scholarly journals Dynamic Ring Exploration with (H,S) View

Algorithms ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 141 ◽  
Author(s):  
Tsuyoshi Gotoh ◽  
Yuichi Sudo ◽  
Fukuhito Ooshita ◽  
Toshimitsu Masuzawa

The researches about a mobile entity (called agent) on dynamic networks have attracted a lot of attention in recent years. Exploration which requires an agent to visit all the nodes in the network is one of the most fundamental problems. While the exploration of dynamic networks with complete information or with no information about network changes has been studied, an agent with partial information about the network changes has not been considered yet despite its practical importance. In this paper, we consider the exploration of dynamic networks by a single agent with partial information about network changes. To the best of our knowledge, this is the very first work to investigate the exploration problem with such partial information. As a first step in this research direction, we focus on 1-interval connected rings as dynamic networks in this paper. We assume that the single agent has partial information called the ( H , S ) view by which it always knows whether or not each of the links within H hops is available in each of the next S time steps. In this setting, we show that H + S ≥ n and S ≥ ⌈ n / 2 ⌉ (n is the size of the network) are necessary and sufficient conditions to explore 1-interval connected rings. Moreover, we investigate the upper and lower bounds of the exploration time. It is proven that the exploration time is O ( n 2 ) for ⌈ n / 2 ⌉ ≤ S < 2 H ′ − 1 , O ( n 2 / H + n H ) for S ≥ max ( ⌈ n / 2 ⌉ , 2 H ′ − 1 ) , O ( n 2 / H + n log H ) for S ≥ n − 1 , and Ω ( n 2 / H ) for any S where H ′ = min ( H , ⌊ n / 2 ⌋ ) .

1992 ◽  
Vol 06 (10) ◽  
pp. 1657-1709 ◽  
Author(s):  
ROBERT R. TUCCI

In this paper, we generalize to 2-mode states the 1-mode state results obtained in a previous paper. We study 2-mode Gaussian density matrices (i.e., density matrices of the form: exponential of a quadratic polynomial in the creation and annihilation operators for the two modes). We find a linear transformation which maps the two annihilation operators, one for each mode, into two new annihilation operators that are uncorrelated and unsqueezed. This allows us to express the density matrix as a product of two 1mode density matrices. We find general conditions under which 2-mode Gaussian density matrices become pure states. Possible pure states include the 2-mode squeezed pure states commonly mentioned in the literature, plus other pure states never mentioned before. We discuss the entropy and thermodynamic laws (Second Law, Fundamental Equation, and Gibbs-Duhem Equation) for the 2-mode states being considered. We study the change in entropy that is produced when a 2-mode Gaussian state is subjected to a measurement of the complex amplitude of one of its two modes. We derive upper and lower bounds for the final (i.e., after the measurement) entropy of the unmeasured mode, and we give necessary and sufficient conditions for the achievement of these bounds. The existence of the bounds is shown to be a consequence of the concavity property of the entropy function.


2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zhengxin Wang ◽  
Yang Cao

This paper studies the consensus problem for a high-order multi-agent systems without or with delays. Consensus protocols, which only depend on the own partial information of agents and partial relative information with its neighbors, are proposed for consensus and quasi-consensus, respectively. Firstly, some lemmas are presented, and then a necessary and sufficient condition for guaranteeing the consensus is established under the consensus protocol without delays. Furthermore, communication delays are considered. Some necessary and sufficient conditions for solving quasi-consensus problem with delays are obtained. Finally, some simulations are given to verify the theoretical results.


2014 ◽  
Vol 17 (08) ◽  
pp. 1450050 ◽  
Author(s):  
GIULIA DI NUNNO ◽  
STEFFEN SJURSEN

We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite activity. The default events are modeled via a counting process in line with large part of the literature in credit risk. In order to deal with both cases of inside and partial information we consider the framework of the anticipating calculus of forward integration. This does not require a priori assumptions typical of the framework of enlargement of filtrations. We find necessary and sufficient conditions for the existence of a locally maximizing portfolio of the expected utility at terminal time. We consider a large class of utility functions. In addition we show that the existence of the solution implies the semi-martingale property of the noises driving the stock. Some discussion on unicity of the maxima is included.


2019 ◽  
Vol 27 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Natalia Pavlovna Bondarenko

AbstractAn integro-differential Dirac system with an integral term in the form of convolution is considered. We suppose that the convolution kernel is known a priori on a part of the interval, and recover it on the remaining part, using a part of the spectrum. We prove the uniqueness theorem, provide an algorithm for the solution of the inverse problem together with necessary and sufficient conditions for its solvability.


1989 ◽  
Vol 39 (2) ◽  
pp. 301-317 ◽  
Author(s):  
G.M. Kelly

With a view to further applications, we give a self-contained account of indexed limits for 2-categories, including necessary and sufficient conditions for 2-categorical completeness. Many important 2-categories fail to be complete but do admit a wide class of limits. Accordingly, we introduce a variety of particular 2-categorical limits of practical importance, and show that certain of these suffice for the existence of indexed lax- and pseudo-limits. Other important 2-categories fail to admit even pseudo-limits, but do admit the weaker bilimits; we end by discussing these.


Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Qinyao Pan ◽  
Jie Zhong ◽  
Shalin Tong ◽  
Bowen Li ◽  
Xiaoxu Liu

It is worth noting that both nodes’ coupling connections and logical updating functions play a vital role in state evolutions of Boolean networks (BNs). In this paper, a new concept named structural controllability (SC) about Boolean control networks (BCNs) with known partial information on nodes’ connections is studied. Then, by referring to semi-tensor product (STP) techniques, several types of SC are presented according to different issues of Boolean functions. Thereafter, several necessary and sufficient conditions are derived for SC of BCNs. Finally, a biological model of the lactose operon in Escherichia coli is simulated to show the effectiveness of the main theoretical results.


Author(s):  
Ross G. Drynan

AbstractThis note generalises the necessary and sufficient conditions for one act to be dominated by another when the two acts available to the decision maker have outcomes contingent on discrete states of nature whose probabilities of occurrence are known only to the extent of linear partial information. The generalisation relates to the dominance of an act by a set of acts. The presentation is in terms of general vector dominance, of which statistical dominance is only a particular case.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jumei Yue ◽  
Yongyi Yan ◽  
He Deng

In this paper, the structure of graphs in terms of k-externally stable set (k-ESS) is investigated by a matrix method based on a new matrix product, called semitensor product of matrices. By defining an eigenvector and an eigenvalue of the node subset of a graph, three necessary and sufficient conditions of k-ESS, minimum k-ESS, and k-kernels of graphs are proposed in a matrix form, respectively. Using these conditions, the concepts of k-ESS matrix, minimum k-ESS matrix, and k-kernel matrix are introduced. These matrices provide complete information of the corresponding structures of a graph. Further, three algorithms are designed, respectively, to find all these three structures of a graph by conducting a series of matrix operation. Finally, the correctness and effectiveness of the results are checked by studying an example. The proposed method and results may offer a new way to investigate the problems related to graph structures in the field of network systems.


2012 ◽  
Vol 23 (07) ◽  
pp. 1250072 ◽  
Author(s):  
MANUEL FERNÁNDEZ-LÓPEZ ◽  
EDUARDO GARCÍA-RÍO

Necessary and sufficient conditions for a gradient Ricci soliton to be Einstein are given, showing that they can be expressed in terms of upper and lower bounds on the behavior of the Ricci tensor when evaluated on the gradient of the potential function of the soliton.


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