On fractionality of the path packing problem

In this paper, we study fractional multiflows in undirected graphs. A fractional multiflow in a graph G with a node subset T, called terminals, is a collection of weighted paths with ends in T such that the total weights of paths traversing each edge does not exceed 1. Well-known fractional path packing problem consists of maximizing the total weight of paths with ends in a subset S of TxT over all fractional multiflows. Together, G,T and S form a network. A network is an Eulerian network if all nodes in N\T have even degrees. A term "fractionality" was defined for the fractional path packing problem by A. Karzanov as the smallest natural number D so that there exists a solution to the problem that becomes integer-valued when multiplied by D. A. Karzanov has defined the class of Eulerian networks in terms of T and S, outside which D is infinite and proved that whithin this class D can be 1,2 or 4. He conjectured that D should be 1 or 2 for this class of networks. In this paper we prove this conjecture.Comment: 18 pages, 5 figures in .eps format, 2 latex files, main file is kc13.tex Resubmission due to incorrectly specified CS type of the article; no changes to the context have been mad

Boosting the Efficiency of Byzantine-tolerant Reliable Communication

Reliable communication is a fundamental primitive in distributed systems prone to Byzantine (i.e. arbitrary, and possibly malicious) failures to guarantee integrity, delivery and authorship of messages exchanged between processes. Its practical adoption strongly depends on the system assumptions. One of the most general (and hence versatile) such hypothesis assumes a set of processes interconnected through an unknown communication network of reliable and authenticated links, and an upper bound on the number of Byzantine faulty processes that may be present in the system, known to all participants. To this date, implementing a reliable communication service in such an environment may be expensive, both in terms of message complexity and computational complexity, unless the topology of the network is known. The target of this work is to combine the Byzantine fault-tolerant topol-ogy reconstruction with a reliable communication primitive, aiming to boost the efficiency of the reliable communication service component after an initial (expensive) phase where the topology is partially reconstructed. We characterize the sets of assumptions that make our objective achievable, and we propose a solution that, after an initialization phase, guarantees reliable communication with optimal message complexity and optimal delivery complexity

Guidelines for the use and interpretation of assays for monitoring autophagy (4th edition)1.

In 2008, we published the first set of guidelines for standardizing research in autophagy. Since then, this topic has received increasing attention, and many scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Thus, it is important to formulate on a regular basis updated guidelines for monitoring autophagy in different organisms. Despite numerous reviews, there continues to be confusion regarding acceptable methods to evaluate autophagy, especially in multicellular eukaryotes. Here, we present a set of guidelines for investigators to select and interpret methods to examine autophagy and related processes, and for reviewers to provide realistic and reasonable critiques of reports that are focused on these processes. These guidelines are not meant to be a dogmatic set of rules, because the appropriateness of any assay largely depends on the question being asked and the system being used. Moreover, no individual assay is perfect for every situation, calling for the use of multiple techniques to properly monitor autophagy in each experimental setting. Finally, several core components of the autophagy machinery have been implicated in distinct autophagic processes (canonical and noncanonical autophagy), implying that genetic approaches to block autophagy should rely on targeting two or more autophagy-related genes that ideally participate in distinct steps of the pathway. Along similar lines, because multiple proteins involved in autophagy also regulate other cellular pathways including apoptosis, not all of them can be used as a specific marker for bona fide autophagic responses. Here, we critically discuss current methods of assessing autophagy and the information they can, or cannot, provide. Our ultimate goal is to encourage intellectual and technical innovation in the field