On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure

A novel structure-based encoding for machine-learning applied to the inference of SH3 domain specificity

MOTIVATION: Unravelling the rules underlying protein-protein and protein-ligand interactions is a crucial step in understanding cell machinery. Peptide recognition modules (PRMs) are globular protein domains which focus their binding targets on short protein sequences and play a key role in the frame of protein-protein interactions. High-throughput techniques permit the whole proteome scanning of each domain, but they are characterized by a high incidence of false positives. In this context, there is a pressing need for the development of in silico experiments to validate experimental results and of computational tools for the inference of domain-peptide interactions. RESULTS: We focused on the SH3 domain family and developed a machine-learning approach for inferring interaction specificity. SH3 domains are well-studied PRMs which typically bind proline-rich short sequences characterized by the PxxP consensus. The binding information is known to be held in the conformation of the domain surface and in the short sequence of the peptide. Our method relies on interaction data from high-throughput techniques and benefits from the integration of sequence and structure data of the interacting partners. Here, we propose a novel encoding technique aimed at representing binding information on the basis of the domain-peptide contact residues in complexes of known structure. Remarkably, the new encoding requires few variables to represent an interaction, thus avoiding the 'curse of dimension'. Our results display an accuracy >90% in detecting new binders of known SH3 domains, thus outperforming neural models on standard binary encodings, profile methods and recent statistical predictors. The method, moreover, shows a generalization capability, inferring specificity of unknown SH3 domains displaying some degree of similarity with the known data

Preserving Creativity in Medicine

Imagination and creativity are essential traits that medicine, and medical insurers, must again learn to recognize and rewar

A neural strategy for the inference of SH3 domain-peptide interaction specificity

The SH3 domain family is one of the most representative and widely studied cases of so-called Peptide Recognition Modules (PRM). The polyproline II motif PxxP that generally characterizes its ligands does not reflect the complex interaction spectrum of the over 1500 different SH3 domains, and the requirement of a more refined knowledge of their specificity implies the setting up of appropriate experimental and theoretical strategies. Due to the limitations of the current technology for peptide synthesis, several experimental high-throughput approaches have been devised to elucidate protein-protein interaction mechanisms. Such approaches can rely on and take advantage of computational techniques, such as regular expressions or position specific scoring matrices (PSSMs) to pre-process entire proteomes in the search for putative SH3 targets. In this regard, a reliable inference methodology to be used for reducing the sequence space of putative binding peptides represents a valuable support for molecular and cellular biologists

DBATE: database of alternative transcripts expression

The use of high-throughput RNA sequencing technology (RNA-seq) allows whole transcriptome analysis, providing an unbiased and unabridged view of alternative transcript expression. Coupling splicing variant-specific expression with its functional inference is still an open and difficult issue for which we created the DataBase of Alternative Transcripts Expression (DBATE), a web-based repository storing expression values and functional annotation of alternative splicing variants. We processed 13 large RNA-seq panels from human healthy tissues and in disease conditions, reporting expression levels and functional annotations gathered and integrated from different sources for each splicing variant, using a variant-specific annotation transfer pipeline. The possibility to perform complex queries by cross-referencing different functional annotations permits the retrieval of desired subsets of splicing variant expression values that can be visualized in several ways, from simple to more informative. DBATE is intended as a novel tool to help appreciate how, and possibly why, the transcriptome expression is shaped. DATABASE URL: http://bioinformatica.uniroma2.it/DBATE/

Optimal Vertex Cover for the Small-World Hanoi Networks

The vertex-cover problem on the Hanoi networks HN3 and HN5 is analyzed with an exact renormalization group and parallel-tempering Monte Carlo simulations. The grand canonical partition function of the equivalent hard-core repulsive lattice-gas problem is recast first as an Ising-like canonical partition function, which allows for a closed set of renormalization group equations. The flow of these equations is analyzed for the limit of infinite chemical potential, at which the vertex-cover problem is attained. The relevant fixed point and its neighborhood are analyzed, and non-trivial results are obtained both, for the coverage as well as for the ground state entropy density, which indicates the complex structure of the solution space. Using special hierarchy-dependent operators in the renormalization group and Monte-Carlo simulations, structural details of optimal configurations are revealed. These studies indicate that the optimal coverages (or packings) are not related by a simple symmetry. Using a clustering analysis of the solutions obtained in the Monte Carlo simulations, a complex solution space structure is revealed for each system size. Nevertheless, in the thermodynamic limit, the solution landscape is dominated by one huge set of very similar solutions.Comment: RevTex, 24 pages; many corrections in text and figures; final version; for related information, see http://www.physics.emory.edu/faculty/boettcher

