Abstract unordered and ordered trees CRDT

Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas of a distributed system are allowed to diverge but should eventually reach the same value if no more mutations occur. A new method to ensure eventual consistency is to design Conflict-free Replicated Data Types (CRDT). In this report, we design a collection of tree CRDT using existing set CRDTs. The remaining concurrency problems particular to tree data structure are resolved using one or two layers of correction algorithm. For each of these layer, we propose different and independent policies. Any combination of set CRDT and policies can be constructed, giving to the distributed application programmer the entire control of the behavior of the shared data in face of concurrent mutations. We also propose to order these trees by adding a positioning layer which is also independent to obtain a collection of ordered tree CRDTs

Evolving Market Performance in Brazilian Futures Contracts Using Relative Efficiency

Marketing,

A fuzzy approach for the network congestion problem

In the recent years, the unpredictable growth of the Internet has moreover pointed out the congestion problem, one of the problems that historicallyha ve affected the network. This paper deals with the design and the evaluation of a congestion control algorithm which adopts a FuzzyCon troller. The analogyb etween Proportional Integral (PI) regulators and Fuzzycon trollers is discussed and a method to determine the scaling factors of the Fuzzycon troller is presented. It is shown that the Fuzzycon troller outperforms the PI under traffic conditions which are different from those related to the operating point considered in the design

Scalable XML Collaborative Editing with Undo short paper

Commutative Replicated Data-Type (CRDT) is a new class of algorithms that ensures scalable consistency of replicated data. It has been successfully applied to collaborative editing of texts without complex concurrency control. In this paper, we present a CRDT to edit XML data. Compared to existing approaches for XML collaborative editing, our approach is more scalable and handles all the XML editing aspects : elements, contents, attributes and undo. Indeed, undo is recognized as an important feature for collaborative editing that allows to overcome system complexity through error recovery or collaborative conflict resolution

Common fixed points of generalized Mizoguchi-Takahashi type contractions in partial metric spaces

We give some common fixed point results for multivalued mappings in the setting of complete partial metric spaces. Our theorems extend and complement analogous results in the existing literature on metric and partial metric spaces. Finally, we provide an example to illustrate the new theory

"Term Partition" for Mathematical Induction

A key new concept, {\em term partition}, allows to design a new method for proving theorems whose proof usually requires mathematical induction. A term partition of a term $t$ is a well-defined splitting of $t$ into a pair $(a,b)$ of terms that describes the {\em language of normal forms of the ground instances of $t$}. If \A {\em monomorphic} set of axioms (rules) and (a,b)$is a term partition of$t$, then the normal form (obtained by using$\Aany ground instance of $t$ can be ``divided'' into the normal forms (obtained by using \Athe corresponding ground instances of a$and$b$. Given a conjecture$t = s$to be checked for inductive validity in a theory$\Aartition $(a,b)$ of $t$ and a partition $(c,d)$ of $s$ is computed. If $a = c$ and $b = d$, then $t = s$ is an inductive theorem of \A The method is conceptually different to the classical theorem proving approaches since it tries to directly mechanize the \omega$-rule. It allows to obtain elegant and natural proofs of a large number of conjectures (including non-linear ones) without additional lemmas and/or generalizations

A genetic algorithm for the design of a fuzzy controller for active queue management

Active queue management (AQM) policies are those policies of router queue management that allow for the detection of network congestion, the notification of such occurrences to the hosts on the network borders, and the adoption of a suitable control policy. This paper proposes the adoption of a fuzzy proportional integral (FPI) controller as an active queue manager for Internet routers. The analytical design of the proposed FPI controller is carried out in analogy with a proportional integral (PI) controller, which recently has been proposed for AQM. A genetic algorithm is proposed for tuning of the FPI controller parameters with respect to optimal disturbance rejection. In the paper the FPI controller design metodology is described and the results of the comparison with random early detection (RED), tail drop, and PI controller are presented