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We analyze a modification of the Richards growth model by introducing a time-dependent perturbation in the growth rate. This modification becomes effective at a special switching time, which represents the first-crossing-time of the Richards growth curve through a given constant boundary. The relevant features of the modified growth model are studied and compared with those of the original one. A sensitivity analysis on the switching time is also performed. Then, we define two different stochastic processes, i.e. a non-homogeneous linear birth-death process and a lognormal diffusion process, such that their means identify to the growth curve under investigation. For the diffusion process, we address the problem of parameters estimation through the maximum likelihood method. The estimates are obtained via meta-heuristic algorithms (namely, Simulated Annealing and Ant Lion Optimizer). A simulation study to validate the estimation procedure is also presented, together with a real application to oil production in France. Special attention is devoted to the approximation of switching time density, viewed as the first-passage-time density for the lognormal process., Comment: 24 pages, 18 figures

We consider a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious epidemic model in which the transmission intensity function is time-dependent. Such a model is well suited to describe some classes of micro-parasitic infections in which individuals never acquire lasting immunity and over the course of the epidemic everyone eventually becomes infected. The stochastic process related to the deterministic model is transformable into a non homogeneous Wiener process so the probability distribution can be obtained. Here we focus on the inference for such process, by providing an estimation procedure for the involved parameters. We point out that the time dependence in the infinitesimal moments of the diffusion process makes classical inference methods inapplicable. The proposed procedure is based on Generalized Method of Moments in order to find suitable estimate for the infinitesimal drift and variance of the transformed process. Several simulation studies are conduced to test the procedure, these include the time homogeneous case, for which a comparison with the results obtained by applying the MLE is made, and cases in which the intensity function are time dependent with particular attention to periodic cases. Finally, we apply the estimation procedure to a real dataset., Comment: 20 pages, 6 figures

Multiple-Input Multiple-Output (MIMO) systems play a crucial role in fifth-generation (5G) mobile communications, primarily achieved through the utilization of precoding matrix techniques. This paper presents precoding techniques employing codebooks in downlink MIMO-5G wireless communications, aiming to enhance network performance to meet the overarching 5G objectives of increased capacity and reduced latency. We conduct a comparative analysis of various precoding techniques outlined by the 5G standard through diverse simulations across different scenarios. These simulations enable us to assess the performance of the different precoding techniques, ultimately revealing the strengths and weaknesses inherent in Type I and Type II codebooks., Comment: 4 pages, 6 figures

Human-level autonomous driving is an ever-elusive goal, with planning and decision making -- the cognitive functions that determine driving behavior -- posing the greatest challenge. Despite a proliferation of promising approaches, progress is stifled by the difficulty of deploying experimental planners in naturalistic settings. In this work, we propose Lab2Car, an optimization-based wrapper that can take a trajectory sketch from an arbitrary motion planner and convert it to a safe, comfortable, dynamically feasible trajectory that the car can follow. This allows motion planners that do not provide such guarantees to be safely tested and optimized in real-world environments. We demonstrate the versatility of Lab2Car by using it to deploy a machine learning (ML) planner and a search-based planner on self-driving cars in Las Vegas. The resulting systems handle challenging scenarios, such as cut-ins, overtaking, and yielding, in complex urban environments like casino pick-up/drop-off areas. Our work paves the way for quickly deploying and evaluating candidate motion planners in realistic settings, ensuring rapid iteration and accelerating progress towards human-level autonomy., Comment: This work has been submitted to the IEEE for possible publication

An algebraic characterization of the contractions of the Poincar\'e group permits a proper construction of a non-relativistic limit of its tachyonic representation. We arrive at a consistent, nonstandard representation of the Galilei group which was disregarded long ago by supposedly unphysical properties. The corresponding quantum (and classical) theory shares with the relativistic one their fundamentals, and serves as a toy model to better comprehend the unusual behavior of the tachyonic representation. For instance, we see that evolution takes place in a spatial coordinate rather than time, as for relativistic tachyons, but the modulus of the three-momentum is the same for all Galilean observers, leading to a new dispersion relation for a Galilean system. Furthermore, the tachyonic objects described by the new representation cannot be regarded as localizable in the standard sense., Comment: 19 pages, 3 figures

