Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive
Tsallis, Constantino; Gell-Mann, Murray; Sato, Yuzuru
2005-01-01
Phase space can be constructed for N equal and distinguishable subsystems that could be probabilistically either weakly correlated or strongly correlated. If they are locally correlated, we expect the Boltzmann-Gibbs entropy SBG ≡ -k Σi pi ln pi to be extensive, i.e., SBG(N) ∝ N for N → ∞. In particular, if they are independent, SBG is strictly additive, i.e., SBG(N) = NSBG(1), ∀N. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy Sq ≡ k[1 - Σi pqi]/(q - 1) (with S1 = SBG) for some special value of q ≠ 1 to be the one which is extensive [i.e., Sq(N) ∝ N for N → ∞]. Another concept which is relevant is strict or asymptotic scale-freedom (or scale-invariance), defined as the situation for which all marginal probabilities of the N-system coincide or asymptotically approach (for N → ∞) the joint probabilities of the (N - 1)-system. If each subsystem is a binary one, scale-freedom is guaranteed by what we hereafter refer to as the Leibnitz rule, i.e., the sum of two successive joint probabilities of the N-system coincides or asymptotically approaches the corresponding joint probability of the (N - 1)-system. The kinds of interplay of these various concepts are illustrated in several examples. One of them justifies the title of this paper. We conjecture that these mechanisms are deeply related to the very frequent emergence, in natural and artificial complex systems, of scale-free structures and to their connections with nonextensive statistical mechanics. Summarizing, we have shown that, for asymptotically scale-invariant systems, it is Sq with q ≠ 1, and not SBG, the entropy which matches standard, clausius-like, prescriptions of classical thermodynamics. PMID:16230624
Scale invariance in biophysics
NASA Astrophysics Data System (ADS)
Stanley, H. Eugene
2000-06-01
In this general talk, we offer an overview of some problems of interest to biophysicists, medical physicists, and econophysicists. These include DNA sequences, brain plaques in Alzheimer patients, heartbeat intervals, and time series giving price fluctuations in economics. These problems have the common feature that they exhibit features that appear to be scale invariant. Particularly vexing is the problem that some of these scale invariant phenomena are not stationary-their statistical properties vary from one time interval to the next or form one position to the next. We will discuss methods, such as wavelet methods and multifractal methods, to cope with these problems. .
The scale invariant generator technique for quantifying anisotropic scale invariance
NASA Astrophysics Data System (ADS)
Lewis, G. M.; Lovejoy, S.; Schertzer, D.; Pecknold, S.
1999-11-01
Scale invariance is rapidly becoming a new paradigm for geophysics. However, little attention has been paid to the anisotropy that is invariably present in geophysical fields in the form of differential stratification and rotation, texture and morphology. In order to account for scaling anisotropy, the formalism of generalized scale invariance (GSI) was developed. Until now there has existed only a single fairly ad hoc GSI analysis technique valid for studying differential rotation. In this paper, we use a two-dimensional representation of the linear approximation to generalized scale invariance, to obtain a much improved technique for quantifying anisotropic scale invariance called the scale invariant generator technique (SIG). The accuracy of the technique is tested using anisotropic multifractal simulations and error estimates are provided for the geophysically relevant range of parameters. It is found that the technique yields reasonable estimates for simulations with a diversity of anisotropic and statistical characteristics. The scale invariant generator technique can profitably be applied to the scale invariant study of vertical/horizontal and space/time cross-sections of geophysical fields as well as to the study of the texture/morphology of fields.
A Scale-Invariant Treatment for Recursive Path Models.
ERIC Educational Resources Information Center
McDonald, Roderick P.; And Others
1993-01-01
A reparameterization is formulated that yields estimates of scale-invariant parameters in recursive path models with latent variables, and (asymptotically) correct standard errors, without the use of constrained optimization. The method is based on the logical structure of the reticular action model. (Author)
Hidden scale invariance of metals
NASA Astrophysics Data System (ADS)
Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.; Pedersen, Ulf R.
2015-11-01
Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general "hidden" scale invariance of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant inverse power-law (IPL) pair interactions. However, crystal packings of several transition metals (V, Cr, Mn, Fe, Nb, Mo, Ta, W, and Hg), most post-transition metals (Ga, In, Sn, and Tl), and the metalloids Si and Ge cannot be explained by the IPL assumption. The virial-energy correlation coefficients of iron and phosphorous are shown to increase at elevated pressures. Finally, we discuss how scale invariance explains the Grüneisen equation of state and a number of well-known empirical melting and freezing rules.
Emerging universe from scale invariance
Del Campo, Sergio; Herrera, Ramón; Guendelman, Eduardo I.; Labraña, Pedro E-mail: guendel@bgu.ac.il E-mail: plabrana@ubiobio.cl
2010-06-01
We consider a scale invariant model which includes a R{sup 2} term in action and show that a stable ''emerging universe'' scenario is possible. The model belongs to the general class of theories, where an integration measure independent of the metric is introduced. To implement scale invariance (S.I.), a dilaton field is introduced. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (S.S.B) of S.I. After S.S.B. of S.I. in the model with the R{sup 2} term (and first order formalism applied), it is found that a non trivial potential for the dilaton is generated. The dynamics of the scalar field becomes non linear and these non linearities are instrumental in the stability of some of the emerging universe solutions, which exists for a parameter range of the theory.
Measuring Scale Invariance between and within Subjects.
ERIC Educational Resources Information Center
Benson, Jeri; Hocevar, Dennis
The present paper represents a demonstration of how LISREL V can be used to investigate scale invariance (1) across time (its relationship to test-retest reliability), and (2) across groups. Five criteria were established to test scale invariance across time and four criteria were established to test scale invariance across groups. Using the…
Scale invariance in road networks
NASA Astrophysics Data System (ADS)
Kalapala, Vamsi; Sanwalani, Vishal; Clauset, Aaron; Moore, Cristopher
2006-02-01
We study the topological and geographic structure of the national road networks of the United States, England, and Denmark. By transforming these networks into their dual representation, where roads are vertices and an edge connects two vertices if the corresponding roads ever intersect, we show that they exhibit both topological and geographic scale invariance. That is, we show that for sufficiently large geographic areas, the dual degree distribution follows a power law with exponent 2.2⩽α⩽2.4 , and that journeys, regardless of their length, have a largely identical structure. To explain these properties, we introduce and analyze a simple fractal model of road placement that reproduces the observed structure, and suggests a testable connection between the scaling exponent α and the fractal dimensions governing the placement of roads and intersections.
Cosmological constant in scale-invariant theories
Foot, Robert; Kobakhidze, Archil; Volkas, Raymond R.
2011-10-01
The incorporation of a small cosmological constant within radiatively broken scale-invariant models is discussed. We show that phenomenologically consistent scale-invariant models can be constructed which allow a small positive cosmological constant, providing certain relation between the particle masses is satisfied. As a result, the mass of the dilaton is generated at two-loop level. Another interesting consequence is that the electroweak symmetry-breaking vacuum in such models is necessarily a metastable ''false'' vacuum which, fortunately, is not expected to decay on cosmological time scales.
Broken Scale Invariance and Anomalous Dimensions
DOE R&D Accomplishments Database
Wilson, K. G.
1970-05-01
Mack and Kastrup have proposed that broken scale invariance is a symmetry of strong interactions. There is evidence from the Thirring model and perturbation theory that the dimensions of fields defined by scale transformations will be changed by the interaction from their canonical values. We review these ideas and their consequences for strong interactions.
Scale invariant density perturbations from cyclic cosmology
NASA Astrophysics Data System (ADS)
Frampton, Paul Howard
2016-04-01
It is shown how quantum fluctuations of the radiation during the contraction era of a comes back empty (CBE) cyclic cosmology can provide density fluctuations which re-enter the horizon during the subsequent expansion era and at lowest order are scale invariant, in a Harrison-Zel’dovich-Peebles sense. It is necessary to be consistent with observations of large scale structure.
Scale invariance in the spectral action
Chamseddine, Ali H.; Connes, Alain
2006-06-15
The arbitrary mass scale in the spectral action for the Dirac operator is made dynamical by introducing a dilaton field. We evaluate all the low-energy terms in the spectral action and determine the dilaton couplings. These results are applied to the spectral action of the noncommutative space defined by the standard model. We show that the effective action for all matter couplings is scale invariant, except for the dilaton kinetic term and Einstein-Hilbert term. The resulting action is almost identical to the one proposed for making the standard model scale invariant as well as the model for extended inflation and has the same low-energy limit as the Randall-Sundrum model. Remarkably, all desirable features with correct signs for the relevant terms are obtained uniquely and without any fine tuning.
Natural inflation with hidden scale invariance
NASA Astrophysics Data System (ADS)
Barrie, Neil D.; Kobakhidze, Archil; Liang, Shelley
2016-05-01
We propose a new class of natural inflation models based on a hidden scale invariance. In a very generic Wilsonian effective field theory with an arbitrary number of scalar fields, which exhibits scale invariance via the dilaton, the potential necessarily contains a flat direction in the classical limit. This flat direction is lifted by small quantum corrections and inflation is realised without need for an unnatural fine-tuning. In the conformal limit, the effective potential becomes linear in the inflaton field, yielding to specific predictions for the spectral index and the tensor-to-scalar ratio, being respectively: ns - 1 ≈ - 0.025(N⋆/60)-1 and r ≈ 0.0667(N⋆/60)-1, where N⋆ ≈ 30- 65 is a number of efolds during observable inflation. This predictions are in reasonable agreement with cosmological measurements. Further improvement of the accuracy of these measurements may turn out to be critical in falsifying our scenario.
From scale invariance to Lorentz symmetry.
Sibiryakov, Sergey
2014-06-20
It is shown that a unitary translationally invariant field theory in 1+1 dimensions, satisfying isotropic scale invariance, standard assumptions about the spectrum of states and operators, and the requirement that signals propagate with finite velocity, possesses an infinite dimensional symmetry given by one or a product of several copies of conformal algebra. In particular, this implies the presence of one or several Lorentz groups acting on the operator algebra of the theory. PMID:24996083
Scale-invariant geometric random graphs
NASA Astrophysics Data System (ADS)
Xie, Zheng; Rogers, Tim
2016-03-01
We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and time, mimicking the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale invariance for geometric random graphs generated this way. Our analysis reveals a dichotomy between scale-free and Poisson distributions of in- and out-degree, the existence of a random number of hub nodes, high clustering, and unusual percolation behavior. These properties are similar to those of empirically observed web graphs.
