Cdot Log Research Articles

BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs

Edge-coloured directed graphs provide an essential structure for modelling and analysis of complex systems arising in many scientific disciplines (e.g. feature-oriented systems, gene regulatory networks, etc.). One of the fundamental problems for edge-coloured graphs is the detection of strongly connected components, or SCCs. The size of edge-coloured graphs appearing in practice can be enormous both in the number of vertices and colours. The large number of vertices prevents us from analysing such graphs using explicit SCC detection algorithms, such as Tarjan's, which motivates the use of a symbolic approach. However, the large number of colours also renders existing symbolic SCC detection algorithms impractical. This paper proposes a novel algorithm that symbolically computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $O(p \cdot n \cdot log~n)$ symbolic steps, where $p$ is the number of colours and $n$ is the number of vertices. We evaluate the algorithm using an experimental implementation based on binary decision diagrams (BDDs). Specifically, we use our implementation to explore the SCCs of a large collection of coloured graphs (up to $2^{48}$) obtained from Boolean networks -- a modelling framework commonly appearing in systems biology.

Distributed Density Peaks Clustering Revisited

Density Peaks (DP) Clustering organizes data into clusters by finding peaks in dense regions. This involves computing density ( <inline-formula><tex-math notation="LaTeX">$\rho$</tex-math></inline-formula> ) and distance ( <inline-formula><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> ) of every point. As such, though DP has been very effective in producing high quality clusters, their complexity is O( <inline-formula><tex-math notation="LaTeX">$N^2$</tex-math></inline-formula> ) where <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> is the number of data points. In this paper, we propose a fast distributed density peaks clustering algorithm, FDDP, based on the z-value index. In FDDP, we first employ the z-value index to map multi-dimensional data points into one dimensional space, and then range-partition the data according to the z-value to balance the load across the processing nodes. We ensure minimal overlapping range to handle computations at the boundary points. We also propose FC, an efficient algorithm that employs a forward computing strategy to calculate <inline-formula><tex-math notation="LaTeX">$\rho$</tex-math></inline-formula> linearly. Additionally, we propose another algorithm, CB, which uses a caching and efficient searching strategy to compute <inline-formula><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> . Moreover, FDDP is able to reduce the time complexity from <inline-formula><tex-math notation="LaTeX">$O(N^2)$</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">$O(N\cdot log(N))$</tex-math></inline-formula> . We provide a theoretical analysis of FDDP and evaluated FDDP empirically. Our experimental results show that FDDP outperforms the state-of-the-art algorithms significantly.

A Logical Key Hierarchy Based Approach to Preserve Content Privacy in Decentralized Online Social Networks

Distributed Online Social Networks (DOSNs) have been proposed to shift the control over user data from a unique entity, the online social network provider, to the users of the DOSN themselves. In this paper we focus on the problem of preserving the privacy of the contents shared to large groups of users. In general, content privacy is enforced by encrypting the content, having only authorized parties being able to decrypt it. When efficiency has to be taken into account, new solutions have to be devised that: i) minimize the re-encryption of the contents published in a group when the composition of the group changes; and, ii) enable a fast distribution of the cryptographic keys to all the members ( $n$ n ) of a group, each time a set of users is removed from or added to the group by the group owner. Current solutions fall short in meeting the above criteria, while our approach requires only $O(d\cdot log_d (n))$ O ( d · l o g d ( n ) ) encryption operations when a user is removed from a group (where $d$ d is an input parameter of the system), and $O(2\cdot log_d (n))$ O ( 2 · l o g d ( n ) ) when a user joins the group. The effectiveness of our approach is evaluated through simulations based on a real online social network.

HUBBLE SPACE TELESCOPEMEASURES OF MASS ACCRETION RATES IN THE ORION NEBULA CLUSTER

The present observational understanding of the evolution of the mass accretion rates (Macc) in pre-main sequence stars is limited by the lack of accurate measurements of Macc over homogeneous and large statistical samples of young stars. Such observational effort is needed to properly constrain the theory of star formation and disk evolution. Based on HST/WFPC2 observations, we present a study of Macc for a sample of \sim 700 sources in the Orion Nebula Cluster, ranging from the Hydrogen-burning limit to M\ast \sim 2M\odot. We derive Macc from both the U-band excess and the H{\alpha} luminosity (LH{\alpha}), after determining empirically both the shape of the typical accretion spectrum across the Balmer jump and the relation between the accretion luminosity (Lacc) and LH{\alpha}, that is Lacc/L\odot = (1.31\pm0.03)\cdotLH{\alpha}/L\odot + (2.63\pm 0.13). Given our large statistical sample, we are able to accurately investigate relations between Macc and the parameters of the central star such as mass and age. We clearly find Macc to increase with stellar mass, and decrease over evolutionary time, but we also find strong evidence that the decay of Macc with stellar age occurs over longer timescales for more massive PMS stars. Our best fit relation between these parameters is given by: log(Macc/M\odot\cdotyr)=(-5.12 \pm 0.86) -(0.46 \pm 0.13) \cdot log(t/yr) -(5.75 \pm 1.47)\cdot log(M\ast/M\odot) + (1.17 \pm 0.23)\cdot log(t/yr) \cdot log(M\ast/M\odot). These results also suggest that the similarity solution model could be revised for sources with M\ast > 0.5M\odot. Finally, we do not find a clear trend indicating environmental effects on the accretion properties of the sources.

A Note on Unsatisfiable k-CNF Formulas with Few Occurrences per Variable

The (k,s)-SAT problem is the satisfiability problem restricted to instances where each clause has exactly k literals and every variable occurs at most s times. It is known that there exists a function f such that for s \leq f(k) all (k,s)-SAT instances are satisfiable, but (k,f(k)+1)-SAT is already NP-complete (k \geq 3). We prove that f(k) = O(2k \cdot log k/k), improving upon the best known upper bound O(2k/kalpha), where alpha=log3 4 - 1 \approx 0.26. The new upper bound is tight up to a log k factor with the best known lower bound Omega(2k/k).