Space Complexity Research Articles

Dynamic community detection algorithm based on hyperbolic graph convolution

PurposeCommunity detection is a key factor in analyzing the structural features of complex networks. However, traditional dynamic community detection methods often fail to effectively solve the problems of deep network information loss and computational complexity in hyperbolic space. To address this challenge, a hyperbolic space-based dynamic graph neural network community detection model (HSDCDM) is proposed.Design/methodology/approachHSDCDM first projects the node features into the hyperbolic space and then utilizes the hyperbolic graph convolution module on the Poincaré and Lorentz models to realize feature fusion and information transfer. In addition, the parallel optimized temporal memory module ensures fast and accurate capture of time domain information over extended periods. Finally, the community clustering module divides the community structure by combining the node characteristics of the space domain and the time domain. To evaluate the performance of HSDCDM, experiments are conducted on both artificial and real datasets.FindingsExperimental results on complex networks demonstrate that HSDCDM significantly enhances the quality of community detection in hierarchical networks. It shows an average improvement of 7.29% in NMI and a 9.07% increase in ARI across datasets compared to traditional methods. For complex networks with non-Euclidean geometric structures, the HSDCDM model incorporating hyperbolic geometry can better handle the discontinuity of the metric space, provides a more compact embedding that preserves the data structure, and offers advantages over methods based on Euclidean geometry methods.Originality/valueThis model aggregates the potential information of nodes in space through manifold-preserving distribution mapping and hyperbolic graph topology modules. Moreover, it optimizes the Simple Recurrent Unit (SRU) on the hyperbolic space Lorentz model to effectively extract time series data in hyperbolic space, thereby enhancing computing efficiency by eliminating the reliance on tangent space.

Measuring Heuristic Accuracy on the Performance of Search Algorithms in Solving 8-Puzzle Problems

The goal of this paper is to examine the effect of heuristic accuracy on the performance of search algorithms in solving 8-puzzle problems. The 8-puzzle is a popular benchmark search problem in Artificial Intelligence, and numerous search strategies have been developed to solve it. This research evaluates the performance of search algorithms using different heuristics to determine the optimal level of heuristic accuracy for solving 8-puzzle problems. Several search algorithms, including uniform cost search and A* search, were implemented and tested using different heuristics. Manhattan and Euclidean distances were chosen as heuristics for A* algorithm. Heuristics play a crucial role in guiding these algorithms towards the solution, and their accuracy can greatly impact the performance of the search. Results revealed that reduction attained in both time and space complexity by A* search with Manhattan heuristic is over 99.1% for the average case, while the reduction in the effective branching factor is over 21.1%. These results from the experiments provide insights into the trade-off between heuristic accuracy and search efficiency, and contribute to a better understanding of the behavior of search algorithms in complex problems

Advances in Computational Methods for Drug Design: A Revolution in Pharmaceutical Development

Computational methods of drug design involve the use of various software and algorithms to predict the properties of drug molecules, screen for potential targets, and optimize drug candidates for therapeutic efficacy, it lowering the cost of drug research and development time. The discovery and development of a novel medicine is a lengthy, complex, expensive, and high-risk process that has no commercial counterpart. CADD has previously been used to uncover drugs that have gone through clinical trials and become innovative medicines for many ailments. CADD approaches are widely divided into two categories: structure-based drug design (SBDD) and ligand-based drug design (LBDD). SBDD is used when the three-dimensional structures of target proteins are available, while LBDD design is used in the absence of receptor 3D information and relies on knowledge of molecules that bind to the biological target of interest. Some applications in CADD are Lead Optimization, Virtual screening (VS), ADMET prediction, and toxicity prediction. Medicinal chemists use a variety of computational approaches to modify the chemical structure of a compound to maximize its in vitro activity, drug discovery is driven by the idea that a ligand with higher binding affinity to a target should be more efficacious than that with lower binding affinity to the same target. Target flexibility is one of the key issues that still need to be resolved in drug discovery. The majority of molecular docking tools give the ligand high flexibility, but they fix or give the protein's residues close to or inside the active site only limited flexibility. It is very difficult to provide complete molecular flexibility to the protein as this increases the space and time complexity of the computation. In conclusion, computational methods have revolutionized the field of drug design by enabling faster, more cost-effective, and more efficient drug discovery