Scale invariant texture descriptors for classifying celiac disease
Hegenbart, Sebastian; Uhl, Andreas; Vécsei, Andreas; Wimmer, Georg
2013-01-01
Scale invariant texture recognition methods are applied for the computer assisted diagnosis of celiac disease. In particular, emphasis is given to techniques enhancing the scale invariance of multi-scale and multi-orientation wavelet transforms and methods based on fractal analysis. After fine-tuning to specific properties of our celiac disease imagery database, which consists of endoscopic images of the duodenum, some scale invariant (and often even viewpoint invariant) methods provide classification results improving the current state of the art. However, not each of the investigated scale invariant methods is applicable successfully to our dataset. Therefore, the scale invariance of the employed approaches is explicitly assessed and it is found that many of the analyzed methods are not as scale invariant as they theoretically should be. Results imply that scale invariance is not a key-feature required for successful classification of our celiac disease dataset. PMID:23481171
The scale-invariant scotogenic model
NASA Astrophysics Data System (ADS)
Ahriche, Amine; McDonald, Kristian L.; Nasri, Salah
2016-06-01
We investigate a minimal scale-invariant implementation of the scotogenic model and show that viable electroweak symmetry breaking can occur while simultaneously generating one-loop neutrino masses and the dark matter relic abundance. The model predicts the existence of a singlet scalar (dilaton) that plays the dual roles of triggering electroweak symmetry breaking and sourcing lepton number violation. Important constraints are studied, including those from lepton flavor violating effects and dark matter direct-detection experiments. The latter turn out to be somewhat severe, already excluding large regions of parameter space. None the less, viable regions of parameter space are found, corresponding to dark matter masses below (roughly) 10 GeV and above 200 GeV.
Discrete scale invariance in supercritical percolation
NASA Astrophysics Data System (ADS)
Schröder, Malte; Chen, Wei; Nagler, Jan
2016-01-01
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order parameter (Chen et al 2014 Phys. Rev. Lett. 112 155701). Here we report the discovery of macrotransition cascades which follow percolation. The order parameter grows in discrete macroscopic steps with positions that can be randomly distributed even in the thermodynamic limit. These transition positions are, however, correlated and follow scaling laws which arise from discrete scale invariance (DSI) and non self-averaging, both traditionally unrelated to percolation. We reveal the DSI in ensemble measurements of these non self-averaging systems by rescaling of the individual realizations before averaging.
Scale invariance and universality of economic fluctuations
NASA Astrophysics Data System (ADS)
Stanley, H. E.; Amaral, L. A. N.; Gopikrishnan, P.; Plerou, V.
2000-08-01
In recent years, physicists have begun to apply concepts and methods of statistical physics to study economic problems, and the neologism “econophysics” is increasingly used to refer to this work. Much recent work is focused on understanding the statistical properties of time series. One reason for this interest is that economic systems are examples of complex interacting systems for which a huge amount of data exist, and it is possible that economic time series viewed from a different perspective might yield new results. This manuscript is a brief summary of a talk that was designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena - scale invariance and universality - can be useful in guiding research on economics. We shall see that while scale invariance has been tested for many years, universality is relatively less frequently discussed. This article reviews the results of two recent studies - (i) The probability distribution of stock price fluctuations: Stock price fluctuations occur in all magnitudes, in analogy to earthquakes - from tiny fluctuations to drastic events, such as market crashes. The distribution of price fluctuations decays with a power-law tail well outside the Lévy stable regime and describes fluctuations that differ in size by as much as eight orders of magnitude. (ii) Quantifying business firm fluctuations: We analyze the Computstat database comprising all publicly traded United States manufacturing companies within the years 1974-1993. We find that the distributions of growth rates is different for different bins of firm size, with a width that varies inversely with a power of firm size. Similar variation is found for other complex organizations, including country size, university research budget size, and size of species of bird populations.
Scale-invariant correlations and the distribution of prime numbers
NASA Astrophysics Data System (ADS)
Holdom, B.
2009-08-01
Negative correlations in the distribution of prime numbers are found to display a scale invariance. This occurs in conjunction with a nonstationary behavior. We compare the prime number series to a type of fractional Brownian motion which incorporates both the scale invariance and the nonstationary behavior. Interesting discrepancies remain. The scale invariance also appears to imply the Riemann hypothesis and we study the use of the former as a test of the latter.
Scale invariance, conformality, and generalized free fields
NASA Astrophysics Data System (ADS)
Dymarsky, Anatoly; Farnsworth, Kara; Komargodski, Zohar; Luty, Markus A.; Prilepina, Valentina
2016-02-01
This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance. An important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen is that trace of the energy-momentum tensor T could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if T is a generalized free field unless the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.
Noninflationary model with scale invariant cosmological perturbations
Peter, Patrick; Pinho, Emanuel J. C.; Pinto-Neto, Nelson
2007-01-15
We show that a contracting universe which bounces due to quantum cosmological effects and connects to the hot big-bang expansion phase, can produce an almost scale invariant spectrum of perturbations provided the perturbations are produced during an almost matter dominated era in the contraction phase. This is achieved using Bohmian solutions of the canonical Wheeler-DeWitt equation, thus treating both the background and the perturbations in a fully quantum manner. We find a very slightly blue spectrum (n{sub S}-1>0). Taking into account the spectral index constraint as well as the cosmic microwave background normalization measure yields an equation of state that should be less than {omega} < or approx. 8x10{sup -4}, implying n{sub S}-1{approx}O(10{sup -4}), and that the characteristic curvature scale of the Universe at the bounce is L{sub 0}{approx}10{sup 3}l{sub Pl}, a region where one expects that the Wheeler-DeWitt equation should be valid without being spoiled by string or loop quantum gravity effects. We have also obtained a consistency relation between the tensor-to-scalar ratio T/S and the scalar spectral index as T/S{approx}4.6x10{sup -2}{radical}(n{sub S}-1), leading to potentially measurable differences with inflationary predictions.
Computing with scale-invariant neural representations
NASA Astrophysics Data System (ADS)
Howard, Marc; Shankar, Karthik
The Weber-Fechner law is perhaps the oldest quantitative relationship in psychology. Consider the problem of the brain representing a function f (x) . Different neurons have receptive fields that support different parts of the range, such that the ith neuron has a receptive field at xi. Weber-Fechner scaling refers to the finding that the width of the receptive field scales with xi as does the difference between the centers of adjacent receptive fields. Weber-Fechner scaling is exponentially resource-conserving. Neurophysiological evidence suggests that neural representations obey Weber-Fechner scaling in the visual system and perhaps other systems as well. We describe an optimality constraint that is solved by Weber-Fechner scaling, providing an information-theoretic rationale for this principle of neural coding. Weber-Fechner scaling can be generated within a mathematical framework using the Laplace transform. Within this framework, simple computations such as translation, correlation and cross-correlation can be accomplished. This framework can in principle be extended to provide a general computational language for brain-inspired cognitive computation on scale-invariant representations. Supported by NSF PHY 1444389 and the BU Initiative for the Physics and Mathematics of Neural Systems,.
The Scale Invariant Synchrotron Jet of Flat Spectrum Radio Quasars
NASA Astrophysics Data System (ADS)
Du, L. M.; Bai, J. M.; Xie, Z. H.; Yi, T. F.; Xu, Y. B.; Xue, R.; Wang, X. H.
2015-06-01
In this paper, the scale invariance of the synchrotron jet of Flat Spectrum Radio Quasars has been studied using a sample of combined sources from FKM04 and from SDSS DR3 catalogue. Since the research of scale invariance has been focused on sub-Eddington cases that can be fitted onto the fundamental plane, while near-Eddington sources such as FSRQs have not been explicitly studied. The extracted physical properties of synchrotron jet of FSRQs have been shown to be scale invariant using our sample. The results are in good agreement with theoretical expectations of Heinz & Sunyaev (2003). Therefore, the jet synchrotron is shown to be scale independent, regardless of the accretion modes. Results in this article thus lend support to the scale invariant model of the jet synchrotron throughout the mass scale of black hole systems.
Scale invariance of subsurface flow patterns and its limitation
NASA Astrophysics Data System (ADS)
Hergarten, S.; Winkler, G.; Birk, S.
2016-05-01
Preferential flow patterns in the subsurface are of great importance for the availability and the quality of water resources. However, knowledge of their spatial structure is still behind their importance, so that understanding the nature of preferential flow patterns is a major issue in subsurface hydrology. Comparing the statistics of river catchment sizes and spring discharges, we found that the morphology of preferential subsurface flow patterns is probably scale invariant and similar to that of dendritic river networks. This result is not limited to karstic aquifers where the occurrence of dendritic structures has been known at least qualitatively for a long time. The scale invariance even seems to be independent of the lithology of the aquifer. However, scale invariance of river patterns seems to be only limited by the continental scale, while scale invariance of subsurface flow patterns breaks down at much smaller scales. The upper limit of scale invariance in subsurface flow patterns is highly variable. We found a range from thousands of square kilometers for limestone aquifers down to less than 1 km2 in the weathered zone and debris accumulations of crystalline rocks.
On time scale invariance of random walks in confined space.
Bearup, Daniel; Petrovskii, Sergei
2015-02-21
Animal movement is often modelled on an individual level using simulated random walks. In such applications it is preferable that the properties of these random walks remain consistent when the choice of time is changed (time scale invariance). While this property is well understood in unbounded space, it has not been studied in detail for random walks in a confined domain. In this work we undertake an investigation of time scale invariance of the drift and diffusion rates of Brownian random walks subject to one of four simple boundary conditions. We find that time scale invariance is lost when the boundary condition is non-conservative, that is when movement (or individuals) is discarded due to boundary encounters. Where possible analytical results are used to describe the limits of the time scaling process, numerical results are then used to characterise the intermediate behaviour. PMID:25481837
Anisotropic scale invariant spacetimes and black holes in Zwei-Dreibein Gravity
NASA Astrophysics Data System (ADS)
Goya, A. F.
2014-09-01
We show that Zwei-Dreibein Gravity (ZDG), a bigravity theory recently proposed by Bergshoeff, de Haan, Hohm, Merbis, and Townsend in ref. [1], admits exact solutions with anisotropic scale invariance. These type of geometries are the three-dimensional analogues of the spacetimes which were proposed as gravity duals for condensed matter systems. In particular, we find Schrödinger invariant spaces as well as Lifshitz spaces with arbitrary dynamical exponent z. We also find black holes that are asymptotically Lifshitz with z = 3, showing that these (non-constant curvature) solutions of New Massive Gravity (NMG) are persistent after the introduction of the infinite tower of higher-curvature terms of ZDG, provided a renormalization of the parameters. Black holes in asymptotically warped Anti-de Sitter spaces are also found. Interestingly, in almost all the geometries studied in this work, the metric associated with the second dreibein turns out to be equivalent, up to a constant global factor, to the first one. This phenomenon has been previously observed in other bigravity theories in asymptotically flat and asymptotically Anti-de Sitter backgrounds. However, for the particular case of the z = 3 Lifshitz black hole, here we found that the second metric corresponds to a different black hole that coincides with the former only in the asymptotic region. In fact, we find a new family of z = 3 black holes that corresponds to a one-parameter deformation of the NMG solution.
Tuning the cosmological constant, broken scale invariance, unitarity
NASA Astrophysics Data System (ADS)
Förste, Stefan; Manz, Paul
2016-06-01
We study gravity coupled to a cosmological constant and a scale but not conformally invariant sector. In Minkowski vacuum, scale invariance is spontaneously broken. We consider small fluctuations around the Minkowski vacuum. At the linearised level we find that the trace of metric perturbations receives a positive or negative mass squared contribution. However, only for the Fierz-Pauli combination the theory is free of ghosts. The mass term for the trace of metric perturbations can be cancelled by explicitly breaking scale invariance. This reintroduces fine-tuning. Models based on four form field strength show similarities with explicit scale symmetry breaking due to quantisation conditions.
