lending desk, or, to obtain additional revenue from a
portfolio such as from the point of view of a long only asset management firm).
Lastly, we run simulations to establish numerical examples for the set of
valuations and for various bidding strategies corresponding to different
auction settings.


  The problem of harmonics generation in nanotargets is considered at the range
of parameters (a nanotarget diameter and a pump laser intensity) when the
oscillation amplitude of an electron in a target is much larger than the target
width. Electron motion in charged nanotargets in the presence of a laser field
of different (non-relativistic) strength is considered. It is demonstarted that
for lasers of infrared frequencies clusters do not posess strong enough
potential to bound electrons with large oscillation amplitudes. Opposite to
clusters, nanofilms were found to be very perspective targets in the problem
considered. A simple analytic model and molecular dynamic simulations showed
increased harmonics generation when the oscillation amplitude of electrons in a
film becomes much larger, than the film width. Different regimes of generation
are briefly discussed.


  The dynamical law obeyed by the one-dimensional physical systems in the scale
relativity approach is reduced to a Riccati nonlinear differential equation.
Applied to the harmonic oscillator potential, we show that such an approach
permits the calculation of the solutions of the scale relativity problem in
terms of the well known solutions of the Schroedinger equation for the harmonic
oscillator.


  Dirichlet-based uncertainty (DBU) models are a recent and promising class of
uncertainty-aware models. DBU models predict the parameters of a Dirichlet
distribution to provide fast, high-quality uncertainty estimates alongside with
class predictions. In this work, we present the first large-scale, in-depth
study of the robustness of DBU models under adversarial attacks. Our results
suggest that uncertainty estimates of DBU models are not robust w.r.t. three
important tasks: (1) indicating correctly and wrongly classified samples; (2)
detecting adversarial examples; and (3) distinguishing between in-distribution
(ID) and out-of-distribution (OOD) data. Additionally, we explore the first
approaches to make DBU models more robust. While adversarial training has a
minor effect, our median smoothing based approach significantly increases
robustness of DBU models.


  We present a new third-order, semi-discrete, central method for approximating
solutions to multi-dimensional systems of hyperbolic conservation laws,
convection-diffusion equations, and related problems. Our method is a
high-order extension of the recently proposed second-order, semi-discrete
method in [16].
  The method is derived independently of the specific piecewise polynomial
reconstruction which is based on the previously computed cell-averages. We
demonstrate our results, by focusing on the new third-order CWENO
reconstruction presented in [21]. The numerical results we present, show the
desired accuracy, high resolution and robustness of our method.


  Large intelligent surface (LIS) has recently emerged as a potential low-cost
solution to reshape the wireless propagation environment for improving the
spectral efficiency. In this paper, we consider a downlink millimeter-wave
(mmWave) multiple-input-multiple-output (MIMO) system, where an LIS is deployed
to assist the downlink data transmission from a base station (BS) to a user
equipment (UE). Both the BS and the UE are equipped with a large number of
antennas, and a hybrid analog/digital precoding/combining structure is used to
reduce the hardware cost and energy consumption. We aim to maximize the
spectral efficiency by jointly optimizing the LIS's reflection coefficients and
the hybrid precoder (combiner) at the BS (UE). To tackle this non-convex
problem, we reformulate the complex optimization problem into a much more
friendly optimization problem by exploiting the inherent structure of the
effective (cascade) mmWave channel. A manifold optimization (MO)-based
algorithm is then developed. Simulation results show that by carefully devising
LIS's reflection coefficients, our proposed method can help realize a favorable
propagation environment with a small channel matrix condition number. Besides,
it can achieve a performance comparable to those of state-of-the-art
algorithms, while at a much lower computational complexity.


  The ability to autonomously explore and navigate a physical space is a
fundamental requirement for virtually any mobile autonomous agent, from
household robotic vacuums to autonomous vehicles. Traditional SLAM-based
approaches for exploration and navigation largely focus on leveraging scene
geometry, but fail to model dynamic objects (such as other agents) or semantic
constraints (such as wet floors or doorways). Learning-based RL agents are an
attractive alternative because they can incorporate both semantic and geometric
information, but are notoriously sample inefficient, difficult to generalize to
novel settings, and are difficult to interpret. In this paper, we combine the
best of both worlds with a modular approach that learns a spatial
representation of a scene that is trained to be effective when coupled with
traditional geometric planners. Specifically, we design an agent that learns to
predict a spatial affordance map that elucidates what parts of a scene are
navigable through active self-supervised experience gathering. In contrast to
most simulation environments that assume a static world, we evaluate our
approach in the VizDoom simulator, using large-scale randomly-generated maps
containing a variety of dynamic actors and hazards. We show that learned
affordance maps can be used to augment traditional approaches for both
exploration and navigation, providing significant improvements in performance.


