Natural Regularity Research Articles

Scat Singing and Vocal Winging: Vowel Phoneme Timbre Dimensions Reflect Physical Natural Regularities

ABSTRACT Speech phoneme perception can be biased to follow production expectations. We propose some vowel-phonemes (such as /i/ as in “deed” and /Ʌ/ as in “dud”) sound, respectively, higher and lower in pitch in part because they are typically vocalized at higher and lower f 0 s, and listener pitch perception is biased toward those production tendencies. Resonant sounds, like vowels, possess two principal spectral pitch qualities: musical note/chroma (reflecting f 0 ), and tone height (reflecting spectral centroid). Participants could exhibit perceptual biases to experience vowel phonemes at differing tone heights related to their typically voiced f 0 s in speech and song, even when they are f 0 -matched. Experiment 1 measures the similarity of 12 f 0 -matched vowel sounds and reconfirms two principal spectral timbre dimensions, one which is related to pitch: tone height/brightness (spectral centroid), and the other, harmonicity/consonance (harmonic overtone alignment). Experiment 2 finds participants vocally mimic high- and low-frequency sinusoidal sounds using the phonemes at height extremes: 8 kHz elicits /i/ and 60 hz elicits /Ʌ/. Participants also mimic consonant and dissonant sounds using the phonemes at harmonicity extremes: 256 hz sinusoid elicits /u/ (“dude”) and an inharmonic cicada call elicits /æ/ (“dad”). Experiment 3 confirms that, in freeform speech and scat singing, /i/, /I/ (“did”), and /Ʌ/ vowel phonemes exhibit characteristic f 0 s that correlate with height ratings in Experiment 1. The overall findings confirm a natural regularity for vowel sounds to have systematically different f 0 s in speech and freeform song. Listeners incorporate this pattern as a perceptual bias when rating tone height of f 0 -matched vowel phonemes and in production when mimicking non-speech sounds, consistent with the scene-parsing principle of perceptual biases matching natural acoustic patterns.

Reduced theory of symmetric and antisymmetric exchange interactions in nanowires

We investigate the behavior of minimizers of perturbed Dirichlet energies supported on a wire generated by a regular simple curve $\gamma$ and defined in the space of $\mathbb{S}^2$-valued functions. The perturbation $K$ is represented by a matrix-valued function defined on $\mathbb{S}^2$ with values in $\RR^{3 \times 3}$. Under natural regularity conditions on $K$, we show that the family of perturbed Dirichlet energies converges, in the sense of $\Gamma$-convergence, to a simplified energy functional on $\gamma$. The reduced energy unveils how part of the antisymmetric exchange interactions contribute to an anisotropic term whose specific shape depends on the curvature of $\gamma$. We also discuss the significant implications of our results for studies of ferromagnetic nanowires when Dzyaloshinskii-Moriya interaction (DMI) is present.

Error analysis for a finite element approximation of the steady p·-Navier–Stokes equations

Abstract In this paper, we examine a finite element approximation of the steady $p(\cdot )$-Navier–Stokes equations ($p(\cdot )$ is variable dependent) and prove orders of convergence by assuming natural fractional regularity assumptions on the velocity vector field and the kinematic pressure. Compared to previous results, we treat the convective term and employ a more practicable discretization of the power-law index $p(\cdot )$. Numerical experiments confirm the quasi-optimality of the a priori error estimates (for the velocity) with respect to fractional regularity assumptions on the velocity vector field and the kinematic pressure.

Multidimensional Quantum Generative Modeling by Quantum Hartley Transform

AbstractAn approach for building quantum models based on the exponentially growing orthonormal basis of Hartley kernel functions is developed. First, a differentiable Hartley feature map parameterized by real‐valued argument that enables quantum models suitable for solving stochastic differential equations and regression problems is designed. Unlike the naturally complex Fourier encoding, the proposed Hartley feature map circuit leads to quantum states with real‐valued amplitudes, introducing an inductive bias and natural regularization. Next, a quantum Hartley transform circuit is proposed as a map between computational and Hartley basis. The developed paradigm is applied to generative modeling from solutions of stochastic differential equations, and utilize the quantum Hartley transform for fine sampling from parameterized distributions through an extended register. Finally, the capability of multivariate quantum generative modeling is demonstrated for both correlated and uncorrelated distributions. As a result, the developed quantum Hartley‐based generative models (QHGMs) offer a distinct quantum approach to generative AI at increasing scale.

