Modeling and Simulation of Tissue Spheroids Fusion Based on the Function Representation Approach

Mathematical modeling for 3D bioprinting allows us to avoid widespread errors and also time and financial losses. It is necessary for such critical processes as tissue spheroids fusion and diffusion of nutrients in them. The reason is that tissue spheroids fusion is the base of the 3D bioprinting technology. In this work, we propose an approach for tissue spheroids fusion modeling considering a need to compromise between fidelity of the geometric form and viability of the whole bioconstruct.

CAD/CAM System for Additive Manufacturing with a Robust and Efficient Topology Optimization Algorithm Based on the Function Representation

Additive manufacturing erases the distance between design ideas and finished parts. However, designers must use several software tools to use these advantages. Moreover, these tools operate with different representations of geometry. This paper describes the architecture of a new CAD/CAM system that uses only the function representation of the geometry (FRep). It provides all widely used design operations and allows an engineer to employ robust and efficient topology optimization algorithms. The developed CAD/CAM system consists of 3D modeling, simulation, topology optimization, and direct manufacturing modules. We successfully printed designed parts and performed mechanical tests of printed parts. The results of tests show good agreement with simulation data. The system makes it possible to create structures with the desired properties in a fast and flexible way. The proposed approach significantly helps in designing additive manufacturing process and saves time for its users.

Learning Aggregation Functions

Learning on sets is increasingly gaining attention in the machine learning community, due to its widespread applicability. Typically, representations over sets are computed by using fixed aggregation functions such as sum or maximum. However, recent results showed that universal function representation by sum- (or max-) decomposition requires either highly discontinuous (and thus poorly learnable) mappings, or a latent dimension equal to the maximum number of elements in the set. To mitigate this problem, we introduce LAF (Learning Aggregation Function), a learnable aggregator for sets of arbitrary cardinality. LAF can approximate several extensively used aggregators (such as average, sum, maximum) as well as more complex functions (e.g. variance and skewness). We report experiments on semi-synthetic and real data showing that LAF outperforms state-of-the-art sum- (max-) decomposition architectures such as DeepSets and library-based architectures like Principal Neighborhood Aggregation, and can be effectively combined with attention-based architectures.

How Discrete Spectrum and Resonances Influence the Asymptotics of the Toda Shock Wave

We rigorously derive the long-time asymptotics of the Toda shock wave in a middle region where the solution is asymptotically finite gap. In particular, we describe the influence of the discrete spectrum in the spectral gap on the shift of the phase in the theta-function representation for this solution. We also study the effect of possible resonances at the endpoints of the gap on this phase. This paper is a continuation of research started in [arXiv:2001.05184].