Binary optical filters for scale invariant pattern recognition
NASA Technical Reports Server (NTRS)
Reid, Max B.; Downie, John D.; Hine, Butler P.
1992-01-01
Binary synthetic discriminant function (BSDF) optical filters which are invariant to scale changes in the target object of more than 50 percent are demonstrated in simulation and experiment. Efficient databases of scale invariant BSDF filters can be designed which discriminate between two very similar objects at any view scaled over a factor of 2 or more. The BSDF technique has considerable advantages over other methods for achieving scale invariant object recognition, as it also allows determination of the object's scale. In addition to scale, the technique can be used to design recognition systems invariant to other geometric distortions.
Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas.
Rohringer, W; Fischer, D; Steiner, F; Mazets, I E; Schmiedmayer, J; Trupke, M
2015-01-01
We present experimental evidence for scale invariant behaviour of the excitation spectrum in phase-fluctuating quasi-1d Bose gases after a rapid change of the external trapping potential. Probing density correlations in free expansion, we find that the temperature of an initial thermal state scales with the spatial extension of the cloud as predicted by a model based on adiabatic rescaling of initial eigenmodes with conserved quasiparticle occupation numbers. Based on this result, we demonstrate that shortcuts to adiabaticity for the rapid expansion or compression of the gas do not induce additional heating. PMID:25867640
Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas
Rohringer, W.; Fischer, D.; Steiner, F.; Mazets, I. E.; Schmiedmayer, J.; Trupke, M.
2015-01-01
We present experimental evidence for scale invariant behaviour of the excitation spectrum in phase-fluctuating quasi-1d Bose gases after a rapid change of the external trapping potential. Probing density correlations in free expansion, we find that the temperature of an initial thermal state scales with the spatial extension of the cloud as predicted by a model based on adiabatic rescaling of initial eigenmodes with conserved quasiparticle occupation numbers. Based on this result, we demonstrate that shortcuts to adiabaticity for the rapid expansion or compression of the gas do not induce additional heating. PMID:25867640
Scale-invariant entropy-based theory for dynamic ordering
Mahulikar, Shripad P. E-mail: spm@aero.iitb.ac.in; Kumari, Priti
2014-09-01
Dynamically Ordered self-organized dissipative structure exists in various forms and at different scales. This investigation first introduces the concept of an isolated embedding system, which embeds an open system, e.g., dissipative structure and its mass and/or energy exchange with its surroundings. Thereafter, scale-invariant theoretical analysis is presented using thermodynamic principles for Order creation, existence, and destruction. The sustainability criterion for Order existence based on its structured mass and/or energy interactions with the surroundings is mathematically defined. This criterion forms the basis for the interrelationship of physical parameters during sustained existence of dynamic Order. It is shown that the sufficient condition for dynamic Order existence is approached if its sustainability criterion is met, i.e., its destruction path is blocked. This scale-invariant approach has the potential to unify the physical understanding of universal dynamic ordering based on entropy considerations.
Levels of complexity in scale-invariant neural signals
NASA Astrophysics Data System (ADS)
Ivanov, Plamen Ch.; Ma, Qianli D. Y.; Bartsch, Ronny P.
2012-02-01
Many physiological systems exhibit complex scale-invariant and nonlinear features characterized long-range power-law correlations, indicating a possibly common control mechanism. It has been suggested that dynamical processes, influenced by inputs and feedback on multiple time scales, may be sufficient to give rise to this complexity. Two examples of physiologic signals that are the output of hierarchical multiscale physiologic systems under neural control are the human heartbeat and human gait. We show that while both cardiac interbeat interval and gait interstride interval time series under healthy conditions have comparable scale-invariant behavior, they still belong to different complexity classes. We compare results from empirical findings and stochastic feedback modeling approaches to cardiac and locomotor dynamics, which provide new insights into the multicomponent neural mechanisms regulating these complex systems.
Gauge coupling unification in a classically scale invariant model
NASA Astrophysics Data System (ADS)
Haba, Naoyuki; Ishida, Hiroyuki; Takahashi, Ryo; Yamaguchi, Yuya
2016-02-01
There are a lot of works within a class of classically scale invariant model, which is motivated by solving the gauge hierarchy problem. In this context, the Higgs mass vanishes at the UV scale due to the classically scale invariance, and is generated via the Coleman-Weinberg mechanism. Since the mass generation should occur not so far from the electroweak scale, we extend the standard model only around the TeV scale. We construct a model which can achieve the gauge coupling unification at the UV scale. In the same way, the model can realize the vacuum stability, smallness of active neutrino masses, baryon asymmetry of the universe, and dark matter relic abundance. The model predicts the existence vector-like fermions charged under SU(3) C with masses lower than 1 TeV, and the SM singlet Majorana dark matter with mass lower than 2.6 TeV.
Manifestly scale-invariant regularization and quantum effective operators
NASA Astrophysics Data System (ADS)
Ghilencea, D. M.
2016-05-01
Scale-invariant theories are often used to address the hierarchy problem. However the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which breaks this symmetry explicitly. We show how to avoid this problem and study the implications of a manifestly scale-invariant regularization in (classical) scale-invariant theories. We use a dilaton-dependent subtraction function μ (σ ) which, after spontaneous breaking of the scale symmetry, generates the usual dimensional regularization subtraction scale μ (⟨σ ⟩) . One consequence is that "evanescent" interactions generated by scale invariance of the action in d =4 -2 ɛ (but vanishing in d =4 ) give rise to new, finite quantum corrections. We find a (finite) correction Δ U (ϕ ,σ ) to the one-loop scalar potential for ϕ and σ , beyond the Coleman-Weinberg term. Δ U is due to an evanescent correction (∝ɛ ) to the field-dependent masses (of the states in the loop) which multiplies the pole (∝1 /ɛ ) of the momentum integral to give a finite quantum result. Δ U contains a nonpolynomial operator ˜ϕ6/σ2 of known coefficient and is independent of the subtraction dimensionless parameter. A more general μ (ϕ ,σ ) is ruled out since, in their classical decoupling limit, the visible sector (of the Higgs ϕ ) and hidden sector (dilaton σ ) still interact at the quantum level; thus, the subtraction function must depend on the dilaton only, μ ˜σ . The method is useful in models where preserving scale symmetry at quantum level is important.
Scale-invariant Lipatov kernels from t-channel unitarity
Coriano, C.; White, A.R.
1994-11-14
The Lipatov equation can be regarded as a reggeon Bethe-Salpeter equation in which higher-order reggeon interactions give higher-order kernels. Infra-red singular contributions in a general kernel are produced by t-channel nonsense states and the allowed kinematic forms are determined by unitarity. Ward identity and infra-red finiteness gauge invariance constraints then determine the corresponding scale-invariant part of a general higher-order kernel.
Observing scale-invariance in non-critical dynamical systems
NASA Astrophysics Data System (ADS)
Gros, C.; Marković, D.
2013-01-01
Recent observation for scale invariant neural avalanches in the brain have been discussed in details in the scientific literature. We point out, that these results do not necessarily imply that the properties of the underlying neural dynamics are also scale invariant. The reason for this discrepancy lies in the fact that the sampling statistics of observations and experiments is generically biased by the size of the basins of attraction of the processes to be studied. One has hence to precisely define what one means with statements like 'the brain is critical' . We recapitulate the notion of criticality, as originally introduced in statistical physics for second order phase transitions, turning then to the discussion of critical dynamical systems. We elucidate in detail the difference between a 'critical system', viz a system on the verge of a phase transition, and a 'critical state', viz state with scaleinvariant correlations, stressing the fact that the notion of universality is linked to critical states. We then discuss rigorous results for two classes of critical dynamical systems, the Kauffman net and a vertex routing model, which both have non-critical states. However, an external observer that samples randomly the phase space of these two critical models, would find scale invariance. We denote this phenomenon as 'observational criticality' and discuss its relevance for the response properties of critical dynamical systems.
Scale invariance in the dynamics of spontaneous behavior
Proekt, Alex; Banavar, Jayanth R.; Maritan, Amos; Pfaff, Donald W.
2012-01-01
Typically one expects that the intervals between consecutive occurrences of a particular behavior will have a characteristic time scale around which most observations are centered. Surprisingly, the timing of many diverse behaviors from human communication to animal foraging form complex self-similar temporal patterns reproduced on multiple time scales. We present a general framework for understanding how such scale invariance may arise in nonequilibrium systems, including those that regulate mammalian behaviors. We then demonstrate that the predictions of this framework are in agreement with detailed analysis of spontaneous mouse behavior observed in a simple unchanging environment. Neural systems operate on a broad range of time scales, from milliseconds to hours. We analytically show that such a separation between time scales could lead to scale-invariant dynamics without any fine tuning of parameters or other model-specific constraints. Our analyses reveal that the specifics of the distribution of resources or competition among several tasks are not essential for the expression of scale-free dynamics. Rather, we show that scale invariance observed in the dynamics of behavior can arise from the dynamics intrinsic to the brain. PMID:22679281
Scale-invariant alternatives to general relativity. II. Dilaton properties
NASA Astrophysics Data System (ADS)
Karananas, Georgios K.; Shaposhnikov, Mikhail
2016-04-01
In the present paper, we revisit gravitational theories which are invariant under TDiffs—transverse (volume-preserving) diffeomorphisms and global scale transformations. It is known that these theories can be rewritten in an equivalent diffeomorphism-invariant form with an action including an integration constant (cosmological constant for the particular case of non-scale-invariant unimodular gravity). The presence of this integration constant, in general, breaks explicitly scale invariance and induces a runaway potential for the (otherwise massless) dilaton, associated with the determinant of the metric tensor. We show, however, that if the metric carries mass dimension [GeV] -2 , the scale invariance of the system is preserved, unlike the situation in theories in which the metric has mass dimension different from -2 . The dilaton remains massless and couples to other fields only through derivatives, without any conflict with observations. We observe that one can define a specific limit for fields and their derivatives (in particular, the dilaton goes to zero, potentially related to the small distance domain of the theory) in which the only singular terms in the action correspond to the Higgs mass and the cosmological constant. We speculate that the self-consistency of the theory may require the regularity of the action, leading to the absence of the bare Higgs mass and cosmological constant, whereas their small finite values may be generated by nonperturbative effects.
Magnetic vortex filaments, universal scale invariants, and the fundamental constants
Lerner, E.J.
1986-12-01
An explanation for the observed scale invariants in the universe is presented. Force-free magnetic vortex filaments are proposed to play a crucial role in the formation of superclusters, clusters, galaxies, and stars by initiating gravitational compression. The critical velocities involved in vortex formation are shown to explain the observed constant orbital velocities of clusters, galaxies, and stars. A second scale invariant nr = C where n is particle density and r is average distance between objects, is also noted here and explained by the model. The model predicts a maximum size for magnetic vortices, which is comparable to the dimensions of the observable universe and a density for such vortices which is close to that actually observed, eliminating any theoretical need for missing mass. On this basis, they present an alternative cosmology to that of the ''Big Bang,'' one which provides a much better fit to recent observations of large-scale structure and motion. The model suggests scale invariants between microscopic and cosmological scales, leading to the derivation of a simple analytical expression for the fundamental constants G, m/sub rho//m/sub e/, and e/sup 2//hc. We conclude that these expressions indicate the existence of vortex phenomena on the particle level.
