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Professor Mrinal Bhave, 2020
No full textDepartment Chair of Chemistry and Biotechnology at Swinburne, Professor Mrinal Bhave, credits her grandfather with sparking her interest in science, when she was growing up in the Indian state of Karnataka.
Photograph originally appeared in the Media Centre Release, 'Love for science leads to lifelong learning' on Monday 10 February 2020.
Photograph shows Professor Mrinal Bhave in front of a bookshelf that has black folders and red bound items. They are wearing a floral top and smiling
Determinants vs. Algebraic Branching Programs
Get PDFWe show that for every homogeneous polynomial of degree d, if it has determinantal complexity at most s, then it can be computed by a homogeneous algebraic branching program (ABP) of size at most O(d⁵s). Moreover, we show that for most homogeneous polynomials, the width of the resulting homogeneous ABP is just s-1 and the size is at most O(ds).
Thus, for constant degree homogeneous polynomials, their determinantal complexity and ABP complexity are within a constant factor of each other and hence, a super-linear lower bound for ABPs for any constant degree polynomial implies a super-linear lower bound on determinantal complexity; this relates two open problems of great interest in algebraic complexity. As of now, super-linear lower bounds for ABPs are known only for polynomials of growing degree [Mrinal Kumar, 2019; Prerona Chatterjee et al., 2022], and for determinantal complexity the best lower bounds are larger than the number of variables only by a constant factor [Mrinal Kumar and Ben Lee Volk, 2022].
While determinantal complexity and ABP complexity are classically known to be polynomially equivalent [Meena Mahajan and V. Vinay, 1997], the standard transformation from the former to the latter incurs a polynomial blow up in size in the process, and thus, it was unclear if a super-linear lower bound for ABPs implies a super-linear lower bound on determinantal complexity. In particular, a size preserving transformation from determinantal complexity to ABPs does not appear to have been known prior to this work, even for constant degree polynomials
Khandar Film indien de Mrinal Sen
No full textVideau André. Khandar Film indien de Mrinal Sen . In: Hommes et Migrations, n°1123, Juin-juillet 1989. L'immigration portugaise en France. p. 99
A Quadratic Lower Bound for Algebraic Branching Programs
Get PDFWe show that any Algebraic Branching Program (ABP) computing the polynomial ∑_{i=1}^n xⁿ_i has at least Ω(n²) vertices. This improves upon the lower bound of Ω(nlog n), which follows from the classical result of Baur and Strassen [Volker Strassen, 1973; Walter Baur and Volker Strassen, 1983], and extends the results of Kumar [Mrinal Kumar, 2019], which showed a quadratic lower bound for homogeneous ABPs computing the same polynomial.
Our proof relies on a notion of depth reduction which is reminiscent of similar statements in the context of matrix rigidity, and shows that any small enough ABP computing the polynomial ∑_{i=1}^n xⁿ_i can be depth reduced to essentially a homogeneous ABP of the same size which computes the polynomial ∑_{i=1}^n xⁿ_i + ε(), for a structured "error polynomial" ε(). To complete the proof, we then observe that the lower bound in [Mrinal Kumar, 2019] is robust enough and continues to hold for all polynomials ∑_{i=1}^n xⁿ_i + ε(), where ε() has the appropriate structure
Chronicling the Self: A Feminist Approach to Mrinal Pande's Daughter's Daughter
Get PDFAutobiography writing is a means for women writers to explore their inner-most recesses of their selves. Mrinal Pande's Daughter's Daughter is a rare type of the portrayal of self-wherein the author creates a fictional self to describe her survival story of being a daughter's daughter. In the autobiography the author maintains a distance with her own self, speaking through a girl of the age span f two to ten. In the story of her 'self', Mrinal Pande, introspects, observes, comments and narrates her past through her mouthpiece, Tinu. The present paper focuses in detail the pain of being a girl child in a patriarchal society and the author's decision not to be a victim of patriarchal domination. 
A travel time study of P waves using deep-focus earthquakes,
Get PDFThesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Science, 1972.Includes bibliographical references (leaves 45-55).by Mrinal Kanti Sengupta.M.S
Researching the roles of wheat proteins (Research at Swinburne)
No full textDr Mrinal Bhave and PhD researcher, Rebecca Alfred, discuss their fascinating work on wheat proteins and talk about the strong relationship between PhD supervisor and candidate
A Quadratic Lower Bound for Homogeneous Algebraic Branching Programs
No full textAn algebraic branching program (ABP) is a directed acyclic graph, with a start vertex s, and end vertex t and each edge having a weight which is an affine form in variables x_1, x_2, ..., x_n over an underlying field. An ABP computes a polynomial in a natural way, as the sum of weights of all paths from s to t, where the weight of a path is the product of the weights of the edges in the path. An ABP is said to be homogeneous if the polynomial computed at every vertex is homogeneous. In this paper, we show that any homogeneous algebraic branching program which computes the polynomial x_1^n + x_2^n + ... + x_n^n has at least Omega(n^2) vertices (and edges).
To the best of our knowledge, this seems to be the first non-trivial super-linear lower bound on the number of vertices for a general homogeneous ABP and slightly improves the known lower bound of Omega(n log n) on the number of edges in a general (possibly non-homogeneous) ABP, which follows from the classical results of Strassen (1973) and Baur--Strassen (1983).
On the way, we also get an alternate and unified proof of an Omega(n log n) lower bound on the size of a homogeneous arithmetic circuit (follows from [Strassen, 1973] and [Baur-Strassen, 1983]), and an n/2 lower bound (n over reals) on the determinantal complexity of an explicit polynomial [Mignon-Ressayre, 2004], [Cai, Chen, Li, 2010], [Yabe, 2015]. These are currently the best lower bounds known for these problems for any explicit polynomial, and were originally proved nearly two decades apart using seemingly different proof techniques
Ergodic control of multidimensional diffusions I. : the existence results
Get PDFBibliography: p. 29-30.Supported in part by ARO Contract No. DAAG29-84-K-005 Supported in part by ARO Contract No. AFOSR 85-0227by Vivek S. Borkar, Mrinal K. Ghosh
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