Computational Problems Research Articles

A Survey on Ring Theory for its Mathematical Foundation and Applications

The origin of the ring theory can be dated to the early 19th century. With the rapid development of technology, more and more complex engineering problems and computer problems need to obtain support and results from more basic mathematics theory. Hence, based on this demand, the researcher discovered that ring theory is a very noteworthy math theory for solving the complicated problems above. This paper investigated the ring theory and related articles based on number theory and corresponding applications, which produces and results in a literature review in this particular direction.

A qubit-efficient variational selected configuration-interaction method

Abstract Finding the ground-state energy of molecules is an important and challenging computational problem for which quantum computing can potentially find efficient solutions. The variational quantum eigensolver (VQE) is a quantum algorithm that tackles the molecular groundstate problem and is regarded as one of the flagships of quantum computing. Yet, to date, only very small molecules were computed via VQE, due to high noise levels in current quantum devices. Here we present an alternative variational quantum scheme that requires significantly less qubits than VQE. The reduction in the qubit number allows for shallower circuits to be sufficient, rendering the method more resistant to noise. The proposed algorithm, termed variational quantum selected-configuration-interaction (VQ-SCI), is based on: (a) representing the target groundstate as a superposition of Slater determinant configurations, encoded directly upon the quantum computational basis states; and (b) selecting a-priory only the most dominant configurations. This is demonstrated through a set of groundstate calculations of the H2, LiH, BeH2, H2O, NH3 and C2H4 molecules in the sto-3g basis set, performed on IBM quantum devices. We show that the VQ-SCI reaches the full configuration interaction energy within chemical accuracy using the lowest number of qubits reported to date. Moreover, when the SCI matrix is generated ‘on the fly’, the VQ-SCI requires exponentially less memory than classical SCI methods. This offers a potential remedy to a severe memory bottleneck problem in classical SCI calculations. Finally, the proposed scheme is general and can be straightforwardly applied for finding the groundstate of any Hermitian matrix, outside the chemical context.

Multi-innovation adaptive Kalman filter algorithm for estimating the SOC of lithium-ion batteries based on singular value decomposition and Schmidt orthogonal transformation

The state of charge (SOC) of lithium battery is a key parameter for effective management of battery management systems (BMS). To address the problems of low precision, complex computation and poor robustness of traditional charging state estimation methods, an enhanced algorithm based on Unscented Kalman filter (UKF) is proposed. The singular value decomposition (SVD) method is adopted to ensure the normal operation of the Unscented Kalman Filter (UKF) algorithm even when the matrix P lacks positive semi-definiteness from a mathematical perspective. This enhancement significantly improves the theoretical robustness of UKF. Schmidt orthogonal transformation is concurrently used to reduce the computational complexity in the sampling point selection process, and the multi-innovation theory is combined with adaptive noise control to further improve the accuracy of SOC estimation. The algorithm is validated using the Urban Dynamometer Driving Schedule (UDDS) condition. The simulation results are excited using Singular value decomposition-multi-innovation adaptive Schmidt orthogonal unscented Kalman filter method (SVD-MIASOUKF). 0.95 % and 1.29 % of maximum errors are obtained at 25 °C and −10 °C, while the maximum errors are 2.46 %–2.99 % using SVD-UKF and UKF. The proposed approach shows faster convergence speed and higher estimation accuracy in comparison to traditional algorithms.

Dynamic Spatial-Temporal Embedding via Neural Conditional Random Field for Multivariate Time Series Forecasting

How to capture dynamic spatial-temporal dependencies remains an open question in multivariate time series (MTS) forecasting. Although recent advanced spatial-temporal graph neural networks (STGNNs) achieve superior forecasting performance, they either consider pre-defined spatial correlations or simply learn static graphs. Some research has tried to learn many adjacent matrices to reveal time-varying spatial correlations, but they generate discrete graphs which cannot encode evolutionary information and also face computational complexity problem. In this article, we propose two significant plugins to help automatically learn enhanced dynamic spatial-temporal embedding of MTS data: (1) a novel neural conditional random field (CRF) layer. We find that the implicit time-varying spatial dependencies are reflected by the explicit changeable links between edges, and we propose the neural CRF to encode such pairwise changeable evolutionary inter-dependencies; (2) a structure adaptive graph convolution (SAGC) that does not require pre-defined graphs to capture semantically richer spatial correlations. Then, we integrate the neural CRF, SAGC with recurrent neural network to develop a new STGNN paradigm termed Adaptive Spatial-Temporal graph neural network with Conditional Random Field (ASTCRF), which can be trained in an end-to-end fashion. We validate the effectiveness, efficiency, and scalability of ASTCRF on five public benchmark MTS datasets.