  Analysis of small-x semi-inclusive DIS hadroproduction suggests that multiple
parton radiation leads to a broadening of transverse momentum distributions
beyond that predicted by a straightforward calculation in the
Collins-Soper-Sterman formalism. This effect can be modeled by a modification
of the resummed form factor in the small-x region. We discuss the impact of
such a modification on the production of electroweak bosons at hadron-hadron
colliders. We show that if substantial small-x broadening is observed in
forward Z boson production in the Tevatron Run-2, it would strongly affect
predicted transverse momentum distributions for W, Z, and Higgs boson
production at the Large Hadron Collider.


  In recent years, Twitter data related to political trends have tentatively
been used to make predictions (poll) about several electoral events. Given $q$
candidates for an election and a time-series of Twitts (short messages), one
can extract the $q$ mean trends and the $q(q+1)/2$ Twitt-to-Twitt correlations,
and look for the statistical models that reproduce these data. On the base of
several electoral events and assuming a stationary regime, we find out the
following: i) the maximization of the entropy singles out a microscopic model
(single-Twitt-level) that coincides with a $q$-state Potts model having
suitable couplings and external fields to be determined via an inverse problem
from the two sets of data; ii) correlations decay as $1/N_{eff}$, where
$N_{eff}$ is a small fraction of the mean number of Twitts; iii) the simplest
statistical models that reproduce these correlations are the multinomial
distribution (MD), characterized by $q$ external fields, and the mean-field
Potts model (MFP), characterized by one coupling; iv) remarkably, this coupling
turns out to be always close to its critical value. This results in a MD or MFP
model scenario that discriminates between cases in which polls are reliable and
not reliable, respectively. More precisely, predictions based on polls should
be avoided whenever the data maps to a MFP because anomalous large fluctuations
(if $q=2$) or sudden jumps (if $q\geq 3$) in the trends might take place as a
result of a second-order or a first-order phase transition of the MFP,
respectively.


  Fine-tuning contextualized representations learned by pre-trained language
models remains a prevalent practice in NLP. However, fine-tuning can lead to
representation degradation (also known as representation collapse), which may
result in instability, sub-optimal performance, and weak generalization.
  In this paper, we propose Representation Projection Invariance (REPINA), a
novel regularization method to maintain the information content of
representation and reduce representation collapse during fine-tuning by
discouraging undesirable changes in the representations. We study the empirical
behavior of the proposed regularization in comparison to 5 comparable baselines
across 13 language understanding tasks (GLUE benchmark and six additional
datasets). When evaluating in-domain performance, REPINA consistently
outperforms other baselines on most tasks (10 out of 13). We also demonstrate
its effectiveness in few-shot settings and robustness to label perturbation. As
a by-product, we extend previous studies of representation collapse and propose
several metrics to quantify it. Our empirical findings show that our approach
is significantly more effective at mitigating representation collapse.


  Let $G_n$ be the Barnes multiple Gamma function of order $n$ and the function
$f_n(z)$ be defined as \begin{align*} f_n(z)=\dfrac{\log G_n(z+1)}{z^n\Log
z},\quad z\in \mathbb{C}\setminus (-\infty,0]. \end{align*} In this work, a
conjecture to find the Stieltjes representation is proposed such that $f_n(z)$
is a Pick function. The conjecture is established for the particular case $n=3$
by examining the properties of $f_3(z)$.


  We report a quantum simulation of the deuteron binding energy on quantum
processors accessed via cloud servers. We use a Hamiltonian from pionless
effective field theory at leading order. We design a low-depth version of the
unitary coupled-cluster ansatz, use the variational quantum eigensolver
algorithm, and compute the binding energy to within a few percent. Our work is
the first step towards scalable nuclear structure computations on a quantum
processor via the cloud, and it sheds light on how to map scientific computing
applications onto nascent quantum devices.


