Sharif Digital Repository

In this article, we consider a secure multi-party computation problem (MPC), where the goal is to offload the computation of an arbitrary polynomial function of some massive private matrices (inputs) to a cluster of workers. The workers are not reliable. Some of them may collude to gain information about the input data (semi-honest workers). The system is initialized by sharing a (randomized) function of each input matrix to each server. Since the input matrices are massive, each share's size is assumed to be at most 1/k fraction of the input matrix, for some k ∈ N. The objective is to minimize the number of workers needed to perform the computation task correctly, such that even if an... 

In this paper, we introduce limited-sharing multiparty computation; in which there is a network of workers (processors) and a set of sources, each having access to a massive matrix as a private input. These sources aim to offload the task of computing a polynomial function of the matrices to the workers, while preserving the privacy of data. We also assume that the load of the link between each source and each worker is upper bounded by a fraction of each input matrix for some cin{1, rac{1}{2},rac{1}{3}, ldots}. The objective is to minimize the number of workers needed to perform the computation, such that even if an arbitrary subset of t-1 workers, for some tin mathbb{N}, collude, they... 

In this article, we consider a secure multi-party computation problem (MPC), where the goal is to offload the computation of an arbitrary polynomial function of some massive private matrices (inputs) to a cluster of workers. The workers are not reliable. Some of them may collude to gain information about the input data (semi-honest workers). The system is initialized by sharing a (randomized) function of each input matrix to each server. Since the input matrices are massive, each share's size is assumed to be at most 1/k fraction of the input matrix, for some k ∈ N. The objective is to minimize the number of workers needed to perform the computation task correctly, such that even if an... 

In a secure multiparty computation (MPC) system, there are some sources, where each one has access to a private input. The sources want to offload the computation of a polynomial function of the inputs to some processing nodes or workers. The processors are unreliable, i.e., a limited number of them may collude to gain information about the inputs. The objective is to minimize the number of required workers to calculate the polynomial, while the colluding workers gain no information about inputs. In this paper, we assume that the inputs are massive matrices, while the workers have the limited computation and storage at each worker. As proxy for that, we assume the link between each source... 

Macroporous styrene-divinylbenzene copolymers with different degree of crosslinking were prepared by suspension polymerization in presence of different binary mixtures of toluene and heptane, as diluent. Specific surface area, bulk and apparent densities, and pore volume of the resulting beads were determined experimentally. Applying the least square method to the experimental data, correlations for prediction of these properties were obtained. Effects of divinylbenzene concentration, diluent to comonomer volume ratio, and composition of the diluent mixture were considered in developing the aforementioned correlations. The influence of the reaction recipe on porous structure of the samples... 

The energy of a graph is defined as the sum of absolute values of all eigenvalues of its adjacency matrix. For a nonempty graph G, S. Akbari, A. Alazemi, M. Andelić and M.A. Hosseinzadeh proposed a conjecture: The energy of the line graph of G is at least |E(G)|+Δ(G)−3, where E(G) is the edge set of G and Δ(G) is the maximum degree of G. In this paper, we give a proof confirming the conjecture, and present a lower bound and an upper bound for the energy of line graphs of regular graphs. © 2023 Elsevier Inc  

Pulsating heat pipe (PHP) is a type of wickless heat pipe that has a simple structure and an outstanding thermal performance. Nanofluid is a type of fluid in which nanoparticles are dispersed in a base fluid and have generally a better thermal conductivity in comparison with its base fluid. In this article, the performance of a nanofluid PHP is investigated. Graphene/water nanofluid with a concentration of 1 mg mL−1 and TiO2 (titania)/water nanofluid with a concentration of 10 mg mL−1 are used as the working fluids. To simultaneously investigate the thermal performance and flow regimes in the PHP, a one-turn copper PHP with a Pyrex glass attached to its adiabatic section is used. A one-turn... 

Pulsating heat pipe (PHP) is a type of wickless heat pipe that has a simple structure and an outstanding thermal performance. Nanofluid is a type of fluid in which nanoparticles are dispersed in a base fluid and have generally a better thermal conductivity in comparison with its base fluid. In this article, the performance of a nanofluid PHP is investigated. Graphene/water nanofluid with a concentration of 1 mg mL −1 and TiO 2 (titania)/water nanofluid with a concentration of 10 mg mL −1 are used as the working fluids. To simultaneously investigate the thermal performance and flow regimes in the PHP, a one-turn copper PHP with a Pyrex glass attached to its adiabatic section is used. A... 

Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and term rank of G, by rk (G) and Rk (G), respectively. van Nuffelen conjectured that for any graph G, χ (G) ≤ rk (G). The first counterexample to this conjecture was obtained by Alon and Seymour. In 2002, Fishkind and Kotlov proved that for any graph G, χ (G) ≤ Rk (G). Here we improve this upper bound and show that χl (G) ≤ (rk (G) + Rk (G)) / 2, where χl (G) is the list chromatic number of G. © 2006 Elsevier B.V. All rights reserved  

Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and the term rank of G, by rk (G) and Rk (G), respectively. It was conjectured [C. van Nuffelen, Amer. Math. Monthly 83 (1976) 265-266], for any graph G, χ (G) ≤ rk (G). The first counterexample to this conjecture was obtained by Alon and Seymour [J. Graph Theor. 13 (1989) 523-525]. Recently, Fishkind and Kotlov [Discrete Math. 250 (2002) 253-257] have proved that for any graph G, χ (G) ≤ Rk (G). In this Note we improve Fishkind-Kotlov upper bound and show that χ (G) ≤ rk(G)+Rk(G)/2. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved  

Numerous operational issues including voltage deviation and instability arise in distribution networks with insufficient reactive support. Static issues have been widely studied for years, and some dynamic ones are recently gaining attention due to the proliferation of distributed generation (DG). In this paper, a two-step reactive compensation planning procedure is proposed to address these challenges. In the first step, passive compensators are optimally sited and sized using a metaheuristic algorithm in order to improve steady-state indices including power efficiency, voltage profile, and static voltage stability. In the second step, a static synchronous compensator (Statcom) is located... 

Let G be a graph and for any natural number r, χs ′ (G, r) denotes the minimum number of colors required for a proper edge coloring of G in which no two vertices with distance at most r are incident to edges colored with the same set of colors. In [Z. Zhang, L. Liu, J. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett. 15 (2002) 623-626] it has been proved that for any tree T with at least three vertices, χs ′ (T, 1) ≤ Δ (T) + 1. Here we generalize this result and show that χs ′ (T, 2) ≤ Δ (T) + 1. Moreover, we show that if for any two vertices u and v with maximum degree d (u, v) ≥ 3, then χs ′ (T, 2) = Δ (T). Also for any tree T with Δ (T) ≥ 3 we prove that χs ′ (T, 3) ≤ 2 Δ... 

The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all noncentral elements of R, and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this article we investigate some graph-theoretic properties of Γ(Mn(F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GLn(F) and SLn(F). We show that Γ(Mn(F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GLn(F)) and Γ(SL n(F)). Also we show... 

An Artificial Neural Network (ANN) model has been designed for predicting the effects of alloying elements (Fe, Si, Al, Mn) on the recrystallization behavior and microstructural changes of 70/30 brass. The model introduced here considers the content of alloying elements, temperature, and time of recrystallization as inputs while percent of recrystallization is presented as output. It is shown that the designed model is able to predict the effect of alloying elements well. It is also shown that all alloying elements strongly affect the recrytallization kinetics, and all slow down the recrystallization process. The effect of alloying elements on the activation energy for recrystallization has... 

A subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper, we prove that a complete graph on 2m (m ≠ 2) vertices K2m can be properly edge-colored with 2m - 1 colors in such a way that the edges of K2m can De partitioned into m multicolored isomorphic spanning trees. © 2006 Society for Industrial and Applied Mathematics  

Packet loss recovery is an important part of P2P video streaming networks due to inevitable packet loss in today's internet and interdependency of data units in compressed video streams. In addition, the architecture of P2P streaming networks, in which the data delivered to the receivers through chain of peers, can intensify the impact of the internet packet loss on the quality of perceived video at the receivers. FEC and ARQ are the two most important techniques that can be used to overcome the side effect of the internet packet loss in P2P video streaming networks. Based on these two techniques, different packet loss recovery strategies can be applied in different overlay hops of a given... 

Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,x)=σi=1 nd(G,i)xi, where d(G,i) is the number of dominating sets of G of size i. A root of D(G,x) is called a domination root of G. We denote the set of distinct domination roots by Z(D(G,x)). Two graphs G and H are said to be D-equivalent, written as G~H, if D(G,x)=D(H,x). The D-equivalence class of G is [G]={H:H~G}. A graph G is said to be D-unique if [G]={G}. In this paper, we show that if a graph G has two distinct domination roots, then Z(D(G,x))={-2,0}. Also, if G is a graph with no pendant vertex and has three distinct domination roots, then Z(D(G,x)). Also, we study the D-equivalence classes of... 

Let R be a ring with identity and M be a unitary left R-module. The intersection graph of submodules of M, denoted by G(M), is defined to be a graph whose vertices are in one to one correspondence with all non-trivial submodules of M and two distinct vertices are adjacent if and only if the corresponding submodules of M have non-zero intersection. In this paper, we consider the intersection graph of submodules of a module. We determine the structure of modules whose clique numbers are finite. We show that if 1 < ω(G(M)) < ∞, then M is a direct sum of a finite module and a cyclic module, where ω(G(M)) denotes the clique number of G(M). We prove that if ω(G(M)) is not finite, then M contains...