Neuronal diversity can improve machine learning for physics and beyond.

Diversity conveys advantages in nature, yet homogeneous neurons typically comprise the layers of artificial neural networks. Here we construct neural networks from neurons that learn their own activation functions, quickly diversify, and subsequently outperform their homogeneous counterparts on image classification and nonlinear regression tasks. Sub-networks instantiate the neurons, which meta-learn especially efficient sets of nonlinear responses. Examples include conventional neural networks classifying digits and forecasting a van der Pol oscillator and physics-informed Hamiltonian neural networks learning Hénon-Heiles stellar orbits and the swing of a video recorded pendulum clock. Such learned diversity provides examples of dynamical systems selecting diversity over uniformity and elucidates the role of diversity in natural and artificial systems.

A Study of Association of Premature Graying of Hair and Osteopenia in North Indian Population.

CONTEXT: Hair graying is one of the signs of human aging and is caused by a progressive loss of pigmentation from growing hair shafts. Studies have shown a correlation of early hair graying with osteopenia, indicating that premature graying could serve as an early marker of osteopenia. AIM: To compare the degree of osteopenia in individuals with premature graying of hair (PGH) compared to ordinary individuals. SETTINGS AND DESIGN: We conducted an observational, case-control study among 132 healthy individuals between 18 and 30 years of age. SUBJECTS AND METHODS: Detailed history and examination of PGH was taken. Bone mineral density (BMD) was assessed using Furuno CM-200 ultrasound bone densitometer. STATISTICAL ANALYSIS: SPSS 21 software was used, and the data were summarized in the form of mean ± standard deviation for quantitative values and percentages for qualitative values. Chi-square test, Student's t-test, analysis of variance, and other appropriate tests were applied for comparison, and P < 0.05 was considered statistically significant. RESULTS: PGH was present in 82 (62.1%) cases, whereas osteopenia was present in 56 (42.4%) cases. The mean age of onset of graying of hair among the cases was 20.62 ± 3.74 years. A higher age group of 25-30 years (P = 0.016) and family history of PGH (P < 0.001) were significant risk factors for PGH. The mean BMD of the case group was 0.76 ± 1.00 and the control group was 0.68 ± 1.11, but the difference was not statistically significant (P = 0.649). CONCLUSION: The study concluded that there is no significant association between osteopenia and PGH.

Physics-enhanced neural networks learn order and chaos.

Artificial neural networks are universal function approximators. They can forecast dynamics, but they may need impractically many neurons to do so, especially if the dynamics is chaotic. We use neural networks that incorporate Hamiltonian dynamics to efficiently learn phase space orbits even as nonlinear systems transition from order to chaos. We demonstrate Hamiltonian neural networks on a widely used dynamics benchmark, the Hénon-Heiles potential, and on nonperturbative dynamical billiards. We introspect to elucidate the Hamiltonian neural network forecasting.

Clinicobacteriological evaluation of leprosy patients with 1-5 skin lesions.

Background: Mycobacterium leprae is a noncultivable mycobacteria, and diagnosis of the disease is based on its clinical and histopathological characteristics and finding the bacteria in skin scrapings and in biopsies taken from the patients. The aim of this study was to shed light on the clinical classification (based on the number of skin lesions) used extensively in the field where patients classified as paucibacillary (PB) were positive on skin smears and histopathology leading to treatment failure and drug resistance. Methods: In this study, we enrolled untreated 62 leprosy patients with 1-5 skin lesions and did a detailed bacterio-histopathological analysis by slit-skin smears (SSSs) and histopathology. Results: Of 62 patients analyzed, 15 patients came out to be multibacillary (MB) and 47 were PB by SSS and histopathology. Conclusion: The findings of the present study showed that the WHO classification of leprosy based on the number of lesions seems to be inappropriate as it considers a number of MB lesions as PB only, thus misleading the treatment strategies. Hence, it is essential that a comprehensive clinicobacteriological assessment of leprosy cases should be done to ensure the appropriate bacillary status and guiding the appropriate treatment strategy.

Small-world networks exhibit pronounced intermittent synchronization.

We report the phenomenon of temporally intermittently synchronized and desynchronized dynamics in Watts-Strogatz networks of chaotic Rössler oscillators. We consider topologies for which the master stability function (MSF) predicts stable synchronized behaviour, as the rewiring probability (p) is tuned from 0 to 1. MSF essentially utilizes the largest non-zero Lyapunov exponent transversal to the synchronization manifold in making stability considerations, thereby ignoring the other Lyapunov exponents. However, for an N-node networked dynamical system, we observe that the difference in its Lyapunov spectra (corresponding to the N - 1 directions transversal to the synchronization manifold) is crucial and serves as an indicator of the presence of intermittently synchronized behaviour. In addition to the linear stability-based (MSF) analysis, we further provide global stability estimate in terms of the fraction of state-space volume shared by the intermittently synchronized state, as p is varied from 0 to 1. This fraction becomes appreciably large in the small-world regime, which is surprising, since this limit has been otherwise considered optimal for synchronized dynamics. Finally, we characterize the nature of the observed intermittency and its dominance in state-space as network rewiring probability (p) is varied.

