The Improved Element-Free Galerkin Method for 3D Helmholtz Equations

The improved element-free Galerkin (IEFG) method is proposed in this paper for solving 3D Helmholtz equations. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty technique is used to enforce the essential boundary conditions. Thus, the final discretized equations of the IEFG method for 3D Helmholtz equations can be derived by using the corresponding Galerkin weak form. The influences of the node distribution, the weight functions, the scale parameters of the influence domain, and the penalty factors on the computational accuracy of the solutions are analyzed, and the numerical results of three examples show that the proposed method in this paper can not only enhance the computational speed of the element-free Galerkin (EFG) method but also eliminate the phenomenon of the singular matrix.

Reverse engineering of a mechanistic model of gene expression using metastability and temporal dynamics

Differentiation can be modeled at the single cell level as a stochastic process resulting from the dynamical functioning of an underlying Gene Regulatory Network (GRN), driving stem or progenitor cells to one or many differentiated cell types. Metastability seems inherent to differentiation process as a consequence of the limited number of cell types. Moreover, mRNA is known to be generally produced by bursts, which can give rise to highly variable non-Gaussian behavior, making the estimation of a GRN from transcriptional profiles challenging. In this article, we present CARDAMOM (Cell type Analysis from scRna-seq Data achieved from a Mixture MOdel), a new algorithm for inferring a GRN from timestamped scRNA-seq data, which crucially exploits these notions of metastability and transcriptional bursting. We show that such inference can be seen as the successive resolution of as many regression problem as timepoints, after a preliminary clustering of the whole set of cells with regards to their associated bursts frequency. We demonstrate the ability of CARDAMOM to infer a reliable GRN from in silico expression datasets, with good computational speed. To the best of our knowledge, this is the first description of a method which uses the concept of metastability for performing GRN inference.

Simulation of RSO Images for Space Situation Awareness (SSA) Using Parallel Processing

With the rapid increase in resident space objects (RSO), there is a growing demand for their identification and characterization to advance space simulation awareness (SSA) programs. Various AI-based technologies are proposed and demonstrated around the world to effectively and efficiently identify RSOs from ground and space-based observations; however, there remains a challenge in AI training due to the lack of labeled datasets for accurate RSO detection. In this paper, we present an overview of the starfield simulator to generate a realistic representation of images from space-borne imagers. In particular, we focus on low-resolution images such as those taken with a commercial-grade star tracker that contains various RSO in starfield images. The accuracy and computational efficiency of the simulator are compared to the commercial simulator, namely STK-EOIR to demonstrate the performance of the simulator. In comparing over 1000 images from the Fast Auroral Imager (FAI) onboard CASSIOPE satellite, the current simulator generates both stars and RSOs with approximately the same accuracy (compared to the real images) as STK-EOIR and, an order of magnitude faster in computational speed by leveraging parallel processing methodologies.

FARCI: Fast and Robust Connectome Inference

The inference of neuronal connectome from large-scale neuronal activity recordings, such as two-photon Calcium imaging, represents an active area of research in computational neuroscience. In this work, we developed FARCI (Fast and Robust Connectome Inference), a MATLAB package for neuronal connectome inference from high-dimensional two-photon Calcium fluorescence data. We employed partial correlations as a measure of the functional association strength between pairs of neurons to reconstruct a neuronal connectome. We demonstrated using in silico datasets from the Neural Connectomics Challenge (NCC) and those generated using the state-of-the-art simulator of Neural Anatomy and Optimal Microscopy (NAOMi) that FARCI provides an accurate connectome and its performance is robust to network sizes, missing neurons, and noise levels. Moreover, FARCI is computationally efficient and highly scalable to large networks. In comparison with the best performing connectome inference algorithm in the NCC, Generalized Transfer Entropy (GTE), and Fluorescence Single Neuron and Network Analysis Package (FluoroSNNAP), FARCI produces more accurate networks over different network sizes, while providing significantly better computational speed and scaling.

Modified KNN-LVQ for Stairs Down Detection Based on Digital Image

Persons with visual impairments need a tool that can detect obstacles around them. The obstacles that exist can endanger their activities. The obstacle that is quite dangerous for the visually impaired is the stairs down. The stairs down can cause accidents for blind people if they are not aware of their existence. Therefore we need a system that can identify the presence of stairs down. This study uses digital image processing technology in recognizing the stairs down. Digital images are used as input objects which will be extracted using the Gray Level Co-occurrence Matrix method and then classified using the KNN-LVQ hybrid method. The proposed algorithm is tested to determine the accuracy and computational speed obtained. Hybrid KNN-LVQ gets an accuracy of 95%. While the average computing speed obtained is 0.07248 (s).

