scholarly journals Path homologies of motifs and temporal network representations

2022 ◽  
Vol 7 (1) ◽  
Author(s):  
Samir Chowdhury ◽  
Steve Huntsman ◽  
Matvey Yutin
Keyword(s):  
Complex Networks ◽  
Directed Acyclic Graphs ◽  
Complete Characterization ◽  
Temporal Network ◽  
Temporal Networks ◽  
Acyclic Graphs ◽  
Bona Fide ◽  
Insight Into ◽  
Theoretical Developments

AbstractPath homology is a powerful method for attaching algebraic invariants to digraphs. While there have been growing theoretical developments on the algebro-topological framework surrounding path homology, bona fide applications to the study of complex networks have remained stagnant. We address this gap by presenting an algorithm for path homology that combines efficient pruning and indexing techniques and using it to topologically analyze a variety of real-world complex temporal networks. A crucial step in our analysis is the complete characterization of path homologies of certain families of small digraphs that appear as subgraphs in these complex networks. These families include all digraphs, directed acyclic graphs, and undirected graphs up to certain numbers of vertices, as well as some specially constructed cases. Using information from this analysis, we identify small digraphs contributing to path homology in dimension two for three temporal networks in an aggregated representation and relate these digraphs to network behavior. We then investigate alternative temporal network representations and identify complementary subgraphs as well as behavior that is preserved across representations. We conclude that path homology provides insight into temporal network structure, and in turn, emergent structures in temporal networks provide us with new subgraphs having interesting path homology.

scholarly journals Adjustment for time-invariant and time-varying confounders in ‘unexplained residuals’ models for longitudinal data within a causal framework and associated challenges

2018 ◽  
Vol 28 (5) ◽  
pp. 1347-1364 ◽  
Author(s):  
KF Arnold ◽  
GTH Ellison ◽  
SC Gadd ◽  
J Textor ◽  
PWG Tennant ◽  
...  
Keyword(s):  
Directed Acyclic Graphs ◽  
Regression Methods ◽  
Modelling Framework ◽  
Acyclic Graphs ◽  
Confounding Variables ◽  
Confounder Adjustment ◽  
Causal Framework ◽  
Distal Outcome ◽  
Time Invariant ◽  
Insight Into

‘Unexplained residuals’ models have been used within lifecourse epidemiology to model an exposure measured longitudinally at several time points in relation to a distal outcome. It has been claimed that these models have several advantages, including: the ability to estimate multiple total causal effects in a single model, and additional insight into the effect on the outcome of greater-than-expected increases in the exposure compared to traditional regression methods. We evaluate these properties and prove mathematically how adjustment for confounding variables must be made within this modelling framework. Importantly, we explicitly place unexplained residual models in a causal framework using directed acyclic graphs. This allows for theoretical justification of appropriate confounder adjustment and provides a framework for extending our results to more complex scenarios than those examined in this paper. We also discuss several interpretational issues relating to unexplained residual models within a causal framework. We argue that unexplained residual models offer no additional insights compared to traditional regression methods, and, in fact, are more challenging to implement; moreover, they artificially reduce estimated standard errors. Consequently, we conclude that unexplained residual models, if used, must be implemented with great care.

scholarly journals CAPRI: Efficient Inference of Cancer Progression Models from Cross-sectional Data

2014 ◽  
Author(s):  
Daniele Ramazzotti ◽  
Giulio Caravagna ◽  
Loes Olde Loohuis ◽  
Alex Graudenzi ◽  
Ilya Korsunsky ◽  
...  
Keyword(s):  
Cancer Progression ◽  
Directed Acyclic Graphs ◽  
The Cancer Genome Atlas ◽  
Scoring Method ◽  
Cross Sectional ◽  
Progression Model ◽  
Acyclic Graphs ◽  
Cancer Genome Atlas ◽  
Atypical Chronic Myeloid Leukemia ◽  
Insight Into

