INSTITUTE SEMINAR DAYS

March 08 and 15, 2017

Venue: Ramanujan Auditorium, IMSc

(scroll below for March 8 schedule)

SCHEDULE March 15, 2017

 Speaker Title 10:00 R Ganesh Kinetic energy of electrons and magnetism 10:15 Arun Kumar Lie algebras and Chromatic polynomials 10:30 Kamal Lodaya Wise's event structure 10:45 Maria Quadeer Random Access Codes - The Quantum Advantage 11:00 D. Indumathi Leptonic CP 11:15 Parameswaran Sankaran Richard Thompson’s groups 11:30 Coffee break 12:00 Meena Mahajan Short proofs with simple arithmetic? 12:15 Anand Pathak Uncovering the mesoscopic organization of the Macaque Brain 12:30 Karimilla BN Residues modulo powers of two in the Young-Fibonacci lattice 12:45 Pinaki Chaudhuri Playing with glass 13:00 Director’s Lunch 14:30 Suresh Dara On Clique Convergence of Graphs 14:45 Lawqueen Kanesh Vertex Cover in the presence of Conflicts 15:00 Pallavi Jain A new neighborhood Search Strategy for Vertex Separation Minimization Problem 15:15 Anantha Padmanabha Epistemic assumptions in systems of unboundedly many agents 15:30 Coffee break 16:00 Vivek Ananth RP Systems modeling of protein secretion system in model filamentous fungus 16:15 Anupama Sharma A game theoretic model for vaccine uptake during an epidemic 16:30 Mukul Laad Hidden Fermi Liquidity and Topological Criticality in the FiniteTemperature Kitaev Model 16:45 Vani Vemparala What happens when you add salt to water?

ABSTRACTS March 15

R Ganesh Kinetic energy of electrons and magnetism

Magnetic heterostructures are very useful for technological applications, e.g., in computer hard drives. They are also an interesting playground for magnetism and transport. We consider a well-known class of heterostructures (e.g., composed of layers of La$_{1-x}$Sr$_x$MnO$_3$ and SrRuO$_3$) and propose a new mechanism for how magnetism arises here. We argue that the kinetic energy of electrons is the driving force -- the system chooses to order ferromagnetically or antiferromagnetically so as to maximise kinetic energy.

Arun Kumar

I will explain how the chromatic polynomial of a graph shows up naturally in the theory of Free Partially Commutative Lie algebras.

Kamal Lodaya Wise's event structure

Daniel Wise works in geometric group theory. He defined a complete square complex which he called X. Jeremie Chalopin, who works in distributed algorithms, and Vicotr Chepoi, who works in geometric graph theory, defined from X an event structure called W, which provides a counterexample to a conjecture of P.S. Thiagarajan in the theory of Petri nets. In this talk we define W.

Random access codes have been studied in classical Information

theory. In my talk I will discuss what Random access codes are and how

using quantum resources one can obtain advantage over their classical

counterpart. I will then briefly discuss our work.

D Indumathi Leptonic CP

I shall try and explain the words "Lepton", "C" and "P" and motivate why they are all so interesting and how they may be relevant to the evolution of the Universe.

Parameswaran Sankaran Richard Thompson's groups

Richard Thompson introduced in 1965 three groups F, T, and V, which have many remarkable properties. I will describe the groups F and T, point out a few of their unusual properties, and their generalizations.

Lawqueen Kanesh Vertex Cover in the presence of Conflicts

Finding a minimum vertex cover in a graph is a popular optimization problem in computer science. In this problem we are given a graph G and a positive integer k and the goal is to test whether there exists a set of at most k vertices such that every edge has at least one end point in it. Such a set is called vertex cover. It is a classical example of NP-Complete problems and known to be Fixed-parameter tractable (FPT). In the conflict version of the problem we are given two graphs  G and H (on same vertex set as G and may be different edge set) and a positive integer  k and the goal is to test whether there exists a vertex cover of size at most k in G such that it is an independent set  H. Is this problem FPT? In my talk I will discuss about such problems with conflicts.

Anand Pathak Uncovering the mesoscopic organization of the Macaque Brain

In higher organisms such as mammals, in order to unravel how their brain carries out various cognitive and motor functions, it is crucial to understand the structural organization of the neurons at different levels of organization and heirarchy. At a morphological level, mammalian brain is compartmentalized into different brain regions (lobes, gyri, nuclei etc.) Neurons of each of the brain regions seem to have extensive connections with neurons of one or more other brain regions. Considering brain regions as nodes and neuronal connections as links, we study the mesoscopic structure of the network of brain regions of macaque monkey. We first obtained an unambigous and comprehensive brain network from the existing database. Our network consists of brain regions of the lowest level of heirarchy and hence having a high spatial resolution. We systematically select Newman Spectral Analysis as an appropriate community detection algorithm to identify the different modules of brain regions. We identify the important regions according to their functional roles with respect to their respective modules. The modules of brain regions appear to be spatially localised as well showing proximity as an important factor determining connectivity. We also explore the core periphery structure of the network.