Multifractality and scale invariance in human heartbeat dynamics
NASA Astrophysics Data System (ADS)
Ching, Emily S. C.; Tsang, Yue-Kin
2007-10-01
Human heart rate is known to display complex fluctuations. Evidence of multifractality in heart rate fluctuations in healthy state has been reported [Ivanov , Nature (London) 399, 461 (1999)]. This multifractal character could be manifested as the dependence of the probability density functions (PDFs) of the interbeat interval increments, which are the differences in two interbeat intervals that are separated by n beats, on n . On the other hand, “scale invariance in the PDFs of detrended healthy human heart rate increments” was recently reported [Kiyono , Phys. Rev. Lett. 93, 178103 (2004)]. In this paper, we clarify that the scale invariance reported is actually exhibited by the PDFs of the increments of the “detrended” integrated healthy interbeat interval and should, therefore, be more accurately referred as the scale invariance or n independence of the PDFs of the sum of n detrended interbeat intervals. Indeed, we demonstrate explicitly that the PDFs of detrended healthy interbeat interval increments are scale or n dependent in accord with its multifractal character. Our work also establishes that this n independence of the PDFs of the sum of n detrended interbeat intervals is a general feature of human heartbeat dynamics, shared by heart rate fluctuations in both healthy and pathological states.
Self-organization in a model of economic system with scale invariant interactions
NASA Astrophysics Data System (ADS)
Pis`mak, Yu. M.
2001-10-01
The method of constructing the local scale invariant stochastic models is proposed. The possible extension of minimal scale-invariant interaction principle for stochastic systems is formulated. A simple scale invariant model that possesses an economical interpretation is considered. Essential characteristics of its self-organization mechanisms are discussed.
Scale Invariance in Landscape Evolution Models Using Stream Power Laws
NASA Astrophysics Data System (ADS)
Kwang, J. S.; Parker, G.
2014-12-01
Landscape evolution models (LEM) commonly utilize stream power laws to simulate river incision with formulations such as E = KAmSn, where E is a vertical incision rate [L/T], K is an erodibility constant [L1-2m/T], A is an upstream drainage area [L2], S is a local channel gradient [-], and m and n are positive exponents that describe the basin hydrology. In our reduced complexity model, the landscape approached equilibrium by balancing an incision rate with a constant, uniform, vertical rock uplift rate at every location in the landscape. From our simulations, for a combination of m and n, the landscape exhibited scale invariance. That is, regardless of the size and scale of the basin, the relief and vertical structure of the landscape remained constant. Therefore, the relief and elevation profile of the landscape at equilibrium were only dependent on the coefficients for erodibility and uplift and an equation that described how upstream area, A, increased as the length of a stream increased. In our analytical 1D models, we utilized two equations that described upslope area, (a) A = Bl, where B is the profile width [L], and l is the stream length from the ridge [L] and (b) A = Clh, Hack's Law, where C is a constant [L2-h] and h is a positive exponent. With these equations, (a) m = n and (b) hm = n resulted in scale invariance. In our numerical 2D models, the relationship between A and l was inherent in the actual structure of the drainage network. From our numerical 2D results, scale invariance occurred when 2m = n. Additionally, using reasonable values from the literature for exponents, n, m and h, resulted in singularities at the ridges in the landscape, which caused truncation error. In consequence, the elevation of the ridge increased as the number of grid cells in the domain increased in the numerical model, and the model was unable to converge. These singularities at the ridges appeared when (a) m ≥ n and (b) hm ≥ n in the analytical model and 2m ≥ n in
Scale invariant behavior in a large N matrix model
NASA Astrophysics Data System (ADS)
Narayanan, Rajamani; Neuberger, Herbert
2016-01-01
Eigenvalue distributions of properly regularized Wilson-loop operators are used to study the transition from UV behavior to IR behavior in gauge theories coupled to matter that potentially have an IR fixed point. We numerically demonstrate the emergence of scale invariance in a matrix model that describes S U (N ) gauge theory coupled to two flavors of massless adjoint fermions in the large N limit. The eigenvalue distribution of Wilson loops of varying sizes cannot be described by a universal lattice beta function connecting the UV to the IR.
Scale-Invariant Correlations in Dynamic Bacterial Clusters
NASA Astrophysics Data System (ADS)
Chen, Xiao; Dong, Xu; Be'er, Avraham; Swinney, Harry L.; Zhang, H. P.
2012-04-01
In Bacillus subtilis colonies, motile bacteria move collectively, spontaneously forming dynamic clusters. These bacterial clusters share similarities with other systems exhibiting polarized collective motion, such as bird flocks or fish schools. Here we study experimentally how velocity and orientation fluctuations within clusters are spatially correlated. For a range of cell density and cluster size, the correlation length is shown to be 30% of the spatial size of clusters, and the correlation functions collapse onto a master curve after rescaling the separation with correlation length. Our results demonstrate that correlations of velocity and orientation fluctuations are scale invariant in dynamic bacterial clusters.
Non-scale-invariant density perturbations from chaotic extended inflation
Mollerach, S. ); Matarrese, S. )
1992-03-15
Chaotic inflation is analyzed in the frame of scalar-tensor theories of gravity. Fluctuations in the energy density arise from quantum fluctuations of the Brans-Dicke field and of the inflaton field. The spectrum of perturbations is studied for a class of models: it is non-scale-invariant and, for certain values of the parameters, it has a peak. If the peak appears at astrophysically interesting scales it may help to reconcile the cold-dark-matter scenario for structure formation with large-scale observations.
Non scale-invariant density perturbations from chaotic extended inflation
NASA Technical Reports Server (NTRS)
Mollerach, Silvia; Matarrese, Sabino
1991-01-01
Chaotic inflation is analyzed in the frame of scalar-tensor theories of gravity. Fluctuations in the energy density arise from quantum fluctuations of the Brans-Dicke field and of the inflation field. The spectrum of perturbations is studied for a class of models: it is non scale-invarient and, for certain values of the parameters, it has a peak. If the peak appears at astrophysically interesting scales, it may help to reconcile the Cold Dark Matter scenario for structure formation with large scale observations.
Critical Scale Invariance in a Healthy Human Heart Rate
NASA Astrophysics Data System (ADS)
Kiyono, Ken; Struzik, Zbigniew R.; Aoyagi, Naoko; Sakata, Seiichiro; Hayano, Junichiro; Yamamoto, Yoshiharu
2004-10-01
We demonstrate the robust scale-invariance in the probability density function (PDF) of detrended healthy human heart rate increments, which is preserved not only in a quiescent condition, but also in a dynamic state where the mean level of the heart rate is dramatically changing. This scale-independent and fractal structure is markedly different from the scale-dependent PDF evolution observed in a turbulentlike, cascade heart rate model. These results strongly support the view that a healthy human heart rate is controlled to converge continually to a critical state.
Scale invariance of human electroencephalogram signals in sleep
NASA Astrophysics Data System (ADS)
Cai, Shi-Min; Jiang, Zhao-Hui; Zhou, Tao; Zhou, Pei-Ling; Yang, Hui-Jie; Wang, Bing-Hong
2007-12-01
In this paper, we investigate the dynamical properties of electroencephalogram (EEG) signals of humans in sleep. By using a modified random walk method, we demonstrate that scale-invariance is embedded in EEG signals after a detrending procedure is applied. Furthermore, we study the dynamical evolution of the probability density function (PDF) of the detrended EEG signals by nonextensive statistical modeling. It displays a scale-independent property, which is markedly different from the usual scale-dependent PDF evolution and cannot be described by the Fokker-Planck equation.
Scale-invariant curvature fluctuations from an extended semiclassical gravity
Pinamonti, Nicola E-mail: siemssen@dima.unige.it; Siemssen, Daniel E-mail: siemssen@dima.unige.it
2015-02-15
We present an extension of the semiclassical Einstein equations which couple n-point correlation functions of a stochastic Einstein tensor to the n-point functions of the quantum stress-energy tensor. We apply this extension to calculate the quantum fluctuations during an inflationary period, where we take as a model a massive conformally coupled scalar field on a perturbed de Sitter space and describe how a renormalization independent, almost-scale-invariant power spectrum of the scalar metric perturbation is produced. Furthermore, we discuss how this model yields a natural basis for the calculation of non-Gaussianities of the considered metric fluctuations.
Evaluation of Scaling Invariance Embedded in Short Time Series
Pan, Xue; Hou, Lei; Stephen, Mutua; Yang, Huijie; Zhu, Chenping
2014-01-01
Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length . Calculations with specified Hurst exponent values of show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias () and sharp confidential interval (standard deviation ). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records. PMID:25549356
Scale invariance of temporal order discrimination using complex, naturalistic events
Kwok, Sze Chai; Macaluso, Emiliano
2015-01-01
Recent demonstrations of scale invariance in cognitive domains prompted us to investigate whether a scale-free pattern might exist in retrieving the temporal order of events from episodic memory. We present four experiments using an encoding-retrieval paradigm with naturalistic stimuli (movies or video clips). Our studies show that temporal order judgement retrieval times were negatively correlated with the temporal separation between two events in the movie. This relation held, irrespective of whether temporal distances were on the order of tens of minutes (Exp 1−2) or just a few seconds (Exp 3−4). Using the SIMPLE model, we factored in the retention delays between encoding and retrieval (delays of 24 h, 15 min, 1.5–2.5 s, and 0.5 s for Exp 1–4, respectively) and computed a temporal similarity score for each trial. We found a positive relation between similarity and retrieval times; that is, the more temporally similar two events, the slower the retrieval of their temporal order. Using Bayesian analysis, we confirmed the equivalence of the RT/similarity relation across all experiments, which included a vast range of temporal distances and retention delays. These results provide evidence for scale invariance during the retrieval of temporal order of episodic memories. PMID:25909581
Scale invariance of temporal order discrimination using complex, naturalistic events.