Da Lógica à Natureza: a posição de Hegel não-romântica e pós-kantiana da Naturphilosophie

This is to lay out the issues involved in an appropriately post-Kantian interpretation of Hegel’s Naturphilosophie, which I translate not as “philosophy of nature” but as “natural philosophy”. Pure thought as Kant argued is empty, but he thought that he could supply pure content to it by the combination of pure intuitions and the unity of self-consciousness. His successors, especially Fichte, did not think that resolved matters, and Hegel tried to make good on what he saw as the failures of Fichte’s attempt to do Kantian philosophy without pure intuitions. Hegel however also saw that one could not begin with self-consciousness per se or with Fichte’s “I.” Instead, Hegel proposed a Logic that would give an internally self-enclosed system of pure thoughts as what was needed to make sense of making sense. Famously, he concluded the system with some not entirely clear ideas about its needing a move to a Naturphilosophie that was not a move in terms of a “transition.” Pure thought thus developed a concept of that which would be external to pure thought itself (like Fichte’s “Not-I”) but still something intrinsically linked to pure thought. This is the very concept of “externality to pure thought itself,” which first appears as space and time. The development of the simple thought of “external to pure thought” leads to a non-empiricist account of nature. Empiricists study regularities of nature in the Humean sense, but these regularities, although existent, are not fully “actual” in that they are not what is doing the work of explanation. What explains the regularities themselves are the various pure objects of the Naturphilosophie: The mechanical, the physical, the chemical and the biological fields of nature, each of which manifests a power [Potenz] that explains why the empirically found regularities in nature actually hold. The basic objects of a true Naturphilosophie present a unified field of investigation that is defined by the field’s powers and which in turn calls out for an empirical investigation of how these powers actually operate in the vast continuum of nature. Each of these distinct fields moreover has its own distinct form of causality, culminating in the causality of freedom in the human realm. It is then suggested that the reason for the transition from Logic to Nature is that pure thought on its own is powerless and finds itself filled with only the shadows of the world as a whole. This has implications for how we think of Hegel’s system as a whole.

A class of space–time discretizations for the stochastic [formula omitted]-Stokes system

The main objective of the present paper is to construct a new class of space–time discretizations for the stochastic p-Stokes system and analyze its stability and convergence properties. We derive regularity results for the approximation that are similar to the natural regularity of solutions. One of the key arguments relies on discrete extrapolation that allows us to relate lower moments of discrete maximal processes. We show that, if the generic spatial discretization is constraint conforming, then the velocity approximation satisfies a best-approximation property in the natural distance. Moreover, we present an example such that the resulting velocity approximation converges with rate 1/2 in time and 1 in space towards the (unknown) target velocity with respect to the natural distance. The theory is corroborated by numerical experiments.

Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov chains: A Banach lattice approach

We establish the existence and uniqueness of quasi-stationary and quasi-ergodic measures for almost surely absorbed discrete-time Markov chains under weak conditions. We obtain our results by exploiting Banach lattice properties of transition functions under natural regularity assumptions.

Optimally localized single-band Wannier functions for two-dimensional Chern insulators

The construction of optimally localized Wannier functions (and Wannier functions in general) for a Chern insulator has been considered to be impossible owing to the fact that the second moment of such functions is generally infinite. In this article, we propose a solution to this problem in the case of a single band isolated from the rest of the band structure. We accomplish this by drawing an analogy between the minimization of the variance and the minimization of the electrostatic energy of a periodic array of point charges in a smooth neutralizing background. In doing so, we obtain a natural regularization of the diverging variance and this leads to an analytical solution to the minimization problem. We demonstrate our results numerically for a particular model system. Furthermore, we show how the optimally localized Wannier functions provide a natural way of evaluating the electric polarization for a Chern insulator. Published by the American Physical Society 2024

