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Unmanned Aerial Vehicles (UAVs) are increasingly adopted in modern communication networks. However, challenges in decision-making and digital modeling continue to impede their rapid advancement. Reinforcement Learning (RL) algorithms face limitations such as low sample efficiency and limited data versatility, further magnified in UAV communication scenarios. Moreover, Digital Twin (DT) modeling introduces substantial decision-making and data management complexities. RL models, often integrated into DT frameworks, require extensive training data to achieve accurate predictions. In contrast to traditional approaches that focus on class boundaries, Diffusion Models (DMs), a new class of generative AI, learn the underlying probability distribution from the training data and can generate trustworthy new patterns based on this learned distribution. This paper explores the integration of DMs with RL and DT to effectively address these challenges. By combining the data generation capabilities of DMs with the decision-making framework of RL and the modeling accuracy of DT, the integration improves the adaptability and real-time performance of UAV communication. Moreover, the study shows how DMs can alleviate data scarcity, improve policy networks, and optimize dynamic modeling, providing a robust solution for complex UAV communication scenarios., Comment: 7 pages, 2 figures

In this paper we investigate an optimal control problem involving a toy model for the protection on a crop field. Precisely, we consider a protection on a crop field and we want to place intervention zones represented by a control, in order to maximise the protection on the field during a given period. Using a relaxation method, we prove that there exists a control which maximises the protection and, moreover, it must be a bang-bang control. Furthermore, with additional assumptions on the crop field geometry, some results on the shape of the optimal intervention are proved using comparison results for elliptic equations via Schwarz and Steiner symmetrizations. Finally, some numerical simulations are performed in order to illustrate those results., Comment: 21 pages

Rapid advances in Machine Learning (ML) have triggered new trends in Autonomous Vehicles (AVs). ML algorithms play a crucial role in interpreting sensor data, predicting potential hazards, and optimizing navigation strategies. However, achieving full autonomy in cluttered and complex situations, such as intricate intersections, diverse sceneries, varied trajectories, and complex missions, is still challenging, and the cost of data labeling remains a significant bottleneck. The adaptability and robustness of humans in complex scenarios motivate the inclusion of humans in the ML process, leveraging their creativity, ethical power, and emotional intelligence to improve ML effectiveness. The scientific community knows this approach as Human-In-The-Loop Machine Learning (HITL-ML). Towards safe and ethical autonomy, we present a review of HITL-ML for AVs, focusing on Curriculum Learning (CL), Human-In-The-Loop Reinforcement Learning (HITL-RL), Active Learning (AL), and ethical principles. In CL, human experts systematically train ML models by starting with simple tasks and gradually progressing to more difficult ones. HITL-RL significantly enhances the RL process by incorporating human input through techniques like reward shaping, action injection, and interactive learning. AL streamlines the annotation process by targeting specific instances that need to be labeled with human oversight, reducing the overall time and cost associated with training. Ethical principles must be embedded in AVs to align their behavior with societal values and norms. In addition, we provide insights and specify future research directions., Comment: 19 pages, 4 figures

Unmanned Aerial Vehicles (UAVs) offer agile, secure and efficient solutions for communication relay networks. However, their modeling and control are challenging, and the mismatch between simulations and actual conditions limits real-world deployment. Moreover, improving situational awareness is essential. Several studies proposed integrating the operation of UAVs with immersive digital technologies such as Digital Twin (DT) and Extended Reality (XR) to overcome these challenges. This paper provides a comprehensive overview of the latest research and developments involving immersive digital technologies for UAVs. We explore the use of Machine Learning (ML) techniques, particularly Deep Reinforcement Learning (DRL), to improve the capabilities of DT for UAV systems. We provide discussion, identify key research gaps, and propose countermeasures based on Generative AI (GAI), emphasizing the significant role of AI in advancing DT technology for UAVs. Furthermore, we review the literature, provide discussion, and examine how the XR technology can transform UAV operations with the support of GAI, and explore its practical challenges. Finally, we propose future research directions to further develop the application of immersive digital technologies for UAV operation., Comment: 12 pages

