A Polymatroid Approach to Separable Convex Optimization with Linear Ascending Constraints

We revisit a problem studied by Padakandla and Sundaresan SIAM J. Optim., August 2009] on the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation problems in wireless communication settings. It is also a special case of an optimization of a separable convex function over the bases of a specially structured polymatroid. We give an alternative proof of the correctness of the algorithm of Padakandla and Sundaresan. In the process we relax some of their restrictions placed on the objective function.

A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem

We revisit the a posteriori error analysis of discontinuous Galerkin methods for the obstacle problem derived in 25]. Under a mild assumption on the trace of obstacle, we derive a reliable a posteriori error estimator which does not involve min/max functions. A key in this approach is an auxiliary problem with discrete obstacle. Applications to various discontinuous Galerkin finite element methods are presented. Numerical experiments show that the new estimator obtained in this article performs better.

Stable isotope evidence for ca. 2.7-Ga-old Archean cap carbonates from the Dharwar Supergroup, southern India

Carbon isotope compositions of carbonate rocks from similar to 2.7-Ga-old Neoarchean Vanivilas Formation of the Dharwar Supergroup presented earlier by us are re-evaluated in this study, besides oxygen isotope compositions of a few silica dolomite pairs. The purpose of such a revisit assumes significance in view of recent field evidences that suggest a glaciomarine origin for the matrix-supported conglomerate member, the Talya conglomerate, which underlies the carbonate rocks of the Vanivilas Formation. An in-depth analysis of carbon isotope data reveals preservation of their pristine character despite the rocks having been subjected to metamorphism to different degrees (from lower greenschist to lower amphibolite facies). The dolomitic member of Vanivilas Formation of Marikanive area is characterized by highly depleted delta C-13 value (up to -5 parts per thousand VPDB) and merits as the Indian example of ca. 2.7-Ga-old cap carbonate. This inference is further supported by estimated low temperature of equilibration documented by a few silica dolomite pairs from the Vanivilas Formation collected near Kalche area. These pairs show evidence for oxygen isotopic equilibrium at low temperatures (similar to 0-20 degrees C) with depleted water (delta O-18 = -21 parts per thousand to -15 parts per thousand VSMOW) of glacial origin. We propose that the mineral pairs were deposited during the deglaciation period when the ocean temperature was in its gradual restoration phase. The dolomite of Marikanive area is the first record of cap carbonates from the Indian subcontinent with Neoarchean antiquity.

Cybernetic Modeling Revisited: A Method for Inferring the Cybernetic Variables u(i) from Experimental Data

The cybernetic modeling framework for the growth of microorganisms provides for an elegant methodology to account for the unknown regulatory phenomena through the use of cybernetic variables for enzyme induction and activity. In this paper, we revisit the assumption of limited resources for enzyme induction (Sigma u(i) = 1) used in the cybernetic modeling framework by presenting a methodology for inferring the individual cybernetic variables u(i) from experimental data. We use this methodology to infer u(i) during the simultaneous consumption of glycerol and lactose by Escherichia coli and then model the fitness trade-offs involved in the recently discovered predictive regulation strategy of microorganisms.

Spatio-temporal Map Formation Based on a Potential Function

We revisit the problem of temporal self organization using activity diffusion based on the neural gas (NGAS) algorithm. Using a potential function formulation motivated by a spatio-temporal metric, we derive an adaptation rule for dynamic vector quantization of data. Simulations results show that our algorithm learns the input distribution and time correlation much faster compared to the static neural gas method over the same data sequence under similar training conditions.