Twice weekly polymerase chain reaction (PCR) surveillance swabs are not as effective as daily antigen testing for containment of severe acute respiratory coronavirus virus 2 (SARS-CoV-2) outbreaks: A modeling study based on real world data from a child and adolescent psychiatry clinic.

OBJECTIVE: In the coronavirus disease 2019 (COVID-19) pandemic, child and adolescent psychiatry wards face the risk of severe acute respiratory coronavirus 2 (SARS-CoV-2) introduction and spread within the facility. In this setting, mask and vaccine mandates are hard to enforce, especially for younger children. Surveillance testing may detect infection early and enable mitigation measures to prevent viral spread. We conducted a modeling study to determine the optimal method and frequency of surveillance testing and to analyze the effect of weekly team meetings on transmission dynamics. DESIGN AND SETTING: Simulation with an agent-based model reflecting ward structure, work processes, and contact networks from a real-world child and adolescent psychiatry clinic with 4 wards, 40 patients, and 72 healthcare workers. METHODS: We simulated the spread of 2 SARS-CoV-2 variants over 60 days under surveillance testing with polymerase chain reaction (PCR) tests and rapid antigen tests in different scenarios. We measured the size, peak, and the duration of an outbreak. We compared medians and percentage of spillover events to other wards from 1,000 simulations for each setting. RESULTS: The outbreak size, peak, and duration were dependent on test frequency, test type, SARS-CoV-2 variant, and ward connectivity. Under surveillance conditions, joint staff meetings and therapists shared between wards did not significantly change median outbreak size under surveillance conditions. With daily antigen testing, outbreaks were mostly confined to 1 ward and median outbreak sizes were lower than with twice-weekly PCR testing (1 vs 22; P < .001). CONCLUSION: Modeling can help to understand transmission patterns and guide local infection control measures.

Neural ordinary differential equations with irregular and noisy data.

Measurement noise is an integral part of collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We discuss a methodology to learn differential equation(s) using noisy and irregularly sampled measurements. In our methodology, the main innovation can be seen in the integration of deep neural networks with the neural ordinary differential equations (ODEs) approach. Precisely, we aim at learning a neural network that provides (approximately) an implicit representation of the data and an additional neural network that models the vector fields of the dependent variables. We combine these two networks by constraints using neural ODEs. The proposed framework to learn a model describing the vector field is highly effective under noisy measurements. The approach can handle scenarios where dependent variables are unavailable at the same temporal grid. Moreover, a particular structure, e.g. second order with respect to time, can easily be incorporated. We demonstrate the effectiveness of the proposed method for learning models using data obtained from various differential equations and present a comparison with the neural ODE method that does not make any special treatment to noise. Additionally, we discuss an ensemble approach to improve the performance of the proposed approach further.

Discovery of nonlinear dynamical systems using a Runge-Kutta inspired dictionary-based sparse regression approach.

In this work, we blend machine learning and dictionary-based learning with numerical analysis tools to discover differential equations from noisy and sparsely sampled measurement data of time-dependent processes. We use the fact that given a dictionary containing large candidate nonlinear functions, dynamical models can often be described by a few appropriately chosen basis functions. As a result, we obtain parsimonious models that can be better interpreted by practitioners, and potentially generalize better beyond the sampling regime than black-box modelling. In this work, we integrate a numerical integration framework with dictionary learning that yields differential equations without requiring or approximating derivative information at any stage. Hence, it is utterly effective for corrupted and sparsely sampled data. We discuss its extension to governing equations, containing rational nonlinearities that typically appear in biological networks. Moreover, we generalized the method to governing equations subject to parameter variations and externally controlled inputs. We demonstrate the efficiency of the method to discover a number of diverse differential equations using noisy measurements, including a model describing neural dynamics, chaotic Lorenz model, Michaelis-Menten kinetics and a parameterized Hopf normal form.

Tomographic X-ray scattering based on invariant reconstruction: analysis of the 3D nanostructure of bovine bone.

Small-angle X-ray scattering (SAXS) is an effective characterization technique for multi-phase nanocomposites. The structural complexity and heterogeneity of biological materials require the development of new techniques for the 3D characterization of their hierarchical structures. Emerging SAXS tomographic methods allow reconstruction of the 3D scattering pattern in each voxel but are costly in terms of synchrotron measurement time and computer time. To address this problem, an approach has been developed based on the reconstruction of SAXS invariants to allow for fast 3D characterization of nanostructured inhomogeneous materials. SAXS invariants are scalars replacing the 3D scattering patterns in each voxel, thus simplifying the 6D reconstruction problem to several 3D ones. Standard procedures for tomographic reconstruction can be directly adapted for this problem. The procedure is demonstrated by determining the distribution of the nanometric bone mineral particle thickness (T parameter) throughout a macroscopic 3D volume of bovine cortical bone. The T parameter maps display spatial patterns of particle thickness in fibrolamellar bone units. Spatial correlation between the mineral nano-structure and microscopic features reveals that the mineral particles are particularly thin in the vicinity of vascular channels.

Greedy low-rank algorithm for spatial connectome regression.

Recovering brain connectivity from tract tracing data is an important computational problem in the neurosciences. Mesoscopic connectome reconstruction was previously formulated as a structured matrix regression problem (Harris et al. in Neural Information Processing Systems, 2016), but existing techniques do not scale to the whole-brain setting. The corresponding matrix equation is challenging to solve due to large scale, ill-conditioning, and a general form that lacks a convergent splitting. We propose a greedy low-rank algorithm for the connectome reconstruction problem in very high dimensions. The algorithm approximates the solution by a sequence of rank-one updates which exploit the sparse and positive definite problem structure. This algorithm was described previously (Kressner and Sirkovic in Numer Lin Alg Appl 22(3):564-583, 2015) but never implemented for this connectome problem, leading to a number of challenges. We have had to design judicious stopping criteria and employ efficient solvers for the three main sub-problems of the algorithm, including an efficient GPU implementation that alleviates the main bottleneck for large datasets. The performance of the method is evaluated on three examples: an artificial "toy" dataset and two whole-cortex instances using data from the Allen Mouse Brain Connectivity Atlas. We find that the method is significantly faster than previous methods and that moderate ranks offer a good approximation. This speedup allows for the estimation of increasingly large-scale connectomes across taxa as these data become available from tracing experiments. The data and code are available online.

RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations.

This paper introduces a new algorithm for solving large-scale continuous-time algebraic Riccati equations (CARE). The advantage of the new algorithm is in its immediate and efficient low-rank formulation, which is a generalization of the Cholesky-factored variant of the Lyapunov ADI method. We discuss important implementation aspects of the algorithm, such as reducing the use of complex arithmetic and shift selection strategies. We show that there is a very tight relation between the new algorithm and three other algorithms for CARE previously known in the literature-all of these seemingly different methods in fact produce exactly the same iterates when used with the same parameters: they are algorithmically different descriptions of the same approximation sequence to the Riccati solution.