Combinatorial Explosion Research Articles

Efficient Search Algorithms for Identifying Synergistic Associations in High-Dimensional Datasets

In recent years, there has been a notably increased interest in the study of multivariate interactions and emergent higher-order dependencies. This is particularly evident in the context of identifying synergistic sets, which are defined as combinations of elements whose joint interactions result in the emergence of information that is not present in any individual subset of those elements. The scalability of frameworks such as partial information decomposition (PID) and those based on multivariate extensions of mutual information, such as O-information, is limited by combinational explosion in the number of sets that must be assessed. In order to address these challenges, we propose a novel approach that utilises stochastic search strategies in order to identify synergistic triplets within datasets. Furthermore, the methodology is extensible to larger sets and various synergy measures. By employing stochastic search, our approach circumvents the constraints of exhaustive enumeration, offering a scalable and efficient means to uncover intricate dependencies. The flexibility of our method is illustrated through its application to two epidemiological datasets: The Young Finns Study and the UK Biobank Nuclear Magnetic Resonance (NMR) data. Additionally, we present a heuristic for reducing the number of synergistic sets to analyse in large datasets by excluding sets with overlapping information. We also illustrate the risks of performing a feature selection before assessing synergistic information in the system.

Research on combined damage characteristics of underwater armor-piercing and explosion based on supercavitating projectile

Recent studies of supercavitating projectiles primarily focus on the formation and evolution of the cavity, as well as its underwater ballistic characteristics, while neglecting the terminal damage effects. Little attention has been given to exploring the combined damage effects of armor-piercing-explosion supercavitating projectiles (APESP). Therefore, this study comparatively analyzes the response processes and failure modes of an underwater aluminum alloy cylindrical shell target under the action of three different types of loads: armor piercing, explosion, and combined armor-piercing and explosion. This study investigates the underwater combined damage mechanisms of the APESP, clarifies each damage phase under the combined effect, discusses the advantages of damage resulting from the combined armor-piercing and explosion effect based on the target responses and damage modes, and explores the reasons for dissipation of explosion energy. The results show that: the APESP combines localized point damage characteristics of armor piercing with overall surface damage features of underwater explosion. Depending on load stages and target responses, the target response process under the action of the APESP can be divided into the hydrodynamic ram phase, penetration phase, shock wave phase, stable vibration phase, and bubble pulsation phase. The entire physical system can be abstracted as a low-frequency series spring system (equivalent to bubble pulsation frequency) with high-frequency external energy input, based on the energy relationship of the medium and the structure. The concept of the 'blower effect' is proposed based on target behavior during the stable vibration phase. Following the application of different loads, the plastic deformation of the target in a stable state is ranked as: underwater explosion > combined armor-piercing and explosion > underwater armor piercing. Supercavity, shell casing and penetration hole will cause the dissipation of explosion energy.

Belief-Rule-Based System with Self-organizing and Multi-temporal Modeling for Sensor-based Human Activity Recognition.

Smart environment is an efficient and cost- effective way to afford intelligent supports for the elderly people. Human activity recognition (HAR) is a crucial aspect of the research field of smart environments, and it has attracted widespread attention lately. The goal of this study is to develop an effective sensor-based HAR model based on the belief-rule-based system (BRBS), which is one of representative rule-based expert systems. Specially, a new belief rule base (BRB) modeling approach is proposed by taking into account the self- organizing rule generation method and the multi-temporal rule representation scheme, in order to address the problem of combination explosion that existed in the traditional BRB modelling procedure and the time correlation found in continuous sensor data in chronological order. The new BRB modeling approach is so called self-organizing and multi-temporal BRB (SOMT-BRB) modeling procedure. A case study is further deducted to validate the effectiveness of the SOMT-BRB modeling procedure. By comparing with some conventional BRBSs and classical activity recognition models, the results show a significant improvement of the BRBS in terms of the number of belief rules, modelling efficiency, and activity recognition accuracy.

