Hartry Field argues that conservative rather than true mathematical sentences facilitate deductions in nominalist (i.e., abstracta-free) science without prejudging its empirical outcomes. In this paper, I identify one branch of mathematics as nonconservative, for its indispensable role in enabling nominalist language about a fundamental scientific property, in a fictional scientific community. The fundamental property is electromagnetic reflectance, and the mathematics is Fourier analysis, which renders reflectance ascribable, and nominalist reflectance claims utterable, by this community. Using a recent characterization (...) of conservativeness by Kenneth Boyce, I argue that infinitudes can be rendered inherently mathematical and non-nominalizable in the fictional community, and that rendering infinitudes inherently mathematical for all real communities would yield a convincing counterexample to Fieldian conservativeness. (shrink)

Center of pressure measurements are often used to identify balance problems. A new method for COP signal analysis using mean frequency is proposed in this paper. The computation of mean frequency is based on the Fourier–Bessel expansion that is suitable for use in non-stationary COP signals. In addition, FB expansion provides better frequency resolution and low frequency detectability. Seventeen subjects were tested under eyes open and eyes closed conditions, with different vibration frequencies applied for the eyes closed condition (...) in order to further perturb sensory information. More accurate estimates of mean frequency were obtained for 200-point segments, with significant increase in mean frequency observed over time as subjects recovered from the initial perturbation of stepping on to the force plate. Subjects were significantly more stable in the mediolateral direction compared to anteroposterior one. Mean frequency as calculated by FB expansion was able to distinguish between eyes open and eyes closed conditions, but no effect of vibration could be detected. (shrink)

Beyond being the first substantial publication on Fourier, this work contains the text of Fourier's seminal paper of 1807 on the propagation of heat, marking the first time it has ever appeared in print. This paper incorporates many of the mathematical creations on which Fourier's fame rests, including derivation of the diffusion equation, the separation of the treatment of surface phenomena from internal phenomena, the use of boundary values and initial conditions, and the development of "Fourier (...) series" and the so-called "Bessel functions."When submitted to the examiners of the Institut de France, the originality of the paper and the surprising nature of some of its mathematical revelations caused great controversy, and it was denied publication both in 1807 and in later years. Fourier had the support, among the examiners, of Laplace and Monge, but Lagrange was adamantly in opposition, so that Fourier's work did not appear in print until 1822, reworked into book form.Fourier's mathematical discoveries are intimately related to his interest in the solution of physical problems and their experimental verification. The mathematical methods he developed in connection with heat diffusion apply to physical situations far beyond the boundaries of this area. Generally, Fourier may be credited with one of the first major extensions of mathematical physics beyond the applications of Newton's laws of motion and universal gravitation.The opening biographical chapter of this book follows Fourier's career up to the submission of the 1807 paper, and the two closing chapters take up his life and work from that point on. Fourier had strong political motivations and spent much of his life in the public service. These chapters trace his political difficulties, both before and after 1807, when he was the prefect of a department of France and was subjected to the dislocations of Napoleon's ups and downs. These chapters also describe aspects of the turbulent but productive development of French science from the Revolution to 1830.The core of the book presents the paper of 1807 in its original French and with the original notation. Grattan-Guinness has divided the paper into sections by the sequence of the problems taken up, and he introduces and, where necessary, closes each section with commentary relevant to Fourier's later work in these areas. The paper itself (cllows the chronology of Fourier's discoveries, and among the topics treated are, in this order: heat diffusion between disjoint bodies and in continuous bodies; the appearance of partial differential equations; the special solution for the lamina; sine and cosine series for an arbitrary function; reflections on the vibrating string problem; solution for the annulus; the full Fourier series for an arbitrary function; reflections on n-body analysis; solution for the sphere; solution for the cylinder; steady-state diffusion in the rectangular prism; time-dependent diffusion in the cube; and Fourier's experimental work. (shrink)

The present research used archaeological data, i.e., the data obtained from kamekan jar burials in the Mikuni Hills of the northern Kyushu area in the Mid- dle Yayoi period, to test the parochial altruism model. This model argued that out-group hate and in-group favor coevolved via prehistoric intergroup conflicts. If this model is accurate, such an out-group hate and in-group favor could be re- flected in the archaeological remains, such as pottery making; the more frequent intergroup conflicts are and the (...) more each group is opposed, the more independent and coherent each group will be and more evident cultural identity could be estab- lished within each group. We employed an elliptic Fourier analysis for the shapes of kamekan jar burials. We examined whether frequent intergroup conflicts in the period influenced kamekan jar pottery between subareas of the Mikuni Hills. The results suggested that the shapes of kamekan jar burials after the KIIIa type are slightly different between subareas, which is partially consistent with the model. However, the results do not support the model directly. (shrink)

In the automatic detection of epileptic seizures, the monitoring of critically ill patients with time varying EEG signals is an essential procedure in intensive care units. There is an increasing interest in using EEG analysis to detect seizure, and in this study we aim to get a better understanding of how to visualize the information in the EEG time-frequency feature, and design and train a novel random forest algorithm for EEG decoding, especially for multiple-levels of illness. Here, we propose (...) an automatic detection framework for epileptic seizure based on multiple time-frequency analysis approaches; it involves a novel random forest model combined with grid search optimization. The short-time Fourier transformation visualizes seizure features after normalization. The dimensionality of features is reduced through principal component analysis before feeding them into the classification model. The training parameters are optimized using grid search optimization to improve detection performance and diagnostic accuracy by in the recognition of three different levels epileptic of conditions (healthy subjects, seizure-free intervals, seizure activity). Our proposed model was used to classify 500 samples of raw EEG data, and multiple cross-validations were adopted to boost the modeling accuracy. Experimental results were evaluated by an accuracy, a confusion matrix, a receiver operating characteristic curve and an area under the curve. The evaluations indicated that our model achieved the more effective classification than some previous typical methods. Such a scheme for computer-assisted clinical diagnosis of seizures has a potential guiding significance, which not only relieves the suffering of patient with epilepsy to improve quality of life, but also helps neurologists reduce their workload. (shrink)