We devise a novel inference algorithm to effectively solve the cancer progression model reconstruction problem. Our empirical analysis of the accuracy and convergence rate of our algorithm, CAncer PRogression Inference (CAPRI), shows that it outperforms the state-of-the-art algorithms addressing similar problems. Motivation: Several cancer-related genomic data have become available (e.g., The Cancer Genome Atlas, TCGA) typically involving hundreds of patients. At present, most of these data are aggregated in a cross-sectional fashion providing all measurements at the time of diagnosis. Our goal is to infer cancer ?progression? models from such data. These models are represented as directed acyclic graphs (DAGs) of collections of ?selectivity? relations, where a mutation in a gene A ?selects? for a later mutation in a gene B. Gaining insight into the structure of such progressions has the potential to improve both the stratification of patients and personalized therapy choices. Results: The CAPRI algorithm relies on a scoring method based on a probabilistic theory developed by Suppes, coupled with bootstrap and maximum likelihood inference. The resulting algorithm is efficient, achieves high accuracy, and has good complexity, also, in terms of convergence properties. CAPRI performs especially well in the presence of noise in the data, and with limited sample sizes. Moreover CAPRI, in contrast to other approaches, robustly reconstructs different types of confluent trajectories despite irregularities in the data. We also report on an ongoing investigation using CAPRI to study atypical Chronic Myeloid Leukemia, in which we uncovered non trivial selectivity relations and exclusivity patterns among key genomic events.

A Note on a Result of Ghosh and Sinha

1980 ◽  
Vol 29 (3-4) ◽  
pp. 169-172
Author(s):  
Bikas Kumar Sinha ◽  
Banshi Badan Mukhopadhyay
Keyword(s):  
Linear Model ◽  
Likelihood Ratio Test ◽  
Covariance Structure ◽  
Complete Characterization ◽  
Alternative Proof ◽  
Design Matrix ◽  
Ratio Test ◽  
Normal Linear Model ◽  
Insight Into

For the usual normal linear model with an lntraclass covariance structure, Ghosh and Sinha (1978) has given a complete characterization of tho design matrix for the robustness of the likelihood ratio test for linear hypotheses. We indicate here an alternative proof of the result which gives a better Insight into the problem.

scholarly journals The linearization problem of a binary quadratic problem and its applications

2021 ◽  
Author(s):  
Hao Hu ◽  
Renata Sotirov
Keyword(s):  
Shortest Path ◽  
Quadratic Function ◽  
Directed Acyclic Graphs ◽  
Complete Characterization ◽  
Shortest Path Problem ◽  
Quadratic Problem ◽  
Lower Bounding ◽  
Linearization Problem ◽  
Binary Quadratic Problem

AbstractWe provide several applications of the linearization problem of a binary quadratic problem. We propose a new lower bounding strategy, called the linearization-based scheme, that is based on a simple certificate for a quadratic function to be non-negative on the feasible set. Each linearization-based bound requires a set of linearizable matrices as an input. We prove that the Generalized Gilmore–Lawler bounding scheme for binary quadratic problems provides linearization-based bounds. Moreover, we show that the bound obtained from the first level reformulation linearization technique is also a type of linearization-based bound, which enables us to provide a comparison among mentioned bounds. However, the strongest linearization-based bound is the one that uses the full characterization of the set of linearizable matrices. We also present a polynomial-time algorithm for the linearization problem of the quadratic shortest path problem on directed acyclic graphs. Our algorithm gives a complete characterization of the set of linearizable matrices for the quadratic shortest path problem.

scholarly journals New insight into the biochemical mechanisms regulating auxin transport in plants

2007 ◽  
Vol 401 (3) ◽  
pp. 613-622 ◽  
Author(s):  
Ian D. Kerr ◽  
Malcolm J. Bennett
Keyword(s):  
Auxin Transport ◽  
Future Research ◽  
Research Directions ◽  
The Past ◽  
Bona Fide ◽  
Future Research Directions ◽  
Biochemical Mechanisms ◽  
Ylacetic Acid ◽  
Insight Into

