Artificial Potential Field (APF) is one of the path planning and obstacle avoidance methods used for its simplicity and effectiveness. The goal’s attractive force and the obstacles’ repulsive forces are modeled and considered to act upon the vehicle or robot. However, in practice, the classical APF faces challenges like local minima. We propose to study several enhancements and their combinations in order to show how they can create even more efficient algorithms to overcome these challenges. Those enhancements include tangential force, inertia-inspired force, and a local minima detection (l.m.d.) and reaction scheme by adding virtual obstacles and dynamically changing coefficients. All of them keep the methods as lightweight as possible while improving the classical APF. The tangential force provides smoother paths and avoids local minima cases. The dynamic change of APF’s parameters, coupled with the addition of virtual obstacles when detecting local minima, provides an efficient way to escape them. The inertia-inspired force can be used to smooth the trajectory when only obstacles in front of the vehicle are taken into account. We defined performance metrics to assess the path completion, path quality, and processing time to compare the proposed enhancements with the base case of classical APF. We benchmarked the proposed methods in different environments for a holonomic robot and a simplified bicycle. The proposed adaptive APF with inertial force extension completed 87.5% of the tests while the classical APF completed only 43.8% of them. On the other side, tangential versions of APF reduce the path length deviation by 8% and the curvature by 20% in simple cases. The code is available on: https://github.com/Glawal/APFproject/tree/paper1.

Directed antennas offer significant energy savings, yet the neighbor-discovery phase requires nontrivial algorithms. Using graph-theoretic analysis, we establish theoretical lower and upper bounds on the time required to reach minimally connected antenna topologies. We develop a Q-learning-based (QL) neighbor-discovery algorithm and introduce two enhancements. First, we propose an adaptive mechanism that dynamically updates the exploration rate epsilon based on changes in Q-tables, enabling a principled balance between exploration and exploitation. Second, we introduce a temporal sector-pruning heuristic that penalizes and prunes unfruitful sector pairs. Experiments are performed in a custom simulator, measuring the time required to reach minimal connectivity. We compare the proposed methods against random walk and baseline QL across regular, dense (King Grid), and irregular, sparse (Random) topologies. Results show that the synergistic integration of pruning and adaptive QL reduces discovery time by about one-third relative to QL on regular and dense graphs. On sparse graphs, baseline QL fails to complete within the threshold time, while the synergistic scheme achieves at least a tenfold speed-up. The synergistic method further outperforms pruning-only QL by 30%-86% and adaptive-only QL by 7%-16% in discovery time.

Model reduction of fast-slow chemical reaction networks based on the quasi-steady state approximation fails when the fast subsystem has first integrals. We call these first integrals approximate conservation laws. In order to define fast subsystems and identify approximate conservation laws, we use ideas from tropical geometry. We prove that any approximate conservation law evolves more slowly than all the species involved in it and therefore represents a supplementary slow variable in an extended system. By elimination of some variables of the extended system, we obtain networks without approximate conservation laws, which can be reduced by standard singular perturbation methods. The field of applications of approximate conservation laws covers the quasi-equilibrium approximation, which is well known in biochemistry. We discuss reductions of slow-fast as well as multiple timescale systems. Networks with multiple timescales have hierarchical relaxation. At a given timescale, our multiple timescale reduction method defines three subsystems composed of (i) slaved fast variables satisfying algebraic equations, (ii) slow driving variables satisfying reduced ordinary differential equations, and (iii) quenched much slower variables that are constant. The algebraic equations satisfied by fast variables define chains of nested normally hyperbolic invariant manifolds. In such chains, faster manifolds are of higher dimension and contain the slower manifolds. Our reduction methods are introduced algorithmically for networks with monomial reaction rates and linear, monomial, or polynomial approximate conservation laws. We propose symbolic algorithms to reshape and rescale the networks such that geometric singular perturbation theory can be applied to them, test the applicability of the theory, and finally reduce the networks. As a proof of concept, we apply this method to a model of the TGF-beta signaling pathway.