We first discuss some technical questions which arise in connection with the construction of undecidable propositions in analysis, in particular in connection with the notion of the normal form of a function representing a predicate. Then it is stressed that while a function f(x) may be computable in the sense of recursive function theory, it may nevertheless have undecidable properties in the realm of Fourier analysis. This has an implication for a conjecture of Penrose's which states that (...) classical physics is computable. (shrink)

The long-periodic/infinite discrete Gabor transform is more effective than the periodic/finite one in many applications. In this paper, a fast and effective approach is presented to efficiently compute the Gabor analysis window for arbitrary given synthesis window in DGT of long-periodic/infinite sequences, in which the new orthogonality constraint between analysis window and synthesis window in DGT for long-periodic/infinite sequences is derived and proved to be equivalent to the completeness condition of the long-periodic/infinite DGT. By using the property of (...) delta function, the original orthogonality can be expressed as a certain number of linear equation sets in both the critical sampling case and the oversampling case, which can be fast and efficiently calculated by fast discrete Fourier transform. The computational complexity of the proposed approach is analyzed and compared with that of the existing canonical algorithms. The numerical results indicate that the proposed approach is efficient and fast for computing Gabor analysis window in both the critical sampling case and the oversampling case in comparison to existing algorithms. (shrink)

We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the recursively enumerable sets using Fourier coefficients of recursive analytic functions that are generated by differential equations and elementary operations.

ABSTRACTThe emergence of dimensional analysis in the early nineteenth century involved a redefinition of the pre-existing concepts of homogeneity and dimensions, which entailed a shift from a qualitative to a quantitative conception of these notions. Prior to the nineteenth century, these concepts had been used as criteria to assess the soundness of operations and relations between geometrical quantities. Notably, the terms in such relations were required to be homogeneous, which meant that they needed to have the same geometrical dimensions. (...) The latter reflected the nature of the quantities in question, such as volume vs area. As natural philosophy came to encompass non-geometrical quantities, the need arose to generalize the concept of homogeneity. In 1822, Jean Baptiste Fourier consequently redefined it to be the condition an equation must satisfy in order to remain valid under a change of units, and the ‘dimension' correspondingly became the power of a conversion factor. When these innovations eventually found an echo in France and Great Britain, in the second half of the century, tensions arose between the former, qualitative understanding of dimensions as reflecting the nature of physical quantities, and the new, quantitative conception based on unit conversion and measurement. The emergence of dimensional analysis thus provides a case study of how existing rules and concepts can find themselves redefined in the context of wider conceptual changes; in the present case this redefinition involved a generalization, but also a shift in meaning which led to conceptual tensions. (shrink)

Reflectance physicalists define reflectance as the intrinsic disposition of a surface to reflect finite-duration light pulses at a given efficiency per wavelength. I criticize the received view of dispositional reflectance (David R. Hilbert’s) for failing to account for what I call “harmonic dispersion,” the inverse relationship of a light pulse's duration to its bandwidth. I argue that harmonic dispersion renders reflectance defined in terms of light pulses an extrinsic disposition. Reflectance defined as the per-wavelength efficiency to reflect the superimposed, infinite-duration, (...) Fourier harmonics of pulses can be an intrinsic disposition of surfaces. This conclusion raises questions about mathematical realism, about which I nevertheless remain neutral. (shrink)

In the following we consider the possibility of interpretating recent non-local interferometric experiments according to the De Broglie causal model. With the help of a simplified mathematical model based on wavelet analysis it is indeed possible to explain it in a causal way. Furthermore we show the distinctions between the two formalisms and discuss some experimental conditions that may make these differences evident.

Aiming at the problem of radar target recognition of High-Resolution Range Profile under low signal-to-noise ratio conditions, a recognition method based on the Constrained Naive Least-Squares Generative Adversarial Network, Short-time Fourier Transform, and Convolutional Neural Network is proposed. Combining the Least-Squares Generative Adversarial Network with the Wasserstein Generative Adversarial Network with Gradient Penalty, the CN-LSGAN is presented and applied to the HRRP denoise. The frequency domain and phase features of HRRP are gained by STFT in order to facilitate feature (...) learning and also match the input data format of the CNN. These experimental results show that the CN-LSGAN has better data augmentation performance and can effectively avoid the model collapse compared to the generative adversarial network and LSGAN. Also, the method has better recognition performance than the one-dimensional CNN method and the Long Short-Term Memory network method. (shrink)

This thesis is devoted to the exploration of the complexity of some mathematical problems using the framework of computable analysis and descriptive set theory. We will especially focus on Weihrauch reducibility as a means to compare the uniform computational strength of problems. After a short introduction of the relevant background notions, we investigate the uniform computational content of problems arising from theorems that lie at the higher levels of the reverse mathematics hierarchy.We first analyze the strength of the open (...) and clopen Ramsey theorems. Since there is not a canonical way to phrase these theorems as multi-valued functions, we identify eight different multi-valued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility.We then discuss some new operators on multi-valued functions and study their algebraic properties and the relations with other previously studied operators on problems. In particular, we study the first-order part and the deterministic part of a problem f, capturing the Weihrauch degree of the strongest multi-valued problem that is reducible to f and that, respectively, has codomain $\mathbb {N}$ or is single-valued.These notions proved to be extremely useful when exploring the Weihrauch degree of the problem $\mathsf {DS}$ of computing descending sequences in ill-founded linear orders. They allow us to show that $\mathsf {DS}$, and the Weihrauch equivalent problem $\mathsf {BS}$ of finding bad sequences through non-well quasi-orders, while being very “hard” to solve, are rather weak in terms of uniform computational strength. We then generalize $\mathsf {DS}$ and $\mathsf {BS}$ by considering $\boldsymbol {\Gamma }$ -presented orders, where $\boldsymbol {\Gamma }$ is a Borel pointclass or $\boldsymbol {\Delta }^1_1$, $\boldsymbol {\Sigma }^1_1$, $\boldsymbol {\Pi }^1_1$. We study the obtained $\mathsf {DS}$ -hierarchy and $\mathsf {BS}$ -hierarchy of problems in comparison with the Baire hierarchy and show that they do not collapse at any finite level.Finally, we work in the context of geometric measure theory and we focus on the characterization, from the point of view of descriptive set theory, of some conditions involving the notions of Hausdorff/Fourier dimension and Salem sets. We first work in the hyperspace $\mathbf {K}$ of compact subsets of $[0,1]$ and show that the closed Salem sets form a $\boldsymbol {\Pi }^0_3$ -complete family. This is done by characterizing the complexity of the family of sets having sufficiently large Hausdorff or Fourier dimension. We also show that the complexity does not change if we increase the dimension of the ambient space and work in $\mathbf {K}$. We also generalize the results by relaxing the compactness of the ambient space and show that the closed Salem sets are still $\boldsymbol {\Pi }^0_3$ -complete when we endow $\mathbf {F}$ with the Fell topology. A similar result holds also for the Vietoris topology.We conclude by analyzing the same notions from the point of view of effective descriptive set theory and Type-2 Theory of Effectivity, and show that the complexities remain the same also in the lightface case. In particular, we show that the family of all the closed Salem sets is $\Pi ^0_3$ -complete. We furthermore characterize the Weihrauch degree of the functions computing Hausdorff and Fourier dimension of closed sets.prepared by Manlio Valenti.E-mail:[email protected]. (shrink)

