arXiv subjects

Krishna Pusuluri

Publications and source records attributed to Krishna Pusuluri.

6 recordsLinked to original sources

arXiv2026

Hierarchical emergence of network bursting in a four-cell central pattern generator model

How can a neural circuit rhythmically burst when none of its constituent neurons can endogenously do so? We address this question through a bottom-up reconstruction of a 4-cell neural circuit modeled after the swim central pattern generator (CPG) of the sea slug \textit{Dendronotus iris}. We first map the intrinsic regimes of a swim interneuron (SiN) model neuron and show that slow mutual inhibition can generate anti-phase bursting in a half-center oscillator (HCO) assembled from tonic-spiking or quiescent cells. A slow--fast phase-space deconstruction explains this pairwise rhythm as a release mechanism. We then move on to CPG parametrization, in which cells 1 and 2 are quiescent, while cells 3 and 4 are tonic spikers but their isolated HCO can only exhibit tonic spiking or suppression. Bursting therefore does not arise at either the cellular or HCO level. It appears only after the two modules are assembled into the complete 4-cell network, where cross excitation, cross inhibition, and rectified electrical coupling act together to support a robust network rhythm-generation. Event-based symbolic encoding and GPU-parallel parameter sweeps show that this higher-order collective state occupies extended parameter domains rather than a single tuned point, and they quantify how the network interactions reshape those domains and the spike counts per burst. Symbolic sweeps identify the healthy range of activity regimes (periodic sequences) and transition boundaries; Lempel--Ziv complexity is used as a descriptor of aperiodic symbolic output rather than as proof of chaos or dynamical instability. Our results establish a hierarchy of rhythm generation---from intrinsic cell dynamics, through conditional HCO bursting, to bursting that emerges only in the fully assembled 4-cell CPG---and provide experimentally accessible predictions for perturbing its chemical and electrical couplings.

q-bio.NC↗

arXiv2023

Intelligent gradient amplification for deep neural networks

Deep learning models offer superior performance compared to other machine learning techniques for a variety of tasks and domains, but pose their own challenges. In particular, deep learning models require larger training times as the depth of a model increases, and suffer from vanishing gradients. Several solutions address these problems independently, but there have been minimal efforts to identify an integrated solution that improves the performance of a model by addressing vanishing gradients, as well as accelerates the training process to achieve higher performance at larger learning rates. In this work, we intelligently determine which layers of a deep learning model to apply gradient amplification to, using a formulated approach that analyzes gradient fluctuations of layers during training. Detailed experiments are performed for simpler and deeper neural networks using two different intelligent measures and two different thresholds that determine the amplification layers, and a training strategy where gradients are amplified only during certain epochs. Results show that our amplification offers better performance compared to the original models, and achieves accuracy improvement of around 2.5% on CIFAR- 10 and around 4.5% on CIFAR-100 datasets, even when the models are trained with higher learning rates.

cs.LG↗

arXiv2021

Ordered intricacy of Shilnikov saddle-focus homoclinics in symmetric systems

Using the technique of Poincaré return maps, we disclose an intricate order of the subsequent homoclinics near the primary homoclinic bifurcation of the Shilnikov saddle-focus in systems with reflection symmetry. We also reveal the admissible shapes of the corresponding bifurcation curves in a parameter plane of such systems. The scalability ratio of geometry and organization is proven to be universal for such homoclinic bifurcations of higher orders. Two applications with similar dynamics due to the Shilnikov saddle-foci, a smooth adaptation of the Chua circuit and a 3D normal form, are used to illustrate the theory

math.DS↗

arXiv2020

Homoclinic chaos in the Rössler model

We study the origin of homoclinic chaos in the classical 3D model proposed by O. Rössler in 1976. Of our particular interest are the convoluted bifurcations of the Shilnikov saddle-foci and how their synergy determines the global unfolding of the model, along with transformations of its chaotic attractors. We apply two computational methods proposed, 1D return maps and a symbolic approach specifically tailored to this model, to scrutinize homoclinic bifurcations, as well as to detect the regions of structurally stable and chaotic dynamics in the parameter space of the Rössler model.

nlin.CD↗

arXiv2018

Unraveling the Chaos-land and its organization in the Rabinovich System

A suite of analytical and computational techniques based on symbolic representations of simple and complex dynamics, is further developed and employed to unravel the global organization of bi-parametric structures that underlie the emergence of chaos in a simplified resonantly coupled wave triplet system, known as the Rabinovich system. Bi-parametric scans reveal the stunning intricacy and intramural connections between homoclinic and heteroclinic connections, and codimension-2 Bykov T-points and saddle structures, which are the prime organizing centers of complexity of the bifurcation unfolding of the given system. This suite includes Deterministic Chaos Prospector (DCP) to sweep and effectively identify regions of simple (Morse-Smale) and chaotic structurally unstable dynamics in the system. Our analysis provides striking new insights into the complex behaviors exhibited by this and similar systems.

nlin.CD↗

arXiv2018

Homoclinic chaos and its organization in a nonlinear optics model

We developed a powerful computational approach to elaborate on onset mechanisms of deterministic chaos due to complex homoclinic bifurcations in diverse systems. Its core is the reduction of phase space dynamics to symbolic binary representations that lets one detect regions of simple and complex dynamics as well as fine organization structures of the latter in parameter space. Massively parallel simulations shorten the computational time to disclose highly detailed bifurcation diagrams to a few seconds.

nlin.CD↗