Tropical Dominating Sets in Vertex-Coloured Graphs

Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various parameters of the graph such as minimum degree and number of edges. We also give upper bounds for random graphs. Last, we give approximability and inapproximability results for general and restricted classes of graphs, and establish a FPT algorithm for interval graphs.Comment: 19 pages, 4 figure

Algorithmic aspects of disjunctive domination in graphs

For a graph $G=(V,E)$, a set $D\subseteq V$ is called a \emph{disjunctive dominating set} of $G$ if for every vertex $v\in V\setminus D$, $v$ is either adjacent to a vertex of $D$ or has at least two vertices in $D$ at distance $2$ from it. The cardinality of a minimum disjunctive dominating set of $G$ is called the \emph{disjunctive domination number} of graph $G$, and is denoted by $\gamma_{2}^{d}(G)$. The \textsc{Minimum Disjunctive Domination Problem} (MDDP) is to find a disjunctive dominating set of cardinality $\gamma_{2}^{d}(G)$. Given a positive integer $k$ and a graph $G$, the \textsc{Disjunctive Domination Decision Problem} (DDDP) is to decide whether $G$ has a disjunctive dominating set of cardinality at most $k$. In this article, we first propose a linear time algorithm for MDDP in proper interval graphs. Next we tighten the NP-completeness of DDDP by showing that it remains NP-complete even in chordal graphs. We also propose a $(\ln(\Delta^{2}+\Delta+2)+1)$-approximation algorithm for MDDP in general graphs and prove that MDDP can not be approximated within $(1-\epsilon) \ln(|V|)$ for any $\epsilon>0$ unless NP $\subseteq$ DTIME$(|V|^{O(\log \log |V|)})$. Finally, we show that MDDP is APX-complete for bipartite graphs with maximum degree $3$

The Use of Premixed Calcium Silicate Bioceramic Sealer with Warm Carrier-Based Technique: A 2-Year Study for Patients Treated in a Master Program

Background: Recently several calcium silicate flowable sealers have been introduced as endodontic materials for the root canal. This clinical study tested the use of a new premixed calcium silicate bioceramic sealer in association with the Thermafil warm carrier-based technique (TF). Epoxy-resin-based sealer with the warm carrier-based technique was the control group. Methodology: Healthy consecutive patients (n = 85) requiring 94 root canal treatments were enrolled in this study and assigned to one filling group (Ceraseal-TF n = 47, AH Plus-TF n = 47) in accordance with operator training and best clinical practice. Periapical X-rays were taken preoperatively, after root canal filling and after 6, 12 and 24 months. Two evaluators blindly assessed the periapical index (PAI) and sealer extrusion in the groups (k = 0.90). Healing rate and survival rate were also evaluated. Chi-square tests was used to analyze significant differences between the groups. Multilevel analysis was performed to evaluate the factors associated with healing status. Results: A total of 89 root canal treatments in 82 patients were analyzed at the end-line (24 months). The total drop-out was 3.6% (3 patients; 5 teeth). A total of 91.1% of healed teeth (PAI 1-2) was observed in Ceraseal-TF, with 88.6% in AH Plus-TF. No significant difference was observed on healing outcome and survival among the two filling groups (p > 0.05). Apical extrusion of the sealers occurred in 17 cases (19.0%). Of these, 6 occurred in Ceraseal-TF (13.3%) and 11 in AH Plus-TF (25.0%). Three Ceraseal extrusions were radiographically undetectable after 24 months. All the AH Plus extrusions did not change during the evaluation time. Conclusions: The combined use of the carrier-based technique and premixed CaSi-based bioceramic sealer showed clinical results comparable with carrier-based technique and epoxy-resin-based sealer. The radiographical disappearance of apically extruded Ceraseal is a possible event in the first 24 months