Semantic segmentation is a fundamental computer vision task with a vast number of applications. State of the art methods increasingly rely on deep learning models, known to incorrectly estimate uncertainty and being overconfident in predictions, especially in data not seen during training. This is particularly problematic in semantic segmentation due to inherent class imbalance. Popular uncertainty quantification approaches are task-agnostic and fail to leverage spatial pixel correlations in uncertainty estimates, crucial in this task. In this work, a novel training methodology specifically designed for semantic segmentation is presented. Training samples are weighted by instance-wise uncertainty masks computed by an ensemble. This is shown to increase performance on minority classes, boost model generalization and robustness to domain-shift when compared to using the inverse of class proportions or no class weights at all. This method addresses the challenges of class imbalance and uncertainty estimation in semantic segmentation, potentially enhancing model performance and reliability across various applications.

We review the book of Ruben Aldrovandi and Jose Geraldo Pereira about Teleparallel Gravity. Teleparallel Gravity is an alternative to General Relativity to describe the gravitational interaction. The difference between General Relativity and Teleparallel Gravity is the fact that General Relativity associates the curvature to the gravitational interaction, whereas in the Teleparallel Gravity the mathematical object associated to gravitational field is the torsion, whose field is the so called Weintzenb\"ock connection. We discuss briefly the advantages of Teleparallel Gravity over General Relativity as well as Weintzenb\"ock connection properties.

Unmanned Aerial Vehicle (UAV) swarms play an effective role in timely data collection from ground sensors in remote and hostile areas. Optimizing the collective behavior of swarms can improve data collection performance. This paper puts forth a new mean field flight resource allocation optimization to minimize age of information (AoI) of sensory data, where balancing the trade-off between the UAVs movements and AoI is formulated as a mean field game (MFG). The MFG optimization yields an expansive solution space encompassing continuous state and action, resulting in significant computational complexity. To address practical situations, we propose, a new mean field hybrid proximal policy optimization (MF-HPPO) scheme to minimize the average AoI by optimizing the UAV's trajectories and data collection scheduling of the ground sensors given mixed continuous and discrete actions. Furthermore, a long short term memory (LSTM) is leveraged in MF-HPPO to predict the time-varying network state and stabilize the training. Numerical results demonstrate that the proposed MF-HPPO reduces the average AoI by up to 45 percent and 57 percent in the considered simulation setting, as compared to multi-agent deep Q-learning (MADQN) method and non-learning random algorithm, respectively., Comment: 13 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:2312.09953

When acquiring an image of a paper document, the image printed on the back page sometimes shows through. The mixture of the front- and back-page images thus obtained is markedly nonlinear, and thus constitutes a good real-life test case for nonlinear blind source separation. This paper addresses a difficult version of this problem, corresponding to the use of "onion skin" paper, which results in a relatively strong nonlinearity of the mixture, which becomes close to singular in the lighter regions of the images. The separation is achieved through the MISEP technique, which is an extension of the well known INFOMAX method. The separation results are assessed with objective quality measures. They show an improvement over the results obtained with linear separation, but have room for further improvement.

This work is devoted to the mathematical study of an optimization problem regarding control strategies of mosquito population in a heterogeneous environment. Mosquitoes are well known to be vectors of diseases, but, in some cases, they have a reduced vector capacity when carrying the endosymbiotic bacterium Wolbachia. We consider a mathematical model of a replacement strategy, consisting in rearing and releasing Wolbachia-infected mosquitoes to replace the wild population. We investigate the question of optimizing the release protocol to have the most effective replacement when the environment is heterogeneous. In other words we focus on the question: where to release, given an inhomogeneous environment, in order to maximize the replacement across the domain. To do so, we consider a simple scalar model in which we assume that the carrying capacity is space dependent. Then, we investigate the existence of an optimal release profile and prove some interesting properties. In particular, neglecting the mobility of mosquitoes and under some assumptions on the biological parameters, we characterize the optimal releasing strategy for a short time horizon, and provide a way to reduce to a one-dimensional optimization problem the case of a long time horizon. Our theoretical results are illustrated with several numerical simulations.

