Question answering (QA) systems have garnered significant attention in recent years due to their potential to bridge the gap between human language understanding and machine intelligence . Consequently, a wide variety of approaches have been developed, each tailored to specific tasks. In this survey paper, we provide a comprehensive overview of three prominent QA paradigms: Extractive , generative, and Visual QA . We discuss the underlying principles, methodologies, applications, challenges, and recent trends in each of these areas. By synthesizing insights from the existing literature and research findings, we aim to provide a holistic understanding of extractive, generative, and Visual QA systems and offer insights into their strengths, limitations, and future directions.

In recent years, there has been a growing interest in analyzing text data from different scientific fields. The significant advancement of Artificial Intelligence in Natural Language Processing enables a systematic categorization of the wealth of scientific papers into fundamental thematic clusters. In this context, topic modeling is playing a crucial role. Unfortunately, the comparative analysis between traditional and advanced topic modeling methods, including well-established techniques like Latent Dirichlet Allocation (LDA) and newer approaches like BERTopic, remains significantly underexplored. This study addresses this gap by conducting a comprehensive analysis of extensive text data focused on sustainable energy research. To achieve this, we compile a unique dataset consisting of thousands of abstracts sourced from PubMed, Scopus, and Web of Science. Our analysis involves a comparison between LDA and the transformer model BERTopic. Importantly, we introduce a novel approach to determine the optimal number of topics, achieved through the maximization of combined semantic scores, and show that the number of topics is considerably lower than from previous approaches. Overall, our study not only contributes methodologically but also enhances our understanding of the principal topics in sustainable energy research.

Question-answering (QA) systems are becoming more and more important because they enable human-computer communication in a natural language. In recent years, significant progress has been made with transformer-based models that leverage deep learning in combination with large amounts of text data. However, a significant challenge with QA systems lies in their complexity rooted in the ambiguity and flexibility of a natural language. This makes even their evaluation a formidable task. For this reason, in this study, we focus on the evaluation of extractive question-answering (EQA) systems by conducting a large-scale analysis of distilBERT using benchmark data provided by the Stanford Question Answering Dataset (SQuAD). Specifically, the main objectives of this paper are fourfold. First, we study the influence of the answer length on the performance and we demonstrate that there is an inverse correlation between both. Second, we study differences in exact match (EM) measures because there are different definitions commonly used in the literature. As a result, we find that despite the fact that all of those measures are named ”exact match” these measures are actually different from each other. Third, we study the practical relevance of these different definitions because due to the ambivalent meaning of ”exact match” in the literature, it is often unclear if reported improvements are genuine or only due to a change in the exact match measure. Importantly, our results show that differences between differently defined EM measures are in the same order of magnitude as reported differences found in the literature. This raises concerns about the robustness of reported results. Fourth, we provide guidelines to improve the experimental design of general EQA studies, aiming to enhance performance evaluation and minimize the potential for spurious results.

In the context of multi-label text classification (MLTC), Binary Relevance (BR) stands out as one of the most intuitive and frequently employed methodologies. It tackles the MLTC task by breaking it down into multiple binary classification problems. However, BR has faced conceptual criticism due to its omission of label dependency information. To address this limitation, numerous studies have concentrated their efforts on enhancing the incorporation of label dependencies and document features. This resulted in substantial improvements in the performance of MLTC models. While the question of whether models incorporating label dependency information consistently outperform BR models remains unanswered, the prevailing opinion suggests their superiority. In this paper, we present evidence that challenges this widely held belief. Our numerical results across various text datasets demonstrate that an optimized binary relevance convolutional neural network (BR-CNN) can outperform advanced multi-label learning models explicitly designed to leverage label dependency information as well as advanced Binary Relevance (BR) models. Our results underscores the competitiveness of a BR-CNN approach for MLTC and emphasizes the versatility of the BR model family as a customizable option. More fundamentally, our findings contribute to the ongoing discourse surrounding label dependency and provide valuable insights into the efficacy of the binary relevance approach.

