arXiv subjects

Karl R. B. Schmitt

Publications and source records attributed to Karl R. B. Schmitt.

5 recordsLinked to original sources

arXiv2019

Predicting Graph Categories from Structural Properties

This paper has been withdrawn from arXiv.org due to a disagreement among the authors related to several peer-review comments received prior to submission on arXiv.org. Even though the current version of this paper is withdrawn, there was no disagreement between authors on the novel work in this paper. One specific issue was the discussion of related work by Ikehara \& Clauset (found on page 8 of the previously posted version). Peer-review comments on a similar version made ALL authors aware that the discussion misrepresented their work prior to submission to arXiv.org. However, some authors choose to post to arXiv a minimally updated version without the consent of all authors or properly addressing this attribution issue. ================ Original Paper Abstract: Complex networks are often categorized according to the underlying phenomena that they represent such as molecular interactions, re-tweets, and brain activity. In this work, we investigate the problem of predicting the category (domain) of arbitrary networks. This includes complex networks from different domains as well as synthetically generated graphs from five different network models. A classification accuracy of $96.6\%$ is achieved using a random forest classifier with both real and synthetic networks. This work makes two important findings. First, our results indicate that complex networks from various domains have distinct structural properties that allow us to predict with high accuracy the category of a new previously unseen network. Second, synthetic graphs are trivial to classify as the classification model can predict with near-certainty the network model used to generate it. Overall, the results demonstrate that networks drawn from different domains (and network models) are trivial to distinguish using only a handful of simple structural properties.

cs.SI↗

arXiv2017

Network Classification and Categorization

To the best of our knowledge, this paper presents the first large-scale study that tests whether network categories (e.g., social networks vs. web graphs) are distinguishable from one another (using both categories of real-world networks and synthetic graphs). A classification accuracy of $94.2\%$ was achieved using a random forest classifier with both real and synthetic networks. This work makes two important findings. First, real-world networks from various domains have distinct structural properties that allow us to predict with high accuracy the category of an arbitrary network. Second, classifying synthetic networks is trivial as our models can easily distinguish between synthetic graphs and the real-world networks they are supposed to model.

cs.SI↗

arXiv2015

A Graph Theoretical Analysis of the Number of Edges in k-dense Graphs

Due to the increasing discovery and implementation of networks within all disciplines of life, the study of subgraph connectivity has become increasingly important. Motivated by the idea of community (or sub-graph) detection within a network/graph, we focused on finding characterizations of k-dense communities. For each edge $uv\in E(G)$, the {\bf edge multiplicity} of $uv$ in $G$ is given by $m_G(uv)=|N_{G}(u)\cap N_{G}(v)|.$ For an integer $k$ with $k\ge 2$, a {\bf $k$-dense community} of a graph $G$, denoted by $DC_k(G)$, is a maximal connected subgraph of $G$ induced by the vertex set $$V_{DC_k(G)} = \{v\in V(G) : \exists u\in V(G)\ {\rm such\ that\} uv\in E(G)\ {\rm and\} m_{DC_{k(G)}}(uv)\ge k-2\}.$$ In this research, we characterize which graphs are $k$-dense but not $(k+1)$-dense for some values of $k$ and study the minimum and maximum number of edges such graphs can have. A better understanding of $k$-dense sub-graphs (or communities) helps in the study of the connectivity of large complex graphs (or networks) in the real world.

math.CO↗

arXiv2013

A hierarchical network heuristic for solving the orientation problem in genome assembly

In the past several years, the problem of genome assembly has received considerable attention from both biologists and computer scientists. An important component of current assembly methods is the scaffolding process. This process involves building ordered and oriented linear collections of contigs (continuous overlapping sequence reads) called scaffolds and relies on the use of mate pair data. A mate pair is a set of two reads that are sequenced from the ends of a single fragment of DNA, and therefore have opposite mutual orientations. When two reads of a mate-pair are placed into two different contigs, one can infer the mutual orientation of these contigs. While several orientation algorithms exist as part of assembly programs, all encounter challenges while solving the orientation problem due to errors from mis-assemblies in contigs or errors in read placements. In this paper we present an algorithm based on hierarchical clustering that independently solves the orientation problem and is robust to errors. We show that our algorithm can correctly solve the orientation problem for both faux (generated) assembly data and real assembly data for {\em R. sphaeroides bacteria}. We demonstrate that our algorithm is stable to both changes in the initial orientations as well as noise in the data, making it advantageous compared to traditional approaches.

q-bio.GN↗

arXiv2009

Complex Dynamics and Synchronization of Delayed-Feedback Nonlinear Oscillators

We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital-signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized even when the coupling between them is changing unpredictably.

nlin.CD↗