Publications

A major obstacle to treating Alzheimer’s disease (AD) is our lack of understanding of the molecular mechanisms underlying selective neuronal vulnerability, a key characteristic of the disease. Here, we present a framework integrating high-quality neuron-type-specific molecular profiles across the lifetime of the healthy mouse, which we generated using bacTRAP, with postmortem human functional genomics and quantitative genetics data. We demonstrate human-mouse conservation of cellular taxonomy at the molecular level for neurons vulnerable and resistant in AD, identify specific genes and pathways associated with AD neuropathology, and pinpoint a specific functional gene module underlying selective vulnerability, enriched in processes associated with axonal remodeling, and affected by amyloid accumulation and aging. We have made all cell-type-specific profiles and functional networks available at http://alz.princeton.edu. Overall, our study provides a molecular framework for understanding the complex interplay between Aβ, aging, and neurodegeneration within the most vulnerable neurons in AD.

A generic flow distribution network typically does not deliver its load at a uniform rate across a service area, instead oversupplying regions near the nutrient source while leaving downstream regions undersupplied. In this work we demonstrate how a local adaptive rule coupling tissue growth with nutrient density results in a flow network that self-organizes to deliver nutrients uniformly. This geometric adaptive rule can be generalized and imported to mechanics-based adaptive models to address the effects spatial gradients in nutrients or growth factors in tissues.

Hot spots, or plasmoids, which form due to magnetic reconnection in current sheets, are conjectured to power frequent X-ray and near-infrared flares from Sgr A*, the black hole in the center of our Galaxy. It is unclear how, where, and when current sheets form in black hole accretion disks. We perform axisymmetric general-relativistic resistive magnetohydrodynamics simulations to model reconnection and plasmoid formation in a range of accretion flows. Current sheets and plasmoids are ubiquitous features that form regardless of the initial magnetic field in the disk, the magnetization in the quasisteady-state phase of accretion, and the spin of the black hole. Within 10 Schwarzschild radii from the event horizon, we observe plasmoids forming, after which they can merge, grow to macroscopic scales of the order of a few Schwarzschild radii, and are ultimately advected along the jet’s sheath or into the disk. Large plasmoids are energized to relativistic temperatures via reconnection and contribute to the jet’s limb brightening. We find that only hot spots forming in magnetically arrested disks can potentially explain the energetics of Sgr A* flares. The flare period is determined by the reconnection rate, which we find to be between $0.01c$ and $0.03c$ in all cases, consistent with studies of reconnection in isolated Harris-type current sheets. We quantify magnetic dissipation and nonideal electric fields, which can efficiently inject nonthermal particles. We show that explicit resistivity allows for converged numerical solutions, such that the electromagnetic energy evolution and dissipation become independent of the grid scale for the extreme resolutions considered here.

We introduce a procedure to systematically search for a local unitary transformation that maps a wave function with a nontrivial sign structure into a positive-real form. The transformation is parametrized as a quantum circuit compiled into a set of one- and two-qubit gates. We design a cost function that maximizes the average sign of the output state and removes its complex phases. The optimization of the gates is performed through automatic differentiation algorithms, widely used in the machine learning community. We provide numerical evidence for significant improvements in the average sign for a two-leg triangular Heisenberg ladder with next-to-nearest-neighbor and ring-exchange interactions. This model exhibits phases where the sign structure can be removed by simple local one-qubit unitaries, but also an exotic Bose-metal phase whose sign structure induces “Bose surfaces” with a fermionic character and a higher entanglement that requires deeper circuits.

Loss of normal tissue architecture is a hallmark of oncogenic transformation1. In developing organisms, tissues architectures are sculpted by mechanical forces during morphogenesis2. However, the origins and consequences of tissue architecture during tumorigenesis remain elusive. In skin, premalignant basal cell carcinomas form ‘buds’, while invasive squamous cell carcinomas initiate as ‘folds’. Here, using computational modelling, genetic manipulations and biophysical measurements, we identify the biophysical underpinnings and biological consequences of these tumour architectures. Cell proliferation and actomyosin contractility dominate tissue architectures in monolayer, but not multilayer, epithelia. In stratified epidermis, meanwhile, softening and enhanced remodelling of the basement membrane promote tumour budding, while stiffening of the basement membrane promotes folding. Additional key forces stem from the stratification and differentiation of progenitor cells. Tumour-specific suprabasal stiffness gradients are generated as oncogenic lesions progress towards malignancy, which we computationally predict will alter extensile tensions on the tumour basement membrane. The pathophysiologic ramifications of this prediction are profound. Genetically decreasing the stiffness of basement membranes increases membrane tensions in silico and potentiates the progression of invasive squamous cell carcinomas in vivo. Our findings suggest that mechanical forces—exerted from above and below progenitors of multilayered epithelia—function to shape premalignant tumour architectures and influence tumour progression.

