My research is focused on complexity in natural as well as intelligent systems. My most recent work involves the evolution of languages and the perception of speech. I maintain an interest in granular physics, with an emphasis on static and dynamical heterogeneities. Other areas of interest concern mechanisms of memory storage and preservation, game-theoretic models of strategic learning, network dynamics and their role in risk minimisation, and optimal encodings on landscapes for NP-complete problems.
Difficult, in particular NP-complete, optimization problems are traditionally solved approximatel... more Difficult, in particular NP-complete, optimization problems are traditionally solved approximately using search heuristics. These are usually slowed down by the rugged landscapes encountered, because local minima arrest the search process. Cover-encoding maps were devised to circumvent this problem by transforming the original landscape to one that is free of local minima and enriched in near-optimal solutions. By definition, these involve the mapping of the original (larger) search space into smaller subspaces, by processes that typically amount to a form of coarse-graining. In this paper, we explore the details of this coarse-graining using formal arguments, as well as concrete examples of cover-encoding maps, that are investigated analytically as well as computationally. Our results strongly suggest that the coarse-graining involved in cover-encoding maps bears a strong resemblance to that encountered in renormalisation group schemes. Given the apparently disparate nature of these two formalisms, these strong similarities are rather startling, and suggest deep mathematical underpinnings that await further exploration.
EPJ News (April 2023) carried this highlight of our paper 'Evolution of grammatical forms: some q... more EPJ News (April 2023) carried this highlight of our paper 'Evolution of grammatical forms: some quantitative approaches' (Eur. Phys. J. B 96:19, 2023).
Grammatical forms are said to evolve via two main mechanisms. These are, respectively, the 'desce... more Grammatical forms are said to evolve via two main mechanisms. These are, respectively, the 'descent' mechanism, where current forms can be seen to have descended (albeit with occasional modifications) from their roots in ancient languages, and the 'contact' mechanism, where evolution in a given language occurs via borrowing from other languages with which it is in contact. We use ideas and concepts from statistical physics to formulate a series of static and dynamical models which illustrate these issues in general terms. The static models emphasise the relative numbers of rules and exceptions, while the dynamical models focus on the emergence of exceptional forms. These unlikely survivors among various competing grammatical forms are winners against the odds. Our analysis suggests that they emerge when the influence of neighbouring languages exceeds the generic tendency towards regularisation within individual languages.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
We investigate the survivor distributions of a spatially extended model of competitive dynamics i... more We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and nonsurvivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterization is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept-the dynamical fugacity. Remarkably, in the large-mass limit, the survivor probability of a node become...
We focus in this work on the study of traffic in open systems using a modified version of an exis... more We focus in this work on the study of traffic in open systems using a modified version of an existing cellular automaton model. We demonstrate that the open system is rather different from the closed system in its 'choice' of a unique steady-state density and velocity distribution, independently of the initial conditions, reminiscent of self-organised criticality. Quantities of interest such as average densities and velocities of cars, exhibit phase transitions between free flow and the jammed state, as a function of the braking probability R in a way that is very different from closed systems. Velocity correlation functions show that the concept of a dynamical cluster, introduced earlier in the context of granular flow is also relevant for traffic flow models.
1. (Dis)respect for gender identity. I was frequently referred to as 'that sand pile woman... more 1. (Dis)respect for gender identity. I was frequently referred to as 'that sand pile woman', which conjured up visions of a laid-back woman lazing on the beach, dabbling in sand. The implication in most such cases was that only a dilettante would dabble in a subject as frivolous as sand, and of course as a woman, I was more than likely to be not completely serious in my pursuit of the sciences. I am sure that my love of subjects outside the sciences, such as music and literature, only added to this perception in certain scientific circles, of an essential light-hearted(and alas, light-headed-) ness!
We have two main aims in this paper. First we use theories of disease spreading on networks to lo... more We have two main aims in this paper. First we use theories of disease spreading on networks to look at the COVID-19 epidemic on the basis of individual contacts -- these give rise to predictions which are often rather different from the homogeneous mixing approaches usually used. Our second aim is to look at the role of social deprivation, again using networks as our basis, in the spread of this epidemic. We choose the city of Kolkata as a case study, but assert that the insights so obtained are applicable to a wide variety of urban environments which are densely populated and where social inequalities are rampant. Our predictions of hotspots are found to be in good agreement with those currently being identfied empirically as containment zones and provide a useful guide for identifying potential areas of concern.
The traditional way of tackling discrete optimization problems is by using local search on suitab... more The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a feature of the typically rugged landscapes encountered arrest the progress of the search process. Another way of tackling optimization problems is by the use of heuristic approximations to estimate a global cost minimum. Here, we present a combination of these two approaches by using cover-encoding maps which map processes from a larger search space to subsets of the original search space. The key idea is to construct cover-encoding maps with the help of suitable heuristics that single out near-optimal solutions and result in landscapes on the larger search space that no longer exhibit trapping local minima. We present cover-encoding maps for the problems of the traveling salesman, number partitioning, maximum matching and maximum clique; the practic...