In recent in vitro experiments on co-culture between breast tumour spheroids and activated immune cells, it was observed that the introduction of the stress hormone cortisol resulted in a decreased immune cell infiltration into the spheroids. Moreover, the presence of cortisol deregulated the normal levels of the pro- and anti-inflammatory cytokines IFN-{\gamma} and IL-10. We present an individual-based model to explore the interaction dynamics between tumour and immune cells under psychological stress conditions. With our model, we explore the processes underlying the emergence of different levels of immune infiltration, with particular focus on the biological mechanisms regulated by IFN-{\gamma} and IL-10. The set-up of numerical simulations is defined to mimic the scenarios considered in the experimental study. Similarly to the experimental quantitative analysis, we compute a score that quantifies the level of immune cell infiltration into the tumour. The results of numerical simulations indicate that the motility of immune cells, their capability to infiltrate through tumour cells, their growth rate and the interplay between these cell parameters can affect the level of immune cell infiltration in different ways. Ultimately, numerical simulations of this model support a deeper understanding of the impact of biological stress-induced mechanisms on immune infiltration.

This paper is devoted to the study of optimal release strategies to control vector-borne diseases, such as dengue, Zika, chikungunya and malaria. Two techniques are considered: the sterile insect one (SIT), which consists in releasing sterilized males among wild vectors in order to perturb their reproduction, and the Wolbachia one (presently used mainly for mosquitoes), which consists in releasing vectors, that are infected with a bacterium limiting their vector capacity, in order to replace the wild population by one with reduced vector capacity. In each case, the time dynamics of the vector population is modeled by a system of ordinary differential equations in which the releases are represented by linear combinations of Dirac measures with positive coefficients determining their intensity. We introduce optimal control problems that we solve numerically using ad-hoc algorithms, based on writing first-order optimality conditions characterizing the best combination of Dirac measures. We then discuss the results obtained, focusing in particular on the complexity and efficiency of optimal controls and comparing the strategies obtained. Mathematical modeling can help testing a great number of scenarios that are potentially interesting in future interventions (even those that are orthogonal to the present strategies) but that would be hard, costly or even impossible to test in the field in present conditions.

This work concerns feedback global stabilization of the sterile insect technique dynamics. The Sterile Insect Technique (SIT) is presently one of the most ecological methods for controlling insect pests responsible for crop destruction and disease transmission worldwide. This technique consists in releasing sterile males among the insect pest population, the aim being to reduce fertility and, consequently, reduce significantly the wild insect population after a few generations.In this work, we study the global stabilization of a pest population at extinction equilibrium by the SIT method and construct explicit feedback laws that stabilize the model. Numerical simulations show the efficiency of our feedback laws.

We study the hypothesis of deformation of the invariance of Lorentz transformations produced by the introduction of a universal minimum velocity relative to a preferred frame. Our goal with this job is to apply this hypothesis to superfluids and study its consequences relating the minimum velocity to the idea of a fluid, with superfluid properties. In previous works we related the minimum velocity to the cosmological constant and even to cosmic inflation. Soon we could generate a hypothetical superfluid capable of modeling with characteristics of a cosmological fluid with dark energy properties. The first excited state of this universal superfluid would be a preferred frame from which all other excited states are observed and then we would have a preferred frame $S_{V}$ associated with the critical Landau velocity, thus implying that the universal minimum velocity coincides with the critical Landau velocity, and the objects observed by the preferred frame are excited states of the superfluid. This coincidence between the concepts of minimum velocity and Landau's critical velocity makes Landau's critical velocity a type of limit velocity, modifying the usual causal structure of restricted relativity. Formulating the phenomena in this preferred frame would have the advantage of providing a simple explanation for astrophysical and cosmological phenomena linked to a causal structure, which emerges from this construction and is very similar to causal structures linked to Gordon geometry and acoustic tachyons. We build a deformed relativistic Lagrangian, demonstrate its relation with a K-essence Lagrangian and calculate the quantities associated with that Lagrangian. We also studied an irrotational fluid and verified the role of enthalpy associated with the minimum velocity structure., Comment: 33 pages, 4 figures

