Oblivious Bounds on the Probability of Boolean Functions

This paper develops upper and lower bounds for the probability of Boolean functions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. We call this approach dissociation and give an exact characterization of optimal oblivious bounds, i.e. when the new probabilities are chosen independent of the probabilities of all other variables. Our motivation comes from the weighted model counting problem (or, equivalently, the problem of computing the probability of a Boolean function), which is #P-hard in general. By performing several dissociations, one can transform a Boolean formula whose probability is difficult to compute, into one whose probability is easy to compute, and which is guaranteed to provide an upper or lower bound on the probability of the original formula by choosing appropriate probabilities for the dissociated variables. Our new bounds shed light on the connection between previous relaxation-based and model-based approximations and unify them as concrete choices in a larger design space. We also show how our theory allows a standard relational database management system (DBMS) to both upper and lower bound hard probabilistic queries in guaranteed polynomial time.Comment: 34 pages, 14 figures, supersedes: http://arxiv.org/abs/1105.281

Approximate Lifted Inference with Probabilistic Databases

This paper proposes a new approach for approximate evaluation of #P-hard queries with probabilistic databases. In our approach, every query is evaluated entirely in the database engine by evaluating a fixed number of query plans, each providing an upper bound on the true probability, then taking their minimum. We provide an algorithm that takes into account important schema information to enumerate only the minimal necessary plans among all possible plans. Importantly, this algorithm is a strict generalization of all known results of PTIME self-join-free conjunctive queries: A query is safe if and only if our algorithm returns one single plan. We also apply three relational query optimization techniques to evaluate all minimal safe plans very fast. We give a detailed experimental evaluation of our approach and, in the process, provide a new way of thinking about the value of probabilistic methods over non-probabilistic methods for ranking query answers.Comment: 12 pages, 5 figures, pre-print for a paper appearing in VLDB 2015. arXiv admin note: text overlap with arXiv:1310.625

GAFit : a computational tool kit for parameterizations of potential energy surfaces

The potential energy surface of a molecular system governs many of its chemical properties, and particularly, the dynamics, that is, the spatial evolution of nuclei with time. Most of the chemical dynamics simulations performed nowadays involve integration of the classical equations of motion, calculating the forces on atoms at each step either directly by electronic structure calculations (i.e., “on-the-fly” or direct dynamics) or from analytical PES (Potential Energy Surfaces). In principle, the direct dynamics approach may be the preferred option for simulations of reactive systems that include a small number of atoms, because one avoids the construction of the analytical surface. The use of analytical PES, however, has a clear advantage in terms of CPU-time costs, being mandatory in molecular dynamics simulations of systems composed by thousands of atoms. Even for small-size systems, the use of an analytical surface may be a convenient choice. If it is developed with care, it may be almost as accurate as the exact surface corresponding to the electronic structure method used as a reference for its construction. The development of analytical PES may be facilitated by using optimization methods, and many research groups have been using them for their particular purposes. However, to our knowledge, there is not a general code that allows users to parametrize analytical surfaces in a relatively easy way. The aim of the present work was to write a suite of programs to assist users in developing analytical surfaces. This suite of programs is called GAFit. GAFit is a package of programs initially developed to facilitate fittings of intermolecular potentials and reparametrizations of semiempirical Hamiltonians. However, it can be easily adjusted for other purposes in which fittings of a series of parameters are needed. The core of the package is the genetic algorithm developed by Marques and co-workers (Marques, J M C; Prudente, F V; Pereira F B; Almeida M M; Maniero A M and Fellows C E. “A new genetic algorithm to be used in the direct fit of potential energy curves to ab initio and spectroscopic data”. In: Journal of Physics B: Atomic, Molecular and Optical Physics 41.8 (2008),p. 085103.). The functionality of the package was extended separating the core itself from the fitting targets. Now, users can choose, upon their programming skills, from introducing their custom potentials directly into code, use an easy pre-coded potential template to do so, or for those with no programming knowledge at all, use an analytical expression or the most used potentials coded just ready to use. A complete set of tools were added to the package to facilitate the creation and configuration of input files. In addition, an external interface was developed to interact with external programs. Using this interface the tools needed to use GAFit to parametrize the MOPAC program were developed. A further MOPAC enhanced interface permits running parallel copies of MOPAC to speed up calculations and face up some problems encountered during the first stage development

