Combinatorial Explosion Research Articles

Discovery of complex oxides via automated experiments and data science

The quest to identify materials with tailored properties is increasingly expanding into high-order composition spaces, with a corresponding combinatorial explosion in the number of candidate materials. A key challenge is to discover regions in composition space where materials have novel properties. Traditional predictive models for material properties are not accurate enough to guide the search. Herein, we use high-throughput measurements of optical properties to identify novel regions in three-cation metal oxide composition spaces by identifying compositions whose optical trends cannot be explained by simple phase mixtures. We screen 376,752 distinct compositions from 108 three-cation oxide systems based on the cation elements Mg, Fe, Co, Ni, Cu, Y, In, Sn, Ce, and Ta. Data models for candidate phase diagrams and three-cation compositions with emergent optical properties guide the discovery of materials with complex phase-dependent properties, as demonstrated by the discovery of a Co-Ta-Sn substitutional alloy oxide with tunable transparency, catalytic activity, and stability in strong acid electrolytes. These results required close coupling of data validation to experiment design to generate a reliable end-to-end high-throughput workflow for accelerating scientific discovery.

Automated Transformation of PDDL Representations

This paper describes a system that automatically transforms a PDDL encoding, calls a planner to solve the transformed representation, and translates the solution back into the original representation. The approach involves counting objects that are indistinguishable, rather than treating them as individuals, which eliminates some unnecessary combinatorial explosion.

Learning software configuration spaces: A systematic literature review

Most modern software systems (operating systems like Linux or Android, Web browsers like Firefox or Chrome, video encoders like ffmpeg, x264 or VLC, mobile and cloud applications, etc.) are highly configurable. Hundreds of configuration options, features, or plugins can be combined, each potentially with distinct functionality and effects on execution time, security, energy consumption, etc. Due to the combinatorial explosion and the cost of executing software, it is quickly impossible to exhaustively explore the whole configuration space. Hence, numerous works have investigated the idea of learning it from a small sample of configurations’ measurements. The pattern “sampling, measuring, learning” has emerged in the literature, with several practical interests for both software developers and end-users of configurable systems. In this systematic literature review, we report on the different application objectives (e.g., performance prediction, configuration optimization, constraint mining), use-cases, targeted software systems, and application domains. We review the various strategies employed to gather a representative and cost-effective sample. We describe automated software techniques used to measure functional and non-functional properties of configurations. We classify machine learning algorithms and how they relate to the pursued application. Finally, we also describe how researchers evaluate the quality of the learning process. The findings from this systematic review show that the potential application objective is important; there are a vast number of case studies reported in the literature related to particular domains or software systems. Yet, the huge variant space of configurable systems is still challenging and calls to further investigate the synergies between artificial intelligence and software engineering.

Bypassing combinatorial explosions in equivalence structure extraction

Bypassing combinatorial explosions in equivalence structure extraction

Independent Markov decomposition: Toward modeling kinetics of biomolecular complexes

To advance the mission of in silico cell biology, modeling the interactions of large and complex biological systems becomes increasingly relevant. The combination of molecular dynamics (MD) simulations and Markov state models (MSMs) has enabled the construction of simplified models of molecular kinetics on long timescales. Despite its success, this approach is inherently limited by the size of the molecular system. With increasing size of macromolecular complexes, the number of independent or weakly coupled subsystems increases, and the number of global system states increases exponentially, making the sampling of all distinct global states unfeasible. In this work, we present a technique called independent Markov decomposition (IMD) that leverages weak coupling between subsystems to compute a global kinetic model without requiring the sampling of all combinatorial states of subsystems. We give a theoretical basis for IMD and propose an approach for finding and validating such a decomposition. Using empirical few-state MSMs of ion channel models that are well established in electrophysiology, we demonstrate that IMD models can reproduce experimental conductance measurements with a major reduction in sampling compared with a standard MSM approach. We further show how to find the optimal partition of all-atom protein simulations into weakly coupled subunits.

