arXiv subjects

Anita Mehta

Publications and source records attributed to Anita Mehta.

At least 19 recordsLinked to original sources

arXiv2024

Speech perception: a model of word recognition

We present a model of speech perception which takes into account effects of correlations between sounds. Words in this model correspond to the attractors of a suitably chosen descent dynamics. The resulting lexicon is rich in short words, and much less so in longer ones, as befits a reasonable word length distribution. We separately examine the decryption of short and long words in the presence of mishearings. In the regime of short words, the algorithm either quickly retrieves a word, or proposes another valid word. In the regime of longer words, the behaviour is markedly different. While the successful decryption of words continues to be relatively fast, there is a finite probability of getting lost permanently, as the algorithm wanders round the landscape of suitable words without ever settling on one.

cond-mat.stat-mech↗

arXiv2023

Optimisation via encodings: a renormalisation group perspective

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.

cs.AI↗

arXiv2023

Evolution of grammatical forms: some quantitative approaches

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.

cond-mat.stat-mech↗

arXiv2020

Hearings and mishearings: decrypting the spoken word

We propose a model of the speech perception of individual words in the presence of mishearings. This phenomenological approach is based on concepts used in linguistics, and provides a formalism that is universal across languages. We put forward an efficient two-parameter form for the word length distribution, and introduce a simple representation of mishearings, which we use in our subsequent modelling of word recognition. In a context-free scenario, word recognition often occurs via anticipation when, part-way into a word, we can correctly guess its full form. We give a quantitative estimate of this anticipation threshold when no mishearings occur, in terms of model parameters. As might be expected, the whole anticipation effect disappears when there are sufficiently many mishearings. Our global approach to the problem of speech perception is in the spirit of an optimisation problem. We show for instance that speech perception is easy when the word length is less than a threshold, to be identified with a static transition, and hard otherwise. We extend this to the dynamics of word recognition, proposing an intuitive approach highlighting the distinction between individual, isolated mishearings and clusters of contiguous mishearings. At least in some parameter range, a dynamical transition is manifest well before the static transition is reached, as is the case for many other examples of complex systems.

cs.CL↗

arXiv2020

Heterogeneous contact networks in COVID-19 spreading: the role of social deprivation

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 identifed empirically as containment zones and provide a useful guide for identifying potential areas of concern.

physics.soc-ph↗

arXiv2020

On the coexistence of competing languages

We investigate the evolution of competing languages, a subject where much previous literature suggests that the outcome is always the domination of one language over all the others. Since coexistence of languages is observed in reality, we here revisit the question of language competition, with an emphasis on uncovering the ways in which coexistence might emerge. We find that this emergence is related to symmetry breaking, and explore two particular scenarios -- the first relating to an imbalance in the population dynamics of language speakers in a single geographical area, and the second to do with spatial heterogeneity, where language preferences are specific to different geographical regions. For each of these, the investigation of paradigmatic situations leads us to a quantitative understanding of the conditions leading to language coexistence. We also obtain predictions of the number of surviving languages as a function of various model parameters.

cond-mat.stat-mech↗

arXiv2018

A neutron tomography study: probing the spontaneous crystallization of randomly packed granular assemblies

We study the spontaneous crystallization of an assembly of highly monodisperse steel spheres under shaking, as it evolves from localized icosahedral ordering towards a packing reaching crystalline ordering. Towards this end, real space neutron tomography measurements on the granular assembly are carried out, as it is systematically subjected to a variation of frequency and amplitude. As expected, we see a presence of localized icosahedral ordering in the disordered initial state (packing fraction around 0.62). As the frequency is increased for both the shaking amplitudes (0.2 and 0.6 mm) studied here, there is a rise in packing fraction, accompanied by an evolution to crystallinity. The extent of crystallinity is found to depend on both the amplitude and frequency of shaking. We find that the icosahedral ordering remains localized and its extent does not grow significantly, while the crystalline ordering grows rapidly as an ordering transition point is approached. In the ordered state, crystalline clusters of both face centered cubic (FCC) and hexagonal close packed (HCP) types are identified, the latter of which grows from stacking faults. Our study shows that an earlier domination of FCC gives way to HCP ordering at higher shaking frequencies, suggesting that despite their coexistence, there is a subtle dynamical competition at play. This competition depends on both shaking amplitude and frequency, as our results as well as those of earlier theoretical simulations demonstrate. It is likely that this involves the very small free energy difference between the two structures.

