Linear approximation of Karnik-Mendel type reduction algorithm

Karnik-Mendel (KM) algorithm is the most used and researched type reduction (TR) algorithm in literature. This algorithm is iterative in nature and despite consistent long term effort, no general closed form formula has been found to replace this computationally expensive algorithm. In this research work, we demonstrate that the outcome of KM algorithm can be approximated by simple linear regression techniques. Since most of the applications will have a fixed range of inputs with small scale variations, it is possible to handle those complexities in design phase and build a fuzzy logic system (FLS) with low run time computational burden. This objective can be well served by the application of regression techniques. This work presents an overview of feasibility of regression techniques for design of data-driven type reducers while keeping the uncertainty bound in FLS intact. Simulation results demonstrates the approximation error is less than 2%. Thus our work preserve the essence of Karnik-Mendel algorithm and serves the requirement of low
computational complexities.

Distinguishing attack on SOBER-128 with linear masking

We present a distinguishing attack against SOBER-128 with linear masking. We found a linear approximation which has a bias of 2^− − 8.8 for the non-linear filter. The attack applies the observation made by Ekdahl and Johansson that there is a sequence of clocks for which the linear combination of some states vanishes. This linear dependency allows that the linear masking method can be applied. We also show that the bias of the distinguisher can be improved (or estimated more precisely) by considering quadratic terms of the approximation. The probability bias of the quadratic approximation used in the distinguisher is estimated to be equal to O(2^− − 51.8), so that we claim that SOBER-128 is distinguishable from truly random cipher by observing O(2^103.6) keystream words.

Improved linear cryptanalysis of reduced-round SIMON-32 and SIMON-48

In this paper we analyse two variants of SIMON family of light-weight block ciphers against variants of linear cryptanalysis and present the best linear cryptanalytic results on these variants of reduced-round SIMON to date. We propose a time-memory trade-off method that finds differential/linear trails for any permutation allowing low Hamming weight differential/linear trails. Our method combines low Hamming weight trails found by the correlation matrix representing the target permutation with heavy Hamming weight trails found using a Mixed Integer Programming model representing the target differential/linear trail. Our method enables us to find a 17-round linear approximation for SIMON-48 which is the best current linear approximation for SIMON-48. Using only the correlation matrix method, we are able to find a 14-round linear approximation for SIMON-32 which is also the current best linear approximation for SIMON-32. The presented linear approximations allow us to mount a 23-round key recovery attack on SIMON-32 and a 24-round Key recovery attack on SIMON-48/96 which are the current best results on SIMON-32 and SIMON-48. In addition we have an attack on 24 rounds of SIMON-32 with marginal complexity.

Extrinsic Analog Synthesis using Piecewise Linear Current-Mode Circuits

A methodology is presented for the synthesis of analog circuits using piecewise linear (PWL) approximations. The function to be synthesized is divided into PWL segments such that each segment can be realized using elementary MOS current-mode programmable-gain circuits. A number of these elementary current-mode circuits when connected in parallel, it is possible to realize piecewise linear approximation of any arbitrary analog function with in the allowed approximation error bounds. Simulation results show a close agreement between the desired function and the synthesized output. The number of PWL segments used for approximation and hence the circuit area is determined by the required accuracy and the smoothness of the resulting function.

linear cryptanalysis of nush block cipher

IEEE Computer Society

Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Cubic approximation for the transverse displacement in BEM for elastic plates analysis

This work presents an application for the plate analysis formulation by BEM where 3 boundary equations are used, written for the transverse displacement w and the normal and tangential derivatives partial derivativew/partial derivativen and partial derivativew/partial derivatives. In this extension, the transverse displacement w is approximated by a cubic polynomial and, as a consequence, partial derivativew/partial derivatives has a quadratic approximation. This alternative BEM formulation improves the analysis of thin plates, when compared to the formulation using the linear approximation for the displacements, mainly in the obtaining of the bending moments at the boundary of the plate. The implementation of this proposal to the computational codes is simple. (C) 2004 Published by Elsevier Ltd.