  We report on an all-electrical measurement of the spin Hall effect in
epitaxial Fe/In_{x}Ga_{1-x}As heterostructures with n-type channel doping (Si)
and highly doped Schottky tunnel barriers. A transverse spin current generated
by an ordinary charge current flowing in the In_{x}Ga_{1-x}As is detected by
measuring the spin accumulation at the edges of the channel. The spin
accumulation is identified through the observation of a Hanle effect in the
Hall voltage measured by pairs of ferromagnetic contacts. We investigate the
bias and temperature dependence of the resulting Hanle signal and determine the
skew and side-jump contributions to the total spin Hall conductivity.


  We analyze mechanisms and regimes of wave packet spreading in nonlinear
disordered media. We predict that wave packets can spread in two regimes of
strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion
equations, and predict a dynamical crossover from strong to weak chaos. The
crossover is controlled by the ratio of nonlinear frequency shifts and the
average eigenvalue spacing of eigenstates of the linear equations within one
localization volume. We consider generalized models in higher lattice
dimensions and obtain critical values for the nonlinearity power, the
dimension, and norm density, which influence possible dynamical outcomes in a
qualitative way.


  We prove that the hyperelliptic mapping class group of a nonorientable
surface of genus $g\geq 4$ has a faithful linear representation of dimension
$g^2-1$ over $\mathbb{R}$.


  Some recent theoretical studies have tended to employ analytically-continuous
{\em gaussian}, or infinite-bandwidth step pulses to examine tunneling process.
The stationary phase method is often employed to this aim. However, {\em
gaussian} functions do not have a well-defined front, such that their speed of
propagation becomes ambiguous. Also, infinite bandwidth signals cannot
propagate through any real physical medium (whose transfer function is
therefore finite) without pulse distortion, which also leads to ambiguities in
determining propagation velocity during the tunneling process. In this
manuscript, we appoint some incompatibilities with the application of the
method of stationary phase in deriving tunneling times which, eventually, can
ruin the {\em superluminal} interpretation of transition times.


  Observations with the James Webb Space Telescope have revealed a high
abundance of bright galaxies at redshift, $z\gtrsim 12$, which has been widely
interpreted as conflicting with the $\Lambda$CDM model. In Cowley et al. (2018)
predictions were made - prior to the JWST observations - for the expected
abundance of these galaxies using the Durham semi-analytic galaxy formation
model, GALFORM, which is known to produce a realistic population of galaxies at
lower redshifts including the present day. Key to this model is the assumption
of a "top-heavy" initial mass function of stars formed in bursts (required to
explain the number counts and redshift distribution of sub-millimetre
galaxies). Here, we compare the rest-frame ultraviolet luminosity functions
derived from JWST observations with those predicted by the Cowley et al. model
up to $z=14$ and make further predictions for $z=16$. We find that below $z\sim
10$, the Cowley et al. predictions agree very well with observations, while
agreement at $z\gtrsim12$ requires extending the model to take into account the
timescale for the growth of obscuring dust grains and its dependence on gas
metallicity. We trace the evolution of these galaxies from $z=14$ to $z=0$ and
find that their descendants typically reside in halos with a median mass of
$10^{13.6}\,h^{-1}\,\mathrm{M_{\odot}}$. The stellar masses of the descendants
range from $10^{7}\,h^{-1}\,\mathrm{M_{\odot}}$ to
$10^{11.5}\,h^{-1}\,\mathrm{M_{\odot}}$. Although these galaxies were all
central galaxies at $z=14$, nearly half of their descendants end up as
satellites in massive halos.


  Tutte's $3$-flow conjecture states that every $4$-edge-connected graph admits
a nowhere-zero $3$-flow. In this paper, we characterize all graphs with
independence number at most $4$ that admit a nowhere-zero $3$-flow. The
characterization of $3$-flow verifies Tutte's $3$-flow conjecture for graphs
with independence number at most $4$ and with order at least $21$. In addition,
we prove that every odd-$5$-edge-connected graph with independence number at
most $3$ admits a nowhere-zero $3$-flow. To obtain these results, we introduce
a new reduction method to handle odd wheels.