Kwok, Sze Chai; Macaluso, Emiliano
2015-07-01
Recent demonstrations of scale invariance in cognitive domains prompted us to investigate whether a scale-free pattern might exist in retrieving the temporal order of events from episodic memory. We present four experiments using an encoding-retrieval paradigm with naturalistic stimuli (movies or video clips). Our studies show that temporal order judgement retrieval times were negatively correlated with the temporal separation between two events in the movie. This relation held, irrespective of whether temporal distances were on the order of tens of minutes (Exp 1-2) or just a few seconds (Exp 3-4). Using the SIMPLE model, we factored in the retention delays between encoding and retrieval (delays of 24 h, 15 min, 1.5-2.5 s, and 0.5 s for Exp 1-4, respectively) and computed a temporal similarity score for each trial. We found a positive relation between similarity and retrieval times; that is, the more temporally similar two events, the slower the retrieval of their temporal order. Using Bayesian analysis, we confirmed the equivalence of the RT/similarity relation across all experiments, which included a vast range of temporal distances and retention delays. These results provide evidence for scale invariance during the retrieval of temporal order of episodic memories. PMID:25909581
Differential rotation and cloud texture: Analysis using generalized scale invariance
Pflug, K.; Lovejoy, S. ); Schertzer, D. )
1993-02-14
The standard picture of atmospheric dynamics is that of an isotropic two-dimensional large scale and an isotropic three-dimensional small scale, the two separated by a dimensional transition called the [open quotes]mesoscale gap.[close quotes] Evidence now suggests that, on the contrary, atmospheric fields, while strongly anisotropic, are nonetheless scale invariant right through the mesoscale. Using visible and infrared satellite cloud images and the formalism of generalized scale invariance (GSI), the authors attempt to quantify the anisotropy for cloud radiance fields in the range 1-1000 km. To do this, the statistical translational invariance of the fields is exploited by studying the anisotropic scaling of lines of constant Fourier amplitude. This allows the investigation of the change in shape and orientation of average structures with scale. For the three texturally-and meteorologically-very different images analyzed, three different generators of anisotropy are found that generally reproduce well the Fourier space anisotropy. Although three cases are a small number from which to infer ensemble-averaged properties, the authors conclude that while cloud radiances are not isotropic (self-similar), they are nonetheless scaling. Since elsewhere (with the help of simulations) it is shown that the generator of the anisotropy is related to the texture, it is argued here that GSI could potentially provide a quantitative basis for cloud classification and modeling. 59 refs., 21 figs., 2 tabs.
A dimension scale-invariant probabilistic model based on Leibniz-like pyramids
NASA Astrophysics Data System (ADS)
Rodríguez, A.; Tsallis, C.
2012-02-01
We introduce a family of dimension scale-invariant Leibniz-like pyramids and (d + 1)-dimensional hyperpyramids (d = 1, 2, 3, …), with d = 1 corresponding to triangles, d = 2 to (tetrahedral) pyramids, and so on. For all values of d, they are characterized by a parameter ν > 0, whose value determines the degree of correlation between N (d + 1)-valued random variables (d = 1 corresponds to binary variables, d = 2 to ternary variables, and so on). There are (d + 1)N different events, and the limit ν → ∞ corresponds to independent random variables, in which case each event has a probability 1/(d + 1)N to occur. The sums of these N (d + 1)-valued random variables correspond to a d-dimensional probabilistic model and generalize a recently proposed one-dimensional (d = 1) model having q -Gaussians (with q = (ν - 2)/(ν - 1) for ν ∈ [1, ∞)) as N → ∞ limit probability distributions for the sum of the N binary variables [A. Rodríguez, V. Schwammle, and C. Tsallis, J. Stat. Mech.: Theory Exp. 2008, P09006; R. Hanel, S. Thurner, and C. Tsallis, Eur. Phys. J. B 72, 263 (2009)]. In the ν → ∞ limit the d-dimensional multinomial distribution is recovered for the sums, which approach a d-dimensional Gaussian distribution for N → ∞. For any ν, the conditional distributions of the d-dimensional model are shown to yield the corresponding joint distribution of the (d-1)-dimensional model with the same ν. For the d = 2 case, we study the joint probability distribution and identify two classes of marginal distributions, one of them being asymmetric and dimension scale-invariant, while the other one is symmetric and only asymptotically dimension scale-invariant. The present probabilistic model is proposed as a testing ground for a deeper understanding of the necessary and sufficient conditions for having q-Gaussian attractors in the N → ∞ limit, the ultimate goal being a neat mathematical view of the causes clarifying the ubiquitous emergence of q
Generalized scale invariance, clouds and radiative transfer on multifractal clouds
Lovejoy, S.; Schertzer, D.
1995-09-01
Recent systematic satellite studies (LANDSAT, AVHRR, METEOSAT) of cloud radiances using (isotropic) energy spectra have displayed excellent scaling from at least about 300m to about 4000km, even for individual cloud pictures. At first sight, this contradicts the observed diversity of cloud morphology, texture and type. The authors argue that the explanation of this apparent paradox is that the differences are due to anisotropy, e.g. differential stratification and rotation. A general framework for anisotropic scaling expressed in terms of isotropic self-similar scaling and fractals and multifractals is needed. Schertzer and Lovejoy have proposed Generalized Scale Invariance (GSI) in response to this need. In GSI, the statistics of the large and small scales of system can be related to each other by a scale changing operator T{sub {lambda}} which depends only on the scale ratio {lambda}{sub i} there is no characteristic size. 3 refs., 1 fig.
Fermi-bounce cosmology and scale-invariant power spectrum
NASA Astrophysics Data System (ADS)
Alexander, Stephon; Bambi, Cosimo; Marcianò, Antonino; Modesto, Leonardo
2014-12-01
We develop a nonsingular bouncing cosmology using a nontrivial coupling of general relativity to fermionic fields. The usual big bang singularity is avoided thanks to a negative energy density contribution from the fermions. Our theory is ghost free since the fermionic operator that generates the bounce is equivalent to torsion, which has no kinetic terms. The physical system consists of standard general relativity plus a topological sector for gravity and fermionic matter described by Dirac fields with a nonminimal coupling. We show that a scale-invariant power spectrum generated in the contracting phase can be recovered by suitable choices of fermion number density and bare mass, thus providing a possible alternative to the inflationary scenario.
Scale-invariant structure of size fluctuations in plants
NASA Astrophysics Data System (ADS)
Picoli, S.; Mendes, R. S.; Lenzi, E. K.; Malacarne, L. C.
2012-03-01
A wide range of physical and biological systems exhibit complex behaviours characterised by a scale-invariant structure of the fluctuations in their output signals. In the context of plant populations, scaling relationships are typically allometric. In this study, we analysed spatial variation in the size of maize plants (Zea Mays L.) grown in agricultural plots at constant densities and found evidence of scaling in the size fluctuations of plants. The findings indicate that the scaling of the probability distribution of spatial size fluctuation exhibits non-Gaussian behaviour compatible with a Lévy stable process. The scaling relationships were observed for spatial scales spanning three orders of magnitude. These findings should provide additional information for the selection and development of empirically accurate models of pattern formation in plant populations.
Classically Scale Invariant Inflation and (A)gravity
NASA Astrophysics Data System (ADS)
Farzinnia, Arsham
2016-07-01
In this talk, I present the minimal classically scale-invariant and CP-symmetric extension of the standard model, containing one additional complex gauge singlet and three flavors of right-handed Majorana neutrinos, incorporated within a renormalizable framework of gravity, consistent with these symmetries; the Agravity. I particularly focus on the slow-roll inflationary paradigm within this framework, by identifying the pseudo-Nambu-Goldstone boson of the (approximate) scale symmetry with the inflaton field, constructing its one-loop effective potential, computing the slow-roll parameters and the inflationary observables, and demonstrating the compatibility of the small field inflation scenario with the latest Planck collaboration data sets.a
Fisher information and the thermodynamics of scale-invariant systems
NASA Astrophysics Data System (ADS)
Hernando, A.; Vesperinas, C.; Plastino, A.
2010-02-01
We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of the Fisher information measure. In such a way a clear analogy between these systems’ thermal properties and those of gases and fluids is seen to emerge in a natural fashion. We focus our attention on the non-interacting scenario, speaking thus of scale-free ideal gases (SFIGs) and present some empirical evidences regarding such disparate systems as electoral results, city populations and total citations in Physics journals, that seem to indicate that SFIGs do exist. We also illustrate the way in which Zipf’s law can be understood in a thermodynamical context as the surface of a finite system. Finally, we derive an equivalent microscopic description of our systems which totally agrees with previous numerical simulations found in the literature.
Transport in fractal media: an effective scale-invariant approach.
Hernandez-Coronado, H; Coronado, M; Herrera-Hernandez, E C
2012-06-01
In this paper an advective-dispersion equation with scale-dependent coefficients is proposed for describing transport through fractals. This equation is obtained by imposing scale invariance and assuming that the porosity, the dispersion coefficient, and the velocity follow fractional power laws on the scale. The model incorporates the empirically found trends in highly heterogeneous media, regarding the dependence of the dispersivity on the scale and the dispersion coefficient on the velocity. We conclude that the presence of nontrivial fractal parameters produces anomalous dispersion, as expected, and that the presence of convective processes induces a reescalation in the concentration and shifts the tracer velocity to different values with respect to the nonfractal case. PMID:23005215
Excitation of flow instabilities due to nonlinear scale invariance
Prasad Datta, Dhurjati; Sen, Sudip
2014-05-15
A novel route to instabilities and turbulence in fluid and plasma flows is presented in kinetic Vlasov-Maxwell model. New kind of flow instabilities is shown to arise due to the availability of new kinetic energy sources which are absent in conventional treatments. The present approach is based on a scale invariant nonlinear analytic formalism developed to address irregular motions on a chaotic attractor or in turbulence in a more coherent manner. We have studied two specific applications of this turbulence generating mechanism. The warm plasma Langmuir wave dispersion relation is shown to become unstable in the presence of these multifractal measures. In the second application, these multifractal measures are shown to induce naturally non-Gaussian, i.e., a stretched, Gaussian distribution and anomalous transport for tracer particles from the turbulent advection-diffusion transport equation in a Vlasov plasma flow.
Near-Milne realization of scale-invariant fluctuations
Magueijo, Joao
2007-12-15
A near-Milne universe produces a very red spectrum of vacuum quantum fluctuations but has the potential to produce near-scale-invariant thermal fluctuations. This happens if the energy and entropy are mildly subextensive, for example, if there is a Casimir contribution. Therefore, one does not need to invoke corrections to Einstein gravity (as in loop quantum cosmology) for a thermal scenario to be viable. Neither do we need the energy to scale like the area, as in scenarios where the thermal fluctuations are subject to a phase transition in the early universe. Some odd features of this model are pointed out: whether they are fatal or merely unusual will need to be investigated further.
Generation of scale invariant magnetic fields in bouncing universes
NASA Astrophysics Data System (ADS)
Sriramkumar, L.; Atmjeet, Kumar; Jain, Rajeev Kumar
2015-09-01
We consider the generation of primordial magnetic fields in a class of bouncing models when the electromagnetic action is coupled non-minimally to a scalar field that, say, drives the background evolution. For scale factors that have the power law form at very early times and non-minimal couplings which are simple powers of the scale factor, one can easily show that scale invariant spectra for the magnetic field can arise before the bounce for certain values of the indices involved. It will be interesting to examine if these power spectra retain their shape after the bounce. However, analytical solutions for the Fourier modes of the electromagnetic vector potential across the bounce are difficult to obtain. In this work, with the help of a new time variable that we introduce, which we refer to as the e-Script N-fold, we investigate these scenarios numerically. Imposing the initial conditions on the modes in the contracting phase, we numerically evolve the modes across the bounce and evaluate the spectra of the electric and magnetic fields at a suitable time after the bounce. As one could have intuitively expected, though the complete spectra depend on the details of the bounce, we find that, under the original conditions, scale invariant spectra of the magnetic fields do arise for wavenumbers much smaller than the scale associated with the bounce. We also show that magnetic fields which correspond to observed strengths today can be generated for specific values of the parameters. But, we find that, at the bounce, the backreaction due to the electromagnetic modes that have been generated can be significantly large calling into question the viability of the model. We briefly discuss the implications of our results.
