Non-uniform Scaling Research Articles

Brownian motion on simple fractal spaces

A class of fractals with non-uniform scaling and a weak form of symmetry is defined. The paper deals with the problem of constructing a diffusion process on this class. A key element in the study is the property of the fractal as an electric network

Recognition of object classes from range data

We develop techniques for recognizing instances of 3D object classes (which may consist of multiple and/or repeated sub-parts with internal degrees of freedom, linked by parameterized transformations), from sets of 3D feature observations. Recognition of a class instance is structured as a search of an interpretation tree in which geometric constraints on pairs of sensed features not only prune the tree, but are used to determine upper and lower bounds on the model parameter values of the instance. A real-valued constraint propagation network unifies the representations of the model parameters, model constraints and feature constraints, and provides a simple and effective mechanism for accessing and updating parameter values. Recognition of objects with multiple internal degrees of freedom, including non-uniform scaling and stretching, articulations, and sub-part repetitions, is demonstrated and analysed for two different types of real range data: 3D edge fragments from a stereo vision system, and position/surface normal data derived from planar patches extracted from a range image.

On the Scaling Heuristic for Reconstruction from Slices

It is demonstrated by example that non-uniform scaling of polygons prior to reconstruction from slices can lead to illegal intersections when the scaling is retracted. But uniform scaling does not suffer from this potential defect.

Non-uniform temporal scaling of hand and finger kinematics during typing.

We examined the manner in which the keystroke kinematics of the hand and the fingers varied with the mean rate of typing by trained typists. We used words and phrases in which only one letter was typed with the right hand and all of the remaining letters were typed using the left hand. We varied the typing rate over a threefold range (intervals between keypresses ranging from 150 ms to 500 ms) with the aid of a metronome. The results from four subjects, and three letters (n, u, and o) were analyzed. We did not find a simple scaling that could account for variations in the velocity profiles with typing rate. For some subjects and some letters, the velocities were independent of typing rate. In other instances, the kinematics did depend on typing rate, but to a much greater extent prior to the time of keypress than afterward. Sometimes the velocity profiles of all of the fingers and of the hand changed in a similar manner as the interval between keypresses was varied. In other instances only the focal movement of the hand and the finger used to press the key depended on the interval, whereas the motions of the other fingers did not. We suggest that the consistencies in the velocity profiles which we observed may simplify the problem of arranging a temporally ordered sequence of goal-directed movements.

The vibrational spectra (100–1500 cm−1) of a series of bicyclo[3.2.1]octanes assigned by means of scaled 3-21G ab initio harmonic force fields

The infrared absorption (vapor phase and solution) and Raman (liquid phase) spectra of bicyclo[3.2.1]octane, 8-oxabicyclo[3.2.1]octane, 6-oxabicyclo[3.2.1]octane, 6,8-dioxabicyclo[3.2.1]octane, and the 7,7-dideutero-substituted derivatives of the last two compounds are reported in the region 100–1500 cm−1 for the first time. The vibrational spectra are assigned almost completely with the guidance of ab initio 3-21G geometries and scaled force fields. A total of 14 force-field scale facors are transferred from smaller molecules, predicting the frequencies with an average error of 7.6 cm−1 (1.2%) for 196 assigned transitions. After optimizing the factors in an overlay refinement involving all six molecules, the frequencies are within 5.7 cm−1 (0.75%) of experiment. The ab initio absorption and Raman intensities are calculated with the 3-21G basis set and are demonstrated to be of such accuracy as to be useful for the spectral assignments. These intensities are calculated with uniformly and nonuniformly scaled force fields and compared to the experimental spectra. The intensities derived from the latter force fields are superior, meaning that nonuniform scaling is preferable at this level of theory for both vibrational frequencies and normal mode descriptions.

Requirements for correlation energy density functionals from coordinate transformations.