TC-Match: Fast Time-Constrained Continuous Subgraph Matching

Continuously monitoring structural patterns in streaming graphs is a critical task in many real-time graph-based applications. In this paper, we study the problem of time-constrained continuous subgraph matching (shorted as TCSM) over streaming graphs. Given a query graph Q with timing order constraint and a data graph stream G , TCSM aims to report all incremental matches of Q in G for each update of G , where a match should obey both structure constraint (i.e., isomorphism) and timing order constraint of Q. Although TCSM has a wide range of applications, such as cyber-attack detection and credit card fraud detection, we note that this problem has not been well addressed. The state-of-the-art bears the limitations of high index space cost and intermediate result maintenance cost. In this paper, we propose TC-Match, an effective approach to TCSM. First, we design a space and time cost-effective index CSS, which is essentially a k -partite graph structure where a node corresponds to an edge in G. By carefully creating links between nodes, we can encapsulate into CSS the partial embedding and timing order information between edges in G. We theoretically show that CSS has polynomial space and construction time complexities. Second, based on the property of CSS, we develop an efficient incremental matching algorithm with an effective node merging optimization. Extensive experiments show that TC-Match can achieve up to 3 orders of magnitude query performance improvement over the baseline methods, and meanwhile the memory consumption is reduced by 48.7%-86.7%.

Quad-functioning parity layout for nanocomputing: A QCA design

Quantum dot cellular automata (QCA) is considered an alternative to conventional technologies like CMOS (Complementary Metal-Oxide-Semiconductor) technology due to its potential for lower power consumption, higher speed, and increased device density. QCA introduces a novel approach to designing nano communication circuits and systems. Nano communications data mistakes are detected via parity generators and checkers. The parity bit of each data block ensures that the number of 1′s is either even or odd. Consequently, the system requires four circuits: an even parity generator, an odd parity generator, an even parity checker, and an odd parity checker. The whole system requires more space and cell complexity. In this work, we propose a QCA architecture that serves as a generator for both even and odd parities, as well as a checker for both even and odd parities. It is a quad-functioning circuit that performs four distinct operations within a single design, utilizing 118 QCA cells and occupying an area of 0.17 μm2. The recommended approach uses an efficient XOR gate, resulting in improvements across several performance metrics. QCAPro calculates energy dissipation and design parameters. The recommended QCA circuit outperformed similar QCA circuits in size, complexity, and energy dissipation. The circuit's design cost functions are also low. There has been a 17% reduction in latency and an 86% improvement in QCA-specific costs when compared to the optimal existing design. Moreover, it necessitates a 40% reduction in majority gate usage. The proposed design may compete effectively with other equivalent higher-order circuit designs by reducing the need for multiple blocks in conventional circuits to execute the same task. This architecture holds potential benefits for nano processors and nano communication networks.

Analysis of visual communication elements in variable font design from the perspective of digital technology

With the maturity of digital technology, the effectiveness of information transmission has received extensive attention. Variable font design is regarded as an extension of graphic design in digital media art, and variable font design is studied from the perspective of information communication design. From the perspective of digital technology, based on the research theory of variable information communication design, combined with the specific methods of font design, the perception, cognitive methods, and aesthetic laws of aesthetic subject vision and psychology in the field of font variable design are discussed. Provide relevant theoretical support for information communication design activities with variable fonts. Based on artificial intelligence technology, a new interactive art expression method is proposed. By analyzing the main expression scenarios of interactive art, namely user information communication scenarios, interactive art push scenarios, interactive art promotion scenarios and personal service scenarios, it provides a scenario application basis for interactive expression, calculate the space complexity, space complexity and resource complexity, according to the complexity calculation results, carry out interaction design from three aspects of visual elements, multimedia elements, and human-computer interaction elements, integrate the topology structure after the interaction is realized, and in the network topology structure. The proposed model consists mainly of visual design, basic design elements, basic visual design, complete design and solution generation. It realizes the expression of interactive art of multimedia elements in display and control. The experimental results show that the interactive element extraction speed of the visual communication expression method based on artificial intelligence technology is increased by 30%, and the flexibility is stronger.