Curvaton reheating mechanism in a scale invariant two measures theory
NASA Astrophysics Data System (ADS)
Guendelman, Eduardo I.; Herrera, Ramón
2016-01-01
The curvaton reheating mechanism in a scale invariant two measures theory defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold which are metric independent is studied. The model involves two scalar matter fields, a dilaton, that transforms under scale transformations and it will be used also as the inflaton of the model and another scalar, which does not transform under scale transformations and which will play the role of a curvaton field. Potentials of appropriate form so that the pertinent action is invariant under global Weyl-scale symmetry are introduced. Scale invariance is spontaneously broken upon integration of the equations of motion. After performing transition to the physical Einstein frame we obtain: (1) For given value of the curvaton field an effective potential for the scalar field with two flat regions for the dilaton which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (2) In the phase corresponding to the early universe, the curvaton has a constant mass and can oscillate decoupled from the dilaton and that can be responsible for both reheating and perturbations in the theory. In this framework, we obtain some interesting constraints on different parameters that appear in our model; (3) For a definite parameter range the model possesses a non-singular "emergent universe" solution which describes an initial phase of evolution that precedes the inflationary phase. Finally we discuss generalizations of the model, through the effect of higher curvature terms, where inflaton and curvaton can have coupled oscillations.
Physical naturalness and dynamical breaking of classical scale invariance
NASA Astrophysics Data System (ADS)
Heikinheimo, Matti; Racioppi, Antonio; Spethmann, Christian; Raidal, Martti; Tuominen, Kimmo
2014-05-01
We propose a model of a confining dark sector, dark technicolor, that communicates with the Standard Model (SM) through the Higgs portal. In this model electroweak (EW) symmetry breaking and dark matter (DM) share a common origin, and the EW scale is generated dynamically. Our motivation to suggest this model is the absence of evidence for new physics from recent Large Hadron Collider (LHC) data. Although the conclusion is far from certain at this point, this lack of evidence may suggest that no mechanism exists at the EW scale to stabilize the Higgs mass against radiative corrections from ultraviolet (UV) physics. The usual reaction to this puzzling situation is to conclude that the stabilizing new physics is either hidden from us by accident, or that it appears at energies that are currently inaccessible, such that nature is indeed fine-tuned. In order to re-examine the arguments that have led to this dichotomy, we review the concept of naturalness in effective field theories, discussing in particular the role of quadratic divergences in relation to different energy scales. This leads us to suggest classical scale invariance as a guideline for model building, implying that explicit mass scales are absent in the underlying theory.
Scale-Invariant Hydrodynamics and Quantum Viscosity in Fermi Gases
NASA Astrophysics Data System (ADS)
Thomas, John
2015-05-01
An optically-trapped gas of spin 1/2-up and spin 1/2-down 6Li atoms, tuned near a collisional (Feshbach) resonance, provides a unique paradigm for testing predictions that cross interdisciplinary boundaries, from high temperature superconductors to nuclear matter. At resonance, the dilute atomic cloud becomes the most strongly interacting, non-relativistic fluid known: Shock waves are produced when two clouds collide. We observe scale-invariant hydrodynamic expansion of a resonantly interacting gas and determine the quantum shear viscosity η = α ℏn , with n the density, as a function of interaction strength and temperature, from nearly the ground state through the superfluid phase transition. We extract the local shear viscosity coefficient α from cloud-averaged data, using iterative methods borrowed from image processing, and observe previously hidden features, which are compared to recent predictions. In collaboration with Ethan Elliott and James Joseph, Physics Department, North Carolina State University. Supported by NSF, DOE, ARO, AFOSR.
Scale invariance of a diode-like tunnel junction
NASA Astrophysics Data System (ADS)
Cabrera, Hugo; Zanin, Danilo Andrea; de Pietro, Lorenzo Giuseppe; Michaels, Thomas; Thalmann, Peter; Ramsperger, Urs; Vindigni, Alessandro; Pescia, Danilo
2013-03-01
In Near Field-Emission SEM (NFESEM), electrostatic considerations favor a diode-like tunnel junction consisting of an atomic-sized source mounted at the apex of a thin wire placed at nanometric distances from a collector. The quantum mechanical tunnel process, instead, can provide a barrier toward miniaturization. In the first place, it deteriorates the generation of electrons by introducing non-linearities within the classically forbidden zone that exponentially increase with decreasing sizes. In addition, in the direct tunnelling regime, i.e. when the distance between emitter and collector d approaches the subnanometer range, a characteristic length appears, making the cross-over from the (almost) scale-invariant electric-field assisted regime to the essentially different STM-regime. We have observed that the experimental data relating the current I to the two experimental variables V (bias voltage between tip and collector) and d can be made (almost) collapse onto a ``scaling curve'' relating I to the single variable V .d-λ , λ being some exponent that depends solely on the geometry of the junction. This scaling property can be used to highlight non-linear aspects of the quantum mechanical tunnelling process.
Viscosity and scale invariance in the unitary Fermi gas
Enss, Tilman; Haussmann, Rudolf; Zwerger, Wilhelm
2011-03-15
We compute the shear viscosity of the unitary Fermi gas above the superfluid transition temperature, using a diagrammatic technique that starts from the exact Kubo formula. The formalism obeys a Ward identity associated with scale invariance which guarantees that the bulk viscosity vanishes identically. For the shear viscosity, vertex corrections and the associated Aslamazov-Larkin contributions are shown to be crucial to reproduce the full Boltzmann equation result in the high-temperature, low fugacity limit. The frequency dependent shear viscosity {eta}({omega}) exhibits a Drude-like transport peak and a power-law tail at large frequencies which is proportional to the Tan contact. The weight in the transport peak is given by the equilibrium pressure, in agreement with a sum rule due to Taylor and Randeria. Near the superfluid transition the peak width is of the order of 0.5T{sub F}, thus invalidating a quasiparticle description. The ratio {eta}/s between the static shear viscosity and the entropy density exhibits a minimum near the superfluid transition temperature whose value is larger than the string theory bound h/(4{pi}k{sub B}) by a factor of about seven.
Rotation and Scale Invariant Wavelet Feature for Content-Based Texture Image Retrieval.
ERIC Educational Resources Information Center
Lee, Moon-Chuen; Pun, Chi-Man
2003-01-01
Introduces a rotation and scale invariant log-polar wavelet texture feature for image retrieval. The underlying feature extraction process involves a log-polar transform followed by an adaptive row shift invariant wavelet packet transform. Experimental results show that this rotation and scale invariant wavelet feature is quite effective for image…
ERIC Educational Resources Information Center
Moses, Tim
2011-01-01
The purpose of this study was to consider the relationships of prediction, measurement, and scaling invariance when these invariances were simultaneously evaluated in psychometric test data. An approach was developed to evaluate prediction, measurement, and scaling invariance based on linear and nonlinear prediction, measurement, and scaling…
Power spectrum scale invariance identifies prefrontal dysregulation in paranoid schizophrenia.
Radulescu, Anca R; Rubin, Denis; Strey, Helmut H; Mujica-Parodi, Lilianne R
2012-07-01
Theory and experimental evidence suggest that complex living systems function close to the boundary of chaos, with erroneous organization to an improper dynamical range (too stiff or chaotic) underlying system-wide dysregulation and disease. We hypothesized that erroneous organization might therefore also characterize paranoid schizophrenia, via optimization abnormalities in the prefrontal-limbic circuit regulating emotion. To test this, we acquired fMRI scans from 35 subjects (N = 9 patients with paranoid schizophrenia and N = 26 healthy controls), while they viewed affect-valent stimuli. To quantify dynamic regulation, we analyzed the power spectrum scale invariance (PSSI) of fMRI time-courses and computed the geometry of time-delay (Poincaré) maps, a measure of variability. Patients and controls showed distinct PSSI in two clusters (k(1) : Z = 4.3215, P = 0.00002 and k(2) : Z = 3.9441, P = 0.00008), localized to the orbitofrontal/medial prefrontal cortex (Brodmann Area 10), represented by β close to white noise in patients (β ≈ 0) and in the pink noise range in controls (β ≈ -1). Interpreting the meaning of PSSI differences, the Poincaré maps indicated less variability in patients than controls (Z = -1.9437, P = 0.05 for k(1) ; Z = -2.5099, P = 0.01 for k(2) ). That the dynamics identified Brodmann Area 10 is consistent with previous schizophrenia research, which implicates this area in deficits of working memory, executive functioning, emotional regulation and underlying biological abnormalities in synaptic (glutamatergic) transmission. Our results additionally cohere with a large body of work finding pink noise to be the normal range of central function at the synaptic, cellular, and small network levels, and suggest that patients show less supple responsivity of this region. PMID:21567663
N-boson spectrum from a discrete scale invariance
NASA Astrophysics Data System (ADS)
Kievsky, A.; Timofeyuk, N. K.; Gattobigio, M.
2014-09-01
We present an analysis of the N-boson spectrum computed using a soft two-body potential, the strength of which has been varied in order to cover an extended range of positive and negative values of the two-body scattering length a close to the unitary limit. The spectrum shows a tree structure of two states, one shallow and one deep, attached to the ground state of the system with one less particle. It is governed by a unique universal function Δ (ξ), already known in the case of three bosons. In the three-particle system the angle ξ, determined by the ratio of the two- and three-body binding energies E3/E2=tan2ξ, characterizes the discrete scale invariance of the system. Extending the definition of the angle to the N-body system as EN/E2=tan2ξ, we study the N-boson spectrum in terms of this variable. The analysis of the results, obtained for up to N =16 bosons, allows us to extract a general formula for the energy levels of the system close to the unitary limit. Interestingly, a linear dependence of the universal function as a function of N is observed at fixed values of a. We show that the finite-range nature of the calculations results in the range corrections that generate a shift of the linear relation between the scattering length a and a particular form of the universal function. We also comment on the limits of applicability of the universal relations.
Scale invariant sheath folds in salt, sediments and shear zones
NASA Astrophysics Data System (ADS)
Alsop, G. I.; Holdsworth, R. E.; McCaffrey, K. J. W.
