Robert Grosseteste: the geometry to solve the complexity of the world

Robert Grosseteste: the geometry to solve the complexity of the world, by Amelia Carolina Sparavigna, Politecnico di Torino, Department of Applied Science and Technology. Italy Abstract: Robert Grosseteste, an English philosopher and scientist, Bishop of Lincoln, is considered as the founder of the scientific thought in medieval Oxford. During the beginning of the XIII century he wrote several scientific papers concerning light and its propagation, where he based the discussion of some phenomena on the use of geometry. Here we will translate and discuss one of his scientific treatises concerning light, entitled De Lineis, Angulis et Figuris, seu Fractionibus et Reflexionibus Radiorum. Since to Grosseteste, the propagation of light had the main role in the creation of the world, the use of its geometry becomes a method to solve the complexity of the physical world. Here we will find an interesting text, where phenomena concerning the intensity of reflected and refracted light seem well-posed, even when compared with the Fresnel theor

On Frequency LTL in Probabilistic Systems

We study frequency linear-time temporal logic (fLTL) which extends the linear-time temporal logic (LTL) with a path operator $G^p$ expressing that on a path, certain formula holds with at least a given frequency p, thus relaxing the semantics of the usual G operator of LTL. Such logic is particularly useful in probabilistic systems, where some undesirable events such as random failures may occur and are acceptable if they are rare enough. Frequency-related extensions of LTL have been previously studied by several authors, where mostly the logic is equipped with an extended "until" and "globally" operator, leading to undecidability of most interesting problems. For the variant we study, we are able to establish fundamental decidability results. We show that for Markov chains, the problem of computing the probability with which a given fLTL formula holds has the same complexity as the analogous problem for LTL. We also show that for Markov decision processes the problem becomes more delicate, but when restricting the frequency bound $p$ to be 1 and negations not to be outside any $G^p$ operator, we can compute the maximum probability of satisfying the fLTL formula. This can be again performed with the same time complexity as for the ordinary LTL formulas.Comment: A paper presented at CONCUR 2015, with appendi

Solving large-scale linear circuit problems via convex optimization

A broad class of problems in circuits, electromagnetics, and optics can be expressed as finding some parameters of a linear system with a specific type. This paper is concerned with studying this type of circuit using the available control techniques. It is shown that the underlying problem can be recast as a rank minimization problem that is NP-hard in general. In order to circumvent this difficulty, the circuit problem is slightly modified so that the resulting optimization becomes convex. This interesting result is achieved at the cost of complicating the structure of the circuit, which introduces a trade-off between the design simplicity and the implementation complexity. When it is strictly required to solve the original circuit problem, the elegant structure of the proposed rank minimization problem allows for employing a celebrated heuristic method to solve it efficiently

Graph editing problems with extended regularity constraints

© 2017 Graph editing problems offer an interesting perspective on sub- and supergraph identification problems for a large variety of target properties. They have also attracted significant attention in recent years, particularly in the area of parameterized complexity as the problems have rich parameter ecologies. In this paper we examine generalisations of the notion of editing a graph to obtain a regular subgraph. In particular we extend the notion of regularity to include two variants of edge-regularity along with the unifying constraint of strong regularity. We present a number of results, with the central observation that these problems retain the general complexity profile of their regularity-based inspiration: when the number of edits k and the maximum degree r are taken together as a combined parameter, the problems are tractable (i.e. in FPT), but are otherwise intractable. We also examine variants of the basic editing to obtain a regular subgraph problem from the perspective of parameterizing by the treewidth of the input graph. In this case the treewidth of the input graph essentially becomes a limiting parameter on the natural k+r parameterization

Robert Grosseteste and his Treatise on Lines, Angles and Figures of the Propagation of Light

Robert Grosseteste, an English philosopher and scientist, Bishop of Lincoln, is considered as the founder of the scientific thought in medieval Oxford. During the beginning of the XIII century he wrote several scientific papers concerning light and its propagation, where he based the description of some phenomena on the use of geometry. Here we will translate and discuss one of his scientific treatises concerning light, which is entitled De Lineis, Angulis et Figuris, seu Fractionibus et Reflexionibus Radiorum. Since to Grosseteste, the propagation of light had the main role in the creation of the world, the use of its geometry becomes a method to solve the complexity of the physical world. However, besides the use of geometry, we will find in this interesting text the description of some phenomena concerning the intensity of reflected and refracted light, which seems well-posed, even when compared with the modern Fresnel theory

Computational complexity of impact size estimation forspreading processes on networks

Spreading processes on networks are often analyzed to understand how the outcome of the process (e.g. the number of affected nodes) depends on structural properties of the underlying network. Most available results are ensemble averages over certain interesting graph classes such as random graphs or graphs with a particular degree distributions. In this paper, we focus instead on determining the expected spreading size and the probability of large spreadings for a single (but arbitrary) given network and study the computational complexity of these problems using reductions from well-known network reliability problems. We show that computing both quantities exactly is intractable, but that the expected spreading size can be efficiently approximated with Monte Carlo sampling. When nodes are weighted to reflect their importance, the problem becomes as hard as the s-t reliability problem, which is not known to yield an efficient randomized approximation scheme up to now. Finally, we give a formal complexity-theoretic argument why there is most likely no randomized constant-factor approximation for the probability of large spreadings, even for the unweighted case. A hybrid Monte Carlo sampling algorithm is proposed that resorts to specialized s-t reliability algorithms for accurately estimating the infection probability of those nodes that are rarely affected by the spreading proces

Decision models on therapies for intensive medicine

Decision support models are crucial in intensive care units as they allow intensivists to make faster and better decisions. The application of optimization models in these areas becomes challenging given its complexity and multidisciplinary nature. The main objective of this study is to use the stochastic Hill Climbing optimization model in order to identify the best medication to treat the Covid Pneumonia problem, considering the top 3 medications administered as well as the cost of treatment. It should be noted that the problem to be analyzed in the optimization model was selected considering that the extracted data is from the time when Covid-19 was ravaging the intensive care units, so it will be the most interesting. The results obtained in this study denote that the n_iterations parameter was crucial in obtaining the optimal solution since all scenarios with this parameter set to a value of 1000 were able to return the optimal solution, unlike the other ones.The work has been supported by FCT – Fundação para a Ciência e Tecnologia within the Project Scope: DSAIPA/DS/0084/2018