MEDOC: A fast, scalable and mathematically exact algorithm for the site-specific prediction of the protonation degree in large disordered proteins.

Intrinsically disordered regions are found in most eukaryotic proteins and are enriched in positively and negatively charged residues. While it is often convenient to assume these residues follow their model-compound pK a values, recent work has shown that local charge effects (charge regulation) can upshift or downshift sidechain pK a values with major consequences for molecular function. Despite this, charge regulation is rarely considered when investigating disordered regions. The number of potential charge microstates that can be populated through acid/base regulation of a given number of ionizable residues in a sequence, N , scales as ∼2 N . This exponential scaling makes the assessment of the full charge landscape of most proteins computationally intractable. To address this problem, we developed MEDOC (Multisite Extent of Deprotonation Originating from Context) to determine the degree of protonation of a protein based on the local sequence context of each ionizable residue. We show that we can drastically reduce the number of parameters necessary to determine the full, analytic, Boltzmann partition function of the charge landscape at both global and site-specific levels. Our algorithm applies the structure of the q -canonical ensemble, combined with novel strategies to rapidly obtain the minimal set of parameters, thereby circumventing the combinatorial explosion of the number of charge microstates even for proteins containing a large number of ionizable amino acids. We apply MEDOC to several sequences, including a global analysis of the distribution of pK a values across the entire DisProt database. Our results show differences in the distribution of predicted pK a values for different amino acids, in agreement with NMR-measured distributions in proteins.

CHA: Conditional Hyper-Adapter method for detecting human–object interaction

Human–object interactions (HOI) detection aims at capturing human–object pairs in images and predicting their actions. It is an essential step for many visual reasoning tasks, such as VQA, image retrieval and surveillance event detection. The challenge of this task is to tackle the compositional learning problem, especially in a few-shot setting. A straightforward approach is designing a group of dedicated models for each specific pair. However, the maintenance of these independent models is unrealistic due to combinatorial explosion. To address the above problems, we propose a new Conditional Hyper-Adapter (CHA) method based on meta-learning. Different from previous works, our approach regards each <verb, object> as an independent sub-task. Meanwhile, we design two kinds of Hyper-Adapter structures to guide the model to learn “how to address the HOI detection”. By combining the different conditions and hypernetwork, the CHA can adaptively generate partial parameters and improve the representation and generalization ability of the model. Finally, our proposed method can be viewed as a plug-and-play module to boost existing HOI detection models on the widely used HOI benchmarks.

Quantum Probabilistic Model Checking for Time-Bounded Properties

Probabilistic model checking (PMC) is a verification technique for analyzing the properties of probabilistic systems. However, existing techniques face challenges in verifying large systems with high accuracy. PMC struggles with state explosion, where the number of states grows exponentially with the size of the system, making large system verification infeasible. While statistical model checking (SMC) avoids PMC’s state explosion problem by using a simulation approach, it suffers from runtime explosion, requiring numerous samples for high accuracy. To address these limitations in verifying large systems with high accuracy, we present quantum probabilistic model checking (QPMC), the first method leveraging quantum computing for PMC with respect to time-bounded properties. QPMC addresses state explosion by encoding PMC problems into quantum circuits that superpose states within qubits. Additionally, QPMC resolves runtime explosion through Quantum Amplitude Estimation, efficiently estimating the probabilities of specified properties. We prove that QPMC correctly solves PMC problems and achieves a quadratic speedup in time complexity compared to SMC.