Within the last decade, several approaches using quaternion numbers to handle and model multiband images in a holistic manner were introduced. The quaternion Fourier transform can be efficiently used to model texture in multidimensional data such as color images. For practical application, multispectral satellite data appear as a primary source for measuring past trends and monitoring changes in forest carbon stocks. In this work, we propose a texture-color descriptor based on the quaternion Fourier transform to extract relevant information (...) from multiband satellite images. We propose a new multiband image texture model extraction, called FOTO++, in order to address biomass estimation issues. The first stage consists in removing noise from the multispectral data while preserving the edges of canopies. Afterward, color texture descriptors are extracted thanks to a discrete form of the quaternion Fourier transform, and finally the support vector regression method is used to deduce biomass estimation from texture indices. Our texture features are modeled using a vector composed with the radial spectrum coming from the amplitude of the quaternion Fourier transform. We conduct several experiments in order to study the sensitivity of our model to acquisition parameters. We also assess its performance both on synthetic images and on real multispectral images of Cameroonian forest. The results show that our model is more robust to acquisition parameters than the classical Fourier Texture Ordination model. Our scheme is also more accurate for aboveground biomass estimation. We stress that a similar methodology could be implemented using quaternion wavelets. These results highlight the potential of the quaternion-based approach to study multispectral satellite images. (shrink)

Music rhythm detection and tracking is an important part of the music comprehension system and visualization system. The music signal is subjected to a short-time Fourier transform to obtain the frequency spectrum. According to the perception characteristics of the human auditory system, the spectrum amplitude is logarithmically processed, and the endpoint intensity curve and the phase information of the peak value are output through half-wave rectification. The Pulse Code Modulation characteristic value is extracted according to the autocorrelation characteristic of (...) the endpoint intensity curve. This article proposes a rhythm detection algorithm based on multipath search and cluster analysis; that is, based on the clustering algorithm, it absorbs the idea of multipath tracking and proposes its own detection and tracking algorithm. It overcomes the weakness of the clustering algorithm that needs to use Musical Instrument Digital Interface auxiliary input to achieve the desired effect. This algorithm completely uses the PCM signal as the input, which is more robust than the clustering algorithm. The whole process is carried out in the time domain, and the amount of calculation is much smaller than the frequency domain calculation of multipath tracking, and the linear relationship with the rhythm of the music is much better than the filter bank algorithm. This algorithm can successfully detect the rhythm of the music with a strong sense of rhythm and can track the specific position of the rhythm point. (shrink)

How might artificial neural networks (ANNs) inform cognitive science? Often cognitive scientists use ANNs but do not examine their internal structures. In this paper, we use ANNs to explore how cognition might represent musical properties. We train ANNs to classify musical chords, and we interpret network structure to determine what representations ANNs discover and use. We find connection weights between input units and hidden units can be described using Fourier phase spaces, a representation studied in musical set theory. We (...) find the total signal coming through these weighted connection weights is a measure of the similarity between two Fourier structures: the structure of the hidden unit's weights and the structure of the stimulus. This is surprising because neither of these Fourier structures is computed by the hidden unit. We then show how output units use such similarity measures to classify chords. However, we also find different types of units—units that use different activation functions—use this similarity measure very differently. This result, combined with other findings, indicates that while our networks are related to the Fourier analysis of musical sets, they do not perform Fourier analyses of the kind usually described in musical set theory. Our results show Fourier representations of music are not limited to musical set theory. Our results also suggest how cognitive psychologists might explore Fourier representations in musical cognition. Critically, such theoretical and empirical implications require researchers to understand how network structure converts stimuli into responses. (shrink)

According to Jody Azzouni’s “deflationary nominalism,” the singular terms of mathematical language applied or unapplied to science refer to nothing at all. What does exist, Azzouni claims, must satisfy the quaternary condition he calls “thick epistemic access” (TEA). In this paper I argue that TEA surreptitiously reifies some mathematical entities. The mathematical entity that I take TEA to reify is the Fourier harmonic, an infinite-duration monochromatic sinusoid applied throughout engineering and physics. I defend the reality of the harmonic, in (...) Azzouni’s account, not by satisfying all four TEA conditions with respect to it, but by showing that the harmonic renders satisfiable the TEA condition called “grounding,” specifically in Azzouni’s (Talking about nothing: numbers, hallucinations, and fictions. New York: Oxford University Press, 2010) example of a human visually perceiving a vase. The harmonic thereby plays what Azzouni calls an “epistemic role,” and merits inclusion in the deflationary nominalist ontology. Against the “coding” objection of Azzouni and Bueno (Br J Philos Sci 67:781–816, 2016), which would nominalize the harmonic to nonexistent status, I reply that in the context of grounding, the coding objection begs the question. (shrink)