The sample efficiency of Bayesian optimization algorithms depends on carefully crafted acquisition functions (AFs) guiding the sequential collection of function evaluations. The best-performing AF can vary significantly across optimization problems, often requiring ad-hoc and problem-specific choices. This work tackles the challenge of designing novel AFs that perform well across a variety of experimental settings. Based on FunSearch, a recent work using Large Language Models (LLMs) for discovery in mathematical sciences, we propose FunBO, an LLM-based method that can be used to learn new AFs written in computer code by leveraging access to a limited number of evaluations for a set of objective functions. We provide the analytic expression of all discovered AFs and evaluate them on various global optimization benchmarks and hyperparameter optimization tasks. We show how FunBO identifies AFs that generalize well in and out of the training distribution of functions, thus outperforming established general-purpose AFs and achieving competitive performance against AFs that are customized to specific function types and are learned via transfer-learning algorithms.

A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e., minimizing the number of T gates that are needed to implement a given circuit. To achieve this, we develop AlphaTensor-Quantum, a method based on deep reinforcement learning that exploits the relationship between optimizing T-count and tensor decomposition. Unlike existing methods for T-count optimization, AlphaTensor-Quantum can incorporate domain-specific knowledge about quantum computation and leverage gadgets, which significantly reduces the T-count of the optimized circuits. AlphaTensor-Quantum outperforms the existing methods for T-count optimization on a set of arithmetic benchmarks (even when compared without making use of gadgets). Remarkably, it discovers an efficient algorithm akin to Karatsuba's method for multiplication in finite fields. AlphaTensor-Quantum also finds the best human-designed solutions for relevant arithmetic computations used in Shor's algorithm and for quantum chemistry simulation, thus demonstrating it can save hundreds of hours of research by optimizing relevant quantum circuits in a fully automated way., Comment: 25 pages main paper + 19 pages appendix

A stochastic diffusion process, whose mean function is a hyperbolastic curve of type I, is presented. Themain characteristics of the process are studied and the problem of maximum likelihood estimation forthe parameters of the process is considered. To this end, the firefly metaheuristic optimization algo-rithm is applied after bounding the parametric space by a stagewise procedure. Some examples basedon simulated sample paths and real data illustrate this development., Comment: 26 pages, 13 figures

Accurately charting the progress of oil production is a problem of great current interest. Oil production is widely known to be cyclical: in any given system, after it reaches its peak, a decline will begin. With this in mind, Marion King Hubbert developed his peak theory in 1956 based on the bell-shaped curve that bears his name. In the present work, we consider a stochasticmodel based on the theory of diffusion processes and associated with the Hubbert curve. The problem of the maximum likelihood estimation of the parameters for this process is also considered. Since a complex system of equations appears, with a solution that cannot be guaranteed by classical numerical procedures, we suggest the use of metaheuristic optimization algorithms such as simulated annealing and variable neighborhood search. Some strategies are suggested for bounding the space of solutions, and a description is provided for the application of the algorithms selected. In the case of the variable neighborhood search algorithm, a hybrid method is proposed in which it is combined with simulated annealing. In order to validate the theory developed here, we also carry out some studies based on simulated data and consider 2 real crude oil production scenarios from Norway and Kazakhstan., Comment: 30 pages, 5 figures

The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is introduced whose mean function is a curve of this type, concretely a transformation of the well-known Gompertz model after introducing in its expression a polynomial term. The maximum likelihood estimation of the parameters of the model is studied, and various criteria are provided for the selection of the degree of the polynomial when real situations are addressed. Finally, some simulated examples are presented., Comment: 17 pages, 28 figures

We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical inference, two procedures to find the maximum likelihood estimates of the unknown parameters are described. One is based on the resolution of the system of the critical points of the likelihood function, and the other is on the maximization of the likelihood function with the simulated annealing algorithm. A simulation study to validate the described strategies for finding the estimates is also presented, with a real application to epidemiological data. Special attention is also devoted to the first-passage-time problem of the considered diffusion process through a fixed boundary., Comment: 37 pages, 36 figures

We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main properties of the curve, such as the limit behavior, the inflection points and the threshold-crossing-time through a fixed boundary. We also present an application in population dynamics of plants based on real data. Then, we define two different birth-death processes, one with linear birth and death rates and the other with quadratic rates, and we analyze their main features. The conditions under which the processes have a mean of multi-sigmoidal logistic type and the first-passage-time problem are also discussed. Finally, with the aim of obtaining a more manageable stochastic description of the growth, we perform a scaling procedure leading to a lognormal diffusion process with mean of multi-sigmoidal logistic type. We finally conduct a detailed probabilistic analysis of this process, Comment: 28 pages, 30 figures