Optimal Location for Tower Crane and Dynamic Trailer Parking in High-Rise Modular Building Construction Project

Optimization of tower crane positioning is essential in precast building construction to ensure that a crane is in the right position to offer the best value for placing precast elements. The first goal is the optimization of transportation distances made by tower cranes, which will address the issues of efficiency and cost. This is done in a way that provides for minimization of the distances that lie between the trailer parking where elements are parked, the tower crane, and the construction installation point. However, current research fails to address the dynamic movement efficiency of trailers, especially when handling multiple trailers and several models of tower cranes, making this scenario an optimization problem that is classified as NP-hard due to the likelihood of causing a combinatorial explosion. This work endeavors to present a new mathematical model that has been applied to the Genetic Algorithm (GA). The ideal demand-generated model is designed to solve the optimal model and position of tower cranes and the prospective positioning of trailers for parking. The feasibility and applicability of the method exploited in the study are also established through a project case study. When adopting the proposed planning model compared to the earlier planning scale, comparisons highlight a small yet significant saving of 6% in time and cost when lifting elements instead of providing them from the trailers by setting up a new on-site stockyard. In addition, a great deal of enhancement is also observed in the final solution aspects, where the developed GA has even reduced the operational time and cost by half a percent each. The results of this research offer best-practice approaches to the position analysis of tower cranes in precast building construction to bring scalability and cost optimization to bear on the construction business.

Interpretable large-scale belief rule base for complex industrial systems modeling with expert knowledge and limited data

Complex system modeling technology is a hot topic. Nowadays, many complex industrial systems present three characteristics: multiple input indicators, limited data and interpretability requirements. With good interpretability, belief rule base (BRB) serves as an efficient tool for modeling complex systems. However, as the number of input indicators of industrial systems increases, BRB suffers from the combinatorial explosion problem, which makes it hard to generate large-scale BRB and optimize it while maintaining its interpretability. For this purpose, an interpretable large-scale BRB is proposed for complex systems with limited data, where expert knowledge can be utilized effectively. First, a framework for generating an initial large-scale BRB using expert knowledge and limited data is developed, including the determination of attribute weight, basic belief degree and rule weight. Afterwards, a new parameter optimization model is designed to reduce the burden of parameter optimization and maintain the interpretability of BRB, where the Adaptive Moment Estimation (Adam) algorithm is adopted to further improve the efficiency of large-scale parameter optimization. Finally, a health assessment case of an inertial navigation system (INS) verifies the proposed method.

An algorithm for multi-target tracking in low-signal-to-clutter-ratio underwater acoustic scenes

To simplify the computational complexity of the Joint Probabilistic Data Association (JPDA) algorithm for multi-target tracking in low-signal-to-clutter-ratio underwater acoustic scenes, and to solve the problem of unstable tracking caused by poor measurement accuracy of active sonar, a trajectory information-based JPDA optimization algorithm (TJPDA) is designed to meet the real-time and stability requirements of practical engineering. The false alarm rate is reduced by accumulating correlated target trajectories in multiple frames, and the influence factor is introduced to modify the correlation probability and simplify the confirmation matrix splitting process. This effectively solves the problem of information combination explosion and trajectory divergence caused by adjacent target interference in low signal-to-clutter-ratio underwater acoustic scenes. The simulation results show that compared with the JPDA algorithm, the TJPDA algorithm not only improves target-tracking accuracy but also reduces computation time, making it more suitable for practical engineering applications.

A hierarchy of metabolite exchanges in metabolic models of microbial species and communities.

The metabolic network of an organism can be analyzed as a constraint-based model. This analysis can be biased, optimizing an objective such as growth rate, or unbiased, aiming to describe the full feasible space of metabolic fluxes through pathway analysis or random flux sampling. In particular, pathway analysis can decompose the flux space into fundamental and formally defined metabolic pathways. Unbiased methods scale poorly with network size due to combinatorial explosion, but a promising approach to improve scalability is to focus on metabolic subnetworks, e.g., cells' metabolite exchanges with each other and the environment, rather than the full metabolic networks. Here, we applied pathway enumeration and flux sampling to metabolite exchanges in microbial species and a microbial community, using models ranging from central carbon metabolism to genome-scale and focusing on pathway definitions that allow direct targeting of subnetworks such as metabolite exchanges (elementary conversion modes, elementary flux patterns, and minimal pathways). Enumerating growth-supporting metabolite exchanges, we found that metabolite exchanges from different pathway definitions were related through a hierarchy, and we show that this hierarchical relationship between pathways holds for metabolic networks and subnetworks more generally. Metabolite exchange frequencies, defined as the fraction of pathways in which each metabolite was exchanged, were similar across pathway definitions, with a few specific exchanges explaining large differences in pathway counts. This indicates that biological interpretation of predicted metabolite exchanges is robust to the choice of pathway definition, and it suggests strategies for more scalable pathway analysis. Our results also signal wider biological implications, facilitating detailed and interpretable analysis of metabolite exchanges and other subnetworks in fields such as metabolic engineering and synthetic biology.