Stacked-gait: A human gait recognition scheme based on stacked autoencoders.

Human gait recognition (HGR) is the mechanism of biometrics that authors extensively employ to recognize an individuals based on their walking traits. HGR has been prominent for the past few years due to its surveillance capability. In HGR, an individual's walking attributes are utilized for identification. HGR is considered a very effective technique for recognition but faces different problematic factors that degrade its performance. The major factors are variations in clothing, carrying, walking, etc. In this paper, a new hybrid method for the classification of HGR is designed called Stacked-Gait. The system is based on six major steps; initially, image resizing is performed to overcome computation problems. In the second step, these images are converted into grey-scale to extract better features. After that, the dataset division is performed into train and test set. In the next step, the training of the autoencoders and feature extraction of the dataset are performed using training data. In the next step, the stacking of two autoencoders is also performed. After that, the stacked encoders are employed to extract features from the test data. Finally, the feature vectors are given as input to various machine learning classifiers for final classification. The method assessment is performed using the CASIA-B dataset and achieved the accuracy of 99.90, 98.10, 97.20, 97.20, 96.70, and 100 percent on 000, 180, 360, 540, 720, and 900 angles. It is pragmatic that the system gives promising results compared to recent schemes.

Communication Complexity of Entanglement-Assisted Multi-Party Computation

We consider a quantum and a classical version of a multi-party function computation problem with n players, where players 2,…,n need to communicate appropriate information to player 1 so that a “generalized” inner product function with an appropriate promise can be calculated. In the quantum version of the protocol, the players have access to entangled qudits but the communication is still classical. The communication complexity of a given protocol is the total number of classical bits that need to be communicated. When n is prime, and for our chosen function, we exhibit a quantum protocol (with complexity (n−1)(logn) bits) and a classical protocol (with complexity ((n−1)2(logn2) bits)). Furthermore, we present an integer linear programming formulation for determining a lower bound on the classical communication complexity. This demonstrates that our quantum protocol is strictly better than classical protocols.

Neural-network approach to running high-precision atomic computations

Modern applications of atomic physics, including the determination of frequency standards and the analysis of astrophysical spectra, require prediction of atomic properties with exquisite accuracy. For complex atomic systems, high-precision calculations are a major challenge due to the exponential scaling of the involved electronic configuration sets. This exacerbates the problem of required computational resources for these computations and makes indispensable the development of approaches to select the most important configurations out of otherwise intractably huge sets. We have developed a neural-network (NN) tool for running high-precision atomic configuration interaction (CI) computations with iterative selection of the most important configurations. Integrated with the established atomic codes, our approach results in computations with significantly reduced computational requirements in comparison with those without NN support. We showcase a number of NN-supported computations for the energy levels of Fe16+ and Ni12+ and demonstrate that our approach can be reliably used and automated for solving specific computational problems for a wide variety of systems. Published by the American Physical Society 2024

TCRcost: a deep learning model utilizing TCR 3D structure for enhanced of TCR-peptide binding.

Predicting TCR-peptide binding is a complex and significant computational problem in systems immunology. During the past decade, a series of computational methods have been developed for better predicting TCR-peptide binding from amino acid sequences. However, the performance of sequence-based methods appears to have hit a bottleneck. Considering the 3D structures of TCR-peptide complexes, which provide much more information, could potentially lead to better prediction outcomes. In this study, we developed TCRcost, a deep learning method, to predict TCR-peptide binding by incorporating 3D structures. TCRcost overcomes two significant challenges: acquiring a sufficient number of high-quality TCR-peptide structures and effectively extracting information from these structures for binding prediction. TCRcost corrects TCR 3D structures generated by protein structure tools, significantly extending the available datasets. The main and side chains of a TCR structure are separately corrected using a long short-term memory (LSTM) model. This approach prevents interference between the chains and accurately extracts interactions among both adjacent and global atoms. A 3D convolutional neural network (CNN) is designed to extract the atomic features relevant to TCR-peptide binding. The spatial features extracted by the 3DCNN are then processed through a fully connected layer to estimate the probability of TCR-peptide binding. Test results demonstrated that predicting TCR-peptide binding from 3D TCR structures is both efficient and highly accurate with an average accuracy of 0.974 on precise structures. Furthermore, the average accuracy on corrected structures was 0.762, significantly higher than the average accuracy of 0.375 on uncorrected original structures. Additionally, the average root mean square distance (RMSD) to precise structures was significantly reduced from 12.753Å for predicted structures to 8.785Å for corrected structures. Thus, utilizing structural information of TCR-peptide complexes is a promising approach to improve the accuracy of binding predictions.