In the debate over whether mathematical facts, properties, or entities explain physical events (in what philosophers call “extra-mathematical” explanations), Aidan Lyon’s (2012) affirmative answer stands out for its employment of the program explanation (PE) methodology of Frank Jackson and Philip Pettit (1990). Juha Saatsi (2012; 2016) objects, however, that Lyon’s examples from the indispensabilist literature are (i) unsuitable for PE, (ii) nominalizable into non-mathematical terms, and (iii) mysterious about the explanatory relation alleged to obtain between the PE’s mathematical explanantia and (...) physical explananda. In this paper, I propose a counterexample to Saatsi’s objections. My counterexample is Frank Jackson’s (1998a) program explanation for color experience, which I argue needs recasting as an extra-mathematical PE due to its implicit reliance on reflectance, a property that suffers conceptual regress unless redefined with Fourier harmonics. Pace Saatsi, I argue that this recast example is an authoritative PE, non-nominalizable, and minimally esoteric. Important for the indispensability debate at large, moreover, is that my counterexample reifies Fourier harmonics without the Enhanced Indispensability Argument (an argument to which Lyon applies PE as a premise). Indispensabilists have long overlooked the conditionalization of a limited mathematical realism on property realism, and my counterexample to Saatsi exploits this conditionalization. (shrink)

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large is intimately related to the infinitely small. Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version (...) of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. (shrink)

The theory of Participatory Discrepancies (or PDs) claims that minute temporal asynchronies (microtiming) in music performance are crucial for prompting bodily entrainment in listeners, which is a fundamental effect of the “groove” experience. Previous research has failed to find evidence to support this theory. The present study tested the influence of varying PD magnitudes on the beat-related body movement behavior of music listeners. 160 participants (79 music experts, 81 non-experts) listened to twelve music clips in either Funk or Swing style. (...) These stimuli were based on two audio recordings (one in each style) of expert drum and bass duo performances. In one series of six clips, the PDs were downscaled from their originally performed magnitude to complete quantization in steps of 20%. In another series of six clips, the PDs were upscaled from their original magnitude to double magnitude in steps of 20%. The intensity of the listeners’ beat-related head movement was measured using video-based motion capture technology and Fourier analysis. A mixed-design four-factor ANOVA showed that the PD manipulations had a significant effect on the expert listeners’ entrainment behavior. The experts moved more when listening to stimuli with PDs that were downscaled by 60% compared to completely quantized stimuli. This finding offers partial support for PD theory: PDs of a certain magnitude do augment entrainment in listeners. But the effect was found to be small to moderately sized, and it affected music expert listeners only. (shrink)

Is it possible to construct an alternative framework for the description of physical reality that is not based on space and time? According to Kant, because of the incorrigibility of the spatiotemporal scheme, the contents of any such alternative will be beyond our cognitive grasp. Nonetheless, the possibility of constructing such a descriptive scheme poses itself as an intriguing challenge. In this paper, we attempt to answer this challenge by exploiting an analytical tool extensively used by physicists and engineers: the (...) utilisation of multiple representations of the same data using integral transforms – for example, the Fourier transform. According to the spectral picture we propose, frequencies and wavelengths, related to time and space by the Fourier transform, form an adequate alternative basis for describing physical systems, and one that is of equal richness to the spatiotemporal picture. Furthermore, the routine use of Fourier analysis applied to familiar physical systems suggests ways in which sense organs might be constructed such that they naturally give rise to a spectral representation of the world. Although we might never be able to imagine perceiving the world in this way, we can nonetheless describe the contents of such a mode of perception and relate them precisely to our own world-view. Hence, we suggest in a Kantian spirit, that the spatiotemporal description of the world is not unique. (shrink)

The cosmic singularity provides negligible evidence for creation in the finite past, and hence theism. A physical theory might have no metric or multiple metrics, so a ‘beginning’ must involve a first moment, not just finite age. Whether one dismisses singularities or takes them seriously, physics licenses no first moment. The analogy between the Big Bang and stellar gravitational collapse indicates that a Creator is required in the first case only if a Destroyer is needed in the second. The need (...) for and progress in quantum gravity and the underdetermination of theories by data make it difficult to take singularities seriously. The singularity exemplifies the sort of gap that is likely to be closed by scientific progress, obviating special divine action. The apparent irrelevance of cardinality to practices of counting infinite sets in classical field theory and Fourier analysis is noted. Introduction The Doctrine of Creation and Its Warrant Cardinality and Sizes of Infinity Modern Cosmology and Creation Tolerance or Intolerance toward Singularities? Leibniz against Incompetent Watchmaker? Induction from Earlier Theories' Breakdown? Stellar Collapse Implies Theistic Destroyer Stacking the Deck for GTR Quantum Gravity Tends to Resolve Singularities Vicious God-of-the-Gaps Character Fluctuating or Inaccessible Warrant Big Bang Cosmology Not Especially Congenial to Faith CiteULike Connotea Del.icio.us What's this? (shrink)

The Dirac δ function has solid roots in nineteenth century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac’s discovery by over a century, and illuminating the nature of Cauchy’s infinitesimals and his infinitesimal definition of δ.

The Heisenberg-Gabor uncertainty principle defines the limits of information resolution in both time and frequency domains. The limit of resolution discloses unique properties of a time series by frequency decomposition. However, classical methods such as Fourier analysis are limited by spectral leakage, particularly in longitudinal data with shifting periodicity or unequal intervals. Wavelet transformation provides a workable compromise by decomposing the signal in both time and frequency through translation and scaling of a basis function followed by correlation or (...) convolution with the original signal. This study aimed to compare the accuracy of predictive models in mental arithmetic in time and frequency domains. Analysis of the author's response time at mental arithmetic using a soroban was modeled for two periods, an initial period, and a return period both separated by an interval of 370 days. The median response times in seconds was longer for all tasks during the TI compared to the TR period, for addition [CTAdd 62 vs 50 s] and summation [CTSum 68 vs 57 s]. Response times were longer for errors regardless of the study period or task. There was an increasing phase difference for the addition and summation tasks during the TI period toward the end of the series 49.65o compared to the TR period where the phase difference between the two tasks was only 2.05o, indicating that both tasks are likely demonstrating similar learning rates during the latter study period. A comparison between time and time/frequency domain forecasts for an additional 100 tasks demonstrated higher accuracy of the maximum overlap discrete wavelet transform model, where the mean absolute percentage error ranged between 5.48 and 8.19% and that for the time domain models [autoregressive integrated moving average, generalized autoregressive conditional heteroscedasticity ] was 6.16–10.80%. (shrink)

