Publications

We use the entropy method to analyse the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy, an energy-like quantity in the kinetic model, we derive a variational bound on relative entropy fluctuations that can be expressed in terms of orientational order parameters. From this bound we show isotropic suspensions are nonlinearly stable for sufficiently low activity, and derive upper bounds on spatiotemporal averages in the unstable regime that are consistent with fully nonlinear simulations. This work highlights the self-organising role of activity in particle suspensions, and places limits on how organised such systems can be.

Diverse neuro-imaging techniques measure different aspects of neural responses with distinct spatial and temporal resolutions. Relating measured neural responses across different methods has been challenging. Here, we take a step towards overcoming this challenge, by comparing the nonlinearity of neural dynamics measured across methods. We used widefield voltage-sensitive dye imaging (VSDI) to measure neural population responses in macaque V1 to visual stimuli with a wide range of temporal waveforms. We found that stimulus-evoked VSDI responses are surprisingly near-additive in time. These results are qualitatively different from the strong sub-additive dynamics previously measured using fMRI and electrocorticography (ECoG) in human visual cortex with a similar set of stimuli. To test whether this discrepancy is specific to VSDI—a signal dominated by subthreshold neural activity, we repeated our measurements using widefield imaging of a genetically encoded calcium indicator (GcaMP6f)—a signal dominated by spiking activity, and found that GCaMP signals in macaque V1 are also near-additive. Therefore, the discrepancies in the extent of sub-additivity between the macaque and the human measurements are unlikely due to differences between sub- and supra-threshold neural responses. Finally, we use a simple yet flexible delayed normalization model to capture these different dynamics across measurements (with different model parameters). The model can potentially generalize to a broader set of stimuli, which aligns with previous suggestion that dynamic gain-control is a canonical computation contributing to neural processing in the brain.

We present a minimally entangled typical thermal state quantum impurity solver for general multiorbital systems at finite temperatures. We introduce an improved estimator for the single-particle Green's function that strongly reduces the large fluctuations at long imaginary time and low temperature, which were a severe limitation of the original algorithm. In combination with the fork tensor product states Ansatz, we obtain a dynamical mean field theory (DMFT) quantum impurity solver, which we benchmark for single and three-band models down to low temperatures, including the effect of spin-orbit coupling in a realistic DMFT computation for the Hund's metal Sr2⁢RuO4 down to low temperatures.

Given an intractable distribution p, the problem of variational inference (VI) is to find the best approximation from some more tractable family Q. Commonly, one chooses Q to be a family of factorized distributions (i.e., the mean-field assumption), even though p itself does not factorize. We show that this mismatch leads to an impossibility theorem: if p does not factorize, then any factorized approximation q∈Q can correctly estimate at most one of the following three measures of uncertainty: (i) the marginal variances, (ii) the marginal precisions, or (iii) the generalized variance (which can be related to the entropy). In practice, the best variational approximation in Q is found by minimizing some divergence D(q,p) between distributions, and so we ask: how does the choice of divergence determine which measure of uncertainty, if any, is correctly estimated by VI? We consider the classic Kullback-Leibler divergences, the more general Rényi divergences, and a score-based divergence which compares ∇logp and ∇logq. We provide a thorough theoretical analysis in the setting where p is a Gaussian and q is a (factorized) Gaussian. We show that all the considered divergences can be

In addition to the ability to generate fluent text in various languages, large language models have been successful at tasks that involve basic forms of logical "reasoning" over their context. Recent work found that selectively removing certain components from weight matrices in pre-trained models can improve such reasoning capabilities. We investigate this phenomenon further by carefully studying how certain global associations tend to be stored in specific weight components or Transformer blocks, in particular feed-forward layers. Such associations may hurt predictions in reasoning tasks, and removing the corresponding components may then improve performance. We analyze how this arises during training, both empirically and theoretically, on a two-layer Transformer trained on a basic reasoning task with noise, a toy associative memory model, and on the Pythia family of pre-trained models tested on simple reasoning tasks.