Perspective on complexity measures targeting read-once branching programs

A model of computation for which reasonable yet still incomplete lower bounds are known is the read-once branching program. Here variants of complexity measures successful in the study of read-once branching programs are defined and studied. Some new or simpler proofs of known bounds are uncovered. Branching program resources and the new measures are compared extensively. The new variants are developed in part in the hope of tackling read-k branching programs for the tree evaluation problem [8]. Other computation problems are studied as well. In particular, a common view of a function studied by Gál [11] and a function studied by Bollig and Wegener [3] leads to the general combinatorics of blocking sets. Technical combinatorial results of independent interest are obtained. New leads towards further progress are discussed. An exponential lower bound for non-deterministic read-k branching programs for the GEN function [17] is also derived, independently from the new measures.

The Multiple Millionaires' Problem: New Algorithmic Approaches and Protocols

We study a fundamental problem in Multi-Party Computation, which we call the Multiple Millionaires Problem (MMP). Given a set of private integer inputs, the problem is to identify the subset of inputs that equal the maximum (or minimum) of that set, without revealing any further information on the inputs beyond what is implied by the desired output. Such a problem is a natural extension of the Millionaires Problem, which is the very first Multi-Party Computation problem that was presented in Andrew Yaos seminal work (FOCS 1982). A closely related problem is MaxP, in which the value of the maximum is sought. We study these fundamental problems and describe several algorithmic approaches and protocols for their solution. In addition, we compare the performance of the protocols under several selected settings. As applications of privacy-preserving computation are more and more commonly implemented in industrial systems, MMP and MaxP become important building blocks in privacy-preserving statistics, machine learning, auctions and other domains. One of the prominent advantages of the protocols that we present here is their simplicity. As they solve fundamental problems that are essential building blocks in various application scenarios, we believe that the presented solutions to those problems, and the comparison between them, will serve well future researchers and practitioners of secure distributed computing.

Research and application of joint-constrained inversion of transient electromagnetic multivariate parameter

Due to the phenomena of stratigraphic inclination, complex structure, and lateral discontinuity of resistivity or layer thickness in most of the coal seams, the traditional one-dimensional transient electromagnetic inversion method has limitations in interpretation accuracy. In addition, two- and three-dimensional inversion and artificial intelligence inversion have problems of large computation and large sample size, respectively, which limit their application in small- and medium-sized engineering exploration. To improve the inversion effect, this study proposes a method of joint-constrained inversion of transient electromagnetic multivariate parameters. This method achieves the joint constraint inversion of the transient electromagnetic multi-parameter by making full use of the geological data and a priori information to construct the initial model and adding the constraints such as the resistivity, the thickness, and the layer interface of each layer in the inversion objective function, and at the same time, taking into account the spatial correlation of the stratigraphic structure between the neighboring measurement points, as well as the transverse and vertical constraints between the measurement points along the direction of the survey line and perpendicular to the survey line. First, a series of typical geoelectric models are established and numerically simulated, and the results are compared with those of the traditional inversion method to verify the applicability and effectiveness of the method. Then, the constrained inversion is carried out on the physical simulation and measured data, and the results are in good agreement with the actual geological conditions. The numerical simulation, physical simulation and measured data inversion results consistently prove that this method can effectively reduce the uncertainty of the inversion at the isolated measuring points, improve the spatial continuity of the formation boundary, and better reflect the actual geoelectric characteristics of the formation.