Nowadays, literature review is a necessary task when trying to solve a given problem. However, an exhaustive literature review is very time-consuming in today’s vast literature landscape. It can take weeks, even if looking only for abstracts or surveys. Moreover, choosing a method among others, and targeting searches within relevant problem and solution domains, are not easy tasks. These are especially true for young researchers or engineers starting to work in their field. Even if surveys that provide methods used to solve a specific problem already exist, an automatic way to do it for any use case is missing, especially for those who don’t know the existing literature. Our proposed tool, SARBOLD-LLM, allows discovering and choosing among methods related to a given problem, providing additional information about their uses in the literature to derive decision-making insights, in only a few hours. The SARBOLD-LLM comprises three modules: (1: Scopus search) paper selection using a keyword selection scheme to query Scopus API; (2: Scoring and method extraction) relevancy and popularity scores calculation and solution method extraction in papers utilizing OpenAI API (GPT 3.5); (3: Analyzes) sensitivity analysis and post-analyzes which reveals trends, relevant papers and methods. Comparing the SARBOLD-LLM to manual ground truth using precision, recall, and F1-score metrics, the performance results of AI in the oncology case study are 0.68, 0.9, and 0.77, respectively. SARBOLD-LLM demonstrates successful outcomes across various domains, showcasing its robustness and effectiveness. The SARBOLD-LLM addresses engineers more than researchers, as it proposes methods and trends without adding pros and cons. It is a useful tool to select which methods to investigate first and comes as a complement to surveys. This can limit the global search and accumulation of knowledge for the end user. However, it can be used as a director or recommender for future implementation to solve a problem.

For polynomial ODE models, we introduce and discuss the concepts of exact and approximate conservation laws, which are the first integrals of the full and truncated sets of ODEs. For fast-slow systems, truncated ODEs describe the fast dynamics. We define compatibility classes as subsets of the state space, obtained by equating the conservation laws to constants. A set of conservation laws is complete when the corresponding compatibility classes contain a finite number of steady states. Complete sets of conservation laws can be used for model order reduction and for studying the multistationarity of the model. We provide algorithmic methods for computing linear, monomial, and polynomial conservation laws of polynomial ODE models and for testing their completeness. The resulting conservation laws and their completeness are either independent or dependent on the parameters. In the latter case, we provide parametric case distinctions. In particular, we propose a new method to compute polynomial conservation laws by comprehensive Gro"\bner systems and syzygies.

We discuss a method to describe the qualitative dynamics of chemical reaction networks in terms of symbolic dynamics. The method, that can be applied to mass-action reaction networks with separated timescales, uses solutions of the partial tropical equilibration problem as proxies for symbolic states. The partial tropical equilibration solutions are found algorithmically. These solutions also provide the scaling needed for slow-fast decomposition and model reduction. Any trace of the model can thus be represented as a sequence of local approximations of the full model. We illustrate the method using as case study a biochemical model of the cell cycle.

We introduce LNetReduce, a tool that simplifies linear dynamic networks. Dynamic networks are represented as digraphs labeled by integer timescale orders. Such models describe deterministic or stochastic monomolecular chemical reaction networks, but also random walks on weighted protein-protein interaction networks, spreading of infectious diseases and opinion in social networks, communication in computer networks. The reduced network is obtained by graph and label rewriting rules and reproduces the full network dynamics with good approximation at all timescales. The tool is implemented in Python with a graphical user interface. We discuss applications of LNetReduce to network design and to the study of the fundamental relation between timescales and topology in complex dynamic networks.Availability: the code, documentation and application examples are available at https://github.com/oradules/LNetReduce.

Homeostasis occurs in a biological system when some output variable remains approximately constant as one or several input parameters change over some intervals. When the variable is exactly constant, one talks about absolute concentration robustness (ACR). A dual and equally important property is multistationarity, which means that the system has multiple steady states and possible outputs, at constant parameters. We propose a new computational method based on interval techniques to find species in biochemical systems that verify homeostasis, and a similar method for testing multistationarity. We test homeostasis, ACR and multistationarity on a large collection of biochemical models from the Biomodels and DOCSS databases. The codes used in this paper are publicly available at: https://github.com/Glawal/IbexHomeo.