The behavior of the density-functional correlation energy under general linear coordinate transformations is considered. It is demonstrated that it is uniform and nonuniform scaling that yield new conditions which are fulfilled by the exact correlation energy functional, besides the well-known requirements of rotational, reflectional, and translational invariance. By considering various types of nonuniform scaling in the limit of the scale factor \ensuremath{\lambda} going to zero and infinity, a set of relations for the correlation energy is derived. These relations, which are easy to test on approximate functionals, are of the type ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}0}$(1/\ensuremath{\lambda})${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}\ensuremath{\lambda}}^{\mathit{x}\mathit{y}}$]=0 and ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{x}}$]=0. In addition, a previous proof is simplified for ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$]=const, which is bounded from below, and we identify the constant as a second-order energy. Here ${\mathit{n}}_{\ensuremath{\lambda}}$(r)=${\ensuremath{\lambda}}^{3}$n(\ensuremath{\lambda}x,\ensuremath{\lambda}y,\ensuremath{\lambda}z), ${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{x}}$(r)=\ensuremath{\lambda}n(\ensuremath{\lambda}x,y,z), and ${\mathit{n}}_{\ensuremath{\lambda}\ensuremath{\lambda}}^{\mathit{x}\mathit{y}}$(r)=${\ensuremath{\lambda}}^{2}$n(\ensuremath{\lambda}x,\ensuremath{\lambda}y,z) where n is the electron density. The limiting relations are not all met by any known approximate correlation energy functional. These relations apply to a correlation energy for addition to a Hartree-Fock calculation as well as to a correlation energy for use as part of a full density-functional calculation.

Approximate noninteracting kinetic energy functionals from a nonuniform scaling requirement

AbstractWe have recently proven an inequality for the exact noninteracting kinetic energy density functional \documentclass{article}\pagestyle{empty}\begin{document}$ T_s [n]:\mathop {\lim }\limits_{x \to \infty } T_s [n_\lambda ^x] \le T_s [n_s^y [n] + T_S^2 [n] < \infty,where{\rm }n_\lambda ^x (x,{\rm }y,{\rm }z) = \lambda n(\lambda x,{\rm }\lambda {\rm y, }\lambda z) $\end{document}. It is known that the gradient expansion through fourth order, T[n], violates this inequality. Toward improving TsGE[n], we have constructed two new functionals, Ts1[n] and Ts2[n], by keeping the zeroth and second orders in TsGE[n] and replacing the fourth order with two simple terms, respectively, so that these new functionals satisfy the inequality. Numerical tests are presented for Ts1[n], Ts2[n], and TsGE[n] and for the gradient expansion through second order. Hartree–Fock and hydrogenic atomic densities are employed.

Nonuniform coordinate scaling requirements for exchange-correlation energy.

Consider the nonuniformly scaled electron density ${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{x}}$(x,y,z)=\ensuremath{\lambda}n(\ensuremath{\lambda}x,y,z), with analogous definitions for ${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{y}}$ and ${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{z}}$. It is shown that it is generally true that ${\mathit{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{x}}$]\ensuremath{\ne}${\mathit{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{y}}$]\ensuremath{\ne}${\mathit{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{z}}$], where ${\mathit{E}}_{\mathrm{xc}}$ is the exact exchange-correlation energy. A corresponding inequality also holds for the correlation component of ${\mathit{E}}_{\mathrm{xc}}$ when the correlation component is defined in one of the meaningful ways. In contrast, equalities always hold for the local-density approximations to these exact functionals. In other words, the local-density approximations for exchange correlation and for correlation alone do not distinguish between nonuniform scaling along different coordinates.

Nonuniform coordinate scaling requirements in density-functional theory.

