Satellite orbit propagation involves predicting a satellite’s future position and velocity based on initial conditions. Traditional physical models, such as SGDP4, simplify the forces that act on the satellite to achieve high computational efficiency at the cost of reduced prediction accuracy, especially over longer time intervals where error accumulates. More sophisticated models like HPOP offer improved accuracy at the cost of high prediction times, rendering them unusable for realtime long-term predictions. Recent advancements have introduced machine learning techniques to refine these predictions and reduce errors. However, they often lack an analysis of model design choices, such as input feature selection and architectural configurations. Existing models do not incorporate features related to the state of celestial bodies, such as the positions of the Moon or Sun, which can influence the satellite’s trajectory. This paper proposes a novel model that integrates such features at both the initial time and throughout the prediction interval, leveraging their potential impact on the orbit of the satellite. The model is based on a neural network architecture employing GRU layers for encoding sequential data about the celestial conditions. Our results demonstrate that the inclusion of these sequential features significantly reduces prediction errors. Additionally, we have evaluated a variety of design choices such as independent sub-models for specific spatial coordinates and time intervals, further enhancing performance. These innovations lead to substantial improvements in both short- and long-term orbit predictions, providing a more robust and accurate alternative for satellite orbit propagation. • Hybrid model integrates SGDP4 with neural networks for improved orbit predictions. • Celestial body positions included as sequences are key features to enhance accuracy. • Separate models per coordinate and time window boost overall predictive performance. • Improved long-term forecast (10h+) while matching or exceeding short-term accuracy.

P systems are non-deterministic, parallel and distributed models of computation inspired by the behaviour and structure of living cells. Spiking neural P systems synthesise the connections that exist between neurons in the human brain, using pulses as a form of transmission of information. Usually, when a spiking neural P system is defined to solve any problem, it is checked in several cases to know if it works for them. But this methodology is not sufficient to verify if the system always works in a correct way. In this work, we introduce a methodology to look for characteristics in computations of spiking neural P systems that can be used to formally verify that the model works as it is intended.

Abstract In the framework of Membrane Computing, several efficient solutions to computationally hard problems have been given. To find new borderlines between families of P systems that can solve them and the ones that cannot is an important task to tackle the P versus NP problem. Adding syntactic and/or semantic ingredients can mean passing from non-efficiency to presumed efficiency. Here, we try to get narrow frontiers, setting the stage to adapt efficient solutions from a family of P systems to another one. In order to do that, a solution to the problem is given by means of a family of tissue P systems with evolutional symport/antiport rules and cell separation with the restriction that both the left-hand side and the right-hand side of the rules have at most two objects; that is, with recognizer P systems from $${\mathcal {TSEC}}(2, 2)$$ TSEC ( 2 , 2 ) . This result improves a previous one, when 3 objects could be used in the left-hand side of the evolutional communication rules

Originally, in P systems the environment plays a passive role; that is, it can only receive objects, without having the ability to send objects to the system. Later, tissue P systems were introduced, where the cells are located in the environment in the sense that they can communicate between each other but also with the environment. In fact, a special alphabet was introduced as a way to symbolize the chemical elements available in it and that can interact with the cells. In the framework of membrane computing, all the objects of this alphabet are present in the environment with an arbitrary multiplicity at the beginning of the computation; that is, there are enough objects of this type in the environment to fire the rules that can be fired by these objects. From the computational complexity point of view, it seems to be a very strong ingredient, since it adds a virtually infinite number of objects to the system in the whole computation. In this paper, we demonstrate that the behaviour of this special alphabet can be simulated by a generation stage ruled by evolutional communication rules and/or division/separation rules, such that the ability of these systems to efficiently solve presumably hard problems is not changed if the environment does not play an active role.

Membrane computing is a massively parallel and non-deterministic bioinspired computing paradigm whose models are called P systems. Validating and testing such models is a challenge which is being overcome by developing simulators. Regardless of their heterogeneity, such simulators require to read and interpret the models to be simulated. To this end, P-Lingua is a high-level P system definition language which has been widely used in the last decade. The P-Lingua ecosystem includes not only the language, but also libraries and software tools for parsing and simulating membrane computing models. Each version of P-Lingua supported new types or variants of P systems. This leads to a shortcoming: Only a predefined list of variants can be used, thus making it difficult for researchers to study custom ones. Moreover, derivation modes cannot be user-defined, i.e, the way in which P system computations should be generated is determined by the simulation algorithm in the source code. The main contribution of this paper is a completely new design of the P-Lingua language, called P-Lingua 5, in which the user can define custom variants and derivation modes, among other improvements such as including procedural programming and simulation directives. It is worth mentioning that it has backward-compatibility with previous versions of the language. A completely new set of command-line tools is provided for parsing and simulating P-Lingua 5 files. Finally, several examples are included in this paper covering the most common P system types.

Dendrite P systems (DeP systems) are a recently introduced neural-like model of computation. They provide an alternative to the more classical spiking neural (SN) P systems. In this paper, we present the first software simulator for DeP systems, and we investigate the key features of the representation of the syntax and semantics of such systems. First, the conceptual design of a simulation algorithm is discussed. This is helpful in order to shade a light on the differences with simulators for SN P systems, and also to identify potential parallelizable parts. Second, a novel simulator implemented within the P-Lingua simulation framework is presented. Moreover, MeCoSim, a GUI tool for abstract representation of problems based on P system models has been extended to support this model. An experimental validation of this simulator is also covered.