Program Dependence Net and on-demand slicing for property verification of concurrent system and software

When checking concurrent software using a finite-state model, we face a formidable state explosion problem. One solution to this problem is dependence-based program slicing, whose use can effectively reduce verification time. It is orthogonal to other model-checking reduction techniques. However, when slicing concurrent programs for model checking, there are conversions between multiple irreplaceable models, and dependencies need to be found for variables irrelevant to the verified property, which results in redundant computation. To resolve this issue, we propose a Program Dependence Net (PDNet) based on Petri net theory. It is a unified model that combines a control-flow structure with dependencies to avoid conversions. For reduction, we present a PDNet slicing method to capture the relevant variables’ dependencies when needed. PDNet and its on-demand slicing in verifying linear temporal logic are used to significantly reduce computation cost. We implement a model-checking tool based on PDNet and its on-demand slicing and validate the advantages of our proposed methods.

Semantic-Aware Dynamic Generation Networks for Few-Shot Human-Object Interaction Recognition.

Recognizing human-object interaction (HOI) aims at inferring various relationships between actions and objects. Although great progress in HOI has been made, the long-tail problem and combinatorial explosion problem are still practical challenges. To this end, we formulate HOI as a few-shot task to tackle both challenges and design a novel dynamic generation method to address this task. The proposed approach is called semantic-aware dynamic generation networks (SADG-Nets). Specifically, SADG-Net first assigns semantic-aware task representations for different batches of data, which further generates dynamic parameters. It obtains the features that highlight intercategory discriminability and intracategory commonality adaptively. In addition, we also design a dual semantic-aware encoder module (DSAE-Module), that is, verb-aware and noun-aware branches, to yield both action and object prototypes of HOI for each task space, which generalizes to novel combinations by transferring similarities among interactions. Extensive experimental results on two benchmark datasets, that is, humans interacting with common objects (HICO)-FS and trento universal HOI (TUHOI)-FS, illustrate that our SADG-Net achieves superior performance over state-of-the-art approaches, which proves its impressive effectiveness on few-shot HOI recognition.

Mitigating adversarial cascades in large graph environments

A significant amount of society’s infrastructure can be modeled using graph structures, from electric and communication grids, to traffic networks, to social networks. Each of these domains are also susceptible to unwanted cascades, whether this be overloaded devices in the power grid or the reach of a social media post containing misinformation. The potential harm of a cascade is compounded when considering a malicious attack by an adversary that is intended to maximize the cascade impact. However, by exploiting knowledge of the cascading dynamics, targets with the largest cascading impact can be preemptively prioritized for defense, and the damage an adversary can inflict can be mitigated. While game theory provides tools for finding an optimal preemptive defense strategy, existing methods struggle to scale to the context of large graph environments because of the combinatorial explosion of possible actions with the size of the graph. Data-driven deep learning approaches can fill this gap, but they demand a large amount of data that is often costly to obtain. We propose a novel data generation approach for the cascading failure security problem that uses counterfactual data augmentation and a sub-game data querying strategy to generate both high quality and a high quantity of training data. We demonstrate that our data generation approach creates up to an order of magnitude more data than naïve querying with double the efficiency. We also introduce a deep learning model based embedding node pairs, and train it on our generated data, showing that it effectively defends from cascades on graphs as large as 1000 nodes. Our deep learning approach achieves a closer approximation to the Nash Equilibrium than existing heuristic methods, for graphs where the ground-truth equilibrium can be calculated.