Glucose is a primary energy source for cancer cells. Several lines of evidence support the idea that monocarboxylate transporters, such as MCT1, elicit metabolic reprogramming of cancer cells in glucose-poor environments, allowing them to reuse lactate, a byproduct of glucose metabolism, as an alternative energy source with serious consequences for disease progression. We employ a synergistic experimental and mathematical modelling approach to explore the evolutionary processes at the root of cancer cell adaptation to glucose deprivation, with particular focus on the mechanisms underlying the increase in MCT1 expression observed in glucose-deprived aggressive cancer cells. Data from in vitro experiments on breast cancer cells are used to inform and calibrate a mathematical model that comprises a partial integro-differential equation for the dynamics of a population of cancer cells structured by the level of MCT1 expression. Analytical and numerical results of this model suggest that environment-induced changes in MCT1 expression mediated by lactate-associated signalling pathways enable a prompt adaptive response of glucose-deprived cancer cells, whilst fluctuations in MCT1 expression due to epigenetic changes create the substrate for environmental selection to act upon, speeding up the selective sweep underlying cancer cell adaptation to glucose deprivation, and may constitute a long-term bet-hedging mechanism., Comment: Main manuscript: 14 pages, 4 figures. Supplementary material: 29 pages, 11 figures, 2 tables

In this paper, we investigate an initial-boundary-value problem of a reaction-diffusion equation in a bounded domain with a Robin boundary condition and introduce some particular parameters to consider the non-zero flux on the boundary. This problem arises in the study of mosquito populations under the intervention of the population replacement method, where the boundary condition takes into account the inflow and outflow of individuals through the boundary. Using phase-plane analysis, the present paper studies the existence and properties of non-constant steady-state solutions depending on several parameters. Then, we use the principle of linearized stability to prove some sufficient conditions for their stability. We show that the long-time efficiency of this control method depends strongly on the size of the treated zone and the migration rate. To illustrate these theoretical results, we provide some numerical simulations in the framework of mosquito population control.

We present a spatial hybrid discrete-continuum modelling framework for the interaction dynamics between tumour cells and cytotoxic T cells, which play a pivotal role in the immune response against tumours. In this framework, tumour cells and T cells are modelled as individual agents while chemokines that drive the chemotactic movement of T cells towards the tumour are modelled as a continuum. We formally derive the continuum counterpart of this model, which is given by a coupled system that comprises an integro-differential equation for the density of tumour cells, a partial differential equation for the density of T cells, and a partial differential equation for the concentration of chemokines. We report on computational results of the hybrid model and show that there is an excellent quantitative agreement between them and numerical solutions of the corresponding continuum model. These results shed light on the mechanisms that underlie the emergence of different levels of infiltration of T cells into the tumour and elucidate how T-cell infiltration shapes anti-tumour immune response. Moreover, to present a proof of concept for the idea that, exploiting the computational efficiency of the continuum model, extensive numerical simulations could be carried out, we investigate the impact of T-cell infiltration on the response of tumour cells to different types of anti-cancer immunotherapy.

We present an individual-based model for the coevolutionary dynamics between CD8+ cytotoxic T lymphocytes (CTLs) and tumour cells. In this model, every cell is viewed as an individual agent whose phenotypic state is modelled by a discrete variable. For tumour cells this variable represents a parameterisation of the antigen expression profiles, while for CTLs it represents a parameterisation of the target antigens of T-cell receptors (TCRs). We formally derive the deterministic continuum limit of this individual-based model, which comprises a non-local partial differential equation for the phenotype distribution of tumour cells coupled with an integro-differential equation for the phenotype distribution of CTLs. The biologically relevant homogeneous steady-state solutions of the continuum model equations are found. The linear-stability analysis of these steady-state solutions is then carried out in order to identify possible conditions on the model parameters that may lead to different outcomes of immune competition and to the emergence of patterns of phenotypic coevolution between tumour cells and CTLs. We report on computational results of the individual-based model, and show that there is a good agreement between them and analytical and numerical results of the continuum model. These results shed light on the way in which different parameters affect the coevolutionary dynamics between tumour cells and CTLs. Moreover, they support the idea that TCR-tumour antigen binding affinity may be a good intervention target for immunotherapy and offer a theoretical basis for the development of anti-cancer therapy aiming at engineering TCRs so as to shape their affinity for cancer targets.

