In previous work of the author and others, max-plus methods have been explored for solution of first-order, nonlinear Hamilton-Jacobi-Bellman partial differential equations (HJB PDEs) and corresponding nonlinear control problems. Although max-plus basis expansion and max-plus finite-element methods provide computational-speed advantages, they still generally suffer from the curse-of-dimensional...

At the beginning of the twentieth century, the quantum nature of thermal electromagnetic radiation was a subject of intense interest. This was sparked by Max Planck’s discovery that the spectral distribution of light emerging from a thermal body could be explained only if the radiators emitting the energy occurred in discrete energy states. This induced Albert Einstein to conclude in 1905 that ...

In this paper, we address the problem of multi-label classification. We consider linear classifiers and propose to learn a prior over the space of labels to directly leverage the performance of such methods. This prior takes the form of a quadratic function of the labels and permits to encode both attractive and repulsive relations between labels. We cast this problem as a structured prediction...

It is well known that various characteristics in risk and queuing process can be formulated as Markov Renewal function. We study the max-position of finitely many Markov Renewal Reward process with countable state space. We define Markov Renewal equation associated with max-posed process. The solutions of the Markov Renewal Reward equation are derived and the asymptotic behaviors of the equatio...

We demonstrate that the minimal state space realization problem in the max algebra can be transformed into an Extended Linear Complementarity Problem (ELCP). We use an algorithm that finds all solutions of an ELCP to find all equivalent minimal state space realizations of a single input single output (SISO) discrete event system. We also give a geometrical description of the set of all minimal ...

In this paper, we introduce the notions of Belluce lattice associated with a bounded $BCK$-algebra and reticulation $BCK$-algebra. To do this, first, define operations $curlywedge ,$ $curlyvee $ $sqcup on $BCK$-algebras study some algebraic properties them. Also, for $A$ Zariski topology Spec(A)$ induced $tau _{A,Max(A)}$ $Max(A)$. We prove $(Max(A),tau_{A,Max(A)})$ is compact topological space...

We analyze, in this work, the performance of a recently introduced weighted Max-SAT solver, Clone, in the Max-SAT evaluation 2007. Clone utilizes a novel bound computation based on formula compilation that allows it to search in a reduced search space. We study how additional techniques from the SAT and Max-SAT literature affect the performance of Clone on problems from the evaluation. We then ...

In this paper we present a simple and efficient implementation of a min-max priority queue, reflected min-max priority queues. The main merits of our construction are threefold. First, the space utilization of the reflected min-max heaps is much better than the naive solution of putting two heaps back-to-back. Second, the methods applied in this structure can be easily used to transform ordinar...

Location problems with Q (in general connicting) criteria are considered. After reviewing previous results of the authors dealing with lexicographic and Pareto location the main focus of the paper is on max-ordering locations. In these location problems the worst of the single objectives is minimized. After discussing some general results (including reductions to single criterion problems and t...