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For any $p\in[1,\infty)$, we prove that the set of simple functions taking at most $k$ different values is proximinal in B\"ochner spaces $L^p(X)$ whenever $X$ is a dual Banach space with $w^*$-sequentially compact unit ball. With additional properties on $X$ and its norm, we show these sets are approximatively $w^*$-compact for $p\in(1,\infty)$ and even approximatively norm-compact under stronger hypothesis.

In this article we study the long time behavior of linear functionals of branching diffusion processesas well as the time reversal of the spinal process by means of spectral properties of the Feynman-Kacsemigroup. We generalize for this non Markovian semigroup the theory of quasi-stationary distribution(q.s.d.) and Q-process. The most amazing result is the identification of the law of the reversal time spinalprocess issued from q.s.d. with the Q-process of the Feynman-Kac semigroup.

We study a semiclassical model of the mixmaster universe. We first derive the quantum model and then introduce its semiclassical approximation. We employ a general integral quantization method that respects the symmetries of the model given by the affine and the Weyl-Heisenberg groups, and can produce a wide class of quantum models. The semiclassical approximation is based on the coherent states. The semiclassical dynamics is complex and cannot be solved by analytical methods. We focus on a key qualitative feature of the dynamics, namely, we investigate whether the primordial anisotropic universe can undergo a spontaneous inflationary phase driven by the anisotropic energy combined with semiclassical corrections. The answer to this question provides a useful perspective on the inflationary paradigm as well as on alternative bouncing models., Comment: 15 pages, 6 figures

In this work we explore the quantum Bianchi type IX-model, its semi-classical features, and its relevance in early cosmology to tentatively explain inflation and production of primordial structures. We specially focus on the analytical and numerical exploration of the dynamical system derived from the phase-space portraits. Afterwards we investigate the reliability of our results with regard to inflation and post inflation scenarii commonly accepted nowadays., Comment: Presented at the 8th Conference of the Polish Society on Relativity. To appear in Acta Physica Polonica B Supplement

A quantum cosmological bouncing model may exhibit an ambiguity stemming from the nonclassical nature of the background evolution: two classically equivalent theories can produce two qualitatively different potentials sourcing the perturbations. We derive explicitly the quantum canonical transformation involving the quantum background to show how it leads to inequivalent theories. We identify the relevant quantum parameter describing the difference and expand upon the ambiguity by calculating the expected power spectra produced for initial quantum vacuum fluctuations in the contracting phase of both potentials. We find that one spectral index corresponds to all values of this parameter but one, while the other thus represents a set of measure zero., Comment: 16 pages, 7 figures, follow-up article to gr-qc 2111.02963, matching published version

For any $p\in[1,\infty]$, we prove that the set of simple functions taking at most $k$ different values is proximinal in $L^p$ for all $k\geq 1$. We introduce the class of uniformly approximable subsets of $L^p$, which is larger than the class of uniformly integrable sets. This new class is characterized in terms of the $p$-variation if $p\in[1,\infty)$ and in terms of covering numbers if $p=\infty$. We study properties of uniformly approximable sets. In particular, we prove that the convex hull of a uniformly approximable bounded set is also uniformly approximable and that this class is stable under H\"older transformations. We also prove that, for $p\in [1,\infty)$, the unit ball of $L^p$ is uniformly approximable if and only if $L^p$ is finite-dimensional, while for $p=\infty$ the unit ball is always uniformly approximable.

By quantizing the background as well as the perturbations in a simple one fluid cosmological model, we show that there exists an ambiguity in the choice of relevant variables, potentially leading to incompatible observational physical predictions. In a classical inflationary background, the exact same canonical transformations lead to unique predictions, so the ambiguity we put forward demands a semiclassical background with a sufficiently strong departure from classical evolution. The latter condition is clearly satisfied by bouncing models. We propose coherent states as the tool for introducing the semiclassical universe. We solve the quantum dynamics of the perturbation modes both analytically and numerically and investigate the amplitude spectra of the perturbations. We study the underlying quantum state, the Bunch-Davies vacuum, from the point of view of late-time observers by means of the Bogolyubov transformations. In particular, we study the phase space probability distributions obtained with the standard coherent states built from instantaneous vacua. We discuss the issue of the temporal phase shift with which the modes emerge from the bounce as sine waves. Finally, we find that the model may be fitted to data and shed light on the physical universe, constraining free parameters of the bouncing universe., Comment: Contribution to the 2022 Cosmology session of the 56th Rencontres de Moriond

Consider hard balls in a bounded rotating drum. If there is no gravitation then there is no Fermi acceleration, i.e., the energy of the balls remains bounded forever. If there is gravitation, Fermi acceleration may arise. A number of explicit formulas for the system without gravitation are given. Some of these are based on an explicit realization, which we derive, of the well-known microcanonical ensemble measure.

