Frequent Subgraph Mining in Outerplanar Graphs

In recent years there has been an increased interest in frequent pattern discovery in large databases of graph structured objects. While the frequent connected subgraph mining problem for tree datasets can be solved in incremental polynomial time, it becomes intractable for arbitrary graph databases. Existing approaches have therefore resorted to various heuristic strategies and restrictions of the search space, but have not identified a practically relevant tractable graph class beyond trees. In this paper, we define the class of so called tenuous outerplanar graphs, a strict generalization of trees, develop a frequent subgraph mining algorithm for tenuous outerplanar graphs that works in incremental polynomial time, and evaluate the algorithm empirically on the NCI molecular graph dataset

Frequent Subgraph Mining in Outerplanar Graphs

In recent years there has been an increased interest in frequent pattern discovery in large databases of graph structured objects. While the frequent connected subgraph mining problem for tree datasets can be solved in incremental polynomial time, it becomes intractable for arbitrary graph databases. Existing approaches have therefore resorted to various heuristic strategies and restrictions of the search space, but have not identified a practically relevant tractable graph class beyond trees. In this paper, we define the class of so called tenuous outerplanar graphs, a strict generalization of trees, develop a frequent subgraph mining algorithm for tenuous outerplanar graphs that works in incremental polynomial time, and evaluate the algorithm empirically on the NCI molecular graph dataset

Effective Privacy Amplification for Secure Classical Communications

We study the practical effectiveness of privacy amplification for classical key-distribution schemes. We find that in contrast to quantum key distribution schemes, the high fidelity of the raw key generated in classical systems allow the users to always sift a secure shorter key if they have an upper bound on the eavesdropper probability to correctly guess the exchanged key-bits. The number of privacy amplification iterations needed to achieve information leak of 10^-8 in existing classical communicators is 2 or 3 resulting in a corresponding slowdown 4 to 8. We analyze the inherent tradeoff between the number of iterations and the security of the raw key. This property which is unique to classical key distribution systems render them highly useful for practical, especially for noisy channels where sufficiently low quantum bit error ratios are difficult to achieve.Comment: 11 pages, 3 figure

An exactly mass conserving space-time embedded-hybridized discontinuous Galerkin method for the Navier-Stokes equations on moving domains

This paper presents a space-time embedded-hybridized discontinuous Galerkin (EHDG) method for the Navier--Stokes equations on moving domains. This method uses a different hybridization compared to the space-time hybridized discontinuous Galerkin (HDG) method we presented previously in (Int. J. Numer. Meth. Fluids 89: 519--532, 2019). In the space-time EHDG method the velocity trace unknown is continuous while the pressure trace unknown is discontinuous across facets. In the space-time HDG method, all trace unknowns are discontinuous across facets. Alternatively, we present also a space-time embedded discontinuous Galerkin (EDG) method in which all trace unknowns are continuous across facets. The advantage of continuous trace unknowns is that the formulation has fewer global degrees-of-freedom for a given mesh than when using discontinuous trace unknowns. Nevertheless, the discrete velocity field obtained by the space-time EHDG and EDG methods, like the space-time HDG method, is exactly divergence-free, even on moving domains. However, only the space-time EHDG and HDG methods result in divergence-conforming velocity fields. An immediate consequence of this is that the space-time EHDG and HDG discretizations of the conservative form of the Navier--Stokes equations are energy stable. The space-time EDG method, on the other hand, requires a skew-symmetric formulation of the momentum advection term to be energy-stable. Numerical examples will demonstrate the differences in solution obtained by the space-time EHDG, EDG, and HDG methods

A locally conservative and energy-stable finite element for the Navier--Stokes problem on time-dependent domains

We present a finite element method for the incompressible Navier--Stokes problem that is locally conservative, energy-stable and pressure-robust on time-dependent domains. To achieve this, the space--time formulation of the Navier--Stokes problem is considered. The space--time domain is partitioned into space--time slabs which in turn are partitioned into space--time simplices. A combined discontinuous Galerkin method across space--time slabs, and space--time hybridized discontinuous Galerkin method within a space--time slab, results in an approximate velocity field that is $H({\rm div})$-conforming and exactly divergence-free, even on time-dependent domains. Numerical examples demonstrate the convergence properties and performance of the method

Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains

This paper presents the first analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains. The analysis is based on non-standard local trace and inverse inequalities that are anisotropic in the spatial and time steps. We prove well-posedness of the discrete problem and provide a priori error estimates in a mesh-dependent norm. Convergence theory is validated by a numerical example solving the advection--diffusion problem on a time-dependent domain for approximations of various polynomial degree

Mitochondrial ROS Signaling in Organismal Homeostasis

Generation, transformation, and utilization of organic molecules in support of cellular differentiation, growth, and maintenance are basic tenets that define life. In eukaryotes, mitochondrial oxygen consumption plays a central role in these processes. During the process of oxidative phosphorylation, mitochondria utilize oxygen to generate ATP from organic fuel molecules but in the process also produce reactive oxygen species (ROS). While ROS have long been appreciated for their damage-promoting, detrimental effects, there is now a greater understanding of their roles as signaling molecules. Here, we review mitochondrial ROS-mediated signaling pathways with an emphasis on how they are involved in various basal and adaptive physiological responses that control organismal homeostasis