For the purpose of improving upon present approximate functionals, nonuniform coordinate scaling is introduced into density-functional theory, where ${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{x}}$(x,y,z)=\ensuremath{\lambda}n(\ensuremath{\lambda}x,y,z) is an example of a nonuniformly scaled electron density. Inequalities are derived for the exact noninteracting kinetic energy ${\mathit{T}}_{\mathit{s}}$[n]. For example, ${\mathit{T}}_{\mathit{s}}$[${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{x}}$]\ensuremath{\le}${\ensuremath{\lambda}}^{2}$${\mathit{T}}_{\mathit{s}}^{\mathit{x}}$[n]+${\mathit{T}}_{\mathit{s}}^{\mathit{y}}$[n]+${\mathit{T}}_{\mathit{s}}$ $^{\mathit{z}}]$, where ${\mathit{T}}_{\mathit{s}}^{\mathit{x}}$,${\mathit{T}}_{\mathit{s}}^{\mathit{y}}$, and ${\mathit{T}}_{\mathit{s}}^{\mathit{z}}$ are the x,y, and z components of ${\mathit{T}}_{\mathit{s}}$. Surprisingly, the gradient expansion through fourth order violates the inequalities. We also observe that the Thomas-Fermi approximation for ${\mathit{T}}_{\mathit{s}}$,${\mathit{T}}_{\mathit{s}}^{\mathrm{TF}}$, and the local-density approximation for the exchange-correlation energy, ${\mathit{E}}_{\mathrm{xc}}^{\mathrm{LDA}}$, do not distinguish between nonuniform scaling along different coordinates. That is, ${\mathit{T}}_{\mathit{s}}^{\mathrm{TF}}$[${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{x}}$]=${\mathit{T}}_{\mathit{s}}^{\mathrm{TF}}$[${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{y}}$] and ${\mathit{E}}_{\mathrm{xc}}^{\mathrm{LDA}}$[${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{x}}$]=${\mathit{E}}_{\mathrm{xc}}^{\mathrm{LDA}}$[${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{y}}$]. In contrast, for the true noninteracting kinetic energy it is proved that ${\mathit{T}}_{\mathit{s}}$[${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{x}}$]\ensuremath{\ne}${\mathit{T}}_{\mathit{s}}$[${\mathit{n}}_{\ensuremath{\lambda}}^{\mathit{y}}$] for a general density without special symmetry, and corresponding inequalities are conjectured to apply as well to the exact ${\mathit{E}}_{\mathrm{xc}}$. Moreover, ${\mathit{T}}_{\mathit{s}}^{\mathrm{TF}}$ incorrectly gives the same value for its x, y, and z components.

Synthesizing Statistical Knowledge from Incomplete Mixed-Mode Data

The difficulties in analyzing and clustering (synthesizing) multivariate data of the mixed type (discrete and continuous) are largely due to: 1) nonuniform scaling in different coordinates, 2) the lack of order in nominal data, and 3) the lack of a suitable similarity measure. This paper presents a new approach which bypasses these difficulties and can acquire statistical knowledge from incomplete mixed-mode data. The proposed method adopts an event-covering approach which covers a subset of statistically relevant outcomes in the outcome space of variable-pairs. And once the covered event patterns are acquired, subsequent analysis tasks such as probabilistic inference, cluster analysis, and detection of event patterns for each cluster based on the incomplete probability scheme can be performed. There are four phases in our method: 1) the discretization of the continuous components based on a maximum entropy criterion so that the data can be treated as n-tuples of discrete-valued features; 2) the estimation of the missing values using our newly developed inference procedure; 3) the initial formation of clusters by analyzing the nearest-neighbor distance on subsets of selected samples; and 4) the reclassification of the n-tuples into more reliable clusters based on the detected interdependence relationships. For performance evaluation, experiments have been conducted using both simulated and real life data.

Vowel‐space normalization procedures and phone‐preserving transformations of synthetic vowels

A variety of speaker‐normalization procedures have been proposed for the recognition of vowels of different speakers and/or the cross‐language comparison of vowel systems. Many such procedures are special cases of affine transformations of coordinates in a two‐(or more) formant space. Results of perceptual experiments are presented indicating that only a limited subset of affine transformations preserve the phonetic identity of a set of synthetic vowels. From a perceptual point of view, many vowel normalization procedures appear to be too powerful in the sense that they can “over‐normalize”" vowels which are phonetically distinct. In particular, rotations of a two‐formant space and/or independent multiplicative scaling of the F1 and F2 axes lead to marked change in phonetic quality. On the other hand, results indicate that uniform multiplicative sealing of F1 and F2 by a single constant is “almost phone‐preserving” in the range of male/female vowel differences. For larger (e.g., male/child) differences, a specific nonuniform scaling similar to that proposed by Fant seems to be required to maintain “perceptual constancy.”