Is it possible to construct an alternative framework for the description of physical reality that is not based on space and time? According to Kant, because of the incorrigibility of the spatiotemporal scheme, the contents of any such alternative will be beyond our cognitive grasp. Nonetheless, the possibility of constructing such a descriptive scheme poses itself as an intriguing challenge. In this paper, we attempt to answer this challenge by exploiting an analytical tool extensively used by physicists and engineers: the (...) utilisation of multiple representations of the same data using integral transforms – for example, the Fourier transform. According to the “spectral” picture we propose, frequencies and wavelengths, related to time and space by the Fourier transform, form an adequate alternative basis for describing physical systems, and one that is of equal richness to the spatiotemporal picture. Furthermore, the routine use of Fourier analysis applied to familiar physical systems suggests ways in which sense organs might be constructed such that they naturally give rise to a spectral representation of the world. Although we might never be able to imagine perceiving the world in this way, we can nonetheless describe the contents of such a mode of perception and relate them precisely to our own world-view. Hence, we suggest in a Kantian spirit, that the spatiotemporal description of the world is not unique. (shrink)

A derivation by Fröhner of non-relativistic quantum mechanics via Fourier analysis applied to probability theory is not extendable to relativistic quantum mechanics because Schrödinger's positive definite probability density ψ*ψ is lost (Dirac's spin 1/2 case being the exception). The nature of the Fourier link then changes; it points to a redefinition of the probability scheme as an information carrying telegraph, the code of which is Born's as extended by Dirac and by Feynman. Hermitian symmetry of the transition (...) amplitude 〈ϕ∣ψ〉 between Dirac representations expresses reciprocity of preparation and measurement (the quantal coding and decoding), two equally active interventions of the physicist; as “the measurement perturbs the system” retrodiction implies retroaction evidenced in “delayed choice.” Reciprocity of knowledge and organization vindicates Wigner's claim that “reciprocal to the action of matter upon mind there exists a direct action of mind upon matter”: psychokinesis, branded by Jaynes as “a psychiatric disorder of the Copenhagen school.” As for factlike irreversibility, it is expressed by the enormity of the change rate from information to negentropy: while gain in knowledge is normal psychokinesis is paranormal. Stapp's recent discussion of psychokinesis in a quantum context should be resumed in association with an EPR correlation; an experimental test is proposed. (shrink)

The present work sets out to discuss in three main steps the roots of the indeterministic paradigm for quantum mechanics as against a causal explanation of reality. The first step is to present the fundamental role played by non-local Fourier analysis in the Copenhagen paradigm. The second is to present wavelet local analysis, a recent formalism that will perhaps allow the development of a new causal paradigm for physics. The third is to present the Heisenberg-Bohr uncertainty relations (...) as a direct mathematical consequence of Fourier non-local analysis. Finally, experimental evidence violating these relations is presented. These results imply that the indeterministic approach has reached its limits. However, they can be explained within a causal framework allowing a more general mathematical formulation for uncertainty relations. (shrink)

Photonic Crystals is the first book to address one of the newest and most exciting developments in physics--the discovery of photonic band-gap materials and their use in controlling the propagation of light. Recent discoveries show that many of the properties of an electron in a semiconductor crystal can apply to a particle of light in a photonic crystal. This has vast implications for physicists, materials scientists, and electrical engineers and suggests such possible developments as an entirely optical computer. Combining cutting-edge (...) research with the basic theoretical concepts behind photonic crystals, the authors present to undergraduates and researchers a concise, readable, and comprehensive text on these novel materials and their applications. The first chapters develop the theoretical tools of photonic crystals in a broad, intuitive fashion, starting from nothing more than Maxwell's equations and Fourier analysis, and include analogies to traditional solid-state physics and quantum theory. There follows an investigation of the unique phenomena that take place within photonic crystals, at defect sites, and at surfaces and interfaces. The authors offer a new treatment of the traditional multilayer film (a one-dimensional photonic crystal), which allows for the extension to higher dimensions and more complex geometries. After exploring the capabilities of photonic crystals to guide and localize light, the authors demonstrate how these notions can be put to work. (shrink)

The present work sets out to discuss in three main steps the roots of the indeterministic paradigm for quantum mechanics as against a causal explanation of reality. The first step is to present the fundamental role played by non-local Fourier analysis in the Copenhagen paradigm. The second is to present wavelet local analysis, a recent formalism that will perhaps allow the development of a new causal paradigm for physics. The third is to present the Heisenberg-Bohr uncertainty relations (...) as a direct mathematical consequence of Fourier non-local analysis. Finally, experimental evidence violating these relations is presented. These results imply that the indeterministic approach has reached its limits. However, they can be explained within a causal framework allowing a more general mathematical formulation for uncertainty relations. (shrink)

Sound symbolism refers to non‐arbitrary mappings between the sounds of words and their meanings and is often studied by pairing auditory pseudowords such as “maluma” and “takete” with rounded and pointed visual shapes, respectively. However, it is unclear what auditory properties of pseudowords contribute to their perception as rounded or pointed. Here, we compared perceptual ratings of the roundedness/pointedness of large sets of pseudowords and shapes to their acoustic and visual properties using a novel application of representational similarity analysis (...) (RSA). Representational dissimilarity matrices (RDMs) of the auditory and visual ratings of roundedness/pointedness were significantly correlated crossmodally. The auditory perceptual RDM correlated significantly with RDMs of spectral tilt, the temporal fast Fourier transform (FFT), and the speech envelope. Conventional correlational analyses showed that ratings of pseudowords transitioned from rounded to pointed as vocal roughness (as measured by the harmonics‐to‐noise ratio, pulse number, fraction of unvoiced frames, mean autocorrelation, shimmer, and jitter) increased. The visual perceptual RDM correlated significantly with RDMs of global indices of visual shape (the simple matching coefficient, image silhouette, image outlines, and Jaccard distance). Crossmodally, the RDMs of the auditory spectral parameters correlated weakly but significantly with those of the global indices of visual shape. Our work establishes the utility of RSA for analysis of large stimulus sets and offers novel insights into the stimulus parameters underlying sound symbolism, showing that sound‐to‐shape mapping is driven by acoustic properties of pseudowords and suggesting audiovisual cross‐modal correspondence as a basis for language users' sensitivity to this type of sound symbolism. (shrink)

