196,075 research outputs found
Exponentially accurate solution tracking for nonlinear ODEs, the higher order Stokes phenomenon and double transseries resummation
No full textWe demonstrate the conjunction of new exponential-asymptotic effects in the context of a second order nonlinear ordinary differential equation with a small parameter. First, we show how to use a hyperasymptotic, beyond-all-orders approach to seed a numerical solver of a nonlinear ordinary differential equation with sufficiently accurate initial data so as to track a specific solution in the presence of an attractor. Second, we demonstrate the necessary role of a higher order Stokes phenomenon in analytically tracking the transition between asymptotic behaviours in a heteroclinic solution. Third, we carry out a double resummation involving both subdominant and sub-subdominant transseries to achieve the two-dimensional (in terms of the arbitrary constants) uniform approximation that allows the exploration of the behaviour of a two parameter set of solutions across wide regions of the independent variable. This is the first time all three effects have been studied jointly in the context of an asymptotic treatment of a nonlinear ordinary differential equation with a parameter. This paper provides an exponential asymptotic algorithm for attacking such problems when they occur. The availability of explicit results would depend on the individual equation under study
INFORMATION CONTENT OF COYOTE BARKS HOWLS
No full textThe information content of coyote (Canis latrans) vocalizations is poorly understood, but has important implications for understanding coyote behavior. Coyotes probably use information present in barks or howls to recognize individuals, but the presence of individually-specific information has not bean demonstrated. We found that coyote barks and howls contained individually specific characteristics: discriminant analysis correctly classified barks of five coyotes 69% of the time and howls of six coyotes 83% of the time. We also investigated the stability of vocalization characteristics at multiple distances from the source. Recordings were played back and re-recorded at 10 m, 600m, and 1,000m. Vocalization features were measured at each distance and analyzed to determine whether characteristics were stable. Most howl characteristics did not change with distance, and regardless of the distance discriminant analysis was 81% accurate at assigning howls among six individuals. Bark characteristics, however, were less stable and it is unlikely that barks could be used for individual recognition over long distances. The disparate results for the two vocalization types suggest that howls and barks serve separate functions. Howls appear optimized to convey information (i.e. data), while barks seem more suitable for attracting attention and acoustic ranging
Incomplete Airy beams: finite-energy from a sharp spectral cutoff
No full textWe present a mathematical analysis of the finite-energy Airy beam with a sharply truncated spectrum, which can be generated by a uniformly illuminated, finite-sized spatial light modulator, or windowed cubic phase mask. The resulting “incomplete Airy beam” is tractable mathematically, and differs from an infinite-energy Airy beam by an additional oscillating modulation and the decay of its fringes. Its propagation can be described explicitly using an incomplete Airy function, from which we derive simple expressions for the beam’s total power and mean position. Asymptotic analysis reveals a simple connection between the cutoff and the region of the beam with Airy-like behavior
The acoustic structure of wolf howls in some eastern Tuscany (central Italy) free ranging packs
No full textItalian wolf howls are described for the first time from observations between 2003-2008 of a population living in eastern Tuscany, central Italy. A sample of 37 howls selected among single responses and 128 howls included in the choruses of 7 free ranging packs was recorded and analysed. The mean fundamental frequency of the howls ranged between 274-908 Hz. Two main structures recognised by means of multivariate explorative analysis, in particular Principal Component and Cluster Analysis, were ascribed to breaking and flat howls. Discriminant Function Analysis was applied to the recognised groups with the aim to find a general rule for classification. Howls with different features were correctly assigned to the groups obtained by explorative analysis in 95.8% of cases. The analysis of the variables characterising the structure of the howls suggests that maximum frequency and range of fundamental frequency are the most important parameters for classification, while duration does not appear to play any significant role
Electronic submission – Analogy with the Severn Bore
No full textIntroducing Elsevier's electronic submission system (EES) to the many erudite academics, clinicians and researchers who contribute to Medical Engineering & Physics (MEP) could have been a bore. I hope the physical scientists amongst you, who will recognise this natural phenomenon as a step function modulated by an Airy function, will forgive the pun. I was brought up in an area of the UK where the river Severn gives rise to the occurrence of a wave that can be equally like riding a roller coaster or a bit of a damp squib. It is thus with that same slightly nervous, queasy feeling that we embarked upon presenting the system to the many people submitting to MEP.During the last quarter there have been many peaks and troughs whilst the system has moved towards a seamless publishing service, but the transients have given way to a stable soliton.The main advantage of EES is the streamlining of effort required by all