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Fluorescent imaging data are currently widely used in neuroscience and other fields. Genetically encoded sensors, based on fluorescent proteins, provide a wide inventory enabling scientiests to image virtually any process in a living cell and extracellular environment. However, especially due to the need for fast scanning, miniaturization, etc, the imaging data can be severly corrupred with multiplicative heteroscedactic noise, reflecting stochastic nature of photon emission and photomultiplier detectors. Deep learning architectures demonstrate outstanding performance in image segmentation and denoising, however they can require large clean datasets for training, and the actual data transformation is not evident from the network architecture and weight composition. On the other hand, some classical data transforms can provide for similar performance in combination with more clear insight in why and how it works. Here we propose an algorithm for denoising fluorescent dynamical imaging data, which is based on multilinear higher-order singular value decomposition (HOSVD) with optional truncation in rank along each axis and thresholding of the tensor of decomposition coefficients. In parallel, we propose a convenient paradigm for validation of the algorithm performance, based on simulated flurescent data, resulting from biophysical modeling of calcium dynamics in spatially resolved realistic 3D astrocyte templates. This paradigm is convenient in that it allows to vary noise level and its resemblance of the Gaussian noise and that it provides ground truth fluorescent signal that can be used to validate denoising algorithms. The proposed denoising method employs truncated HOSVD twice: first, narrow 3D patches, spanning the whole recording, are processed (local 3D-HOSVD stage), second, 4D groups of 3D patches are collaboratively processed (non-local, 4D-HOSVD stage). The effect of the first pass is twofold: first, a significant part of noise is removed at this stage, second, noise distribution is transformed to be more Gaussian-like due to linear combination of multiple samples in the singular vectors. The effect of the second stage is to further improve SNR. We perform parameter tuning of the second stage to find optimal parameter combination for denoising.

The objective of this article is to develop a model for a realistic description of a mixed flow of two types of vehicles (cars and trucks) on multi-lane highways, taking into account differences not only in the technical characteristics of vehicles (dimensions, maximum speed), but also differences in driving strategies. The article includes a literature review, including publications of recent years, confirming the relevance of modeling heterogeneous traffic flows.

The new model takes into account that trucks have a lower maximum speed compared to cars and are slower to start. They are less maneuverable, so it is more difficult for them to change lanes. In addition, the movement of trucks can be regulated by some restrictive rules, for example, a ban on driving in left lanes.

The model is based on the cellular automata theory, which allows for a comprehensive description of the features of individual flow components. At each time step, the state of the automaton cells is updated in two stages — changing lanes and moving forward. The algorithms of both substeps for cars and trucks differ. Each vehicle is assigned a number of parameters: vehicle type, length, maximum speed, lane change strategy, in-lane movement strategy.

The model is implemented as a software package that allows simulating traffic on various sections of the road network — intersections, sections with narrowing and widening of the road, entrances and exits from the highway. In this work, a road section with a varying number of lanes and a straight multi-lane section with a virtual detector were selected for testing the model. The results are presented in the form of local speed-density and flow-density diagrams, as well as spatiotemporal speed diagrams.

To test the model, a number of problems with different percentages of passenger cars and trucks are solved, which allows demonstrating a drop in the capacity of elements of the road network with an increase in the share of trucks in the flow. The cases of uniform distribution by lanes and the restriction to the right lane for trucks are simulated. The positive effect of introducing a ban on the movement of trucks in left lanes on a multi-lane highway is illustrated.