In the present paper we describe a class of algorithms for the solution of Laplace's equation on polygonal domains with Neumann boundary conditions. It is well known that in such cases the solutions have singularities near the corners which poses a challenge for many existing methods. If the boundary data is smooth on each edge of the polygon, then in the vicinity of each corner the solution to the corresponding boundary integral equation has an expansion in terms of certain (analytically available) singular powers. Using the known behavior of the solution, universal discretizations have been constructed for the solution of the Dirichlet problem. However, the leading order behavior of solutions to the Neumann problem is $O(t^{\mu})$ for $\mu \in (-1/2,0)$ depending on the angle at the corner (compared to $O(C+t^{\mu})$ with $\mu>1/2$ for the Dirichlet problem); this presents a significant challenge in the design of universal discretizations. Our approach is based on using the discretization for the Dirichlet problem in order to compute a solution in the "weak sense" by solving an adjoint linear system; namely, it can be used to compute inner products with smooth functions accurately, but it cannot be interpolated. Furthermore we present a procedure to obtain accurate solutions arbitrarily close to the corner, by solving a sequence of small local subproblems in the vicinity of that corner. The results are illustrated with several numerical examples.

One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the continuous Fourier transform of the unknown object. Making use of prior information about the sample (such as its support), a natural goal is to recover the phase through computational means, after which the unknown object can be visualized at high resolution. While many algorithms have been proposed for this phase retrieval problem, careful analysis of its well-posedness has received relatively little attention. In this paper, we show that the problem is, in general, not well-posed and describe some of the underlying issues that are responsible for the ill-posedness. We then show how this analysis can be used to develop experimental protocols that lead to better conditioned inverse problems.

We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle collisions. This algorithm extends the well-known complementarity method for non-smooth multi-body dynamics to resolve collisions in dense rigid body suspensions. This approach formulates the collision resolution problem as a linear complementarity problem with geometric `non-overlapping' constraints imposed at each timestep. It is then reformulated as a constrained quadratic programming problem and the Barzilai-Borwein projected gradient descent method is applied for its solution. This framework is designed to be applicable for any convex particle shape, e.g., spheres and spherocylinders, and applicable to any Stokes mobility solver, including the Rotne-Prager-Yamakawa approximation, Stokesian Dynamics, and PDE solvers (e.g., boundary integral and immersed boundary methods). In particular, this method imposes Newton's Third Law and records the entire contact network. Further, we describe a fast, parallel, and spectrally-accurate boundary integral method tailored for spherical particles, capable of resolving lubrication effects. We show weak and strong parallel scalings up to 8×104 particles with approximately 4×107 degrees of freedom on 1792 cores. We demonstrate the versatility of this framework with several examples, including sedimentation of particle clusters, and active matter systems composed of ensembles of particles driven to rotate.

We present a theoretical formulation of the frequency domain multidimensional pump-probe analog spectroscopy, which utilizes the spectral– temporal entanglement features of the biphoton sources. It has been shown, via a compact multi-time, convolutional Green’s function expression and the accompanying numerical simulations, that utilizing the correlation properties of non-classical sources offers a viable scheme for the exploration of dissipative kinetics of the cavity confined quantum aggregates. The cooperative and competitive modifications brought in by the photonic cavity mode and the auxiliary vibrational modes into the scattering and dephasing properties of the exciton– polaritons have been explored via their signatures in the multidimensional correlation maps. The study offers a new parameter window for the investigation of the dynamical polariton characteristics and warrants the usage of multi-mode entanglement properties of the external photonic sources in future studies.

Elucidating the carrier density at which strongly bound excitons dissociate into a plasma of uncorrelated electron-hole pairs is a central topic in the many-body physics of semiconductors. However, there is a lack of information on the high-density response of excitons absorbing in the near-to-mid ultraviolet, due to the absence of suitable experimental probes in this elusive spectral range. Here, we present a unique combination of many-body perturbation theory and state-of-the-art ultrafast broadband ultraviolet spectroscopy to unveil the interplay between the ultraviolet-absorbing two-dimensional excitons of anatase TiO2 and a sea of electron-hole pairs. We discover that the critical density for the exciton Mott transition in this material is the highest ever reported in semiconductors. These results deepen our knowledge of the exciton Mott transition and pave the route toward the investigation of the exciton phase diagram in a variety of wide-gap insulators.