ABSTRACT. DNA methylation is a modification of the biochemical environment of a nucleotide that can occur at so-called CpG sites in the DNA strand. Just as a genetic mutation, it can benefit or harm the organism, depending on where exactly it happens and to which extent. Our work focuses on two questions regarding the patterns of methylation in certain DNA sequences: is the size of (de-)methylated clusters depending on reactions with other CpG sites? And can these reactions alter epigenetic variation, i.e. population-wide methylation patterns? To describe the methylome evolution within one individual (on a single cell basis), but also intergenerational developments, we formulate two mathematical models and corresponding master equations: one considering the influence of a single neighbouring CpG site and one regarding both nearest neighbours. We illustrate and quantify the models with numerical simulations, which are then also used for the investigation of our research questions. Eventually we did find that for the chosen parameters, the cluster size increases if neighbouring interactions are involved. Also we found hints for the epigenetic variation being larger compared to a model that only considers exclusively spontaneous methylation processes. To allow further research on this topic using the code that was created during this project, it is made available in a public GitHub repository (see https://github.com/yifanchn/methylation_pattern_modelling_pub).

ABSTRACT. Protein structure prediction is one of the most important scientific problems, on the one hand it is one of the NP-hard problems, and on the other hand it has a wide range of applications, including drug discovery and the development of biotechnology. A significant breakthrough in this area has occurred with the use of machine learning algorithms. Unlike traditional methods based on physical principles, these data-driven approaches use statistics and pattern recognition to predict protein structures, interactions, and functions.

This study presents a new approach to protein structure prediction by integrating the Landscape Modification (LM) method with the Adam optimizer for OpenFold. We compare the performance of standard Adam, LM, and LM with Simulated Annealing (LM SA) on different datasets and computational conditions. Our empirical results show that LM and LM SA outperform the standard Adam on these metrics.

Funded by Singapore MoE Tier 1 grant entitled "MAPLE" with grant number 22-5715-P0001.

ABSTRACT. Nowadays, microbiological systems have become important objects of interdisciplinary research in mathematical biology and bioinformatics, and can be analyzed by means of in silico study with the implementation of computational experiments. Design of mathematical models of bacterial biomass growth under external inhibition can help predict states of the microbiological system, reduce antibiotic use and hence avoid antimicrobial resistance. The present study was undertaken to develop a mathematical model of nutrient-dependent dynamics of bacteria cultured on media, taking into account external surface growth inhibition. The mathematical problem statement includes governing equations to define spatial-temporal distributions of bacterial biomass concentration, nutrient concentration, time-dependent dose of antibiotic concentration, and characteristics of bacterial quorum sensing. We proposed a joint numerical scheme based on finite difference methods and specialized program application implemented with Matlab software. A series of computational experiments were performed to describe distributions of key chemical compounds characterizing bacterial surface growth exposed to antibiotics and predict strategies of antibiotic treatment.

ABSTRACT. The multidimensional study of major groups of microorganisms has recently gained high importance due to modern challenges from viruses and pathogen bacteria. Biofilms as the predominant life-form of bacteria (estimates suggest that 99% of all bacteria exist in biofilm communities) provide bacteria survival and formation of resistance factors. In the context of exploring behavioral patterns, the relevant problem is represented by design and implementation of simulation models of growth and development of biofilm structures. The current study focuses on the further development of the 3D hybrid simulation model of biofilm formation for the bacterial community taking into account the surface spreading mechanism. The proposed model modification is based on the cellular automaton algorithm of biofilm evolution, a discrete analogy for the diffusion model of nutrient consumption, and an additional inoculation mechanism regulated by bacterial quorum sensing. The proposed algorithm allows one to conduct simulations under variations of key model parameters: the initial nutrient level, the probability of additional inoculation, and the radius of random inoculation transfer. A series of computation experiments were performed to indicate biofilm formation from the point of view of ensuring optimality factors: maximum space occupation with minimal resource consumption.

ABSTRACT. The number of customer-machine interactions has increased dramatically over the last decade. With the introduction of fully functional Generative AI, such as ChatGPT, Copilot, Gemini, the number of the interactions and the amount of information will further increase in the nearest future.

In this work, I suggest an algorithm (optimizing layers) that can effectively minimize the number of questions asked from a user by machine with the goal to optimize the amount information used and stored by API server running the Generative AI. As a result, the cost of using the services reduces for the users as well as for the service providers.

The HPC (high performance computing) experiments have shown a significant role of the optimizing layers for effective user-machine interactions and their services.

