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By using white noise analysis, we study the integral kernel $\xi(x)$, $x\in\mathbb{R}^{d}$, of stochastic currents corresponding to fractional Brownian motion with Hurst parameter $H\in(0,1)$. For $x\in\mathbb{R}^{d}\backslash\{0\}$ and $d\ge1$ we show that the kernel $\xi(x)$ is well-defined as a Hida distribution for all $H\in(0,1/2]$. For $x=0$ and $d=1$, $\xi(0)$ is a Hida distribution for all $H\in(0,1)$. For $d\ge2$, then $\xi(0)$ is a Hida distribution only for $H\in(0,1/d)$. To cover the case $H\in[1/d,1)$ we have to truncate the delta function so that $\xi^{(N)}(0)$ is a Hida distribution whenever $2N(H-1)+Hd>1$., Comment: 17 pages

Starting with the overall wave function expression for the electron in an Aharonov-Bohm potential, we derive a version of the Kuramoto Model describing the phase dynamics of the bound state of the quantum mechanical system., Comment: 14 pages, 6 figures, 1 table

We construct the Feynman integral for the Schr\"odinger propagator in the polar conjugate momentum space, which describes the bound state Aharonov-Bohm effect, as a well-defined white noise functional., Comment: 28 pages, 1 figure

This paper investigates a broad class of non-Gaussian measures, $ \mu_\Psi$, associated with a family of generalized Wright functions, $_m\Psi_q$. First, we study these measures in Euclidean spaces $\mathbb{R}^d$, then define them in an abstract nuclear triple $\mathcal{N}\subset\mathcal{H}\subset\mathcal{N}'$. We study analyticity, invariance properties, and ergodicity under a particular group of automorphisms. Then we show the existence of an Appell system which allows the extension of the non-Gaussian Hilbert space $L^2(\mu_\Psi)$ to the nuclear triple consisting of test functions' and distributions' spaces, $(\mathcal{N})^{1}\subset L^2(\mu_\Psi)\subset(\mathcal{N})_{\mu_\Psi}^{-1}$. Thanks to this triple, we can study Donsker's delta as a well-defined object in the space of distributions $(\mathcal{N})_{\mu_\Psi}^{-1}$.

In this paper, we investigate the Green measure for a class of non-Gaussian processes in $\mathbb{R}^{d}$. These measures are associated with the family of generalized grey Brownian motions $B_{\beta,\alpha}$, $0<\beta\le1$, $0<\alpha\le2$. This family includes both fractional Brownian motion, Brownian motion, and other non-Gaussian processes. We show that the perpetual integral exists with probability $1$ for $d\alpha>2$ and $1<\alpha\le2$. The Green measure then generalizes those measures of all these classes., Comment: 13 pages

In the last two decades, much effort has been dedicated to studying curves and surfaces according to their angle with a given direction. However, most findings were obtained using a case-by-case approach, and it is often unclear what are consequences of the specificities of the ambient manifold and what could be generic. In this work, we propose a theoretical framework to unify parts of these findings. We study curves and surfaces by prescribing the angle they make with a parallel transported vector field. We show that the characterization of Euclidean helices in terms of their curvature and torsion is also valid in any Riemannian manifold. Among other properties, we prove that surfaces making a constant angle with a parallel transported direction are extrinsically flat ruled surfaces. We also investigate the relation between their geodesics and the so-called slant helices; we prove that surfaces of constant angle are the rectifying surface of a slant helix, i.e., the ruled surface with rulings given by the Darboux vector field of the directrix. We characterize rectifying surfaces of constant angle; in other words, when their geodesics are slant helices. As a corollary, we show that if every geodesic of a surface of constant angle is a slant helix, then the ambient manifold is flat. Finally, we characterize surfaces in the product of a Riemannian surface with the real line making a constant angle with the vertical real direction., Comment: 27 pages. Keywords: Helix, Slant helix, Surface of constant angle, Rectifying surface