Multi-Domain Multi-Scale Diffusion Model for Low-Light Image Enhancement

Diffusion models have achieved remarkable progress in low-light image enhancement. However, there remain two practical limitations: (1) existing methods mainly focus on the spatial domain for the diffusion process, while neglecting the essential features in the frequency domain; (2) conventional patch-based sampling strategy inevitably leads to severe checkerboard artifacts due to the uneven overlapping. To address these limitations in one go, we propose a Multi-Domain Multi-Scale (MDMS) diffusion model for low-light image enhancement. In particular, we introduce a spatial-frequency fusion module to seamlessly integrates spatial and frequency information. By leveraging the Multi-Domain Learning (MDL) paradigm, our proposed model is endowed with the capability to adaptively facilitate noise distribution learning, thereby enhancing the quality of the generated images. Meanwhile, we propose a Multi-Scale Sampling (MSS) strategy that follows a divide-ensemble manner by merging the restored patches under different resolutions. Such a multi-scale learning paradigm explicitly derives patch information from different granularities, thus leading to smoother boundaries. Furthermore, we empirically adopt the Bright Channel Prior (BCP) which indicates natural statistical regularity as an additional restoration guidance. Experimental results on LOL and LOLv2 datasets demonstrate that our method achieves state-of-the-art performance for the low-light image enhancement task. Codes are available at https://github.com/Oliiveralien/MDMS.

Analytical and Numerical Investigation of Two-Dimensional Heat Transfer with Periodic Boundary Conditions

A two-dimensional heat diffusion problem with a heat source that is a quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are employed. As the problem is nonlinear, Picard’s successive approximation theorem is utilized. We demonstrate the existence, uniqueness, and constant dependence of the solution on the data using the generalized Fourier method under specific conditions of natural regularity and consistency imposed on the input data. For the numerical solution, an implicit finite difference scheme is used. The results obtained from the analytical and numerical solutions closely match each other.

An inverse time-dependent source problem for a time-fractional diffusion equation with nonlocal boundary conditions

In this paper, we investigate an inverse time-dependent source problem for a time-fractional diffusion equation with nonlocal boundary and integral over-determination conditions. The fractional derivative is described in the generalized Caputo sense. The nonlocal boundary conditions are regular but not strongly regular. The special thing about this problem is: the system of eigenfunctions is not complete, but the system of eigen-and associated functions forming a basis in L2 (0,1). Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown by using the generalized Fourier method, the estimates of Mittag-Leffler function and Banach’s contraction mapping principle.

Effects of GLP1RAs on pregnancy rate and menstrual cyclicity in women with polycystic ovary syndrome: a meta-analysis and systematic review

PurposeThis study was aimed to assess the effectiveness of Glucagon-like peptide 1 receptor agonists on pregnancy rate, menses, anthropometric and hormonal parameters in PCOS patients.MethodsWe conducted searches of the published literature in PubMed, EMBASE, Cochrane Library, Web of Science up to September 2022. Data from randomized controlled trials were obtained to assess the effects of GLP1RAs in PCOS women. Weighted mean difference, standardized mean difference, and risks ratio were employed for effect size estimation using a random-effects model.ResultsA total of 840 patients with 469 individuals in GLP1RAs group and 371 individuals in control group from 11 RCTs were included. GLP1RAs usage was associated with an improvement in natural pregnancy rate (RR: 1.72, 95% CI 1.22 to 2.43, P = 0.002, I2 = 0%) and menstrual regularity (SMD: 1.72, 95% CI 0.60 to 2.85, P < 0.001, I2 = 95.6%). There were no statistically significant differences in total pregnancy rate, IVF pregnancy rate between two groups, but total PR elevated in a short time after GLP1RAs as shown in subgroup analysis. Randomization to GLP1RAs treatment was associated with great improvement in HOMA-IR, BMI, WC, SHBG and a slight reduction in TT compared to control group. A decrease in TBF was seen in European population. GLP1RAs monotherapy was not superior to metformin when it came to fT, DHEAS, FAI.ConclusionsPrescription of GLP1RAs improves natural pregnancy rate, menstrual cyclicity and insulin sensitivity, anthropometrics, hormonal indexes in PCOS women.