Massively multiplayer online games (MMOGs) played on the Web provide a new form of social, computer-mediated interactions that allow the connection of millions of players worldwide. The rules governing team-based MMOGs are typically complex and nondeterministic giving rise to an intricate dynamical behavior. However, due to the novelty and complexity of MMOGs, their behavior is understudied. In this article, we investigate the MMOG World of Tanks Blitz by using a combined approach based on data science and complex adaptive systems. We analyze data on the population level to get insights into organizational principles of the game and its game mechanics. For this reason, we study the scaling behavior and the predictability of system variables. As a result, we find a power-law behavior on the population level revealing long-range interactions between system variables. Furthermore, we identify and quantify the predictability of summary statistics of the game and its decomposition into explanatory variables. This reveals a heterogeneous progression through the tiers and identifies only a single system variable as key driver for the win rate.

In recent years, many applications are using various forms of deep learning models. Such methods are usually based on traditional learning paradigms requiring the consistency of properties among the feature spaces of the training and test data and also the availability of large amounts of training data, e.g., for performing supervised learning tasks. However, many real-world data do not adhere to such assumptions. In such situations transfer learning can provide feasible solutions, e.g., by simultaneously learning from data-rich source data and data-sparse target data to transfer information for learning a target task. In this paper, we survey deep transfer learning models with a focus on applications to text data. First, we review the terminology used in the literature and introduce a new nomenclature allowing the unequivocal description of a transfer learning model. Second, we introduce a visual taxonomy of deep learning approaches that provides a systematic structure to the many diverse models introduced until now. Furthermore, we provide comprehensive information about text data that have been used for studying such models because only by the application of methods to data, performance measures can be estimated and models assessed.

Large-scale perturbation databases, such as Connectivity Map (CMap) or Library of Integrated Network-based Cellular Signatures (LINCS), provide enormous opportunities for computational pharmacogenomics and drug design. A reason for this is that in contrast to classical pharmacology focusing at one target at a time, the transcriptomics profiles provided by CMap and LINCS open the door for systems biology approaches on the pathway and network level. In this article, we provide a review of recent developments in computational pharmacogenomics with respect to CMap and LINCS and related applications.

Briefings in Bioinformatics (2017) doi: 10.1093/bib/bbw112 In the article above, the last name of ‘Galina Glazko’ was misspelled as ‘Galina Galzko’. The name has been corrected online and in print. The authors apologize for this error.

BACKGROUND: Gene set analysis (in a form of functionally related genes or pathways) has become the method of choice for analyzing omics data in general and gene expression data in particular. There are many statistical methods that either summarize gene-level statistics for a gene set or apply a multivariate statistic that accounts for intergene correlations. Most available methods detect complex departures from the null hypothesis but lack the ability to identify the specific alternative hypothesis that rejects the null. RESULTS: GSAR (Gene Set Analysis in R) is an open-source R/Bioconductor software package for gene set analysis (GSA). It implements self-contained multivariate non-parametric statistical methods testing a complex null hypothesis against specific alternatives, such as differences in mean (shift), variance (scale), or net correlation structure. The package also provides a graphical visualization tool, based on the union of two minimum spanning trees, for correlation networks to examine the change in the correlation structures of a gene set between two conditions and highlight influential genes (hubs). CONCLUSIONS: Package GSAR provides a set of multivariate non-parametric statistical methods that test a complex null hypothesis against specific alternatives. The methods in package GSAR are applicable to any type of omics data that can be represented in a matrix format. The package, with detailed instructions and examples, is freely available under the GPL (> = 2) license from the Bioconductor web site.

BACKGROUND: sgnesR (Stochastic Gene Network Expression Simulator in R) is an R package that provides an interface to simulate gene expression data from a given gene network using the stochastic simulation algorithm (SSA). The package allows various options for delay parameters and can easily included in reactions for promoter delay, RNA delay and Protein delay. A user can tune these parameters to model various types of reactions within a cell. As examples, we present two network models to generate expression profiles. We also demonstrated the inference of networks and the evaluation of association measure of edge and non-edge components from the generated expression profiles. RESULTS: The purpose of sgnesR is to enable an easy to use and a quick implementation for generating realistic gene expression data from biologically relevant networks that can be user selected. CONCLUSIONS: sgnesR is freely available for academic use. The R package has been tested for R 3.2.0 under Linux, Windows and Mac OS X.