We present a conceptually novel approach to achieve selective area epitaxy of GaN nanowires. The approach is based on the fact that these nanostructures do not form in plasma-assisted molecular beam epitaxy on structurally and chemically uniform cation-polar substrates. By in situ depositing and nitridating Si on a Ga-polar GaN film, we locally reverse the polarity to induce the selective area epitaxy of N-polar GaN nanowires. We show that the nanowire number density can be controlled over several orders of magnitude by varying the amount of pre-deposited Si. Using this growth approach, we demonstrate the synthesis of single-crystalline and uncoalesced nanowires with diameters as small as 20 nm. The achievement of nanowire number densities low enough to prevent the shadowing of the nanowire sidewalls from the impinging fluxes paves the way for the realization of homogeneous core-shell heterostructures without the need of using ex situ pre-patterned substrates.

In this paper, we study the quasi-invariant property of a class of non-Gaussian measures. These measures are associated with the family of generalized grey Brownian motions. We identify the Cameron--Martin space and derive the explicit Radon-Nikodym density in terms of the Wiener integral with respect to the fractional Brownian motion. Moreover, we show an integration by parts formula for the derivative operator in the directions of the Cameron--Martin space. As a consequence, we derive the closability of both the derivative and the corresponding gradient operators., Comment: 36 pages, 1 figure

This work is concerned with the existence of mild solutions and the uniqueness of distributional solutions to nonlinear Fokker-Planck equations with nonlocal operators $\Psi(-\Delta)$, where $\Psi$ is a Bernstein function. As applications, the existence and uniqueness of solutions to the corresponding nonlinear martingale problems are proved. Furthermore, it is shown that these solutions form a nonlinear Markov process in the sense of McKean such that their one-dimensional time marginal law densities are the solutions to the nonlocal nonlinear Fokker-Planck equation. Hence, McKean's program envisioned in his PNAS paper from 1966 is realized for these nonlocal PDEs., Comment: arXiv admin note: text overlap with arXiv:2210.05612

Rob\^oCIn has participated in RoboCup Small Size League since 2019, won its first world title in 2022 (Division B), and is currently a three-times Latin-American champion. This paper presents our improvements to defend the Small Size League (SSL) division B title in RoboCup 2023 in Bordeaux, France. This paper aims to share some of the academic research that our team developed over the past year. Our team has successfully published 2 articles related to SSL at two high-impact conferences: the 25th RoboCup International Symposium and the 19th IEEE Latin American Robotics Symposium (LARS 2022). Over the last year, we have been continuously migrating from our past codebase to Unification. We will describe the new architecture implemented and some points of software and AI refactoring. In addition, we discuss the process of integrating machined components into the mechanical system, our development for participating in the vision blackout challenge last year and what we are preparing for this year.

Visual Question Answering (VQA) is an emerging area of interest for researches, being a recent problem in natural language processing and image prediction. In this area, an algorithm needs to answer questions about certain images. As of the writing of this survey, 25 recent studies were analyzed. Besides, 6 datasets were analyzed and provided their link to download. In this work, several recent pieces of research in this area were investigated and a deeper analysis and comparison among them were provided, including results, the state-of-the-art, common errors, and possible points of improvement for future researchers., Comment: 30 pages. arXiv admin note: text overlap with arXiv:2104.00926, arXiv:2110.02526, arXiv:2108.02059, arXiv:1908.01801 by other authors

Over the last few years, the number of works about deep learning applied to the medical field has increased enormously. The necessity of a rigorous assessment of these models is required to explain these results to all people involved in medical exams. A recent field in the machine learning area is explainable artificial intelligence, also known as XAI, which targets to explain the results of such black box models to permit the desired assessment. This survey analyses several recent studies in the XAI field applied to medical diagnosis research, allowing some explainability of the machine learning results in several different diseases, such as cancers and COVID-19.