This paper examines the analysis of property regimes in the thought of the French philosopher, Francois Huet, as presented especially in his one major work on that subject, Le Regne Social du Christianisme . There, Huet developed his concern with social issues which began in the mid-1840s, when he was Professor of Philosophy at the University of Ghent. From 1846, he formed a study group of students now known as the ‘Huet Society’, which discussed social questions such as property (...) rights and inheritance, and considered various reform proposals in the works of Fourier, Proudhon, Saint-Simon and others. In the aftermath of the 1848 Revolutions, Huet resigned his Chair following an official campaign against his allegedly subversive views. From 1850 until his death in 1869, Huet lived in Paris where he concentrated on his studies, producing a large number of published works. Apart from Le Regne, those works were concerned principally with Catholic theology, at least until 1864 when Huet renounced his faith and sought to develop a version of pantheism. However, in La Science de l'esprit , which immediately preceded that renunciation, Huet restated at length and in virtually identical form the core argument of Le Regne. Even in one of his last works, La Revolution Religieuse , moreover, Huet expressed his continuing endorsement of its ‘fundamental idea’ of ‘a guarantee of property to all’, and argued that after fifteen years it was still in advance of current liberal critiques of property regimes. (shrink)

Plastic waste is a significant environmental problem for almost all countries; therefore, protecting the environment from the problem is crucial. The most sensible solution to these problems is substituting the natural aggregates with substantial plastic waste in various building materials. This study aimed to optimise the mixed design ratio of cement brick containing plastic waste as aggregate replacement. Plastic cement brick mixtures were prepared by the incorporation of four different types of plastic waste such as polyethylene terephthalate (PET), high-density polyethylene, (...) low-density polyethylene and polypropylene into cement bricks with different cement contents (150, 300 and 450 g) and plastic replacement percentages (0, 3 and 6%). Compressive strength and water absorption of the plastic cement bricks were analysed using a statistical model through the response surface methodology. It revealed the optimum cement brick mixed design is C3-1% PET with the compressive strength of 27.50 MPa and water absorption of 1.16%. The optimised plastic cement brick also satisfied the general ASTM C62-17 requirements for building bricks despite the higher porosity observed by the scanning electron microscopy. The results from Fourier transform infrared spectroscopy analysis also showed that the addition of the plastic waste into cement brick was unlikely to modify the chemical compound within the cement brick mixtures. Thus, the proposed mathematical model can predict the required hardened properties of plastic cement bricks and could lead to greater utilisation of plastic waste in building materials. (shrink)

Machine learning, deep learning and neural networks are extensively applied for the development of many fields. Though their technologies are improved greatly, they are often said to be opaque in terms of explainability. Their explainable neural functions will be essential to realization in the networks. In this paper, it is shown that the bio-inspired networks are useful for the explanation of tracking and classification of features. First, the asymmetric network with nonlinear functions is created based on the bio-inspired retinal network. (...) They have orthogonal properties useful for the tracking of features compared with the conventional symmetric networks, which is also proposed on the biological functions. Next, the analysis for the independence of the subspaces between the Fourier bases and the asymmetric network bases is performed. It was that the asymmetric networks have better performances in the classification compared with the symmetric ones. Further, the layered asymmetric networks generate the higher dimensional orthogonal bases that improve the classification accuracies by the replacements of bases. Finally, we classified Reuters collections data applying the explainable processing steps, which consist of the linear discriminations and the sparse coding with nearest neighbor relation for classification. (shrink)

ABSTRACT This article examines the reaction to Owen’s work in the circle associated with the liberal Journal des Économistes. It attempts to reconstruct the liberal argument against utopian socialist schemes of ‘regeneration’ and ‘redistribution’, and against those associated with Robert Owen in particular. It focuses on the works of Louis Reybaud (1799–1879) and Adolphe Blanqui (1798–1854) and their critical engagement with the writings of Saint-Simon, Fourier and Owen. It offers a detailed analysis of Reybaud’s Études sur les réformateurs, (...) ou socialistes modernes (1840), which did much to popularise the term ‘socialist’ in France, and Blanqui’s Histoire de l’économie politique en Europe depuis les anciens jusqu’à nos jours (1837). The article’s central argument is that these works appeared at an inflection point in the history of liberal political economy in France. Both started from the premise, shared with the socialist authors they were analysing, but increasingly suspect to liberal economic opinion, that the solution to the social question lay in the proper harnessing of the spirit of association as opposed to unregulated competition. The question at issue for Blanqui and Reybaud was what form this ‘associationism’ should take. (shrink)

In this study, voluntary and involuntary visual attention focused on different interpretations of a bistable image, were investigated using magnetoencephalography. A Necker cube with sinusoidally modulated pixels' intensity in the front and rear faces with frequencies 6.67 Hz and 8.57 Hz, respectively, was presented to 12 healthy volunteers, who interpreted the cube as either left- or right-oriented. The tags of these frequencies and their second harmonics were identified in the average Fourier spectra of the MEG data recorded from the (...) visual cortex. In the first part of the experiment, the subjects were asked to voluntarily control their attention by interpreting the cube orientation as either being on the left or right. Accordingly, we observed the dominance of the corresponding spectral component, and voluntary attention performance was measured. In the second part of the experiment, the subjects were asked to focus their gaze on a red marker at the center of the cube image without putting forth effort in its interpretation. The alternation of the dominant spectral energies at the second harmonics of the stimulation frequencies was treated as changes in the cube orientation. Based on the results of the first experimental stage and using a wavelet analysis, we developed a method which allowed us to identify the currently perceived cube orientation. Finally, we characterized involuntary attention using the distribution of dominance times when focusing attention on one of the cube orientations, which was related to voluntary attention performance and brain noise. In particular, we confirmed our hypothesis that higher attention performance is associated with stronger brain noise. (shrink)

