Whether County Lockdown Could Deter the Contagion of COVID-19 in the USA

Aim

Whether to lock down a country or not during COVID-19 pandemic becomes a vital issue, since it affects people’s daily life. The objective of this research is to design a measurement that could be utilised to predict the efficacy of a lockdown decision.

Methods

One would expect that the effectiveness of lockdown lies in the assumption that the virus spreads from one area to another area in a rippling way. If the virus spreads in a radiating way, then lockdown should be an effective countermeasure to contain the pandemic. On the other hand, if it spreads indiscernibly or randomly, then a lockdown decision would have lesser or little effect on the containment. We mainly combine graphs and metric to compute correlation matrices, which would measure whether the virus spreads in a rippling way. The metric used is to measure the boundary (or county) distances between counties. We take 3073 counties and equivalents in the USA and explore the property of contagion with respect to distance. The distance between any two counties is measured by the number of neighbours (or counties) between them. Then, we study the relation between contagion and distances. The relation between distance (complexity of neighbouring) and confirmed cases (contagion) is further explored.

Results

Then, we study the relation between contagion and distances. The relation between distance (complexity of neighbouring) and confirmed cases (contagion) could be explored. Our research shows county lockdown in the USA plays no important role in containing the spread of coronavirus for the time being.

Conclusion

Rippling effect in the USA regarding COVID-19 is not significant. This indicates other robust approaches or policies should be taken into consideration, rather than a simple lockdown policy.

Topoly: Python package to analyze topology of polymers

The increasing role of topology in (bio)physical properties of matter creates a need for an efficient method of detecting the topology of a (bio)polymer. However, the existing tools allow one to classify only the simplest knots and cannot be used in automated sample analysis. To answer this need, we created the Topoly Python package. This package enables the distinguishing of knots, slipknots, links and spatial graphs through the calculation of different topological polynomial invariants. It also enables one to create the minimal spanning surface on a given loop, e.g. to detect a lasso motif or to generate random closed polymers. It is capable of reading various file formats, including PDB. The extensive documentation along with test cases and the simplicity of the Python programming language make it a very simple to use yet powerful tool, suitable even for inexperienced users. Topoly can be obtained from https://topoly.cent.uw.edu.pl.

Damage Localization and Severity Assessment of a Cable-Stayed Bridge Using a Message Passing Neural Network

Cable-stayed bridges are damaged by multiple factors such as natural disasters, weather, and vehicle load. In particular, if the stayed cable, which is an essential and weak component of the cable-stayed bridge, is damaged, it may adversely affect the adjacent cables and worsen the bridge structure condition. Therefore, we must accurately determine the condition of the cable with a technology-based evaluation strategy. In this paper, we propose a deep learning model that allows us to locate the damaged cable and estimate its cross-sectional area. To obtain the data required for the deep learning training, we use the tension data of the reduced area cable, which are simulated in the Practical Advanced Analysis Program (PAAP), a robust structural analysis program. We represent the sensor data of the damaged cable-stayed bridge as a graph composed of vertices and edges using tension and spatial information of the sensors. We apply the sensor geometry by mapping the tension data to the graph vertices and the connection relationship between sensors to the graph edges. We employ a Graph Neural Network (GNN) to use the graph representation of the sensor data directly. GNN, which has been actively studied recently, can treat graph-structured data with the most advanced performance. We train the GNN framework, the Message Passing Neural Network (MPNN), to perform two tasks to identify damaged cables and estimate the cable areas. We adopt a multi-task learning method for more efficient optimization. We show that the proposed technique achieves high performance with the cable-stayed bridge data generated from PAAP.

Brain microvasculature has a common topology with local differences in geometry that match metabolic load

The microvasculature underlies the supply networks that support neuronal activity within heterogeneous brain regions. What are common versus heterogeneous aspects of the connectivity, density, and orientation of capillary networks? To address this, we imaged, reconstructed, and analyzed the microvasculature connectome in whole adult mice brains with sub-micrometer resolution. Graph analysis revealed common network topology across the brain that leads to a shared structural robustness against the rarefaction of vessels. Geometrical analysis, based on anatomically accurate reconstructions, uncovered a scaling law that links length density, i.e., the length of vessel per volume, with tissue-to-vessel distances. We then derive a formula that connects regional differences in metabolism to differences in length density and, further, predicts a common value of maximum tissue oxygen tension across the brain. Last, the orientation of capillaries is weakly anisotropic with the exception of a few strongly anisotropic regions; this variation can impact the interpretation of fMRI data.

SeBioGraph: Semi-supervised Deep Learning for the Graph via Sustainable Knowledge Transfer

Semi-supervised deep learning for the biomedical graph and advanced manufacturing graph is rapidly becoming an important topic in both academia and industry. Many existing types of research focus on semi-supervised link prediction and node classification, as well as the application of these methods in sustainable development and advanced manufacturing. To date, most manufacturing graph neural networks are mainly evaluated on social and information networks, which improve the quality of network representation y integrating neighbor node descriptions. However, previous methods have not yet been comprehensively studied on biomedical networks. Traditional techniques fail to achieve satisfying results, especially when labeled nodes are deficient in number. In this paper, a new semi-supervised deep learning method for the biomedical graph via sustainable knowledge transfer called SeBioGraph is proposed. In SeBioGraph, both node embedding and graph-specific prototype embedding are utilized as transferable metric space characterized. By incorporating prior knowledge learned from auxiliary graphs, SeBioGraph further promotes the performance of the target graph. Experimental results on the two-class node classification tasks and three-class link prediction tasks demonstrate that the SeBioGraph realizes state-of-the-art results. Finally, the method is thoroughly evaluated.

Closed Formulas for Some New Degree Based Topological Descriptors Using M-polynomial and Boron Triangular Nanotube

In this article, we provide new formulas to compute the reduced reciprocal randić index, Arithmetic geometric1 index, SK index, SK 1 index, SK 2 index, edge version of the first zagreb index, sum connectivity index, general sum connectivity index, and the forgotten index using the M-polynomial and finding these topological indices for a boron triangular nanotube. We also elaborate the results with graphical representations.

Assessing wildland-urban interface fire risk

Recent wildfire events, in the United States (USA) and around the world, have resulted in thousands of homes destroyed and many lives lost, leaving communities and policy makers, once again, with the question as to how to manage wildfire risk. This is particularly important given the prevalent trend of increased fire frequency and intensity. Current approaches to managing wildfires focus on fire suppression and managing fuel build-up in wildlands. However, reliance on these strategies alone has clearly proven inadequate. As such, focus should be shifted towards minimizing potential losses to communities. Achieving this goal, however, requires detailed understanding of the factors that contribute to community vulnerability and the interplay between probability of ignition, vulnerability and calculated risk. In this study, we evaluate wildfire risk for four different communities across the USA for the duration of May to September to communicate a different perspective of risk assessment. We show, for the first time, that community risk is closely related to wind speed and direction, pattern of surrounding wildland vegetation, and buildings layout. The importance of the findings lies in the need for exploring unique viable solutions to reduce risk for every community independently as opposed to embracing a generalized approach as is currently the case.

Creating effective interrupted time series graphs: Review and recommendations

Introduction

Interrupted Time Series (ITS) studies may be used to assess the impact of an interruption, such as an intervention or exposure. The data from such studies are particularly amenable to visual display and, when clearly depicted, can readily show the short‐ and long‐term impact of an interruption. Further, well‐constructed graphs allow data to be extracted using digitizing software, which can facilitate their inclusion in systematic reviews and meta‐analyses.

Aim

We provide recommendations for graphing ITS data, examine the properties of plots presented in ITS studies, and provide examples employing our recommendations.

Methods and results

Graphing recommendations from seminal data visualization resources were adapted for use with ITS studies. The adapted recommendations cover plotting of data points, trend lines, interruptions, additional lines and general graph components. We assessed whether 217 graphs from recently published (2013‐2017) ITS studies met our recommendations and found that 130 graphs (60%) had clearly distinct data points, 100 (46%) had trend lines, and 161 (74%) had a clearly defined interruption. Accurate data extraction (requiring distinct points that align with axis tick marks and labels that allow the points to be interpreted) was possible in only 72 (33%) graphs.

Conclusion

We found that many ITS graphs did not meet our recommendations and could be improved with simple changes. Our proposed recommendations aim to achieve greater standardization and improvement in the display of ITS data, and facilitate re‐use of the data in systematic reviews and meta‐analyses.

Application of data visualization recommendations can improve quality of interrupted time series graphs.

Well‐designed graphs accurately depict time series data, any impact of the interruption, and the results of the analysis.

Well‐designed graphs facilitate data extraction for use in systematic reviews and reproducibility.

An assessment of graphs included in interrupted time series studies (published between 2013 and 2017) found that graphs often do not meet core graphing recommendations.

DEEP MULTIMODAL BRAIN NETWORK LEARNING FOR JOINT ANALYSIS OF STRUCTURAL MORPHOMETRY AND FUNCTIONAL CONNECTIVITY

Learning from the multimodal brain imaging data attracts a large amount of attention in medical image analysis due to the proliferation of multimodal data collection. It is widely accepted that multimodal data can provide complementary information than mining from a single modality. However, unifying the image-based knowledge from the multimodal data is very challenging due to different image signals, resolution, data structure, etc.. In this study, we design a supervised deep model to jointly analyze brain morphometry and functional connectivity on the cortical surface and we name it deep multimodal brain network learning (DMBNL). Two graph-based kernels, i.e., geometry-aware surface kernel (GSK) and topology-aware network kernel (TNK), are proposed for processing the cortical surface morphometry and brain functional network. The vertex features on the cortical surface from GSK is pooled and feed into TNK as its initial regional features. In the end, the graph-level feature is computed for each individual and thus can be applied for classification tasks. We test our model on a large autism imaging dataset. The experimental results prove the effectiveness of our model.

Context-Specific Nested Effects Models

Advances in systems biology have made clear the importance of network models for capturing knowledge about complex relationships in gene regulation, metabolism, and cellular signaling. A common approach to uncovering biological networks involves performing perturbations on elements of the network, such as gene knockdown experiments, and measuring how the perturbation affects some reporter of the process under study. In this article, we develop context-specific nested effects models (CSNEMs), an approach to inferring such networks that generalizes nested effects models (NEMs). The main contribution of this work is that CSNEMs explicitly model the participation of a gene in multiple contexts, meaning that a gene can appear in multiple places in the network. Biologically, the representation of regulators in multiple contexts may indicate that these regulators have distinct roles in different cellular compartments or cell cycle phases. We present an evaluation of the method on simulated data as well as on data from a study of the sodium chloride stress response in Saccharomyces cerevisiae.

Information Management in Healthcare and Environment: Towards an Automatic System for Fake News Detection

Comments and information appearing on the internet and on different social media sway opinion concerning potential remedies for diagnosing and curing diseases. In many cases, this has an impact on citizens’ health and affects medical professionals, who find themselves having to defend their diagnoses as well as the treatments they propose against ill-informed patients. The propagation of these opinions follows the same pattern as the dissemination of fake news about other important topics, such as the environment, via social media networks, which we use as a testing ground for checking our procedure. In this article, we present an algorithm to analyse the behaviour of users of Twitter, the most important social network with respect to this issue, as well as a dynamic knowledge graph construction method based on information gathered from Twitter and other open data sources such as web pages. To show our methodology, we present a concrete example of how the associated graph structure of the tweets related to World Environment Day 2019 is used to develop a heuristic analysis of the validity of the information. The proposed analytical scheme is based on the interaction between the computer tool—a database implemented with Neo4j—and the analyst, who must ask the right questions to the tool, allowing to follow the line of any doubtful data. We also show how this method can be used. We also present some methodological guidelines on how our system could allow, in the future, an automation of the procedures for the construction of an autonomous algorithm for the detection of false news on the internet related to health.

Potential Confounders in the Analysis of Brazilian Adolescent's Health: A Combination of Machine Learning and Graph Theory

The prevalence of health problems during childhood and adolescence is high in developing countries such as Brazil. Social inequality, violence, and malnutrition have strong impact on youth health. To better understand these issues we propose to combine machine-learning methods and graph analysis to build predictive networks applied to the Brazilian National Student Health Survey (PenSE 2015) data, a large dataset that consists of questionnaires filled by the students. By using a combination of gradient boosting machines and centrality hub metric, it was possible to identify potential confounders to be considered when conducting association analyses among variables. The variables were ranked according to their hub centrality to predict the other variables from a directed weighted-graph perspective. The top five ranked confounder variables were “gender”, “oral health care”, “intended education level”, and two variables associated with nutrition habits—“eat while watching TV” and “never eat fast-food”. In conclusion, although causal effects cannot be inferred from the data, we believe that the proposed approach might be a useful tool to obtain novel insights on the association between variables and to identify general factors related to health conditions.

Leveraging User-Friendly Network Approaches to Extract Knowledge From High-Throughput Omics Datasets

Recent technological advances for the acquisition of multi-omics data have allowed an unprecedented understanding of the complex intricacies of biological systems. In parallel, a myriad of computational analysis techniques and bioinformatics tools have been developed, with many efforts directed towards the creation and interpretation of networks from this data. In this review, we begin by examining key network concepts and terminology. Then, computational tools that allow for their construction and analysis from high-throughput omics datasets are presented. We focus on the study of functional relationships such as co-expression, protein-protein interactions, and regulatory interactions that are particularly amenable to modeling using the framework of networks. We envisage that many potential users of these analytical strategies may not be completely literate in programming languages and code adaptation, and for this reason, emphasis is given to tools' user-friendliness, including plugins for the widely adopted Cytoscape software, an open-source, cross-platform tool for network analysis, visualization, and data integration.

Automatic Graph-Based Modeling of Brain Microvessels Captured With Two-Photon Microscopy

Graph models of cerebral vasculature derived from two-photon microscopy have shown to be relevant to study brain microphysiology. Automatic graphing of these microvessels remain problematic due to the vascular network complexity and two-photon sensitivity limitations with depth. In this paper, we propose a fully automatic processing pipeline to address this issue. The modeling scheme consists of a fully-convolution neural network to segment microvessels, a three-dimensional surface model generator, and a geometry contraction algorithm to produce graphical models with a single connected component. Based on a quantitative assessment using NetMets metrics, at a tolerance of 60 μm, false negative and false positive geometric error 19 rates are 3.8% and 4.2%, respectively, whereas false nega- 20 tive and false positive topological error rates are 6.1% and 4.5%, respectively. Our qualitative evaluation confirms the efficiency of our scheme in generating useful and accurate graphical models.

A Novel Computational Model for Predicting microRNA-Disease Associations Based on Heterogeneous Graph Convolutional Networks

Identifying the interactions between disease and microRNA (miRNA) can accelerate drugs development, individualized diagnosis, and treatment for various human diseases. However, experimental methods are time-consuming and costly. So computational approaches to predict latent miRNA-disease interactions are eliciting increased attention. But most previous studies have mainly focused on designing complicated similarity-based methods to predict latent interactions between miRNAs and diseases. In this study, we propose a novel computational model, termed heterogeneous graph convolutional network for miRNA-disease associations (HGCNMDA), which is based on known human protein-protein interaction (PPI) and integrates four biological networks: miRNA-disease, miRNA-gene, disease-gene, and PPI network. HGCNMDA achieved reliable performance using leave-one-out cross-validation (LOOCV). HGCNMDA is then compared to three state-of-the-art algorithms based on five-fold cross-validation. HGCNMDA achieves an AUC of 0.9626 and an average precision of 0.9660, respectively, which is ahead of other competitive algorithms. We further analyze the top-10 unknown interactions between miRNA and disease. In summary, HGCNMDA is a useful computational model for predicting miRNA-disease interactions.

You Can't See Me: Anonymizing Graphs Using the Szemerédi Regularity Lemma

Complex networks gathered from our online interactions provide a rich source of information that can be used to try to model and predict our behavior. While this has very tangible benefits that we have all grown accustomed to, there is a concrete privacy risk in sharing potentially sensitive data about ourselves and the people we interact with, especially when this data is publicly available online and unprotected from malicious attacks. k-anonymity is a technique aimed at reducing this risk by obfuscating the topological information of a graph that can be used to infer the nodes' identity. In this paper we propose a novel algorithm to enforce k-anonymity based on a well-known result in extremal graph theory, the Szemerédi regularity lemma. Given a graph, we start by computing a regular partition of its nodes. The Szemerédi regularity lemma ensures that such a partition exists and that the edges between the sets of nodes behave almost randomly. With this partition, we anonymize the graph by randomizing the edges within each set, obtaining a graph that is structurally similar to the original one yet the nodes within each set are structurally indistinguishable. We test the proposed approach on real-world networks extracted from Facebook. Our experimental results show that the proposed approach is able to anonymize a graph while retaining most of its structural information.

Protein Sequence Comparison and DNA-binding Protein Identification with Generalized PseAAC and Graphical Representation

AIM AND OBJECTIVE

The rapid increase in the amount of protein sequence data available leads to an urgent need for novel computational algorithms to analyze and compare these sequences. This study is undertaken to develop an efficient computational approach for timely encoding protein sequences and extracting the hidden information.

METHODS

Based on two physicochemical properties of amino acids, a protein primary sequence was converted into a three-letter sequence, and then a graph without loops and multiple edges and its geometric line adjacency matrix were obtained. A generalized PseAAC (pseudo amino acid composition) model was thus constructed to characterize a protein sequence numerically.

RESULTS

By using the proposed mathematical descriptor of a protein sequence, similarity comparisons among β-globin proteins of 17 species and 72 spike proteins of coronaviruses were made, respectively. The resulting clusters agreed well with the established taxonomic groups. In addition, a generalized PseAAC based SVM (support vector machine) model was developed to identify DNA-binding proteins. Experiment results showed that our method performed better than DNAbinder, DNA-Prot, iDNA-Prot and enDNA-Prot by 3.29-10.44% in terms of ACC, 0.056-0.206 in terms of MCC, and 1.45-15.76% in terms of F1M. When the benchmark dataset was expanded with negative samples, the presented approach outperformed the four previous methods with improvement in the range of 2.49-19.12% in terms of ACC, 0.05-0.32 in terms of MCC, and 3.82- 33.85% in terms of F1M.

CONCLUSION

These results suggested that the generalized PseAAC model was very efficient for comparison and analysis of protein sequences, and very competitive in identifying DNA-binding proteins.

Proximity of restored hedgerows interacts with local floral diversity and species' traits to shape long-term pollinator metacommunity dynamics

Disconnected habitat fragments are poor at supporting population and community persistence; restoration ecologists, therefore, advocate for the establishment of habitat networks across landscapes. Few empirical studies, however, have considered how networks of restored habitat patches affect metacommunity dynamics. Here, using a 10-year study on restored hedgerows and unrestored field margins within an intensive agricultural landscape, we integrate occupancy modelling with network theory to examine the interaction between local and landscape characteristics, habitat selection and dispersal in shaping pollinator metacommunity dynamics. We show that surrounding hedgerows and remnant habitat patches interact with the local floral diversity, bee diet breadth and bee body size to influence site occupancy, via colonisation and persistence dynamics. Florally diverse sites and generalist, small-bodied species are most important for maintaining metacommunity connectivity. By providing the first in-depth assessment of how a network of restored habitat influences long-term population dynamics, we confirm the conservation benefit of hedgerows for pollinator populations and demonstrate the importance of restoring and maintaining habitat networks within an inhospitable matrix.

On a two-truths phenomenon in spectral graph clustering

Spectral graph clustering—clustering the vertices of a graph based on their spectral embedding—is of significant current interest, finding applications throughout the sciences. But as with clustering in general, what a particular methodology identifies as “clusters” is defined (explicitly, or, more often, implicitly) by the clustering algorithm itself. We provide a clear and concise demonstration of a “two-truths” phenomenon for spectral graph clustering in which the first step—spectral embedding—is either Laplacian spectral embedding, wherein one decomposes the normalized Laplacian of the adjacency matrix, or adjacency spectral embedding given by a decomposition of the adjacency matrix itself. The two resulting clustering methods identify fundamentally different (true and meaningful) structure.

Clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering—clustering the vertices of a graph based on their spectral embedding—is commonly approached via K-means (or, more generally, Gaussian mixture model) clustering composed with either Laplacian spectral embedding (LSE) or adjacency spectral embedding (ASE). Recent theoretical results provide deeper understanding of the problem and solutions and lead us to a “two-truths” LSE vs. ASE spectral graph clustering phenomenon convincingly illustrated here via a diffusion MRI connectome dataset: The different embedding methods yield different clustering results, with LSE capturing left hemisphere/right hemisphere affinity structure and ASE capturing gray matter/white matter core–periphery structure.

Connectivity in fMRI: Blind Spots and Breakthroughs

In recent years, driven by scientific and clinical concerns, there has been an increased interest in the analysis of functional brain networks. The goal of these analyses is to better understand how brain regions interact, how this depends upon experimental conditions and behavioral measures and how anomalies (disease) can be recognized. In this paper, we provide, first, a brief review of some of the main existing methods of functional brain network analysis. But rather than compare them, as a traditional review would do, instead, we draw attention to their significant limitations and blind spots. Then, second, relevant experts, sketch a number of emerging methods, which can break through these limitations. In particular we discuss five such methods. The first two, stochastic block models and exponential random graph models, provide an inferential basis for network analysis lacking in the exploratory graph analysis methods. The other three addresses: network comparison via persistent homology, time-varying connectivity that distinguishes sample fluctuations from neural fluctuations, and network system identification that draws inferential strength from temporal autocorrelation.

Epigenetic inheritance systems contribute to the evolution of a germline

Differentiation within multicellular organisms is controlled by epigenetic markers transmitted across cell division. The process of differentiation will modify these epigenetic markers so that information that one cell type possesses can be lost in the transition to another. Many of the systems that encode these markers also exist in unicellular organisms but do not control differentiation. Thus, during the evolution of multicellularity, epigenetic inheritance systems were probably exapted for their current use in differentiation. We show that the simultaneous use of an information carrier for differentiation and transmission across generations can lead to the evolution of cell types that do not directly contribute to the progeny of the organism and ergo a germ-soma distinction. This shows that an intrinsic instability during a transition from unicellularity to multicellularity may contribute to widespread evolution of a germline and its maintenance, a phenomenon also relevant to the evolution of eusociality. The difference in epigenetic information contents between different cell lines in a multicellular organism is also relevant for the full-success cloning of higher animals, as well as for the maintenance of single germlines over evolutionary timescales.This article is part of the themed issue 'The major synthetic evolutionary transitions'.

Some new sharp bounds for the spectral radius of a nonnegative matrix and its application

In this paper, we give some new sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. Using these bounds, we obtain some new and improved bounds for the signless Laplacian spectral radius of a graph or a digraph.

How to describe univariate data

Univariate analysis has the purpose to describe a single variable distribution in one sample. It is the first important step of every clinical trial. In this short review, we focus on this analysis, the methods that authors should use to report this type of data, information that they should not miss and mistakes that they must avoid.

Effect of Resting-State fNIRS Scanning Duration on Functional Brain Connectivity and Graph Theory Metrics of Brain Network

As an emerging brain imaging technique, functional near infrared spectroscopy (fNIRS) has attracted widespread attention for advancing resting-state functional connectivity (FC) and graph theoretical analyses of brain networks. However, it remains largely unknown how the duration of the fNIRS signal scanning is related to stable and reproducible functional brain network features. To answer this question, we collected resting-state fNIRS signals (10-min duration, two runs) from 18 participants and then truncated the hemodynamic time series into 30-s time bins that ranged from 1 to 10 min. Measures of nodal efficiency, nodal betweenness, network local efficiency, global efficiency, and clustering coefficient were computed for each subject at each fNIRS signal acquisition duration. Analyses of the stability and between-run reproducibility were performed to identify optimal time length for each measure. We found that the FC, nodal efficiency and nodal betweenness stabilized and were reproducible after 1 min of fNIRS signal acquisition, whereas network clustering coefficient, local and global efficiencies stabilized after 1 min and were reproducible after 5 min of fNIRS signal acquisition for only local and global efficiencies. These quantitative results provide direct evidence regarding the choice of the resting-state fNIRS scanning duration for functional brain connectivity and topological metric stability of brain network connectivity.

An Effective Computational Method Incorporating Multiple Secondary Structure Predictions in Topology Determination for Cryo-EM Images

A key idea in de novo modeling of a medium-resolution density image obtained from cryo-electron microscopy is to compute the optimal mapping between the secondary structure traces observed in the density image and those predicted on the protein sequence. When secondary structures are not determined precisely, either from the image or from the amino acid sequence of the protein, the computational problem becomes more complex. We present an efficient method that addresses the secondary structure placement problem in presence of multiple secondary structure predictions and computes the optimal mapping. We tested the method using 12 simulated images from α-proteins and two Cryo-EM images of α-β proteins. We observed that the rank of the true topologies is consistently improved by using multiple secondary structure predictions instead of a single prediction. The results show that the algorithm is robust and works well even when errors/misses in the predicted secondary structures are present in the image or the sequence. The results also show that the algorithm is efficient and is able to handle proteins with as many as 33 helices.