Taking advantage of the fact that the cardinalities of hidden variables in network scenarios can be assumed to be finite without loss of generality, a numerical tool for finding explicit local models that reproduce a given statistical behaviour was developed. The numerical procedure was then validated using families of statistical behaviours for which the network-local boundary is known, in the bilocal scenario. Furthermore, the critical visibility for 3 notable distributions mixed with a uniform random noise is investigated in the triangle network without inputs. We provide conjectures for the critical visibilities of the Greenberger-Horne-Zeilinger (GHZ) and W distributions (which are roots of 4th degree polynomials), as well as a lower bound estimate of the critical visibility of the Elegant Joint Measurement distribution. The developed codes and documentation are publicly available at github.com/mariofilho281/localmodels, Comment: 10 pages and 8 figures. Updated to match the published version

In this paper we study the existence of Green measures for Markov processes with a nonlocal jump generator. The jump generator has no second moment and satisfies a suitable condition on its Fourier transform. We also study the same problem for certain classes of random time changes Markov processes with jump generator., Comment: 20 pages

In this paper we use a biorthogonal approach to the analysis of the infinite dimensional fractional Poisson measure $\pi_{\sigma}^{\beta}$, $0<\beta\leq1$, on the dual of Schwartz test function space $\mathcal{D}'$. The Hilbert space $L^{2}(\pi_{\sigma}^{\beta})$ of complex-valued functions is described in terms of a system of generalized Appell polynomials $\mathbb{P}^{\sigma,\beta,\alpha}$ associated to the measure $\pi_{\sigma}^{\beta}$. The kernels $C_{n}^{\sigma,\beta}(\cdot)$, $n\in\mathbb{N}_{0}$, of the monomials may be expressed in terms of the Stirling operators of the first and second kind as well as the falling factorials in infinite dimensions. Associated to the system $\mathbb{P}^{\sigma,\beta,\alpha}$, there is a generalized dual Appell system $\mathbb{Q}^{\sigma,\beta,\alpha}$ that is biorthogonal to $\mathbb{P}^{\sigma,\beta,\alpha}$. The test and generalized function spaces associated to the measure $\pi_{\sigma}^{\beta}$ are completely characterized using an integral transform as entire functions., Comment: 39 pages, 1 figure

In this paper, we use a biorthogonal approach (Appell system) to construct and characterize the spaces of test and generalized functions associated to the fractional Poisson measure $\pi_{\lambda,\beta}$, that is, a probability measure in the set of natural (or real) numbers. The Hilbert space $L^{2}(\pi_{\lambda,\beta})$ of complex-valued functions plays a central role in the construction, namely, the test function spaces $(N)_{\pi_{\lambda,\beta}}^{\kappa}$, $\kappa\in[0,1]$ is densely embedded in $L^{2}(\pi_{\lambda,\beta})$. Moreover, $L^{2}(\pi_{\lambda,\beta})$ is also dense in the dual $((N)_{\pi_{\lambda,\beta}}^{\kappa})'=(N)_{\pi_{\lambda,\beta}}^{-\kappa}$. Hence, we obtain a chain of densely embeddings $(N)_{\pi_{\lambda,\beta}}^{\kappa}\subset L^{2}(\pi_{\lambda,\beta})\subset(N)_{\pi_{\lambda,\beta}}^{-\kappa}$. The characterization of these spaces is realized via integral transforms and chain of spaces of entire functions of different types and order of growth. Wick calculus extends in a straightforward manner from Gaussian analysis to the present non-Gaussian framework. Finally, in Appendix B we give an explicit relation between (generalized) Appell polynomials and Bell polynomials., Comment: 32 pages, 0 figures

In this paper we study stochastic currents of Brownian motion $\xi(x)$, $x\in\mathbb{R}^{d}$, by using white noise analysis. For $x\in\mathbb{R}^{d}\backslash\{0\}$ and for $x=0\in\mathbb{R}$ we prove that the stochastic current $\xi(x)$ is a Hida distribution. Moreover for $x=0\in\mathbb{R}^{d}$ with $d>1$ we show that the stochastic current is not a Hida distribution., Comment: 10 pages