We consider here spiking neural P systems with a non-synchronized (i.e., asynchronous) use of rules: in any step, a neuron can apply or not apply its rules which are enabled by the number of spikes it contains (further spikes can come, thus changing the rules enabled in the next step). Because the time between two firings of the output neuron is now irrelevant, the result of a computation is the number of spikes sent out by the system, not the distance between certain spikes leaving the system. The additional non-determinism introduced in the functioning of the system by the nonsynchronization is proved not to decrease the computing power in the case of using extended rules (several spikes can be produced by a rule). That is, we obtain again the equivalence with Turing machines (interpreted as generators of sets of (vectors of) numbers). However, this problem remains open for the case of restricted spiking neural P systems, whose rules can only produce one spike. On the other hand we prove that asynchronous systems, with extended rules, and where each neuron is either bounded or unbounded, are not computationally complete. For these systems, the configuration reachability, membership (in terms of generated vectors), emptiness, infiniteness, and disjointness problems are shown to be decidable. However, containment and equivalence are undecidable. In short, an SN P system consists of a set of neurons placed in the nodes of a directed graph and sending signals (spikes, denoted in what follows by the symbol a) along the arcs of the graph (they are called synapses). Thus, the architecture is that of a tissue-like P system, with only one kind of object present in the cells (the reader is referred to [18] for an introduction to membrane computing and to [23] for the up-to-date information about this research area). The objects evolve by means of standard spiking rules, which are of the form E/a c → a; d, where E is a regular expression over {a} and c, d are natural numbers, c ≥ 1, d ≥ 0. The meaning is that a neuron containing k spikes such that a k ∈ L(E), k ≥ c, can consume c spikes and produce one spike, after a delay of d steps. This spike is sent to all neurons connected by an outgoing synapse from the neuron where the rule was applied. There also are forgetting rules, of the form a s → λ, with the meaning that s ≥ 1 spikes are removed, provided that the neuron contains exactly s spikes. Extended rules were considered in [4], [17]: these rules are of the form E/a c → a p ; d, with the meaning that when using the rule, c spikes are consumed and p spikes are produced. Because p can be 0 or greater than 0, we obtain a generalization of both standard spiking and forgetting rules. In this paper we consider extended spiking rules with restrictions on the type of the regular expressions used. In particular, we consider two types of rules. The first type are called bounded rules and are of the form a i /a c → a p ; d, where 1 ≤ c ≤ i, p ≥ 0, and d ≥ 0. We also consider unbounded rules of the form a i (a j) * /a c → a p ; d...

We construct a family of extremely simple bijections that yield Cayley's famous formula for counting trees. The weight preserving properties of these bijections furnish a number of multivariate generating functions for weighted Cayley trees. Essentially the same idea is used to derive bijective proofs and q-analogues for the number of spanning trees of other graphs, including the complete bipartite and complete tripartite graphs. These bijections also allow the calculation of explicit formulas for the expected number of various statistics on Cayley trees.

The Smith-Waterman algorithm for local sequence alignment is one of the most important techniques in computational molecular biology. This ingenious dynamic programming approach was designed to reveal the highly conserved fragments by discarding poorly conserved initial and terminal segments. However, the existing notion of local similarity has a serious flaw: it does not discard poorly conserved intermediate segments. The Smith-Waterman algorithm finds the local alignment with maximal score but it is unable to find local alignment with maximum degree of similarity (e.g. maximal percent of matches). Moreover, there is still no efficient algorithm that answers the following natural question: do two sequences share a (sufficiently long) fragment with more than 70% of similarity? As a result, the local alignment sometimes produces a mosaic of well-conserved fragments artificially connected by poorly-conserved or even unrelated fragments. This may lead to problems in comparison of long genomic sequences and comparative gene prediction as recently pointed out by Zhang et al. (Bioinformatics, 15, 1012-1019, 1999). In this paper we propose a new sequence comparison algorithm (normalized local alignment ) that reports the regions with maximum degree of similarity. The algorithm is based on fractional programming and its running time is O(n2log n). In practice, normalized local alignment is only 3-5 times slower than the standard Smith-Waterman algorithm.

