Multifunctions of bounded variation

Consider control systems described by a differential equation with a control term or, more generally, by a differential inclusion with velocity set F(t,x). Certain properties of state trajectories can be derived when it is assumed that F(t,x) is merely measurable w.r.t. the time variable t . But sometimes a refined analysis requires the imposition of stronger hypotheses regarding the time dependence. Stronger forms of necessary conditions for minimizing state trajectories can be derived, for example, when F(t,x) is Lipschitz continuous w.r.t. time. It has recently become apparent that significant addition properties of state trajectories can still be derived, when the Lipschitz continuity hypothesis is replaced by the weaker requirement that F(t,x) has bounded variation w.r.t. time. This paper introduces a new concept of multifunctions F(t,x) that have bounded variation w.r.t. time near a given state trajectory, of special relevance to control. We provide an application to sensitivity analysis

Speculative Segmented Sum for Sparse Matrix-Vector Multiplication on Heterogeneous Processors

Sparse matrix-vector multiplication (SpMV) is a central building block for scientific software and graph applications. Recently, heterogeneous processors composed of different types of cores attracted much attention because of their flexible core configuration and high energy efficiency. In this paper, we propose a compressed sparse row (CSR) format based SpMV algorithm utilizing both types of cores in a CPU-GPU heterogeneous processor. We first speculatively execute segmented sum operations on the GPU part of a heterogeneous processor and generate a possibly incorrect results. Then the CPU part of the same chip is triggered to re-arrange the predicted partial sums for a correct resulting vector. On three heterogeneous processors from Intel, AMD and nVidia, using 20 sparse matrices as a benchmark suite, the experimental results show that our method obtains significant performance improvement over the best existing CSR-based SpMV algorithms. The source code of this work is downloadable at https://github.com/bhSPARSE/Benchmark_SpMV_using_CSRComment: 22 pages, 8 figures, Published at Parallel Computing (PARCO

CSR5: An Efficient Storage Format for Cross-Platform Sparse Matrix-Vector Multiplication

Sparse matrix-vector multiplication (SpMV) is a fundamental building block for numerous applications. In this paper, we propose CSR5 (Compressed Sparse Row 5), a new storage format, which offers high-throughput SpMV on various platforms including CPUs, GPUs and Xeon Phi. First, the CSR5 format is insensitive to the sparsity structure of the input matrix. Thus the single format can support an SpMV algorithm that is efficient both for regular matrices and for irregular matrices. Furthermore, we show that the overhead of the format conversion from the CSR to the CSR5 can be as low as the cost of a few SpMV operations. We compare the CSR5-based SpMV algorithm with 11 state-of-the-art formats and algorithms on four mainstream processors using 14 regular and 10 irregular matrices as a benchmark suite. For the 14 regular matrices in the suite, we achieve comparable or better performance over the previous work. For the 10 irregular matrices, the CSR5 obtains average performance improvement of 17.6\%, 28.5\%, 173.0\% and 293.3\% (up to 213.3\%, 153.6\%, 405.1\% and 943.3\%) over the best existing work on dual-socket Intel CPUs, an nVidia GPU, an AMD GPU and an Intel Xeon Phi, respectively. For real-world applications such as a solver with only tens of iterations, the CSR5 format can be more practical because of its low-overhead for format conversion. The source code of this work is downloadable at https://github.com/bhSPARSE/Benchmark_SpMV_using_CSR5Comment: 12 pages, 10 figures, In Proceedings of the 29th ACM International Conference on Supercomputing (ICS '15

Multifunctions of Bounded Variation, Preliminary Version I

Consider control systems described by a differential equation with a control term or, more generally, by a differential inclusion with velocity set $F(t,x)$. Certain properties of state trajectories can be derived when, in addition to other hypotheses, it is assumed that $F(t,x)$ is merely measurable w.r.t. the time variable $t$. But sometimes a refined analysis requires the imposition of stronger hypotheses regarding the $t$ dependence of $F(t,x)$. Stronger forms of necessary conditions for state trajectories that minimize a cost can derived, for example, if it is hypothesized that $F(t,x)$ is Lipschitz continuous w.r.t. $t$. It has recently become apparent that interesting addition properties of state trajectories can still be derived, when the Lipschitz continuity hypothesis is replaced by the weaker requirement that $F(t,x)$ has bounded variation w.r.t. $t$. This paper introduces a new concept of multifunctions $F(t,x)$ that have bounded variation w.r.t. $t$ near a given state trajectory, of special relevance to control system analysis. Properties of such multifunctions are derived and their significance is illustrated by an application to sensitivity analysis.Comment: Preliminary version of a article which will submitted to a journal for publicatio

Decomposition of Differential Games

This paper provides a decomposition technique for the purpose of simplifying the solution of certain zero-sum differential games. The games considered terminate when the state reaches a target, which can be expressed as the union of a collection of target subsets; the decomposition consists of replacing the original target by each of the target subsets. The value of the original game is then obtained as the lower envelope of the values of the collection of games resulting from the decomposition, which can be much easier to solve than the original game. Criteria are given for the validity of the decomposition. The paper includes examples, illustrating the application of the technique to pursuit/evasion games, where the decomposition arises from considering the interaction of individual pursuer/evader pairs.Comment: 10 pages, 2 figure

