In this joint work with Pramod Eyyunni and Sanoli Gun, we pursue the study initiated by P. E., M. K. Das and B. R. Patil on the study of N(x, H) which is the number of values of Euler’s totient function in the interval (x, x+H].
It is a standard result that the set of values of Euler’s function has a zero asymptotic density, which implies that N(x, H) is usually o(H). However, K. Ford, S. Konyagin and C. Pomerance have shown that N(x, H) is at most H(1/4 + o(1)) as H tends to infinity, uniformly in x. The question has been raised to know whether the constant can be replaced by 0. We give some support to the conjecture that the constant 1/4 in the above mentioned result is best possible by showing that this is the case if one takes for granted a standard conjecture of L. Dickson that suitable linear functions may simultaneously take prime values.
The bluejeans Meeting URL
In this thesis we consider several (di)graph cut problems and study them from the perspective of parameterized complexity and kernelization. The goal of the study is three-fold: first to extend the otherwise limited understanding of parameterized cut problems on directed graphs, second to present novel applications of the rich toolkit available for undirected cut problems and third to develop tools that allow to reuse the algorithms to solve the respective problems in the presence of an additional constraint.
The concrete questions addressed in the thesis are inspired from some major open problems and concerns in the area. Some of these being the famously active open problem of the existence of a polynomial kernel for Directed Feedback Vertex/Arc Set, sub-exponentiality in FPT beyond tournaments, parameterized algorithms for partitioning problems beyond the classical partitioning problems, the existence of single exponential FPT algorithms for stable versions of classical cut problems and the parameterized complexity of Stable Multicut. We address the above questions either in full or extend all possible results known in literature that take steps to come closer to resolving the actual question.
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[Google Meet Link]: meet.google.com/mqw-rrug-fje
[Download title and abstract of the talk]: www.imsc.res.in/~asamal/seminar/UddipanSarma_Aug13_2020.pdf
Information encoded in the dynamics of signaling pathways often elicit critical cell fate decisions. For instance, sustained dynamics of TGF β pathway impart growth inhibition, a property abrogated in diseases like cancer.To understand how cells encode the extracellular input and transmit its information to elicit appropriate responses, we acquired quantitative time‐resolved measurements of pathway activation at the single‐cell level. We compared the signaling dynamics of thousands of individual cells and build mathematical models to understand the regulatory processes controlling the cell specific dynamics, both sustained and transient. Our combined experimental and theoretical study revealed that the response to a given dose of TGF β is determined specifically by the levels of defined signaling proteins in individual cells. Heterogeneity in signaling protein expression led to decomposition of cells into classes with qualitatively distinct signaling dynamics and corresponding phenotypic outcome. Also, negative feedback regulators promote heterogeneous TGF β signaling, as SMAD7 (a negative regulator of the pathway) knock‐out specifically affected the signal duration in a subpopulation of genetically identical cells. Taken together, our study established a quantitative framework that allows predicting and testing sources of cellular signaling heterogeneity.
Webinar link: https://us02web.zoom.us/j/85402825387
Given a finite group G, it is a result of Frobenius and Schur that all complex irreducible representations of G may be defined over the reals if and only if the character degree sum of G is equal to the number of involutions of G. We use this result and generatingfunctionology to study the real representations of finite groups of Lie type, and to obtain some new combinatorial identities. We will begin with examples of Weyl groups, then discuss joint work with Jason Fulman on finite general linear and unitary groups, and then give more recent results for finite symplectic and orthogonal groups.
[Google Meet Link]: meet.google.com/ewb-smyc-dog
[Download title and abstract of the talk]: https://www.imsc.res.in/~asamal/seminar/SudipKundu_Aug18_2020.pdf
Morethan 20% caloric intake of the whole world population comes fromrice; however, this rice production is under several biotic andabiotic stresses. Thus, society needs efficient stress tolerant highyield rice cultivars. A deep understanding of the rice cellular andplant physiology, and how its outcome depends on the interactions ofseveral levels of different cellular networks will help the ricebiotechnologist to achieve this goal. Towards this aim, the focus ofthis presentation would be use of analytical techniques to understandthe rice cellular physiology.