We consider a non homogeneous Gompertz diffusion process whose parameters are modified by generally time-dependent exogenous factors included in the infinitesimal moments. The proposed model is able to describe tumor dynamics under the effect of anti-proliferative and/or cell death-induced therapies. We assume that such therapies can modify also the infinitesimal variance of the diffusion process. An estimation procedure, based on a control group and two treated groups, is proposed to infer the model by estimating the constant parameters and the time-dependent terms. Moreover, several concatenated hypothesis tests are considered in order to confirm or reject the need to include time-dependent functions in the infinitesimal moments. Simulations are provided to evaluate the efficiency of the suggested procedures and to validate the testing hypothesis. Finally, an application to real data is considered., Comment: 44 pages, 63 figures. Includes Material Supplementary

Recently a general growth curve including the well known growth equations, such as Malthus, logistic, Bertallanfy, Gompertz, has been studied. We now propose two stochastic formulations of this growth equation. They are obtained starting from a suitable parametrization of the deterministic model, by adding an additive and multiplicative noise respectively. For these processes we focus attention on the First Passage Time from a barrier and on the First Exit Time from a region delimited by two barriers. We consider thresholds, generally time dependent, for which there exist closed-forms of the probability densities of the first passage time and of the first exit time., Comment: 25 pages, 17 figures

The momentum space associated with "tachyonic particles" proves to be rather intricate, departing very much from the ordinary dual to Minkowski space directly parametrized by space-time translations of the Poincar\'e group. In fact, although described by the constants of motion (Noether invariants) associated with space-time translations, they depend non-trivially on the parameters of the rotation subgroup. However, once the momentum space is parametrized by the Noether invariants, it behaves exactly as that of ordinary particles. On the other hand, the evolution parameter is no longer the one associated with time translation, whose Noether invariant, $P_o$, is now a basic one. Evolution takes place in a spatial direction. These facts not only make difficult the computation of the corresponding representation, but also force us to a sound revision of several traditional ingredients related to Cauchy hypersurface, scalar product and, of course, causality. After that, the theory becomes consistent and could shed new light on some special physical situations like inflation or traveling inside a black hole., Comment: 13 pages

In the not so unlikely scenario of total compromise of computers accessible to a group of users, they might be tempted to resort to human-computable paper-and-pencil cryptographic methods aided by a classic Tabula Recta, which helps to perform addition and subtraction directly with letters. But do these classic algorithms, or some new ones using the same simple tools, have any chance against computer-aided cryptanalysis? In this paper I discuss how some human-computable algorithms can indeed afford sufficient security in this situation, drawing conclusions from computer-based statistical analysis. Three kinds of algorithms are discussed: those that concentrate entropy from shared text sources, stream ciphers based on arithmetic of non-binary spaces, and hash-like algorithms that may be used to generate a password from a challenge text., Comment: 18 pages, 3 figures

In Physical Human--Robot Interaction (pHRI) grippers, humans and robots may contribute simultaneously to actions, so it is necessary to determine how to combine their commands. Control may be swapped from one to the other within certain limits, or input commands may be combined according to some criteria. The Assist-As-Needed (AAN) paradigm focuses on this second approach, as the controller is expected to provide the minimum required assistance to users. Some AAN systems rely on predicting human intention to adjust actions. However, if prediction is too hard, reactive AAN systems may weigh input commands into an emergent one. This paper proposes a novel AAN reactive control system for a robot gripper where input commands are weighted by their respective local performances. Thus, rather than minimizing tracking errors or differences to expected velocities, humans receive more help depending on their needs. The system has been tested using a gripper attached to a sensitive robot arm, which provides evaluation parameters. Tests consisted of completing an on-air planar path with both arms. After the robot gripped a person's forearm, the path and current position of the robot were displayed on a screen to provide feedback to the human. The proposed control has been compared to results without assistance and to impedance control for benchmarking. A statistical analysis of the results proves that global performance improved and tracking errors decreased for ten volunteers with the proposed controller. Besides, unlike impedance control, the proposed one does not significantly affect exerted forces, command variation, or disagreement, measured as the angular difference between human and output command. Results support that the proposed control scheme fits the AAN paradigm, although future work will require further tests for more complex environments and tasks.