Detection of Cyber-Attacks in a Discrete Event System Based on Deep Learning

This paper addresses the problem of cyber-attack detection in a discrete event system by proposing a novel model. The model utilizes graph convolutional networks to extract spatial features from event sequences. Subsequently, it employs gated recurrent units to re-extract spatio-temporal features from these spatial features. The obtained spatio-temporal features are then fed into an attention model. This approach enables the model to learn the importance of different event sequences, ensuring that it is sufficiently general for identifying cyber-attacks, obviating the need to specify attack types. Compared with traditional methods that rely on synchronous product computations to synthesize diagnosers, our deep learning-based model circumvents state explosion problems. Our method facilitates real-time and efficient cyber-attack detection, eliminating the necessity to specifically identify system states or distinguish attack types, thereby significantly simplifying the diagnostic process. Additionally, we set an adjustable probability threshold to determine whether an event sequence has been compromised, allowing for customization to meet diverse requirements. Experimental results demonstrate that the proposed method performs well in cyber-attack detection, achieving over 99.9% accuracy at a 1% threshold and a weighted F1-score of 0.8126, validating its superior performance.

Network medicine-based epistasis detection in complex diseases: ready for quantum computing.

Most heritable diseases are polygenic. To comprehend the underlying genetic architecture, it is crucial to discover the clinically relevant epistatic interactions (EIs) between genomic single nucleotide polymorphisms (SNPs)(1-3). Existing statistical computational methods for EI detection are mostly limited to pairs of SNPs due to the combinatorial explosion of higher-order EIs. With NeEDL (network-based epistasis detection via local search), we leverage network medicine to inform the selection of EIs that are an order of magnitude more statistically significant compared to existing tools and consist, on average, of five SNPs. We further show that this computationally demanding task can be substantially accelerated once quantum computing hardware becomes available. We apply NeEDL to eight different diseases and discover genes (affected by EIs of SNPs) that are partly known to affect the disease, additionally, these results are reproducible across independent cohorts. EIs for these eight diseases can be interactively explored in the Epistasis Disease Atlas (https://epistasis-disease-atlas.com). In summary, NeEDL demonstrates the potential of seamlessly integrated quantum computing techniques to accelerate biomedical research. Our network medicine approach detects higher-order EIs with unprecedented statistical and biological evidence, yielding unique insights into polygenic diseases and providing a basis for the development of improved risk scores and combination therapies.

Adaptive random-grid and progressive color secret sharing with CNN super-resolution on a many-core system

This study introduces an innovative method combining Convolutional Neural Networks (CNN) with random grid generation for enhanced visual secret sharing. Our approach supports color images, reduces processing time, and offers non-pixel expansion and flexible share combinations. Utilizing GPU computation, it significantly improves practicality and efficiency by operating in a feed-forward manner, avoiding complex optimization. Experimental results demonstrate superior metrics: maximum PSNR of 32 dB, 99% NCC correlation with benchmarks, 2.9% NAE, and SSIM of 98%. We achieve substantial speedups– 493 × for 256 × 256 and 3145 × for 1024 × 1024 images–compared to sequential models. The scheme exhibits robustness against attacks, evidenced by CMY component and share histogram similarities, and scalability shown in combinatorial explosion visualization. These findings underscore the efficacy and efficiency of our approach, advancing secure image sharing applications significantly.

A data-driven approach for volume feature recognition based on cell graph

ABSTRACT Machining feature recognition is one of the key technologies for realizing automated process planning. The machining feature represented by volume contains more complete information due to its property of forming a closed region which facilitates subsequent process planning. The existing volume feature recognition approaches mainly rely on expert-defined rules to combine volumes into the desired feature. When dealing with some complex parts, volume feature recognition faces combinatorial explosion, and it is difficult to formulate complete combination rules manually. This research proposes a novel data-driven approach for volume machining feature recognition. The proposed approach does not require manually defined rules and can learn various complex volume combination rules from the data, which can be implicitly represented by the structure and parameters of the data-driven model. The volume machining feature recognition is first converted to machining feature subgraph (MFS) detection by creating the zone graph. MFS detection can then be achieved by graph edge cut. Finally, the edge cut is modeled as a binary classification deep learning problem, which is solved by graph neural network. Two datasets are created, and case studies are carried out on them. The results show that the proposed approach is effective for volume machining feature recognition.

