Algorithms to Compute the Lyndon Array

We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these algorithms execute in quadratic time in the worst case, the third achieves linear time, but at the expense of prior computation of both the suffix array and the inverse suffix array of x. We then go on to describe two variants of a new algorithm that avoids prior computation of global data structures and executes in worst-case n log n time. Experimental evidence suggests that all but one of these five algorithms require only linear execution time in practice, with the two new algorithms faster by a small factor. We conjecture that there exists a fast and worst-case linear-time algorithm to compute the Lyndon array that is also elementary (making no use of global data structures such as the suffix array)

Numerical modelling of electric conductance of a thin sheet

In this paper the numeric modelling of total resistance of a thin sheet, with local conductivity in randomly distributed grains higher then is that of the basic matrix, is presented. The 2D model is formed by a structure of longitudinal and transversal conductors interconnected in nodes of a square net. In all nodes, using iteration procedure, the potential is determined from which the conductance of sheet is computed between two touching electrodes. The described model can be used to imitate the behaviour of heterogeneous thin conducting sheets prepared by different techniques. The model was verified in some cases where the net resistance is well known from the theory

On the maximal sum of exponents of runs in a string

A run is an inclusion maximal occurrence in a string (as a subinterval) of a repetition $v$ with a period $p$ such that $2p \le |v|$. The exponent of a run is defined as $|v|/p$ and is $\ge 2$. We show new bounds on the maximal sum of exponents of runs in a string of length $n$. Our upper bound of $4.1n$ is better than the best previously known proven bound of $5.6n$ by Crochemore & Ilie (2008). The lower bound of $2.035n$, obtained using a family of binary words, contradicts the conjecture of Kolpakov & Kucherov (1999) that the maximal sum of exponents of runs in a string of length $n$ is smaller than $2n$Comment: 7 pages, 1 figur

The BaBar Event Building and Level-3 Trigger Farm Upgrade

The BaBar experiment is the particle detector at the PEP-II B-factory facility at the Stanford Linear Accelerator Center. During the summer shutdown 2002 the BaBar Event Building and Level-3 trigger farm were upgraded from 60 Sun Ultra-5 machines and 100MBit/s Ethernet to 50 Dual-CPU 1.4GHz Pentium-III systems with Gigabit Ethernet. Combined with an upgrade to Gigabit Ethernet on the source side and a major feature extraction software speedup, this pushes the performance of the BaBar event builder and L3 filter to 5.5kHz at current background levels, almost three times the original design rate of 2kHz. For our specific application the new farm provides 8.5 times the CPU power of the old system.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 4 pages, 1 eps figure, PSN MOGT00

Amperometric separation-free immunosensor for real-time environmental monitoring

Immunoanalytical techniques have found widespread use due to the characteristics of specificity and wide applicability for many analytes, from large polymer antigens, to simple haptens, and even single atoms. Electrochemical sensors offer benefits of technical simplicity, speed and convenience via direct transduction to electronic equipment. Together, these two systems offer the possibility of a convenient, ubiquitous assay technique with high selectivity. However, they are still not widely used, mainly due to the complexity of the associated immunoassay methodologies. A separation-free immunoanalytical technique is described here, which has allowed for the analysis of atrazine in real time and in both quasi-equilibrium and stirred batch configurations. It illustrated that determinations as low as 0.13 muM (28 ppb) could be made using equilibrium incubation with an analytical range of 0.1-10 muM. Measurements could be made between 1 and 10 mM within several minutes using a real-time, stirred batch method. This system offers the potential for fast, simple, cost-effective biosensors for the analysis of many substances of environmental, biomedical and pharmaceutical concern. (C) 2001 Elsevier Science B.V. All rights reserved

Efficient Online Timed Pattern Matching by Automata-Based Skipping

The timed pattern matching problem is an actively studied topic because of its relevance in monitoring of real-time systems. There one is given a log $w$ and a specification $\mathcal{A}$ (given by a timed word and a timed automaton in this paper), and one wishes to return the set of intervals for which the log $w$, when restricted to the interval, satisfies the specification $\mathcal{A}$. In our previous work we presented an efficient timed pattern matching algorithm: it adopts a skipping mechanism inspired by the classic Boyer--Moore (BM) string matching algorithm. In this work we tackle the problem of online timed pattern matching, towards embedded applications where it is vital to process a vast amount of incoming data in a timely manner. Specifically, we start with the Franek-Jennings-Smyth (FJS) string matching algorithm---a recent variant of the BM algorithm---and extend it to timed pattern matching. Our experiments indicate the efficiency of our FJS-type algorithm in online and offline timed pattern matching