Publications

This dissertation investigates two fundamental aspects of neural population coding: adaptive coding efficiency and stochastic representational geometry. We introduce a theory for adaptive statistical whitening revolving around a gain control mechanism, based on a novel overcomplete matrix factorization of the whitening transform. From this theory, we derive an online whitening algorithm that maps directly onto a recurrent neural network with primary neurons and an over-complete, auxiliary set of gain-modulating interneurons. Further elaborating on this framework, we integrate adaptive gain control with existing theories of adaptive whitening into a single unified adaptation objective using synaptic plasticity in a multi-timescale mechanistic model. This model adapts to changing sensory statistics by modifying gains and synapses at varying rates, resulting in improved adaptive whitening responses that is robust to non-stationary environments. Leveraging V1 population adaptation data, we demonstrate that propagation of single neuron gain changes through recurrent network structures is sufficient to explain the entire set of observed adaptation effects. Finally, we shift our focus to stochastic representational geometry, and introduce a family of distance metrics for comparing geometry between stochastic neural networks. These metrics are based on concepts from optimal transport theory and provide unique insights into the representations of noisy artificial and biological neural networks. Taken together, this thesis advances our understanding of neural population coding by examining the adaptive coding efficiency and the stochastic geometry of neural representations, with possible implications to the fields of neuroscience and machine learning.

The circumgalactic medium (CGM) plays a pivotal role in regulating gas flows around galaxies and thus shapes their evolution. However, the details of how galaxies and their CGM co-evolve remain poorly understood. We present a new time-dependent two-zone model that self-consistently tracks not just mass and metal flows between galaxies and their CGM but also the evolution of the global thermal and turbulent kinetic energy of the CGM. Our model accounts for heating and turbulence driven by both supernova winds and cosmic accretion as well as radiative cooling, turbulence dissipation, and halo outflows due to CGM overpressurization. We demonstrate that, depending on parameters, the CGM can undergo a phase transition (``thermalization'') from a cool, turbulence-supported phase to a virial-temperature, thermally-supported phase. This CGM phase transition is largely determined by the ability of radiative cooling to balance heating from supernova winds and turbulence dissipation. We perform an initial calibration of our model to the FIRE-2 cosmological hydrodynamical simulations and show that it can approximately reproduce the baryon cycles of the simulated halos. In particular, we find that, for these parameters, the phase transition occurs at high-redshift in ultrafaint progenitors and at low redshift in classical Mvir∼1011M⊙ dwarfs, while Milky Way-mass halos undergo the transition at z≈0.5. We see a similar transition in the simulations though it is more gradual, likely reflecting radial dependence and multi-phase gas not captured by our model. We discuss these and other limitations of the model and possible future extensions.

Sensation of light is essential for all organisms. The eye-less nematode Caenorhabditis elegans detects UV and blue light to evoke escape behavior. The photosensor LITE-1 absorbs UV photons with an unusually high extinction coefficient, involving essential tryptophans. Here, we modeled the structure and dynamics of LITE-1 using AlphaFold2-multimer and molecular dynamics (MD) simulations and performed mutational and behavioral assays in C. elegans to characterize its function. LITE-1 resembles olfactory and gustatory receptors from insects, recently shown to be tetrameric ion channels. We identified residues required for channel gating, light absorption, and mechanisms of photo-oxidation, involving a likely binding site for the peroxiredoxin PRDX-2. Furthermore, we identified the binding pocket for a putative chromophore. Several residues lining this pocket have previously been established as essential for LITE-1 function. A newly identified critical cysteine pointing into the pocket represents a likely chromophore attachment site. We derived a model for how photon absorption, via a network of tryptophans and other aromatic amino acids, induces an excited state that is transferred to the chromophore. This evokes conformational changes in the protein, possibly leading to a state receptive to oxidation of cysteines and, jointly, to channel gating. Electrophysiological data support the idea that LITE-1 is a photon and H2O2-coincidence detector. Other proteins with similarity to LITE-1, specifically C. elegans GUR-3, likely use a similar mechanism for photon detection. Thus, a common protein fold and assembly, used for chemoreception in insects, possibly by binding of a particular compound, may have evolved into a light-activated ion channel.

Stellar obliquity, the angle between a planet's orbital axis and its host star's spin axis, traces the formation and evolution of a planetary system. In transiting-exoplanet observations, only the sky-projected stellar obliquity can be measured, but this can be deprojected using an estimate of the stellar obliquity. In this paper, we introduce a flexible, hierarchical Bayesian framework that can be used to infer the stellar obliquity distribution solely from sky-projected stellar obliquities, including stellar inclination measurements when available. We demonstrate that while a constraint on the stellar inclination is crucial for measuring the obliquity of an individual system, it is not required for robust determination of the population-level stellar obliquity distribution. In practice, the constraints on the stellar obliquity distribution are mainly driven by the sky-projected stellar obliquities. When applying the framework to all systems with measured sky-projected stellar obliquity, which are mostly hot Jupiter systems, we find that the inferred population-level obliquity distribution is unimodal and peaked at zero degrees. Misaligned systems have nearly isotropic stellar obliquities with no strong clustering near 90°. The diverse range of stellar obliquities prefers dynamic mechanisms, such as planet-planet scattering after a convergent disk migration, which could produce both prograde and retrograde orbits of close-in planets with no strong inclination concentrations other than that at 0°.