SPIN-Based Linear Temporal Logic Path Planning for Ground Vehicle Missions with Motion Constraints on Digital Elevation Models.

Linear temporal logic (LTL) formalism can ensure the correctness of mobile robot planning through concise, readable, and verifiable mission specifications. For uneven terrain, planning must consider motion constraints related to asymmetric slope traversability and maneuverability. However, even though model checker tools like the open-source Simple Promela Interpreter (SPIN) include search optimization techniques to address the state explosion problem, defining a global LTL property that encompasses both mission specifications and motion constraints on digital elevation models (DEMs) can lead to complex models and high computation times. In this article, we propose a system model that incorporates a set of uncrewed ground vehicle (UGV) motion constraints, allowing these constraints to be omitted from LTL model checking. This model is used in the LTL synthesizer for path planning, where an LTL property describes only the mission specification. Furthermore, we present a specific parameterization for path planning synthesis using a SPIN. We also offer two SPIN-efficient general LTL formulas for representative UGV missions to reach a DEM partition set, with a specified or unspecified order, respectively. Validation experiments performed on synthetic and real-world DEMs demonstrate the feasibility of the framework for complex mission specifications on DEMs, achieving a significant reduction in computation cost compared to a baseline approach that includes a global LTL property, even when applying appropriate search optimization techniques on both path planners.

Machine learning-guided multi-site combinatorial mutagenesis enhances the thermostability of pectin lyase

Enhancing the thermostability of enzymes is crucial for industrial applications. Methods such as directed evolution are often limited by the huge sequence space and combinatorial explosion, making it difficult to obtain optimal mutants. In recent years, machine learning (ML)-guided protein engineering has become an attractive tool because of its ability to comprehensively explore the sequence space of enzymes and discover superior mutants. This study employed ML to perform combinatorial mutation design on the pectin lyase PMGL-Ba from Bacillus licheniformis, aiming to improve its thermostability. First, 18 single-point mutants with enhanced thermostability were identified through semi-rational design. Subsequently, the initial library containing a small number of low-order mutants was utilized to construct an ML model to explore the combinatorial sequence space (theoretically 196,608 mutants) of single-point mutants. The results showed that the ML-predicted second library was successfully enriched with highly thermostable combinatorial mutants. After one iteration of learning, the best-performing combinatorial mutant in the third library, P36, showed a 67-fold and 39-fold increase in half-life at 75 °C and 80 °C, respectively, as well as a 2.1-fold increase in activity. Structural analysis and molecular dynamics simulations provided insights into the improved performance of the engineered enzyme.

DNA sequences alignment method using sparse index on pan-genome graph.

The graph of sequences represents the genetic variations of pan-genome concisely and space-efficiently than multiple linear reference genome. In order to accelerate aligning reads to the graph, an index of graph-based reference genomes is used to obtain candidate locations. However, the potential combinatorial explosion of nodes on the sequence graph leads to increasing the index space and maximum memory usage of alignment process considerably, especially for large-scale datasets. For this, existing methods typically attempt to prune complex regions, or extend the length of seeds, which sacrifices the recall of alignment algorithm despite reducing space usage slightly. We present the Sparse-index of Graph (SIG) and alignment algorithm SIG-Aligner, capable of indexing and aligning at the lower memory cost. SIG builds the non-overlapping minimizers index inside nodes of sequence graph and SIG-Aligner filters out most of the false positive matches by the method based on the pigeonhole principle. Compared to Giraffe, the results of computational experiments show that SIG achieves a significant reduction in index memory space ranging from 50% to 75% for the human pan-genome graphs, while still preserving superior or comparable accuracy of alignment and the faster alignment time.