Karimilla BN  Residues modulo powers of two in the Young-Fibonacci lattice

We study the subgraph of the Young-Fibonacci graph induced by elements with

odd f-statistic (the f-statistic of an element w of a differential graded

poset is the number of saturated chains from the minimal element of the

poset to w). We show that this subgraph is a binary tree. Moreover, the odd

residues of the f-statistics in a row of this tree equidistribute modulo any

power two. This is equivalent to a purely number theoretic result about the

equidistribution of residues modulo powers of two among the products of

distinct odd numbers less than a fixed number.

Pinaki Chaudhuri  Playing with glass

Suresh Dara On Clique Convergence of Graphs

Let G be a graph and K_G be the set of all cliques of G, then the clique graph of G denot

ed by K(G) is the graph with vertex set K_G and two elements Q_i, Q_j in K_G form an edge

if and only if Q_i and Q_j are disjoint. Iterated clique graphs are defined by K^0(G)=G,

and K^n(G)=K(K^{n-1}(G)) for n>0. We prove a necessary and sufficient condition for a

clique graph K(G) to be complete when G=G_1+G_2, give a partial characterization for

clique divergence of the join of graphs and prove that if G_1, G_2 are Clique-Helly

graphs different from K_1 and G=G_1 Box G_2, then K^2(G) = G.  In particular we show that,

when G_1, G_2 are two graphs and G=G_1+G_2:

1. K(G) is complete if and only if either K(G_1) is complete or K(G_2) is complete.

2. If K(G_1), K(G_2) are not complete, then K^2(G_1)+K^2(G_2) is an induced subgraph of K^2(G).

3. If G_1, G_2 are Clique-Helly graphs different from K_1 and G=G_1 Box G_2, then K^2(G) = G.

Meena Mahajan Short proofs with simple arithmetic?

"Play this way and you WILL win. I can PROVE it, but it may take time."

There's a simple 2-player game, and one coach is sure that her player

can always win. She even tells the player what strategy to use. The

player suspects the coach of ulterior motives, and isn't convinced the

strategy really works. How fast can the coach convince him?

Pallavi Jain A new neighborhood Search Strategy for Vertex Separation Minimization Problem.

Vertex Separation Minimization Problem (VSMP) consists of embedding vertices of a graph G=(V,E) onto a path such that maximum vertex cut over all the regions is minimized. It is an NP-complete problem in general. VSMP finds applications in VLSI design, graph drawing and computer language compiler design. In this talk, we will present a variant of variable neighborhood search strategy for VSMP. Construction heuristics play a very important role in the metaheuristic techniques as they are responsible for generating initial solution which lead to faster convergence. We will also present some construction heuristics which outperforms state of the art metaheuristic. The algorithm returns optimal solution for several classes of graphs, on which we know exact  results. Extensive experiments have also been conducted on Harwell-Boeing graphs which are a subset of public domain Matrix Market library. Results indicate that it outperforms the results provided by state of the art algorithms.

Anantha Padmanabha Epistemic assumptions in unboundedly many agents

How does rumour spread in a social network? How does a process in a distributed system know that it has answered all its requests (and no more will come)?  Questions like these need to reason about nested knowledge assertions of the form “A knows that B knows P”. We discuss what assumptions we can make about such knowledge statements: for instance, whatever is known to an agent must be true. We further discuss how these assumptions lift to the setting with unboundedly many agents.

Vivek Ananth RP  Systems modeling of protein secretion system in model filamentous fungus

Protein secretion is a fundamental biological process involved in host pathogenesis, immune response, cellular communication and cellular homeostasis. In eukaryotes, the traffic of the proteins destined for extracellular space are processed, packaged and delivered via an intricate network spanning several organelles. From an application perspective, elucidating this protein secretion machinery in filamentous fungi is critical for development of hypersecretion strains for novel enzymes. Towards this goal we have mapped the protein secretion system in the filamentous fungus Neurospora crassa. Our computational pipeline involved a combination of genomics tools and literature mining. This effort has led to assignment of function to several proteins of unknown function in N. crassa. Subsequent analysis of next generation RNA-seq and ChIP-seq data within the network context shed new insights on the regulation of the protein secretion system in N. crassa. In summary, our integrative analysis provides a systems perspective on the protein secretion machinery in N. crassa. (Work done with M. Karthikeyan and Areejit Samal)

