Remotely pumped optical distribution networks: a distributed amplifier model

Optical distribution networks using remotely pumped erbium-doped fiber amplifiers (EDFAs) with a single pump source at the head end can conveniently provide signal gain without adding to the power-consumption cost and management complexity of having multiple locally pumped EDFAs in densely populated metropolitan areas. We introduce an analytical model for understanding the basic physical foundations of remotely pumped network design and for analyzing the number of users that can be supported using such a remote-pumping scheme

Semantic Bidirectionalization Revisited

A bidirectional transformation is a pair of mappings between source and view data objects, one in each direction. When the view is modified, the source is updated accordingly with respect to some laws. Over the years, a lot of effort has been made to offer better language support for programming such transformations, essentially allowing the programmers to construct one mapping of the pair and have the other automatically generated. As an alternative to creating specialized new languages, one can try to analyse and transform programs written in general purpose languages, and "bidirectionalize" them. Among others, a technique termed as semantic bidirectionalization stands out in term of user-friendliness. The unidirectional program can be written using arbitrary language constructs, as long as the function is polymorphic and the language constructs respect parametricity. The free theorem that follows from the polymorphic type of the program allows a kind of forensic examination of the transformation, determining its effect without examining its implementation. This is convenient, in the sense that the programmer is not restricted to using a particular syntax; but it does require the transformation to be polymorphic. In this paper, we revisit the idea of semantic bidirectionalization and reveal the elegant principles behind the current state-of-the-art techniques. Guided by the findings, we derive much simpler implementations that scale easily

A Feature-Based Analysis on the Impact of Set of Constraints for e-Constrained Differential Evolution

Different types of evolutionary algorithms have been developed for constrained continuous optimization. We carry out a feature-based analysis of evolved constrained continuous optimization instances to understand the characteristics of constraints that make problems hard for evolutionary algorithm. In our study, we examine how various sets of constraints can influence the behaviour of e-Constrained Differential Evolution. Investigating the evolved instances, we obtain knowledge of what type of constraints and their features make a problem difficult for the examined algorithm.Comment: 17 Page

Algebraic and geometric space-time analogies in nonlinear optical pulse propagation

We extend recently developed algebraic space time analogies for the dispersive and nonlinear propagation of optical breathers. Geometrical arguments can explain the similarity of evolutionary behavior between spatial and temporal phenomena even when strict algebraic translation of solutions may not be possible. This explanation offers a new set of tools for understanding and predicting the evolutionary structure of self-consistent Gaussian breathers in nonlinear optical fibers

Approximating the Expansion Profile and Almost Optimal Local Graph Clustering

Spectral partitioning is a simple, nearly-linear time, algorithm to find sparse cuts, and the Cheeger inequalities provide a worst-case guarantee for the quality of the approximation found by the algorithm. Local graph partitioning algorithms [ST08,ACL06,AP09] run in time that is nearly linear in the size of the output set, and their approximation guarantee is worse than the guarantee provided by the Cheeger inequalities by a polylogarithmic $\log^{\Omega(1)} n$ factor. It has been a long standing open problem to design a local graph clustering algorithm with an approximation guarantee close to the guarantee of the Cheeger inequalities and with a running time nearly linear in the size of the output. In this paper we solve this problem; we design an algorithm with the same guarantee (up to a constant factor) as the Cheeger inequality, that runs in time slightly super linear in the size of the output. This is the first sublinear (in the size of the input) time algorithm with almost the same guarantee as the Cheeger's inequality. As a byproduct of our results, we prove a bicriteria approximation algorithm for the expansion profile of any graph. Let $\phi(\gamma) = \min_{\mu(S) \leq \gamma}\phi(S)$. There is a polynomial time algorithm that, for any $\gamma,\epsilon>0$, finds a set $S$ of measure $\mu(S)\leq 2\gamma^{1+\epsilon}$, and expansion $\phi(S)\leq \sqrt{2\phi(\gamma)/\epsilon}$. Our proof techniques also provide a simpler proof of the structural result of Arora, Barak, Steurer [ABS10], that can be applied to irregular graphs. Our main technical tool is that for any set $S$ of vertices of a graph, a lazy $t$-step random walk started from a randomly chosen vertex of $S$, will remain entirely inside $S$ with probability at least $(1-\phi(S)/2)^t$. This itself provides a new lower bound to the uniform mixing time of any finite states reversible markov chain

A New Regularity Lemma and Faster Approximation Algorithms for Low Threshold Rank Graphs

Kolla and Tulsiani [KT07,Kolla11} and Arora, Barak and Steurer [ABS10] introduced the technique of subspace enumeration, which gives approximation algorithms for graph problems such as unique games and small set expansion; the running time of such algorithms is exponential in the threshold-rank of the graph. Guruswami and Sinop [GS11,GS12], and Barak, Raghavendra, and Steurer [BRS11] developed an alternative approach to the design of approximation algorithms for graphs of bounded threshold-rank, based on semidefinite programming relaxations in the Lassere hierarchy and on novel rounding techniques. These algorithms are faster than the ones based on subspace enumeration and work on a broad class of problems. In this paper we develop a third approach to the design of such algorithms. We show, constructively, that graphs of bounded threshold-rank satisfy a weak Szemeredi regularity lemma analogous to the one proved by Frieze and Kannan [FK99] for dense graphs. The existence of efficient approximation algorithms is then a consequence of the regularity lemma, as shown by Frieze and Kannan. Applying our method to the Max Cut problem, we devise an algorithm that is faster than all previous algorithms, and is easier to describe and analyze