Relation of drift velocity to low-field mobility and high-field saturation velocity

From an investigation of the behavior of the momentum distribution function of electrons or holes under scattering rate and momentum scaling transformations, a number of interesting results are derived concerning the parameterization of drift-velocity–vs–electric-field relations in terms of mobility and saturation velocity. Indeed it is determined that saturation velocity is invariant under scaling of the magnitude of the scattering rates, which alters mobility, while mobility is invariant under scaling of the magnitude of the momentum, which alters saturation velocity. This independence between mobility and saturation velocity is utilized to generalize to interfaces velocity-field relations valid the the bulk. Using the transformation of drift velocity under both rate and momentum scaling, partial experimental data can be used to predict high-field saturation velocities. These velocities need not be reduced due to higher scattering rates as much as their low-field counterparts. Nonzero magnetic fields and nonuniform scaling are also considered.

Continuum contribution to polarizabilities and scaling

AbstractThe role of the continuum, so important in ground‐state properties, is known to be less important and may even be negligible in the computation of polarizabilities and other higher negative moments of the oscillator strength distribution. This can be rationalized in terms of the solutions of the inhomogeneous equation generating the moments as an alternative to the dominating first term in an eigenfunction expansion. This leads in a natural form to the approximation Fϕ0(1 + w(r)) for the perturbed wave function where 1 + w(r) represents a nonuniform scaling of the unperturbed function ϕ0.

Piecewise--planar representation of vowel formant frequencies.

The first three formant frequencies for 778 steady-state tokens of 30 nonretroflex vowel types uttered by a female speaker are found to lie close to a piecewise-planar surface (expressed numerically as 0.634F1 +0.603F2 -- 0.485F3 -- 366 = 0, for F2 greater than 0.027F1 +1692 and 0.686F1 -- 0.528F2 -- 0.501F3 +1569 = 0, otherwise). The rms distance of the vowels from this surface is only 86 Hz. The intersection between the two planes is a line of nearly constant F2, corresponding closely to the F2 of a uniform vocal tract of the same length as our speaker's. The piecewise-planar representation also suggests a way to test the hypotheses of uniform and nonuniform formant-frequency scaling between speakers.

Charge Separation Effects on the Profile of a Perpendicular Shock Wave

The profile of a plasma shock wave propagating perpendicular to a magnetic field is studied using a system of moment equations derived from a pair of Boltzmann equations for electrons and ions. The system, rigorously closed for weak shocks, describes a fully ionized plasma in which a long list of dissipative mechanisms and Hall effects are coupled. The charge separation effect which is automatically excluded by the usual weak shock scaling [P. N. Hu, Phys. Fluids 9, 89 (1966) and H. Grad and P. N. Hu, Phys. Fluids 10, 2596 (1967)] is retained in this description by a special nonuniform scaling of the Debye length relative to the shock strength. The shock profiles are obtained from an equation with two essential parameters (combining five dimensionless parameters which occur in the problem). The magnetic field profiles cover the entire range from collision-dominated monotonic profiles to damped oscillatory profiles and the limiting collisionless case of purely oscillatory and solitary wave profiles. The profiles of the electric field and the charge density can also be oscillatory or monotonic, and, in some parameter ranges, have long downstream tails, extending far beyond where the velocity and the magnetic field are undisturbed.