Albert Abraham Michelson (1852-1931), the American optical physicist best known for his precise determination of the velocity of light and for his experiments concerning aether drift, is less often acknowledged as the creator of new spectroscopic instrumentation and new spectroscopies. He devised a new method of light analysis relying upon his favourite instrument – a particular configuration of optical interferometer – and published investigations of spectral line separation, Doppler-broadening and simple high-resolution spectra (1887-1898). Contemporaries did not pursue his method. (...) Michelson himself discarded the technique by the end of the decade, promoting a new device, the ‘echelon spectroscope’, as a superior instrument. High-resolution spectroscopy was taken up by others at the turn of the century using the echelon, Fabry-Pérot etalon and similar instruments. Michelson’s ‘Light Wave Analysis’ was largely forgotten, but was rediscovered c1950 and developed over the following three decades into a technique rechristened ‘Fourier transform spectroscopy’. This paper presents Michelson’s interferometric work as a continuum of personal interests and historical context as an example of 'research technology' and 'peripheral science'. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Fabuler la fin du monde: La puissance critique des fictions d’apocalypse by Jean-Paul EngélibertCyril CamusJean-Paul Engélibert. Fabuler la fin du monde: La puissance critique des fictions d’apocalypse [Fabulating the end of the world: The critical power of apocalypse fiction]. Paris: Éditions La Découverte, 2019. 239 pp. Print. 20€. ISBN 978-2-348-03719-1.Jean-Paul Engélibert is a well-established expert on apocalyptic and postapocalyptic fiction. His exploration of the genre thus far includes (...) the monograph Apocalypses sans royaume: Politique des fictions de la fin du monde, XX–XXIe siècles (2013), numerous articles, as well as the essay collection L’Apocalypse: Une imagination politique, XIXe–XXIe siècles (2018), which he co-edited. In his latest book, Fabuler la fin du monde, he returns to several texts and aspects of the genre previously covered, delving deeper into what he calls “fictions of the end of the world.” In the ten chapters, gathered in five parts, he approaches his subject as a seasoned scholar in the field of comparative literature, and his analysis draws from comparisons between modern fiction’s representation of apocalypse and biblical literature’s visions of apocalypse and messianism. The book also offers ecocritical insights into the specter of Anthropocenic manifestations in fiction, with reflections on the interrelated genres of utopia and dystopia, theories of cinema, and philosophical writings on the catastrophic history of the twentieth and twenty-first centuries.The range of fictional works discussed is wide, including Jean-Baptiste Cousin de Grainville’s Le dernier homme (1805); Mary Shelley’s Frankenstein (1818); Émile Souvestre’s Le monde tel qu’il sera (1846); Didier de Chousy’s Ignis (1883); Robert Merle’s Malevil (1972); José Saramago’s Blindness (1995); Antoine Volodine’s Minor Angels (1999); Don DeLillo’s Cosmopolis (2003); Cormac McCarthy’s The Road (2006); Céline Minard’s Le dernier monde (2007); Davide [End Page 163] Longo’s The Last Man Standing (2010); and Margaret Atwood’s MaddAddam trilogy (Oryx and Crake [2003], The Year of the Flood [2009], and MaddAddam [2013]). Engélibert also touches on feature-length movies such as Stanley Kramer’s On the Beach (1959), Lars von Trier’s Melancholia (2011), Abel Ferrara’s 4:44 Last Day on Earth (2012), and Mamoru Oshii’s Ghost in the Shell (1995), as well as on other literary and audiovisual fictions, such as E. M. Forster’s short story “The Machine Stops” (1909), Edward Bond’s dramatic trilogy The War Plays (1985), and the first season (2014) of Damon Lindelof and Tom Perrotta’s TV series The Leftovers (2014–17).Engélibert’s exegeses of the genre build around two aspects of the evolving relationship of apocalyptic narratives to the context of their production. Apocalypse (in the sense of “the end of the world” rather than the etymological sense of “revelation”) is no longer primarily a religious myth: the creation and use of the atomic bomb during the Second World War, the theorization of the Anthropocene, and the mainstreaming of concerns over climate change have made the term “apocalypse” a very real, tangible prospect for the future. Engélibert relies on Günther Anders’s Die atomare Drohung (1981) to highlight the importance of the A-bomb in bringing home the reality of potential annihilation to people’s collective consciousness. Yet his second contextual/historical point is that the Anthropocene (albeit unnamed at the time) actually started with the Industrial Revolution, and that thinkers and polemicists such as Charles Fourier or Eugène Huzar, as well as contemporary fiction writers, were already acknowledging the environmental impact of humans and their economic/industrial/technological activity as threats to human and nonhuman life, and to the health of the planetary system itself.1Citing the work of Jean-Baptiste Fressoz and Christophe Bonneuil on the history of climate science, Engélibert analyzes in detail several nineteenth-century novels (namely Le Dernier homme, Frankenstein, Le monde tel qu’il sera, and Ignis) and one early-twentieth-century story (Forster’s “The Machine Stops”) that denounce the harm that the idol of the time, Progress, was already wreaking on nature and human life... (shrink)

Kropotkin's anarchism looked to a future defined by communalism. However, his understanding of this potential communal future has rarely been subject to analysis. Particularly important was his distinction between communalism and the tradition of communal experimentation in the US, which drew heavily on the ideas of Charles Fourier. Kropotkin was influenced by Fourier, but thought that attempts to found phalanstèries had been disastrous, vitiating the power of communalist propaganda. To defend the idea of a communal future, Kropotkin (...) therefore advanced a tripartite critique of the US model of utopian experimentation. The image of American utopianism he created consequently served as a useful rhetorical device, allowing him to advance a counter-image of the anarchist communal theory that lay at the heart of his political theory. (shrink)

