Narrowing down the Hardness Barrier of Synthesizing Elementary Net Systems

Elementary net system feasibility is the problem to decide for a given automaton A if there is a certain boolean Petri net with a state graph isomorphic to A. This is equivalent to the conjunction of the state separation property (SSP) and the event state separation property (ESSP). Since feasibility, SSP and ESSP are known to be NP-complete in general, there was hope that the restriction of graph parameters for A can lead to tractable and practically relevant subclasses. In this paper, we analyze event manifoldness, the amount of occurrences that an event can have in A, and state degree, the number of allowed successors and predecessors of states in A, as natural input restrictions. Recently, it has been shown that all three decision problems, feasibility, SSP and ESSP, remain NP-complete for linear A where every event occurs at most three times. Here, we show that these problems remain hard even if every event occurs at most twice. Nevertheless, this has to be paid by relaxing the restriction on state degree, allowing every state to have two successor and two predecessor states. As we also show that SSP becomes tractable for linear A where every event occurs at most twice the only open cases left are ESSP and feasibilty for the same input restriction

Born-Again Tree Ensembles

The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix possible sources of mistakes and biases. Tree ensembles offer a good prediction quality in various domains, but the concurrent use of multiple trees reduces the interpretability of the ensemble. Against this background, we study born-again tree ensembles, i.e., the process of constructing a single decision tree of minimum size that reproduces the exact same behavior as a given tree ensemble in its entire feature space. To find such a tree, we develop a dynamic-programming based algorithm that exploits sophisticated pruning and bounding rules to reduce the number of recursive calls. This algorithm generates optimal born-again trees for many datasets of practical interest, leading to classifiers which are typically simpler and more interpretable without any other form of compromise.Comment: "Born-Again Tree Ensembles", proceedings of ICML 2020. The associated source code is available at: https://github.com/vidalt/BA-Tree

On the Nonlinear Tribological Jerk Dynamics at Sliding Interfaces

As the world desires the next industrial revolution, the potential threats that will undermine energy efficient innovations include detrimental frictional effects that exacerbate wear, hasten equipment breakdowns, and worsen heat dissipation. Capturing the inherently nonlinear manifestations of friction fundamentally has been difficult. A fundamental modeling scheme elucidating friction will bolster novel technologies synthesizing wear resistant materials and lubricants needed for sustainable energy efficiency. Frictional dissipation at dynamical sliding interfaces has been studied for generations. Interfacial sliding frictional effects are prevalent in natural and artificial phenomena such as earthquake, hip and knee joints, and the moving parts of energy-producing and energy-consuming equipment. Hitherto, despite significant research efforts, no consensus fundamental modeling technique exists that deterministically ties friction with system degradation. Yet, elucidating the basic physics of nonlinear friction-resisted motion will clarify how heat generation, efficiency, lubrication, wear, and material lifetime evolve in sliding contacts. In this study, we unify Newtonian mechanics with classical thermodynamics to elicit nonlinear tribological jerk dynamics at a sliding interface. Jerk, the rate of change of acceleration has been elusive in classical mechanics. By showing jerk originating in a friction-resisted motion a new fundamental scientific modeling tool emerges. For example, although Coulomb\u27s law of friction precludes significant friction-velocity coupling our reassessment using jerk dynamics results shows otherwise. We find Coulomb\u27s law may seemingly be an oversimplification by reproducing the Stribeck effect known to capture friction-velocity coupling. Furthermore, negative frictional jerk opposes relative motion while positive lubricating jerk supports relative motion. A frictionless unconstrained motion recaptures constant acceleration Newtonian-Galilean mechanics. Using the kinematic and dynamic results as inputs, we quantified wear and wear rates, subsurface temperature and mechanical sliding efficiency. Our modeling results quantitatively match experimental results from tribometer and thermal compliance tests very well. We constructed an analytical algebraic partitioning technique to solve the jerk balance equations which are third order and nonlinear ordinary differential equations. The algebraic technique works well and may facilitate engineering and scientific modeling efforts. By placing jerk in basic physics context, we proffer a fundamental tool that likely will transform how relative motions in artificial and natural phenomena are modeled

Computer Aided Verification

The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic

Magnetism, FeS colloids, and Origins of Life

A number of features of living systems: reversible interactions and weak bonds underlying motor-dynamics; gel-sol transitions; cellular connected fractal organization; asymmetry in interactions and organization; quantum coherent phenomena; to name some, can have a natural accounting via $physical$ interactions, which we therefore seek to incorporate by expanding the horizons of `chemistry-only' approaches to the origins of life. It is suggested that the magnetic 'face' of the minerals from the inorganic world, recognized to have played a pivotal role in initiating Life, may throw light on some of these issues. A magnetic environment in the form of rocks in the Hadean Ocean could have enabled the accretion and therefore an ordered confinement of super-paramagnetic colloids within a structured phase. A moderate H-field can help magnetic nano-particles to not only overcome thermal fluctuations but also harness them. Such controlled dynamics brings in the possibility of accessing quantum effects, which together with frustrations in magnetic ordering and hysteresis (a natural mechanism for a primitive memory) could throw light on the birth of biological information which, as Abel argues, requires a combination of order and complexity. This scenario gains strength from observations of scale-free framboidal forms of the greigite mineral, with a magnetic basis of assembly. And greigite's metabolic potential plays a key role in the mound scenario of Russell and coworkers-an expansion of which is suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed Krishnaswami Alladi, Springer 201

Synthesizing species trees from gene trees using the parameterized and graph-theoretic approaches

Gene trees describe how parts of the species have evolved over time, and it is assumed that gene trees have evolved along the branches of the species tree. However, some of gene trees are often discordant with the corresponding species tree due to the complicated evolution history of genes. To overcome this obstacle, median problems have emerged as a major tool for synthesizing species trees by reconciling discordance in a given collection of gene trees. Given a collection of gene trees and a cost function, the median problem seeks a tree, called median tree, that minimizes the overall cost to the gene trees. Median tree problems are typically NP-hard, and there is an increased interest in making such median tree problems available for large-scale species tree construction. In this thesis work, we first show that the gene duplication median tree problem satisfied the weaker version of the Pareto property and propose a parameterized algorithm to solve the gene duplication median tree problem. Second, we design two efficient methods to handle the issues of applying the parameterized algorithm to unrooted gene trees which are sampled from the different species. Third, we introduce the graph-theoretic formulation of the Robinson-Foulds median tree problem and a new tree edit operation. Fourth, we propose a new metric between two phylogenetic trees and examine the statistical properties of the metric. Finally, we propose a new clustering criteria in a bipartite network and propose a new NP-hard problem and its ILP formulation

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications