Topological properties for a perturbed first order sweeping process

In this paper, we consider a perturbed sweeping process for a class of subsmooth moving sets. The perturbation is general and takes the form of a sum of a single-valued mapping and a set-valued mapping. In the first result, we study some topological proprieties of the attainable set, the set-valued mapping considered here is upper semi-continuous with convex values. In the second result, we treat the autonomous problem under assumptions that do not require the convexity of the values and that weaken the assumption on the upper semi-continuity. Then, we deduce a solution of the time optimality problem.

An Optimal Lysis Time Maximizes Bacteriophage Fitness in Quasi-continuous Culture

ABSTRACTOptimality models have a checkered history in evolutionary biology. While optimality models have been successful in providing valuable insight into the evolution of a wide variety of biological traits, a common objection is that optimality models are overly simplistic and ignore organismal genetics. We revisit evolutionary optimization in the context of a major bacteriophage life history trait, lysis time. Lysis time refers to the period spanning phage infection of a host cell and its lysis, whereupon phage progeny are released. Lysis time, therefore, directly determines phage fecundity assuming progeny assembly rate is maximized. Noting that previous tests of lysis time optimality rely on batch culture, we implemented a quasi-steady state system to observe productivity of a panel of isogenic phage λ mutants differing in lysis time. We report that λ phage productivity in our experiments is maximized around an optimal lysis time of 65 min, which is the lysis time of the λ “wildtype” strain. We discuss this finding in light of recent results that lysis time variation is also minimized in the λ “wildtype” strain.

Time-optimality by distance-optimality for parabolic control systems

The equivalence of time-optimal and distance-optimal control problems is shown for a class of parabolic control systems. Based on this equivalence, an approach for the efficient algorithmic solution of time-optimal control problems is investigated. Numerical examples are provided to illustrate that the approach works well in practice.

Pushing revisited: Differential flatness, trajectory planning, and stabilization

We prove that quasi-static pushing with a sticking contact and ellipsoid approximation of the limit surface is differential flat. Both graphical and algebraic derivations are given. A major conclusion is that the pusher–slider system is reducible to the Dubins car problem where the sticking contact constraints translate to bounded curvature. Planning is as easy as computing a Dubins curve with the additional benefit of time-optimality. For trajectory stabilization, we design closed-loop control using dynamic feedback linearization or open-loop control using two contact points as a form of mechanical feedback. We conduct robotic experiments using objects with different pressure distributions, shape, and contact materials placed at different initial poses that require difficult switching action maneuvers to the goal pose. The average error is within 1.67 mm in translation and 0.5° in orientation over 60 experimental trials. We also show an example of pushing among obstacles using a RRT planner with exact steering.

A stream-based method to detect differences between XML documents

Detecting differences between XML documents is one of most important research topics for XML. Since XML documents are generally considered to be organized in a tree structure, most previous research has attempted to detect differences using tree-matching algorithms. However, most tree-matching algorithms have inadequate performance owing to limitations in terms of the execution time, optimality and scalability. This study proposes a stream-based difference detection method in which an XML binary encoding algorithm is used to provide improved performance relative to that of previous tree-matching algorithms. A tree-structured analysis of XML is not essential in order to detect differences. We use a D-Path algorithm that has an optimal result quality for difference detection between two streams and has a lower time complexity than tree-based methods. We then modify the existing XML binary encoding method to tokenize the stream and the algorithm in order to support more operations than D-Path algorithm does. The experimental results reveal greater efficiency for the proposed method relative to tree-based methods. The execution time is at least 4 times faster than state-of-the-art tree-based methods. In addition, the scalability is much more efficient.