Publications

PELICAN is a novel permutation equivariant and Lorentz invariant or covariant aggregator network designed to overcome common limitations found in architectures applied to particle physics problems. Compared to many approaches that use non-specialized architectures that neglect underlying physics principles and require very large numbers of parameters, PELICAN employs a fundamentally symmetry group-based architecture that demonstrates benefits in terms of reduced complexity, increased interpretability, and raw performance. We present a comprehensive study of the PELICAN algorithm architecture in the context of both tagging (classification) and reconstructing (regression) Lorentz-boosted top quarks, including the difficult task of specifically identifying and measuring the $W$-boson inside the dense environment of the Lorentz-boosted top-quark hadronic final state. We also extend the application of PELICAN to the tasks of identifying quark-initiated vs.~gluon-initiated jets, and a multi-class identification across five separate target categories of jets. When tested on the standard task of Lorentz-boosted top-quark tagging, PELICAN outperforms existing competitors with much lower model complexity and high sample efficiency. On the less common and more complex task of 4-momentum regression, PELICAN also outperforms hand-crafted, non-machine learning algorithms. We discuss the implications of symmetry-restricted architectures for the wider field of machine learning for physics.

Acute kidney injury (AKI) is a major risk factor for long-term adverse outcomes, including chronic kidney disease. In mouse models of AKI, maladaptive repair of the injured proximal tubule (PT) prevents complete tissue recovery. However, evidence for PT maladaptation and its etiological relationship with complications of AKI is lacking in humans. We performed single-nucleus RNA sequencing of 120,985 nuclei in kidneys from 17 participants with AKI and seven healthy controls from the Kidney Precision Medicine Project. Maladaptive PT cells, which exhibited transcriptomic features of dedifferentiation and enrichment in pro-inflammatory and profibrotic pathways, were present in participants with AKI of diverse etiologies. To develop plasma markers of PT maladaptation, we analyzed the plasma proteome in two independent cohorts of patients undergoing cardiac surgery and a cohort of marathon runners, linked it to the transcriptomic signatures associated with maladaptive PT, and identified nine proteins whose genes were specifically up- or down-regulated by maladaptive PT. After cardiac surgery, both cohorts of patients had increased transforming growth factor–β2 (TGFB2), collagen type XXIII-α1 (COL23A1), and X-linked neuroligin 4 (NLGN4X) and had decreased plasminogen (PLG), ectonucleotide pyrophosphatase/phosphodiesterase 6 (ENPP6), and protein C (PROC). Similar changes were observed in marathon runners with exercise-associated kidney injury. Postoperative changes in these markers were associated with AKI progression in adults after cardiac surgery and post-AKI kidney atrophy in mouse models of ischemia-reperfusion injury and toxic injury. Our results demonstrate the feasibility of a multiomics approach to discovering noninvasive markers and associating PT maladaptation with adverse clinical outcomes.

Soft materials are usually defined as materials made of mesoscopic entities, often self-organised, sensitive to thermal fluctuations and to weak perturbations. Archetypal examples are colloids, polymers, amphiphiles, liquid crystals, foams. The importance of soft materials in everyday commodity products, as well as in technological applications, is enormous, and controlling or improving their properties is the focus of many efforts. From a fundamental perspective, the possibility of manipulating soft material properties, by tuning interactions between constituents and by applying external perturbations, gives rise to an almost unlimited variety in physical properties. Together with the relative ease to observe and characterise them, this renders soft matter systems powerful model systems to investigate statistical physics phenomena, many of them relevant as well to hard condensed matter systems. Understanding the emerging properties from mesoscale constituents still poses enormous challenges, which have stimulated a wealth of new experimental approaches, including the synthesis of new systems with, e.g. tailored self-assembling properties, or novel experimental techniques in imaging, scattering or rheology. Theoretical and numerical methods, and coarse-grained models, have become central to predict physical properties of soft materials, while computational approaches that also use machine learning tools are playing a progressively major role in many investigations. This Roadmap intends to give a broad overview of recent and possible future activities in the field of soft materials, with experts covering various developments and challenges in material synthesis and characterisation, instrumental, simulation and theoretical methods as well as general concepts.

Black-box variational inference is widely used in situations where there is no proof that its stochastic optimization succeeds. We suggest this is due to a theoretical gap in existing stochastic optimization proofs—namely the challenge of gradient estimators with unusual noise bounds, and a composite non-smooth objective. For dense Gaussian variational families, we observe that existing gradient estimators based on reparameterization satisfy a quadratic noise bound and give novel convergence guarantees for proximal and projected stochastic gradient descent using this bound. This provides rigorous guarantees that methods similar to those used in practice converge on realistic inference problems.

Here we introduce a variation of the trap model of supercooled liquids based on softness, a particle-based variable identified by machine learning that quantifies the local structural environment and energy barrier for the particle to rearrange. As in the trap model, we assume that each particle's softness, and hence energy barrier, evolves independently. We show that our model makes qualitatively reasonable predictions of behaviors such as the dependence of fragility on density in a model supercooled liquid. We also show failures of the model, indicating in some cases signs that softness may be missing important information, and in other cases features that may only be explained by correlations neglected in the trap model.