Physics simulation capabilities of LLMs

Large Language Models (LLMs) can solve some undergraduate-level to graduate-level physics textbook problems and are proficient at coding. Combining these two capabilities could one day enable AI systems to simulate and predict the physical world. We present an evaluation of state-of-the-art (SOTA) LLMs on PhD-level to research-level computational physics problems. We condition LLM generation on the use of well-documented and widely-used packages to elicit coding capabilities in the physics and astrophysics domains. We contribute ∼50 original and challenging problems in celestial mechanics (with REBOUND), stellar physics (with MESA), 1D fluid dynamics (with Dedalus) and non-linear dynamics (with SciPy). Since our problems do not admit unique solutions, we evaluate LLM performance on several soft metrics: counts of lines that contain different types of errors (coding, physics, necessity and sufficiency) as well as a more educational’ Pass-Fail metric focused on capturing the salient physical ingredients of the problem at hand. As expected, today's SOTA LLM (GPT4) zero-shot fails most of our problems, although about 40% of the solutions could plausibly get a passing grade. About 70%–90% of the code lines produced are necessary, sufficient and correct (coding & physics). Physics and coding errors are the most common, with some unnecessary or insufficient lines. We observe significant variations across problem class and difficulty. We identify several failure modes of GPT4 in the computational physics domain, such as poor physical units handling, poor code versioning, tendency to hallucinate plausible sub-modules, lack of physical justification for global run parameters (e.g., simulation time, or upper-lower bounds for parametric exploration) and inability to define steady-state or stopping conditions reliably. Our reconnaissance work provides a snapshot of current computational capabilities in classical physics and points to obvious improvement targets if AI systems are ever to reach a basic level of autonomy in physics simulation capabilities.

On an Empirical Likelihood Based Solution to the Approximate Bayesian Computation Problem

On an Empirical Likelihood Based Solution to the Approximate Bayesian Computation Problem

A method to balancing robotic mixed-model assembly lines: Practical constraints, computational challenges, and performance estimation

This paper considers a robotic assembly line with various practical constraints. These have been previously modeled mathematically, but extending it to consider mixed-model production presents two challenges: computational costs increase substantially with problem size, and devising a theoretical model for practical performance is difficult within mathematical programming. This paper seeks to bridge those gaps,by proposing a method based on fixing, constraining, and optimizing mixed-integer programming instances. Simulations and linear relaxations are used to measure performance and estimate room for improvement. The resulting solution for the large-size industrial case study reached approximately 5% better throughput than a mixed-model benchmark approach, which represents around 85% of the estimated improvement potential for starting from that initial solution. Furthermore, an exhaustive set of tests was performed to demonstrate the proposed method’s efficacy. Hence, the method managed to optimize a rather challenging computational problem that combines the complexity of relevant practical constraints with theoretical difficulties in estimating the performance of solutions.

Procedimentos para modelagem BIM de lajes nervuradas de concreto armado em edificações

It is impossible not to admit that commercial computational tools for structural analysis and detailing have become indispensable in the various applications of Structural Engineering nowadays. The importance of these tools equipped with graphical interfaces based on the BIM (Building Information Modeling) environment is mainly due to the flexibility and ease in making common corrections and changes during the elaboration stage, as well as the proposition of different structural conceptions, not always innovative, but almost always bold, as in the case of reinforced concrete ribbed slabs. The use of ribbed slabs in reinforced concrete is an old practice in Structural Engineering, which has encouraged the adaptation of commercial computational tools, both in the development of structurally consistent mathematical formulations, as well as in the development of specific databases, equipped with information from mold manufacturers and materials intended for the execution of this type of slabs. It is highly efficient in building structures in which there are numerous problems of interference of structural elements with elements of installations, such as large-diameter pipes for wastewater, sewage, gas, fire, and even air conditioning ducts, exhaust and architectural elements. This efficiency is mainly due to the fact that large beams are not considered in their supports, making the lower face of the slab practically without obstacles to the building pipes, and is also due to the low average thickness of concrete used in the pavement compared to conventional rectangular supported slabs and flat mushroom slabs. However, it is not always possible to obtain an optimal final result, even with all the adaptations previously described, mainly due to executive and computational modeling problems. This work intends to present a possible structural modeling methodology, which provides results within the limits of the feasibility of the slab, both in the construction aspect of the computational structural model, as well as the possibility of using materials from manufacturers and labor, using a commercial computational tool for structural analysis and detailing.