Quantum computational speed of a nanowires system with Rashba interaction in the presence of a magnetic field

The present research is designed to examine the dynamic of the quantum computational speed in a nanowire system through the orthogonality speed when three distinct types of magnetic fields are applied: the strong magnetic field, the weak magnetic field, and no magnetic field. Moreover, we investigate the action of the magnetic fields, the spin-orbit coupling, and the system’s initial states on the orthogonality speed. The observed results reveal that a substantial correlation between the intensity of the spin-orbit coupling and the dynamics of the orthogonality speed, where the orthogonality speed decreasing as the spin-orbit coupling increases. Furthermore, the initial states of the nanowire system are critical for regulating the speed of transmuting the information and computations.

CompAIRR: ultra-fast comparison of adaptive immune receptor repertoires by exact and approximate sequence matching

Adaptive immune receptor (AIR) repertoires (AIRRs) record past immune encounters with exquisite specificity. Therefore, identifying identical or similar AIR sequences across individuals is a key step in AIRR analysis for revealing convergent immune response patterns that may be exploited for diagnostics and therapy. Existing methods for quantifying AIRR overlap do not scale with increasing dataset numbers and sizes. To address this limitation, we developed CompAIRR, which enables ultra-fast computation of AIRR overlap, based on either exact or approximate sequence matching. CompAIRR improves computational speed 1000-fold relative to the state of the art and uses only one-third of the memory: on the same machine, the exact pairwise AIRR overlap of 104 AIRRs with 105 sequences is found in ~17 minutes, while the fastest alternative tool requires 10 days. CompAIRR has been integrated with the machine learning ecosystem immuneML to speed up various commonly used AIRR-based machine learning applications.

Development of a Modelica-based simplified building model for district energy simulations

Urban Building Energy Simulation (UBES) is an efficient tool to investigate and subsequently reduce energy demand of urban areas. Nevertheless, UBES has always been a challenging task due the trade-off between accuracy, computational speed and parametrization. In order to reduce these computation and parameterization requirements, model reduction and simplification methods aim at representing building behaviour with an acceptable accuracy, but using less equations and input parameters. This paper presents the development and validation results of a simplified urban simulation model based on the ISO 13790 Standard and written in the Modelica language. The model describes the thermo-physical behaviour of buildings by means of an equivalent electric network consisting of five resistances and one capacitance. The validation of the model was carried out using four cases of the ANSI/ASHRAE Standard 140. In general, the model shows good accuracy and the validation provided values within the acceptable ranges.

SpatialDE2: Fast and localized variance component analysis of spatial transcriptomics

Spatial transcriptomics is now a mature technology, allowing to assay gene expression changes in the histological context of complex tissues. A canonical analysis workflow starts with the identification of tissue zones that share similar expression profiles, followed by the detection of highly variable or spatially variable genes. Rapid increases in the scale and complexity of spatial transcriptomic datasets demand that these analysis steps are conducted in a consistent and integrated manner, a requirement that is not met by current methods. To address this, we here present SpatialDE2, which unifies the mapping of tissue zones and spatial variable gene detection as integrated software framework, while at the same time advancing current algorithms for both of these steps. Formulated in a Bayesian framework, the model accounts for the Poisson count noise, while simultaneously offering superior computational speed compared to previous methods. We validate SpatialDE2 using simulated data and illustrate its utility in the context of two real-world applications to the spatial transcriptomics profiles of the mouse brain and human endometrium.

Comparison and Analysis of Neural Solver Methods for Differential Equations in Physical Systems

Differential equations are ubiquitous in many fields of study, yet not all equations, whether ordinary or partial, can be solved analytically. Traditional numerical methods such as time-stepping schemes have been devised to approximate these solutions. With the advent of modern deep learning, neural networks have become a viable alternative to traditional numerical methods. By reformulating the problem as an optimisation task, neural networks can be trained in a semi-supervised learning fashion to approximate nonlinear solutions. In this paper, neural solvers are implemented in TensorFlow for a variety of differential equations, namely: linear and nonlinear ordinary differential equations of the first and second order; Poisson’s equation, the heat equation, and the inviscid Burgers’ equation. Different methods, such as the naive and ansatz formulations, are contrasted, and their overall performance is analysed. Experimental data is also used to validate the neural solutions on test cases, specifically: the spring-mass system and Gauss’s law for electric fields. The errors of the neural solvers against exact solutions are investigated and found to surpass traditional schemes in certain cases. Although neural solvers will not replace the computational speed offered by traditional schemes in the near future, they remain a feasible, easy-to-implement substitute when all else fails.