  Excess heat will be an important heat source in future carbon-neutral
district heating systems. A barrier to excess heat integration is the lack of
appropriate scheduling and pricing systems for these producers, which generally
have small capacity and limited flexibility. In this work, we formulate and
analyze two methods for scheduling and pricing excess heat producers:
self-scheduling and market participation. In the former, a price signal is sent
to excess heat producers, based on which they determine their optimal schedule.
The latter approach allows excess heat producers to participate in a market
clearing. In a realistic case study of the Copenhagen district heating system,
we investigate market outcomes for the two excess heat integration paradigms
under increasing excess heat penetration. An important conclusion is that in
systems of high excess heat penetration, simple price signal methods will not
suffice, and more sophisticated price signals or coordinated dispatch become a
necessity.


  (Abridged abstract) We present an analysis of the X-ray emission of the
rapidly rotating giant star YY Mensae observed by Chandra HETGS and XMM-Newton.
Although no obvious flare was detected, the X-ray luminosity changed by a
factor of two between the XMM-Newton and Chandra observations taken 4 months
apart. The coronal abundances and the emission measure distribution have been
derived from three different methods using optically thin collisional
ionization equilibrium models. The abundances show an inverse first ionization
potential (FIP) effect. We further find a high N abundance which we interpret
as a signature of material processed in the CNO cycle. The corona is dominated
by a very high temperature (20-40 MK) plasma, which places YY Men among the
magnetically active stars with the hottest coronae. Lower temperature plasma
also coexists, albeit with much lower emission measure. Line broadening is
reported, which we interpret as Doppler thermal broadening, although rotational
broadening due to X-ray emitting material high above the surface could be
present as well. We use two different formalisms to discuss the shape of the
emission measure distribution. The first one infers the properties of coronal
loops, whereas the second formalism uses flares as a statistical ensemble. We
find that most of the loops in the corona of YY Men have their maximum
temperature equal to or slightly larger than about 30 MK. We also find that
small flares could contribute significantly to the coronal heating in YY Men.
Although there is no evidence of flare variability in the X-ray light curves,
we argue that YY Men's distance and X-ray brightness does not allow us to
detect flares with peak luminosities Lx <= 10^{31} erg/s with current
detectors.


  We propose the Wigner separability entropy as a measure of complexity of a
quantum state. This quantity measures the number of terms that effectively
contribute to the Schmidt decomposition of the Wigner function with respect to
a chosen phase space decomposition. We prove that the Wigner separability
entropy is equal to the operator space entanglement entropy, measuring
entanglement in the space of operators, and, for pure states, to twice the
entropy of entanglement. The quantum to classical correspondence between the
Wigner separability entropy and the separability entropy of the classical phase
space Liouville density is illustrated by means of numerical simulations of
chaotic maps. In this way, the separability entropy emerges as an extremely
broad complexity quantifier in both the classical and quantum realms.


The supersymmetric extensions of the Schr\"odinger algebra are reviewed.


  Let $S$ be a subset of $\overline{\mathbb Z}$, the ring of all algebraic
integers. A polynomial $f \in \mathbb Q[X]$ is said to be integral-valued on
$S$ if $f(s) \in \overline{\mathbb Z}$ for all $s \in S$. The set
$\text{Int}_{\mathbb Q}(S,\overline{\mathbb Z})$ of all integral-valued
polynomials on $S$ forms a subring of $\mathbb Q[X]$ containing $\mathbb Z[X]$.
We say that $\text{Int}_{\mathbb Q}(S,\overline{\mathbb Z})$ is trivial if
$\text{Int}_{\mathbb Q}(S,\overline{\mathbb Z}) = \mathbb Z[X]$, and nontrivial
otherwise. We give a collection of necessary and sufficient conditions on $S$
in order $\text{Int}_{\mathbb Q}(S,\overline{\mathbb Z})$ to be nontrivial. Our
characterizations involve, variously, topological conditions on $S$ with
respect to fixed extensions of the $p$-adic valuations to $\overline{\mathbb
Q}$; pseudo-monotone sequences contained in $S$; ramification indices and
residue field degrees; and the polynomial closure of $S$ in $\overline{\mathbb
Z}$.