Non-fullerene acceptor (NFA)-based ternary bulk heterojunction solar cells (TSC) are the most efficient organic solar cells (OSCs) today due to their broader absorption and quantum efficiencies (QE) often surpassing those of corresponding binary blends. We study how the energetics driving charge transfer at the electron donor:electron acceptor (D/A) interfaces impact the QE in blends of PBDB-T-2F donor with several pairs of lower bandgap NFAs. As in binary blends, the ionization energy offset between donor and acceptor ({\Delta}IE) controls the QE and maximizes for {\Delta}IE > 0.5 eV. However, {\Delta}IE is not controlled by the individual NFAs IEs but by their average, weighted for their blending ratio. Using this property, we improved the QE of a PBDB-T-2F:IEICO binary blend that had an insufficient {\Delta}IE for charge generation by adding a deep IE third component: IT-4F. Combining two NFAs enables to optimize the D/A energy alignment and cells' QE without molecular engineering., Comment: S Karuthedath and S H K Paleti contributed equally. MS: 35 pages, 9 figures. SI: 21 pages, 23 figures - updates: added a model scheme as Fig1, updated T1 EQE and blends PL in Fig 2 (former 1). Added Figure (5): charge generation upon acceptor excitation. Corrected {\Delta}IEs in fig7 and 9 (a few tens of meV off). Added more blends to show generality (2 groups, 10 blends compositions)

By quantising the background as well as the perturbations in a simple one fluid model, we show that there exists an ambiguity in the choice of relevant variables, potentially leading to incompatible observational physical predictions. In a classical or quantum inflationary background, the exact same canonical transformations lead to unique predictions, so the ambiguity we put forward demands a semiclassical background with a sufficiently strong departure from classical evolution. The latter condition happens to be satisfied in bouncing scenarios, which may thus be having predictability issues. Inflationary models could evade such a problem because of the monotonic behavior of their scale factor; they do, however, initiate from a singular state which bouncing scenarios aim at solving., Comment: 13 pages, 7 figures

In this work, we demonstrate the formation of a "red-phase" poly[2-methoxy, 5-(2'- ethyl-hexoxy)-1,4-phenylene vinylene-PPV] (MEH-PPV) embedded into a host matrix of highly entangled ultra-high molecular weight polystyrene (MEH-PPV/UHMW PS pseudogel) that allows the simple processing of the MEH-PPV solutions. We processed a "red-phase" in the gel, the gel shows that the features what have beed demonstrated in the solution can be observed in the processable gel for optoelectronics applications. [Yamagata, Hajime, and Hestand, Nicholas J. and Spano, Frank C. and Kohler, Anna and Scharsich, Christina and Hoffmann, Sebastian T. and Bassler, Heinz, The Journal of Chemical Physics, 2013, 139, 114903]

Precise determination of the solid-state microstructure of semiconducting polymers is of paramount importance for the further development of these materials in various organic electronic technologies. Yet, prior characterization of the ordering of semiconducting polymers often resulted in conundrums in which X-ray scattering and microscopy yielded seemingly contradicting results. Here, based on fast scanning calorimetry, we introduce for the first time the concept of the semi-para-crystallinity and measurement of the degree of para-crystallinity (ordered volume/mass fraction) in a set of materials that previously eluded understanding. In combination with lattice distortion determination within para-crystals (g-parameter from X-ray scattering) and nanomorphology, the complete solid-state microstructure is correlated with device properties. Our data show that the long-range charge carrier transport in these materials is more sensitive to the interconnection of para-crystal units than to the amount of structural order itself.

Bisexual Galton-Watson processes are discrete Markov chains where reproduction events are due to mating of males and females. Owing to this interaction, the standard branching property of Galton-Watson processes is lost. We prove tightness for conveniently rescaled bisexual Galton-Watson processes, based on recent techniques developed by Bansaye, Caballero and M{\'e}l{\'e}ard. We also identify the possible limits of these rescaled processes as solutions of a stochastic system, coupling two equations through singular coefficients in Poisson terms added to square roots as coefficients of Brownian motions. Under some additional integrability assumptions, pathwise uniqueness of this limiting system of stochastic differential equations and convergence of the rescaled processes are obtained. Two examples corresponding to mutual fidelity are considered.

