On the Complexity of Quadratization for Polynomial Differential Equations

Chemical reaction networks (CRNs) are a standard formalism used in chemistry and biology to reason about the dynamics of molecular interaction networks. In their interpretation by ordinary differential equations, CRNs provide a Turing-complete model of analog computattion, in the sense that any computable function over the reals can be computed by a finite number of molecular species with a continuous CRN which approximates the result of that function in one of its components in arbitrary precision. The proof of that result is based on a previous result of Bournez et al. on the Turing-completeness of polyno-mial ordinary differential equations with polynomial initial conditions (PIVP). It uses an encoding of real variables by two non-negative variables for concentrations, and a transformation to an equivalent quadratic PIVP (i.e. with degrees at most 2) for restricting ourselves to at most bimolecular reactions. In this paper, we study the theoretical and practical complexities of the quadratic transformation. We show that both problems of minimizing either the number of variables (i.e., molecular species) or the number of monomials (i.e. elementary reactions) in a quadratic transformation of a PIVP are NP-hard. We present an encoding of those problems in MAX-SAT and show the practical complexity of this algorithm on a benchmark of quadratization problems inspired from CRN design problems

Effects of oral capsaicinoids and capsinoids supplementation on resistance and high intensity interval training: A systematic review of randomized controlled trials

Oral capsaicinoids and capsinoids supplementation has been studied recently for a plausible ergogenic impact on sports performance. However, non-aggregated literature has focused on the impact of this substances in healthy humans’ performance. The aim of the present systematic review was to explore the effects of capsaicinoids and capsinoids on resistance training (RT) and HIIT exercise. Studies searches were performed in the PubMed/MEDLINE, Scopus and Web of Science electronic databases. Studies where healthy subjects consumed capsaicinoids or capsinoids acutely or chronically compared to placebo before a RT or HIIT intervention were included. The methodological quality of the included studies was assessed with PEDro checklist. A total of 7 excellent-good quality placebo-controlled trials (i.e., 5 RT and 2 HIIT experiments) were included. The most prevalent protocol used capsaicin (i.e., 6 capsacin and 1 capsiate studies) and acute (i.e., 5 of 7 interventions) supplementation designs. Positive effects were only noted for capsaicin in repetitions until failure (+14.4 to +21.7%), total weight lifted (+13.0 to +23.3%), perceived effort (-6.4%), fatigue index (+15.0%) and peak torque (+6.1%) compared to placebo. Neuromuscular HIIT variables (e.g., total and medium sprint time) were not highly affected by capsaicin except the time to reach 90% VO2 peak (+61.2%) and the number of efforts performed (+14.7%). Collectively, our findings suggest a positive effect of 12 mg of capsaicin on strength endurance, total weight lifted and perceived effort variables in healthy males after acute (i.e., 45 minutes pre-exercise) supplementation

Hybrid Rules with Well-Founded Semantics

A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive negation for logic programs. Hybrid rules are normal clauses extended with constraints in the bodies; constraints are certain formulae in the language of the external theory. A hybrid program is a pair of a set of hybrid rules and an external theory. Instances of the framework are obtained by specifying the class of external theories, and the class of constraints. An example instance is integration of (non-disjunctive) Datalog with ontologies formalized as description logics. The paper defines a declarative semantics of hybrid programs and a goal-driven formal operational semantics. The latter can be seen as a generalization of SLS-resolution. It provides a basis for hybrid implementations combining Prolog with constraint solvers. Soundness of the operational semantics is proven. Sufficient conditions for decidability of the declarative semantics, and for completeness of the operational semantics are given

Trend-based analysis of a population model of the AKAP scaffold protein

We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system

Dietary supplementation habits in international natural bodybuilders during pre-competition

Bodybuilding is characterized by high-rates of sport supplementation. This is the first study to compare the supplementation patterns of winners (WB) and non-winners (NWB) among international natural bodybuilders during contest preparation. Fifty-six natural bodybuilders (5 women) (age = 28.85 ± 8.03 years; final body mass = 71.50 ± 10.28 kg), 19 WB (athletes who had achieved victory in an official natural bodybuilding championship at least once) and 37 NWB (athletes who never achieved victory), from 18 countries (55.36% from Spain) responded to this cross-sectional online survey related to their nutritional habits, strategies and supplementation practices. WB were significantly older (p = 0.024), completed more competitive seasons (p = 0.027) and participated in more competitions in the last contest year (p = 0.011). There were no significant differences between WB and NWB for years training for bodybuilding (p = 0.055), weeks of dieting for competition (p = 0.392), and body weight at the start (p = 0.553) and end (p = 0.330) of the season. Beverage and supplement consumption, purchasing patterns, and information sources did not differ between groups (p > 0.05). In conclusion, natural bodybuilding WB tended to be older and had more competitive experience, but shared similar supplementation protocols to NWB. Athletes’ supplementation patterns were influenced by different sources of information. However, these natural bodybuilders mainly purchased their supplements through the internet without guidance from a coach or dietitian

Synthesis, electrochemical and photochromic behaviour of a series of (1,4-dithiafulven-6-yl)substituted 3H-naphtho[2,1-b]pyran derivatives

The synthesis and electrochemical and photochromic properties of new 3,3-diphenyl-8-(1,4-dithiafulven-6-yl)-[3H]-naphtho[2,1-b]pyran derivatives containing differently substituted dithiafulvenyl units are described. An example of electrochemical dimerization is shown which gives access to electroactive bichromophoric systems. Such systems could allow the study of the interplay of photochromic and electrochemical properties

Reversibility in Chemical Reactions

open access bookIn this chapter we give an overview of techniques for the modelling and reasoning about reversibility of systems, including outof- causal-order reversibility, as it appears in chemical reactions. We consider the autoprotolysis of water reaction, and model it with the Calculus of Covalent Bonding, the Bonding Calculus, and Reversing Petri Nets. This exercise demonstrates that the formalisms, developed for expressing advanced forms of reversibility, are able to model autoprotolysis of water very accurately. Characteristics and expressiveness of the three formalisms are discussed and illustrated

Generating Random Logic Programs Using Constraint Programming

Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs, experimental evaluations are limited to only a few programs. Existing methods to generate random logic programs are limited to propositional programs and often impose stringent syntactic restrictions. We present a novel approach to generating random logic programs and random probabilistic logic programs using constraint programming, introducing a new constraint to control the independence structure of the underlying probability distribution. We also provide a combinatorial argument for the correctness of the model, show how the model scales with parameter values, and use the model to compare probabilistic inference algorithms across a range of synthetic problems. Our model allows inference algorithm developers to evaluate and compare the algorithms across a wide range of instances, providing a detailed picture of their (comparative) strengths and weaknesses.Comment: This is an extended version of the paper published in CP 202