The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

A brief survey on numerical methods for solving singularly perturbed problems

Automated dynamic malware analysis is a common approach for detecting malicious software. However, many malware samples identify the presence of the analysis environment and evade detection by not performing any malicious activity. Recently, an approach to the automated detection of such evasive malware was proposed. In this approach, a malware sample is analyzed in multiple analysis environments, including a bare-metal environment, and its various behaviors are compared. Malware whose behavior deviates substantially is identified as evasive malware. However, a malware analyst still needs to re-analyze the identified evasive sample to understand the technique used for evasion. Different tools are available to help malware analysts in this process. However, these tools in practice require considerable manual input along with auxiliary information. This manual process is resource-intensive and not scalable. In this paper, we present MalGene, an automated technique for extracting analysis evasion signatures. MalGene leverages algorithms borrowed from bioinformatics to automatically locate evasive behavior in system call sequences. Data flow analysis and data mining techniques are used to identify call events and data comparison events used to perform the evasion. These events are used to construct a succinct evasion signature, which can be used by an analyst to quickly understand evasions. Finally, evasive malware samples are clustered based on their underlying evasive techniques. We evaluated our techniques on 2810 evasive samples. We were able to automatically extract their analysis evasion signatures and group them into 78 similar evasion techniques.

https://dl.acm.org/doi/pdf/10.1145/2810103.2813642

MalGene: Automatic Extraction of Malware Analysis Evasion Signature

Review of wavelet methods for the solution of reaction–diffusion problems in science and engineering

In this paper, we review many recent developments and further applications of nonstandard finite difference (NSFD) methods encountered in the past decade. In particular, it is a follow up article of the one published in 2005 [K.C. Patidar, On the use of non-standard finite difference methods, J. Differ. Equ. Appl. 11 (2005), pp. 735–758]. It also includes those research contributions in this field that are very significant and published prior to the above article but were not included in the above paper simply because we did not have access to them when we wrote the above article. We also give a detailed account on various definitions/notions of NSFD methods appeared in the literature in past two decades. All contributions are listed chronologically except that in some instances we have grouped certain works to show connectivity in those fields. While categorizing these research contributions, we considered a number of different application areas. Moreover, due to space limitations, firstly, we have not i...

Nonstandard finite difference methods: recent trends and further developments

We develop a general discrete inequality based on the entropy idea in hyperbolic conservation laws, and demonstrate that enforcing this auxiliary inequality can be utilized for a number of steady and time-dependent problems. We demonstrate that, for any existing central difference based method, addition of this auxiliary inequality at the discrete level, enables one to achieve several desired purposes. Firstly, the violation of the inequality allows us to determine unphysical regions in the numerical solution without any a-priori knowledge of the solution. Secondly, the sign of the discrete production also functions as an excellent indicator for mesh adaptation in several problems in general and singular perturbation problems in particular. Thirdly, the operator can be used to derive robust schemes for convection dominated problems. Most importantly, all these are achieved without any ad-hoc, user introduced, parameters. We provide a range of numerical results demonstrating the efficacy of the method and its applicability to both steady and time dependent problems.

An Auxiliary Inequality Based Method for Stabilization and Mesh-Adaptation of Steady and Time-Dependent Differential Equations

In this paper, we develop a SIRS age-structured model with infective immigrants. We consider a fraction of the juvenile immigrants and a fraction of the adult immigrants to be infective. We calculate the equilibrium points and then check the stability of these points. The reproduction number is calculated using the Next- Generation Method. Mathematical simulation for the model is also conducted using MATLAB. It is observed that an increase in the infective immigrants does not affect the total infective persons in the population. However, there is an increase in the infective population if the rate of immigration is increased. Also, the recovered population increases as the recovery rate increases. It is seen that as the mosquito population increases due to an increase in their birth rate, the infective human population also increases.

An SIRS Age-Structured Model for Vector-Borne Diseases with Infective Immigrants

Authentication among the various communicating devices within wireless sensor networks during broadcasting is most significant among the other primary security services. This authentication during broadcasting services allows multiple mobile end‐devices to transmit messages dynamically and securely for fasten consumer tracking and sustaining privacy of the data transferred in the insecure sensor network. To enhance this authentication protocol for secure end‐users message distribution, this research work has introduced a novel identity (ID) based cryptographic technique that employs ElGmal‐elliptic‐curve cryptography and digital signature without implementing bilinear paring operation to reduce huge burden of computation overhead. Additionally, to accelerate the performance of the proposed authentication protocol, the size of the signature along with the encryption key is minimized. Eventually, the authentication protocol provides comparatively less computational complexity with secure and faster key management. The performance analysis supports the aforesaid claim as well as reflects the supremacy of the proposed scheme over the handover authentication protocol and bilinear pairings based authentication schemes.

Enhanced pairing‐free identity‐based broadcast authentication protocol in WSN using ElGamal ECC

Applying Efforts for Behavior-Based Authentication for Mobile Cloud Security

Traditional information retrieval methods become inadequate for increasing vast amount of data. Without knowing what could be in the documents; it is difficult to formulate effective queries for analyzing and extracting useful information from the data. This survey focused on some of the present strategies used for filtering documents. Starting with different types of text features this paper has discussed about recent developments in the field of classification of text documents. This paper gives a concise study of methods proposed by different researchers. Here various preprocessing steps were also discussed with a comprehensive and comparative understanding of existing literature.

/pdf/a-survey-on-various-features-and-techniques-of-text-content-20tjpgw9ll.pdf

Vivek Kumar

Papers

An Auxiliary Inequality Based Method for Stabilization and Mesh-Adaptation of Steady and Time-Dependent Differential Equations

An SIRS Age-Structured Model for Vector-Borne Diseases with Infective Immigrants

Enhanced pairing‐free identity‐based broadcast authentication protocol in WSN using ElGamal ECC

Applying Efforts for Behavior-Based Authentication for Mobile Cloud Security

A Survey on Various Features and Techniques of Text Content Classification