IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

We introduce the notion of Q-commuting operators which includes commuting operators. We prove a generalized version of the commutant lifting theorem and Ando's dilation theorem in the context of Q-commuting operators. © 2020 University of Szeged. All rights reserved.

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Department of Mathematics

Acta Scientiarum Mathematicarum

On a generalization of Ando's dilation theorem

We study properties and the structure of some special classes of homomorphisms on C*-algebras. These maps are *-preserving up to conjugation by a symmetry. Making use of these homomorphisms, we prove a new structure theorem for completely bounded maps from a unital C*-algebra into the algebra of all bounded linear maps on a Hilbert space. Finally we provide alternative proofs for some of the known results about completely bounded maps and improve on them. © 2017 Mathematical Sciences Publishers.

Pacific Journal of Mathematics

Regular representations of completely bounded maps

We consider the tensorial Schur productR∘ ⊗S= [ rij⊗ sij] for R∈ Mn(A) , S∈ Mn(B) , with A,BunitalC∗-algebras, verify that such a ‘tensorial Schur product’ of positive operators is again positive, and then use this fact to prove (an apparently marginally more general version of) the classical result of Choi that a linear map ϕ: Mn→ Md is completely positive if and only if [ϕ(Eij)]∈Mn(Md)+, where of course  Eij: 1 ≤ i, j≤ n denotes the usual system of matrix units in Mn(: = Mn(C)). We also discuss some other corollaries of the main result. © 2015, Springer Basel.

Fulltext

Positivity

On a tensor-analogue of the Schur product

One may ask which maps between Hilbert modules allow for a completely positive extension to a map acting block-wise between the associated (extended) linking algebras. In these notes we investigate in particular those CP-extendable maps where the 22-corner of the extension can be chosen to be a homomorphism, the CP-H-extendable maps. We show that they coincide with the maps considered by Asadi [4], by Bhat, Ramesh, and Sumesh [9], and by Skeide [28]. We also give an intrinsic characterization that generalizes the characterization by Abbaspour Tabadkan and Skeide [1] of homomorphically extendable maps as those which are ternary homomorphisms. For general strictly CP-extendable maps we give a factorization theorem that generalizes those of Asadi, of Bhat, Ramesh, and Sumesh, and of Skeide for CP-H-extendable maps. This theorem may be viewed as a unification of the representation theory of the algebra of adjointable operators and the KSGNS-construction. Then, we examine semigroups of CP-H-extendable maps, so-called CPH-semigroups. As an application, we illustrate their relation with a new sort of generalized dilation of CP-semigroups, CPH-dilations.

Journal of Mathematical Analysis and Applications

CP-H-extendable maps between Hilbert modules and CPH-semigroups

Bures had defined a metric on the set of normal states on a von Neumann algebra using GNS representations of states. This notion has been extended to completely positive maps between C*-algebras by Kretschmann, Schlingemann and Werner. We present a Hilbert C*-module version of this theory. We show that we do get a metric when the completely positive maps under consideration map to a von Neumann algebra. Further, we include several examples and counter examples. We also prove a rigidity theorem, showing that representation modules of completely positive maps which are close to the identity map contain a copy of the original algebra. © 2013 World Scientific Publishing Company.

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Bures distance for completely positive maps

We strengthen Mohammad B. Asadi's analogue of Stinespring's theorem for certain maps on Hilbert C*-modules. We also show that any two minimal Stinespring representations are unitarily equivalent. We illustrate the main theorem with an example. © by THETA, 2012.

Department of Aerospace Engineering

Journal of Operator Theory

Stinespring's theorem for maps on Hilbert C*- modules

Sporulation is an important cellular response to stress that is also significant from a bioreactor operation viewpoint. While sporulating organisms are known to show an enhanced sporulation response under several stress situations, the sporulation response to shear stress has not been investigated thus far. Such a study could be of interest since shear stress, to a greater or lesser degree, is always present in bioreactor operation. In this article, we investigate the sporulation extents of the Gram-positive bacteria Bacillus subtilis at various defined shear levels. We show that, contrary to expectations, shear inhibits sporulation. We found an inverse correlation between the shear rate-dependent specific intracellular reactive oxygen species level (siROS), and the sporulation extent. A 10-fold increase in siROS resulted in about 17-fold decrease in sporulation extent. The involvement of reactive oxygen species (ROS) in sporulation was unknown thus far. Further, through experiments that specifically increased and reduced intracellular ROS (iROS), we established that siROS is responsible for the inhibition of sporulation under shear stress. In addition, we found that shear induced siROS regulated the expression levels of the general stress proteins Ctc and σB Based on the above, we hypothesize that siROS may regulate suppression of sporulation under high shear by altering σB and Ctc expression levels, and a model for the same is presented. © 2004 Wiley Periodicals, Inc.