Shortchanging America's Health 2008: A State-by-State Look at How Federal Public Health Dollars Are Spent

Examines public health indicators in each state, in combination with federal and state funding for programs to promote health. Includes state rankings by funding per capita, percentage of population who are uninsured, disease rates, and other indicators

Zdravstvena njega žene u postpartalnom periodu

Postpartalna zdravstvena skrb žene počinje već nakon samog poroda u rodilištu, a obuhvaća pregled tijekom hospitalizacije, kontrolne preglede nakon šest tjedana, nadzor babinjače u njenom domu putem patronažne zdravstvene zaštite te edukaciju i zdravstveni odgoj babinjače. Kod provođenja postpartalne zdravstvene skrbi iznimno je važna uloga patronažne sestre čiji su ključni zadaci kontrola i praćenje fizioloških zbivanja kako kod žene, tako i kod novorođenčeta te naročito pružanje potpore u slučaju postojanja problema te edukacija o normalnom procesu oporavka nakon poroda i mogućim poteškoćama i komplikacijama. Patronažna skrb se nastavlja na skrb koja je započela u rodilištu i od iznimne je važnosti za zdravlje majke i novorođenčeta. Vrlo je bitno da ona bude pravovremena i kontinuirana te ju treba započeti što ranije, već po dolasku iz rodilišta jer su u tom periodu potrebe majke, djeteta i cijele njene obitelji najveće. Patronažna sestrinska skrb uključuje procjenu, planiranje i na kraju provedbu mjera potrebnih za unapređenje i zaštitu zdravlja. Neki od brojnih zadataka patronažne sestre u tom razdoblju su praćenje općeg zdravstvenog stanja žene, tjelesnih i psihičkih promjena, procjena obiteljske situacije, procjena rizika za nastanak mogućih komplikacija te njihovo rano prepoznavanje. U periodu nakon poroda žene su iznimno osjetljive, ponekad im se javlja nedostatak samopouzdanja te sumnja u vlastitu sposobnost roditeljstva. Zahtjevi koji se pred njih postavljaju su vrlo veliki, javlja se umor, iscrpljenost, opterećenost kućanskim poslovima, briga oko starije djece i mnoge druge obaveze. Upravo tu je ključna uloga patronažne sestre koja svojim empatijskim pristupom, pruţanjem pomoći i potpore ženi pomaže u uspješnom svladavanju ovih problema.Postpartum health care begins after the birth in the maternity ward, and includes a review during hospitalization, the inspections after six weeks, supervision of purpera in her home through home visiting health care and education. With the implementation of postpartum health care is extremely important role of home care nurses whose key tasks are control and monitoring of physiological occurrence in both, women and newborn and in particular to provide support in case of problems and education about the normal process of recovery after delivery and possible difficulties and complications. Home care nurses continues care that began in the hospital and is extremely important for the health of mothers and newborns. Health care must be timely and continuous, and should be initiated as early as possible, on arrival from the hospital, because in this period the needs of mother, child and the entire family are the largest. Home care nursing care includes assessment, planning and on-site implementation of the measures necessary for the promotion and protection of health. Some of the many tasks of home care nurses in this period are monitoring the general health status of women, physical and psychological changes, the assessment of the family situation, the assessment of the risk of possible complications and their early recognition. In the period after childbirth women are extremely sensitive, sometimes they occur lack of confidence and doubt in their own parenthood ability. The requirements placed upon them are very large. There is fatigue, exhaustion, the burden on household chores and taking care of older children and many other duties. The key role of home care nurses is their empathetic approach, providing assistance and support in successfully solving postpartal problems

The Hamiltonian Inclusion for Nonconvex Velocity Sets

Since Clarke's 1973 proof of the Hamiltonian inclusion for optimal control problems with convex velocity sets, there has been speculation (and, more recently, speculation relating to a stronger, partially convexified version of the Hamiltonian inclusion) as to whether these necessary conditions are valid in the absence of the convexity hypothesis. The issue was in part resolved by Clarke himself when, in 2005, he showed that $L^{\infty}$ local minimizers satisfy the Hamiltonian inclusion. In this paper it is shown, by counterexample, that the Hamiltonian inclusion (and so also the stronger partially convexified Hamiltonian inclusion) are not in general valid for nonconvex velocity sets when the local minimizer in question is merely a $W^{1,1}$ local minimizer, not an $L^{\infty}$ local minimizer. The counterexample demonstrates that the need to consider $L^{\infty}$ local minimizers, not $W^{1,1}$ local minimizers, in the proof of the Hamiltonian inclusion for nonconvex velocity sets is fundamental, not just a technical restriction imposed by currently available proof techniques. The paper also establishes the validity of the partially convexified Hamiltonian inclusion for $W^{1,1}$ local minimizers under a normality assumption, thereby correcting earlier assertions in the literature

Minimax optimal control

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