ABSTRACT. This paper introduces Phoenix-OC, a novel optimal control software for the solution of large-scale, multi-phase Optimal Control (OC) problems. Phoenix-OC employs segmented collocation methods for the state discretization and B-Splines for the control parameterization. Each of the parameterized controls is allowed to have a distinct degree and knot grid. Additionally, control derivatives of arbitrary order can be utilized in the model, as well as constraint and cost functions. User-defined functions can be modeled either through an automatic differentiation framework or, alternatively, via a generic C interface supporting the utilization of virtually arbitrary functions, external models, etc. Among other features, the software inherently supports table data interpolation, the computation of post-optimal sensitivities for parametric OC problems, bi-level optimization, homotopy formulations, parallel batch runs, and job dependencies. Furthermore, jobs can be executed locally or through a job scheduler on computer clusters.

Phoenix-OC operates on the Phoenix-Core engine - a generic sparse evaluation framework for both the evaluation and derivative computation of vector-valued functions. Central to this computational engine is the notion of an Extended Sparsity Pattern (ESP). This novel type of sparsity pattern extends traditional binary-valued sparsity patterns to a new type of floating-point pattern, allowing for advanced structure exploitation. The exploitation of sparse structures based on the ESP, combined with the multi-level parallelism implemented in Phoenix-OC, yields high performance across a range of representative benchmarks from engineering applications.

ABSTRACT. A problem of safe aircraft flows merging in the approach zone is studied. It is supposed that the air routes of aircraft flows have a branched structure, that is, there can be multiple paths that lead an aircraft from the entry point of the flow to the final point of the scheme. There may be several merge points, at which the original and/or merged earlier aircraft flows join. At each point of the air route scheme, a safe passage of vessels must be provided, that is, the presence of the safe time interval between the instants of aircraft passage must be guaranteed. Regulation of the arrival instants of vessels is carried out by changing their velocities, routes or usage of special scheme elements: holding areas, point-merge schemes, path alignments. In the problem, some model is considered taking into account directions from an air traffic controller to a pilot connected with changing the aircraft's velocity and/or route. The resultant schedule of the aircraft arrivals to the scheme points is optimized from the point of view of some criterion. The criterion minimizes the deviations of aircraft arrivals to the final point of the scheme from the nominal ones and the number of directions from an air traffic controller to pilots. The methodology for constructing the model of such a problem is proposed within the mixed integer linear programming framework. Results of numerical modeling are given.

ABSTRACT. In this age where data is growing at an astronomical rate, with unfettered access to digital information, complexities have been introduced to scientific computations, analysis,and inferences. This is because such data could not be easily processed with traditionalapproaches. However, with innovative designs brought to the fore by NVIDIA and othermarket players in recent times, there have been productions of state-of-the-art GPUs suchas NVIDIA A100 Tensor Core GPU, Tesla V100, and NVIDIA H100 that seamlessly handle complex mathematical simulations and computations, Artificial Intelligence, Machine Learning, and high-performance computing, producing highly improved speed and efficiency, with room for scalability. These innovations have made it possible to efficiently deploy many parallel programming models like shared memory, distributed memory, data parallelization, and Partitioned Global Address Space (PGAS) with high-performance metrics. In this work, we analyzed the parquet-formatted New York City yellow taxi dataset on a RAPIDS and DASK-supported distributed data-parallel training platform using NVIDIA multi-GPUs. The dataset was used to train Extreme Gradient Boosting (XGBoost), RandomForest Regressor, and Elastic Net models for trip fare predictions. Our models achieved notableperformance metrics. The XGBoost achieved a mean squared error of 11.38 and R-squared of 0.9678. The model training and evaluation time took 38.51 seconds despite the huge size of the training dataset, showing how computationally efficient the system was. The model results for the RandomForest MSE was 21.96, and the R-squared was 0.9378. In the bid to show the scalability and versatility of our experimental design to different machine learning domains, our GPU-accelerated training was extended to image classification tasks by using MobileNet-V3-Large pre-trained architecture on a CIFAR-100 dataset. We achieved a ROC AUC of over 95% for the implementation. This work advances the state-of-the-art in parallel computing through implementation of RAPIDS and DASK frameworks on a distributed data-parallel training platform making use of NVIDIA multi-GPUs. The work is built on a well established theoretical framework using Amdahl and Gustafon’s laws on parallel computation.By integrating RAPIDS and DASK, we contribute to advancing parallel computing capabilities, offering potential applications in smart city development and the field of logistics and transportation management services where rapid fare predictions are very important. The contribution could also be extended to the field of image classification, vision systems, object detection and embedded systems for mobile applications.