Inclusão de pilares numa formulação do método dos elementos de contorno para análise linear de pavimentos de edifícios

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Provisos for classic linear oscillator design methods. New linear oscillator design based on the NDF/RRT

In this paper, the classic oscillator design methods are reviewed, and their strengths and weaknesses are shown. Provisos for avoiding the misuse of classic methods are also proposed. If the required provisos are satisfied, the solutions provided by the classic methods (oscillator start-up linear approximation) will be correct. The provisos verification needs to use the NDF (Network Determinant Function). The use of the NDF or the most suitable RRT (Return Relation Transponse), which is directly related to the NDF, as a tool to analyze oscillators leads to a new oscillator design method. The RRT is the "true" loop-gain of oscillators. The use of the new method is demonstrated with examples. Finally, a comparison of NDF/RRT results with the HB (Harmonic Balance) simulation and practical implementation measurements prove the universal use of the new methods.

Approximation of Univariate Set-Valued Functions - an Overview

2000 Mathematics Subject Classification: 26E25, 41A35, 41A36, 47H04, 54C65.

An improved distinguisher for dragon

Dragon stream cipher is one of the focus ciphers which have reached Phase 2 of the eSTREAMproject. In this paper, we present a new method of building a linear distinguisher for Dragon. The distinguisher is constructed by exploiting the biases of two S-boxes and the modular addition which are basic components of the nonlinear function F. The bias of the distinguisher is estimated to be around 2−75.32 which is better than the bias of the distinguisher presented by Englund and Maximov. We have shown that Dragon is distinguishable from a random cipher by using around 2150.6 keystream words and 259 memory. In addition, we present a very efficient algorithm for computing the bias of linear approximation of modular addition.

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Reservoir Operation for Hydropower Optimization: A Chance-Constrained Approach

This paper presents a chance-constrained linear programming formulation for reservoir operation of a multipurpose reservoir. The release policy is defined by a chance constraint that the probability of irrigation release in any period equalling or exceeding the irrigation demand is at least equal to a specified value P (called reliability level). The model determines the maximum annual hydropower produced while meeting the irrigation demand at a specified reliability level. The model considers variation in reservoir water level elevation and also the operating range within which the turbine operates. A linear approximation for nonlinear power production function is assumed and the solution obtained within a specified tolerance limit. The inflow into the reservoir is considered random. The chance constraint is converted into its deterministic equivalent using a linear decision rule and inflow probability distribution. The model application is demonstrated through a case study.

Robust Approach for Identification of Bad Data in State Estimation Using SLP Technique

This paper proposes a new approach for solving the state estimation problem. The approach is aimed at producing a robust estimator that rejects bad data, even if they are associated with leverage-point measurements. This is achieved by solving a sequence of Linear Programming (LP) problems. Optimization is carried via a new algorithm which is a combination of “upper bound optimization technique" and “an improved algorithm for discrete linear approximation". In this formulation of the LP problem, in addition to the constraints corresponding to the measurement set, constraints corresponding to bounds of state variables are also involved, which enables the LP problem more efficient in rejecting bad data, even if they are associated with leverage-point measurements. Results of the proposed estimator on IEEE 39-bus system and a 24-bus EHV equivalent system of the southern Indian grid are presented for illustrative purpose.

Cyclical Features of Uzawa-Lucas Endogenous Growth Model

This paper analyzes the cyclical properties of a generalized version of Uzawa-Lucas endogenous growth model. We study the dynamic features of different cyclical components of this model characterized by a variety of decomposition methods. The decomposition methods considered can be classified in two groups. On the one hand, we consider three statistical filters: the Hodrick-Prescott filter, the Baxter-King filter and Gonzalo-Granger decomposition. On the other hand, we use four model-based decomposition methods. The latter decomposition procedures share the property that the cyclical components obtained by these methods preserve the log-linear approximation of the Euler-equation restrictions imposed by the agent’s intertemporal optimization problem. The paper shows that both model dynamics and model performance substantially vary across decomposition methods. A parallel exercise is carried out with a standard real business cycle model. The results should help researchers to better understand the performance of Uzawa-Lucas model in relation to standard business cycle models under alternative definitions of the business cycle.