The transport of the plant hormone auxin has been under intense investigation since its identification 80 years ago. Studies have gradually refined our understanding of the importance of auxin transport in many aspects of plant signalling and development, and the focus has intensified in recent years towards the identification of the proteins involved in auxin transport and their functional mechanism. Within the past 18 months, the field has progressed rapidly, with confirmation that several distinct classes of proteins, previously dubbed as ‘putative auxin permeases’ or ‘auxin transport facilitators’, are bona fide transporters of IAA (indol-3-ylacetic acid). In this review we will appraise the recent transport data and highlight likely future research directions, including the characterization of auxiliary proteins necessary for the regulation of auxin transporters.

scholarly journals Faster algorithms for counting subgraphs in sparse graphs

Algorithmica ◽  
2021 ◽  
Author(s):  
Marco Bressan
Keyword(s):  
Directed Acyclic Graphs ◽  
Counting Problem ◽  
Sparse Graphs ◽  
Acyclic Graphs ◽  
Degeneracy Graphs ◽  
Counting Algorithms ◽  
Complete Bipartite Graphs ◽  
Host Graph ◽  
Pattern Graph

AbstractGiven a k-node pattern graph H and an n-node host graph G, the subgraph counting problem asks to compute the number of copies of H in G. In this work we address the following question: can we count the copies of H faster if G is sparse? We answer in the affirmative by introducing a novel tree-like decomposition for directed acyclic graphs, inspired by the classic tree decomposition for undirected graphs. This decomposition gives a dynamic program for counting the homomorphisms of H in G by exploiting the degeneracy of G, which allows us to beat the state-of-the-art subgraph counting algorithms when G is sparse enough. For example, we can count the induced copies of any k-node pattern H in time $$2^{O(k^2)} O(n^{0.25k + 2} \log n)$$ 2 O ( k 2 ) O ( n 0.25 k + 2 log n ) if G has bounded degeneracy, and in time $$2^{O(k^2)} O(n^{0.625k + 2} \log n)$$ 2 O ( k 2 ) O ( n 0.625 k + 2 log n ) if G has bounded average degree. These bounds are instantiations of a more general result, parameterized by the degeneracy of G and the structure of H, which generalizes classic bounds on counting cliques and complete bipartite graphs. We also give lower bounds based on the Exponential Time Hypothesis, showing that our results are actually a characterization of the complexity of subgraph counting in bounded-degeneracy graphs.

Skeletal elements of crinoid echinoderms: High-resolution structural and microanalytical results

1983 ◽  
Vol 41 ◽  
pp. 194-195
Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor
Keyword(s):  
High Resolution ◽  
Marine Invertebrates ◽  
Sea Urchins ◽  
Structural Features ◽  
Sea Stars ◽  
High Resolution Tem ◽  
Relationship Of ◽  
The Relationship ◽  
Insight Into

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.

Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites

1982 ◽  
Vol 10 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. Kumar ◽  
C. W. Bert
Keyword(s):  
Response Characteristic ◽  
Cord Compression ◽  
Complete Characterization ◽  
Strain Response ◽  
Strain Gages ◽  
Experimental Characterization ◽  
Rubber Composites ◽  
Stress Strain ◽  
Strain Data

Abstract Unidirectional cord-rubber specimens in the form of tensile coupons and sandwich beams were used. Using specimens with the cords oriented at 0°, 45°, and 90° to the loading direction and appropriate data reduction, we were able to obtain complete characterization for the in-plane stress-strain response of single-ply, unidirectional cord-rubber composites. All strains were measured by means of liquid mercury strain gages, for which the nonlinear strain response characteristic was obtained by calibration. Stress-strain data were obtained for the cases of both cord tension and cord compression. Materials investigated were aramid-rubber, polyester-rubber, and steel-rubber.

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