Towards a transferable fermionic neural wavefunction for molecules.

Deep neural networks have become a highly accurate and powerful wavefunction ansatz in combination with variational Monte Carlo methods for solving the electronic Schrödinger equation. However, despite their success and favorable scaling, these methods are still computationally too costly for wide adoption. A significant obstacle is the requirement to optimize the wavefunction from scratch for each new system, thus requiring long optimization.

Assessing the heterogeneity in the transmission of infectious diseases from time series of epidemiological data.

Structural features and the heterogeneity of disease transmissions play an essential role in the dynamics of epidemic spread. But these aspects can not completely be assessed from aggregate data or macroscopic indicators such as the effective reproduction number. We propose in this paper an index of effective aggregate dispersion (EffDI) that indicates the significance of infection clusters and superspreading events in the progression of outbreaks by carefully measuring the level of relative stochasticity in time series of reported case numbers using a specially crafted statistical model for reproduction.

Integral representations of shallow neural network with rectified power unit activation function.

In this paper we characterize the set of functions that can be represented by infinite width neural networks with RePU activation function max(0,x), when the network coefficients are regularized by an ℓ (quasi)norm. Compared to the more well-known ReLU activation function (which corresponds to p=1), the RePU activation functions exhibit a greater degree of smoothness which makes them preferable in several applications. Our main result shows that such representations are possible for a given function if and only if the function is κ-order Lipschitz and its R-norm is finite.

Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks.

The Schrödinger equation describes the quantum-mechanical behaviour of particles, making it the most fundamental equation in chemistry. A solution for a given molecule allows computation of any of its properties. Finding accurate solutions for many different molecules and geometries is thus crucial to the discovery of new materials such as drugs or catalysts.

Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies.

Due to the ongoing COVID-19 pandemic, demand for diagnostic testing has increased drastically, resulting in shortages of necessary materials to conduct the tests and overwhelming the capacity of testing laboratories. The supply scarcity and capacity limits affect test administration: priority must be given to hospitalized patients and symptomatic individuals, which can prevent the identification of asymptomatic and presymptomatic individuals and hence effective tracking and tracing policies. We describe optimized group testing strategies applicable to SARS-CoV-2 tests in scenarios tailored to the current COVID-19 pandemic and assess significant gains compared to individual testing.

Scattered manifold-valued data approximation.

We consider the problem of approximating a function from an Euclidean domain to a manifold by scattered samples [Formula: see text], where the data sites [Formula: see text] are assumed to be locally close but can otherwise be far apart points scattered throughout the domain. We introduce a natural approximant based on combining the moving least square method and the Karcher mean. We prove that the proposed approximant inherits the accuracy order and the smoothness from its linear counterpart.