In this article we study stability properties of $g_O$, the standard Green kernel for $O$ an open regular set in $R^d$. In $d\ge 3$ we show that $g_O^\beta$ is again a Green kernel of a Markov Feller process, for any power $\beta\in [1,d/(d-2))$. In dimension $d=2$, if $O$ is an open Greenian regular set, we show the same result for $g_O^\beta$, for any $\beta\ge 1$ and for the kernel $\exp(\alpha g_O)$, when $\alpha \in (0,2\pi)$., Comment: 30 pages

In this article we present a new characterization of inverse M-matrices, inverse row diagonally dominant M-matrices and inverse row and column diagonally dominant M-matrices, based on the positivity of certain inner products., Comment: 9 pages

Recent demonstrations of inverted thermal activation of charge mobility in polymer field-effect transistors have excited the interest in transport regimes not limited by thermal barriers. However, rationalization of the limiting factors to access such regimes is still lacking. An improved understanding in this area is critical for development of new materials, establishing processing guidelines, and broadening of the range of applications. Here we show that precise processing of a diketopyrrolopyrrole-tetrafluorobenzene-based electron transporting copolymer results in single crystal-like and voltage-independent mobility with vanishing activation energy above 280 K. Key factors are uniaxial molecular alignment and thermal annealing at temperatures within the melting endotherm of films. Experimental and computational evidence converge toward a picture of electrons being delocalized within crystalline domains of increased size. Residual energy barriers introduced by disordered regions are bypassed in the direction of molecular alignment by a more efficient interconnection of the ordered domains following the annealing process.

The High Cadence Transient Survey (HiTS) aims to discover and study transient objects with characteristic timescales between hours and days, such as pulsating, eclipsing and exploding stars. This survey represents a unique laboratory to explore large etendue observations from cadences of about 0.1 days and to test new computational tools for the analysis of large data. This work follows a fully \textit{Data Science} approach: from the raw data to the analysis and classification of variable sources. We compile a catalog of ${\sim}15$ million object detections and a catalog of ${\sim}2.5$ million light-curves classified by variability. The typical depth of the survey is $24.2$, $24.3$, $24.1$ and $23.8$ in $u$, $g$, $r$ and $i$ bands, respectively. We classified all point-like non-moving sources by first extracting features from their light-curves and then applying a Random Forest classifier. For the classification, we used a training set constructed using a combination of cross-matched catalogs, visual inspection, transfer/active learning and data augmentation. The classification model consists of several Random Forest classifiers organized in a hierarchical scheme. The classifier accuracy estimated on a test set is approximately $97\%$. In the unlabeled data, $3\,485$ sources were classified as variables, of which $1\,321$ were classified as periodic. Among the periodic classes we discovered with high confidence, 1 $\delta$-scutti, 39 eclipsing binaries, 48 rotational variables and 90 RR-Lyrae and for the non-periodic classes we discovered 1 cataclysmic variables, 630 QSO, and 1 supernova candidates. The first data release can be accessed in the project archive of HiTS., Comment: 22 pages including 10 figures and 9 tables. Accepted for publication in AJ. For associated files, see http://astro.cmm.uchile.cl/HiTS/

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are limit points of $n$-player equilibria, but we also exhibit a remarkable class of mean field equilibria that are not limits, thus questioning their interpretation as "large $n$" equilibria., Comment: Forthcoming in 'Annals of Applied Probability'

IRT models are being increasingly used worldwide for test construction and scoring. The study examines the practical implications of estimating individual scores in a paper-and-pencil high-stakes test using 2PL and 3PL models, specifically whether the principle of consistent order holds when scoring with IRT. The principle states that student A, who answers the same (or a larger) number of items of greater difficulty than student B, should outscore B. Results of analyses conducted using actual scores from the Chilean national admission test in mathematics indicate the principle does not hold when scoring with 2PL or 3PL models. Students who answer more items and of greater difficulty may be assigned lower scores. The findings can be explained by examining the mathematical models, since estimated ability scores are an increasing function of the accumulated estimated discriminations for the correct items, not their difficulty. For high stakes tests the decision to use complex model should therefore be a matter of serious deliberation for policy makers and test experts, since fairness and transparency may be compromised., Comment: 15 pages, 8 figures, 1 table

