Leonardo Lanzi

On computing the diameter of real-world undirected graphs

We propose a new algorithm for the classical problem of computing the diameter of undirected unweighted graphs, namely, the maximum distance among all the pairs of nodes, where the distance of a pair of nodes is the number of edges contained in the shortest path connecting these two nodes. Although its worst-case complexity is O(nm) time, where n is the number of nodes and m is the number of edges of the graph, we experimentally show that our algorithm works in O(m) time in practice, requiring few breadth-first searches to complete its task on almost 200 real-world graphs.

Differential and double-differential dielectric spectroscopy to measure complex permittivity in transmission lines

This article presents and compares two differential methods for measuring the complex permittivity of dielectric materials: In the first method, two measuring cells built as coaxial transmission lines of identical cross section and terminations but different lengths are filled with a sample of the dielectric material. The complex dielectric permittivity is determined from the scattering parameter measurements and the length difference between the two cells, neglecting the resistive losses due to the cells. The second method is a double-differential one: Repeating measurements on the same cells empty, no other knowledge or limiting assumption is required.

A comparison between potentiostatic circuits with grounded work or auxiliary electrode

Potentiostatic circuit configurations with work electrodes and auxiliary electrodes at ground potential have been reviewed and compared. Though the former is by far the best known and most used, the latter was more convenient and accurate in interfacial capacity measurements.

Finding the diameter in real-world graphs experimentally turning a lower bound into an upper bound

The diameter of an unweighted graph is the maximum pairwise distance among its connected vertices. It is one of the main measures in real-world graphs and complex networks. The double sweep is a simple method to find a lower bound for the diameter. It chooses a random vertex and performs two breadth-first searches (BFSes), returning the maximum length among the shortest paths thus found. We propose an algorithm called fringe, which uses few BFSes to find a matching upper bound for almost all the graphs in our dataset of 44 real-world graphs. In the few graphs it cannot, we perform an exhaustive search of the diameter using a cluster of machines for a total of 40 cores. In all cases, the diameter is surprisingly equal to the lower bound found after very few executions of the double sweep method. The lesson learned is that the latter can be used to find the diameter of real-world graphs in many more cases than expected, and our fringe algorithm can quickly validate this finding for most of them.

On computing the diameter of real-world directed (weighted) graphs

In this paper we propose a new algorithm for computing the diameter of directed unweighted graphs. Even though, in the worst case, this algorithm has complexity O(nm), where n is the number of nodes and m is the number of edges of the graph, we experimentally show that in practice our method works in O(m) time. Moreover, we show how to extend our algorithm to the case of directed weighted graphs and, even in this case, we present some preliminary very positive experimental results.

A comparison of three algorithms for approximating the distance distribution in real-world graphs

The distance for a pair of vertices in a graph G is the length of the shortest path between them. The distance distribution for G specifies how many vertex pairs are at distance h, for all feasible values h. We study three fast randomized algorithms to approximate the distance distribution in large graphs. The Eppstein-Wang (EW) algorithm exploits sampling through a limited (logarithmic) number of Breadth-First Searches (BFSes). The Size-Estimation Framework (SEF) by Cohen employs random ranking and least-element lists to provide several estimators. Finally, the Approximate Neighborhood Function (ANF) algorithm by Palmer, Gibbons, and Faloutsos makes use of the probabilistic counting technique introduced by Flajolet and Martin, in order to estimate the number of distinct elements in a large multiset. We investigate how good is the approximation of the distance distribution, when the three algorithms are run in similar settings. The analysis of ANF derives from the results on the probabilistic counting method, while the one of sef is given by Cohen. For what concerns EW (originally designed for another problem), we extend its simple analysis in order to bound its error with high probability and to show its convergence. We then perform an experimental study on 30 real-world graphs, showing that our implementation of ew combines the accuracy of sef with the performance of ANF.

A new insight on the dynamics of sodium dodecyl sulfate aqueous micellar solutions by dielectric spectroscopy

Aqueous sodium dodecyl sulfate micellar solutions were investigated by a recently developed double-differential dielectric spectroscopy technique in the frequency range 100 MHz-3 GHz at 22 degrees C, in the surfactant concentration range 29.8-524 mM, explored for the first time above 104 mM. The micellar contribution to dielectric spectra was analyzed according to three models containing, respectively, a single Debye relaxation, a Cole-Cole relaxation and a double Debye relaxation. The single Debye model is not accurate enough. Both Cole-Cole and double Debye models fit well the experimental dielectric spectra. With the double Debye model, two characteristic relaxation times were identified: the slower one, in the range 400-900 ps, is due to the motion of counterions bound to the micellar surface (lateral motion); the faster one, in the range 100-130 ps, is due to interfacial bound water. Time constants and amplitudes of both processes are in fair agreement with Grosses theoretical model, except at the largest concentration values, where interactions between micelles increase. For each sample, the volume fraction of bulk water and the effect of bound water as well as the conductivity in the low frequency limit were computed. The bound water increases as the surfactant concentration increases, in quantitative agreement with the micellar properties. The number of water molecules per surfactant molecule was also computed. The conductivity values are in agreement with Kallays model over the whole surfactant concentration range.

Electronic linearization of piezoelectric actuators and noise budget in scanning probe microscopy

The maximum resolution achievable with a scanning probe microscope is limited by the probe size, by the mechanism of interaction with the sample, as is widely known, and by the electronic noise in the instrument. The evaluation of this noise for the three motion axes of a linearized high resolution scanning electrochemical microscope has been carried through and the intrinsic maximum resolution is discussed.

Implementation on a desktop computer of the real time feedback control loop of a scanning probe microscope

A software package has been developed to implement the real time feedback control loop needed in scanning probe microscopy on a general purpose desktop computer of the current high-speed/multicore generation. The main features of the implementation of both the feedback loop and the control of the experiment on the same computer are discussed. The package can work with several general purpose data acquisition boards and can be extended in a modular way to further board models; timing performance has been tested with several hardware configurations and some applications common in scanning probe microscopy. The package is available under an Open Source license.

Performance Evaluation of a Chord-Based JXTA Implementation

In this paper, we propose a new implementation of the JXTA framework, based on the integration of the original JXTA version with the Chord DHT management protocol. The resulting new JXTA implementation is experimentally compared with the original one, by referring to the JXTA performance model proposed by Halepovic et al. in 2004: the results give strong evidence to the fact that the JXTA rendezvous protocol performances can be improved up to one order of magnitude by replacing the original loosely-consistent DHT with the real Chord DHT.