Losslessness and stability of LDI ladders and filters

The stability of digital ladder filters close in form, via the lossless discrete integrator (LDI) transformation, to doubly terminatedLC Cauer ladder low-pass filters is studied. The LDI transformation does not necessarily map stable analogue into stable digital filters. Necessary and sufficient conditions for these digital filter to be lossless and for a corresponding doubly terminated filter to be stable are given. LDIs are often used in the design of switched capacitor (SC) filters. For this case we provide a threshold sampling rate above which the SC LDI filter retains the stability of the analogue filter. In spite of the stability problem with the LDI mapping, it has been observed that when applied to simulate analogue filters the resulting filter is stable. It can now be argued that, in these cases, other factors in the determination of the sampling rate leads typically to a choice that is also sufficiently above the threshold rate for stability. The theory described is also useful to derive more general digital filters and to perform the design of stable LDI filters exclusively in the Z-plane without reference to analogue prototypes.This work was partly supported by the U.S.-Israel Binational Science Foundation under Grant No. 88-425.     

Random Cayley graphs and expanders

For every 1 > δ > 0 there exists a c = c(δ) > 0 such that for every group G of order n, and for a set S of c(δ) log n random elements in the group, the expected value of the second largest eigenvalue of the normalized adjacency matrix of the Cayley graph X(G, S) is at most (1 - δ). This implies that almost every such a graph is an ?(δ)-expander. For Abelian groups this is essentially tight, and explicit constructions can be given in some cases. © 1994 John Wiley & Sons, Inc.     

Evaluating the Influence of Warmup on Singing Voice Quality Using Acoustic Measures

Vocal warmup is generally accepted as vital for singing performance. However, only a limited number of studies have evaluated this effect quantitatively. In this study, we evaluated the effect of vocal warmup on voice production, among young female singers, using a set of acoustic parameters. Warmup reduced frequency-perturbation (p < 0.001) and amplitude-perturbation values (p < 0.05). In addition, warmup increased singer's formant amplitude (p < 0.05) and improved noise-to-harmonic ratio (p < 0.05). Tone-matching accuracy, however, was not affected by warmup. The effect of vocal warmup on frequency-perturbation parameters was more evident among mezzo-soprano singers than it was among soprano singers. It was also more evident in the low pitch-range than in the higher pitch-ranges (p < 0.05). The results of this study provide valid support for the advantageous effect of vocal warmup on voice quality and present acoustic analysis as a valuable and sensitive tool for quantifying this effect.     

Crack growth resistance of shape memory alloys by means of a cohesive zone model

Crack growth resistance of shape memory alloys (SMAs) is dominated by the transformation zone in the vicinity of the crack tip. In this study, the transformation toughening behavior of a slowly propagating crack in an SMA under plane strain conditions and mode I deformation is numerically investigated. A small-scale transformation zone is assumed. A cohesive zone model is implemented to simulate crack growth within a finite element scheme. Resistance curves are obtained for a range of parameters that specify the cohesive traction-separation constitutive law. It is found that the choice of the cohesive strength t₀ has a great influence on the toughening behavior of the material. Moreover, the reversibility of the transformation can significantly reduce the toughening of the alloy. The shape of the initial transformation zone, as well as that of a growing crack is determined. The effect of the Young's moduli ratio of the martensite and austenite phases is examined.     

Schur-positive sets of permutations via products and grid classes

Characterizing sets of permutations whose associated quasisymmetric function is symmetric and Schur-positive is a long-standing problem in algebraic combinatorics. In this paper, we present a general method to construct Schur-positive sets and multisets, based on geometric grid classes and the product operation. Our approach produces many new instances of Schur-positive sets and provides a broad framework that explains the existence of known such sets that until now were sporadic cases.     

On Lipschitz extension from finite subsets

We prove that for every n ∈ ? there exists a metric space (X, d _X), an n-point subset S ? X, a Banach space (Z, \({\left\| \right\|_Z}\)) and a 1-Lipschitz function f: S → Z such that the Lipschitz constant of every function F: X → Z that extends f is at least a constant multiple of \(\sqrt {\log n} \). This improves a bound of Johnson and Lindenstrauss [JL84]. We also obtain the following quantitative counterpart to a classical extension theorem of Minty [Min70]. For every α ∈ (1/2, 1] and n ∈ ? there exists a metric space (X, d _X), an n-point subset S ? X and a function f: S → ?₂ that is α-Hölder with constant 1, yet the α-Hölder constant of any F: X → ?₂ that extends f satisfies \({\left\| F \right\|_{Lip\left( \alpha \right)}} > {\left( {\log n} \right)^{\frac{{2\alpha - 1}}{{4\alpha }}}} + {\left( {\frac{{\log n}}{{\log \log n}}} \right)^{{\alpha ^2} - \frac{1}{2}}}\). We formulate a conjecture whose positive solution would strengthen Ball’s nonlinear Maurey extension theorem [Bal92], serving as a far-reaching nonlinear version of a theorem of König, Retherford and Tomczak-Jaegermann [KRTJ80]. We explain how this conjecture would imply as special cases answers to longstanding open questions of Johnson and Lindenstrauss [JL84] and Kalton [Kal04].     

Novel algorithms for the network lifetime problem in wireless settings

One of the major concerns in wireless ad-hoc networks design is energy efficiency. Wireless devices are typically equipped with a limited energy supply sufficient only for a limited amount of time which is reversely proportional to the transmission power of the device. The network lifetime is defined as the time the first device runs out of its initial energy charge. In this paper we study the maximum network lifetime problem for broadcast and data gathering in wireless settings. We provide polynomial time approximation algorithms, with guaranteed performance bounds while considering omnidirectional and unidirectional transmissions. We also consider an extended variant of the maximum lifetime problem, which simultaneously satisfies additional constraints, such as bounded hop-diameter and degree of the routing tree, and minimizing the total energy used in a single transmission. Finally, we evaluate the performance of some of our algorithms through simulations.     

Enumeration and randomized constructions of hypertrees

Over 30 years ago, Kalai proved a beautiful d‐dimensional analog of Cayley's formula for the number of n‐vertex trees. He enumerated d‐dimensional hypertrees weighted by the squared size of their (d ? 1)‐dimensional homology group. This, however, does not answer the more basic problem of unweighted enumeration of d‐hypertrees, which is our concern here. Our main result, Theorem 1.4, significantly improves the lower bound for the number of d‐hypertrees. In addition, we study a random 1‐out model of d‐complexes where every (d ? 1)‐dimensional face selects a random d‐face containing it, and show that it has a negligible d‐dimensional homology.     

Q-switching an all-fiber laser using acousto-optic null coupler

A new method for Q-switching an all-fiber laser is presented. It is based on induced acoustic long period grating operating on a null coupler, which acts as acoustically controlled tunable output coupler. Q-switching is achieved by switching on and off the acoustic wave in a burst mode, thereby generating laser pulses that are ~400 times shorter than the acoustically controlled coupler’s rise time. Output pulse energy of 22 μJ and temporal width of ~100 ns were measured at a wavelength of 1.54 μm.     

Statistics on wreath products and generalized binomial-stirling numbers

Various statistics on wreath products are defined via canonical words, “colored” right to left minima and “colored” descents. It is shown that refined counts with respect to these statistics have nice recurrence formulas of binomial-Stirling type. These extended Stirling numbers determine (via matrix inversion) dual systems, which are also shown to have combinatorial realizations within the wreath product. The above setting also gives rise to a MacMahon-type equi-distribution theorem over subsets with prescribed statistics. Partially supported by Minerva Grant No. 8441 and by EC's IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272. Partially supported by EC's IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272.