Eagle

Object sensitivity is widely used as a context abstraction for computing the points-to information context-sensitively for object-oriented programming languages such as Java. Due to the combinatorial explosion of contexts in large object-oriented programs, k -object-sensitive pointer analysis (under k -limiting), denoted k -obj , is often inefficient even when it is scalable for small values of k , where k ⩽ 2 holds typically. A recent popular approach for accelerating k -obj trades precision for efficiency by instructing k -obj to analyze only some methods in a program context-sensitively, determined heuristically by a pre-analysis. In this article, we investigate how to develop a fundamentally different approach, Eagle , for designing a pre-analysis that can make k -obj run significantly faster while maintaining its precision. The novelty of Eagle is to enable k -obj to analyze a method with partial context sensitivity (i.e., context-sensitively for only some of its selected variables/allocation sites) by solving a context-free-language (CFL) reachability problem based on a new CFL-reachability formulation of k -obj . By regularizing one CFL for specifying field accesses and using another CFL for specifying method calls, we have formulated Eagle as a fully context-sensitive taint analysis (without k -limiting) that is both effective (by selecting the variables/allocation sites to be analyzed by k -obj context-insensitively so as to reduce the number of context-sensitive facts inferred by k -obj in the program) and efficient (by running linearly in terms of the number of pointer assignment edges in the program). As Eagle represents the first precision-preserving pre-analysis, our evaluation focuses on demonstrating its significant performance benefits in accelerating k -obj for a set of popular Java benchmarks and applications, with call graph construction, may-fail-casting, and polymorphic call detection as three important client analyses.

Predicting plasmid persistence in microbial communities by coarse-grained modeling.

Plasmids are a major type of mobile genetic elements (MGEs) that mediate horizontal gene transfer. The stable maintenance of plasmids plays a critical role in the functions and survival for microbial populations. However, predicting and controlling plasmid persistence and abundance in complex microbial communities remain challenging. Computationally, this challenge arises from the combinatorial explosion associated with the conventional modeling framework. Recently, a plasmid-centric framework (PCF) has been developed to overcome this computational bottleneck. This framework enables the derivation of a simple metric, the persistence potential, to predict plasmid persistence and abundance. Here, we discuss how PCF can be extended to account for plasmid interactions. We also discuss how such model-guided predictions of plasmid fates can benefit from the development of new experimental tools and data-driven computational methods.

Visual analytics of set data for knowledge discovery and member selection support

Visual analytics (VA) is a visually assisted exploratory analysis approach in which knowledge discovery is executed interactively between the user and system in a human-centered manner. The purpose of this study is to develop a method for the VA of set data aimed at supporting knowledge discovery and member selection. A typical target application is a visual support system for team analysis and member selection, by which users can analyze past teams and examine candidate lineups for new teams. Because there are several difficulties, such as the combinatorial explosion problem, developing a VA system of set data is challenging. In this study, we first define the requirements that the target system should satisfy and clarify the accompanying challenges. Then we propose a method for the VA of set data, which satisfies the requirements. The key idea is to model the generation process of sets and their outputs using a manifold network model. The proposed method visualizes the relevant factors as a set of topographic maps on which various information is visualized. Furthermore, using the topographic maps as a bidirectional interface, users can indicate their targets of interest in the system on these maps. We demonstrate the proposed method by applying it to basketball teams, and compare with a benchmark system for outcome prediction and lineup reconstruction tasks. Because the method can be adapted to individual application cases by extending the network structure, it can be a general method by which practical systems can be built.

Extension of Fermat\u2019s last theorem in Minkowski natural spaces

Minkowski natural (N + 1)-dimensional spaces constitute the framework where the extension of Fermat’s last theorem is discussed. Based on empirical experience obtained via computational results, some hints about the extension of Fermat’s theorem from (2 + 1)-dimensional Minkowski spaces to (N + 1)-dimensional ones. Previous experience permits to conjecture that the theorem can be extended in (3 + 1) spaces, new results allow to do the same in (4 + 1) spaces, with an anomaly present here but difficult to find in higher dimensions. In (N + 1) dimensions with N > 4 there appears an increased difficulty to find Fermat vectors, there is discussed a possible source of such an obstacle, separately of the combinatorial explosion associated to the generation of natural vectors of high dimension.