Based on the feature and communication of neurons in animal neural systems, spiking neural P systems (SN P systems) were proposed as a kind of powerful computing model. Considering the length of axons and the information transmission speed on synapses, SN P systems with delay on synapses (SNP-DS systems) are proposed in this work. Unlike the traditional SN P systems, where all the postsynaptic neurons receive spikes at the same instant from their presynaptic neuron, the postsynaptic neurons in SNP-DS systems would receive spikes at different instants, depending on the delay time on the synapses connecting them. It is proved that the SNP-DS systems are universal as number generators. Two small universal SNP-DS systems, with standard or extended rules, are constructed to compute functions, using 56 and 36 neurons, respectively. Moreover, a simulator has been provided, in order to check the correctness of these two SNP-DS systems, thus providing an experimental validation of the universality of the systems designed.

Biological membranes play an active role in the evolution of cells over time. In the framework of Membrane Computing, P systems with active membranes capture this idea, and the possibility to increase the number of membranes during a computation. Classically, it has been considered, by using divisi on rules, inspired in the mitosis process. Initially, the membranes in these models are supposed to have an electrical polarization (positive, negative or neutral) and the semantics is minimalist, in the sense that rules are applied in parallel, but in one transition step, each membrane can be the subject of at most one rule of types communication, dissolution or division. This paper focuses on polarizationless P systems with active membranes in which membrane creation rules are considered instead of membrane division rules as a mechanism to construct an exponential workspace, expressed both in terms of number of objects and membranes, in linear time. Moreover, the minimalist semantics is considered and some complexity results are provided in this framework, allowing to tackle the P versus NP problem from a new perspective. An original frontier of the efficiency in this context is unveiled in this paper: allowing membrane creation rules to be applicable in any membrane of the system, instead of restricting them to only elementary membranes, yields a significant boost on the computational power. More precisely, only problems in P can be efficiently solved in the restricted case, while in the non-restricted case an efficient and uniform solution to a PSPACE-complete problem is provided.

Polarizationless P systems with active membranes are non-cooperative systems, that is, the left-hand side of their rules have a single object. Usually, these systems make use of division rules as a mechanism to produce an exponential workspace in linear time. Division rules are inspired by cell div ision, a process of nuclear division that occurs when a parent cell divides to produce two identical daughter cells. On the other hand, separation rules are inspired by the membrane fission process, a mechanism by which a biological membrane is split into two new ones in such a manner that the contents of the initial membrane is distributed between the new membranes. In this paper, separation rules are used instead of division rules. The computational efficiency of these models is studied and the role of the (minimal) cooperation in object evolution rules is explored from a computational complexity point of view.

Membrane computing is a computing paradigm providing a class of distributed parallel computing devices of a biochemical type whose process units represent biological membranes. In the cell-like basic model, a hierarchical membrane structure formally described by a rooted tree is considered. It is w ell known that families of such systems where the number of membranes can only decrease during a computation (for instance by dissolving membranes), can only solve in polynomial time problems in class P. P systems with active membranes is a variant where membranes play a central role in their dynamics. In the seminal version, membranes have an electrical polarization (positive, negative, or neutral) associated in any instant, and besides being dissolved, they can also replicate by using division rules. These systems are computationally universal, that is, equivalent in power to deterministic Turing machines, and computationally efficient, that is, able to solve computationally hard problems in polynomial time. If polarizations in membranes are removed and dissolution rules are forbidden, then only problems in class P can be solved in polynomial time by these systems (even in the case when division rules for non-elementary membranes are permitted). In that framework it has been shown that by considering minimal cooperation (left-hand side of such rules consists of at most two symbols) and minimal production (only one object is produced by the application of such rules) in object evolution rules, such systems provide efficient solutions to NP-complete problems. In this paper, minimal cooperation and minimal production in communication rules instead of object evolution rules is studied, and the computational efficiency of these systems is obtained in the case where division rules for non-elementary membranes are permitted.

Inspired by mitosis process and membrane fission processes, cell-like P systems with symport/antiport rules and membrane division rules or membrane separation rules have been introduced, respectively. These computation systems have two key features: the ability to have infinite copies of some objects (within an active environment) and to generate an exponential workspace in polynomial time. In this work, we extend the P-Lingua framework for simulating that kind of P systems taking into account these two features. Consequently, a new simulator has been developed and included in pLinguaCore library. The functioning of the simulator has been checked by simulating efficient solutions to SAT problem using a family of cell-like P systems with symport/antiport rules and membrane division rules or membrane separation rules. The corresponding MeCoSim based application is also provided.

P systems have been proven to be useful as modeling tools in many fields, such as Systems Biology and Ecological Modeling. For such applications, the acceleration of P system simulation is often desired, given the computational needs derived from the

Sevilla carpets have already been used to compare different solutions of the Subset Sum problem: either designed in the framework of P systems with active membranes (both in the case of membrane division and membrane creation), and in the framework of tissue-like P systems with cell division. Recently, the degree of parallelism and other descriptive complexity details have been found to be relevant when designing parallel simulators running on GPUs. We present here a new way to use the information provided by Sevilla carpets in this context, and a script that allows to generate them automatically from P-Lingua files.