cond-mat.soft↗

arXiv2018

Patterning the insect eye: from stochastic to deterministic mechanisms

While most processes in biology are highly deterministic, stochastic mechanisms are sometimes used to increase cellular diversity, such as in the specification of sensory receptors. In the human and Drosophila eye, photoreceptors sensitive to various wavelengths of light are distributed randomly across the retina. Mechanisms that underlie stochastic cell fate specification have been analysed in detail in the Drosophila retina. In contrast, the retinas of another group of dipteran flies exhibit highly ordered patterns. Species in the Dolichopodidae, the "long-legged" flies, have regular alternating columns of two types of ommatidia (unit eyes), each producing corneal lenses of different colours. Individual flies sometimes exhibit perturbations of this orderly pattern, with "mistakes" producing changes in pattern that can propagate across the entire eye, suggesting that the underlying developmental mechanisms follow local, cellular-automaton-like rules. We hypothesize that the regulatory circuitry patterning the eye is largely conserved among flies such that the difference between the Drosophila and Dolichopodidae eyes should be explicable in terms of relative interaction strengths, rather than requiring a rewiring of the regulatory network. We present a simple stochastic model which, among its other predictions, is capable of explaining both the random Drosophila eye and the ordered, striped pattern of Dolichopodidae.

q-bio.CB↗

arXiv2018

Storing and retrieving long-term memories: cooperation and competition in synaptic dynamics

We first review traditional approaches to memory storage and formation, drawing on the literature of quantitative neuroscience as well as statistical physics. These have generally focused on the fast dynamics of neurons; however, there is now an increasing emphasis on the slow dynamics of synapses, whose weight changes are held to be responsible for memory storage. An important first step in this direction was taken in the context of Fusi's cascade model, where complex synaptic architectures were invoked, in particular, to store long-term memories. No explicit synaptic dynamics were, however, invoked in that work. These were recently incorporated theoretically using the techniques used in agent-based modelling, and subsequently, models of competing and cooperating synapses were formulated. It was found that the key to the storage of long-term memories lay in the competitive dynamics of synapses. In this review, we focus on models of synaptic competition and cooperation, and look at the outstanding challenges that remain.

q-bio.NC↗

arXiv2018

Cover-Encodings of Fitness Landscapes

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 practical feasibility of our method is demonstrated by simulations of adaptive walks on the corresponding encoded landscapes which find the global minima for these problems.

cond-mat.dis-nn↗

arXiv2014

The clash of the Titans: how preferential attachment helps the survival of the smallest

We examine the effects of preferential attachment on a model of competing clusters. In the original model, cluster masses grow at the expense of their neighbours; on a lattice, this is known to result in the asymptotic survival and indefinite growth of clusters which are isolated from each other. The presence of preferential attachment results in an inhomogeneous topology, where hubs monopolize the connections, while most other nodes are sparsely connected. Interestingly, this results in the protection of the less massive clusters from annihilation, to which the hubs are doomed.

physics.soc-ph↗

arXiv2014

Shaking-induced crystallization of dense sphere packings

We use a hybrid Monte Carlo algorithm to simulate the shaking of spheres at different vibrational amplitudes, and find that spontaneous crystallisation occurs in specific dynamical regimes. Several crystallising transitions are typically observed, leading to end states which can be fully or partially ordered, depending on the shaking amplitude, which we investigate using metrics of global and local order. At the lowest amplitudes, crystallisation is incomplete, at least for our times of observation. For amplitude ranges where crystallisation is complete, there is typically a competition between hexagonal close packed (hcp) or face-centered cubic (fcc) ordering. It is seen that fcc ordering typically predominates; in fact for an optimal range of amplitudes, spontaneous crystallisation into a pure fcc state is observed. An interesting feature is the breakdown of global order when there is juxtaposition of fully developed hcp and fcc order locally: we suggest that this is due to the interfaces between the different domains of order, which play the same role as dislocations.

