Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis

In this paper, we discuss the mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. The Schrödinger equation and Heisenberg uncertainty principles are structured within local fractional operators.

Sexual dimorphism of the human mandible: demonstration by elliptical Fourier analysis.

A new quantitative approach of the mandibular sexual dimorphism, based on computer-aided image analysis and elliptical Fourier analysis of the mandibular outline in lateral view is presented. This method was applied to a series of 117 dentulous mandibles from 69 male and 48 female individuals native of Rhenish countries. Statistical discriminant analysis of the elliptical Fourier harmonics allowed the demonstration of a significant sexual dimorphism in 97.1% of males and 91.7% of females, i.e. in a higher proportion than in previous studies using classical metrical approaches. This original method opens interesting perspectives for increasing the accuracy of sex identification in current anthropological practice and in forensic procedures.

Analisi morfometrica classica ed EFA (Elliptic Fourier Analysis) degli otoliti del genere Mullus in Alto - Medio Adriatico.

L’obiettivo del presente lavoro di tesi è stato quello di analizzare i campioni di otoliti delle due specie del genere Mullus (Mullus barbatus e Mullus surmuletus) per mezzo dell’Analisi Ellittica di Fourier (EFA) e l’analisi di morfometria classica con gli indici di forma, al fine di verificare la simmetria tra l’otolite destro e sinistro in ognuna delle singole specie di Mullus e se varia la forma in base alla taglia dell’individuo. Con l’EFA è stato possibile mettere a confronto le forme degli otoliti facendo i confronti multipli in base alla faccia, al sesso e alla classe di taglia. Inoltre è stato fatto un confronto tra le forme degli otoliti delle due specie. Dalle analisi EFA è stato possibile anche valutare se gli esemplari raccolti appartenessero tutti al medesimo stock o a stock differenti. Gli otoliti appartengono agli esemplari di triglia catturati durante la campagna sperimentale MEDITS 2012. Per i campioni di Mullus surmuletus, data la modesta quantità, sono stati analizzati anche gli otoliti provenienti dalla campagna MEDITS 2014 e GRUND 2002. I campioni sono stati puliti e analizzati allo stereomicroscopio con telecamera e collegato ad un PC fornito di programma di analisi di immagine. Dalle analisi di morfometria classica sugli otoliti delle due specie si può sostenere che in generale vi sia una simmetria tra l’otolite destro e sinistro. Dalle analisi EFA sono state riscontrate differenze significative in tutti i confronti, anche nel confronto tra le due specie. I campioni sembrano però appartenere al medesimo stock. In conclusione si può dire che l’analisi di morfometria classica ha dato dei risultati congrui con quello che ci si aspettava. I risultati dell’analisi EFA invece hanno evidenziato delle differenze significative che dimostrano una superiore potenza discriminante. La particolare sensibilità dell’analisi dei contorni impone un controllo di qualità rigoroso durante l’acquisizione delle forme.

Fourier analysis of the aerodynamic behavior of cup anemometers

The calibration results (the transfer function) of an anemometer equipped with several cup rotors were analyzed and correlated with the aerodynamic forces measured on the isolated cups in a wind tunnel. The correlation was based on a Fourier analysis of the normal-to-the-cup aerodynamic force. Three different cup shapes were studied: typical conical cups, elliptical cups and porous cups (conical-truncated shape). Results indicated a good correlation between the anemometer factor, K, and the ratio between the first two coefficients in the Fourier series decomposition of the normal-to-the-cup aerodynamic force

Computer program to perform Fourier analysis of x-ray data /

"U.S. Atomic Energy Commission Contract AT(29-1)-1106."

Double Fourier analysis for Emotion Identification in Voiced Speech

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech -- Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions -- A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds -- Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions -- Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it -- Finally features related with emotions in voiced speech are extracted and presented

Analysis of β-amyloid (Aβ) deposition in the temporal lobe in Alzheimer's disease using Fourier (spectral) analysis

To determine the spatial pattern of ß-amyloid (Aß) deposition throughout the temporal lobe in Alzheimer's disease (AD). Methods: Sections of the complete temporal lobe from six cases of sporadic AD were immunolabelled with antibody against Aß. Fourier (spectral) analysis was used to identify sinusoidal patterns in the fluctuation of Aß deposition in a direction parallel to the pia mater or alveus. Results: Significant sinusoidal fluctuations in density were evident in 81/99 (82%) analyses. In 64% of analyses, two frequency components were present with density peaks of Aß deposits repeating every 500–1000 µm and at distances greater than 1000 µm. In 25% of analyses, three or more frequency components were present. The estimated period or wavelength (number of sample units to complete one full cycle) of the first and second frequency components did not vary significantly between gyri of the temporal lobe, but there was evidence that the fluctuations of the classic deposits had longer periods than the diffuse and primitive deposits. Conclusions: (i) Aß deposits exhibit complex sinusoidal fluctuations in density in the temporal lobe in AD; (ii) fluctuations in Aß deposition may reflect the formation of Aß deposits in relation to the modular and vascular structure of the cortex; and (iii) Fourier analysis may be a useful statistical method for studying the patterns of Aß deposition both in AD and in transgenic models of disease.