Simulating the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm with limited entanglement using tensor networks

Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time evolution is perfectly unitary and that the full Hilbert space is available. However, in practice, the available entanglement may be limited, leading to a reduced fidelity of the quantum algorithms. To simulate the execution of quantum algorithms with limited entanglement, tensor-network methods provide a useful framework, since they allow us to restrict the entanglement in a quantum circuit. Thus, we here use tensor networks to analyze the fidelity of the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm as the entanglement is reduced, and we map out the entanglement that is generated during the execution of each algorithm. In all three cases, we find that the algorithms can be executed with high fidelity even if the entanglement is somewhat reduced. For example, the quantum counting algorithm can be executed with a high fidelity beyond a certain threshold level of entanglement. Our results provide an understanding of the entanglement that is required to execute the three algorithms, and our simulations based on tensor networks can easily be applied to other algorithms. Published by the American Physical Society 2024

Space-time reconstruction for lensless imaging using implicit neural representations

Many computational imaging inverse problems are challenged by noise, model mismatch, and other imperfections that decrease reconstruction quality. For data taken sequentially in time, instead of reconstructing each frame independently, space-time algorithms simultaneously reconstruct multiple frames, thereby taking advantage of temporal redundancy through space-time priors. This helps with denoising and provides improved reconstruction quality, but often requires significant computational and memory resources. Designing effective but flexible temporal priors is also challenging. Here, we propose using an implicit neural representation to model dynamics and act as a computationally tractable and flexible space-time prior. We demonstrate this approach on video captured with a lensless imager, DiffuserCam, and show improved reconstruction results and robustness to noise compared to frame-by-frame methods.

L-FNNG: Accelerating Large-Scale KNN Graph Construction on CPU-FPGA Heterogeneous Platform

Due to the high complexity of constructing exact k -nearest neighbor graphs, approximate construction has become a popular research topic. The NN-Descent algorithm is one of the representative in-memory algorithms. To effectively handle large datasets, existing state-of-the-art solutions combine the divide-and-conquer approach and the NN-Descent algorithm, where large datasets are divided into multiple partitions, and a subgraph is constructed for each partition before all the subgraphs are merged, reducing the memory pressure significantly. However, such solutions fail to address inefficiencies in large-scale k -nearest neighbor graph construction. In this paper, we propose L-FNNG, a novel solution for accelerating large-scale k -nearest neighbor graph construction on CPU-FPGA heterogeneous platform. The CPU is responsible for dividing data and determining the order of partition processing, while the FPGA executes all construction tasks to utilize the acceleration capability fully. To accelerate the execution of construction tasks, we design an efficient FPGA accelerator, which includes the Block-based Scheduling (BS) and Useless Computation Aborting (UCA) techniques to address the problems of memory access and computation in the NN-Descent algorithm. We also propose an efficient scheduling strategy that includes a KD-tree-based data partitioning method and a hierarchical processing method to address scheduling inefficiency. We evaluate L-FNNG on a Xilinx Alveo U280 board hosted by a 64-core Xeon server. On multiple large-scale datasets, L-FNNG achieves, on average, 2.3× construction speedup over the state-of-the-art GPU-based solution.

Quantum embedding method with transformer neural network quantum states for strongly correlated materials

The neural-network quantum states (NNQS) method is rapidly emerging as a powerful tool in quantum mechanisms. While significant advancements have been achieved in simulating simple molecules using NNQS, the ab initio simulation of complex solid-state materials remains challenging. Here in this work, we have adopted the periodic density matrix embedding theory to extend the NNQS method to deal with complex solid-state systems. Our approach notably reduces the computational problem size while maintaining high accuracy. We have validated the accuracy and efficiency of our method against traditional methodologies and experimental data in extended systems, and have investigated the magnetic ordering and charge density wave state in transition metal compounds. The findings from our research indicate that the integration of quantum embedding with intuitive chemical fragmentation can significantly enhance the NNQS simulation of realistic materials.

Multicellular artificial neural network-type architectures demonstrate computational problem solving.

Here, we report a modular multicellular system created by mixing and matching discrete engineered bacterial cells. This system can be designed to solve multiple computational decision problems. The modular system is based on a set of engineered bacteria that are modeled as an 'artificial neurosynapse' that, in a coculture, formed a single-layer artificial neural network-type architecture that can perform computational tasks. As a demonstration, we constructed devices that function as a full subtractor and a full adder. The system is also capable of solving problems such as determining if a number between 0 and 9 is a prime number and if a letter between A and L is a vowel. Finally, we built a system that determines the maximum number of pieces of a pie that can be made for a given number of straight cuts. This work may have importance in biocomputer technology development and multicellular synthetic biology.