A Construction Optimization for Laser SLAM Based on Odometer Constraint Fusion

The traditional laser SLAM (Simultaneous Localization and Mapping) algorithm uses the global relative poses and local ones to form residual blocks. Its constructed map is not smooth enough and the constraint construction is too simplex under some special scenarios. Thus, this paper proposes an odometer constraint fusion method called FOSLAM (Fusion Odometer SLAM) to construct residual blocks between constrains and solve the nonlinear least squares by Ceres. The effectiveness and accuracy of this method have been verified through comparative experiments. Experimental results showed that without increasing the time and space complexity, by involving the odometer constraint into the SLAM optimization process, the convergence of scan matching scores can be improved and the constructed grid map edges are smoother and the jagged phenomenon can be reduced. Under sophisticated scene, FOSLAM is able to acquire more accurate maps and laser odometer trajectory than Cartographer method. Therefore, it is suitable to be used on indoor robot for cleaning and inspection and can be further deployed on autonomous unmanned vehicles involving spatial visualization and neuro-heuristic guidance.

Low-depth Clifford circuits approximately solve MaxCut

We introduce a quantum-inspired approximation algorithm for MaxCut based on low-depth Clifford circuits. We start by showing that the solution unitaries found by the adaptive quantum approximation optimization algorithm (ADAPT-QAOA) for the MaxCut problem on weighted fully connected graphs are (almost) Clifford circuits. Motivated by this observation, we devise an approximation algorithm for MaxCut, ADAPT-Clifford, that searches through the Clifford manifold by combining a minimal set of generating elements of the Clifford group. Our algorithm finds an approximate solution of MaxCut on an N-vertex graph by building a depth O(N) Clifford circuit. The algorithm has runtime complexity O(N2) and O(N3) for sparse and dense graphs, respectively, and space complexity O(N2), with improved solution quality achieved at the expense of more demanding runtimes. We implement ADAPT-Clifford and characterize its performance on graphs with positive and signed weights. The case of signed weights is illustrated with the paradigmatic Sherrington-Kirkpatrick model, for which our algorithm finds solutions with ground-state mean energy density corresponding to ∼94% of the Parisi value in the thermodynamic limit. The case of positive weights is investigated by comparing the cut found by ADAPT-Clifford with the cut found with the Goemans-Williamson (GW) algorithm. For both sparse and dense instances we provide copious evidence that, up to hundreds of nodes, ADAPT-Clifford finds cuts of lower energy than GW. Published by the American Physical Society 2024

Linear Matching of JavaScript Regular Expressions

Modern regex languages have strayed far from well-understood traditional regular expressions: they include features that fundamentally transform the matching problem. In exchange for these features, modern regex engines at times suffer from exponential complexity blowups, a frequent source of denial-of-service vulnerabilities in JavaScript applications. Worse, regex semantics differ across languages, and the impact of these divergences on algorithmic design and worst-case matching complexity has seldom been investigated. This paper provides a novel perspective on JavaScript's regex semantics by identifying a larger-than-previously-understood subset of the language that can be matched with linear time guarantees. In the process, we discover several cases where state-of-the-art algorithms were either wrong (semantically incorrect), inefficient (suffering from superlinear complexity) or excessively restrictive (assuming certain features could not be matched linearly). We introduce novel algorithms to restore correctness and linear complexity. We further advance the state-of-the-art in linear regex matching by presenting the first nonbacktracking algorithms for matching lookarounds in linear time: one supporting captureless lookbehinds in any regex language, and another leveraging a JavaScript property to support unrestricted lookaheads and lookbehinds. Finally, we describe new time and space complexity tradeoffs for regex engines. All of our algorithms are practical: we validated them in a prototype implementation, and some have also been merged in the V8 JavaScript implementation used in Chrome and Node.js.

Two-dimensional data partitioning for non-negative matrix tri-factorization

As a two-sided clustering and dimensionality reduction paradigm, Non-negative Matrix Tri-Factorization (NMTF) has attracted much attention in machine learning and data mining researchers due to its excellent performance and reliable theoretical support. Unlike Non-negative Matrix Factorization (NMF) methods applicable to one-sided clustering only, NMTF introduces an additional factor matrix and uses the inherent duality of data to realize the mutual promotion of sample clustering and feature clustering, thus showing great advantages in many scenarios (e.g., text co-clustering). However, the existing methods for solving NMTF usually involve intensive matrix multiplication, which is characterized by high time and space complexities, that is, there are limitations of slow convergence of the multiplicative update rules and high memory overhead. In order to solve the above problems, this paper develops a distributed parallel algorithm with a 2-dimensional data partition scheme for NMTF (i.e., PNMTF-2D). Experiments on multiple text datasets show that the proposed PNMTF-2D can substantially improve the computational efficiency of NMTF (e.g., the average iteration time is reduced by up to 99.7% on Amazon) while ensuring the effectiveness of convergence and co-clustering.