Anupama Sharma A game theoretic model for vaccine uptake during an epidemic

Vaccination is a core component of any preventive strategy designed to optimize public health in the face of epidemics. A major factor influencing the successful implementation of any immunisation program is public perception, especially when individuals receive no additional incentives from the government. In such instances, the decision of an individual to get vaccinated is mostly based on their own perception of the personal cost and benefits involved. Game theory provides a systematic framework to study this dilemma of ”well-informed and rational” agents. To understand voluntary vaccinating behaviour in more detail, we integrate a game theoretic model of decision-making with a model for disease spreading. Previous modelling approaches that utilized coupled behaviour-incidence frameworks assume that individuals either follow the rule of thumb or imitate their neighbours when deciding whether to be vaccinated. However, as epidemics evolve with time, the cost and benefits of vaccinating also evolve and can give rise to an adaptive vaccinating behaviour that cannot be captured by imitation. We propose a epidemic model for adaptive vaccinating behaviour where both processes, epidemic and immunisation, co-evolve with time and are coupled in a way that they form a feedback loop. We consider an SIR model for the propagation of a (vaccine-preventable) disease, and a game theoretic model with time-variant payoffs that governs whether an agent decides to get vaccinated. We simulate this model on a random static network, assuming all nodes are rational agents and have complete information about disease prevalence and the immune state of their neighbours. Based on this information, agents take a decision in the attempt to maximise their payoff. We find that rational-decision making can lead to the emergence of voluntary vaccination in response to an epidemic outbreak. In addition, the source of information plays an important role in this emergence of this behaviour. For slowly spreading diseases, i.e. diseases with low R0, decisions based on the local rather than global prevalence of the disease results in a significant drop in the number of infected individuals.

Mukul Laad Hidden Fermi Liquidity and Topological Criticality in the Finite Temperature Kitaev Model

The fate of exotic spin liquid states with fractionalized excitations at finite temperature ($T$) is of great interest, since signatures of fractionalization manifest in finite-temperature ($T$) dynamics in real systems, above the tiny magnetic ordering scales. Here, we study a Jordan-Wigner fermionized Kitaev spin liquid at finite $T$ employing combined Exact diagonalization and Monte Carlo simulation methods. We uncover $(i)$ checkerboard or stripy-ordered flux crystalline phases, depending on density of flux, and $(ii)$ establish, surprisingly, that: $(a)$ the finite-$T$ version of the $T=0$ transition from a gapless to gapped phases in the Kitaev model is a Mott transition of the fermions, belonging to the two-dimensional Ising universality class.  These transitions correspond to a topological transitions between a string condensate and a dilute closed string state $(b)$ the Mott insulator'' phase is a precise realization of Laughlin's gossamer (here, $p$-wave) superconductor (SC), and $(c)$ the Kitaev Toric Code phase is a {\it fully} Gutzwiller-projected $p$-wave SC.  These findings establish the finite-$T$ QSL phases in the $D=2$ to be {\it hidden} Fermi liquid(s) of JW fermions.

Vani Vemparala What happens when you add salt to water?

changes much of its structure.
But why should I care, you wonder;
come to my talk and you may discover.

SCHEDULE March 08, 2017

 Speaker Title 09:30 G Baskaran Element of Surprise 09:45 Prathamesh Turaga Of Legendrian Knots and First Order Theorem Provers 10:00 N P Swaroop Bounding the roots of polynomials 10:15 R Janaki Learning to be modular: Interplay between dynamics of synaptic strengths and neuronal activity in the brain results in its modular connection topology 10:30 COFFEE BREAK 10:45 Chandrashekar KA Modularity promotes the recurrence of epidemics 11:00 Madhusudhan Raman Tunneling and Tori 11:15 Ramanathan S Thinniyam The graph reconstruction conjecture 11:30 H Saveetha Fragmentation of Vector Mesons 11:45 COFFEE BREAK 12:00 Aravinda S On the origin of nonclassicality in single systems 12:15 KN Raghavan A plug for heaps 12:30 R Krithika Lossy Kernels 12:45 Ankit Agrawal Human genome organization in a nutshell 13:00 LUNCH BREAK 14:30 Tanmay Mitra On the origin of decisions and memory in the Eukaryotic Cell 14:45 Arindam Mallick Simulation of Dirac Hamiltonian and Neutrino Oscillation by Quantum Walk 15:00 Shakti N Menon Noisy games: Phase transitions and critical phenomena 15:15 R Rajesh Hard core lattice gas models 15:30 HIGH TEA

ABSTRACTS March 8

Bismuth, a colorful elemental solid, continues to surprise physicists.

