An optimal local approximation algorithm for max-min linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0 for nonnegative matrices A and C. We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs. The approximation ratio of our algorithm is the best possible for any local algorithm; there is a matching unconditional lower bound.

Epoch extraction from linear prediction residual for identification of closed glottis interval

In voiced speech analysis epochal information is useful in accurate estimation of pitch periods and the frequency response of the vocal tract system. Ideally, linear prediction (LP) residual should give impulses at epochs. However, there are often ambiguities in the direct use of LP residual since samples of either polarity occur around epochs. Further, since the digital inverse filter does not compensate the phase response of the vocal tract system exactly, there is an uncertainty in the estimated epoch position. In this paper we present an interpretation of LP residual by considering the effect of the following factors: 1) the shape of glottal pulses, 2) inaccurate estimation of formants and bandwidths, 3) phase angles of formants at the instants of excitation, and 4) zeros in the vocal tract system. A method for the unambiguous identification of epochs from LP residual is then presented. The accuracy of the method is tested by comparing the results with the epochs obtained from the estimated glottal pulse shapes for several vowel segments. The method is used to identify the closed glottis interval for the estimation of the true frequency response of the vocal tract system.

Local approximability of max-min and min-max linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0. In a min-max LP, the objective is to minimise ρ subject to Ax ≤ ρ1, Cx ≥ 1, and x ≥ 0. The matrices A and C are nonnegative and sparse: each row ai of A has at most ΔI positive elements, and each row ck of C has at most ΔK positive elements. We study the approximability of max-min LPs and min-max LPs in a distributed setting; in particular, we focus on local algorithms (constant-time distributed algorithms). We show that for any ΔI ≥ 2, ΔK ≥ 2, and ε > 0 there exists a local algorithm that achieves the approximation ratio ΔI (1 − 1/ΔK) + ε. We also show that this result is the best possible: no local algorithm can achieve the approximation ratio ΔI (1 − 1/ΔK) for any ΔI ≥ 2 and ΔK ≥ 2.

A new classification and linear sequence of extant gymnosperms

A new classification and linear sequence of the gymnosperms based on previous molecular and morphological phylogenetic and other studies is presented. Currently accepted genera are listed for each family and arranged according to their (probable) phylogenetic position. A full synonymy is provided, and types are listed for accepted genera. An index to genera assists in easy access to synonymy and family placement of genera.

A linear sequence of extant families and genera of lycophytes and ferns

Throughout the history of the classification of extant ferns (monilophytes) and lycophytes, familial and generic concepts have been in great flux. For the organisation of lycophytes and ferns in herbaria, books, checklists, indices and spore banks and on the internet, this poses a problem, and a standardized linear sequence of these plants is therefore in great need. We provide here a linear classification to the extant lycophytes and ferns based on current phylogenetic knowledge; this provides a standardized guide for organisation of fern collections into a more natural sequence. Two new families, Diplaziopsidaceae and Rhachidosoraceae, are here introduced.

A method for estimation of the radius of elastic-plastic boundary around cold-worked holes

The radius of an elastic-plastic boundary was measured by the strain gage method around the cold-worked region in L72-aluminum alloy. The relative radial expansion was varied from 2.5 to 6.5 percent during the cold-working process using mandrel and split sleeve. The existing theoretical studies in this area are reviewed. The experimental results are compared with existing experimental data of various investigators and with various theoretical formulations. A model is developed to predict the radius of elastic-plastic boundary, and the model is assessed by comparing with the present experiments.

On duality in linear fractional programming

In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.

Nonnegative integral solution of linear equations

A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.

A Bilinear Constitutive Model for Isotropic Bimodulus Materials

Proper formulation of stress-strain relations, particularly in tension-compression situations for isotropic biomodulus materials, is an unresolved problem. Ambartsumyan's model [8] and Jones' weighted compliance matrix model [9] do not satisfy the principle of coordinate invariance. Shapiro's first stress invariant model [10] is too simple a model to describe the behavior of real materials. In fact, Rigbi [13] has raised a question about the compatibility of bimodularity with isotropy in a solid. Medri [2] has opined that linear principal strain-principal stress relations are fictitious, and warned that the bilinear approximation of uniaxial stress-strain behavior leads to ill-working bimodulus material model under combined loading. In the present work, a general bilinear constitutive model has been presented and described in biaxial principal stress plane with zonewise linear principal strain-principal stress relations. Elastic coefficients in the model are characterized based on the signs of (i) principal stresses, (ii) principal strains, and (iii) on the value of strain energy component ratio ER greater than or less than unity. The last criterion is used in tension-compression and compression-tension situations to account for different shear moduli in pure shear stress and pure shear strain states as well as unequal cross compliances.

An efficient algorithm for linear programming

A simple but efficient algorithm is presented for linear programming. The algorithm computes the projection matrix exactly once throughout the computation unlike that of Karmarkar’s algorithm where in the projection matrix is computed at each and every iteration. The algorithm is best suitable to be implemented on a parallel architecture. Complexity of the algorithm is being studied.

On numerical implementation of an isotropic elastic-viscoplastic constitutive model for bulk metallic glasses

An efficient algorithm within the finite deformation framework is developed for finite element implementation of a recently proposed isotropic, Mohr-Coulomb type material model, which captures the elastic-viscoplastic, pressure sensitive and plastically dilatant response of bulk metallic glasses. The constitutive equations are first reformulated and implemented using an implicit numerical integration procedure based on the backward Euler method. The resulting system of nonlinear algebraic equations is solved by the Newton-Raphson procedure. This is achieved by developing the principal space return mapping technique for the present model which involves simultaneous shearing and dilatation on multiple potential slip systems. The complete stress update algorithm is presented and the expressions for viscoplastic consistent tangent moduli are derived. The stress update scheme and the viscoplastic consistent tangent are implemented in the commercial finite element code ABAQUS/Standard. The accuracy and performance of the numerical implementation are verified by considering several benchmark examples, which includes a simulation of multiple shear bands in a 3D prismatic bar under uniaxial compression.