Publications

Recently the SP (Stochastic Polyak step size) method has emerged as a competitive adaptive method for setting the step sizes of SGD. SP can be interpreted as a method specialized to interpolated models, since it solves the interpolation equations. SP solves these equation by using local linearizations of the model. We take a step further and develop a method for solving the interpolation equations that uses the local second-order approximation of the model. Our resulting method SP2 uses Hessian-vector products to speed-up the convergence of SP. Furthermore, and rather uniquely among second-order methods, the design of SP2 in no way relies on positive definite Hessian matrices or convexity of the objective function. We show SP2 is competitive both in experiments and in theory.
We show SP2 is very competitive on matrix completion, non-convex test problems and logistic regression. We also provide a convergence theory on sums-of-quadratics.

Drosophila oogenesis is a powerful and tractable model for studies of cell and developmental biology due to the multitude of well-characterized events in both germline and somatic cells, the ease of genetic manipulation in fruit flies, and the large number of egg chambers produced by each fly. Recent improvements in live imaging and ex vivo culturing protocols have enabled researchers to conduct more detailed, longer-term studies of egg chamber development, enabling insights into fundamental biological processes. Here, we present a protocol for dissection, culturing, and imaging of late-stage egg chambers to study intercellular and directional cytoplasmic flow during “nurse cell dumping.” This critical developmental process towards the latter stages of oogenesis (stages 10b/11) results in rapid growth of the oocyte and shrinkage of the nurse cells and is accompanied by dynamic changes in cell shape.

This is a handbook of simple proofs of the convergence of gradient and stochastic gradient descent type methods. We consider functions that are Lipschitz, smooth, convex, strongly convex, and/or Polyak-Łojasiewicz functions. Our focus is on

Fluorescent protein biomaterials have important applications such as bioimaging in pharmacological studies. Self-assembly of proteins, especially into fibrils, is known to produce fluorescence in the blue band. Capable of self-assembly into nanofibers, we have shown we can modulate its aggregation into mesofibers by encapsulation of a small hydrophobic molecule. Conversely, azobenzenes are hydrophobic small molecules that are virtually non-fluorescent in solution due to their highly efficient photoisomerization. However, they demonstrate fluorogenic properties upon confinement in nanoscale assemblies by reducing the non-radiative photoisomerization. Here, we report the fluorescence of a hybrid protein-small molecule system in which azobenzene is confined in our protein assembly leading to fiber thickening and increased fluorescence. We show our engineered protein Q encapsulates AzoCholine, bearing a photoswitchable azobenzene moiety, in the hydrophobic pore to produce fluorescent mesofibers. This study further investigates the photocontrol of protein conformation as well as fluorescence of an azobenze-containing biomaterial.

The fluid–structure interactions between flexible fibres and viscous flows play an essential role in various biological phenomena, medical problems and industrial processes. Of particular interest is the case of particles transported freely in time-dependent flows. This work elucidates the dynamics and morphologies of actin filaments under oscillatory shear flows by combining microfluidic experiments, numerical simulations and theoretical modelling. Our work reveals that, in contrast to steady shear flows, in which small orientational fluctuations from a flow-aligned state initiate tumbling and deformations, the periodic flow reversal allows the filament to explore many different configurations at the beginning of each cycle. Investigation of filament motion during half time periods of oscillation highlights the critical role of the initial filament orientation on the emergent dynamics. This strong coupling between orientation and deformation results in new deformation regimes and novel higher-order buckling modes absent in steady shear flows. The primary outcome of our analysis is the possibility of suppression of buckling instabilities for certain combinations of the oscillation frequency and initial filament orientation, even in very strong flows. We explain this unusual behaviour through a weakly nonlinear Landau theory of buckling, in which we treat the filaments as inextensible Brownian Euler–Bernoulli rods whose hydrodynamics is described by local slender-body theory.

The nucleation of actin filament branches by the Arp2/3 complex involves activation through nucleation promotion factors (NPFs), recruitment of actin monomers, and binding of the complex to the side of actin filaments. Because of the large system size and processes that involve flexible regions and diffuse components, simulations of branch formation using all-atom molecular dynamics are challenging. We applied a coarse-grained model that retains amino-acid level information and allows molecular dynamics simulations in implicit solvent, with globular domains represented as rigid bodies and flexible regions allowed to fluctuate. We used recent electron microscopy structures of the inactive Arp2/3 complex bound to NPF domains and to mother actin filament for the activated Arp2/3 complex. We studied interactions of Arp2/3 complex with the activating VCA domain of the NPF Wiskott-Aldrich syndrome protein, actin monomers, and actin filament. We found stable configurations with one or two actin monomers bound along the branch filament direction and with CA domain of VCA associated to the strong and weak binding sites of the Arp2/3 complex, supporting prior structural studies and validating our approach. We reproduced delivery of actin monomers and CA to the Arp2/3 complex under different conditions, providing insight into mechanisms proposed in previous studies. Simulations of active Arp2/3 complex bound to a mother actin filament indicate the contribution of each subunit to the binding. Addition of the C-terminal tail of Arp2/3 complex subunit ArpC2, which is missing in the cryo-EM structure, increased binding affinity, indicating a possible stabilizing role of this tail.