Recent discovery of superconductivity at an ultra low temperature

of 0.5 milli Kelvin in bismuth will be reviewed and a suggestion made

that what the TIFR group has observed is only the tip of an iceberg.

Prathamesh Turaga Of Legendrian Knots and First Order Theorem Provers

Legendrian knots are knots in a contact manifold such that the tangent at

each point lies in the associated contact hyperplane at the point. First

Order Theorem Provers refers to computer softwares that can prove results or

produce counter examples of statements expressed in first order logic,

with the axioms of the theory as the input.

In this talk, I will discuss a new class of `combinatorial' invariants that

we discovered (in a joint work with Dheeraj Kulkarni) of Legendrian knots,

that we call Legendrian racks. These invariants can be seen as a

modification of the rack invariants of (topological) knots called quandles.

The distinguishing feature of these invariants is that through these

invariants, one can use first order theorem provers to distinguish

Legendrian knots. This talk shall contain a discussion both the mathematical

and computational aspects of our work, and the interactions between the two.

It will also contain a demonstration of the computational part of the work.

N P Swaroop  Bounding the roots of polynomials

Proving upper bounds on the roots of polynomials is a  classical problem in Computer Algebra. Not only are root bounds interesting from a mathematical  perspective but they also have algorithmic applications. In this talk, I will give a brief overview of the well known root bounds and their algorithmic efficiency.

R Janaki Learning to be modular: Interplay between dynamics of synaptic strengths and neuronal activity in the brain results in its modular connection topology

Neurons in the brain are connected in intricate arrangements, communicating with each other mostly through chemical synapses. The collective dynamics of neuronal networks - responsible for the cognitive and other functions of the brain - is strongly influenced by their connection topology. Motivated by reports that at least some parts of the brain may be wired in a modular fashion, we first show that the occurrence of modularity promotes the dynamical balance between excitation and inhibition in neuronal networks. In other words, the range of values for the fraction of inhibitory neurons in the network that will result in a high probability of persistent activity is considerably amplified by modular organization of the connection topology. We then explore the possibility that this modularity arises in a self-organized manner when a set of neurons interacting with each other spontaneously organize themselves into densely inter-connected communities with sparser connections to other communities. For this purpose, in parallel with action potential generating models of individual neurons, we investigate spike-time dependent plasticity (STDP) synaptic dynamics for evolving the connectivity organization between neurons. Note that STDP is considered to be the principal mechanism by which neurons strengthen or weaken connections, and thereby ”learn” according to the Hebbian paradigm (”neurons that fire together, wire together”). We show that, beginning from a homogeneous globally connected network, the interplay of neuronal dynamics and STDP results in the spontaneous emergence of modules in the network.

Chandrashekar KA Modularity promotes the recurrence of epidemics

The long-term evolution of epidemic processes depends crucially on the structure of contact networks. As empirical evidence indicates that human populations exhibit strong community organization, we investigate here how such communities affect the likelihood of epidemic recurrence. Through  numerical simulations on real social networks and theoretical arguments using spectral methods, we demonstrate that highly contagious diseases that would have otherwise died out rapidly can persist indefinitely for an optimal range of modularity in contact networks.

Quantum mechanics predicts that particles can tunnel through classically insurmountable barriers, and that the probabilities for such processes are exponentially small. We consider a class of polynomial potentials --- in which particles exhibit both oscillatory motion about and tunneling between local minima --- and associate to each pair of such motions a torus. Recent work has shown that on using results from classical geometry, one can relate these two very different kinds of motion in a precise manner. The same considerations allow us to conclude that these motions are governed by familiar elliptic functions, but in "alternative bases", whose study was pioneered by Ramanujan. We conclude with hints that this simple set-up is related to, among other things, discrete subgroups of SL(2,R) and N=2 SQCD theories.

Ramanathan S Thinniyam The graph reconstruction conjecture

"Graphs are uniquely determined by their multi set of one vertex deleted subgraphs." This innocuous sounding conjecture has remained open for more than 70 years despite many partial results. Why is

this so?