Firstly,I will discuss how integration of different omics data and networktheory can not only unravel various regulatory interactionsconnecting phenotypic changes with cellular and / or molecular eventstriggered by stress, but also provides a framework to deepen ourunderstanding of stress cellular physiology. However, this techniquewill not be very useful to understand the cellular metabolism andthus, we use two different metabolic modelling tools, namely fluxbalance analysis (FBA) and elementary flux mode (EFM) analysistechniques.
Secondly,I will describe how we create a structural metabolic model thatcontains the reactions that participate in photorespiration in theplastid, peroxisome, mitochondrion and cytosol, and the metaboliteexchanges between them, and analyse this model (i) to understandbiochemical basis of leafammonium accumulation and chlorosis in GS2 mutant type and (ii) toaddress the impact of photorespiration on metabolism.We also provide a formal demonstration that photorespiration itselfdoes not impact on the CO2:O2 ratio (assimilation quotient), exceptin those modes associated with concomitant nitrate reduction.
[Google Meet Link]: meet.google.com/mjp-apqy-vdc
[Download title and abstract of the talk]: www.imsc.res.in/~asamal/seminar/SangramBagh_Aug20_2020.pdf
The molecular connectivity between genes and proteins inside a cell shows a good degree of resemblance with complex electrical circuits. This inspires the possibility of engineering a cell similar to an engineering device. In this talk, we discuss our recent effort to hardware implement artificial neural network (ANN) with engineered bacteria. The abstract mathematical rules of artificial neural network (ANN) are implemented through software, various material based neuromorphic chips, photonics and in-vitro DNA computation. Here we demonstrate the physical realization of ANN in living bacterial cells. We created a single layer ANN using engineered bacteria, where a single bacterium works as an artificial neuron and demonstrated complex chemical information processing with decoders and encoders. To our knowledge, this is the first ANN created by artificial bacterial neurons. Thus, it may have significance creating engineered biological cells as ANN enabled hardware.
On the other hand, synthetically engineered microbial cells have numerous projected applications in space bioengineering. Microgravity is a unique property of space. Biological solutions to space travel must consider microgravity as an important component. Here we have created the first biological or biochemical or molecular microgravity sensor in Escherichia coli applying synthetic gene circuits.
Part-1: Many galaxies contain interstellar magnetic fields with energy densities comparable to those of thermal motions, turbulence, and cosmic rays. These fields are amplified from small seed fields, and then maintained, by a turbulent dynamo. Intriguingly, they can be coherent on scales of up to several kiloparsecs, much larger than the correlation scale of turbulence. I will present dynamo models that may help to explain various properties of the large-scale components of galactic magnetic fields, and discuss how such models will be extended in the near future. I will then explain how collaborators and I are combining galaxy formation models and dynamo models to understand how the magnetic fields of galaxies evolved, as a population, over the history of the Universe.
Part-2: Common envelope evolution begins when a star, usually a giant, engulfs a companion. This is followed by a rapid inspiral of the companion and core of the giant, owing to gas dynamical friction drag. Liberated orbital energy is transferred to the envelope, helping to unbind it. The progenitors of many astrophysical phenomena, including luminous red novae, certain types of planetary nebulae, and most compact object coalescences observable through gravitational waves, are believed to involve common envelope events. I will present the results of high-resolution 3D global hydrodynamical simulations of common envelope evolution, with a focus on drag force evolution, envelope unbinding, and accretion of gas onto the companion.
We discuss various types of multiple Dirichlet series with arithmetical coefficients
on the numerators. The properties of those Dirichlet series surely depend on what
kind of coefficients is on the numerators. Some of them can be continued
meromorphically in the whole space, while some others have natural boundaries.
One of the most interesting cases is that the coefficients are von Mangold functions.
