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Linear programming for UAVs search path planning in livestock health monitoring
No full textInternational audienceUAV-Assisted Livestock Monitoring is a highly relevant and essential application. It involves deploying autonomous Unmanned Aerial Vehicles (UAVs) to gather remote information from various sensors and IoT devices attached to the livestock's necks. Such information includes the health status indicators of the cattle like temperature, respiration rate, images or videos of the activity, etc. The practical implementation of this application presents several challenges. One significant obstacle is the lack of accurate cattle position information. Employing the Global Positioning System (GPS) has limitations like the high cost, and the need for a reliable network connection, which may not be available in all rural areas.Even using passive tags like RFID tags is not very practical due to their limited reading distance. Thus, the imperfect knowledge of the cattle location forces the UAV to perform area exploration and cattle searches. The focus of this research work is to design a model that determines the optimal UAV search path to localize cattle. We denote this issue as UAV Cattle Search (UCS) path planning. In a previous work, we addressed the UCS problem assuming a single stationary cattle (denoted UCS-ST problem). We now extend this problem with two new assumptions : (i) a single moving cattle (UCS-SMT problem), and (ii) two moving cattle (UCS-TMT problem). For each of these problems, we elaborate a Mixed-Integer Linear Programming formulation (MILP) where the objective function is the total expected search time.Minimizing the search time is crucial for successful search missions. However, to the best of our knowledge, the literature did not focus on finding the fastest path while guaranteeing the target localization. Thus, in the conducted work, we focused on the time required for a UAV to locate a target and formulated an objective function aiming at reducing this time. We implemented the models using mathematical optimization software. Running different instances, our models find optimal solutions that guarantee accurate cattle localization while minimizing the expected search time for graphs including up to 36 vertices (UCS-ST). We have been inspired by established formulations in the literature addressing related problems such as the Travelling Salesman Problem and Optimal Search path. However, to the best of our knowledge, the exact linear formulations of our specific problems have never been proposed
When Are Two Scores Better Than One? Investigating Ensembles of Diffusion Models
No full textInternational audienceDiffusion models now generate high-quality, diverse samples, with an increasing focus on more powerful models. Although ensembling is a well-known way to improve supervised models, its application to unconditional score-based diffusion models remains largely unexplored. In this work we investigate whether it provides tangible benefits for generative modelling. We find that while ensembling the scores generally improves the score-matching loss and model likelihood, it fails to consistently enhance perceptual quality metrics such as FID on image datasets. We confirm this observation across a breadth of aggregation rules using Deep Ensembles, Monte Carlo Dropout, on CIFAR-10 and FFHQ. We attempt to explain this discrepancy by investigating possible explanations, such as the link between score estimation and image quality. We also look into tabular data through random forests, and find that one aggregation strategy outperforms the others. Finally, we provide theoretical insights into the summing of score models, which shed light not only on ensembling but also on several model composition techniques (e.g. guidance)
Code Generation via Meta-programming in Dependently Typed Proof Assistants
No full textDependently typed proof assistants offer powerful meta-programming features, which allow users to implement proof automationor compile-time code generation. This paper surveys meta-programmingframeworks in Rocq, Agda, and Lean, with seven implementations of arunning example: deriving instances for the Functor typeclass. This example is fairly simple, but realistic enough to highlight recurring difficulties with meta-programming: conceptual limitations of frameworks suchas term representation – and in particular binder representation –, meta-language expressiveness, and verifiability, as well as current limitationssuch as API completeness, learning curve, and prover state management,which could in principle be remedied. We conclude with insights regarding features an ideal meta-programming framework should provide
Morphological subphenotypes of acute pancreatitis-related acute respiratory distress syndrome
No full textInternational audienceNo abstract availabl
A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges
No full textIn this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (symmetric) nonlinear exchange terms. We propose a new and rather direct functional inequalities approach to prove the exponential decay of a relative entropy, and thus the convergence of the solution towards the stationary state selected by the total mass of the initial datum
Matrix-Free Delassus Operations: Scalable and Memory-Efficient Algorithms
No full textThe Delassus matrix, closely related to the operational-space inertia matrix, is a fundamental quantity in robotics with applications in simulation, system identification, and control. Traditional approaches compute and store this matrix explicitly, either in sparse or dense form. In this work, we depart from this convention by treating the Delassus matrix as a matrix-free operator. We derive efficient algorithms with low computational complexity that multiply the Delassus matrix or its damped inverse by an input vector or matrix. Unlike approaches based on explicit matrix construction, our method achieves a linear memory footprint, making it scalable to problems with thousands of constraints and suitable for execution on resourcelimited hardware. We implement these matrix-free operations on top of the open-source Pinocchio library and evaluate their performance against state-of-the-art methods that rely on explicit matrix computation. Our benchmarks demonstrate substantial speedups, ranging from 2x to over 400x, in contact-rich scenarios
Quantum Coherence Spaces Revisited: A von Neumann (Co)Algebraic Approach
No full textInternational audienceWe describe a categorical model of MALL (Multiplicative Additive Linear Logic) inspired by the Heisenberg-Schrödinger duality of finite-dimensional quantum theory. Proofs of formulas with positive logical polarity correspond to CPTP (completely positive trace-preserving) maps in our model, i.e. the quantum operations in the Schrödinger picture, whereas proofs of formulas with negative logical polarity correspond to CPU (completely positive unital) maps, i.e. the quantum operations in the Heisenberg picture. The mathematical development is based on noncommutative geometry and finite-dimensional von Neumann (co)algebras, which can be defined as special kinds of (co)monoid objects internal to the category of finite-dimensional operator spaces
A Floyd-Warshall Approach to Value Computation in Markov Decision Processes (Extended Version)
No full textInternational audienceValue and policy iteration are classical algorithms to maximize the average discounted reward of an MDP. They rely on a breadth-first exploration strategy in the future of each state to update its value and possibly change the action policy at this state. This paper revisits this paradigm and examines a depth-first search strategy. It reformulates the average reward computation as an integral over (future) paths that is better expressed in the formalism of weighted automata. Policy evaluation can then be solved by a Floyd-Warshall algorithm, which gathers at once the rewards along possibly infinite runs. This reformulation opens the way to new approximation schemes for the value function. The same formalism also gives access to other quantities of interest, as the gradient of the average reward with respect to model or policy parameters, or the variance of the reward. The behaviors and performances of this value estimation scheme are illustrated on several benchmarks