Природные закономерности почвенно-растительного покрова юго-западных отрогов Баджальского хребта

Expert assessment has been performed using the cartographic method in a key area of the Badjal Rige southwestern spurs. The basic natural regularities of the soil and vegetation cover have been identified, including heterogeneity and contrasting change of soil and vegetation complexes within the limits of vertical zoning; belt-zone differentiation (alpine, subalpine, and taiga); wide distribution of corroms; maximum diversity and high dynamism of floodplain soil and plant complexes. The article presents a 1 : 40,000-scale vegetation map; it is based on the ecological and phytocenotic classification of vegetation. The main mapped units are association groups and their combinations. The legend reflects 13 divisions of the vegetation cover. Corroms occupy the largest areas (24.9 %). The subalpine zone vegetation makes 20.9 % of the total area. Mountain taiga forests take 32.9 % of the total mapped territory, including spruce forests (7.3 %), larch forests (21.9 %), and birch-larch forests (3.7 %). Larch woodlands are responsible for slightly less than 3 % of the territory; sphagnum oligotrophic bogs, for 0.5 %. Floodplain forests are spread over the area of 12.5 %; that includes spruce forests (4.8 %), chosenia-poplar-larch forests (4.5 %), and poplarlarch forests (3.2 %). 4.4 % of the area is pebbled. There are 5 types and 13 subtypes of soils represented in the soil cover. Dystric histosols and leptic folic histosols form the soil background. Soils are characterized by the presence of organogenic-coarse humus or dry peaty horizons. Organic matter content is high or very high. The reaction of the soil solution varies from very acidic to acidic. Based on the vegetation map, soil areas are roughly quantified. In terms of the set of soil and plant complexes as well as their regular change in vertical zoning, the area under discussion is the reference territory. Represented here is the Okhotsk type of land cover zoning, which is typical for the Far East with its monsoonal climate.

The God of Chance and Purpose: Divine Involvement in a Secular Evolutionary World

The God of Chance and Purpose: Divine Involvement in a Secular Evolutionary World

Analysis of compressible bubbly flows. Part I: construction of a microscopic model

In this note, we introduce a microscopic model for the motion of gas bubbles in a viscous fluid. By interpreting a bubble as a compressible fluid with infinite shear viscosity, we derive a pde/ode system coupling the density/velocity/pressure in the surrounding fluid with the linear/angular velocities and radii of the bubbles. We provide a 1D analogue of the system and construct an existence theory for this simplified system in a natural regularity framework. The second part of the paper is a preparatory work for the derivation of an averaged or macroscopic model.

Average long-term background contents of chemical elements and organic substances in the flows of the natural component of the “Suspension of rivers” environment flowing into Lake Baikal reservoirs

The physical and chemical state of the waters of Lake Baikal and the flows of the natural component of the environment flowing into and out is one of the most important elements of the chemical interaction of lake water substances with the environment. To study the natural regularities of the distribution of matter in the “substances of Baikal waters – substances of the flows of the natural component of the environment” megasystem, it is necessary to know the background components in the substance of the flows and their amount. The average long-term content of chemical elements and organic matter was estimated in mg/l. The method for calculating average long-term contents (mg/l, %) of chemical elements and organic (Na+, K+, Ca2+, Mg2+, Al, Si, Mn2+, Fetot, SO42-, HCO3-, Cl-, NO3-, PO43-, H+, O2, As, B, Cr, Cu, Cd, Hg, Pb, Sr, Zn, Co, U, V, Br, Rb, Mo, Corg, Norg, Porg, Sorg, CO2, Ti) in natural component flows environment “suspension of the rivers” flowing into the Southern, Selenginsky, Middle, Northern reservoirs of Baikal was developed. The results of analysis of the chemical composition of suspended substances in rivers for 1976-2001 were used. Natural indicators of the contents of chemical elements and organic matter in the suspended substance of rivers are important for comparative assessments, especially under the increased anthropogenic load. The data are necessary for assessing the scale of river chemical input with river suspension into the reservoirs of Baikal and calculating the contribution of the natural environment flows “River suspension” to the chemical balances of the lake reservoirs.

Curved thin-film limits of chiral Dirichlet energies

We investigate the curved thin-film limit of a family of perturbed Dirichlet energies in the space of H1 Sobolev maps defined in a tubular neighborhood of an (n−1)-dimensional submanifold N of Rn and with values in an (m−1)-dimensional submanifold M of Rm. The perturbation K that we consider is represented by a matrix-valued function defined on M and with values in Rm×n. Under natural regularity hypotheses on N, M, and K, we show that the family of these energies converges, in the sense of Γ-convergence, to an energy functional on N of an unexpected form, which is of particular interest in the theory of magnetic skyrmions. As a byproduct of our results, we get that in the curved thin-film limit, antisymmetric exchange interactions also manifest under an anisotropic term whose specific shape depends both on the curvature of the thin film and the curvature of the target manifold. Various types of antisymmetric exchange interactions in the variational theory of micromagnetism are a source of inspiration and motivation for our work.