PDZ domains are protein-protein interaction modules widely used to assemble membranous signaling complexes including those found in the neuronal synapse. PDZ-containing genes encoded in metazoan genomes vastly outnumber those in prokaryotes, plants, and fungi. By comparing 40 proteomes to track the evolutionary history of the PDZ domain, we observed that the variety of associations between PDZ and other domains expands greatly along the stem leading to metazoans and choanoflagellates. We asked whether the expansion of PDZ domains was due to random or specific sequence changes. Studying the sequence signatures of 58 PDZ lineages that are common to bilaterian animals, we showed that six common amino acid residues are able to classify 96% of PDZ domains to their correct evolutionary lineage. In PDZ domain-ligand cocrystals, four of these "classifying positions" lie in direct contact with the -1 and -3 residues of the ligand. This suggests coevolution of the more flexible regions of the binding interaction as a central mechanism of specialization inherent within the PDZ domain. To identify these positions, we devised two independent algorithms--a metric termed within-clade entropy (WCE) and an average mutual information (AvgMI) score--that both reached similar results. Extending these tools to the choanoflagellate, Monosiga brevicollis, we compared its PDZ domains with their putative metazoan orthologs. Interestingly, the M. brevicollis genes lack conservation at the classifying positions suggesting dissociation between domain organization in multidomain proteins and specific changes within the PDZ domain.

Abstract-The increasing popularity of social networks has initiated a fertile research area in information extraction and data mining. Although such analysis can facilitate better understanding of sociological, behavioral, and other interesting phenomena, there is a growing concern about personal privacy being breached, thereby requiring effective anonymization techniques. In this paper, we consider edge weight anonymization in social graphs. Our approach builds a linear programming (LP) model which preserves properties of the graph that are expressible as linear functions of the edge weights. Such properties form the foundations of many important graph-theoretic algorithms such as shortest paths, k-nearest neighbors, minimum spanning tree, etc. Off-the-shelf LP solvers can then be used to find solutions to the resulting model where the computed solution constitutes the weights in the anonymized graph. As a proof of concept, we choose the shortest paths problem, and experimentally evaluate the proposed techniques using real social network data sets.

Given strings S1, S2, and P, the constrained longest common subsequence problem for S1 and S2 with respect to P is to find a longest common subsequence lcs of S1 and S2 which contains P as a subsequence. We present an algorithm which improves the time complexity of the problem from the previously known O(rn2m2) to O(rnm) where r, n, and m are the lengths of P, S1, and S2, respectively. As a generalization of this, we extend the definition of the problem so that the lcs sought contains a subsequence whose edit distance from P is less than a given parameter d. For the latter problem, we propose an algorithm whose time complexity is O(drnm).

The recognition problem for visibility graphs of simple polygons is not known to be in NP, nor is it known to be NP-hard. It is, however, known to be in PSPACE. Further, every such visibility graph can be dismantled as a sequence of visibility graphs of convex fans. Any nondegenerate configuration of n points can be associated with a maximal chain in the weak Bruhat order of the symmetric group S n. The visibility graph of any simple polygon defined on this configuration is completely determined by this maximal chain via a one-to-one correspondence between maximal chains and balanced tableaux of a certain shape. In the case of staircase polygons (special convex fans), we define a class of graphs called persistent graphs and show that the visibility graph of a staircase polygon is persistent. We then describe a polynomial-time algorithm that recovers a representative maximal chain in the weak Bruhat order from a given persistent graph, thus characterizing the class of persistent graphs. The question of recovering a staircase polygon from a given persistent graph, via a maximal chain, is studied in the companion paper [4]. The overall goal of both papers is to offer a characterization of visibility graphs of convex fans.

Abstract. In search for "realistic" bio-inspired computing models, we consider asynchronous spiking neural P systems, in the hope to get a class of computing devices with decidable properties. However, although the non-synchronization is known in general to decrease the computing power, in the case of using extended rules (several spikes can be produced by a rule) we obtain again the equivalence with Turing machines (interpreted as generators of sets of vectors of numbers). The problem remains open for the case of restricted spiking neural P systems, whose rules can only produce one spike. On the other hand, we prove that asynchronous spiking neural P systems, with a specific way of halting, using extended rules and where each neuron is either bounded or unbounded, are equivalent to partially blind counter machines and, therefore, have many decidable properties. Spiking Neural P Systems -An Informal PresentationIn the present paper we continue the investigation of spiking neural P systems (SN P systems, in short). A survey of results and the biological motivations for these systems can be found in [5] and [2]. In the meantime, two main research directions were particularly active in this area of membrane computing: looking for classes of systems with tractable (for instance, decidable) properties, and looking for the possibility of using SN P systems for efficiently solving computationally hard problems. Along the second research line are the investigations related to the possibility of simulating an SN P system by a Turing machine with a polynomial slowdown (preliminary results can be found in [3]) and those trying to improve the efficiency of SN P systems, e.g., by enhancing the parallelism of the system (see, for instance, [7]).In this paper we report several recent results concerning the first topic mentioned above -specifically, removing the synchronization (common in many membrane computing models), calling them asynchronous SN P systems. These