Intra-tumour heterogeneity (ITH) has a strong impact on the efficacy of the immune response against solid tumours. The number of sub-populations of cancer cells expressing different antigens and the percentage of immunogenic cells (i.e. tumour cells that are effectively targeted by immune cells) in a tumour are both expressions of ITH. Here, we present a spatially explicit stochastic individual-based model of the interaction dynamics between tumour cells and CD8+ T cells, which makes it possible to dissect out the specific impact of these two expressions of ITH on anti-tumour immune response. The set-up of numerical simulations of the model is defined so as to mimic scenarios considered in previous experimental studies. Moreover, the ability of the model to qualitatively reproduce experimental observations of successful and unsuccessful immune surveillance is demonstrated. First, the results of numerical simulations of this model indicate that the presence of a larger number of sub-populations of tumour cells that express different antigens is associated with a reduced ability of CD8+ T cells to mount an effective anti-tumour immune response. Second, the presence of a larger percentage of tumour cells that are not effectively targeted by CD8+ T cells may reduce the effectiveness of anti-tumour immunity. Ultimately, the mathematical model presented in this paper may provide a framework to help biologists and clinicians to better understand the mechanisms that are responsible for the emergence of different outcomes of immunotherapy.

In order to prevent the propagation of human diseases transmitted by mosquitoes (such as dengue or zika), one possible solution is to act directly on the mosquito population. In this work, we consider an invasive species (the mosquitoes) and we study two strategies to eradicate the population in the whole space by a local intervention. The dynamics of the population is modeled through a bistable reaction diffusion equation in an one dimensional setting and both strategies are based on the same idea : we act on a moving interval. The action of the first strategy is to kill as many individuals as we can in this moving interval. The action of the second strategy is to release sterile males in this moving interval. For both strategies, we manage to generate traveling waves that propagate in the opposite direction relative to the one of the natural invasive traveling wave. These cases correspond to succeeding in eradicating the invasive species. Furthermore, for the first strategy, we fully characterize the minimal size of the interval. All the results are illustrated by numerical simulations.

Mosquitoes are responsible for the transmission of many diseases such as dengue fever, zika or chigungunya. One way to control the spread of these diseases is to use the sterile insect technique (SIT), which consists in a massive release of sterilized male mosquitoes. This strategy aims at reducing the total population over time, and has the advantage being specific to the targeted species, unlike the use of pesticides.In this article, we study the optimal release strategies in order to maximize the efficiency of this technique.We consider simplified models that describe the dynamics of eggs, males, females and sterile males in order to optimize the release protocol. We determine in a precise way optimal strategies, which allows us to tackle numerically the underlying optimization problem in a very simple way. We also present some numerical simulations to illustrate our results.

We formulate a general SEIR epidemic model in a heterogenous population characterized by some trait in a discrete or continuous subset of a space R d. The incubation and recovery rates governing the evolution of each homogenous subpopulation depend upon this trait, and no restriction is assumed on the contact matrix that defines the probability for an individual of a given trait to be infected by an individual with another trait. Our goal is to derive and study the final size equation fulfilled by the limit distribution of the population. We show that this limit exists and satisfies the final size equation. The main contribution is to prove the uniqueness of this solution among the distributions smaller than the initial condition. We also establish that the dominant eigenvalue of the next-generation operator (whose initial value is equal to the basic reproduction number) decreases along every trajectory until a limit smaller than 1. The results are shown to remain valid in presence of diffusion term. They generalize previous works corresponding to finite number of traits (including metapopulation models) or to rank 1 contact matrix (modeling e.g. susceptibility or infectivity presenting heterogeneity independently of one another).

