Expert Rule Versus Majority Rule Under Partial Information, II

The main purpose of this paper is clarifying the connection between some characteristics of a deciding body and the probability of its making correct decisions. In our model a group of decision makers is required to select one of two alternatives. We assume the probabilities of the decision makers being correct are independent random variables distributed according to the same given distribution rule. This distribution belongs to a general family, containing the uniform distribution as a particular case. We investigate the behavior of the probability of the expert rule being optimal, as well as that of the majority rule, both as functions of the distribution parameter and the group size. The main result is that for any value of the distribution parameter the expert rule is far more likely to be optimal than the majority rule, especially as the deciding body becomes larger.     

Average speaking fundamental frequency in soprano singers with and without symptoms of vocal attrition

Nineteen trained soprano singers aged 18–30 years vocalized tasks designed to assess average speaking fundamental frequency (SFF) during spontaneous speaking and reading. Vocal range and perceptual characteristics while singing with low intensity and high frequency were also assessed, and subjects completed a survey of vocal habits/symptoms. Recorded signals were digitized prior to being analyzed for SFF using the Kay Computerized Speech Lab program. Subjects were assigned to a normal voice or impaired voice group based on ratings of perceptual tasks and survey results. Data analysis showed group differences in mean SFF, no differences in vocal range, higher mean SFF values for reading than speaking, and 58% ability to perceive speaking in low pitch. The role of speaking in too low pitch as causal for vocal symptoms and need for voice classification differentiation in vocal performance studies are discussed.     

Voice quality changes following phonatory-respiratory effort treatment (LSVT) versus respiratory effort treatment for individuals with Parkinson disease.

Perceptual ratings of hoarseness and breathiness were used to assess the efficacy of two intensive methods for treating dysarthrophonia in individuals with idiopathic Parkinson disease. One method emphasized phonatory-respiratory effort (the Lee Silverman Voice Treatment, LSVT) and the other emphasized respiratory effort alone (RET). Perceptual ratings were performed by two expert listeners based on random order presentation of the patients' pretreatment and posttreatment recordings of the "Rainbow Passage." The listeners were blinded to the patients and their treatment group. Statistically significant pretreatment to posttreatment improvement in hoarseness and breathiness was observed in the LSVT group but not in the RET group. The present findings are consistent with acoustic and physiologic findings reported previously, providing further evidence for the efficacy of the LSVT.     

Ascending Hnn Extensions of Finitely Generated Free Groups Are Hopfian

It is shown that every ascending HNN extension of a finitelygenerated free group is Hopfian. An important ingredient inthe proof is that under certain hypotheses on the group H, ifG is an ascending HNN extension of H, then cd(G) = cd(H) + 1.     

Wetting, mixing, and phase transitions in Langmuir-Gibbs films

Millimolar bulk concentrations of the surfactant cetyltrimethylammonium bromide (CTAB) induce spreading of alkanes, H(CH(2))(n)H (denoted C(n)) 12< or =n< or =21, on the water surface, which is not otherwise wet by these alkanes. The novel Langmuir-Gibbs film (LGF) formed is a liquidlike monolayer comprising both alkanes and CTAB tails. Upon cooling, an ordering transition occurs, yielding a hexagonally packed, quasi-2D crystal. For 11< or =n< or =17 this surface-frozen LGF is a crystalline monolayer. For 18< or =n< or =21 the LGF is a bilayer with a crystalline, pure-alkane, upper monolayer, and a liquidlike lower monolayer. The phase diagram and film structure were determined by x-ray, ellipsometry, and surface tension measurements. A thermodynamic theory accounts quantitatively for the observations.     

Groups with small Dehn functions and bipartite chord diagrams

We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function n²log n. Some of these groups have undecidable conjugacy problem. Our groups are multiple HNN extensions of free groups. We show that n²log n is the smallest Dehn function of a multiple HNN extension of a free group with undecidable conjugacy problem. Both authors were supported in part by the NSF grants DMS 0245600 and DMS 0455881. In addition, the research of the first author was supported in part by the Russian Fund for Basic Research 05-01-00895, the research of the second author was supported in part by the NSF grant DMS 9978802 and the US-Israeli BSF grant 1999298. Received: February 2005; Revision: September 2005; Accepted: September 2005     

On definability in some lattices of semigroup varieties

An identity of the form x ₁?x _n ??x _1?? x _2?? ?x _n?? where ?? is a non-trivial permutation on the set {1,??,n} is called a permutation identity. If u??v is a permutation identity, then ?(u??v) [respectively r(u??v)] is the maximal length of the common prefix [suffix] of the words u and v. A variety that satisfies a permutation identity is called permutative. If $\mathcal{V}$ is a permutative variety, then $\ell=\ell(\mathcal{V})$ [respectively $r=r(\mathcal{V})$ ] is the least ? [respectively r] such that $\mathcal{V}$ satisfies a permutation identity ?? with ?(??)=? [respectively r(??)=r]. A?variety that consists of nil-semigroups is called a nil-variety. If ?? is a set of identities, then $\operatorname {var}\varSigma$ denotes the variety of semigroups defined by ??. If $\mathcal{V}$ is a variety, then $L (\mathcal{V})$ denotes the lattice of all subvarieties of $\mathcal{V}$ . For ?,r??0 and n>1 let $\mathfrak{B}_{\ell,r,n}$ denote the set that consists of n! identities of the form $$t_1\cdots t_\ell x_1x_2 \cdots x_n z_{1}\cdots z_{r}\approx t_1\cdots t_\ell x_{1\pi}x_{2\pi} \cdots x_{n\pi}z_{1}\cdots z_{r}, $$ where ?? is a permutation on the set {1,??,n}. We prove that for each permutative nil-variety $\mathcal{V}$ and each $\ell\ge\ell(\mathcal{V})$ and $r\ge r(\mathcal{V})$ there exists n>1 such that $\mathcal{V}$ is definable by a first-order formula in $L(\operatorname{var}{\mathfrak{B}}_{l,r,n})$ if ???r or $\mathcal{V}$ is definable up to duality in $L(\operatorname{var}{\mathfrak{B}}_{\ell,r,n})$ if ?=r.     

Optimality of the Expert Rule Under Partial Information

We study the uncertain dichotomous choice model. In this model a group of decision makers is required to select one of two alternatives. The applications of this model are relevant to a wide variety of areas, such as medicine, management and banking. The decision rule may be the simple majority rule; however, it is also possible to assign more weight to the opinion of members known to be more qualified. The extreme example of such a rule is the expert decision rule. We are concerned with the probability of the expert rule to be optimal. Our purpose is to investigate the behaviour of this probability as a function of the group size for several rather general types of distributions. One such family of distributions is that where the density function of the correctness probability is a polynomial (on the interval [1/2,1]). Our main result is an explicit formula for the probability in question. This contains formerly known results as very special cases.     

Diagram groups and directed 2-complexes: Homotopy and homology

We show that diagram groups can be viewed as fundamental groups of spaces of positive paths on directed 2-complexes (these spaces of paths turn out to be classifying spaces). Thus diagram groups are analogs of second homotopy groups, although diagram groups are as a rule non-Abelian. Part of the paper is a review of the previous results from this point of view. In particular, we show that the so-called rigidity of the R. Thompson's group F and some other groups is similar to the flat torus theorem. We find several finitely presented diagram groups (even of type F_∞) each of which contains all countable diagram groups. We show how to compute minimal presentations and homology groups of a large class of diagram groups. We show that the Poincaré series of these groups are rational functions. We prove that all integer homology groups of all diagram groups are free Abelian.