Low frequency oscillation is an important attribute of human brain activity, and the amplitude of low frequency fluctuation is an effective method to reflect the characteristics of low frequency oscillation, which has been widely used in the treatment of brain diseases and other fields. However, due to the low accuracy of the current analysis methods for low frequency signal extraction of ALFF, we propose the Fourier-based synchrosqueezing transform, which is often used in the field of signal processing to (...) extract the ALFF of the low frequency power spectrum of the whole-time dimension. The low frequency characteristics of the extracted signal are compared with those of FSST and fast Fourier transform through the resting-state data. It is clear that the signal extracted by FSST has more low frequency characteristics, which is significantly different from FFT. (shrink)

Michel Foucault's The History of Sexuality-the first volume of which was published in 1976-exerts a vast influence across the humanities and social sciences. However, Foucault's interest in the history of sexuality began as early as the 1960s, when he taught two courses on the subject. These lectures offer crucial insight into the development of Foucault's thought yet have remained unpublished until recently. This book presents Foucault's lectures on sexuality for the first time in English. In the first series, held at (...) the University of Clermont-Ferrand in 1964, Foucault asks how sexuality comes to be constituted as a scientific body of knowledge within Western culture and why it derived from the analysis of "perversions"-morbidity, homosexuality, fetishism. The subsequent course, held at the experimental university at Vincennes in 1969, shows how Foucault's theories were reoriented by the events of May 1968; he refocuses on the regulatory nature of the discourse of sexuality and how it serves economic, social, and political ends. Examining creators of political and literary utopias in the nineteenth and twentieth centuries, from Sade to Fourier to Marcuse, who attempted to integrate "natural" sexualities, including transgressive forms, into social and economic life, Foucault elaborates a double critique of the naturalization and the liberation of sexuality. Together, the lectures span a range of interests, from abnormality to heterotopias to ideology, and they offer an unprecedented glimpse into the evolution of Foucault's transformative thinking on sexuality. (shrink)

The aim of this paper is to analyze the philosophical arguments that underpin the four political transformations of Mexico. This analysis provides a detailed account of the difficulties Mexico has had for consolidating the principles of freedom and equality. In what follows, I track the origin of the Mexican left in the 19th century from authors, such as Ignacio Ramírez, to concerns that appear within two contrasting moral Cartillas, the first one written by Alfonso Reyes, and the second one, (...) that of Fourier, brought to Mexico by Plotinus Rhodakanaty. Subsequently, I propose a possible link between anarchism and the political and moral philosophy that underpins the ideology of Andrés Manuel López Obrador. I shall highlight the tensions within the ideology of the fourth transformation, especially those existing between government centralization and the weakening of some institutions, the latter, a premise inherited from the anarchist ideology. (shrink)

This book examines the different areas of knowledge, traditions, and conceptual resources that contributed to the building of Max Planck's theory of radiation. It presents an insightful comparative analysis that not only sheds light upon a fundamental chapter in the history of modern physics, but also enlarges our understanding of how theoreticians work. Coverage offers a deep investigation into the technical aspects behind the theory and extends in time the notion of quantum revolution. It also presents a full-fledged discussion (...) of the combinatorial part of Planck's theory and places emphasis on the epistemological role of mathematical practices. By painstakingly reconstructing both the electromagnetic and the combinatorial part of Planck's black-body theory, the author shows how some apparently merely technical resources, such as the Fourier series, effectively contributed to shape the final form of Planck's theory. For decades, historians have debated the conditions of possibility of Max Planck's discovery as a paradigmatic example of scientific revolution. In particular, the use of combinatorics, which eventually paved the way for the introduction of the quantum hypothesis, has remained a puzzle for experts. This book presents a fresh perspective on this important debate that will appeal to historians and philosophers of science. (shrink)

Marx believed that what most clearly distinguished him and Engels from the nineteenth-century French socialists was that their version of socialism was “scientific” while the latters' was Utopian. What he intended by this contrast is roughly the following: French socialists such as Proudhon and Fourier constructed elaborate visions of a future socialist society without an adequate understanding of existing capitalist society. For Marx, on the other hand, socialism was not an idea or an ideal to be realized, but a (...) natural outgrowth of the existing capitalist order. Marx's historical materialism is a systematic attempt to discover the laws governing the inner dynamics of capitalism and class societies generally. Although this theory issues in a prediction of the ultimate triumph of socialism, it is a commonplace that Marx had little to say about the details of post-capitalist society. Nevertheless, some of its features can be discerned from his critical analysis of capitalism and what its replacement entails. (shrink)

Aims to show graduate students and researchers the vital benefits of integrating mathematics into their study and experience of the physical world. This book details numerous topics from the frontiers of modern physics and mathematics such as convergence, Green functions, complex analysis, Fourier series and Fourier transform, tensors, and others.

This is the first in a series of papers in which a method of harmonic analysis in terms of functions over the groupSU(2) is applied to the description of interaction between matter and the electromagnetic field. Carmeli'sSU(2) formulation of Maxwell's equations is extended to anSU(2) formulation of the equations for the electromagnetic vector potential. The four functions which describe the vector potential are expanded in a generalized Fourier series [SU(2) harmonic analysis] and the equations for the coefficients (...) are derived. These equations are not independent of each other, but in a given order they can be solved consecutively one at a time. (shrink)

In The Manifesto of the Communist Party the founders of Marxism demarcated in a principled way the qualitatively different forms of Utopian socialism. They critically analyzed "feudal socialism," petty-bourgeois socialist Utopias, bourgeois pseudo-socialism and, finally, the critical-Utopian socialism of St. Simon, Fourier, and Owen, which was one of the theoretical sources of the scientific ideology of the working class. This analysis shows that as early as the first half of the nineteeth century ideologies that were foreign to the (...) working class frequently appeared under the banner of socialism. In some cases this socialism had an imaginary, purely phraseological character. In others, it represented a petty bourgeois interpretation of the proletarian liberation movement. But critical-utopian socialism was the reflection of "the first instinctive yearnings of the proletariat for a universal reconstruction of society." This class characterization of the various modifications of socialist doctrine during the epoch of the West European bourgeois democratic revolutions has great methodological significance for understanding the whole subsequent evolution of the ideology of capitalism. (shrink)