Auditory category learning is robust across training regimes

Multiple lines of research have developed training approaches that foster category learning, with important translational implications for education. Increasing exemplar variability, blocking or interleaving by category-relevant dimension, and providing explicit instructions about diagnostic dimensions each have been shown to facilitate category learning and/or generalization. However, laboratory research often must distill the character of natural input regularities that define real-world categories. As a result, much of what we know about category learning has come from studies with simplifying assumptions. We challenge the implicit expectation that these studies reflect the process of category learning of real-world input by creating an auditory category learning paradigm that intentionally violates some common simplifying assumptions of category learning tasks. Across five experiments and nearly 300 adult participants, we used training regimes previously shown to facilitate category learning, but here drew from a more complex and multidimensional category space with tens of thousands of unique exemplars. Learning was equivalently robust across training regimes that changed exemplar variability, altered the blocking of category exemplars, or provided explicit instructions of the category-diagnostic dimension. Each drove essentially equivalent accuracy measures of learning generalization following 40 min of training. These findings suggest that auditory category learning across complex input is not as susceptible to training regime manipulation as previously thought.

Facies control of the reservoir properties distribution in the carbonate rocks of epicontinental platforms

Background: It is difficult to imagine the modern world without hydrocarbon raw materials. Oil and gas production is not only the basis of a powerful fuel and energy complex but also the main source of foreign exchange earnings and a leading component of the budget for many countries. Carbonate rocks strike the imagination by their diversity, but at the same time they cause many problems: they are extremely variable from the point of view of reservoirs. The main problems of productive carbonate members are heterogeneity; distribution of reservoirs in the form of lenses with different configurations and strikes as well as hydrodynamic connections between the lenses is often chaotic. All of the listed problems of carbonate reservoirs are associated with secondary processes. Aim: The project aims to assess the reservoir properties of carbonate rocks from the point of view of facies zoning on the example of Ovinparm rocks. Materials and methods: In this work, we used: rock material from 8 wells (475 m), 14 wells with hydrodynamic data and a 3D seismic cube. Results: Based on the data obtained, the principles of facies diagnostics of the epicontinental platform deposits of were developed, facies of epicontinental platforms were identified, rock material was linked to logging data, a facies model and a facies map were built, a sequence stratigraphic analysis was carried out, and the regularity of the selective nature of the manifestation of secondary processes depending on the characteristics of the conditions for the accumulation of facies of epicontinental platforms was revealed, promising zones were identified taking into account the facies zoning and the intensity of the passage of secondary processes in the study area. Conclusion: By understanding how the reservoir properties are related to carbonate depositional conditions, we can predict the most interesting zones and determine the main secondary processes leading to such improved or degraded reservoir properties.

Elastica Models for Color Image Regularization

The choice of a proper regularization measure plays an important role in the field of image processing. One classical approach treats color images as two- dimensional surfaces embedded in a five-dimensional spatial-chromatic space. In this case, a natural regularization term arises as the image surface area. Choosing the chromatic coordinates as dominating over the spatial ones, we can think of the image spatial coordinates could as a parameterization of the image surface manifold in a three-dimensional color space. Minimizing the area of the image manifold leads to the Beltrami flow or mean curvature flow of the image surface in the three-dimensional color space, while minimizing the elastica of the image surface yields an additional interesting regularization. Recently, we proposed a color elastica model, which minimizes both the surface area and the elastica of the image manifold. In this paper, we propose to modify the color elastica and introduce two new models for color image regularization. The revised measures are motivated by the relations between the color elastica model, Euler’s elastica model, and the total variation model for gray level images. Compared to our previous color elastica model, the new models are direct extensions of Euler’s elastica model to color images. The proposed models are nonlinear and challenging to minimize. To overcome this difficulty, two operator-splitting methods are suggested. Specifically, nonlinearities are decoupled by the introduction of new vector- and matrix-valued variables. Then, the minimization problems are converted to initial value problems which are time-discretized by operator splitting. Each subproblem, after splitting, either has a closed-form solution or can be solved efficiently. The effectiveness and advantages of the proposed models are demonstrated by comprehensive experiments. The benefits of incorporating the elastica of the image surface as regularization terms compared to common alternatives are empirically validated.