Under a sufficiently large load, a solid material will flow via rearrangements, where particles change neighbors. Such plasticity is most easily described in the athermal, quasistatic limit of zero temperature and infinitesimal loading rate, where rearrangements occur only when the system becomes mechanically unstable. For disordered solids, the instabilities marking the onset of rearrangements have long been believed to be fold instabilities, in which an energy barrier disappears and the frequency of a normal mode of vibration vanishes continuously. Here, we report that there exists another, anomalous, type of instability caused by the breaking of a “stabilizing bond,” whose removal creates an unstable vibrational mode. For commonly studied systems, such as those with harmonic finite-range interparticle interactions, such “discontinuous instabilities” are not only inevitable, they often dominate the modes of failure. Stabilizing bonds are a subset of all the bonds in the system and are prevalent in disordered solids generally. Although they do not trigger discontinuous instabilities in systems with vanishing stiffness at the interaction cutoff, they are, even in those cases, local indicators of incipient mechanical failure. They therefore provide an accurate structural predictor of instabilities not only of the discontinuous type but of the fold type as well.

We present efficient methods for Brillouin zone integration with a non-zero but possibly very small broadening factor η, focusing on cases in which downfolded Hamiltonians can be evaluated efficiently using Wannier interpolation. We describe robust, high-order accurate algorithms automating convergence to a user-specified error tolerance ϵ, emphasizing an efficient computational scaling with respect to η. After analyzing the standard equispaced integration method, applicable in the case of large broadening, we describe a simple iterated adaptive integration algorithm effective in the small η regime. Its computational cost scales as O(log3(η−1)) as η → 0+ in three dimensions, as opposed to O(η−3) for equispaced integration. We argue that, by contrast, tree-based adaptive integration methods scale only as O(log(η−1)/η2) for typical Brillouin zone integrals. In addition to its favorable scaling, the iterated adaptive algorithm is straightforward to implement, particularly for integration on the irreducible Brillouin zone, for which it avoids the tetrahedral meshes required for tree-based schemes. We illustrate the algorithms by calculating the spectral function of SrVO3 with broadening on the meV scale.

Mutations in signal transduction pathways lead to various diseases including cancers. MEK1 kinase, encoded by the human MAP2K1 gene, is one of the central components of the MAPK pathway and more than a hundred somatic mutations in the MAP2K1 gene were identified in various tumors. Germline mutations deregulating MEK1 also lead to congenital abnormalities, such as the cardiofaciocutaneous syndrome and arteriovenous malformation. Evaluating variants associated with a disease is a challenge, and computational genomic approaches aid in this process. Establishing evolutionary history of a gene improves computational prediction of disease-causing mutations; however, the evolutionary history of MEK1 is not well understood. Here, by revealing a precise evolutionary history of MEK1, we construct a well-defined dataset of MEK1 metazoan orthologs, which provides sufficient depth to distinguish between conserved and variable amino acid positions. We matched known and predicted disease-causing and benign mutations to evolutionary changes observed in corresponding amino acid positions and found that all known and many suspected disease-causing mutations are evolutionarily intolerable. We selected several variants that cannot be unambiguously assessed by automated prediction tools but that are confidently identified as “damaging” by our approach, for experimental validation in Drosophila. In all cases, evolutionary intolerant variants caused increased mortality and severe defects in fruit fly embryos confirming their damaging nature. We anticipate that our analysis will serve as a blueprint to help evaluate known and novel missense variants in MEK1 and that our approach will contribute to improving automated tools for disease-associated variant interpretation.

Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is analyzed in the limit of slow surface diffusion. Using the tools of formal asymptotics and calculus of variations, we study the characteristic wave-pinning behavior of this system on three dynamical timescales. On the short timescale, generation of an interface separating high- and low-concentration domains is established under suitable conditions. Intermediate timescale dynamics are shown to lead to a uniform growth or shrinking of these domains to sizes that are fixed by global parameters. Finally, the long timescale dynamics reduce to area-preserving geodesic curvature flow that may lead to multi-interface steady state solutions. These results provide a foundation for studying cell polarization and related phenomena in biologically relevant geometries.

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.

An established normative approach for understanding the algorithmic basis of neural computation is to derive online algorithms from principled computational objectives and evaluate their compatibility with anatomical and physiological observations. Similarity matching objectives have served as successful starting points for deriving online algorithms that map onto neural networks (NNs) with point neurons and Hebbian/anti-Hebbian plasticity. These NN models account for many anatomical and physiological observations; however, the objectives have limited computational power and the derived NNs do not explain multi-compartmental neuronal structures and non-Hebbian forms of plasticity that are prevalent throughout the brain. In this article, we unify and generalize recent extensions of the similarity matching approach to address more complex objectives, including a large class of unsupervised and self-supervised learning tasks that can be formulated as symmetric generalized eigenvalue problems or nonnegative matrix factorization problems. Interestingly, the online algorithms derived from these objectives naturally map onto NNs with multi-compartmental neurons and local, non-Hebbian learning rules. Therefore, this unified extension of the similarity matching approach provides a normative framework that facilitates understanding multi-compartmental neuronal structures and non-Hebbian plasticity found throughout the brain.