A generalized disjunctive programming model for the optimal design of reverse electrodialysis process for salinity gradient-based power generation

Reverse electrodialysis (RED) is an emerging electro-membrane technology that generates electricity out of salinity differences between two solutions, a renewable source known as salinity gradient energy. Realizing full-scale RED would require more techno-economic and environmental assessments that consider full process design and operational decision space from the RED stack to the entire system. This work presents an optimization model formulated as a Generalized Disjunctive Programming (GDP) problem that incorporates a finite difference RED stack model from our research group to define the cost-optimal process design. The solution to the GDP problem provides the plant topology and the RED units´ working conditions that maximize the net present value of the RED process for given RED stack parameters and site-specific conditions. Our results show that, compared with simulation-based approaches, mathematical programming techniques are efficient and systematic to assist early-stage research and to extract optimal design and operation guidelines for large-scale RED implementation.This work was supported by the LIFE Programme of the European Union (LIFE19 ENV/ES/000143); the MCIN/AEI/10.13039/501100011033 and “European Union NextGenerationEU/PRTR” (PDC2021–120786-I00); and by the MCIN/AEI/10.13039/501100011033 and “ESF Investing in your future” (PRE2018–086454)

Unifying metabolic networks, regulatory constraints, and resource allocation

Metabolic and gene regulatory networks are two classic models of systems biology. Biologically, gene regulatory networks are the control system of protein expression while metabolic networks, especially the genome-scale reconstructions consist of thousands of enzymatic reactions breaking down nutrients into precursors and energy to support the cellular survival. Metabolic-genetic networks, in addition, include the translational processes as an integrated model of classical metabolic networks and the gene expression machinery. Conversely, genetic regulation is also affected by the metabolic activities that provide feedbacks and precursors to the regulatory system. Thus, the two systems are highly interactive and depend on each other. Up to now, various efforts have been made to bridge the two network types. Yet, the dynamic integration of metabolic networks and genetic regulation remains a major challenge in computational systems biology. This PhD thesis is a contribution to mathematical modeling approaches for studying metabolic-regulatory systems. Inspired by regulatory flux balance analysis (rFBA), we first propose an analytic pipeline to explore the optimal solution space in rFBA. Then, our efforts focus on the dynamic combination of metabolic networks together with enzyme production costs and genetic regulation. For this purpose, we first explore the intuitive idea that incorporates Boolean regulatory rules while iterating resource balance analysis. However, with the iterative strategy, the gene expression states are only updated in discrete time steps. Furthermore, formalizing the metabolic-regulatory networks (MRNs) by hybrid automata provides a new mathematical framework that allows the quantitative integration of the metabolic-genetic network with the genetic regulation in a hybrid discrete-continuous system. For the application of this theoretical formalization, we develop a constraint-based approach regulatory dynamic enzyme-cost flux balance analysis (r-deFBA) as an optimal control strategy for the hybrid automata representing MRNs. This allows the prediction of optimal regulatory state transitions, dynamics of metabolism, and resource allocation capable of achieving a maximal biomass production over a time interval. Finally, this PhD project ends with a chapter on perspectives; we apply the theory of product automata to model the dynamics at population-level, integrating continuous metabolism and discrete regulatory states

Computational approaches to complex biological networks

The need of understanding and modeling the biological networks is one of the raisons d'\ueatre and of the driving forces behind the emergence of Systems Biology. Because of its holistic approach and because of the widely different level of complexity of the networks, different mathematical methods have been developed during the years. Some of these computational methods are used in this thesis in order to investigate various properties of different biological systems. The first part deals with the prediction of the perturbation of cellular metabolism induced by drugs. Using Flux Balance Analysis to describe the reconstructed genome-wide metabolic networks, we consider the problem of identifying the most selective drug synergisms for given therapeutic targets. The second part of this thesis considers gene regulatory and large social networks as signed graphs (activation/deactivation or friendship/hostility are rephrased as positive/negative coupling between spins). Using the analogy with an Ising spin glass an analysis of the energy landscape and of the content of \u201cdisorder\u201d 'is carried out. Finally, the last part concerns the study of the spatial heterogeneity of the signaling pathway of rod photoreceptors. The electrophysiological data produced by our collaborators in the Neurobiology laboratory have been analyzed with various dynamical systems giving an insight into the process of ageing of photoreceptors and into the role diffusion in the pathway