cond-mat.stat-mech↗

arXiv2013

Synaptic metaplasticity underlies tetanic potentiation in Lymnaea: a novel paradigm

We present a mathematical model which explains and interprets a novel form of short-term potentiation, which was found to be use-, but not time-dependent, in experiments done on Lymnaea neurons. The high degree of potentiation is explained using a model of synaptic metaplasticity, while the use-dependence (which is critically reliant on the presence of kinase in the experiment) is explained using a model of a stochastic and bistable biological switch.

physics.bio-ph↗

arXiv2013

Learning theories reveal loss of pancreatic electrical connectivity in diabetes as an adaptive response

Cells of almost all solid tissues are connected with gap junctions which permit the direct transfer of ions and small molecules, integral to regulating coordinated function in the tissue. The pancreatic islets of Langerhans are responsible for secreting the hormone insulin in response to glucose stimulation. Gap junctions are the only electrical contacts between the beta-cells in the tissue of these excitable islets. It is generally believed that they are responsible for synchrony of the membrane voltage oscillations among beta-cells, and thereby pulsatility of insulin secretion. Most attempts to understand connectivity in islets are often interpreted, bottom-up, in terms of measurements of gap junctional conductance. This does not, however explain systematic changes, such as a diminished junctional conductance in type 2 diabetes. We attempt to address this deficit via the model presented here, which is a learning theory of gap junctional adaptation derived with analogy to neural systems. Here, gap junctions are modelled as bonds in a beta-cell network, that are altered according to homeostatic rules of plasticity. Our analysis reveals that it is nearly impossible to view gap junctions as homogeneous across a tissue. A modified view that accommodates heterogeneity of junction strengths in the islet can explain why, for example, a loss of gap junction conductance in diabetes is necessary for an increase in plasma insulin levels following hyperglycemia.

physics.bio-ph↗

arXiv2013

Bridges in three-dimensional granular packings: experiments and simulations

In this letter, we present the first experimental study of bridge structures in three-dimensional dry granular packings. When bridges are small, they are predominantly 'linear', and have an exponential size distribution. Larger, predominantly 'complex' bridges, are confirmed to follow a power-law size distribution. Our experiments, which use X-ray tomography, are in good agreement with the simulations presented here, for the distribution of sizes, end-to-end lengths, base extensions and orientations of predominantly linear bridges. Quantitative differences between the present experiment and earlier simulations suggest that packing fraction is an important determinant of bridge structure.

cond-mat.soft↗

arXiv2012

A two-species model of a two-dimensional sandpile surface: a case of asymptotic roughening

We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains (ρ(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is flat on average, so that there is no bias due to gravity. We find anomalous scaling: the expected logarithmic smoothing at short length and time scales gives way to roughening in the asymptotic limit, where novel and non-trivial exponents are found.

cond-mat.stat-mech↗

arXiv2012

Landscape encodings enhance optimization

Hard combinatorial optimization problems deal with the search for the minimum cost solutions (ground states) of discrete systems under strong constraints. A transformation of state variables may enhance computational tractability. It has been argued that these state encodings are to be chosen invertible to retain the original size of the state space. Here we show how redundant non-invertible encodings enhance optimization by enriching the density of low-energy states. In addition, smooth landscapes may be established on encoded state spaces to guide local search dynamics towards the ground state.

cond-mat.dis-nn↗

arXiv2012

Spectral properties of zero temperature dynamics in a model of a compacting granular column

The compacting of a column of grains has been studied using a one-dimensional Ising model with long range directed interactions in which down and up spins represent orientations of the grain having or not having an associated void. When the column is not shaken (zero 'temperature') the motion becomes highly constrained and under most circumstances we find that the generator of the stochastic dynamics assumes an unusual form: many eigenvalues become degenerate, but the associated multi-dimensional invariant spaces have but a single eigenvector. There is no spectral expansion and a Jordan form must be used. Many properties of the dynamics are established here analytically; some are not. General issues associated with the Jordan form are also taken up.

cond-mat.stat-mech↗