Difficult, in particular NP-complete, optimization problems are traditionally solved approximatel... more Difficult, in particular NP-complete, optimization problems are traditionally solved approximately using search heuristics. These are usually slowed down by the rugged landscapes encountered, because local minima arrest the search process. Cover-encoding maps were devised to circumvent this problem by transforming the original landscape to one that is free of local minima and enriched in near-optimal solutions. By definition, these involve the mapping of the original (larger) search space into smaller subspaces, by processes that typically amount to a form of coarse-graining. In this paper, we explore the details of this coarse-graining using formal arguments, as well as concrete examples of cover-encoding maps, that are investigated analytically as well as computationally. Our results strongly suggest that the coarse-graining involved in cover-encoding maps bears a strong resemblance to that encountered in renormalisation group schemes. Given the apparently disparate nature of these two formalisms, these strong similarities are rather startling, and suggest deep mathematical underpinnings that await further exploration.
EPJ News (April 2023) carried this highlight of our paper 'Evolution of grammatical forms: some q... more EPJ News (April 2023) carried this highlight of our paper 'Evolution of grammatical forms: some quantitative approaches' (Eur. Phys. J. B 96:19, 2023).
Grammatical forms are said to evolve via two main mechanisms. These are, respectively, the 'desce... more Grammatical forms are said to evolve via two main mechanisms. These are, respectively, the 'descent' mechanism, where current forms can be seen to have descended (albeit with occasional modifications) from their roots in ancient languages, and the 'contact' mechanism, where evolution in a given language occurs via borrowing from other languages with which it is in contact. We use ideas and concepts from statistical physics to formulate a series of static and dynamical models which illustrate these issues in general terms. The static models emphasise the relative numbers of rules and exceptions, while the dynamical models focus on the emergence of exceptional forms. These unlikely survivors among various competing grammatical forms are winners against the odds. Our analysis suggests that they emerge when the influence of neighbouring languages exceeds the generic tendency towards regularisation within individual languages.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
We investigate the survivor distributions of a spatially extended model of competitive dynamics i... more We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and nonsurvivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterization is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept-the dynamical fugacity. Remarkably, in the large-mass limit, the survivor probability of a node become...
We focus in this work on the study of traffic in open systems using a modified version of an exis... more We focus in this work on the study of traffic in open systems using a modified version of an existing cellular automaton model. We demonstrate that the open system is rather different from the closed system in its 'choice' of a unique steady-state density and velocity distribution, independently of the initial conditions, reminiscent of self-organised criticality. Quantities of interest such as average densities and velocities of cars, exhibit phase transitions between free flow and the jammed state, as a function of the braking probability R in a way that is very different from closed systems. Velocity correlation functions show that the concept of a dynamical cluster, introduced earlier in the context of granular flow is also relevant for traffic flow models.
1. (Dis)respect for gender identity. I was frequently referred to as 'that sand pile woman... more 1. (Dis)respect for gender identity. I was frequently referred to as 'that sand pile woman', which conjured up visions of a laid-back woman lazing on the beach, dabbling in sand. The implication in most such cases was that only a dilettante would dabble in a subject as frivolous as sand, and of course as a woman, I was more than likely to be not completely serious in my pursuit of the sciences. I am sure that my love of subjects outside the sciences, such as music and literature, only added to this perception in certain scientific circles, of an essential light-hearted(and alas, light-headed-) ness!
We have two main aims in this paper. First we use theories of disease spreading on networks to lo... more We have two main aims in this paper. First we use theories of disease spreading on networks to look at the COVID-19 epidemic on the basis of individual contacts -- these give rise to predictions which are often rather different from the homogeneous mixing approaches usually used. Our second aim is to look at the role of social deprivation, again using networks as our basis, in the spread of this epidemic. We choose the city of Kolkata as a case study, but assert that the insights so obtained are applicable to a wide variety of urban environments which are densely populated and where social inequalities are rampant. Our predictions of hotspots are found to be in good agreement with those currently being identfied empirically as containment zones and provide a useful guide for identifying potential areas of concern.
The traditional way of tackling discrete optimization problems is by using local search on suitab... more The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a feature of the typically rugged landscapes encountered arrest the progress of the search process. Another way of tackling optimization problems is by the use of heuristic approximations to estimate a global cost minimum. Here, we present a combination of these two approaches by using cover-encoding maps which map processes from a larger search space to subsets of the original search space. The key idea is to construct cover-encoding maps with the help of suitable heuristics that single out near-optimal solutions and result in landscapes on the larger search space that no longer exhibit trapping local minima. We present cover-encoding maps for the problems of the traveling salesman, number partitioning, maximum matching and maximum clique; the practic...
We have two main aims in this paper. First we use theories of disease spreading on networks to lo... more We have two main aims in this paper. First we use theories of disease spreading on networks to look at the COVID-19 epidemic on the basis of individual contacts-these give rise to predictions which are often rather different from the homogeneous mixing approaches usually used. Our second aim is to look at the role of social deprivation, again using networks as our basis, in the spread of this epidemic. We choose the city of Kolkata as a case study, but assert that the insights so obtained are applicable to a wide variety of urban environments which are densely populated and where social inequalities are rampant. Our predictions of hotspots are found to be in good agreement with those currently being identified empirically as containment zones and provide a useful guide for identifying potential areas of concern.
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