Hearing in the mind's ear: A PET investigation of musical imagery and perception

Neuropsychological studies have suggested that imagery processes may be mediated by neuronal mechanisms similar to those used in perception. To test this hypothesis, and to explore the neural basis for song imagery, 12 normal subjects were scanned using the water bolus method to measure cerebral blood flow (CBF) during the performance of three tasks. In the control condition subjects saw pairs of words on each trial and judged which word was longer. In the perceptual condition subjects also viewed pairs of words, this time drawn from a familiar song; simultaneously they heard the corresponding song, and their task was to judge the change in pitch of the two cued words within the song. In the imagery condition, subjects performed precisely the same judgment as in the perceptual condition, but with no auditory input. Thus, to perform the imagery task correctly an internal auditory representation must be accessed. Paired-image subtraction of the resulting pattern of CBF, together with matched MRI for anatomical localization, revealed that both perceptual and imagery. tasks produced similar patterns of CBF changes, as compared to the control condition, in keeping with the hypothesis. More specifically, both perceiving and imagining songs are associated with bilateral neuronal activity in the secondary auditory cortices, suggesting that processes within these regions underlie the phenomenological impression of imagined sounds. Other CBF foci elicited in both tasks include areas in the left and right frontal lobes and in the left parietal lobe, as well as the supplementary motor area. This latter region implicates covert vocalization as one component of musical imagery. Direct comparison of imagery and perceptual tasks revealed CBF increases in the inferior frontal polar cortex and right thalamus. We speculate that this network of regions may be specifically associated with retrieval and/or generation of auditory information from memory.

Decomposing Blaschke Products And Polynomials

The goal of this paper is to contribute to the understanding of complex polynomials and Blaschke products, two very important function classes in mathematics. For a polynomial, $f,$ of degree $n,$ we study when it is possible to write $f$ as a composition $f=g\circ h$, where $g$ and $h$ are polynomials, each of degree less than $n.$ A polynomial is defined to be \emph{decomposable }if such an $h$ and $g$ exist, and a polynomial is said to be \emph{indecomposable} if no such $h$ and $g$ exist. We apply the results of Rickards in \cite{key-2}. We show that $$C_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,(z-z_{1})(z-z_{2})...(z-z_{n})\,\mbox{is decomposable}\},$$ has measure $0$ when considered a subset of $\mathbb{R}^{2n}.$ Using this we prove the stronger result that $$D_{n}=\{(z_{1},z_{2},...,z_{n})\in\mathbb{C}^{n}\,|\,\mbox{There exists\,}a\in\mathbb{C}\,\,\mbox{with}\,\,(z-z_{1})(z-z_{2})...(z-z_{n})(z-a)\,\mbox{decomposable}\},$$ also has measure zero when considered a subset of $\mathbb{R}^{2n}.$ We show that for any polynomial $p$, there exists an $a\in\mathbb{C}$ such that $p(z)(z-a)$ is indecomposable, and we also examine the case of $D_{5}$ in detail. The main work of this paper studies finite Blaschke products, analytic functions on $\overline{\mathbb{D}}$ that map $\partial\mathbb{D}$ to $\partial\mathbb{D}.$ In analogy with polynomials, we discuss when a degree $n$ Blaschke product, $B,$ can be written as a composition $C\circ D$, where $C$ and $D$ are finite Blaschke products, each of degree less than $n.$ Decomposable and indecomposable are defined analogously. Our main results are divided into two sections. First, we equate a condition on the zeros of the Blaschke product with the existence of a decomposition where the right-hand factor, $D,$ has degree $2.$ We also equate decomposability of a Blaschke product, $B,$ with the existence of a Poncelet curve, whose foci are a subset of the zeros of $B,$ such that the Poncelet curve satisfies certain tangency conditions. This result is hard to apply in general, but has a very nice geometric interpretation when we desire a composition where the right-hand factor is degree 2 or 3. Our second section of finite Blaschke product results builds off of the work of Cowen in \cite{key-3}. For a finite Blaschke product $B,$ Cowen defines the so-called monodromy group, $G_{B},$ of the finite Blaschke product. He then equates the decomposability of a finite Blaschke product, $B,$ with the existence of a nontrivial partition, $\mathcal{P},$ of the branches of $B^{-1}(z),$ such that $G_{B}$ respects $\mathcal{P}$. We present an in-depth analysis of how to calculate $G_{B}$, extending Cowen's description. These methods allow us to equate the existence of a decomposition where the left-hand factor has degree 2, with a simple condition on the critical points of the Blaschke product. In addition we are able to put a condition of the structure of $G_{B}$ for any decomposable Blaschke product satisfying certain normalization conditions. The final section of this paper discusses how one can put the results of the paper into practice to determine, if a particular Blaschke product is decomposable. We compare three major algorithms. The first is a brute force technique where one searches through the zero set of $B$ for subsets which could be the zero set of $D$, exhaustively searching for a successful decomposition $B(z)=C(D(z)).$ The second algorithm involves simply examining the cardinality of the image, under $B,$ of the set of critical points of $B.$ For a degree $n$ Blaschke product, $B,$ if this cardinality is greater than $\frac{n}{2}$, the Blaschke product is indecomposable. The final algorithm attempts to apply the geometric interpretation of decomposability given by our theorem concerning the existence of a particular Poncelet curve. The final two algorithms can be implemented easily with the use of an HTML

Nonlethal Screening of Bat-Wing Skin with the Use of Ultraviolet Fluorescence to Detect Lesions Indicative of White-Nose Syndrome

Definitive diagnosis of the bat disease white-nose syndrome (WNS) requires histologic analysis to identify the cutaneous erosions caused by the fungal pathogen Pseudogymnoascus [formerly Geomyces] destructans (Pd). Gross visual inspection does not distinguish bats with or without WNS, and no nonlethal, on-site, preliminary screening methods are available for WNS in bats. We demonstrate that long-wave ultraviolet (UV) light (wavelength 366-385 nm) elicits a distinct orange yellow fluorescence in bat-wing membranes (skin) that corresponds directly with the fungal cupping erosions in histologic sections of skin that are the current gold standard for diagnosis of WNS. Between March 2009 and April 2012, wing membranes from 168 North American bat carcasses submitted to the US Geological Survey National Wildlife Health Center were examined with the use of both UV light and histology. Comparison of these techniques showed that 98.8% of the bats with foci of orange yellow wing fluorescence (n=80) were WNS-positive based on histologic diagnosis; bat wings that did not fluoresce under UV light (n=88) were all histologically negative for WNS lesions. Punch biopsy samples as small as 3 mm taken from areas of wing with UV fluorescence were effective for identifying lesions diagnostic for WNS by histopathology. In a nonlethal biopsy-based study of 62 bats sampled (4-mm diameter) in hibernacula of the Czech Republic during 2012, 95.5% of fluorescent (n=22) and 100% of nonfluorescent (n=40) wing samples were confirmed by histopathology to be WNS positive and negative, respectively. This evidence supports use of long-wave UV light as a nonlethal and field-applicable method to screen bats for lesions indicative of WNS. Further, UV fluorescence can be used to guide targeted, nonlethal biopsy sampling for follow-up molecular testing, fungal culture analysis, and histologic confirmation of WNS.