Exploiting ambipolar electrical conductivity based on graphene field-effect transistors has raised enormous interest for high-frequency (HF) analog electronics. Controlling the device polarity, by biasing the graphene transistor around the vertex of the V-shaped transfer curve, enables to redesign and highly simplify conventional analog circuits, and simultaneously to seek for multifunctionalities specially in the HF domain. We present, here, new insights for the design of different HF applications such as power amplifiers, mixers, frequency multipliers, phase shifters, and modulators that specifically leverage the inherent ambipolarity of graphene-based transistors., Comment: 31 pages, 7 figures

We present some simple proofs of the well-known expressions for \[ \zeta(2k) = \sum_{m=1}^\infty \frac{1}{m^{2k}}, \qquad \beta(2k+1) = \sum_{m=0}^\infty \frac{(-1)^m}{(2m+1)^{2k+1}}, \] where $k = 1,2,3,\dots$, in terms of the Bernoulli and Euler polynomials. The computation is done using only the defining properties of these polynomials and employing telescoping series. The same method also yields integral formulas for $\zeta(2k+1)$ and $\beta(2k)$. In addition, the method also applies to series of type \[ \sum_{m\in\mathbb{Z}} \frac{1}{(2m-\mu)^s}, \qquad \sum_{m\in\mathbb{Z}} \frac{(-1)^m}{(2m+1-\mu)^s}, \] in this case using Apostol-Bernoulli and Apostol-Euler polynomials., Comment: 24 pages, to appear in "Orthogonal Polynomials and Special Functions: In Memory of Jos\'e Carlos Petronilho''

In this paper, we introduce the first learning-based planner to drive a car in dense, urban traffic using Inverse Reinforcement Learning (IRL). Our planner, DriveIRL, generates a diverse set of trajectory proposals, filters these trajectories with a lightweight and interpretable safety filter, and then uses a learned model to score each remaining trajectory. The best trajectory is then tracked by the low-level controller of our self-driving vehicle. We train our trajectory scoring model on a 500+ hour real-world dataset of expert driving demonstrations in Las Vegas within the maximum entropy IRL framework. DriveIRL's benefits include: a simple design due to only learning the trajectory scoring function, relatively interpretable features, and strong real-world performance. We validated DriveIRL on the Las Vegas Strip and demonstrated fully autonomous driving in heavy traffic, including scenarios involving cut-ins, abrupt braking by the lead vehicle, and hotel pickup/dropoff zones. Our dataset will be made public to help further research in this area.

The combination of graphene with silicon in hybrid devices has attracted attention extensively over the last decade. Most of such devices were proposed for photonics and radiofrequency applications. In this work, we present a unique technology of graphene-on-silicon heterostructures and their properties as solution-gated transistors. The graphene-on-Silicon field-effect transistors (GoSFETs) were fabricated exploiting various conformations of drain-source regions doping and channel material dimensions. The fabricated devices were electrically characterized demonstrating hybrid behavior with features specific to both graphene and silicon. Although GoSFET's transconductance and carrier's mobility were found to be lower than in conventional silicon and graphene field-effect transistors (SiFETs and GFETs), it was demonstrated that the combination of both materials within the hybrid channel contribute uniquely to the charge carrier transport. A comprehensive physics-based compact modeling was specifically developed, showing excellent agreement with the experimental data. The model is employed to rationalize the observed hybrid behavior as the theoretical results from the electrostatics and the carrier transport under a drift-diffusion approach show that graphene acts as a shield for the silicon channel, giving rise to a non-uniform potential distribution along it, especially at the subthreshold region. This graphene screening effect is shown to strongly affect the device subthreshold swing when compared against a conventional SiFET due to a non-negligible diffusion current in this operation regime.

Perelomov coherent states for equally spaced, infinite homogeneous waveguide arrays with Euclidean E(2) symmetry are defined, and a new resolution of the identity is obtained. The key point to construct this novel resolution of the identity is the fact that coherent states satisfy the Helmholtz equation (in coherent states labels), and thus every coherent state belongs to a one-parameter family uniquely determined by the Cauchy initial data of the coherent state in a one-dimensional Cauchy set. For this reason we call \textit{Cauchy coherent} states to these initial data. The novel, non-local resolution of the identity in terms of Cauchy coherent states is provided using frame theory. It is also shown that Perelomov coherent states for the Eucliean E(2) group have a simple and natural physical realization in these waveguide arrays., Comment: Latex file, 19 pages, 12 figures, references updated. Minor corrections performed. Submission to SciPost