Sharif Digital Repository

Let A be a subset of the constructive real line. What are the necessary and sufficient conditions for the set A such that A is continuously separated from other reals, i.e., there exists a continuous function f with f -1(0) = A? In this paper, we study the notions of closed sets and closure maps in constructive reverse mathematics  

Clustering is the process of grouping data objects into set of disjoint classes called clusters so that objects within a class are highly similar with one another and dissimilar with the objects in other classes. The k-means algorithm is a simple and efficient algorithm that is widely used for data clustering. However, its performance depends on the initial state of centroids and may trap in local optima. In order to overcome local optima obstacles, a lot of studies have been done in clustering. The Fashion Algorithm is one effective method for searching problem space to find a near optimal solution. This paper presents a hybrid optimization algorithm based on Generalized Fashion Algorithm... 

In the context of intuitionistic analysis, we consider the set F consisting of all continuous functions φ{symbol} from [0, 1] to R such that φ{symbol} (0) = 0 and φ{symbol} (1) = 1, and the set I0 consisting of φ{symbol}'s in F where there exists x ∈ [0, 1] such that φ{symbol} (x) = frac(1, 2). It is well-known that there are weak counterexamples to the intermediate value theorem, and with Brouwer's continuity principle we have I0 ≠ F. However, there exists no satisfying answer to I0¬ ¬ =? F. We try to answer to this question by reducing it to a schema (which we call ED) about intuitionistic decidability that asserts "there exists an intuitionistically enumerable set that is not... 

A bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit. We claim that the existence of Specker sequences crucially depends on the properties of intuitionistic decidable sets. We propose a schema (which we call ED) about intuitionistic decidability that asserts "there exists an intuitionistic enumerable set that is not intuitionistic decidable" and show that the existence of a Specker sequence is equivalent to ED. We show that... 

Employing femtocell technology noticeably improves both the indoor coverage and the overall cellular network's capacity. In the downlink scenario, when macrocell users (MUs) are far from the macro base station (MBS) and close to the femto access points (FAPs), the transmitted signals of FAPs to their users cause severe interference on MUs. One solution to overcome this issue is serving MUs by neighbouring FAPs. Generally femtocells are selfish and have no desire to allocate their resources to MUs. In this study, a framework to motivate femtocells to share their free resources with MUs is proposed. In this framework, the femtocells are assumed to belong to a specific unit. The unit encourages... 

A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. In each call between a pair of connected agents, the two agents share all the secrets they have learnt. In dynamic gossip problems, dynamic connection graphs are enabled by permitting agents to spread as well the telephone numbers of other agents they know. This paper characterizes different distributed epistemic protocols in terms of the (largest) class of graphs where each protocol is successful, i.e. where the protocol necessarily ends up with all agents knowing all secrets. © 2016 Elsevier B.V  

A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. The goal is for all agents to get to know all secrets, in which case we call the execution of the protocol successful. We consider distributed and dynamic gossip protocols. In distributed gossip, the agents themselves instead of a global scheduler determine whom to call. In dynamic gossip, not only secrets are exchanged but also telephone numbers (agent identities). This results in increased graph connectivity. We define six such distributed dynamic gossip protocols, and we characterize them in terms of the topology of the graphs on which they are successful, wherein we distinguish...