Department Of Biotechnology

Biotechnology and Bioengineering

Intracellular reactive oxygen species mediate suppression of sporulation in Bacillus subtilis under shear stress

Reactive oxygen (free radical) species such as hydroxyl, superoxide or peroxyl radicals significantly affect cell function and, therefore, determine bioreactor productivities. The specific intracellular reactive oxygen species (ROS) levels as well as the ROS type, during the log and stationary phases of several Xanthomonas campestris (both untreated and HOCl-treated cells) cultivations in the bioreactor, with and without antioxidants, were measured through electron spin resonance (ESR) spectroscopy. Depending on the cultivation conditions, intracellular hydroxyl or superoxide radicals at different levels were detected. The oxygen supply during the cultivations was through need-based, pulse additions of hydrogen peroxide (H2O2), which was subsequently decomposed by culture catalase to yield oxygen. Using data from all cultivations, it was found that the growth rate constant decreased with the log-phase intracellular ROS level; the specific productivity of xanthan gum was found to be optimal at an intracellular ROS level of 0.33 mmol per g cell in the stationary phase. The rheology of the xanthan gum produced in various cultivations is discussed. Further, a model, which can simulate and predict the specific total intracellular ROS level in the cultivations with untreated cells have been developed. © 2002 Elsevier Science Ltd. All rights reserved.

Process Biochemistry

Free radical aspects of Xanthomonas campestris cultivation with liquid phase oxygen supply strategy

Responses of bacterial (Bacillus subtilis) cells under different shear levels, from both the macro and genetic viewpoints, have been presented. The responses were studied using a novel, couette flow bioreactor (CFB), in which the entire cultivation can be performed under defined shear conditions. Oxygen supply, the normal limiting factor for entire cultivations under defined shear conditions, has been achieved by passing air through a poly(tetrafluoroethylene) (PTFE) membrane fixed on the inner cylinder of the CFB. More importantly, analyses of the oxygen transfer capabilities as well as the shear rates show that in this CFB, the effects of defined shear can be studied without interference from the effects of oxygen supply. Further, the shake flask can be used as a proper control for studying the shear effects, mainly because the shear rate in the shake flask under normal shaker operating conditions of 190 rpm has been estimated to be a negligible 0.028 s-1 compared to a value of 445 s-1 at the lowest rpm employed in the CFB. At the macro level the cell size decreased by almost 50% at 1482 s-1 compared to that at 0.028 s-1, the growth rate increased by 245%, and the maximum cell concentration increased by 190% when the shear rate was increased from 0.028 to 1482 s-1. The specific intracellular catalase level increased by 335% and protease by 87% at 1482 s-1 as compared to the control cultures at a shear rate 0.028 s-1. In addition, the specific intracellular reactive oxygen species level (siROS) at the highest shear rate was 9.3-fold compared to the control conditions. At the genetic level we have established the involvement of the transcription factor, σB, in the bacterial responses to shear stress, which was unknown in the literature thus far; the σB expression correlated inversely with the siROS. Further, through experiments with ROS quenchers, we showed that ROS regulated σB expression under shear.

Biotechnology Progress

Macro-Level and Genetic-Level Responses of Bacillus subtilis to Shear Stress

Alternative methods of oxygen supply are of crucial importance, especially in viscous fermentations and shear-sensitive fermentations. A method of oxygen supply that completely eliminates the gas-liquid transport resistance has been presented. The method involves a need-based liquid-phase decomposition of hydrogen peroxide to provide the necessary oxygen. When Xanthomonas campestris was cultivated (viscous cultivation) using this method of oxygen supply, dissolved oxygen (DO) levels were maintained above the setpoint of 50% throughout the cultivation, whereas the conventional cultivation was able to meet culture oxygen demand only for about 6 h in a 72-h fermentation. Furthermore, the maximum specific growth rate and xanthan yields in the novel cultivation were 89% and 169%, respectively, of those obtained in conventional cultivation. A mathematical model was also developed to simulate and predict results in fermentations employing the presented methodology. In addition, studies with HOCI pretreatments indicated that monofunctional catalase may be responsible for the decomposition of H2O2 supplied externally to cells; HOCI pretreatments also increased the tolerance of cells to H2O2. The decomposition kinetics of externally supplied H2O2 was Michaelis-Menten in nature with v(max) = 1.196 x 10-6 M s-1 and K(m) = 0.21 mM. The catalase concentration was estimated to be 3.4 x 10-10 mol/g of cells.Alternative methods of oxygen supply are of crucial importance, especially in viscous fermentations and shear-sensitive fermentations. A method of oxygen supply that completely eliminates the gas-liquid transport resistance has been presented. The method involves a need-based liquid-phase decomposition of hydrogen peroxide to provide the necessary oxygen. When Xanthomonas campestris was cultivated (viscous cultivation) using this method of oxygen supply, dissolved oxygen (DO) levels were maintained above the setpoint of 50% throughout the cultivation, whereas the conventional cultivation was able to meet culture oxygen demand only for about 6 h in a 72-h fermentation. Furthermore, the maximum specific growth rate and xanthan yields in the novel cultivation were 89% and 169%, respectively, of those obtained in conventional cultivation. A mathematical model was also developed to simulate and predict results in fermentations employing the presented methodology. In addition, studies with HOCl pre-treatments indicated that monofunctional catalase may be responsible for the decomposition of H2O2 supplied externally to cells; HOCl pretreatments also increased the tolerance of cells to H2O2. The decomposition kinetics of externally supplied H2O2 was Michaelis-Menten in nature with vmax = 1.196×10-6 M s-1 and Km = 0.21 mM. The catalase concentration was estimated to be 3.4×10-10 mol/g of cells.