Effect Of Linear Transformation Research Articles

Rectangle Attack Against Type‐I Generalized Feistel Structures

Type-I generalized Feistel networks (GFN) are widely used frameworks in symmetric-key primitive designs such as CAST-256 and Lesamnta. Different from the extensive studies focusing on specific block cipher instances, the analysis against Type-I GFN structures gives generic security evaluation of the basic frameworks and concentrates more on the effect of linear transformation. Currently, works in this field mainly evaluate the security against impossible differential attack, zero-correlation linear attack, meet-in-the-middle attack and yoyo game attack, while its security evaluation against rectangle attack is still missing. In this paper, we filled this gap and gave the first structural analytical results of Type-I GFN against rectangle attack. By exploiting its structural properties, we proved there exists a boomerang switch for Type-I GFN for the first time, which is independent of the round functions. Then we turned the boomerang switch into chosen plaintext setting and proposed a new rectangle attack model. By appending 1 more round in the beginning of the boomerang switch, we constructed a rectangle distinguisher and a key recovery attack could be performed.

On weighted cumulative residual extropy: characterization, estimation and testing

This paper considers a new generalization of cumulative residual extropy (CRJ) introduced by Jahanshahi et al. [On cumulative residual extropy. Probab Eng Inf Sci. 2019. DOI:10.1017/S0269964819000196], called weighted cumulative residual extropy (WCRJ). This paper studies some properties of WCRJ of continuous lifetime distributions. Several results including various bounds, inequalities, and effects of linear transformations are obtained. Conditional WCRJ and some of its properties are discussed. Related studies of survival analysis are covered. Also, we propose an empirical version of the WCRJ to estimate this measure of uncertainty. Based on the asymptotic distribution of empirical WCRJ, a new test statistic is given for testing the equality of two cumulative distribution functions. The power of the proposed test statistic is compared to other traditional and new competing approaches. Some simulations are carried out to show how this newly proposed method is more powerful than the others for moderate to large sample sizes.

Interval extropy and weighted interval extropy

Recently, Extropy was introduced by Lad, Sanfilippo and Agr\`o as a complement dual of Shannon Entropy. In this paper, we propose dynamic versions of Extropy for doubly truncated random variables as measures of uncertainty called Interval Extropy and Weighted Interval Extropy. Some characterizations of random variables related to these new measures are given. Several examples are shown. These measures are evaluated under the effect of linear transformations and, finally, some bounds for them are presented.

Weighted Cumulative Residual (Past) Inaccuracy For Minimum (Maximum) of Order Statistics

In this paper, we propose a measure of weighted cumulative residual inaccuracy between survival function of the first-order statistic and parent survival function $\bar{F}$. We also consider weighted cumulative inaccuracy measure between distribution of the last- order statistic and parent distribution $F$. For these concepts, we obtain some reliability properties and characterization results such as relationships with other functions, bounds, stochastic ordering and effect of linear transformation. Dynamic versions of these weighted measures are considered.

Some Results on Dynamic Weighted Varma’s Entropy and its Applications

SYNOPTIC ABSTRACTRecently, the concept of dynamic Varma’s entropy has been proposed in the literature. In this article, we propose weighted forms of Varma’s and dynamic Varma’s entropy measures. We discuss several properties of proposed measures, including uniquely determine property, effect of linear transformation, and bounds. We also discuss some new ageing classes, characterization results, and relationship of proposed measures with some well-known reliability measures.

On weighted cumulative past (residual) inaccuracy for record values

In this paper, we propose the weighted cumulative past (residual) inaccuracy for record values. For this concept, we obtain some properties and characterization results such as relationships with other reliability functions, bounds, stochastic ordering and effect of linear transformation. Dynamic versions of this weighted measure are considered. We also study a problem of estimating the weighted cumulative past inaccuracy by means of the empirical cumulative inaccuracy for lower record values.

A Simple and Robust Approach for Expected Shortfall Estimation

In risk management, estimating Expected Shortfall (ES), though important and indispensable, is difficult when a sample size is small. This paper makes efforts to create a recipe for such challenge. A tail-based normal approximation with explicit formulas is derived by matching a specific quantile and mean excess square of the sample observations. To enhance the estimation accuracy, we then propose an adjusted tail-based normal approximation based on the sample's tail weight. The adjusted tailed-based normal approximation is robust and efficient in the sense that it can be applied to various heavy-tailed distributions, such as student's t, lognormal, Gamma, Weibull, etc., and the errors are very small. In addition, compared to two common ES estimators --- mean of excessive losses and extreme value theory estimator, the proposed approach achieves more accurate estimates with significantly smaller errors, especially at high confidence levels. Another appealing feature of the approach is that it works very well with small sample size. Effects of linear transformations on the ES estimator are also investigated to guarantee the practicality and further validate this new approach.