We present an approach to tame the growth of entanglement during time evolution by tensor network methods. It combines time evolution in the complex plane with a perturbative and controlled reconstruction of correlation functions on the real time axis. We benchmark our approach on the single impurity Anderson model. Compared to purely real time evolution, the complex time evolution significantly reduces the required bond dimension to obtain the spectral function. Notably, our approach yields self-energy results with high precision at low frequencies, comparable to numerical renormalization group results, and it successfully captures the exponentially small Kondo energy scale.

The Kondo lattice is one of the classic examples of strongly correlated electronic systems. We conduct a controlled study of the Kondo lattice in one dimension, highlighting the role of excitations created by the composite fermion operator. Using time-dependent matrix product state methods, we compute various correlation functions and contrast them with both large-N mean-field theory and the strong-coupling expansion. We show that the composite fermion operator creates long-lived, charge-e and spin-1/2 excitations, which cover the low-lying single-particle excitation spectrum of the system. Furthermore, spin excitations can be thought to be composed of such fractionalized quasiparticles with a residual interaction which tend to disappear at weak Kondo coupling.

Microtubules are essential cytoskeletal filaments involved in cell motility, division, and intracellular transport. These biomolecular assemblies can exhibit complex structural be-haviors influenced by various biophysical factors. However, simulating microtubule systems at the atomistic scale is challenging due to their large spatial scales. Here, we present an approach utilizing the Martini 3 Coarse-Grained (CG) model coupled with an appropriate elastic network to simulate microtubule-based systems accurately. By iteratively optimiz-ing the elastic network parameters, we matched the structural fluctuations of CG hetero-dimer building blocks to their atomistic counterparts. Our efforts culminated in a ∼ 200nm microtubule built with ∼ 6 million interaction-centers that could reproduce experimentally observed mechanical properties. Our aim is to employ these CG simulations to investigate specific biophysical phenomena at a microscopic level. These microscopic perspectives can provide valuable insights into the underlying mechanisms and contribute to our knowledge of microtubule-associated processes in cellular biology. With MARTINI 3 CG simulations, we can bridge the gap between computational efficiency and molecular detail, enabling in-vestigations into these biophysical processes over longer spatio-temporal scales with amino acid-level insights.

Can fluorescence lifetime imaging microscopy (FLIM) detect associations between the metabolic state of cumulus cell (CC) samples and the clinical outcome of the corresponding embryos?

FLIM can detect significant variations in the metabolism of CC associated with the corresponding embryos that resulted in a clinical pregnancy versus those that did not.

Human ability to recognize complex visual patterns arises through transformations performed by successive areas in the ventral visual cortex. Deep neural networks trained endto-end for object recognition approach human capabilities, and offer the best descriptions to date of neural responses in the late stages of the hierarchy. But these networks provide a poor account of the early stages, compared to traditional hand-engineered models, or models optimized for coding efficiency or prediction. Moreover, the gradient backpropagation used in end-to-end learning is generally considered to be biologically implausible. Here, we overcome both of these limitations by developing a bottom-up self-supervised training methodology that operates independently on successive layers. Specifically, we maximize feature similarity between pairs of locally-deformed natural image patches, while decorrelating features across patches sampled from other images. Crucially, the deformation amplitudes are adjusted proportionally to receptive field sizes in each layer, thus matching the task complexity to the capacity at each stage of processing. In comparison with architecturematched versions of previous models, we demonstrate that our layerwise complexity-matched learning (LCL) formulation produces a two-stage model (LCL-V2) that is better aligned with selectivity properties and neural activity in primate area V2. We demonstrate that the complexity-matched learning paradigm is responsible for much of the emergence of the improved biological alignment. Finally, when the two-stage model is used as a fixed front end for a deep network trained to perform object recognition, the resultant model (LCL-V2Net) is significantly better than standard end-to-end self-supervised, supervised, and adversarially-trained models in terms of generalization to out-of-distribution tasks and alignment with human behavior. Our code and pre-trained checkpoints are available at https://github.com/nikparth/LCL-V2.git