Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasi-cliques from a graph is a robust way to detect densely connected structures with applications in bioinformatics and social network analysis. However, enumerating quasi-cliques in a graph is a challenging problem, even harder than the problem of enumerating cliques. We consider the enumeration of top- k degree-based quasi-cliques and make the following contributions: (1) we show that even the problem of detecting whether a given quasi-clique is maximal (i.e., not contained within another quasi-clique) is NP-hard. (2) We present a novel heuristic algorithm K ernel QC to enumerate the k largest quasi-cliques in a graph. Our method is based on identifying kernels of extremely dense subgraphs within a graph, followed by growing subgraphs around these kernels, to arrive at quasi-cliques with the required densities. (3) Experimental results show that our algorithm accurately enumerates quasi-cliques from a graph, is much faster than current state-of-the-art methods for quasi-clique enumeration (often more than three orders of magnitude faster), and can scale to larger graphs than current methods.

We classify the functions f : N 2 → N which are stably computable by output-oblivious Stochastic Chemical Reaction Networks (CRNs), i.e., systems of reactions in which output species are never reactants. While it is known that precisely the semilinear functions are stably computable by CRNs, such CRNs sometimes rely on initially producing too many output species, and then consuming the excess in order to reach a correct stable state. These CRNs may be difficult to integrate into larger systems: if the output of a CRN C becomes the input to a downstream CRN C , then C could inadvertently consume too many outputs before C stabilizes. If, on the other hand, C is output-oblivious then C may consume C's output as soon as it is available. In this work we prove that a semilinear function f : N 2 → N is stably computable by an output-oblivious CRN with a leader if and only if it is both increasing and either grid-affine (intuitively, its domains are congruence classes), or the minimum of a finite set of fissure functions (intuitively, functions behaving like the min function).

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In this paper, we present the CET-LATS (Compressing Evolution of TINs from Location Aware Time Series) system, which enables testing the impacts of various compression approaches on evolving Triangulated Irregular Networks (TINs). Specifically, we consider the settings in which values measured in distinct locations and at different time instants, are represented as time series of the corresponding measurements, generating a sequence of TINs. Different compression techniques applied to location-specific time series may have different impacts on the representation of the global evolution of TINs-depending on the distance functions used to evaluate the distortion. CET-LATS users can view and analyze compression vs. (im)precision trade-offs over multiple compression methods and distance functions, and decide which method works best for their application. We also provide an option to investigate the impact of the choice of a compression method on the quality of prediction. Our prototype is a web-based system using Flask, a lightweight Python framework, relying on Apache Spark for data management and JSON files to communicate with the front-end, enabling extensibility in terms of adding new data sources as well as compression techniques, distance functions and prediction methods. CCS CONCEPTS • Information systems → Spatial-temporal systems; Web applications.

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