Each ATTACK GRAPH represents a collection of possible ATTACK scenarios in a computer network. In this paper, we use WEIGHTED ATTACK GRAPHs (WAGs) for vulnerability assessment of computer networks. In these directed GRAPHs, a weight is assigned to each exploit by the security analyst. The weight of an exploit is proportionate to the cost required to prevent that exploit. The aim of analyzing a WEIGHTED ATTACK GRAPH is to find a critical set of exploits such that the sum of their weights is minimum and by preventing them no ATTACK scenario is possible. In this paper, we propose a greedy algorithm, a genetic algorithm with a greedy mutation operator, and a genetic algorithm with a dynamic fitness function for analyzing the WEIGHTED ATTACK GRAPHs. The proposed algorithms are used to analyze a sample WEIGHTED ATTACK GRAPH and several randomly generated large-scale WEIGHTED ATTACK GRAPHs. The results of experiments show that the proposed genetic algorithms outperform the greedy algorithm and find a critical set of exploits with less total weight. Finally, we compare the performance of the second genetic algorithm with an approximation algorithm for analyzing several randomly generated large-scale simple ATTACK GRAPHs. The results of experiments show that our proposed genetic algorithm has better performance than the approximation algorithm and finds a critical set of exploits with less cardinality.

In this paper, the WEIGHTED Szeged indices of Cartesian product and Corona product of two connected GRAPHs are obtained. Using the results obtained here, the WEIGHTED Szeged indices of the hypercube of dimension n, Hamming GRAPH, C4 nanotubes, nanotorus, grid, t-fold bristled, sunlet, fan, wheel, bottleneck GRAPHs and some classes of bridge GRAPHs are computed.

This paper represents a technique for finding optimal paths with multiple indexes in a GRAPH. Up to the present time, all optimal paths have been determined upon one index, say, distance for which an evaluation method exists. In this paper firstly we define multiple indexes for each edge in such a way that anyone can treat the factor for assigning an optimal path. Here, we use Data Envelopment Analysis (DEA) technique for designing a model that can identify optimal paths with multiple indexes, and separate them from the other paths.

The Bertz indices, derived by counting the number of connecting edges of line GRAPHs of a molecule were used in deriving the QSPR models for the physicochemical properties of alkanes. The inability of these indices to identify the hetero centre in a chemical compound restricted their applications to hydrocarbons only. In the present work, a novel molecular descriptor has been derived from the WEIGHTED line GRAPH of the molecular structure and applied in correlating the physicochemical properties of alkane isomers with these descriptors. A weight is tagged at the vertex of the line GRAPH, which consequently modifies the weight of the edge. These descriptors were found to classify the alkane isomers and served well in deriving the QSPR models for various physicochemical properties. The mathematical calculations include the quantitative treatment on the role of substituents (alkyl) in governing the properties under study of the alkane isomers. Further, the use of WEIGHTED line GRAPH in the enumeration of the topological index opens up a new vista on application to heteroatomic systems.

There are various engineering applications dealing with the prototype problem of finding the best p-medians in a WEIGHTED GRAPH. However, the heuristic developments are still of concern due to their complexity. This paper utilizes genetic algorithm as a well-known reliable evolutionary search for such a purpose. Problem formulation is studied, introducing a characteristic GRAPH and specialized genotype representation called\Direct Index Coding". The genetic operators are also modified due to problem requirements, and further tuned using a simulated annealing approach. Such an enhanced evolutionary search tool is then applied to a number of examples to show its effectiveness regarding the exact results, and to compare efficiency between tuned and non-tuned GA.

Performing risk assessment of computer networks is inevitable in the process of network hardening. To do efficient ATTACK prevention, risk evaluation must be done in an accurate and quantitative manner. Such risk assessment requires thorough understanding of ATTACK’s causes or vulnerabilities and their related characteristics. But, one major problem is that, there are vulnerabilities that are known by ATTACKers but there is no information about them in databases like NVD (National Vulnerability Database). Such vulnerabilities are referred to as unknown or zero day ATTACKs. Existing standards like NVD ignore the effect of unknown ATTACKs in risk assessment of computer networks. In this paper, by defining some ATTACK GRAPH based security metrics, we proposed an innovative method for risk evaluation of multi-step Zero-Day ATTACKs. Proposed method by predicting the intrinsic features of Zero-Day ATTACKs makes their risk estimation possible. Considering the effect of Temporal features of vulnerabilities have made our approach a Dynamic Risk Estimator.

Today, the rapid growth of dependence of human life on the cyberspace has raised the attention of the enemies of every society to the threats in this space. Several cyberATTACKs that have taken place in countries such as Estonia, Georgia and the Islamic Republic of Iran in the past, warn that the future of cyberspace will not be free of threats and ATTACKs. Deterrence has always been a very important issue for all countries. In this practical and developmental research, we present Strategical Deterrence model in cyberspace. The game theory will help us model and analyze the deterrent model and descriptive and mathematical inferences will be used to analyze the model. Finally, in this paper, a strategical model for deterrence in cyberspace will be presented in four stages: the current, optimal, gap analysis and warning stages based on the signaling game with incomplete information. Finally after describing each components of the model and their relationship with each other, it has been shown that the amount of equilibrium can indicate the status of the players in the three situation of conflict, balance and mutual weakness, and only in two situation of balance and mutual weakness, the deterrence will exist.

An Euclidean GRAPH associated with a molecule is defined by a WEIGHTED GRAPH with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster GRAPHs and then Randic computed complexity indices of them (1973, 2001). In this paper, with a simple method, we calculate the automorphism group of some WEIGHTED GRAPHs.

Background: Prostate cancer is the third leading cause of death and is the most common cause of cancer in elderly men. Regarding to the low accuracy of screening methods such as prostate-specific antigen (PSA), Digital Rectal Examination (DRE) and trans rectal ultrasound (TRUS) in detection and localization of tumor, Magnetic Resonance Imaging (MRI) and Diffusion WEIGHTED Imaging (DWI) attracted many attentions in the past years. DWI reveals micro-molecular diffusion, which is the Brownian motion of the spins in biologic tissues. This technique can delineate pathologic lesions with high tissue contrast against generally suppressed background signal. In this paper, the value of DWI in detection of prostate cancer is studied.Methods: In this cross-sectional study, the studied population are suspicious patients to prostate cancer based on high Prostatic Specific Antigen level or abnormal Digital Rectal Examination who refered for prostate biopsy to radiology department of Hazrate- Rasoul Hospital during the year 2011. The results of DWI are compared to biopsy results for all patients.Results: Eighty five patients are selected. The DWI sensitivity in detecting of prostate cancer is 100%, specificity 97.1% and positive and negative predictive values are 89.5% and 100%, respectively. The results showed that if DWI reports the prostate cancer as negative, the result was highly reliable and if it reports as positive, although the report was not 100% reliable, but it still had high reliability, more than 90%.Conclusion: DWI had high accuracy in detecting prostate cancer for patients with cancer. Also the accuracy of this method for patients without prostate cancer was acceptable compared to the other common methods.