Quantum K-Nearest Neighbors: Utilizing QRAM and SWAP-Test Techniques for Enhanced Performance

This work introduces a quantum K-Nearest Neighbor (K-NN) classifier algorithm. The algorithm utilizes angle encoding through a Quantum Random Access Memory (QRAM) using n number of qubit addresses with O(log(n)) space complexity. It incorporates Grover’s algorithm and the quantum SWAP-Test to identify similar states and determine the nearest neighbors with high probability, achieving Om search complexity, where m is the qubit address. We implement a simulation of the algorithm using IBM’s Qiskit with GPU support, applying it to the Iris and MNIST datasets with two different angle encodings. The experiments employ multiple QRAM cell sizes (8, 16, 32, 64, 128) and perform ten trials per size. According to the performance, accuracy values in the Iris dataset range from 89.3 ± 5.78% to 94.0 ± 1.56%. The MNIST dataset’s mean binary accuracy values range from 79.45 ± 18.84% to 94.00 ± 2.11% for classes 0 and 1. Additionally, a comparison of the results of this proposed approach with different state-of-the-art versions of QK-NN and the classical K-NN using Scikit-learn. This method achieves a 96.4 ± 2.22% accuracy in the Iris dataset. Finally, this proposal contributes an experimental result to the state of the art for the MNIST dataset, achieving an accuracy of 96.55 ± 2.00%. This work presents a new implementation proposal for QK-NN and conducts multiple experiments that yield more robust results than previous implementations. Although our average performance approaches still need to surpass the classic results, an experimental increase in the size of QRAM or the amount of data to encode is not achieved due to limitations. However, our results show promising improvement when considering working with more feature numbers and accommodating more data in the QRAM.

Capturing the Diversity of Mesoscale Trade Wind Cumuli Using Complementary Approaches From Self‐Supervised Deep Learning

AbstractAt mesoscale, trade wind clouds organize with various spatial arrangements, shaping their effect on Earth's energy budget. Representing their fine‐scale dynamics even at 1 km scale climate simulations remains challenging. However, geostationary satellites (GS) offer high‐resolution cloud observation for gaining insights into trade wind cumuli from long‐term records. To capture the observed organizational variability, this work proposes an integrated framework using a continuous followed by discrete self‐supervised deep learning approach, which exploits cloud optical depth from GS measurements. We aim to simplify the entire mesoscale cloud spectrum by reducing the image complexity in the feature space and meaningfully partitioning it into seven classes whose connection to environmental conditions is illustrated with reanalysis data. Our framework facilitates comparing human‐labeled mesoscale classes with machine‐identified ones, addressing uncertainties in both methods. It advances previous methods by exploring transitions between regimes, a challenge for physical simulations, and illustrates a case study of sugar‐to‐flower transitions.

An Improved Unbounded-DP Algorithm for the Unbounded Knapsack Problem with Bounded Coefficients

Benchmark instances for the unbounded knapsack problem are typically generated according to specific criteria within a given constant range R, and these instances can be referred to as the unbounded knapsack problem with bounded coefficients (UKPB). In order to increase the difficulty of solving these instances, the knapsack capacity C is usually set to a very large value. While current efficient algorithms primarily center on the Fast Fourier Transform (FFT) and (min,+)-convolution method, there is a simpler method worth considering. In this paper, based on the basic Unbounded-DP algorithm, we utilize a recent branch and bound (B&B) result and basic theory of linear Diophantine equation, and propose an improved Unbounded-DP algorithm with time complexity of O(R4) and space complexity of O(R3). Additionally, the algorithm can also solve the All-capacities unbounded knapsack problem within the complexity O(R4+C). In particular, the proof techniques required by the algorithm are primarily covered in the first-year mathematics curriculum, which is convenient for subsequent researchers to grasp.