ABSTRACT. Despite many years of intensive study, the nature of the low-temperature phase in frustrated spin systems, particularly nearest-neighbor models, remains an unsolved problem. To accurately determine the properties of interacting spin systems in thermodynamic equilibrium, it is essential to calculate the partition function, which encapsulates complete information about all possible states of the system. However, the exact computation of the partition function is often infeasible due to the exponentially large number of states and the complexity of defining the generating function. This challenge is further exacerbated in frustrated systems by large relaxation times, a rugged energy landscape, and the macroscopic degeneracy of ground states.

In this work, we present a novel methodology for studying the low-temperature phase of frustrated spin glass models using convolutional neural networks (CNNs). We analyze the performance and accuracy of the proposed method in different models of spin glasses, taking into account different sizes of models and distributions of the exchange integral J. By leveraging CNNs, we demonstrate advancements in modeling complex spin interactions, offering a promising avenue for unraveling the elusive properties of frustrated systems.

ABSTRACT. Linear motion guide ways are crucial components in various applications. The applications include Machining, Cutting, Packing, medical, robotics, automation to name a few. Stiffness and damping are factors affecting the performance of guide ways. These two factors are studied by many researchers worldwide and results obtained are available for further developments. Our research focuses on developing an experimental set up to test the linear motion guide ways for deflection and vibration velocity under loading conditions. The results obtained from experiment set up are validated by building a mathematical model in Matlab. The results obtained by experiment and model are having a good agreement. As non-linearity is considered the real-life behavior of the guide ways can be predicted.

ABSTRACT. Algorithms for the numerical solution of contact static problems of deformable solid mechanics are constructed. The contact interaction of the body system was considered either using variants of the domain decomposition method or using the mortar method (a variant of the Lagrange multiplier method). The developed algorithms are used to simulate the thermomechanical state of a fuel element section, considering creep, plasticity and cracking. The results of calculations for axisymmetric and three-dimensional formulations of the problem for the operation mode of a fuel element with constant heat release in fuel pellets are presented.

ABSTRACT. This paper presents a comprehensive study on the convergence analysis, and discretization error calculation for the three-dimensional (3D) Burgers’ equation solved using the Alternating Direction Implicit (ADI) finite difference method and Thomas algorithm, implemented in parallel on a GPU using CUDA C with various optimization strategies, in particular in memory usage. The applied methodology consists of developing an algorithm to solve the 3D Burgers equation in three meshes to calculate the order of convergence and the convergence error. The result is a comparison of the convergence analysis of our method with the convergence analysis applying the explicit method. In addition, it is verified that the solution is convergent, and the scheme’s order is approximately two. This work contributes to the field of numerical methods and high-performance computing by validating the efficiency and accuracy of the ADI method combined with the Thomas algorithm for solving the 3D Burgers’ equation on modern GPU architectures.

ABSTRACT. Speech enhancement aims at noise reduction and extracting the desired target speaker from the noisy mixture in a complex recording environment. Microphone array (MA) beamforming is commonly used in almost all acoustic equipment, such as hearing aids, surveillance device, teleconference system, mobile - phone, voice - controlled, smart home. MA beamforming techniques use the a priori information about the properties of surrounding environment, the designed MA distribution, the direction of arrival (DoA) of interest useful signal to achieve a better noise reduction and speech enhancement at the same time. Generalized Sidelobe Canceller (GSC) beamformer effi ciently remove background noise while saving the original clean speech component in an annoying recording scenario. However, due to undetermined factors, the overall GSC beamformer’s performance often degraded in realistic recording schemes. In this paper, the authors proposed exploiting the Bayesian estimator of short time spectral amplitude (STSA) to gain the amplitude of beamformer’s output signal. The resulting results showed that the suggested method can use the Bayesian estimator to improve the speech quality in the term of the signal-to-noise ratio (SNR) from 7.9 to 15.3 dB and reduce the speech distortion to 14.1 dB. The numer- ical results indicate the advantage of the author’s approach to overcome the drawback of GSC beamformer in real-life application as compared to state-of-the-art solutions.

ABSTRACT. This work presents a class of computational techniques for solving the radiative heat transfer in heterogeneous media with moving interfaces. The novelty of this work is demonstrating the significance of radiation in participating media at high temperature with thermal and optical properties evolving in time subject to dynamic interfaces. The governing equations consist of an integro-differential equation for the radiative transfer, a heat equation with discontinuous coefficients, and a dynamic equation for the moving interfaces. For the numerical solution, we consider the discrete ordinates method for the angle discretization, the cell-centred finite volume for the space discretization, and the implicit backward-difference formula for the time integration. The nonlinear algebraic equations resulting from these discretizations are dealt with using a Newton-based algorithm. Two test examples of radiative heat transfer in heterogeneous media with moving interfaces are used to examine the performance of the proposed methodology. The obtained results demonstrate the high accuracy and efficiency of the coupled solvers.