H Saveetha  Fragmentation of Vector Mesons

Protons and neutrons are not elementary: they are composed of sub-structures (elementary particles) called quarks and gluons. The latter are not freely seen in nature. Hence, quarks and gluons, when produced, immediately hadronise into composite hadrons such as protons. We present details of a simple model based on SU(3) symmetry that addresses the issue of vector meson fragmentation. This has implications for understanding exotic signatures such as Quark Gluon Plasma.

Aravinda S  On the origin of nonclassicality in single systems

In the framework of certain general probability theories of single systems, we identify various nonclassical features such as incompatibility, multiple pure-state decomposability, measurement dis- turbance, no-cloning and the impossibility of certain universal operations, with the non-simpliciality of the state space. This is shown to naturally suggest an underlying simplex as an ontological model. Contextuality turns out to be an independent nonclassical feature, arising from the intransitivity of compatibility.

KN Raghavan A plug for heaps

This talk is an attempt at publicity for the videos of the ongoing (but about to conclude) lecture course by Xavier Viennot on "Commutations and Heaps of Pieces".  The lectures are jam-packed with new proofs of classical theorems,   myriad applications---from zeta functions of graphs, to Coxeter groups and Lie algebras, to statistical physics---and open questions.    I will showcase the elegance of the theory by deriving from it a famous result of Stanley that "the number of colourings by -1 colours" of a graph equals the number of its acyclic orientations.

R Krithika  Lossy Kernels

Many real-world computational problems are NP-hard and we do not expect efficient algorithms for solving them. One of the popular approaches to solving such problems is the following: first apply reduction rules that transform the input instance to an instance of smaller size and then solve the smaller instance. The sequence of steps that reduce the given large instance to a smaller one is called a kernelization algorithm. As the goal is to eventually solve the original instance, the application of a kernelization algorithm is typically followed by an exact or approximation algorithm that finds a solution to the reduced instance. Lossy kernelization is a recently introduced mathematical framework that quantifies the efficiency of kernelization algorithms by quantifying how a solution to the reduced instance relates to a solution of the original instance. In this talk, we will discuss how lossy kernelization provides a way to design and analyze preprocessing heuristics.

Ankit Agrawal Human genome organization in a nutshell

Genome organization in interphase state of cell cycle are non-random. Size, activity and loops of chromosomes define these non-random nuclear architecture. We have found after extensive simulation that positioning of  large and short chromosomes are controlled by loops and activity respectively.

Tanmay Mitra On the origin of decisions and memory in the Eukaryotic Cell

Learning, wherein repeated exposure to sustained stimulation eventually results in an altered response, is usually associated with multi-cellular organisms, e.g., those possessing a nervous system. However, simpler forms of learning, e.g., sensitization and adaptation, may appear in more rudimentary systems. In this work we report novel results on how the response of a crucial part of the eukaryotic intra-cellular signaling network, can change on receiving a signal repeatedly over an extended period of time. Depending on circumstances, this can result in either an enhanced response (sensitization) or a diminished one (adaptation). On withdrawal of stimulus, the changed response takes an long time to decay, indicating the existence of long-range memory. Taken in conjunction with previous analogies made between the intra-cellular signaling network and nervous systems, this provides an intriguing perspective on how the signaling network of a cell can function as its "brain" and has implications for how an immune cell can learn to respond to pathogen while not attacking its own self tissues.

Arindam Mallick Simulation of Dirac Hamiltonian and Neutrino Oscillation by Quantum Walk

Simulations of one quantum system by an other has implications in realization of quantum machine that can imitate any other quantum system and solve problems that are not accessible to classical computers. In this talk I will present an algorithm for simulation of Dirac cellular automaton, a local space-time discretized theory of Dirac particle dynamics [1]. Extending the algorithm which uses split-step quantum walk as protocol, I will present a scheme to simulate three flavor neutrino oscillation and analyze the evolution of entanglement between spin and space degrees of freedom [2].

Ref:

[1] Scientific Reports 6, 25779 (2016)

[2] Eur. Phys. J. C, Vol. 77  No. 2, 85 (2017)

Shakti N Menon Noisy games: Phase transitions and critical phenomena

I will discuss the collective dynamics in networks of agents interacting via Prisoner's Dilemma or Stag-Hunt games, and whose individual strategies evolve via a stochastic update scheme. We find that such systems exhibit three distinct regimes characterized by unique temporal strategies (always cooperate, always defect or fluctuate). We have studied the nature of the resulting phase diagram as the network is rewired from a regular lattice to a random network using the Watts-Strogatz small-world rewiring scheme. Furthermore, we have characterized the resulting phase transitions in detail and have observed the existence of a "tricritical point".

R Rajesh Hard core lattice gas  models

Previous Institute Seminar Week (2012)