DReSS: a method to quantitatively describe the influence of structural perturbations on state spaces of genetic regulatory networks

Structures of genetic regulatory networks are not fixed. These structural perturbations can cause changes to the reachability of systems’ state spaces. As system structures are related to genotypes and state spaces are related to phenotypes, it is important to study the relationship between structures and state spaces. However, there is still no method can quantitively describe the reachability differences of two state spaces caused by structural perturbations. Therefore, Difference in Reachability between State Spaces (DReSS) is proposed. DReSS index family can quantitively describe differences of reachability, attractor sets between two state spaces and can help find the key structure in a system, which may influence system’s state space significantly. First, basic properties of DReSS including non-negativity, symmetry and subadditivity are proved. Then, typical examples are shown to explain the meaning of DReSS and the differences between DReSS and traditional graph distance. Finally, differences of DReSS distribution between real biological regulatory networks and random networks are compared. Results show most structural perturbations in biological networks tend to affect reachability inside and between attractor basins rather than to affect attractor set itself when compared with random networks, which illustrates that most genotype differences tend to influence the proportion of different phenotypes and only a few ones can create new phenotypes. DReSS can provide researchers with a new insight to study the relation between genotypes and phenotypes.

Network comparison and the within-ensemble graph distance

Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years, a multitude of diverse, ad hoc solutions to this problem have been introduced. Here, we propose that simple and well-understood ensembles of random networks—such as Erdős–Rényi graphs, random geometric graphs, Watts–Strogatz graphs, the configuration model and preferential attachment networks—are natural benchmarks for network comparison methods. Moreover, we show that the expected distance between two networks independently sampled from a generative model is a useful property that encapsulates many key features of that model. To illustrate our results, we calculate this within-ensemble graph distance and related quantities for classic network models (and several parameterizations thereof) using 20 distance measures commonly used to compare graphs. The within-ensemble graph distance provides a new framework for developers of graph distances to better understand their creations and for practitioners to better choose an appropriate tool for their particular task.

A Whole-Brain and Cross-Diagnostic Perspective on Functional Brain Network Dysfunction

A wide variety of mental disorders have been associated with resting-state functional network alterations, which are thought to contribute to the cognitive changes underlying mental illness. These observations appear to support theories postulating large-scale disruptions of brain systems in mental illness. However, existing approaches isolate differences in network organization without putting those differences in a broad, whole-brain perspective. Using a graph distance approach—connectome-wide similarity—we found that whole-brain resting-state functional network organization is highly similar across groups of individuals with and without a variety of mental diseases. This similarity was observed across autism spectrum disorder, attention-deficit hyperactivity disorder, and schizophrenia. Nonetheless, subtle differences in network graph distance were predictive of diagnosis, suggesting that while functional connectomes differ little across health and disease, those differences are informative. These results suggest a need to reevaluate neurocognitive theories of mental illness, with a role for subtle functional brain network changes in the production of an array of mental diseases. Such small network alterations suggest the possibility that small, well-targeted alterations to brain network organization may provide meaningful improvements for a variety of mental disorders.

OHKWR: Offline Handwritten Kannada Words Recognition using SVM Classifier with CNN

In field of handwriting recognition, Robust algorithms for recognition and character segmentation are presented for multilingual Indian archive images of Devanagari and Latin scripts. These report basically suffer from their format organizations, low print and local skews quality and contain intermixed messages (machine-printed and manually written). In order to overcome these drawbacks, a character segmentation algorithm is proposed for kannada handwriting recognition. In this work, in initial steps we are obtained the segmentation paths by using the characters of structural property and also the graph distance theory whereas overlapped and connected character are separated. Finally, we are calculated results by using the SVM classifier. In proposed recognition of character, they are three new geometrical shapes based on new features such as center pixel of character is obtained by first and second feature and third feature is calculation purpose we are used in neighborhood information of text pixels. Benchmarking results represent that proposed algorithms have best work identified with other contemporary methodologies, where best recognition rates and segmentation are obtained.

A New Study of Parikh Matrices Restricted to Terms

Parikh matrices as an extension of Parikh vectors are useful tools in arithmetizing words by numbers. This paper presents a further study of Parikh matrices by restricting the corresponding words to terms formed over a signature. Some [Formula: see text]-equivalence preserving rewriting rules for such terms are introduced. A characterization of terms that are only [Formula: see text]-equivalent to themselves is studied for binary signatures. Graphs associated to the equivalence classes of [Formula: see text]-equivalent terms are studied with respect to graph distance. Finally, the preservation of [Formula: see text]-equivalence under the term self-shuffle operator is studied.

Anomalous diffusion of random walk on random planar maps

We prove that the simple random walk on the uniform infinite planar triangulation (UIPT) typically travels graph distance at most $$n^{1/4 + o_n(1)}$$ n 1 / 4 + o n ( 1 ) in n units of time. Together with the complementary lower bound proven by Gwynne and Miller (2017) this shows that the typical graph distance displacement of the walk after n steps is $$n^{1/4 + o_n(1)}$$ n 1 / 4 + o n ( 1 ) , as conjectured by Benjamini and Curien (Geom Funct Anal 2(2):501–531, 2013. arXiv:1202.5454). More generally, we show that the simple random walks on a certain family of random planar maps in the $$\gamma $$ γ -Liouville quantum gravity (LQG) universality class for $$\gamma \in (0,2)$$ γ ∈ ( 0 , 2 ) —including spanning tree-weighted maps, bipolar-oriented maps, and mated-CRT maps—typically travels graph distance $$n^{1/d_\gamma + o_n(1)}$$ n 1 / d γ + o n ( 1 ) in n units of time, where $$d_\gamma $$ d γ is the growth exponent for the volume of a metric ball on the map, which was shown to exist and depend only on $$\gamma $$ γ by Ding and Gwynne (Commun Math Phys 374:1877–1934, 2018. arXiv:1807.01072). Since $$d_\gamma > 2$$ d γ > 2 , this shows that the simple random walk on each of these maps is subdiffusive. Our proofs are based on an embedding of the random planar maps under consideration into $${\mathbb {C}}$$ C wherein graph distance balls can be compared to Euclidean balls modulo subpolynomial errors. This embedding arises from a coupling of the given random planar map with a mated-CRT map together with the relationship of the latter map to SLE-decorated LQG.

Hypernetwork science via high-order hypergraph walks

We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods which then generalize to hypergraphs include connected component analyses, graph distance-based metrics such as closeness centrality, and motif-based measures such as clustering coefficients. We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods. Lastly, we apply three generative models to the data and find that basic hypergraph properties, such as density and degree distributions, do not necessarily control these new structural measurements. Our work demonstrates how analyses of hypergraph-structured data are richer when utilizing tools tailored to capture hypergraph-native phenomena, and suggests one possible avenue towards that end.