Error reachable set based stabilization of switched linear systems with bounded peak disturbances

This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.

A Simple Method to Derive Minimal Cut Sets for a Non-coherent Fault Tree

Minimal cut sets （or prime implicants： minimal combinations of basic event conditions leading to system failure） are important information for reliability/safety analysis and design. To obtain minimal cut sets for general non-coherent fault trees, including negative basic events or multi-valued basic events, a special procedure such as the consensus rule must be applied to the results obtained by logical operations for coherent fault trees, which will require more steps and time. This paper proposes a simple method for a non-coherent fault tree, whose top event is represented as an AND combination of monotonic sub-trees. A ＂monotonic＂ sub-tree means that it does not have both positive and negative representations for each basic event. It is proven that minimal cut sets can be obtained by a conventional method for coherent fault trees. An illustrative example of a simple event tree analysis shows the detail and characteristics of the proposed method.

Minimal feasible sets in variable resource constrained projects

To determine the reasonable resource dependent relations between activities for the purpose of exactly computing the total floats and the free floats of activities, correctly identifying critical activities and critical sequences in a project schedule with variable resource constraints, the concept of the minimal feasible set （MFS） is proposed and the properties of MFS are discussed. The methods to identify optimal MFSs and resource links are then studied. Furthermore, MFS is generalized to the situation that the preconditions of MFS are not satisfied. Contrastive results show that in establishing resource links and resolving floats, MFS is at least not inferior to other methods in all cases and is superior in most situations.

MINIMAL ESSENTIAL SETS AND ESSENTIAL COMPONENTS OF THE EQUILIBRIA OF PRODUCTION ECONOMIES

The purpose of this paper is to give a further study on the stability of production economies. The new results were given by considering the 'set-valued' stability of equilibria. It is proved that there exists at least one minimal essential set of equilibrium points of the economy and every minimal essential set is connected. Based on these results, it is easy to prove that there is at least one essential component of the set of equilibrium points.

CALCULATION OF FUZZY RELIABILITY IN THE CASE OF RANDOM STRESS AND FUZZY FATIGUE STRENGTH

The fuzzy sets theory is introduced into the fatigue reliability analysis. The concepts of maximizing set and minimizing set are developed to decide the ordering value of each fuzzy number, and these values can be used to determine the order of the fuzzy numbers. On the basis of the works mentioned above, the membership function defining the fuzzy safety event can be calculated, and then the fuzzy reliability in the case of stress and fuzzy fatigue strength is deduced. An example is given to illustrate the method.

Essential cellular modules for the proliferation of the primitive cell

Bacteria appeared early in the evolution of cellular life on planet Earth, and therefore the universally essential genes or biological pathways found across bacterial domains may represent fundamental genetic or cellular systems used in early life. The essential genes and the minimal gene set required to support bacterial life have recently been experimentally and computationally identified. It is, however,still hard to estimate the ancient genes present in primitive cells compared to the essential genes in contemporary bacteria, because we do not know how ancestral primitive cells lived and proliferated, and therefore cannot directly evaluate the essentiality of the genes in ancestral primitive cells. The cell wall is normally essential for bacterial proliferation and cellular division of walled bacterial cells is normally highly controlled by the essential FtsZ cell division machinery. But, bacteria are capable of reverting to their cell wall deficient ancestral form, called the ＂L-form＂. Unlike ＂normal＂ cells, L-forms divide by a simple physical mechanism based on the effects of membrane dynamics, suggesting a mode of primitive proliferation before the appearance of the cell wall. In this review, we summarize the experimental and computational investigations of minimal gene sets and discuss the minimal cellular modules required to support the proliferation of primitive cells, based on L-form proliferation.

An Adherence Semigroup

By a dynamical system we mean a pair of (X,T), whereX is compact Hausdorff space. In this paper we define an adherence semigroupA(X,T--X x, which is the set of all pointwise limit of subnets of(T n)n∈N. We will prove some commonness between adherence semigroup and Ellis semigroup.

RDF(S) repository privacy protection via inference control

The privacy protection of resource description framework （schema） （RDF（S） ） repository is an emerging topic in database security area. In this paper, entailment rules are investigated based on RDF（S） repository firstly. Then, an idea that uses reasoning closure to judge whether the privacy disclosure caused by inference is existed is proposed. Furthermore, the definitions of impli- cation conditions and information measure of triple statements which gains data hiding algorithm with combining proposition logic reasoning theory are introduced. Meanwhile, a conversion method from conjunctive normal form to disjunctive normal form based minimal hitting sets of set cluster is aiso proposed. Finally, the experimental results show that our algorithm can prevent privacy disclosure of RDF（S） repository effectively.

