75 citations · 138 across the 11 of their papers we have counts for
11 papers
Emergent frequency-dependent selection predicts mutation outcomes in complex ecological communities
Shing Yan Li, Zhijie Feng, Akshit Goyal +1
Ecological interactions can dramatically alter evolutionary outcomes in complex communities. Yet, the framework of population genetics largely neglects interactions from a species-…
A universal niche geometry governs the response of ecosystems to environmental perturbations
Akshit Goyal, Jason W. Rocks, Pankaj Mehta
How ecosystems respond to environmental perturbations is a fundamental question in ecology, made especially challenging due to the strong coupling between species and their environ…
Phase transition to chaos in complex ecosystems with non-reciprocal species-resource interactions
Emmy Blumenthal, Jason W. Rocks, Pankaj Mehta
Non-reciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. Here, we investigate the effects of non-reciprocity…
Geometry of ecological coexistence and niche differentiation
Emmy Blumenthal, Pankaj Mehta
A fundamental problem in ecology is to understand how competition shapes biodiversity and species coexistence. Historically, one important approach for addressing this question has…
Emergent competition shapes the ecological properties of multi-trophic ecosystems
Zhijie Feng, Robert Marsland, Jason W. Rocks +1
Ecosystems are commonly organized into trophic levels -- organisms that occupy the same level in a food chain (e.g., plants, herbivores, carnivores). A fundamental question in theo…
Integrating local energetics into Maxwell-Calladine constraint counting to design mechanical metamaterials
Jason W. Rocks, Pankaj Mehta
The Maxwell-Calladine index theorem plays a central role in our current understanding of the mechanical rigidity of discrete materials. By considering the geometric constraints eac…
Thermodynamic origins of topological protection in nonequilibrium stochastic systems
Pankaj Mehta, Jason Rocks
Topological protection has emerged as an organizing principle for understanding and engineering robust collective behavior in electronic and material systems. Recent work suggests…
Bias-variance decomposition of overparameterized regression with random linear features
Jason W. Rocks, Pankaj Mehta
In classical statistics, the bias-variance trade-off describes how varying a model's complexity (e.g., number of fit parameters) affects its ability to make accurate predictions. A…
The Geometry of Over-parameterized Regression and Adversarial Perturbations
Jason W. Rocks, Pankaj Mehta
Classical regression has a simple geometric description in terms of a projection of the training labels onto the column space of the design matrix. However, for over-parameterized…
The Perturbative Resolvent Method: spectral densities of random matrix ensembles via perturbation theory
Wenping Cui, Jason W. Rocks, Pankaj Mehta
We present a simple, perturbative approach for calculating spectral densities for random matrix ensembles in the thermodynamic limit we call the Perturbative Resolvent Method (PRM)…
Memorizing without overfitting: Bias, variance, and interpolation in over-parameterized models
Jason W. Rocks, Pankaj Mehta
The bias-variance trade-off is a central concept in supervised learning. In classical statistics, increasing the complexity of a model (e.g., number of parameters) reduces bias but…