no code implementations • 8 Mar 2024 • Wenping Cui, Robert Marsland III, Pankaj Mehta
We then shift our focus by analyzing these same models in "high-dimensions" (i. e. in the limit where the number of species and resources in the ecosystem becomes large) and discuss how such complex ecosystems can be analyzed using methods from the statistical physics of disordered systems such as the cavity method and Random Matrix Theory.
no code implementations • 2 Mar 2024 • 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 environment.
1 code implementation • 21 Apr 2023 • Emmy Blumenthal, Pankaj Mehta
A fundamental problem in ecology is to understand how competition shapes biodiversity and species coexistence.
no code implementations • 6 Mar 2023 • Zhijie Feng, Robert Marsland III, Jason W. Rocks, Pankaj Mehta
Ecosystems are commonly organized into trophic levels -- organisms that occupy the same level in a food chain (e. g., plants, herbivores, carnivores).
no code implementations • 10 Mar 2022 • Jason W. Rocks, Pankaj Mehta
We show that the linear random features model exhibits three phase transitions: two different transitions to an interpolation regime where the training error is zero, along with an additional transition between regimes with large bias and minimal bias.
no code implementations • 11 Oct 2021 • Pankaj Mehta, Robert Marsland III
Recent work suggests that cross-feeding -- the secretion and consumption of metabolic biproducts by microbes -- is essential for understanding microbial ecology.
no code implementations • 25 Mar 2021 • 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.
no code implementations • 2 Mar 2021 • Jim Wu, Pankaj Mehta, David Schwab
Niche and neutral theory are two prevailing, yet much debated, ideas in ecology proposed to explain the patterns of biodiversity.
no code implementations • 23 Dec 2020 • Alexander Golden, Allyson E. Sgro, Pankaj Mehta
We find that the spatial distribution of the drive signal controls the frequency ranges over which oscillators synchronize to the drive and that boundary conditions strongly influence synchronization to external drives for the CGLE.
Pattern Formation and Solitons
1 code implementation • 1 Dec 2020 • Robert Marsland III, Owen Howell, Andreas Mayer, Pankaj Mehta
Regulatory T cells (Tregs) play a crucial role in mediating immune response.
no code implementations • 26 Oct 2020 • Jason W. Rocks, Pankaj Mehta
In both models, increasing the number of fit parameters leads to a phase transition where the training error goes to zero and the test error diverges as a result of the variance (while the bias remains finite).
1 code implementation • 2 Aug 2019 • Owen Howell, Cui Wenping, Robert Marsland III, Pankaj Mehta
Machine learning methods have had spectacular success on numerous problems.
1 code implementation • 1 Apr 2019 • Wenping Cui, Robert Marsland III, Pankaj Mehta
In 1972, Robert May triggered a worldwide research program studying ecological communities using random matrix theory.
7 code implementations • 23 Mar 2018 • Pankaj Mehta, Marin Bukov, Ching-Hao Wang, Alexandre G. R. Day, Clint Richardson, Charles K. Fisher, David J. Schwab
The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists.
no code implementations • 12 Sep 2016 • David J. Schwab, Pankaj Mehta
", Lin and Tegmark claim to show that the mapping between deep belief networks and the variational renormalization group derived in [arXiv:1410. 3831] is invalid, and present a "counterexample" that claims to show that this mapping does not hold.
no code implementations • 3 Nov 2014 • Charles K. Fisher, Pankaj Mehta
Identifying small subsets of features that are relevant for prediction and/or classification tasks is a central problem in machine learning and statistics.
4 code implementations • 14 Oct 2014 • Pankaj Mehta, David J. Schwab
Here, we show that deep learning is intimately related to one of the most important and successful techniques in theoretical physics, the renormalization group (RG).
no code implementations • 30 Jul 2014 • Charles K. Fisher, Pankaj Mehta
Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning.