scholarly journals Fingerprints of cancer by persistent homology

2019 ◽  
Author(s):  
A. Carpio ◽  
L. L. Bonilla ◽  
J. C. Mathews ◽  
A. R. Tannenbaum
Keyword(s):  
Persistent Homology ◽  
Betti Numbers ◽  
Critical Value ◽  
Topological Data Analysis ◽  
Gene Expressions ◽  
Tissue Samples ◽  
Filtration Parameter ◽  
Different Types ◽  
Parameter Values ◽  
Single Cluster

AbstractWe have carried out a topological data analysis of gene expressions for different databases based on the Fermat distance between the z scores of different tissue samples. There is a critical value of the filtration parameter at which all clusters collapse in a single one. This critical value for healthy samples is gapless and smaller than that for cancerous ones. After collapse in a single cluster, topological holes persist for larger filtration parameter values in cancerous samples. Barcodes, persistence diagrams and Betti numbers as functions of the filtration parameter are different for different types of cancer and constitute fingerprints thereof.

scholarly journals Using Topological Data Analysis (TDA) and Persistent Homology to Analyze the Stock Markets in Singapore and Taiwan

2021 ◽  
Vol 9 ◽  
Author(s):  
Peter Tsung-Wen Yen ◽  
Siew Ann Cheong
Keyword(s):  
Data Analysis ◽  
Stock Markets ◽  
Persistent Homology ◽  
Betti Numbers ◽  
Stock Index ◽  
Topological Data Analysis ◽  
Series Data ◽  
Topological Features ◽  
Market Crashes ◽  
Topological Data

In recent years, persistent homology (PH) and topological data analysis (TDA) have gained increasing attention in the fields of shape recognition, image analysis, data analysis, machine learning, computer vision, computational biology, brain functional networks, financial networks, haze detection, etc. In this article, we will focus on stock markets and demonstrate how TDA can be useful in this regard. We first explain signatures that can be detected using TDA, for three toy models of topological changes. We then showed how to go beyond network concepts like nodes (0-simplex) and links (1-simplex), and the standard minimal spanning tree or planar maximally filtered graph picture of the cross correlations in stock markets, to work with faces (2-simplex) or any k-dim simplex in TDA. By scanning through a full range of correlation thresholds in a procedure called filtration, we were able to examine robust topological features (i.e. less susceptible to random noise) in higher dimensions. To demonstrate the advantages of TDA, we collected time-series data from the Straits Times Index and Taiwan Capitalization Weighted Stock Index (TAIEX), and then computed barcodes, persistence diagrams, persistent entropy, the bottleneck distance, Betti numbers, and Euler characteristic. We found that during the periods of market crashes, the homology groups become less persistent as we vary the characteristic correlation. For both markets, we found consistent signatures associated with market crashes in the Betti numbers, Euler characteristics, and persistent entropy, in agreement with our theoretical expectations.

scholarly journals Topological data analysis of vascular disease: A theoretical framework

2019 ◽  
Author(s):  
John Nicponski ◽  
Jae-Hun Jung
Keyword(s):  
Data Analysis ◽  
Vascular Disease ◽  
Projection Method ◽  
Persistent Homology ◽  
Theoretical Development ◽  
Topological Data Analysis ◽  
Real Patient ◽  
Different Types ◽  
Spherical Projection ◽  
Topological Data

AbstractVascular disease is a leading cause of death world wide and therefore the treatment thereof is critical. Understanding and classifying the types and levels of stenosis can lead to more accurate and better treatment of vascular disease. Some clinical techniques to measure stenosis from real patient data are invasive or of low accuracy.In this paper, we propose a new methodology, which can serve as a supplementary way of diagnosis to existing methods, to measure the degree of vascular disease using topological data analysis. We first proposed the critical failure value, which is an application of the 1-dimensional homology group to stenotic vessels as a generalization of the percent stenosis. We demonstrated that one can take important geometric data including size information from the persistent homology of a topological space. We conjecture that we may use persistent homology as a general tool to measure stenosis levels for many different types of stenotic vessels.We also proposed the spherical projection method, which is meant to allow for future classification of different types and levels of stenosis. We showed empirically using the spectral approximation of different vasculatures that this projection could provide a new medical index that measures the degree of vascular disease. Such a new index is obtained by calculating the persistence of the 2-dimensional homology of flows. We showed that the spherical projection method can differentiate between different cases of flows and reveal hidden patterns about the underlying blood flow characteristics, that is not apparent in the raw data. We showed that persistent homology can be used in conjunction with this technique to classify levels of stenosis.The main interest of this paper is to focus on the theoretical development of the framework for the proposed method using a simple set of vascular data.

scholarly journals Persistent Homology Analysis of RNA

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Adane L. Mamuye ◽  
Matteo Rucco ◽  
Luca Tesei ◽  
Emanuela Merelli
Keyword(s):  
Data Analysis ◽  
Rna Folding ◽  
Persistent Homology ◽  
Betti Numbers ◽  
Structural Features ◽  
Topological Data Analysis ◽  
Analysis Tool ◽  
Global Features ◽  
Folding Space ◽  
Topological Data

AbstractTopological data analysis has been recently used to extract meaningful information frombiomolecules. Here we introduce the application of persistent homology, a topological data analysis tool, for computing persistent features (loops) of the RNA folding space. The scaffold of the RNA folding space is a complex graph from which the global features are extracted by completing the graph to a simplicial complex via the notion of clique and Vietoris-Rips complexes. The resulting simplicial complexes are characterised in terms of topological invariants, such as the number of holes in any dimension, i.e. Betti numbers. Our approach discovers persistent structural features, which are the set of smallest components to which the RNA folding space can be reduced. Thanks to this discovery, which in terms of data mining can be considered as a space dimension reduction, it is possible to extract a new insight that is crucial for understanding the mechanism of the RNA folding towards the optimal secondary structure. This structure is composed by the components discovered during the reduction step of the RNA folding space and is characterized by minimum free energy.

scholarly journals Classification of apatite structures via topological data analysis: a framework for a ‘Materials Barcode’ representation of structure maps

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Scott Broderick ◽  
Ruhil Dongol ◽  
Tianmu Zhang ◽  
Krishna Rajan
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Crystal Chemistry ◽  
Persistent Homology ◽  
Hierarchical Classification ◽  
Topological Data Analysis ◽  
Learning Tool ◽  
Coordination Polyhedra ◽  
Machine Learning Tool ◽  
Topological Data

AbstractThis paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Using the apatite chemistry as a template, we track through the use of persistent homology the topological connectivity of input crystal chemistry descriptors on defining similarity between different stoichiometries of apatites. It is shown that TDA automatically identifies a hierarchical classification scheme within apatites based on the commonality of the number of discrete coordination polyhedra that constitute the structural building units common among the compounds. This information is presented in the form of a visualization scheme of a barcode of homology classifications, where the persistence of similarity between compounds is tracked. Unlike traditional perspectives of structure maps, this new “Materials Barcode” schema serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds.

Multi-omics approach to post-CABG renal impairment

2020 ◽  
Vol 41 (Supplement_2) ◽  
Author(s):  
C Boerschel ◽  
B Geelhoed ◽  
L Conradi ◽  
E Girdauskas ◽  
C Mueller ◽  
...  
Keyword(s):  
Renal Impairment ◽  
Leucine Zipper ◽  
Mixed Model ◽  
Artery Bypass ◽  
Bypass Graft ◽  
Control Cell ◽  
Integrated Approach ◽  
Cell Renewal ◽  
Gene Expressions ◽  
Tissue Samples

Abstract Background Renal impairment is a common complication after CABG (coronary artery bypass graft) surgery associated with an adverse outcome. Purpose To further characterize the molecular framework of the disease through omics analyses. Methods In N=165 CABG patients we performed multi-omics-analyses in preoperatively collected blood and tissue samples as well as 991 creatinine measurements. We used multivariable mixed-model regression analyses to analyse post-operative creatinine increase and to find common genetic polymorphisms, transcripts, metabolites and/or proteins associated with changes in postoperative creatinine increase. Multiple testing was accounted for by setting a 5%-limit on the false discovery rate (FDR) using the Benjamini-Hochberg procedure. Results Post-operative increase of log transformed creatinine was 0.035 (8%); 95% confidence interval (CI) 0.025, 0.045; P<0.001. We identified 55 gene expressions and two proteins associated with post-CABG renal impairment. On the metabolomic and single nucleotide point mutation (SNP) level, no relevant targets were found. The three most important identified gene expressions were MIR3202.1 (beta of log transformed creatinine increase per standard deviation gene expression increase −0.034; 95% CI: −0.048, 0.020; P<0.001), LOC105374386 (−0.032; 95% CI: −0.046, 0.019; P<0.001) and maternal embryonic leucine zipper kinase (MELK) (−0.022; 95% CI: −0.032, 0.013; P<0.001). Expression of all three was associated with a lower risk of post-CABG renal impairment. The same applies to the identified protein CAPRIN2 (−0.042; 95% CI: −0.062, 0.022; P<0.001), while expression of the protein TUBB6 was associated with a higher risk (0.033; 95% CI: 0.017, 0.048; P<0.001). Conclusions In an integrated approach we identified omics-biomarkers for the prediction of renal impairment after CABG surgery. The underlying pathophysiological associations of these genes and proteins are not fully understood. MELK might be an interesting target for further investigations, as it plays a prominent role in cell cycle control, cell proliferation, apoptosis, cell migration and cell renewal. Our results may help to better identify individuals at risk and lay the methodological groundwork for further omics analyses. Funding Acknowledgement Type of funding source: None

scholarly journals Differential Expression of Peroxisomal Proteins in Distinct Types of Parotid Gland Tumors

2021 ◽  
Vol 22 (15) ◽  
pp. 7872
Author(s):  
Malin Tordis Meyer ◽  
Christoph Watermann ◽  
Thomas Dreyer ◽  
Steffen Wagner ◽  
Claus Wittekindt ◽  
...  
Keyword(s):  
Redox Balance ◽  
Matrix Proteins ◽  
Parotid Tumor ◽  
Gene Expressions ◽  
Tissue Samples ◽  
Cellular Redox ◽  
Tumor Subtypes ◽  
Parotid Tumors ◽  
Aggressive Tumors

Salivary gland cancers are rare but aggressive tumors that have poor prognosis and lack effective cure. Of those, parotid tumors constitute the majority. Functioning as metabolic machinery contributing to cellular redox balance, peroxisomes have emerged as crucial players in tumorigenesis. Studies on murine and human cells have examined the role of peroxisomes in carcinogenesis with conflicting results. These studies either examined the consequences of altered peroxisomal proliferators or compared their expression in healthy and neoplastic tissues. None, however, examined such differences exclusively in human parotid tissue or extended comparison to peroxisomal proteins and their associated gene expressions. Therefore, we examined differences in peroxisomal dynamics in parotid tumors of different morphologies. Using immunofluorescence and quantitative PCR, we compared the expression levels of key peroxisomal enzymes and proliferators in healthy and neoplastic parotid tissue samples. Three parotid tumor subtypes were examined: pleomorphic adenoma, mucoepidermoid carcinoma and acinic cell carcinoma. We observed higher expression of peroxisomal matrix proteins in neoplastic samples with exceptional down regulation of certain enzymes; however, the degree of expression varied between tumor subtypes. Our findings confirm previous experimental results on other organ tissues and suggest peroxisomes as possible therapeutic targets or markers in all or certain subtypes of parotid neoplasms.

scholarly journals Topological Segmentation of Time-Varying Functional Connectivity Highlights the Role of Preferred Cortical Circuits

2020 ◽  
Author(s):  
Jacob Billings ◽  
Manish Saggar ◽  
Shella Keilholz ◽  
Giovanni Petri
Keyword(s):  
Functional Connectivity ◽  
Brain Function ◽  
Persistent Homology ◽  
Brain Regions ◽  
Topological Data Analysis ◽  
Time Varying ◽  
Imaging Data ◽  
Experimental Conditions ◽  
Common Time ◽  
Brain Imaging Data

Functional connectivity (FC) and its time-varying analogue (TVFC) leverage brain imaging data to interpret brain function as patterns of coordinating activity among brain regions. While many questions remain regarding the organizing principles through which brain function emerges from multi-regional interactions, advances in the mathematics of Topological Data Analysis (TDA) may provide new insights into the brain’s spontaneous self-organization. One tool from TDA, “persistent homology”, observes the occurrence and the persistence of n-dimensional holes presented in the metric space over a dataset. The occurrence of n-dimensional holes within the TVFC point cloud may denote conserved and preferred routes of information flow among brain regions. In the present study, we compare the use of persistence homology versus more traditional TVFC metrics at the task of segmenting brain states that differ across a common time-series of experimental conditions. We find that the structures identified by persistence homology more accurately segment the stimuli, more accurately segment volunteer performance during experimentally defined tasks, and generalize better across volunteers. Finally, we present empirical and theoretical observations that interpret brain function as a topological space defined by cyclic and interlinked motifs among distributed brain regions, especially, the attention networks.

scholarly journals Topological data analysis for true step detection in periodic piecewise constant signals

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180027 ◽  
Author(s):  
Firas A. Khasawneh ◽  
Elizabeth Munch
Keyword(s):  
Data Analysis ◽  
Persistent Homology ◽  
Topological Data Analysis ◽  
Future Research ◽  
Accurate Identification ◽  
Piecewise Constant ◽  
Higher Dimensional ◽  
Powerful Approach ◽  
Hadamard Transforms ◽  
Topological Data

This paper introduces a simple yet powerful approach based on topological data analysis for detecting true steps in a periodic, piecewise constant (PWC) signal. The signal is a two-state square wave with randomly varying in-between-pulse spacing, subject to spurious steps at the rising or falling edges which we call digital ringing. We use persistent homology to derive mathematical guarantees for the resulting change detection which enables accurate identification and counting of the true pulses. The approach is tested using both synthetic and experimental data obtained using an engine lathe instrumented with a laser tachometer. The described algorithm enables accurate and automatic calculations of the spindle speed without any choice of parameters. The results are compared with the frequency and sequency methods of the Fourier and Walsh–Hadamard transforms, respectively. Both our approach and the Fourier analysis yield comparable results for pulses with regular spacing and digital ringing while the latter causes large errors using the Walsh–Hadamard method. Further, the described approach significantly outperforms the frequency/sequency analyses when the spacing between the peaks is varied. We discuss generalizing the approach to higher dimensional PWC signals, although using this extension remains an interesting question for future research.

Hypernetwork models based on random hypergraphs

2019 ◽  
Vol 30 (08) ◽  
pp. 1950052
Author(s):  
Feng Hu ◽  
Jin-Li Guo ◽  
Fa-Xu Li ◽  
Hai-Xing Zhao
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
World Systems ◽  
Uniform Hypergraphs ◽  
Different Types ◽  
Powerful Means ◽  
Simulation Results ◽  
Parameter Values ◽  
Random Hypergraphs

Hypernetworks are ubiquitous in real-world systems. They provide a powerful means of accurately depicting networks of different types of entity and will attract more attention from researchers in the future. Most previous hypernetwork research has been focused on the application and modeling of uniform hypernetworks, which are based on uniform hypergraphs. However, random hypernetworks are generally more common, therefore, it is useful to investigate the evolution mechanisms of random hypernetworks. In this paper, we construct three dynamic evolutional models of hypernetworks, namely the equal-probability random hypernetwork model, the Poisson-probability random hypernetwork model and the certain-probability random hypernetwork model. Furthermore, we analyze the hyperdegree distributions of the three models with mean-field theory, and we simulate each model numerically with different parameter values. The simulation results agree well with the results of our theoretical analysis, and the findings indicate that our models could help understand the structure and evolution mechanisms of real systems.

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