Multiple-node basin stability in complex dynamical networks.

Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g., a synchronized state) to large perturbations is critical in the operation of many real-world networked dynamical systems such as ecosystems, power grids, the human brain, etc. This necessitates the development of appropriate quantifiers of stability of multiple stable states of such systems. Motivated by the concept of basin stability (BS) [P. J. Menck et al., Nat. Phys. 9, 89 (2013)1745-247310.1038/nphys2516], we propose here the general framework of multiple-node basin stability for gauging the global stability and robustness of networked dynamical systems in response to nonlocal perturbations simultaneously affecting multiple nodes of a system. The framework of multiple-node BS provides an estimate of the critical number of nodes that, when simultaneously perturbed, significantly reduce the capacity of the system to return to the desired stable state. Further, this methodology can be applied to estimate the minimum number of nodes of the network to be controlled or safeguarded from external perturbations to ensure proper operation of the system. Multiple-node BS can also be utilized for probing the influence of spatially localized perturbations or targeted attacks to specific parts of a network. We demonstrate the potential of multiple-node BS in assessing the stability of the synchronized state in a deterministic scale-free network of Rössler oscillators and a conceptual model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics.

Balance of Interactions Determines Optimal Survival in Multi-Species Communities.

We consider a multi-species community modelled as a complex network of populations, where the links are given by a random asymmetric connectivity matrix J, with fraction 1 - C of zero entries, where C reflects the over-all connectivity of the system. The non-zero elements of J are drawn from a Gaussian distribution with mean µ and standard deviation σ. The signs of the elements Jij reflect the nature of density-dependent interactions, such as predatory-prey, mutualism or competition, and their magnitudes reflect the strength of the interaction. In this study we try to uncover the broad features of the inter-species interactions that determine the global robustness of this network, as indicated by the average number of active nodes (i.e. non-extinct species) in the network, and the total population, reflecting the biomass yield. We find that the network transitions from a completely extinct system to one where all nodes are active, as the mean interaction strength goes from negative to positive, with the transition getting sharper for increasing C and decreasing σ. We also find that the total population, displays distinct non-monotonic scaling behaviour with respect to the product µC, implying that survival is dependent not merely on the number of links, but rather on the combination of the sparseness of the connectivity matrix and the net interaction strength. Interestingly, in an intermediate window of positive µC, the total population is maximal, indicating that too little or too much positive interactions is detrimental to survival. Rather, the total population levels are optimal when the network has intermediate net positive connection strengths. At the local level we observe marked qualitative changes in dynamical patterns, ranging from anti-phase clusters of period 2 cycles and chaotic bands, to fixed points, under the variation of mean µ of the interaction strengths. We also study the correlation between synchronization and survival, and find that synchronization does not necessarily lead to extinction. Lastly, we propose an effective low dimensional map to capture the behavior of the entire network, and this provides a broad understanding of the interplay of the local dynamical patterns and the global robustness trends in the network.

Synchronization in time-varying networks.

We study the stability of the synchronized state in time-varying complex networks using the concept of basin stability, which is a nonlocal and nonlinear measure of stability that can be easily applied to high-dimensional systems [P. J. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nature Phys. 9, 89 (2013)]. The time-varying character is included by stochastically rewiring each link with the average frequency f. We find that the time taken to reach synchronization is lowered and the stability range of the synchronized state increases considerably in dynamic networks. Further we uncover that small-world networks are much more sensitive to link changes than random ones, with the time-varying character of the network having a significant effect at much lower rewiring frequencies. At very high rewiring frequencies, random networks perform better than small-world networks and the synchronized state is stable over a much wider window of coupling strengths. Lastly we show that the stability range of the synchronized state may be quite different for small and large perturbations, and so the linear stability analysis and the basin stability criterion provide complementary indicators of stability.

Taming explosive growth through dynamic random links.

We study the dynamics of a collection of nonlinearly coupled limit cycle oscillators relevant to a wide class of systems, ranging from neuronal populations to electrical circuits, over network topologies varying from a regular ring to a random network. We find that for sufficiently strong coupling strengths the trajectories of the system escape to infinity in the regular ring network. However when a fraction of the regular connections are dynamically randomized, the unbounded growth is suppressed and the system remains bounded. Further, we find a scaling relation between the critical fraction of random links necessary for successful prevention of explosive behavior and the network rewiring time-scale. These results suggest a mechanism by which blow-ups may be controlled in extended oscillator systems.