Motivated by experimental observations in 3D/organoid cultures derived from glioblastoma, we develop a mathematical model where tumour aggregate formation is obtained as the result of nutrient-limited cell proliferation coupled with chemotaxis-based cell movement. The introduction of a chemotherapeutic treatment induces mechanical changes at the cell level, with cells undergoing a transition from rigid bodies to semi-elastic entities. We analyse the influence of these individual mechanical changes on the properties of the aggregates obtained at the population level by introducing a nonlinear volume-filling chemotactic system of partial differential equations. The elastic properties of the cells are taken into account through the so-called squeezing probability, which allows us to change the packing capacity of the aggregates, depending on the concentration of the treatment in the extracellular microenvironment. We explore two scenarios for the effect of the treatment: firstly, the treatment acts only on the mechanical properties of the cells and, secondly, we assume it also prevents cell proliferation. A linear stability analysis enables us to study the ability of the system to create patterns. We provide numerical simulations in 1D and 2D that illustrate the shrinking of the aggregates due to the presence of the treatment.

The sterile insect technique consists in massive release of sterilized males in the aim to reduce the size of mosquitoes population or even eradicate it. In this work, we investigate the feasability of using the sterile insect technique as a barrier against reinvasion. More precisely, we provide some numerical simulations and mathematical results showing that performing the sterile insect technique on a band large enough may stop reinvasion.

Vector control plays a central role in the fight against vector-borne diseases and, in particular, arboviruses. The use of the endosymbiotic bacterium Wolbachia has proven effective in preventing the transmission of some of these viruses between mosquitoes and humans, making it a promising control tool. The Incompatible Insect Technique (IIT) consists in replacing the wild population by a population carrying the aforementioned bacterium, thereby preventing outbreaks of the associated vector-borne diseases. In this work, we consider a two species model incorporating both Wolbachia infected and wild mosquitoes. Our system can be controlled thanks to a term representing an artificial introduction of Wolbachia-infected mosquitoes. Under the assumption that the birth rate of mosquitoes is high, we may reduce the model to a simpler one on the proportion of infected mosquitoes. We investigate minimal cost-time strategies to achieve a population replacement both analytically and numerically for the simplified 1D model and only numerically for the full 2D system

In this article, we consider a simplified model of time dynamics for a mosquito population subject to the artificial introduction of {\itshape Wolbachia}-infected mosquitoes, in order to fight arboviruses transmission.Indeed, it has been observed that when some mosquito populations are infected by some {\itshape Wolbachia} bacteria, various reproductive alterations are induced in mosquitoes, including cytoplasmic incompatibility. Some of these {\itshape Wolbachia} bacteria greatly reduce the ability of insects to become infected with viruses such as the dengue ones, cutting down their vector competence and thus effectively stopping local dengue transmission.The behavior of infected and uninfected mosquitoes is assumed to be driven by a compartmental system enriched with the presence of an internal control source term standing for releases of infected mosquitoes, distributed in time. We model and design an optimal releasing control strategy with the help of a least square problem. In a nutshell, one wants to minimize the number of uninfected mosquitoes at a given horizon of time, under some relevant biological constraints. We derive properties of optimal controls, highlight a limit problem providing useful asymptotic properties of optimal controls. We numerically illustrate the relevance of our approach.

In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of vector, \textit{Aedes} mosquitoes in this case. Among possible actions, two techniques consist in releasing mosquitoes to reduce the size of the population (Sterile Insect Technique) or in replacing the wild population by a population carrying a bacteria, called \textit{Wolbachia}, blocking the transmission of viruses from mosquitoes to human. This paper is concerned with the question of optimizing the release protocol for these two strategies with the aim of getting as close as possible to the objectives. Starting from a mathematical model describing the dynamics of the population, we include the control function and introduce the cost functional for both \textit{population replacement} and \textit{Sterile Insect Technique} problems. Next, we establish some properties of the optimal control and illustrate them with some numerical simulations.