We report the discovery of distant RR Lyrae stars, including the most distant known in the Milky Way, using data taken in the $g-$band with the Dark Energy Camera as part of the High cadence Transient Survey (HiTS; 2014 campaign). We detect a total of 173 RR Lyrae stars over a ~120 deg^2 area, including both known RR Lyrae and new detections. The heliocentric distances d_H of the full sample range from 9 to >200 kpc, with 18 of them beyond 90 kpc. We identify three sub-groups of RR Lyrae as members of known systems: the Sextans dwarf spheroidal galaxy, for which we report 46 new discoveries, and the ultra-faint dwarf galaxies Leo IV and Leo V. Following an MCMC methodology, we fit spherical and ellipsoidal profiles of the form rho(R) ~ R^n to the radial density distribution of RR Lyrae in the Galactic halo. The best fit corresponds to the spherical case, for which we obtain a simple power-law index of n=-4.17^{+0.18}_{-0.20}, consistent with recent studies made with samples covering shorter distances. The pulsational properties of the outermost RR Lyrae in the sample (d_H>90 kpc) differ from the ones in the halo population at closer distances. The distribution of the stars in a Period-Amplitude diagram suggest they belong to Oosterhoff-intermediate or Oosterhoff II groups, similar to what is found in the ultra-faint dwarf satellites around the Milky Way. The new distant stars discovered represent an important addition to the few existing tracers of the Milky Way potential in the outer halo., Comment: Accepted for publication in The Astrophysical Journal

In this paper we consider diffusions on the half line (0, $\infty$) such that the expectation of the arrival time at the origin is uniformly bounded in the initial point. This implies that there is a well defined diffusion process starting from infinity, which takes finite values at positive times. We study the behaviour of hitting times of large barriers and in a dual way, the behaviour of the process starting at infinity for small time. In particular we prove that the process coming down from infinity is in small time governed by a specific deterministic function. Suitably normalized fluctuations of the hitting times are asymptotically Gaussian. We also derive the tail of the distribution of the hitting time of the origin and a Yaglom limit for the diffusion starting from infinity. We finally prove that the distribution of this process killed at the origin is absolutely continuous with respect to the speed measure. The density is expressed in terms of the eigenvalues and eigenfunctions of the generator of the killed diffusion.

We obtain a closed-form formula for the quasi-stationary distribution of the classical Shiryaev martingale diffusion considered on the positive half-line $[A,+\infty)$ with $A>0$ fixed; the state space's left endpoint is assumed to be the killing boundary. The formula is obtained analytically as the solution of the appropriate singular Sturm-Liouville problem; the latter was first considered in Section 7.8.2 of Collet et al. (2013), but has heretofore remained unsolved., Comment: To appear in Theory of Probability and Its Applications, 16 pages, 15 figures

In traditional work on numerical schemes for solving stochastic differential equations (SDEs), it is usually assumed that the coefficients are globally Lipschitz. This assumption has been used to establish a powerful analysis of the numerical approximations of the solutions of stochastic differential equations. In practice, however, the globally Lipschitz assumption on the coefficients is on occasion too stringent a requirement to meet. Some Brownian motion driven SDEs used in applications have coefficients that are Lipschitz only on compact sets. Reflecting the importance of the locally Lipschitz case, it has been well studied in recent years, yet some simple to state, fundamental results remain unproved. We attempt to fill these gaps in this paper, establishing both a rate of convergence, but also we find the asymptotic normalized error process of the error process arising from a sequence of approximations. The result is analogous to the original result of this type, established in KT1991-2 back in 1991. This result was improved in 1998 in JJ1998, and recently(2009) it was partially extended in AN. As we indicate, the results in our paper provide the basis of a statistical analysis of the error; in this spirit we give conditions for a finite variance., Comment: 26 pages

Because final properties of nanoscale polymeric structures are largely determined by the solid-state microstructure of the confined polymer, it is imperative not only to understand how the microstructure of polymers develops under nanoscale confinement but also to establish means to manipulate it. Here we present a series of processing strategies, adapted from methods used in bulk polymer processing, that allow to control the solidification of polymer nanostructures. Firstly, we show that supramolecular nucleating agents can be readily used to modify the crystallization kinetics of confined poly(vinylidene fluoride) (PVDF). In addition, we demonstrate that microstructural features that are not traditionally affected by nucleating agents, such as the orientation of crystals, can be tuned with the crystallization temperature applied. Interestingly, we also show that high crystallization temperatures and long annealing periods induce the formation of the modification of PVDF, hence enabling the simple production of ferro/piezoelectric nanostructures. We anticipate that the approaches presented here can open up a plethora of new possibilities for the processing of polymer-based nanostructures with tailored properties and functionalities.