In this case there is a connection between the relevant Dirichlet series and Goldbach’s
problem. I will report the contents of my several papers, written jointly with various
people, some are rather old, while some are quite new.
Mathematics Seminar | IMSc Webinar
Aug 27 16:00-17:00
Ram Rup Sarkar | National Chemical Laboratory, Pune
[Google Meet Link]: meet.google.com/zsc-phes-bhh
[Download title and abstract of the talk]: http://www.imsc.res.in/~asamal/seminar/RamRupSarkar_Aug27_2020.pdf
Cancer cells exhibit characteristic phenotypic plasticity that allows adaptive cellular reprogramming facilitating rapid proliferation, evading immunosurveillance and survival under stress. Cancer metabolism, an emerging hallmark of cancer cells, is one such adaptation that exhibit distinctive phenotypic changes and have been considered as signatures for different cancer cells. Metabolites can directly influence stress response pathways, chromatin modifications and gene expression that collectively drive tumor development. We will be discussing about the metabolic complexities in cancer with reference to a particular type of brain cancers known as glioblastomas. Metabolic alterations like the Warburg effect, Glutaminolysis, etc., help glioblastomas to survive stringent conditions. However, it is difficult to design a holistic experimental setup that could capture multiple pathways simultaneously. In recent years, this limitation is largely being handled by computational and mathematical biology study of large-scale comprehensive signaling and metabolic networks. In this lecture, we will discuss about the two broadly classified computational techniques to address this biological problem: (i) Steady-state modelling approach and (ii) Dynamic modelling approach.
In the first part of the lecture, we will discuss about a popularly used steady state approach known as Constraint-Based Metabolic Modelling. This approach makes use of linear optimization to formulate the cancer metabolic network in mathematical form. The technique provides a holistic perspective of the pathway behavior and changes in a context specific metabolic network of glioblastoma. A network consisting of 13 pathways including Glycolysis, TCA, Oxidative phosphorylation, Glycine-serine metabolism, Cysteine metabolism and Glutamate metabolism pathways was reconstructed . The model was used to interpret biological questions like the differences in pathways during a normal and a glioblastoma scenario, essential metabolites for glioblastoma growth and combinations of metabolic reactions that could be used for treatment or as drug targets. The pathways were observed to be re-routed towards glutathione pathway, which is the anti-oxidant machinery of the cell. Essentiality analysis displayed that cystine and glucose were essential for glioblastoma growth in the given context. The combination of glycine-serine pathway enzymes was highlighted as combinatorial therapeutic targets.
In the second part of the lecture, we will discuss about dynamic modelling approach using ordinary differential equation (ODE). This approach requires the detailed understanding of the biological system and the knowledge of parameter values like concentration, rate kinetics, etc. We have used this approach to build an ODE model for glioblastoma to understand the effect of changing concentration of Reactive Oxygen Species (ROS) in determining the pro-apoptotic or anti-apoptotic fate of gliomas . The model consists of a smaller subset of metabolic pathways that were considered in the constraint-based model, which are relevant to the anti-oxidant machinery. A total of 25 rate equations with Michaelis-Menten and modified Michaelis-Menten equations were formulated, that consisted of 35 variables and 123 parameters. Analysis of the model show that the regulation of certain parameters along with the thiol (GSH/GSSG) and redox (NADPH/NADP+) ratio could determine the dual behavior of ROS in gliomas.
1. Bhowmick, R., Subramanian, A., & Sarkar, R. R. (2015). Exploring the differences in metabolic behavior of astrocyte and glioblastoma: A flux balance analysis approach. Systems and Synthetic Biology, 9, 159 - 177, DOI:10.1007/s11693-015-9183-9.
2. Bhowmick, R., & Sarkar, R. R. (2020). Differential suitability of reactive oxygen species and the role of glutathione in regulating paradoxical behavior in gliomas: A mathematical perspective. PloSOne, 15(6), e0235204. DOI: https://doi.org/10.1371/journal.pone.0235204.