  A general strategy for the determination of Tc oxidation state by new
approach involving X-ray absorption near edge spectroscopy (XANES) at the Tc L3
edge is shown. A comprehensive series of 99Tc compounds, ranging from oxidation
states I to VII, was measured and subsequently simulated within the framework
of crystal-field multiplet theory. The observable trends in the absorption edge
energy shift in combination with the spectral shape allow for a deeper
understanding of complicated Tc coordination chemistry. This approach can be
extended to numerous studies of Tc systems as this method is one of the most
sensitive methods for accurate Tc oxidation state and ligand characterization.


  Recently demonstrated metal-semiconductor heterojunctions with few-atom
thickness show their promise as 2D Schottky contacts for future integrated
circuits and nanoelectronics. The theory for 3D Schottky contacts, however,
fails on these low-dimensional systems. Here, we propose a new model that
yields carrier distribution and potential profile across the 2D
metal-semiconductor heterojunction under the equilibrium condition, based on
the input from first-principle calculations. Our calculation also suggests
that, at the same forward bias, the current density of a stack of 2D
graphene-phosphorene Schottky diodes may be ten thousand times higher than that
of a traditional 3D Schottky diode and offer less energy dissipation.


  We investigate and improve self-supervision as a drop-in replacement for
ImageNet pretraining, focusing on automatic colorization as the proxy task.
Self-supervised training has been shown to be more promising for utilizing
unlabeled data than other, traditional unsupervised learning methods. We build
on this success and evaluate the ability of our self-supervised network in
several contexts. On VOC segmentation and classification tasks, we present
results that are state-of-the-art among methods not using ImageNet labels for
pretraining representations.
  Moreover, we present the first in-depth analysis of self-supervision via
colorization, concluding that formulation of the loss, training details and
network architecture play important roles in its effectiveness. This
investigation is further expanded by revisiting the ImageNet pretraining
paradigm, asking questions such as: How much training data is needed? How many
labels are needed? How much do features change when fine-tuned? We relate these
questions back to self-supervision by showing that colorization provides a
similarly powerful supervisory signal as various flavors of ImageNet
pretraining.


  Computing all-pairs shortest paths is a fundamental and much-studied problem
with many applications. Unfortunately, despite intense study, there are still
no significantly faster algorithms for it than the $\mathcal{O}(n^3)$ time
algorithm due to Floyd and Warshall (1962). Somewhat faster algorithms exist
for the vertex-weighted version if fast matrix multiplication may be used.
Yuster (SODA 2009) gave an algorithm running in time $\mathcal{O}(n^{2.842})$,
but no combinatorial, truly subcubic algorithm is known.
  Motivated by the recent framework of efficient parameterized algorithms (or
"FPT in P"), we investigate the influence of the graph parameters clique-width
($cw$) and modular-width ($mw$) on the running times of algorithms for solving
All-Pairs Shortest Paths. We obtain efficient (and combinatorial) parameterized
algorithms on non-negative vertex-weighted graphs of times
$\mathcal{O}(cw^2n^2)$, resp. $\mathcal{O}(mw^2n + n^2)$. If fast matrix
multiplication is allowed then the latter can be improved to
$\mathcal{O}(mw^{1.842}n + n^2)$ using the algorithm of Yuster as a black box.
The algorithm relative to modular-width is adaptive, meaning that the running
time matches the best unparameterized algorithm for parameter value $mw$ equal
to $n$, and they outperform them already for $mw \in \mathcal{O}(n^{1 -
\varepsilon})$ for any $\varepsilon > 0$.


  Spiking Neural P systems are a class of membrane computing models inspired
directly by biological neurons. Besides the theoretical progress made in this
new computational model, there are also numerous applications of P systems in
fields like formal verification, artificial intelligence, or cryptography.
Motivated by all the use cases of SN P systems, in this paper, we present a new
privacy-preserving protocol that enables a client to compute a linear function
using an SN P system hosted on a remote server. Our protocol allows the client
to use the server to evaluate functions of the form t_1k + t_2 without
revealing t_1, t_2 or k and without the server knowing the result. We also
present an SN P system to implement any linear function over natural numbers
and some security considerations of our protocol in the honest-but-curious
security model.