Fluid-structure interactions between active and passive components are important for many biological systems to function. A particular example is chromatin in the cell nucleus, where ATP-powered processes drive coherent motions of the chromatin fiber over micron lengths. Motivated by this system, we develop a multiscale model of a long flexible polymer immersed in a suspension of active force dipoles as an analog to a chromatin fiber in an active fluid – the nucleoplasm. Linear analysis identifies an orientational instability driven by hydrodynamic and alignment interactions between the fiber and the suspension, and numerical simulations show activity can drive coherent motions and structured conformations. These results demonstrate how active and passive components, connected through fluid-structure interactions, can generate coherent structures and self-organize on large scales.

This work addresses the question of uniqueness of the minimizers of a convex but not strictly convex integral functional with linear growth in a two-dimensional setting. The integrand -- whose precise form derives directly from the theory of perfect plasticity -- behaves quadratically close to the origin and grows linearly once a specific threshold is reached. Thus, in contrast with the only existing literature on uniqueness for functionals with linear growth, that is that which pertains to the generalized least gradient, the integrand is not a norm. We make use of hyperbolic conservation laws hidden in the structure of the problem to tackle uniqueness. Our argument strongly relies on the regularity of a vector field -- the Cauchy stress in the terminology of perfect plasticity -- which allows us to define characteristic lines, and then to employ the method of characteristics. Using the detailed structure of the characteristic landscape evidenced in our preliminary study \cite{BF}, we show that this vector field is actually continuous, save for possibly two points. The different behaviors of the energy density at zero and at infinity imply an inequality constraint on the Cauchy stress. Under a barrier type convexity assumption on the set where the inequality constraint is saturated, we show that uniqueness holds for pure Dirichlet boundary data, a stronger result than that of uniqueness for a given trace on the whole boundary since our minimizers can fail to attain the boundary data.

We obtain asymptotically sharp error estimates for the consistency error of the Target Measure Diffusion map (TMDmap) (Banisch et al. 2020), a variant of diffusion maps featuring importance sampling and hence allowing input data drawn from an arbitrary density. The derived error estimates include the bias error and the variance error. The resulting convergence rates are consistent with the approximation theory of graph Laplacians. The key novelty of our results lies in the explicit quantification of all the prefactors on leading-order terms. We also prove an error estimate for solutions of Dirichlet BVPs obtained using TMDmap, showing that the solution error is controlled by consistency error. We use these results to study an important application of TMDmap in the analysis of rare events in systems governed by overdamped Langevin dynamics using the framework of transition path theory (TPT). The cornerstone ingredient of TPT is the solution of the committor problem, a boundary value problem for the backward Kolmogorov PDE. Remarkably, we find that the TMDmap algorithm is particularly suited as a meshless solver to the committor problem due to the cancellation of several error terms in the prefactor formula. Furthermore, significant improvements in bias and variance errors occur when using a quasi-uniform sampling density. Our numerical experiments show that these improvements in accuracy are realizable in practice when using $\delta$-nets as spatially uniform inputs to the TMDmap algorithm.

Neurons in early sensory areas rapidly adapt to changing sensory statistics, both by normalizing the variance of their individual responses and by reducing correlations between their responses. Together, these transformations may be viewed as an adaptive form of statistical whitening. Existing mechanistic models of adaptive whitening exclusively use either synaptic plasticity or gain modulation as the biological substrate for adaptation; however, on their own, each of these models has significant limitations. In this work, we unify these approaches in a normative multi-timescale mechanistic model that adaptively whitens its responses with complementary computational roles for synaptic plasticity and gain modulation. Gains are modified on a fast timescale to adapt to the current statistical context, whereas synapses are modified on a slow timescale to match structural properties of the input statistics that are invariant across contexts. Our model is derived from a novel multi-timescale whitening objective that factorizes the inverse whitening matrix into basis vectors, which correspond to synaptic weights, and a diagonal matrix, which corresponds to neuronal gains. We test our model on synthetic and natural datasets and find that the synapses learn optimal configurations over long timescales that enable adaptive whitening on short timescales using gain modulation.

All organisms make temporal predictions, and their evolutionary fitness level depends on the accuracy of these predictions. In the context of visual perception, the motions of both the observer and objects in the scene structure the dynamics of sensory signals, allowing for partial prediction of future signals based on past ones. Here, we propose a self-supervised representation-learning framework that extracts and exploits the regularities of natural videos to compute accurate predictions. We motivate the polar architecture by appealing to the Fourier shift theorem and its group-theoretic generalization, and we optimize its parameters on next-frame prediction. Through controlled experiments, we demonstrate that this approach can discover the representation of simple transformation groups acting in data. When trained on natural video datasets, our framework achieves better prediction performance than traditional motion compensation and rivals conventional deep networks, while maintaining interpretability and speed. Furthermore, the polar computations can be restructured into components resembling normalized simple and direction-selective complex cell models of primate V1 neurons. Thus, polar prediction offers a principled framework for understanding how the visual system represents sensory inputs in a form that simplifies temporal prediction.