One-dimensional monotone nonautonomous dynamical systems

This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous(cocycle) dynamical systems. A description of the structures of their invariant sets, omega limit sets,Bohr/Levitan almost periodic and almost automorphic motions, global attractors, and pinched and minimalsets is given. An application of our general results is given to scalar differential and difference equations.

Directed Dominating Set Problem Studied by Cavity Method:Warning Propagation and Population Dynamics

The minimal dominating set for a digraph(directed graph) is a prototypical hard combinatorial optimization problem. In a previous paper, we studied this problem using the cavity method. Although we found a solution for a given graph that gives very good estimate of the minimal dominating size, we further developed the one step replica symmetry breaking theory to determine the ground state energy of the undirected minimal dominating set problem. The solution space for the undirected minimal dominating set problem exhibits both condensation transition and cluster transition on regular random graphs. We also developed the zero temperature survey propagation algorithm on undirected Erds-Rnyi graphs to find the ground state energy. In this paper we continue to develope the one step replica symmetry breaking theory to find the ground state energy for the directed minimal dominating set problem. We find the following.(i) The warning propagation equation can not converge when the connectivity is greater than the core percolation threshold value of 3.704. Positive edges have two types warning, but the negative edges have one.(ii) We determine the ground state energy and the transition point of the Erd?os-R′enyi random graph.(iii) The survey propagation decimation algorithm has good results comparable with the belief propagation decimation algorithm.

Statistical mechanics of the directed 2-distance minimal dominating set problem

The directed L-distance minimal dominating set(MDS) problem has wide practical applications in the fields of computer science and communication networks. Here, we study this problem from the perspective of purely theoretical interest. We only give results for an Erdós Rényi(ER)random graph and regular random(RR) graph, but this work can be extended to any type of network. We develop spin glass theory to study the directed 2-distance MDS problem. First, we find that the belief propagation(BP) algorithm does not converge when the inverse temperatureβ exceeds a threshold on either an ER random network or RR network. Second, the entropy density of replica symmetric theory has a transition point at a finite β on a regular random graph when the arc density exceeds 2 and on an ER random graph when the arc density exceeds3.3;there is no entropy transition point(or β = ■) in other circumstances. Third, the results of the replica symmetry(RS) theory are in agreement with those of BP algorithm while the results of the BP decimation algorithm are better than those of the greedy heuristic algorithm.

Numerical Simulation to Reliability Analysis of Fault-Tolerant Repairable System

In the traditional method for the reliability analysis of fault-tolerant system,the system structure is described by means of binary decision diagram (BDD) and Markov process,and then the reliability indexes are calculated.However,as the size of system augments,the size of state space will increase exponentially.Additionally,Markov approach requires that the failure and repair time of the components obey an exponential distribution.In this study,by combining dynamic fault tree (DFT) and numerical simulation based on the minimal sequence cut set (MSCS),a new method to evaluate reliability of fault-tolerant system with repairable components is proposed.The method presented does not depend on Markov model,so that it can effectively solve the problem of the state-space combination explosion.Moreover,it is suitable for systems whose failure and repair time obey an arbitrary distribution.Therefore,our method is more flexible than the traditional method.At last,an example is given to verify the method.

A general framework for computing maximal contractions

This paper investigates the problem of computing all maximal contractions of a given formula set F with re- spect to a consistent set A of atomic formulas and negations of atomic formulas. We first give a constructive definition of minimal inconsistent subsets and propose an algorithmic framework for computing all minimal inconsistent subsets of any given formula set. Then we present an algorithm to com- pute all maximal contractions from minimal inconsistent sub- sets. Based on the algorithmic framework and the algorithm, we propose a general framework for computing all maximal contractions. The computability of the minimal inconsistent subset and maximal contraction problems are discussed. Fi- nally, we demonstrate the ability of this framework by apply- ing it to the first-order language without variables and design an algorithm for the computation of all maximal contractions.

Commutative Rings Whose Zero-divisor Graph Is a Proper Refinement of a Star Graph

A graph is called a proper refinement of a star graph if it is a refinement of a star graph, but it is neither a star graph nor a complete graph. For a refinement of a star graph G with center c, let G＊ be the subgraph of G induced on the vertex set V（G） ／ {c or end vertices adjacent to c}. In this paper, we study the isomorphic classification of some finite commutative local rings R by investigating their zero-divisor graphs G=Г（R）, which is a proper refinement of a star graph with exactly one center c. We determine all finite commutative local rings R such that G＊ has at least two connected components. We prove that the diameter of the induced graph G＊ is two if Z（R）2 ≠{0}, Z（R）3 = {0} and Gc is connected. We determine the structure of R which has two distinct nonadjacent vertices a, fl C Z（R）＊／{c} such that the ideal [N（a）N（β）]{0} is generated by only one element of Z（R）＊／{c}. We also completely determine the correspondence between commutative rings and finite complete graphs Kn with some end vertices adjacent to a single vertex of Kn.