Transcriptome sequencing (RNA-seq) is gradually replacing microarrays for high-throughput studies of gene expression. The main challenge of analyzing microarray data is not in finding differentially expressed genes, but in gaining insights into the biological processes underlying phenotypic differences. To interpret experimental results from microarrays, gene set analysis (GSA) has become the method of choice, in particular because it incorporates pre-existing biological knowledge (in a form of functionally related gene sets) into the analysis. Here we provide a brief review of several statistically different GSA approaches (competitive and self-contained) that can be adapted from microarrays practice as well as those specifically designed for RNA-seq. We evaluate their performance (in terms of Type I error rate, power, robustness to the sample size and heterogeneity, as well as the sensitivity to different types of selection biases) on simulated and real RNA-seq data. Not surprisingly, the performance of various GSA approaches depends only on the statistical hypothesis they test and does not depend on whether the test was developed for microarrays or RNA-seq data. Interestingly, we found that competitive methods have lower power as well as robustness to the samples heterogeneity than self-contained methods, leading to poor results reproducibility. We also found that the power of unsupervised competitive methods depends on the balance between up- and down-regulated genes in tested gene sets. These properties of competitive methods have been overlooked before. Our evaluation provides a concise guideline for selecting GSA approaches, best performing under particular experimental settings in the context of RNA-seq.

MOTIVATION: Data from RNA-seq experiments provide us with many new possibilities to gain insights into biological and disease mechanisms of cellular functioning. However, the reproducibility and robustness of RNA-seq data analysis results is often unclear. This is in part attributed to the two counter acting goals of (i) a cost efficient and (ii) an optimal experimental design leading to a compromise, e.g. in the sequencing depth of experiments. RESULTS: We introduce an R package called samExploreR that allows the subsampling (m out of n bootstraping) of short-reads based on SAM files facilitating the investigation of sequencing depth related questions for the experimental design. Overall, this provides a systematic way for exploring the reproducibility and robustness of general RNA-seq studies. We exemplify the usage of samExploreR by studying the influence of the sequencing depth and the annotation on the identification of differentially expressed genes. AVAILABILITY AND IMPLEMENTATION: samExploreR is available as an R package from Bioconductor. CONTACT: [email protected] information: Supplementary data are available at Bioinformatics online.

BACKGROUND: It is generally acknowledged that a functional understanding of a biological system can only be obtained by an understanding of the collective of molecular interactions in form of biological networks. Protein networks are one particular network type of special importance, because proteins form the functional base units of every biological cell. On a mesoscopic level of protein networks, modules are of significant importance because these building blocks may be the next elementary functional level above individual proteins allowing to gain insight into fundamental organizational principles of biological cells. RESULTS: In this paper, we provide a comparative analysis of five popular and four novel module detection algorithms. We study these module prediction methods for simulated benchmark networks as well as 10 biological protein interaction networks (PINs). A particular focus of our analysis is placed on the biological meaning of the predicted modules by utilizing the Gene Ontology (GO) database as gold standard for the definition of biological processes. Furthermore, we investigate the robustness of the results by perturbing the PINs simulating in this way our incomplete knowledge of protein networks. CONCLUSIONS: Overall, our study reveals that there is a large heterogeneity among the different module prediction algorithms if one zooms-in the biological level of biological processes in the form of GO terms and all methods are severely affected by a slight perturbation of the networks. However, we also find pathways that are enriched in multiple modules, which could provide important information about the hierarchical organization of the system.

Urothelial cancer (UC) is highly recurrent and can progress from non-invasive (NMIUC) to a more aggressive muscle-invasive (MIUC) subtype that invades the muscle tissue layer of the bladder. We present a proof of principle study that network-based features of gene pairs can be used to improve classifier performance and the functional analysis of urothelial cancer gene expression data. In the first step of our procedure each individual sample of a UC gene expression dataset is inflated by gene pair expression ratios that are defined based on a given network structure. In the second step an elastic net feature selection procedure for network-based signatures is applied to discriminate between NMIUC and MIUC samples. We performed a repeated random subsampling cross validation in three independent datasets. The network signatures were characterized by a functional enrichment analysis and studied for the enrichment of known cancer genes. We observed that the network-based gene signatures from meta collections of protein-protein interaction (PPI) databases such as CPDB and the PPI databases HPRD and BioGrid improved the classification performance compared to single gene based signatures. The network based signatures that were derived from PPI databases showed a prominent enrichment of cancer genes (e.g., TP53, TRIM27 and HNRNPA2B1). We provide a novel integrative approach for large-scale gene expression analysis for the identification and development of novel diagnostical targets in bladder cancer. Further, our method allowed to link cancer gene associations to network-based expression signatures that are not observed in gene-based expression signatures.