Dynamic response of hull girder subjected to combined underwater explosion and wave induced load

Underwater explosion (UNDEX) is one of the major threats to the vitality and sustained combat ability of the warship in the marine military confrontation with both attack and defense. Although there have been plenty of researches focusing on the UNDEX load and its damage effect, the failure mechanism of the structure under the combined UNDEX and wave induced load, especially in extreme sea conditions, is still unrevealed. In this paper, a method for calculating the dynamic response of the hull girder subjected to the combined UNDEX and wave induced load is proposed, in which the acoustic–structure interaction method was employed for determining the UNDEX load, and the wave induced response of hull girder was derived by using hydrodynamic to structure (HTS) calculation procedure. The synergistic effect of the combination of different levels of wave induced load and the underwater explosion was analyzed. It is found that the hull girder is more dangerous under the combined UNDEX and wave induced load, especially in the severe wave level. The damage severity of the hull girder will be underestimated without considering the synergistic effect of the combined loads.

PATSQL

SQL is one of the most popular tools for data analysis, and it is now used by an increasing number of users without having expertise in databases. Several studies have proposed programming-by-example approaches to help such non-experts to write correct SQL queries. While existing methods support a variety of SQL features such as aggregation and nested query, they suffer a significant increase in computational cost as the scale of example tables increases. In this paper, we propose an efficient algorithm utilizing properties known in relational algebra to synthesize SQL queries from input and output tables. Our key insight is that a projection operator in a program sketch can be lifted above other operators by applying transformation rules in relational algebra, while preserving the semantics of the program. This enables a quick inference of appropriate columns in the projection operator, which is an essential component in synthesis but causes combinatorial explosions in prior work. We also introduce a novel form of constraints and its top-down propagation mechanism for efficient sketch completion. We implemented this algorithm in our tool PATSQL and evaluated it on 226 queries from prior benchmarks and Kaggle's tutorials. As a result, PATSQL solved 68% of the benchmarks and found 89% of the solutions within a second. Our tool is available at https://naist-se.github.io/patsql/.

Novel bionanocomposite of polycaprolactone reinforced with steam-exploded microfibrillated cellulose modified with ZnO

Polycaprolactone (PCL) bionanocomposites reinforced with microfibrillated cellulose (MFC), either plain or modified with 2 wt% of zinc oxide (ZnO) nanoparticles, were first time developed for possible application as multifunctional packing. The MFC was obtained by an alkali treatment, a steam explosion process, and ZnO modification applied to parchment (PAR), a husk waste from the coffee industry. X-ray diffraction (XDR), thermogravimetric analysis (TGA/DTG), differential scanning calorimetry (DSC), scanning electron microscopy (SEM), tensile tests, and CO2 permeability characterized the MFCs and the bionanocomposites. As for the MCFs, the crystallinity index of 50.6% measured by XRD for the plain PAR fiber increases with the combined alkaline treatment and steam explosion (CFA/EXP) to 68.2%, and further with ZnO modification (ZnO-CFA/EXP) to 80.1%. TGA/DTG displays a rising onset of thermal degradation from 214 to 306 °C, as well as maximum degradation rate from 330 to 350 °C, for PAR and ZnO-CFA/EXP, respectively. Regarding the nanocomposites, the addition of 3 wt% of alkali/steam explosion and ZnO-modified CFA/EXP contributes to enhancing thermal stability. Tensile tests disclosed improved mechanical properties of the novel nanocomposites as compared to the PCL matrix. In particular, Young's modulus rose from 88.5 to 169.5 MPa for the plain PCL and PCL reinforced with 3(ZnO-CFA/EXP), respectively. SEM images evidenced the participation of cellulose micro and nanofibrils in the PCL matrix. Approximately 20% reduction in the CO2 permeability coefficient of both PCL and its 3CFA/EXP nanocomposite compared with 3(ZnO-CFA/EXP) proved that the ZnO nanoparticles provide a gas barrier to the nanocomposite, a convenient property for food packing.

