OBDD-Based Representation of Interval Graphs

A graph $G = (V,E)$ can be described by the characteristic function of the edge set $\chi_E$ which maps a pair of binary encoded nodes to 1 iff the nodes are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store $\chi_E$ can lead to a (hopefully) compact representation. Given the OBDD as an input, symbolic/implicit OBDD-based graph algorithms can solve optimization problems by mainly using functional operations, e.g. quantification or binary synthesis. While the OBDD representation size can not be small in general, it can be provable small for special graph classes and then also lead to fast algorithms. In this paper, we show that the OBDD size of unit interval graphs is $O(\ | V \ | /\log \ | V \ |)$ and the OBDD size of interval graphs is $O(\ | V \ | \log \ | V \ |)$which both improve a known result from Nunkesser and Woelfel (2009). Furthermore, we can show that using our variable order and node labeling for interval graphs the worst-case OBDD size is$\Omega(\ | V \ | \log \ | V \ |)$. We use the structure of the adjacency matrices to prove these bounds. This method may be of independent interest and can be applied to other graph classes. We also develop a maximum matching algorithm on unit interval graphs using$O(\log \ | V \ |)$operations and a coloring algorithm for unit and general intervals graphs using$O(\log^2 \ | V \ |)$ operations and evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic Concepts 201

Weighted Automata and Logics for Infinite Nested Words

Nested words introduced by Alur and Madhusudan are used to capture structures with both linear and hierarchical order, e.g. XML documents, without losing valuable closure properties. Furthermore, Alur and Madhusudan introduced automata and equivalent logics for both finite and infinite nested words, thus extending B\"uchi's theorem to nested words. Recently, average and discounted computations of weights in quantitative systems found much interest. Here, we will introduce and investigate weighted automata models and weighted MSO logics for infinite nested words. As weight structures we consider valuation monoids which incorporate average and discounted computations of weights as well as the classical semirings. We show that under suitable assumptions, two resp. three fragments of our weighted logics can be transformed into each other. Moreover, we show that the logic fragments have the same expressive power as weighted nested word automata.Comment: LATA 2014, 12 page

Explicit connection actions in multiparty session types

This work extends asynchronous multiparty session types (MPST) with explicit connection actions to support protocols with op- tional and dynamic participants. The actions by which endpoints are connected and disconnected are a key element of real-world protocols that is not treated in existing MPST works. In addition, the use cases motivating explicit connections often require a more relaxed form of mul- tiparty choice: these extensions do not satisfy the conservative restric- tions used to ensure safety in standard syntactic MPST. Instead, we de- velop a modelling-based approach to validate MPST safety and progress for these enriched protocols. We present a toolchain implementation, for distributed programming based on our extended MPST in Java, and a core formalism, demonstrating the soundness of our approach. We discuss key implementation issues related to the proposed extensions: a practi- cal treatment of choice subtyping for MPST progress, and multiparty correlation of dynamic binary connections

Metric-like Lagrangian Formulations for Higher-Spin Fields of Mixed Symmetry

We review the structure of local Lagrangians and field equations for free bosonic and fermionic gauge fields of mixed symmetry in flat space. These are first presented in a constrained setting extending the metric formulation of linearized gravity, and then the ($\gamma$-)trace constraints on fields and gauge parameters are eliminated via the introduction of auxiliary fields. We also display the emergence of Weyl-like symmetries in particular classes of models in low space-time dimensions.Comment: 136 pages, LaTeX. References added. Final version to appear in La Rivista del Nuovo Cimento

On oblivious branching programs with bounded repetition that cannot efficiently compute CNFs of bounded treewidth

In this paper we study complexity of an extension of ordered binary decision diagrams (OBDDs) called c-OBDDs on CNFs of bounded (primal graph) treewidth. In particular, we show that for each k ≥ 3 there is a class of CNFs of treewidth k for which the equivalent c-OBDDs are of size Ω(nk/(8c−4)). Moreover, this lower bound holds if c-OBDDs are non-deterministic and semantic. Our second result uses the above lower bound to separate the above model from sentential decision diagrams (SDDs). In order to obtain the lower bound, we use a structural graph parameter called matching width. Our third result shows that matching width and pathwidth are linearly related

The beginning of time? Evidence for catastrophic drought in Baringo in the early nineteenth century

New developments in the collection of palaeo-data over the past two decades have transformed our understanding of climate and environmental history in eastern Africa. This article utilises instrumental and proxy evidence of historical lake-level fluctuations from Baringo and Bogoria, along with other Rift Valley lakes, to document the timing and magnitude of hydroclimate variability at decadal to century time scales since 1750. These data allow us to construct a record of past climate variation not only for the Baringo basin proper, but also across a sizable portion of central and northern Kenya. This record is then set alongside historical evidence, from oral histories gathered amongst the peoples of northern Kenya and the Rift Valley and from contemporary observations recorded by travellers through the region, to offer a reinterpretation of human activity and its relationship to environmental history in the nineteenth century. The results reveal strong evidence of a catastrophic drought in the early nineteenth century, the effects of which radically alters our historical understanding of the character of settlement, mobility and identity within the Baringo–Bogoria basin

Systems analysis reveals a transcriptional reversal of the mesenchymal phenotype induced by SNAIL-inhibitor GN-25

Abstract Background HMLEs (HMLE-SNAIL and Kras-HMLE, Kras-HMLE-SNAIL pairs) serve as excellent model system to interrogate the effect of SNAIL targeted agents that reverse epithelial-to-mesenchymal transition (EMT). We had earlier developed a SNAIL-p53 interaction inhibitor (GN-25) that was shown to suppress SNAIL function. In this report, using systems biology and pathway network analysis, we show that GN-25 could cause reversal of EMT leading to mesenchymal-to-epithelial transition (MET) in a well-recognized HMLE-SNAIL and Kras-HMLE-SNAIL models. Results GN-25 induced MET was found to be consistent with growth inhibition, suppression of spheroid forming capacity and induction of apoptosis. Pathway network analysis of mRNA expression using microarrays from GN-25 treated Kras-HMLE-SNAIL cells showed an orchestrated global re-organization of EMT network genes. The expression signatures were validated at the protein level (down-regulation of mesenchymal markers such as TWIST1 and TWIST2 that was concurrent with up-regulation of epithelial marker E-Cadherin), and RNAi studies validated SNAIL dependent mechanism of action of the drug. Most importantly, GN-25 modulated many major transcription factors (TFs) such as inhibition of oncogenic TFs Myc, TBX2, NR3C1 and led to enhancement in the expression of tumor suppressor TFs such as SMAD7, DD1T3, CEBPA, HOXA5, TFEB, IRF1, IRF7 and XBP1, resulting in MET as well as cell death. Conclusions Our systems and network investigations provide convincing pre-clinical evidence in support of the clinical application of GN-25 for the reversal of EMT and thereby reducing cancer cell aggressiveness