MOTIVATION: To date, gene set analysis approaches primarily focus on identifying differentially expressed gene sets (pathways). Methods for identifying differentially coexpressed pathways also exist but are mostly based on aggregated pairwise correlations or other pairwise measures of coexpression. Instead, we propose Gene Sets Net Correlations Analysis (GSNCA), a multivariate differential coexpression test that accounts for the complete correlation structure between genes. RESULTS: In GSNCA, weight factors are assigned to genes in proportion to the genes' cross-correlations (intergene correlations). The problem of finding the weight vectors is formulated as an eigenvector problem with a unique solution. GSNCA tests the null hypothesis that for a gene set there is no difference in the weight vectors of the genes between two conditions. In simulation studies and the analyses of experimental data, we demonstrate that GSNCA captures changes in the structure of genes' cross-correlations rather than differences in the averaged pairwise correlations. Thus, GSNCA infers differences in coexpression networks, however, bypassing method-dependent steps of network inference. As an additional result from GSNCA, we define hub genes as genes with the largest weights and show that these genes correspond frequently to major and specific pathway regulators, as well as to genes that are most affected by the biological difference between two conditions. In summary, GSNCA is a new approach for the analysis of differentially coexpressed pathways that also evaluates the importance of the genes in the pathways, thus providing unique information that may result in the generation of novel biological hypotheses. AVAILABILITY AND IMPLEMENTATION: Implementation of the GSNCA test in R is available upon request from the authors.

Abstract Summary: NetBioV (Network Biology Visualization) is an R package that allows the visualization of large network data in biology and medicine. The purpose of NetBioV is to enable an organized and reproducible visualization of networks by emphasizing or highlighting specific structural properties that are of biological relevance. Availability and implementation: NetBioV is freely available for academic use. The package has been tested for R 2.14.2 under Linux, Windows and Mac OS X. It is available from Bioconductor. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

Cancer is a complex disease that has proven to be difficult to understand on the single-gene level. For this reason a functional elucidation needs to take interactions among genes on a systems-level into account. In this study, we infer a colon cancer network from a large-scale gene expression data set by using the method BC3Net. We provide a structural and a functional analysis of this network and also connect its molecular interaction structure with the chromosomal locations of the genes enabling the definition of cis- and trans-interactions. Furthermore, we investigate the interaction of genes that can be found in close neighborhoods on the chromosomes to gain insight into regulatory mechanisms. To our knowledge this is the first study analyzing the genome-scale colon cancer network.

BACKGROUND: Over the last few years transcriptome sequencing (RNA-Seq) has almost completely taken over microarrays for high-throughput studies of gene expression. Currently, the most popular use of RNA-Seq is to identify genes which are differentially expressed between two or more conditions. Despite the importance of Gene Set Analysis (GSA) in the interpretation of the results from RNA-Seq experiments, the limitations of GSA methods developed for microarrays in the context of RNA-Seq data are not well understood. RESULTS: We provide a thorough evaluation of popular multivariate and gene-level self-contained GSA approaches on simulated and real RNA-Seq data. The multivariate approach employs multivariate non-parametric tests combined with popular normalizations for RNA-Seq data. The gene-level approach utilizes univariate tests designed for the analysis of RNA-Seq data to find gene-specific P-values and combines them into a pathway P-value using classical statistical techniques. Our results demonstrate that the Type I error rate and the power of multivariate tests depend only on the test statistics and are insensitive to the different normalizations. In general standard multivariate GSA tests detect pathways that do not have any bias in terms of pathways size, percentage of differentially expressed genes, or average gene length in a pathway. In contrast the Type I error rate and the power of gene-level GSA tests are heavily affected by the methods for combining P-values, and all aforementioned biases are present in detected pathways. CONCLUSIONS: Our result emphasizes the importance of using self-contained non-parametric multivariate tests for detecting differentially expressed pathways for RNA-Seq data and warns against applying gene-level GSA tests, especially because of their high level of Type I error rates for both, simulated and real data.