Generating Believable Stories in Large Domains

Planning-based techniques are a very powerful tool for automated story generation. However, as the number of possible actions increases, traditional planning techniques suffer from a combinatorial explosion due to large branching factors. In this work, we apply Monte Carlo Tree Search (MCTS) techniques to generate stories in domains with large numbers of possible actions (100+). Our approach employs a Bayesian story evaluation method to guide the planning towards believable stories that reach a user defined goal. We generate stories in a novel domain with different type of story goals. Our approach shows an order of magnitude improvement in performance over traditional search techniques.

Bio-Inspired Data Mining for Optimizing GPCR Function Identification

GPCR are the largest family of cell surface receptors; many of them still remain orphans. The GPCR functions prediction represents a very important bioinformatics task. It consists in assigning to the protein, the corresponding functional class. This classification step requires a good protein representation method and a robust classification algorithm. However the complexity of this task could be increased because of the great number of GPCRs features in most databases, which produce combinatorial explosion. In order to reduce complexity and optimize classification, the authors propose to use bio-inspired metaheuristics for both the feature selection and the choice of the best couple (feature extraction strategy (FES), data mining algorithm (DMA)). The authors propose also to use the BAT algorithm for extracting the pertinent features and the Genetic Algorithm to choose the best couple. They compared the results they we obtained with two existing algorithms. Experimental results indicate the efficiency of the proposed system.

A novel nonlinear causal inference approach using vector‐based belief rule base

When using the belief rule base (BRB) methodology to deal with the nonlinear causal inference problems, combinatorial explosion often occurs due to overnumbered antecedent attributes, resulting in poor performance. Therefore, this paper proposes a novel nonlinear causal inference approach based on vector-based BRB. In the modeling process of BRB, the original attributes are ranked by contribution rate and transformed into attribute vectors. Meanwhile, combined with the k-means method, appropriate referential vectors are obtained. Thereby a vector-based BRB can be established. In the inference process of BRB, the idea of full activation of vector-based rules is presented. By calculating the spatial matching degree of the testing sample and the referential vectors, activation weights of the rules which are used in the evidential reasoning algorithm are acquired. Experimental results of a nonlinear function with four-dimensional input and the pipeline leakage detection data show the effectiveness and superiority of the proposed approach.

CoCEC: An Automatic Combinational Circuit Equivalence Checker Based on the Interactive Theorem Prover

Checking the equivalence of two Boolean functions, or combinational circuits modeled as Boolean functions, is often desired when reliable and correct hardware components are required. The most common approaches to equivalence checking are based on simulation and model checking, which are constrained due to the popular memory and state explosion problems. Furthermore, such tools are often not user-friendly, thereby making it tedious to check the equivalence of large formulas or circuits. An alternative is to use mathematical tools, called interactive theorem provers, to prove the equivalence of two circuits; however, this requires human effort and expertise to write multiple output functions and carry out interactive proof of their equivalence. In this paper, we (1) define two simple, one formal and the other informal, gate-level hardware description languages, (2) design and develop a formal automatic combinational circuit equivalence checker (CoCEC) tool, and (3) test and evaluate our tool. The tool CoCEC is based on human-assisted theorem prover Coq, yet it checks the equivalence of circuit descriptions purely automatically through a human-friendly user interface. It either returns a machine-readable proof (term) of circuits’ equivalence or a counterexample of their inequality. The interface enables users to enter or load two circuit descriptions written in an easy and natural style. It automatically proves, in few seconds, the equivalence of circuits with as many as 45 variables (3.5 × 10 13 states). CoCEC has a mathematical foundation, and it is reliable, quick, and easy to use. The tool is intended to be used by digital logic circuit designers, logicians, students, and faculty during the digital logic design course.