Using Constraint Propagation to Bound Linear Programs

We present an approach to compute bounds on the optimal value of linear programs based on constraint propagation. Given a feasible dual solution, we apply constraint propagation to the complementary slackness conditions and, if propagation succeeds to prove these conditions infeasible, the infeasibility certificate (in the sense of Farkas’ lemma) is reconstructed from the propagation history. This certificate is a dual-improving direction, which allows us to improve the bound. As constraint propagation need not always detect infeasibility of a linear inequality system, the method is not guaranteed to converge to a global solution of the linear program but only to an upper bound, whose tightness depends on the structure of the program and the used propagation method. The approach is suited for large sparse linear programs (such as LP relaxations of combinatorial optimization problems), for which the classical LP algorithms may be infeasible, if only for their super-linear space complexity. The approach can be seen as a generalization of the Virtual Arc Consistency (VAC) algorithm to bound the LP relaxation of the Weighted CSP (WCSP). We newly apply it to the LP relaxation of the Weighted Max-SAT problem, experimentally showing that the obtained bounds are often not far from optima of the relaxation and proving that they are exact for known tractable subclasses of Weighted Max-SAT.

An exploration of the self-similarity of traditional settlements: the case of Xiaoliangjiang Village in Jingxing, Hebei, China

In order to retain the characteristics and style of traditional settlements and respect their layout and structure, it is necessary to carry out original planning and expansion of traditional settlements. This model of planning and expansion aims to protect the unique character of the settlement, maintain its original historical and cultural value, and integrate with the surrounding environment. Early research on the space complexity of settlements was dominated by qualitative analysis, and the depth of quantitative research on the spatial form of traditional settlements was insufficient. This article takes Xiaoliangjiang Village in Jingxing County, Shijiazhuang City, Hebei Province, which entered the fifth batch of the list of Chinese traditional villages list, as the research object. The spatial relationship of the settlement was obtained through field surveys and drone oblique photography, and the spatial morphological elements of Xiaoliangjiang Village were analyzed and extracted. Based on three quantitative theories of spatial form, namely topology theory, fractal theory, and space syntax, the self-similarity of settlements is analyzed from the perspectives of buildings, streets, and spaces. The research uses Matlab and DepthMap software to quantitatively analyze the spatial form of Xiaoliangjiang Village and obtains data. Through the analysis of data, it was found that Xiaoliangjiang Village has self-similarity at three levels: buildings, roads and settlement spaces. The buildings iteratively generate various forms of architectural courtyards through the basic “L”-shaped pattern. The spatial structures at all levels of roads and settlement space in Xiaoliangjiang Village are relatively similar, in line with the bottom-up traditional settlement evolutionary law. By studying settlement self-similarity, people can better understand the formation mechanism of traditional settlement space structure and its evolution law. At the same time, it enriches the research perspective of traditional settlements and provides technical support for analyzing the self-similarity of traditional settlements and settlement protection planning.

Recurrent quantum embedding neural network and its application in vulnerability detection

In recent years, deep learning has been widely used in vulnerability detection with remarkable results. These studies often apply natural language processing (NLP) technologies due to the natural similarity between code and language. Since NLP usually consumes a lot of computing resources, its combination with quantum computing is becoming a valuable research direction. In this paper, we present a Recurrent Quantum Embedding Neural Network (RQENN) for vulnerability detection. It aims to reduce the memory consumption of classical models for vulnerability detection tasks and improve the performance of quantum natural language processing (QNLP) methods. We show that the performance of RQENN achieves the above goals. Compared with the classic model, the space complexity of each stage of its execution is exponentially reduced, and the number of parameters used and the number of bits consumed are significantly reduced. Compared with other QNLP methods, RQENN uses fewer qubit resources and achieves a 15.7% higher accuracy in vulnerability detection.

Intelligent design exploration method for complex engineered system architecture generation

ABSTRACT Owing to the discontinuous specificity and complexity of architecture design space, the issue of selecting and combining components comprising the engineered system, numerous constraints and associations need to be accounted for, adding up to a complex and substantial cognitive load on the system architects, which makes it challenging to tackle the current demand of adaptive improvements or innovative upgrading of the existing mature architectural solutions. To this end, this paper proposes an intelligent design exploration method for complex system architecture generation with reinforcement learning. The architectural design space (ADS) is identified by defining the dimensions of ADS, including model, quantity, and design chain, as well as the mathematical boundaries and representation to facilitate computable intelligent design exploration. On this basis, by adopting AI techniques primarily based on reinforcement learning, a massive and reliable architectural scheme is rapidly generated, and a more satisfying and robust architectural solution is selected by accessing the fuzzy Pareto frontier. Validation of the method is demonstrated through a case study of a launch vehicle's first and second-stage separation system. This research contributes valuable insights to overcoming the limitations of traditional techniques and enhancing the efficiency of the generative design and decision-making for complex engineered system architecture.