Dynamical analysis of compositions

This paper analyzes musical opus from the point of view of two mathematical tools, namely the entropy and the multidimensional scaling (MDS). The Fourier analysis reveals a fractional dynamics, but the time rhythm variations are diluted along the spectrum. The combination of time-window entropy and MDS copes with the time characteristics and is well suited to treat a large volume of data. The experiments focus on a large number of compositions classified along three sets of musical styles, namely “Classical”, “Jazz”, and “Pop & Rock” compositions. Without lack of generality, the present study describes the application of the tools and the sets of musical compositions in a methodology leading to clear conclusions, but extensions to other possibilities are straightforward. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments toward a dynamical analysis of musical compositions.

FMRI 3D registration based on Fourier space subsets using neural networks

In this work, we present a neural network (NN) based method designed for 3D rigid-body registration of FMRI time series, which relies on a limited number of Fourier coefficients of the images to be aligned. These coefficients, which are comprised in a small cubic neighborhood located at the first octant of a 3D Fourier space (including the DC component), are then fed into six NN during the learning stage. Each NN yields the estimates of a registration parameter. The proposed method was assessed for 3D rigid-body transformations, using DC neighborhoods of different sizes. The mean absolute registration errors are of approximately 0.030 mm in translations and 0.030 deg in rotations, for the typical motion amplitudes encountered in FMRI studies. The construction of the training set and the learning stage are fast requiring, respectively, 90 s and 1 to 12 s, depending on the number of input and hidden units of the NN. We believe that NN-based approaches to the problem of FMRI registration can be of great interest in the future. For instance, NN relying on limited K-space data (possibly in navigation echoes) can be a valid solution to the problem of prospective (in frame) FMRI registration.

Particle swarm optimization: dynamical analysis through fractional calculus

This chapter considers the particle swarm optimization algorithm as a system, whose dynamics is studied from the point of view of fractional calculus. In this study some initial swarm particles are randomly changed, for the system stimulation, and its response is compared with a non-perturbed reference response. The perturbation effect in the PSO evolution is observed in the perspective of the fitness time behaviour of the best particle. The dynamics is represented through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence upon the global dynamics is also analyzed. Two main issues are reported: the PSO dynamics when the system is subjected to random perturbations, and its modelling with fractional order transfer functions.

Analysis of micro- and nano-structures of the corneal surface of Drosophila and its mutants by atomic force microscopy and optical diffraction.

Drosophila melanogaster is a model organism instrumental for numerous biological studies. The compound eye of this insect consists of some eight hundred individual ommatidia or facets, ca. 15 µm in cross-section. Each ommatidium contains eighteen cells including four cone cells secreting the lens material (cornea). High-resolution imaging of the cornea of different insects has demonstrated that each lens is covered by the nipple arrays--small outgrowths of ca. 200 nm in diameter. Here we for the first time utilize atomic force microscopy (AFM) to investigate nipple arrays of the Drosophila lens, achieving an unprecedented visualization of the architecture of these nanostructures. We find by Fourier analysis that the nipple arrays of Drosophila are disordered, and that the seemingly ordered appearance is a consequence of dense packing of the nipples. In contrast, Fourier analysis confirms the visibly ordered nature of the eye microstructures--the individual lenses. This is different in the frizzled mutants of Drosophila, where both Fourier analysis and optical imaging detect disorder in lens packing. AFM reveals intercalations of the lens material between individual lenses in frizzled mutants, providing explanation for this disorder. In contrast, nanostructures of the mutant lens show the same organization as in wild-type flies. Thus, frizzled mutants display abnormal organization of the corneal micro-, but not nano-structures. At the same time, nipples of the mutant flies are shorter than those of the wild-type. We also analyze corneal surface of glossy-appearing eyes overexpressing Wingless--the lipoprotein ligand of Frizzled receptors, and find the catastrophic aberration in nipple arrays, providing experimental evidence in favor of the major anti-reflective function of these insect eye nanostructures. The combination of the easily tractable genetic model organism and robust AFM analysis represents a novel methodology to analyze development and architecture of these surface formations.

Fourier transform convolution integrals applied to generalized Born molecular volume.

Generalized Born methods are currently among the solvation models most commonly used for biological applications. We reformulate the generalized Born molecular volume method initially described by (Lee et al, 2003, J Phys Chem, 116, 10606; Lee et al, 2003, J Comp Chem, 24, 1348) using fast Fourier transform convolution integrals. Changes in the initial method are discussed and analyzed. Finally, the method is extensively checked with snapshots from common molecular modeling applications: binding free energy computations and docking. Biologically relevant test systems are chosen, including 855-36091 atoms. It is clearly demonstrated that, precision-wise, the proposed method performs as good as the original, and could better benefit from hardware accelerated boards.