2007-10-01
Sheath folds are developed in a broad spectrum of geological environments in which material flow occurs, including gravity-driven surficial deformation in ignimbrites, unconsolidated sediments and salt, together with deeper level ductile shear zones in metamorphic rocks. This study represents the first geometric comparison of sheath folds in these different settings across a wide range of scales. Elliptical closures defining eye-folds represent ( y- z) cross sections through highly-curvilinear sheath folds. Our analysis of the published literature, coupled with field observations, reveals remarkably similar ellipticities ( R yz) for sheath folds in metamorphic shear zones ( R yz 4.23), salt ( R yz 4.29), sediment slumps ( R yz 4.34), glaciotectonites ( R yz 4.48), and ignimbrites ( R yz 4.34). Nested eye-folds across this range of materials ( N = 1800) reveal distinct and consistent differences in ellipticity from the outer- ( R yz) to the inner-most ( R y' z' ) elliptical "rings" of individual sheath folds. The variation in ratios from outer to inner rings ( R' = R yz/ R y' z' ) in gravity-driven surficial flows typically displays a relative increase in ellipticity to define cats-eye-folds ( R' < 1) similar to those observed during simple and general shear in metamorphic rocks. We show that sheath folds develop across a range of scales within these different environments, and display elliptical ratios ( R yz) that are remarkably constant ( R2 > 0.99) across 9 orders of magnitude (sheath y axes range from ˜0.1 mm to >75 km). Our findings lead us to conclude that the geometric properties of sheath folds are scale invariant and primarily controlled by the type and amount of strain, with R' also reflecting the rheological significance of layering associated with original buckle fold mechanisms. The scaling pattern of sheath folds reflects the length scales of the precursor buckle folds (and width of deformation zones) across a broad range of materials and
Saremi, Saeed; Sejnowski, Terrence J
2016-05-01
Natural images are scale invariant with structures at all length scales.We formulated a geometric view of scale invariance in natural images using percolation theory, which describes the behavior of connected clusters on graphs.We map images to the percolation model by defining clusters on a binary representation for images. We show that critical percolating structures emerge in natural images and study their scaling properties by identifying fractal dimensions and exponents for the scale-invariant distributions of clusters. This formulation leads to a method for identifying clusters in images from underlying structures as a starting point for image segmentation. PMID:26415153
Saremi, Saeed; Sejnowski, Terrence J.
2016-01-01
Natural images are scale invariant with structures at all length scales. We formulated a geometric view of scale invariance in natural images using percolation theory, which describes the behavior of connected clusters on graphs. We map images to the percolation model by defining clusters on a binary representation for images. We show that critical percolating structures emerge in natural images and study their scaling properties by identifying fractal dimensions and exponents for the scale-invariant distributions of clusters. This formulation leads to a method for identifying clusters in images from underlying structures as a starting point for image segmentation. PMID:26415153
The neural correlates of processing scale-invariant environmental sounds at birth.
Gervain, Judit; Werker, Janet F; Black, Alexis; Geffen, Maria N
2016-06-01
Sensory systems are thought to have evolved to efficiently represent the full range of sensory stimuli encountered in the natural world. The statistics of natural environmental sounds are characterized by scale-invariance: the property of exhibiting similar patterns at different levels of observation. The statistical structure of scale-invariant sounds remains constant at different spectro-temporal scales. Scale-invariance plays a fundamental role in how efficiently animals and human adults perceive acoustic signals. However, the developmental origins and brain correlates of the neural encoding of scale-invariant environmental sounds remain unexplored. Here, we investigate whether the human brain extracts the statistical property of scale-invariance. Synthetic sounds generated by a mathematical model to respect scale-invariance or violate it were presented to newborns. In alternating blocks, the two sound types were presented together in an alternating fashion, whereas in non-alternating blocks, only one type of sound was presented. Newborns' brain responses were measured using near-infrared spectroscopy. We found that scale-invariant and variable-scale sounds were discriminated by the newborn brain, as suggested by differential activation in the left frontal and temporal areas to alternating vs. non-alternating blocks. These results indicate that newborns already detect and encode scale-invariance as a characteristic feature of acoustic stimuli. This suggests that the mathematical principle of efficient coding of information guides the auditory neural code from the beginning of human development, a finding that may help explain how evolution has prepared the brain for perceiving the natural world. PMID:26956907
General conditions for scale-invariant perturbations in an expanding universe
Geshnizjani, Ghazal; Kinney, William H.; Dizgah, Azadeh Moradinezhad E-mail: whkinney@buffalo.edu
2011-11-01
We investigate the general properties of expanding cosmological models which generate scale-invariant curvature perturbations in the presence of a variable speed of sound. We show that in an expanding universe, generation of a super-Hubble, nearly scale-invariant spectrum of perturbations over a range of wavelengths consistent with observation requires at least one of three conditions: (1) accelerating expansion, (2) a speed of sound faster than the speed of light, or (3) super-Planckian energy density.
Inflation and reheating in theories with spontaneous scale invariance symmetry breaking
NASA Astrophysics Data System (ADS)
Rinaldi, Massimiliano; Vanzo, Luciano
2016-07-01
We study a scale-invariant model of quadratic gravity with a nonminimally coupled scalar field. We focus on cosmological solutions and find that scale invariance is spontaneously broken and a mass scale naturally emerges. Before the symmetry breaking, the Universe undergoes an inflationary expansion with nearly the same observational predictions of Starobinsky's model. At the end of inflation, the Hubble parameter and the scalar field converge to a stable fixed point through damped oscillations and the usual Einstein-Hilbert action is recovered. The oscillations around the fixed point can reheat the Universe in various ways, and we study in detail some of these possibilities.
NASA Astrophysics Data System (ADS)
Patil, Sandeep Baburao; Sinha, G. R.
2016-07-01
India, having less awareness towards the deaf and dumb peoples leads to increase the communication gap between deaf and hard hearing community. Sign language is commonly developed for deaf and hard hearing peoples to convey their message by generating the different sign pattern. The scale invariant feature transform was introduced by David Lowe to perform reliable matching between different images of the same object. This paper implements the various phases of scale invariant feature transform to extract the distinctive features from Indian sign language gestures. The experimental result shows the time constraint for each phase and the number of features extracted for 26 ISL gestures.
Dynamics of Two Dimensional Bose Gases and the Role of Scale Invariance
NASA Astrophysics Data System (ADS)
Maki, Jeff
2016-05-01
The controllable study of dynamics has become commonplace in cold atom experiments. However, the theoretical exploration of dynamics has relied heavily on numerical simulations due to the vast complexity of dynamical many body problems. The situation is simplified in two dimensional Bose gases thanks to the presence of scale invariance. This symmetry is presumed to have an important effect on the dynamics of the system but has yet to be studied in the context of cold gases. In this talk we report a study of interacting two dimensional Bose gases and the role scale invariance plays on the system's dynamics.
Nonlocal matching condition and scale-invariant spectrum in bouncing cosmology
Chu, C.-S.; Furuta, K.; Lin, F.-L.
2006-05-15
In cosmological scenarios such as the pre-big bang scenario or the ekpyrotic scenario, a matching condition between the metric perturbations in the pre-big bang phase and those in the post big bang phase is often assumed. Various matching conditions have been considered in the literature. Nevertheless obtaining a scale-invariant CMB spectrum via a concrete mechanism remains impossible. In this paper, we examine this problem from the point of view of local causality. We begin with introducing the notion of local causality and explain how it constrains the form of the matching condition. We then prove a no-go theorem: independent of the details of the matching condition, a scale-invariant spectrum is impossible as long as the local causality condition is satisfied. In our framework, it is easy to show that a violation of local causality around the bounce is needed in order to give a scale-invariant spectrum. We study a specific scenario of this possibility by considering a nonlocal effective theory inspired by noncommutative geometry around the bounce and show that a scale-invariant spectrum is possible. Moreover we demonstrate that the magnitude of the spectrum is compatible with observations if the bounce is assumed to occur at an energy scale which is a few orders of magnitude below the Planckian energy scale.
Zhang, Wenqing; Qiu, Lu; Xiao, Qin; Yang, Huijie; Zhang, Qingjun; Wang, Jianyong
2012-11-01
By means of the concept of the balanced estimation of diffusion entropy, we evaluate the reliable scale invariance embedded in different sleep stages and stride records. Segments corresponding to waking, light sleep, rapid eye movement (REM) sleep, and deep sleep stages are extracted from long-term electroencephalogram signals. For each stage the scaling exponent value is distributed over a considerably wide range, which tell us that the scaling behavior is subject and sleep cycle dependent. The average of the scaling exponent values for waking segments is almost the same as that for REM segments (∼0.8). The waking and REM stages have a significantly higher value of the average scaling exponent than that for light sleep stages (∼0.7). For the stride series, the original diffusion entropy (DE) and the balanced estimation of diffusion entropy (BEDE) give almost the same results for detrended series. The evolutions of local scaling invariance show that the physiological states change abruptly, although in the experiments great efforts have been made to keep conditions unchanged. The global behavior of a single physiological signal may lose rich information on physiological states. Methodologically, the BEDE can evaluate with considerable precision the scale invariance in very short time series (∼10^{2}), while the original DE method sometimes may underestimate scale-invariance exponents or even fail in detecting scale-invariant behavior. The BEDE method is sensitive to trends in time series. The existence of trends may lead to an unreasonably high value of the scaling exponent and consequent mistaken conclusions. PMID:23214843
Scaling and scale invariance of conservation laws in Reynolds transport theorem framework
NASA Astrophysics Data System (ADS)
Haltas, Ismail; Ulusoy, Suleyman
2015-07-01
Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.
Scaling and scale invariance of conservation laws in Reynolds transport theorem framework.
Haltas, Ismail; Ulusoy, Suleyman
2015-07-01
Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework. PMID:26232979
NASA Astrophysics Data System (ADS)
Tallapragada, Phanindra; Hasabnis, Nilesh; Katuri, Kalyan; Sudarsanam, Senbagaraman; Joshi, Ketaki; Ramasubramanian, Melur
2015-08-01
The hydrodynamic separation of spherical particles in flows at low Reynolds numbers is a very active area of research in microfluidic engineering due to the many important biomedical applications. In particular, curved channels such as spiral channels are of growing interest because the lift and drag force exerted on inertial particles can be used to hydrodynamically separate the particles. In this paper we present a scale invariant classification of the lateral focusing of particles in highly curved spiral micro channels with a square cross section. We then use this scale invariant classification to demonstrate the separation of particles in two-particle mixtures across a large range of sizes. We thus show that our results can be used to systematically design the geometry of devices and select flow parameters to separate particles by size in a mixture.
Scale-invariant scalar spectrum from the nonminimal derivative coupling with fourth-order term
NASA Astrophysics Data System (ADS)
Myung, Yun Soo; Moon, Taeyoon
2015-08-01
In this paper, an exactly scale-invariant spectrum of scalar perturbation generated during de Sitter spacetime is found from the gravity model of the nonminimal derivative coupling with fourth-order term. The nonminimal derivative coupling term generates a healthy (ghost-free) fourth-order derivative term, while the fourth-order term provides an unhealthy (ghost) fourth-order derivative term. The Harrison-Zel’dovich spectrum obtained from Fourier transforming the fourth-order propagator in de Sitter space is recovered by computing the power spectrum in its momentum space directly. It shows that this model provides a truly scale-invariant spectrum, in addition to the Lee-Wick scalar theory.
Direct detection of singlet dark matter in classically scale-invariant standard model
NASA Astrophysics Data System (ADS)
Endo, Kazuhiro; Ishiwata, Koji
2015-10-01
Classical scale invariance is one of the possible solutions to explain the origin of the electroweak scale. The simplest extension is the classically scale-invariant standard model augmented by a multiplet of gauge singlet real scalar. In the previous study it was shown that the properties of the Higgs potential deviate substantially, which can be observed in the International Linear Collider. On the other hand, since the multiplet does not acquire vacuum expectation value, the singlet components are stable and can be dark matter. In this letter we study the detectability of the real singlet scalar bosons in the experiment of the direct detection of dark matter. It is shown that a part of this model has already been excluded and the rest of the parameter space is within the reach of the future experiment.