MOTIVATION: The analysis of differentially expressed gene sets became a routine in the analyses of gene expression data. There is a multitude of tests available, ranging from aggregation tests that summarize gene-level statistics for a gene set to true multivariate tests, accounting for intergene correlations. Most of them detect complex departures from the null hypothesis but when the null hypothesis is rejected, the specific alternative leading to the rejection is not easily identifiable. RESULTS: In this article we compare the power and Type I error rates of minimum-spanning tree (MST)-based non-parametric multivariate tests with several multivariate and aggregation tests, which are frequently used for pathway analyses. In our simulation study, we demonstrate that MST-based tests have power that is for many settings comparable with the power of conventional approaches, but outperform them in specific regions of the parameter space corresponding to biologically relevant configurations. Further, we find for simulated and for gene expression data that MST-based tests discriminate well against shift and scale alternatives. As a general result, we suggest a two-step practical analysis strategy that may increase the interpretability of experimental data: first, apply the most powerful multivariate test to find the subset of pathways for which the null hypothesis is rejected and second, apply MST-based tests to these pathways to select those that support specific alternative hypotheses. CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Evidence suggests that in prokaryotes sequence-dependent transcriptional pauses affect the dynamics of transcription and translation, as well as of small genetic circuits. So far, a few pause-prone sequences have been identified from in vitro measurements of transcription elongation kinetics. RESULTS: Using a stochastic model of gene expression at the nucleotide and codon levels with realistic parameter values, we investigate three different but related questions and present statistical methods for their analysis. First, we show that information from in vivo RNA and protein temporal numbers is sufficient to discriminate between models with and without a pause site in their coding sequence. Second, we demonstrate that it is possible to separate a large variety of models from each other with pauses of various durations and locations in the template by means of a hierarchical clustering and a random forest classifier. Third, we introduce an approximate likelihood function that allows to estimate the location of a pause site. CONCLUSIONS: This method can aid in detecting unknown pause-prone sequences from temporal measurements of RNA and protein numbers at a genome-wide scale and thus elucidate possible roles that these sequences play in the dynamics of genetic networks and phenotype.

BACKGROUND: Structural measures for networks have been extensively developed, but many of them have not yet demonstrated their sustainably. That means, it remains often unclear whether a particular measure is useful and feasible to solve a particular problem in network biology. Exemplarily, the classification of complex biological networks can be named, for which structural measures are used leading to a minimal classification error. Hence, there is a strong need to provide freely available software packages to calculate and demonstrate the appropriate usage of structural graph measures in network biology. RESULTS: Here, we discuss topological network descriptors that are implemented in the R-package QuACN and demonstrate their behavior and characteristics by applying them to a set of example graphs. Moreover, we show a representative application to illustrate their capabilities for classifying biological networks. In particular, we infer gene regulatory networks from microarray data and classify them by methods provided by QuACN. Note that QuACN is the first freely available software written in R containing a large number of structural graph measures. CONCLUSION: The R package QuACN is under ongoing development and we add promising groups of topological network descriptors continuously. The package can be used to answer intriguing research questions in network biology, e.g., classifying biological data or identifying meaningful biological features, by analyzing the topology of biological networks.

Identification of differentially expressed pathways from expression data is an important problem because it allows us to gain insights into the functional working mechanism of cells beyond the detection of differentially expressed genes. In this paper we present a brief guide to methods for the pathway analysis of expression data. Despite the vast amount of different statistical methods that have been developed so far, there is a considerable similarity among them, allowing a systematic classification and a reduction to a few null hypotheses that are effectively tested. Systems biology aims to find emergent phenomena by the integration of heterogeneous data. In general, data integration itself is a part of any scientific inference: its elementary steps are the integration of observations (measurements) into the context of biological knowledge. However, in the case of systems biology, the scale of integration is many folds higher, resulting in a prodigious number of new computational approaches for the simultaneous analyses of heterogeneous data. In this paper we discuss one popular way of integrating biological knowledge into large-scale genome-wide measurements, namely the identification of functionally related genes (pathways) enriched or differentially expressed in gene expression data [1]. It should be noted that the approaches discussed are also applicable to the analyses of, e.g., RNA-seq, metabolomics or proteomics data and, generally, different types of biological measurements when preexisting biological knowledge is available. In the early stages of methodological developments for gene expression data analyses, most approaches were focused on producing so-called gene lists. This is a set of individual genes called differentially expressed as identified by univariate test statistics (e.g., a t-test) [2]–[4]. Instead, more recent approaches clearly reflect systems biology's trend of data integration and interpretation [5]–[7], focusing on sets of functionally related genes (e.g., from the same signaling or metabolic pathway) rather than individual genes. The purpose of this paper is to provide a brief guide to methods for the analysis of differentially expressed pathways or gene sets, which we simply call pathway-based methods. For this reason, we emphasize an illustration of the methods rather than their technical description. The reader is encouraged to follow the cited literature for technical details.