involved, not least the authors and reviewers. For authors it speeds up submission and turn-around of reviews. Authors can upload electronic copy written using a variety of word-processing software. The system automatically converts the files to portable document format (pdf). Conversion of complicated figures and mathematical formulae are also handled efficiently. To date very few problems have arisen and those that have occurred have been swiftly and satisfactorily resolved by our author support team.Reviewers are able to receive an abstract along with their invitation to review before agreeing to act as a referee. Both editors and reviewers can electronically view the full manuscript, search for similar articles and submit reports to the editorial office. Manuscripts are passed securely to the production office keeping their unique identifying number and authors can view progress of their work throughout the editorial process.Thus, as publication lead times improve even further we look forward to receiving your manuscripts and publishing the cutting edge research for which MEP is renowned
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Improving individual identification of wolves (Canis lupus) using the fundamental frequency and amplitude of their howls: a new survey method
No full textMany bioacoustic studies have been able to identify individual mammals from variations in the fundamental frequency (F0) of their vocalizations. Other characteristics of vocalization which encode individuality, such as amplitude, are less frequently used because of problems with background noise and recording fidelity over distance. In this thesis, I investigate whether the inclusion of amplitude variables improves the accuracy of individual howl identification in captive Eastern grey wolves (Canis lupus lycaon). I also explore whether the use of a bespoke code to extract the howl features, combined with histogram-derived principal component analysis (PCA) values, can improve current individual wolf howl identification accuracies. From a total of 89 solo howls from six captive individuals, where distances between wolf and observer were short, I achieved 95.5% (+9.0% improvement) individual identification accuracy of captive wolves using discriminant function analysis (DFA) to classify simple scalar variables of F0 and normalized amplitudes. Moreover, this accuracy was increased to 100% when using histogram-derived PCA values of F0 and amplitudes of the first harmonic
Valuation of soccer spread bets
No full textSimple statistical and probabilistic arguments are used to value the most commonly traded online soccer spread bets. Such markets typically operate dynamically during the course of a match and accurate valuations must, therefore, reflect the changing state of the match. Both goals and corners are assumed to evolve as Poisson processes with constant means. Although many of the bets that are typically traded are relatively easy to value, some (including the 'four flags' market) require more detailed analysis. Examples are given of the evolution of the spread during typical matches and theoretical predictions are shown to compare closely to spreads quoted by online bookmakers during some of the important matches of the EURO2004 tournament
On the resurgence properties of the uniform asymptotic expansion of Bessel functions of high order
No full textFor the coefficients An(‘) and Bn(‘), that occur in the uniform asymptotic expansions of Bessel functions of large order, we give asymptotic expansions as n M X. The coefficients in these asymptotic expansions are again Am>(‘) and Bm(‘), and the asymptotic base consists of functions Apq(n,‘), which can be seen as new generalizations of the Airy function. We describe the asymptotic behaviour of the functions Apq(n, ‘), as n to infinity, and we compute the Taylor-series expansions of Apq(n, ‘) at ‘ = 0. Two numerical examples are included
Axial and focal-plane diffraction catastrophe integrals
No full textExact expressions in terms of Bessel functions are found for some of the diffraction catastrophe integrals that decorate caustics in optics and mechanics. These are the axial and focal-plane sections of the elliptic and hyperbolic umbilic diffraction catastrophes, and symmetric elliptic and hyperbolic unfoldings of the X_9 diffraction catastrophes. These representations reveal unexpected relations between the integrals
When is a Stokes line not a Stokes line?
No full textDuring the course of a Stokes phenomenon, an asymptotic expansion can change its form as a further series, prefactored by an exponentially small term and a Stokes multiplier, appears in the representation. The initially exponentially small contribution may nevertheless grow to dominate the behaviour for other values of the asymptotic or associated parameters.We introduce the concept of a higher order Stokes phenomenon, at which a Stokes multiplier itself can change value. We show that the higher order Stokes phenomenon can be used to explain the apparent sudden birth of Stokes lines at regular points, why some Stokes lines are irrelevant to a given problem and why it is indispensible to the proper derivation of expansions that involve three or more possible asymptotic contributions. We provide an example of how the higher order Stokes phenomenon can have important effects on the large time behaviour of linear partial differential equations.Subsequently we apply these techniques to Burgers equation, a non-linear partial differential equation developed to model turbulent fluid flow. We find that the higher order Stokes phenomenon plays a major, yet very subtle role in the smoothed shock wave formation of this equation
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