  Quantum key distribution (QKD) allows for communication with security
guaranteed by quantum theory. The main theoretical problem in QKD is to
calculate the secret key rate for a given protocol. Analytical formulas are
known for protocols with symmetries, since symmetry simplifies the analysis.
However, experimental imperfections break symmetries, hence the effect of
imperfections on key rates is difficult to estimate. Furthermore, it is an
interesting question whether (intentionally) asymmetric protocols could
outperform symmetric ones. Here, we develop a robust numerical approach for
calculating the key rate for arbitrary discrete-variable QKD protocols.
Ultimately this will allow researchers to study "unstructured" protocols, that
is, those that lack symmetry. Our approach relies on transforming the key rate
calculation to the dual optimization problem, which dramatically reduces the
number of parameters and hence the calculation time. We illustrate our method
by investigating some unstructured protocols for which the key rate was
previously unknown.


  Education at all levels is facing several challenges in most countries, such
as low quality, high costs, lack of educators, and unsatisfied student demand.
Traditional approaches are becoming unable to deliver the required education.
Several causes for this inefficiency can be identified. I argue that beyond
specific causes, the lack of effective education is related to complexity.
However, information technology is helping us overcome this complexity.


  Low energy nuclear reactions in the neighborhood of metallic hydride surfaces
may be induced by ultra-low momentum neutrons. Heavy electrons are absorbed by
protons or deuterons producing ultra low momentum neutrons and neutrinos. The
required electron mass renormalization is provided by the interaction between
surface electron plasma oscillations and surface proton oscillations. The
resulting neutron catalyzed low energy nuclear reactions emit copious prompt
gamma radiation. The heavy electrons which induce the initially produced
neutrons also strongly absorb the prompt nuclear gamma radiation, re-emitting
soft photons. Nuclear hard photon radiation away from the metallic hydride
surfaces is thereby strongly suppressed.


  We consider the problem of sampling transition paths between two given
metastable states of a molecular system, e.g. a folded and unfolded protein or
products and reactants of a chemical reaction. Due to the existence of high
energy barriers separating the states, these transition paths are unlikely to
be sampled with standard Molecular Dynamics (MD) simulation. Traditional
methods to augment MD with a bias potential to increase the probability of the
transition rely on a dimensionality reduction step based on Collective
Variables (CVs). Unfortunately, selecting appropriate CVs requires chemical
intuition and traditional methods are therefore not always applicable to larger
systems. Additionally, when incorrect CVs are used, the bias potential might
not be minimal and bias the system along dimensions irrelevant to the
transition. Showing a formal relation between the problem of sampling molecular
transition paths, the Schr\"odinger bridge problem and stochastic optimal
control with neural network policies, we propose a machine learning method for
sampling said transitions. Unlike previous non-machine learning approaches our
method, named PIPS, does not depend on CVs. We show that our method successful
generates low energy transitions for Alanine Dipeptide as well as the larger
Polyproline and Chignolin proteins.


  The electron self-energy of the t1u states in A3C60 (A=K, Rb) is calculated
using the so-called GW approximation. The calculation is performed within a
model which considers the t1u charge carrier plasmon at 0.5 eV and takes into
account scattering of the electrons within the t1u band. A moderate reduction
(35 %) of the t1u band width is obtained.


  We present results for meson spectral functions at non-zero momentum at
temperatures both below and above Tc, obtained in quenched simulations for a
number of valence quark masses. For the lightest quark masses, a clear
difference between the spectral functions on cold and hot lattices is observed.


  We study the following problem: for given integers $d$, $k$ and graph $G$,
can we reduce some fixed graph parameter $\pi$ of $G$ by at least $d$ via at
most $k$ graph operations from some fixed set $S$? As parameters we take the
chromatic number $\chi$, clique number $\omega$ and independence number
$\alpha$, and as operations we choose the edge contraction ec and vertex
deletion vd. We determine the complexity of this problem for $S=\{\mbox{ec}\}$
and $S=\{\mbox{vd}\}$ and $\pi\in \{\chi,\omega,\alpha\}$ for a number of
subclasses of perfect graphs. We use these results to determine the complexity
of the problem for $S=\{\mbox{ec}\}$ and $S=\{\mbox{vd}\}$ and $\pi\in
\{\chi,\omega,\alpha\}$ restricted to $H$-free graphs.