We consider the numerical solution of a nonlocal partial differential equation which models the process of collective spontaneous emission in a two-level atomic system containing a single photon. We reformulate the problem as an integro-differential equation for the atomic degrees of freedom, and describe an efficient solver for the case of a Gaussian atomic density. The problem of history dependence arising from the integral formulation is addressed using sum-of-exponentials history compression. We demonstrate the solver on two systems of physical interest: in the first, an initially-excited atom decays into a photon by spontaneous emission, and in the second, a photon pulse is used to an excite an atom, which then decays.

Recent experiments have revealed that neural population codes in many brain areas continuously change even when animals have fully learned and stably perform their tasks. This representational ‘drift’naturally leads to questions about its causes, dynamics and functions. Here we explore the hypothesis that neural representations optimize a representational objective with a degenerate solution space, and noisy synaptic updates drive the network to explore this (near-)optimal space causing representational drift. We illustrate this idea and explore its consequences in simple, biologically plausible Hebbian/anti-Hebbian network models of representation learning. We find that the drifting receptive fields of individual neurons can be characterized by a coordinated random walk, with effective diffusion constants depending on various parameters such as learning rate, noise amplitude and input statistics. Despite such drift, the representational similarity of population codes is stable over time. Our model recapitulates experimental observations in the hippocampus and posterior parietal cortex and makes testable predictions that can be probed in future experiments.

Interpreting and modelling astronomical catalogues requires an understanding of the catalogues' completeness or selection function: objects of what properties had a chance to end up in the catalogue. Here we set out to empirically quantify the completeness of the overall Gaia DR3 catalogue. This task is not straightforward because Gaia is the all-sky optical survey with the highest angular resolution to date and no consistent ``ground truth'' exists to allow direct comparisons. However, well-characterised deeper imaging enables an empirical assessment of Gaia's G-band completeness across parts of the sky. On this basis, we devised a simple analytical completeness model of Gaia as a function of the observed G magnitude and position over the sky, which accounts for both the effects of crowding and the complex Gaia scanning law. Our model only depends on a single quantity: the median magnitude M10 in a patch of the sky of catalogued sources with 𝚊𝚜𝚝𝚛𝚘𝚖𝚎𝚝𝚛𝚒𝚌_𝚖𝚊𝚝𝚌𝚑𝚎𝚍_𝚝𝚛𝚊𝚗𝚜𝚒𝚝𝚜 ≤10. M10 reflects elementary completeness decisions in the Gaia pipeline and is computable from the Gaia DR3 catalogue itself and therefore applicable across the whole sky. We calibrate our model using the Dark Energy Camera Plane Survey (DECaPS) and test its predictions against Hubble Space Telescope observations of globular clusters. We find that our model predicts Gaia's completeness values to a few per cent across the sky. We make the model available as a part of the 𝚐𝚊𝚒𝚊𝚜𝚏 Python package built and maintained by the GaiaUnlimited project: $\texttt{this https URL}$

Hamiltonian Monte Carlo (HMC) is a widely used sampler for continuous probability distributions. In many cases, the underlying Hamiltonian dynamics exhibit a phenomenon of resonance which decreases the efficiency of the algorithm and makes it very sensitive to hyperparameter values. This issue can be tackled efficiently, either via the use of trajectory length randomization (RHMC) or via partial momentum refreshment. The second approach is connected to the kinetic Langevin diffusion, and has been mostly investigated through the use of Generalized HMC (GHMC). However, GHMC induces momentum flips upon rejections causing the sampler to backtrack and waste computational resources. In this work we focus on a recent algorithm bypassing this issue, named Metropolis Adjusted Langevin Trajectories (MALT). We build upon recent strategies for tuning the hyperparameters of RHMC which target a bound on the Effective Sample Size (ESS) and adapt it to MALT, thereby enabling the first user-friendly deployment of this algorithm. We construct a method to optimize a sharper bound on the ESS and reduce the estimator variance. Easily compatible with parallel implementation, the resultant Adaptive MALT algorithm is competitive in terms of ESS rate and hits useful tradeoffs in memory usage when compared to GHMC, RHMC and NUTS.