Evaluation of GlassNet for physics‐informed machine learning of glass stability and glass‐forming ability

AbstractGlassy materials form the basis of many modern applications, including nuclear waste immobilization, touch‐screen displays, and optical fibers, and also hold great potential for future medical and environmental applications. However, their structural complexity and large composition space make design and optimization challenging for certain applications. Of particular importance for glass processing and design is an estimate of a given composition's glass‐forming ability (GFA). However, there remain many open questions regarding the underlying physical mechanisms of glass formation, especially in oxide glasses. It is apparent that a proxy for GFA would be highly useful in glass processing and design, but identifying such a surrogate property has proven itself to be difficult. While glass stability (GS) parameters have historically been used as a GFA surrogate, recent research has demonstrated that most of these parameters are not accurate predictors of the GFA of oxide glasses. Here, we explore the application of an open‐source pre‐trained neural network model, GlassNet, that can predict the characteristic temperatures necessary to compute GS with reasonable performance and assess the feasibility of using these physics‐informed machine learning (PIML)‐predicted GS parameters to estimate GFA. In doing so, we track the uncertainties at each step of the computation—from the original ML prediction errors to the compounding of errors during GS estimation, and finally to the final estimation of GFA. While GlassNet exhibits reasonable accuracy on all individual properties, we observe a large compounding of error in the combination of these individual predictions for the PIML prediction of GS, finding that random forest models offer similar accuracy to GlassNet. We also break down the performance of GlassNet on different glass families and find that the error in GS prediction is correlated with the error in crystallization peak temperature prediction. Lastly, we utilize this finding to assess the relationship between top‐performing GS parameters and GFA for two ternary glass systems: sodium borosilicate and sodium iron phosphate glasses. We conclude that to obtain true ML predictive capability of GFA, significantly more data needs to be collected.

Accelerate rotation invariant sliced Gromov-Wasserstein distance by an alternative optimization method

The traditional Wasserstein distance is inadequate for comparing two distributions in different metric spaces. The Gromov-Wasserstein distance (GWD), which evolves from the Gromov-Hausdorff distance, constructs intraspace pairs to ensure comparability. However, solving the GWD requires tackling a complex nonconvex quadratic problem, a process that typically demands significant time and space complexity. The sliced Gromov-Wasserstein distance (SGW) addresses the efficiency issues of GWD by employing a projection-slice method. Unfortunately, slicing destroys the crucial rotation invariance property of GWD. The rotation invariant sliced Gromov-Wasserstein distance (RISGW) restores it by enumerating the alignments of the distributions. Inspired by our observations, we introduce BRISGW, a novel batch rotation invariant sliced Gromov-Wasserstein distance that alternately iterates and approximates the underlying best alignment both effectively and efficiently. We theoretically prove the feasibility the proposed our approach. Moreover, significant experimental results show that the proposed method outperforms the state-of-the-art methods.

Consistency approximation: Incremental feature selection based on fuzzy rough set theory

Fuzzy Rough Set Theory (FRST)-based feature selection has been widely used as a preprocessing step to handle dynamic and large datasets. However, large-scale or high-dimensional datasets remain intractable for FRST-based feature selection approaches due to high space complexity and unsatisfactory classification performance. To overcome these challenges, we propose a Consistency Approximation (CA)-based framework for incremental feature selection. By exploring CA, we introduce a novel significance measure and a tri-accelerator. The CA-based significance measure provides a mechanism for each sample in the universe to keep members with different class labels within its fuzzy neighbourhood as far as possible, while keeping members with the same label as close as possible. Furthermore, our tri-accelerator reduces the search space and decreases the computational space with a theoretical lower bound. The experimental results demonstrate the superiority of our proposed algorithm compared to state-of-the-art methods on efficiency and classification accuracy, especially for large-scale and high-dimensional datasets.