Almost automorphically-forced flows on S^(1) or R in one-dimensional almost periodic semilinear heat equations

In this paper,we consider the asymptotic dynamics of the skew-product semiflow generated by the following time almost periodically-forced scalar reaction-diffusion equation:u_(t)=u_(xx)+f(t,u,u_(x)),t>0,0<x<L(0.1)with the periodic boundary condition u(t,0)=u(t,L),u_(x)(t,0)=u_(x)(t,L),(0.2)where f is uniformly almost periodic in t.In particular,we study the topological structure of the limit sets of the skew-product semiflow.It is proved that any compact minimal invariant set(throughout this paper,we refer to it as a minimal set)can be residually embedded into an invariant set of some almost automorphically-forced flow on a circle S^(1)=R/LZ(see Definition 2.4 for“residually embedded”).Particularly,if f(t,u,p)=f(t,u,-p),then the flow on a minimal set can be embedded into an almost periodically-forced minimal flow on R(see Definition 2.4 for“embedded”).Moreover,it is proved that the ω-limit set of any bounded orbit contains at most two minimal sets that cannot be obtained from each other by phase translation.In addition,we further consider the asymptotic dynamics of the skew-product semiflow generated by(0.1)with the Neumann boundary condition u_(x)(t,0)=u_(x)(t,L)=0 or the Dirichlet boundary condition u(t,0)=u(t,L)=0.For such a system,it has been known that theω-limit set of any bounded orbit contains at most two minimal sets.By applying the new results for(0.1)+(0.2),under certain direct assumptions on f,we prove in this paper that the flow on any minimal set of(0.1)with the Neumann boundary condition or the Dirichlet boundary condition can be embedded into an almost periodically-forced minimal flow on R.Finally,a counterexample is given to show that even for quasi-periodically-forced equations,the results we obtain here cannot be further improved in general.

PEJA:Progressive Energy-Efficient Join Processing for Sensor Networks

Sensor networks are widely used in many applications to collaboratively collect information from the physical environment. In these applications, the exploration of the relationship and linkage of sensing data within multiple regions can be naturally expressed by joining tuples in these regions. However, the highly distributed and resource-constraint nature of the network makes join a challenging query. In this paper, we address the problem of processing join query among different regions progressively and energy-efficiently in sensor networks. The proposed algorithm PEJA （Progressive Energy-efficient Join Algorithm） adopts an event-driven strategy to output the joining results as soon as possible, and alleviates the storage shortage problem in the in-network nodes. It also installs filters in the joining regions to prune unmatchable tuples in the early processing phase, saving lots of unnecessary transmissions. Extensive experiments on both synthetic and real world data sets indicate that the PEJA scheme outperforms other join algorithms, and it is effective in reducing the number of transmissions and the delay of query results during the join processing.

Reasoning with Inconsistent Ontologies

Reasoning with inconsistent ontologies involves using an inconsistency reasoner to get meaningful answers from inconsistent ontologies. This paper introduces an improved inconsistency reasoner, which selects consistent subsets using minimal inconsistent sets and a resolution method, to improve the run-time performance of the reasoning processing. A minimal inconsistent set contains a minimal explanation for the inconsistency of a given ontology. Thus, it can replace the consistency checking operation, which is executed frequently in existing approaches. When selecting subsets of the inconsistent ontology, formulas which can be directly or indirectly resolved with the negation of the query formula are selected because only those formulas affect the consequences of the reasoner. Therefore, the complexity of the reasoning processing is significantly reduced. Tests show that the run-time performance of the inconsistency reasoner is significantly improved.

Ranks of Repeated-Root Constacyclic Code

By the discussion of division in F2m[u]/〈u4〉,the minimal spanning set and the rank of a（1＋u＋u2）-constacyclic code with an arbitrary length N=2en over F2m[u]/〈u4〉 are determined based on the factorization of（xn-1） over F2m.

Exact Reliability Formulas for Linear Consecutive-k-out-of-n: F Systems

A consecutive k out of n: F System, with n linearly arranged i. i. d. components, is examined. This paper gives an exact formula for computing the system's reliability directly. Complexity of this algorithm is an O(n k). Further more, the system's reliability can be computed more quickly and more effectively from this formula than those previously given.