Effect of linear transformation on nonlinear behavior of continuous prestressed beams with external FRP cables

Abstract In continuous prestressed members, linear transformation of the cable line is an interesting topic that has not yet been adequately addressed. This paper presents a numerical study on the flexural response of two-span continuous externally fiber reinforced polymer (FRP) prestressed concrete beams having various linearly transformed cable profiles, with emphasis on the redistribution of moments. The study is conducted by using a robust computational method that has been validated against experimental tests. The results confirm that the cable shift by linear transformation does not affect the basic performance at all stages of loading up to failure. The secondary moments are shown to vary linearly with the cable shift. The development of moment redistribution over the center support is significantly affected by linear transformation. An upward cable shift leads to a decrease in moment redistribution at ultimate. The results indicate that the effect of linear transformation on moment redistribution is neglected or incorrectly included in various design codes.

On weighted cumulative residual entropy

To overcome the drawbacks of a shift-independent information measure, Di Crescenzo and Longobardi (2006) proposed weighted differential entropy. Motivated by this, the cumulative residual entropy can be generalized to weighted cumulative residual entropy. In this communication, we consider the weighted cumulative residual entropy and its dynamic version. These measures are useful in neurology and reliability engineering. Several results including bounds, inequalities, effects of linear transformations are obtained. Further, we propose two new classes of distributions and study closure and reversed closure properties. Finally, dynamic weighted cumulative residual entropy of residual lifetime of a series system is studied.

On Shift-Dependent Cumulative Entropy Measures

Measures of cumulative residual entropy (CRE) and cumulative entropy (CE) about predictability of failure time of a system have been introduced in the studies of reliability and life testing. In this paper, cumulative distribution and survival function are used to develop weighted forms of CRE and CE. These new measures are denominated as weighted cumulative residual entropy (WCRE) and weighted cumulative entropy (WCE) and the connections of these new measures with hazard and reversed hazard rates are assessed. These information-theoretic uncertainty measures are shift-dependent and various properties of these measures are studied, including their connections with CRE, CE, mean residual lifetime, and mean inactivity time. The notions of weighted mean residual lifetime (WMRL) and weighted mean inactivity time (WMIT) are defined. The connections of weighted cumulative uncertainties with WMRL and WMIT are used to calculate the cumulative entropies of some well-known distributions. The joint versions of WCE and WCRE are defined which have the additive properties similar to those of Shannon entropy for two independent random lifetimes. The upper boundaries of newly introduced measures and the effect of linear transformations on them are considered. Finally, empirical WCRE and WCE are proposed by virtue of sample mean, sample variance, and order statistics to estimate the new measures of uncertainty. The consistency of these estimators is studied under specific choices of distributions.

On the application of linear transformations for genetic algorithms optimization

This paper discusses new results about the effect of linear transformations (LTs) over the representation, the spectrum and the performance of standard genetic algorithms (GAs). Unitary LTs are used to set the basic outcomes and, although they can be used for theoretic GA-hard problems, their applicability is shown to be quite limited. Nevertheless, the redundancy of problems can be exploited by means of non-unitary LTs. We also propose an heuristic for construction of non-unitary LTs. Several experiments are performed in order to discuss the theoretical results of the paper.

PERFORMANCE ANALYSIS FOR DIRECTIONAL RESIDUAL BASED FAULT ISOLATION

Generalized likelihood ratio test (GLRT) for directional residual based fault isolation is studied in this paper. The conditional probability of correct fault isolation is used to measure the performance of the test. The explicit form of this probability is derived with the help of two GLRT invariant properties and the standard fault isolation subspace. The effect of linear transformation is studied as well.

Effects of Linear Transformations on the Divergence of Bounded Sequences and Functions

Effects of Linear Transformations on the Divergence of Bounded Sequences and Functions

Effects of linear transformations on the divergence of bounded sequences and functions

where { xi } is a sequence of complex elements and the Kn,i are complex numbers, has been widely studied, and the conditions which must be fulfilled by the Kn,i in order that the property of convergence of the sequence may remain invariant were given by Schur [I ].t In recent studies by Hurwitz [2, 3] and Knopp [4] modes of measuring the divergence of bounded sequences were given, and the conditions on the Kn,i were found under which the divergence of the sequence { yn } is no greater than that of {Xn}. In this paper the effects of the transformations will be investigated with fewer restrictions on the Kn,i than those imposed by earlier writers. The problem will be approached by means of the new concept of the limit circle defined as follows: The limit circle of a bounded sequence of complex elements is the (unique) circle of least radius which contains within or on its boundary the limit points of the sequence. The limit circle of a bounded function F(y) of the complex variable y as y->t (finite or infinite) is analogously defined in terms of the limit points of F(y) as y->t; this concept will be used in the study of transformations of sequences and functions into functions. 2. Sequence to function transformations. Instead of the transformation mentioned in the introduction we shall study the following more general transformation S. Let T be a set of points in the complex plane having a limit point to (finite or infinite) not belonging to T. We shall speak of a point t in T as being sufficiently advanced if for some a >0, jt toI < when to is finite, or j i/tI < 5 when to is infinite. Then let Ki(t) be a set of complex numbers defined for i= 1, 2, ... , and each t in T, and such that