MOTIVATION: The inference of regulatory networks from large-scale expression data holds great promise because of the potentially causal interpretation of these networks. However, due to the difficulty to establish reliable methods based on observational data there is so far only incomplete knowledge about possibilities and limitations of such inference methods in this context. RESULTS: In this article, we conduct a statistical analysis investigating differences and similarities of four network inference algorithms, ARACNE, CLR, MRNET and RN, with respect to local network-based measures. We employ ensemble methods allowing to assess the inferability down to the level of individual edges. Our analysis reveals the bias of these inference methods with respect to the inference of various network components and, hence, provides guidance in the interpretation of inferred regulatory networks from expression data. Further, as application we predict the total number of regulatory interactions in human B cells and hypothesize about the role of Myc and its targets regarding molecular information processing.

MOTIVATION: Recently, many univariate and several multivariate approaches have been suggested for testing differential expression of gene sets between different phenotypes. However, despite a wealth of literature studying their performance on simulated and real biological data, still there is a need to quantify their relative performance when they are testing different null hypotheses. RESULTS: In this article, we compare the performance of univariate and multivariate tests on both simulated and biological data. In the simulation study we demonstrate that high correlations equally affect the power of both, univariate as well as multivariate tests. In addition, for most of them the power is similarly affected by the dimensionality of the gene set and by the percentage of genes in the set, for which expression is changing between two phenotypes. The application of different test statistics to biological data reveals that three statistics (sum of squared t-tests, Hotelling's T(2), N-statistic), testing different null hypotheses, find some common but also some complementing differentially expressed gene sets under specific settings. This demonstrates that due to complementing null hypotheses each test projects on different aspects of the data and for the analysis of biological data it is beneficial to use all three tests simultaneously instead of focusing exclusively on just one.

BACKGROUND: Identification of the structural domains of proteins is important for our understanding of the organizational principles and mechanisms of protein folding, and for insights into protein function and evolution. Algorithmic methods of dissecting protein of known structure into domains developed so far are based on an examination of multiple geometrical, physical and topological features. Successful as many of these approaches are, they employ a lot of heuristics, and it is not clear whether they illuminate any deep underlying principles of protein domain organization. Other well-performing domain dissection methods rely on comparative sequence analysis. These methods are applicable to sequences with known and unknown structure alike, and their success highlights a fundamental principle of protein modularity, but this does not directly improve our understanding of protein spatial structure. RESULTS: We present a novel graph-theoretical algorithm for the identification of domains in proteins with known three-dimensional structure. We represent the protein structure as an undirected, unweighted and unlabeled graph whose nodes correspond to the secondary structure elements and edges represent physical proximity of at least one pair of alpha carbon atoms from two elements. Domains are identified as constrained partitions of the graph, corresponding to sets of vertices obtained by the maximization of the cycle distributions found in the graph. When a partition is found, the algorithm is iteratively applied to each of the resulting subgraphs. The decision to accept or reject a tentative cut position is based on a specific classifier. The algorithm is applied iteratively to each of the resulting subgraphs and terminates automatically if partitions are no longer accepted. The distribution of cycles is the only type of information on which the decision about protein dissection is based. Despite the barebone simplicity of the approach, our algorithm approaches the best heuristic algorithms in accuracy. CONCLUSION: Our graph-theoretical algorithm uses only topological information present in the protein structure itself to find the domains and does not rely on any geometrical or physical information about protein molecule. Perhaps unexpectedly, these drastic constraints on resources, which result in a seemingly approximate description of protein structures and leave only a handful of parameters available for analysis, do not lead to any significant deterioration of algorithm accuracy. It appears that protein structures can be rigorously treated as topological rather than geometrical objects and that the majority of information about protein domains can be inferred from the coarse-grained measure of pairwise proximity between elements of secondary structure elements.