arXiv subjects

Suman Kulkarni

Publications and source records attributed to Suman Kulkarni.

5 recordsLinked to original sources

arXiv2024

Towards principles of brain network organization and function

The brain is immensely complex, with diverse components and dynamic interactions building upon one another to orchestrate a wide range of functions and behaviors. Understanding patterns of these complex interactions and how they are coordinated to support collective neural activity and function is critical for parsing human and animal behavior, treating mental illness, and developing artificial intelligence. Rapid experimental advances in imaging, recording, and perturbing neural systems across various species now provide opportunities and challenges to distill underlying principles of brain organization and function. Here, we take stock of recent progresses and review methods used in the statistical analysis of brain networks, drawing from fields of statistical physics, network theory and information theory. Our discussion is organized by scale, starting with models of individual neurons and extending to large-scale networks mapped across brain regions. We then examine the organizing principles and constraints that shape the biological structure and function of neural circuits. Finally, we describe current opportunities aimed at improving models in light of recent developments and at bridging across scales to contribute to a better understanding of brain networks.

q-bio.NC↗

arXiv2023

Information content of note transitions in the music of J. S. Bach

Music has a complex structure that expresses emotion and conveys information. Humans process that information through imperfect cognitive instruments that produce a gestalt, smeared version of reality. How can we quantify the information contained in a piece of music? Further, what is the information inferred by a human, and how does that relate to (and differ from) the true structure of a piece? To tackle these questions quantitatively, we present a framework to study the information conveyed in a musical piece by constructing and analyzing networks formed by notes (nodes) and their transitions (edges). Using this framework, we analyze music composed by J. S. Bach through the lens of network science and information theory. Regarded as one of the greatest composers in the Western music tradition, Bach's work is highly mathematically structured and spans a wide range of compositional forms, such as fugues and choral pieces. Conceptualizing each composition as a network of note transitions, we quantify the information contained in each piece and find that different kinds of compositions can be grouped together according to their information content and network structure. Moreover, we find that the music networks communicate large amounts of information while maintaining small deviations of the inferred network from the true network, suggesting that they are structured for efficient communication of information. We probe the network structures that enable this rapid and efficient communication of information--namely, high heterogeneity and strong clustering. Taken together, our findings shed new light on the information and network properties of Bach's compositions. More generally, our framework serves as a stepping stone for exploring musical complexities, creativity and the structure of information in a range of complex systems.

physics.soc-ph↗

arXiv2022

Finite-size scaling functions of the phase transition in the ferromagnetic Ising model on random regular graphs

We discuss the finite-size scaling of the ferromagnetic Ising model on random regular graphs. These graphs are locally tree-like, and in the limit of large graphs, the Bethe approximation gives the exact free energy per site. In the thermodynamic limit, the Ising model on these graphs show a phase transition. This transition is rounded off for finite graphs. We verify the scaling theory prediction that this rounding off is described in terms of the scaling variable $[T/T_c -1] S^{1/2}$ (where $T$ and $T_c$ are the temperature and the critical temperature respectively, and $S$ is the number of sites in the graph), and $\textit{not}$ in terms of a power of the diameter of the graph, which varies as $\log S$. We determine the theoretical scaling functions for the specific heat capacity and the magnetic susceptibility of the absolute value of the magnetization in closed form and compare them to Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2021

On the reliability of parameter estimates in the first observing run of Advanced LIGO

Accurate parameter estimation is key to maximizing the scientific impact of gravitational-wave astronomy. Parameters of a binary merger are typically estimated using Bayesian inference. It is necessary to make several assumptions when doing so, one of which is that the the detectors output stationary Gaussian noise. We test the validity of these assumptions by performing percentile-percentile tests in both simulated Gaussian noise and real detector data in the first observing run of Advanced LIGO (O1). We add simulated signals to 512s of data centered on each of the three events detected in O1 -- GW150914, GW151012, and GW151226 -- and check that the recovered credible intervals match statistical expectations. We find that we are able to recover unbiased parameter estimates in the real detector data, indicating that the assumption of Gaussian noise does not adversely effect parameter estimates. However, we also find that both the parallel-tempered sampler emcee_pt and the nested sampler dynesty struggle to produced unbiased parameter estimates for GW151226-like signals, even in simulated Gaussian noise. The emcee_pt sampler does produce unbiased estimates for GW150914-like signals. This highlights the importance of performing percentile-percentile tests in different targeted areas of parameter space.

gr-qc↗

arXiv2019

Extreme events in stochastic transport on networks

Extreme events are emergent phenomena in multi-particle transport processes on complex networks. In practice, such events could range from power blackouts to call drops in cellular networks to traffic congestion on roads. All the earlier studies of extreme events on complex networks have focused only on the nodal events. If random walks are used to model transport process on a network, it is known that degree of the nodes determines the extreme event properties. In contrast, in this work, it is shown that extreme events on the edges display a distinct set of properties from that of the nodes. It is analytically shown that the probability for the occurrence of extreme events on an edge is independent of the degree of the nodes linked by the edge and is dependent only on the total number of edges on the network and the number of walkers on it. Further, it is also demonstrated that non-trivial correlations can exist between the extreme events on the nodes and the edges. These results are in agreement with the numerical simulations on synthetic and real-life networks.

physics.soc-ph↗