Random mask-based estimation of the distribution algorithm for stacked auto-encoder one-step pre-training

The deep learning techniques have received great achievements in computer vision, natural language processing, etc. The success of deep neural networks depends on the sufficient training of parameters. The traditional way of neural network training is a gradient-based algorithm, which suffers the disadvantage of gradient disappearing, especially for the deeper neural network. Recently, a heuristic algorithm has been proposed for deeper neural network optimization. In this paper, a random mask and elitism univariate continuous estimation of distribution algorithm based on the Gaussian model is proposed to pre-train staked auto-encoder, and then a Stochastic Gradient Descent (SGD) based fine-tuning process is carried out for local searching. In the improved estimation of the distribution algorithm, two individual update strategies are defined; one group of individuals is generated according to the constructed probabilistic model, and another is updated according to the statistics of advanced individuals that aim to reduce the probability of combination explosion and time consumption according to the mask information. In the simulations, different architectures, different mask ratios and different promising individual ratios are adopted to testify the effectiveness of the improved algorithm. According to simulation results, the estimation of thr distribution algorithm has a steady optimization ability for the shallow and stacked auto-encoder by one-step pre-training combining SGD based fine-tuning for the MNIST dataset. The proposed model will achieve a state-of-the-art performance on Fashion-MNIST.

Improved approximate rips filtrations with shifted integer lattices and cubical complexes

Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes is expensive because of a combinatorial explosion in the complex size. For n points in mathbb {R}^d, we present a scheme to construct a 2-approximation of the filtration of the Rips complex in the L_infty -norm, which extends to a 2d^{0.25}-approximation in the Euclidean case. The k-skeleton of the resulting approximation has a total size of n2^{O(dlog k +d)}. The scheme is based on the integer lattice and simplicial complexes based on the barycentric subdivision of the d-cube. We extend our result to use cubical complexes in place of simplicial complexes by introducing cubical maps between complexes. We get the same approximation guarantee as the simplicial case, while reducing the total size of the approximation to only n2^{O(d)} (cubical) cells. There are two novel techniques that we use in this paper. The first is the use of acyclic carriers for proving our approximation result. In our application, these are maps which relate the Rips complex and the approximation in a relatively simple manner and greatly reduce the complexity of showing the approximation guarantee. The second technique is what we refer to as scale balancing, which is a simple trick to improve the approximation ratio under certain conditions.

Arguments for the unsuitability of convolutional neural networks for non-local tasks

Convolutional neural networks have established themselves over the past years as the state of the art method for image classification, and for many datasets, they even surpass humans in categorizing images. Unfortunately, the same architectures perform much worse when they have to compare parts of an image to each other to correctly classify this image.Until now, no well-formed theoretical argument has been presented to explain this deficiency. In this paper, we will argue that convolutional layers are of little use for such problems, since comparison tasks are global by nature, but convolutional layers are local by design. We will use this insight to reformulate a comparison task into a sorting task and use findings on sorting networks to propose a lower bound for the number of parameters a neural network needs to solve comparison tasks in a generalizable way. We will use this lower bound to argue that attention, as well as iterative/recurrent processing, is needed to prevent a combinatorial explosion.

Evolutionary algorithm-based generation of optimum peptide sequences with dengue virus inhibitory activity.

Background: There is currently no effective dengue virus (DENV) therapeutic. We aim to develop a genetic algorithm-based framework for the design of peptides with possible DENV inhibitory activity. Methods & results: A Python-based tool (denominated AutoPepGEN) based on a DENV support vector machineclassifier as the objective function was implemented. AutoPepGEN was applied to the design of three- to seven-amino acid sequences and ten peptides wereselected. Peptide-protease (DENV) docking and Molecular Mechanics-Generalized Born Surface Areacalculations wereperformed for the selected sequences and favorable binding energies wereobserved. Conclusion: It is hoped that AutoPepGEN will serve as an in silico alternative to the experimental design of positional scanning combinatorial libraries, known to be prone to a combinatorial explosion. AutoPepGEN is available at: https://github.com/sjbarigye/AutoPepGEN.