Nonuniform Scaling of an Approximate H2+ Wavefunction

Nonuniform Scaling of an Approximate H2+ Wavefunction

The Effect of Temperature on the Oxygen Consumption of an Insect, Melanoplus differentialis

Previous article No AccessThe Effect of Temperature on the Oxygen Consumption of an Insect, Melanoplus differentialisEdith RogersEdith Rogers Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Volume 2, Number 2Apr., 1929 Article DOIhttps://doi.org/10.1086/physzool.2.2.30151358 Views: 5Total views on this site Citations: 12Citations are reported from Crossref Journal History This article was published in Physiological Zoology (1928-1998), which is continued by Physiological and Biochemical Zoology (1999-present). PDF download Crossref reports the following articles citing this article:Yadong Zhang, Zongkun Li, Wei Ge, Xudong Chen, Hongyin Xu, Hongyan Guan Evaluation of the impact of extreme floods on the biodiversity of terrestrial animals, Science of The Total Environment 790 (Oct 2021): 148227.https://doi.org/10.1016/j.scitotenv.2021.148227Devin B. Preston, Steven G. Johnson Generalist grasshoppers from thermally variable sites do not have higher thermal tolerance than grasshoppers from thermally stable sites - A study of five populations, Journal of Thermal Biology 88 (Feb 2020): 102527.https://doi.org/10.1016/j.jtherbio.2020.102527Steven G. Kuntz, Michael B. Eisen Oxygen changes drive non-uniform scaling in Drosophila melanogaster embryogenesis, F1000Research 4 (Oct 2015): 1102.https://doi.org/10.12688/f1000research.7221.1H.L. Contreras, T.J. Bradley Transitions in insect respiratory patterns are controlled by changes in metabolic rate, Journal of Insect Physiology 56, no.55 (May 2010): 522–528.https://doi.org/10.1016/j.jinsphys.2009.05.018Margaret Keister, John Buck RESPIRATION: SOME EXOGENOUS AND ENDOGENOUS EFFECTS ON RATE OF RESPIRATION, (Jan 1974): 469–509.https://doi.org/10.1016/B978-0-12-591606-6.50014-8 A. Glenn Richards The Generality of Temperature Effects on Developmental Rate and on Oxygen Consumption in Insect Eggs, Physiological Zoology 37, no.22 (Sep 2015): 199–211.https://doi.org/10.1086/physzool.37.2.30152331B. P. Uvarov RECENT ADVANCES IN ACRIDOLOGY: ANATOMY AND PHYSIOLOGY OF ACRIDIDAE., Transactions of the Royal Entomological Society of London 99, no.11 (Apr 2009): 1–73.https://doi.org/10.1111/j.1365-2311.1948.tb01224.x James P. Goodrich , and Joseph Hall Bodine A Determination of the Temperature Coefficients for Oxygen Uptake of Normal and Blocked Embryos and Eggs (Orthoptera), Physiological Zoology 12, no.33 (Sep 2015): 312–318.https://doi.org/10.1086/physzool.12.3.30151506J. R. BUSVINE THE TOXICITY OF ETHYLENE OXIDE TO CALANDRA ORYZAE, C. GRANARIA, TRIBOLIUM CASTANEUM, AND CIMEX LECTULARIUS, Annals of Applied Biology 25, no.33 (Aug 1938): 605–632.https://doi.org/10.1111/j.1744-7348.1938.tb04372.xLouis W. Kleinman The effect of temperature upon the respiratory quotients of nymphs of the grasshopper, Chortophaga viridifasciata DeGeer, and larvae of the Japanese beetle, Popillia japonica Newman, with reference to changes during hibernation, Journal of Cellular and Comparative Physiology 4, no.22 (Feb 1934): 221–235.https://doi.org/10.1002/jcp.1030040206 Joseph Hall Bodine Hibernation and Diapause in Certain Orthoptera. II. Response to Temperature during Hibernation and Diapause, Physiological Zoology 5, no.44 (Sep 2015): 538–548.https://doi.org/10.1086/physzool.5.4.30151184B. P. Uvarov INSECTS AND CLIMATE., Transactions of the Royal Entomological Society of London 79, no.11 (Apr 2009): 1–232.https://doi.org/10.1111/j.1365-2311.1931.tb00696.x