Titius-Bode laws in the solar system. 1: Scale invariance explains everything
NASA Astrophysics Data System (ADS)
Graner, F.; Dubrulle, B.
1994-02-01
According to the Titius-Bode law, the planetary distances to the sun follow a geometric progression. We review the major interpretations and explanations of the law. We show that most derivations of Titius-Bode law are implicitely based on the assumption of both rotational and scale invariance. In absence of any radial length scale, linear instabilities cause periodic perturbations in the variable x = ln(r/r0). Since maxima equidistant in x obey a geometric progression in the variable r, Titius-Bode type of laws are natural outcome of the linear regime of systems in which both symmetries are present; we discuss possible nonlinear corrections to the law. Thus, if Titius-Bode law is real, it is probably only a consequence of the scale invariance of the disk which gave rise to the planets.
Scale-invariant cosmological perturbations from Horava-Lifshitz gravity without inflation
Mukohyama, Shinji
2009-06-15
Based on the renormalizable theory of gravitation recently proposed by Horava, we present a simple scenario to generate almost scale-invariant, super-horizon curvature perturbations. The anisotropic scaling with dynamical critical exponent z = 3 implies that the amplitude of quantum fluctuations of a free scalar field generated in the early epoch of the expanding universe is insensitive to the Hubble expansion rate and, thus, scale-invariant. Those fluctuations are later converted to curvature perturbations by the curvaton mechanism or/and the modulated decay of heavy particles/oscillating fields. This scenario works, for example, for power law expansion a{proportional_to}t {sup p} with p>1/3 and, thus, does not require inflation. Also, this scenario does not rely on any additional assumptions such as the detailed balance condition.
Void probability as a function of the void's shape and scale-invariant models
NASA Technical Reports Server (NTRS)
Elizalde, E.; Gaztanaga, E.
1991-01-01
The dependence of counts in cells on the shape of the cell for the large scale galaxy distribution is studied. A very concrete prediction can be done concerning the void distribution for scale invariant models. The prediction is tested on a sample of the CfA catalog, and good agreement is found. It is observed that the probability of a cell to be occupied is bigger for some elongated cells. A phenomenological scale invariant model for the observed distribution of the counts in cells, an extension of the negative binomial distribution, is presented in order to illustrate how this dependence can be quantitatively determined. An original, intuitive derivation of this model is presented.
Bellay, Timothy; Klaus, Andreas; Seshadri, Saurav; Plenz, Dietmar
2015-01-01
Spontaneous fluctuations in neuronal activity emerge at many spatial and temporal scales in cortex. Population measures found these fluctuations to organize as scale-invariant neuronal avalanches, suggesting cortical dynamics to be critical. Macroscopic dynamics, though, depend on physiological states and are ambiguous as to their cellular composition, spatiotemporal origin, and contributions from synaptic input or action potential (AP) output. Here, we study spontaneous firing in pyramidal neurons (PNs) from rat superficial cortical layers in vivo and in vitro using 2-photon imaging. As the animal transitions from the anesthetized to awake state, spontaneous single neuron firing increases in irregularity and assembles into scale-invariant avalanches at the group level. In vitro spike avalanches emerged naturally yet required balanced excitation and inhibition. This demonstrates that neuronal avalanches are linked to the global physiological state of wakefulness and that cortical resting activity organizes as avalanches from firing of local PN groups to global population activity. PMID:26151674
Reconstruction of a nonminimal coupling theory with scale-invariant power spectrum
Qiu, Taotao
2012-06-01
A nonminimal coupling single scalar field theory, when transformed from Jordan frame to Einstein frame, can act like a minimal coupling one. Making use of this property, we investigate how a nonminimal coupling theory with scale-invariant power spectrum could be reconstructed from its minimal coupling counterpart, which can be applied in the early universe. Thanks to the coupling to gravity, the equation of state of our universe for a scale-invariant power spectrum can be relaxed, and the relation between the parameters in the action can be obtained. This approach also provides a means to address the Big-Bang puzzles and anisotropy problem in the nonminimal coupling model within Jordan frame. Due to the equivalence between the two frames, one may be able to find models that are free of the horizon, flatness, singularity as well as anisotropy problems.
Observation of the Efimovian expansion in scale-invariant Fermi gases.
Deng, Shujin; Shi, Zhe-Yu; Diao, Pengpeng; Yu, Qianli; Zhai, Hui; Qi, Ran; Wu, Haibin
2016-07-22
Scale invariance plays an important role in unitary Fermi gases. Discrete scaling symmetry manifests itself in quantum few-body systems such as the Efimov effect. Here, we report on the theoretical prediction and experimental observation of a distinct type of expansion dynamics for scale-invariant quantum gases. When the frequency of the harmonic trap holding the gas decreases continuously as the inverse of time t, the expansion of the cloud size exhibits a sequence of plateaus. The locations of these plateaus obey a discrete geometric scaling law with a controllable scale factor, and the expansion dynamics is governed by a log-periodic function. This marked expansion shares the same scaling law and mathematical description as the Efimov effect. PMID:27463669
A new dynamics of electroweak symmetry breaking with classically scale invariance
NASA Astrophysics Data System (ADS)
Haba, Naoyuki; Ishida, Hiroyuki; Kitazawa, Noriaki; Yamaguchi, Yuya
2016-04-01
We propose a new dynamics of the electroweak symmetry breaking in a classically scale invariant version of the standard model. The scale invariance is broken by the condensations of additional fermions under a strong coupling dynamics. The electroweak symmetry breaking is triggered by negative mass squared of the elementary Higgs doublet, which is dynamically generated through the bosonic seesaw mechanism. We introduce a real pseudo-scalar singlet field interacting with additional fermions and Higgs doublet in order to avoid massless Nambu-Goldstone bosons from the chiral symmetry breaking in a strong coupling sector. We investigate the mass spectra and decay rates of these pseudo-Nambu-Goldstone bosons, and show they can decay fast enough without cosmological problems. We further show that our model can make the electroweak vacuum stable.
Observation of the Efimovian expansion in scale-invariant Fermi gases
NASA Astrophysics Data System (ADS)
Deng, Shujin; Shi, Zhe-Yu; Diao, Pengpeng; Yu, Qianli; Zhai, Hui; Qi, Ran; Wu, Haibin
2016-07-01
Scale invariance plays an important role in unitary Fermi gases. Discrete scaling symmetry manifests itself in quantum few-body systems such as the Efimov effect. Here, we report on the theoretical prediction and experimental observation of a distinct type of expansion dynamics for scale-invariant quantum gases. When the frequency of the harmonic trap holding the gas decreases continuously as the inverse of time t, the expansion of the cloud size exhibits a sequence of plateaus. The locations of these plateaus obey a discrete geometric scaling law with a controllable scale factor, and the expansion dynamics is governed by a log-periodic function. This marked expansion shares the same scaling law and mathematical description as the Efimov effect.
Exact scale-invariant background of gravitational waves from cosmic defects.
Figueroa, Daniel G; Hindmarsh, Mark; Urrestilla, Jon
2013-03-01
We demonstrate that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum. Cosmic defects, created after a phase transition in the early universe, are such a scaling source. We emphasize that the result is independent of the topology of the cosmic defects, the order of phase transition, and the nature of the symmetry broken, global or gauged. As an example, using large-scale numerical simulations, we calculate the scale-invariant gravitational wave power spectrum generated by the dynamics of a global O(N) scalar theory. The result approaches the large N theoretical prediction as N(-2), albeit with a large coefficient. The signal from global cosmic strings is O(100) times larger than the large N prediction. PMID:23521248
NASA Technical Reports Server (NTRS)
Sohrab, Siavash H.; Piltch, Nancy (Technical Monitor)
2000-01-01
A scale-invariant model of statistical mechanics is applied to present invariant forms of mass, energy, linear, and angular momentum conservation equations in reactive fields. The resulting conservation equations at molecular-dynamic scale are solved by the method of large activation energy asymptotics to describe the hydro-thermo-diffusive structure of laminar premixed flames. The predicted temperature and velocity profiles are in agreement with the observations. Also, with realistic physico-chemical properties and chemical-kinetic parameters for a single-step overall combustion of stoichiometric methane-air premixed flame, the laminar flame propagation velocity of 42.1 cm/s is calculated in agreement with the experimental value.
Scale-invariant hidden local symmetry, topology change, and dense baryonic matter
NASA Astrophysics Data System (ADS)
Paeng, Won-Gi; Kuo, Thomas T. S.; Lee, Hyun Kyu; Rho, Mannque
2016-05-01
When scale symmetry is implemented into hidden local symmetry in low-energy strong interactions to arrive at a scale-invariant hidden local symmetric (HLS) theory, the scalar f0(500 ) may be interpreted as pseudo-Nambu-Goldstone (pNG) boson, i.e., dilaton, of spontaneously broken scale invariance, joining the pseudoscalar pNG bosons π and the matter fields V =(ρ ,ω ) as relevant degrees of freedom. Implementing the skyrmion-half-skyrmion transition predicted at large Nc in QCD at a density roughly twice the nuclear matter density found in the crystal simulation of dense skyrmion matter, we determine the intrinsically density-dependent "bare parameters" of the scale-invariant HLS Lagrangian matched to QCD at a matching scale ΛM. The resulting effective Lagrangian, with the parameters scaling with the density of the system, is applied to nuclear matter and dense baryonic matter relevant to massive compact stars by means of the double-decimation renormalization-group Vlow k formalism. We satisfactorily postdict the properties of normal nuclear matter and more significantly predict the equation of state of dense compact-star matter that quantitatively accounts for the presently available data coming from both the terrestrial and space laboratories. We interpret the resulting structure of compact-star matter as revealing how the combination of hidden-scale symmetry and hidden local symmetry manifests itself in compressed baryonic matter.
On scale invariant features and sequential Monte Carlo sampling for bronchoscope tracking
NASA Astrophysics Data System (ADS)
Luó, Xióngbiao; Feuerstein, Marco; Kitasaka, Takayuki; Natori, Hiroshi; Takabatake, Hirotsugu; Hasegawa, Yoshinori; Mori, Kensaku
2011-03-01
This paper presents an improved bronchoscope tracking method for bronchoscopic navigation using scale invariant features and sequential Monte Carlo sampling. Although image-based methods are widely discussed in the community of bronchoscope tracking, they are still limited to characteristic information such as bronchial bifurcations or folds and cannot automatically resume the tracking procedure after failures, which result usually from problematic bronchoscopic video frames or airway deformation. To overcome these problems, we propose a new approach that integrates scale invariant feature-based camera motion estimation into sequential Monte Carlo sampling to achieve an accurate and robust tracking. In our approach, sequential Monte Carlo sampling is employed to recursively estimate the posterior probability densities of the bronchoscope camera motion parameters according to the observation model based on scale invariant feature-based camera motion recovery. We evaluate our proposed method on patient datasets. Experimental results illustrate that our proposed method can track a bronchoscope more accurate and robust than current state-of-the-art method, particularly increasing the tracking performance by 38.7% without using an additional position sensor.
Apparent Low-Energy Scale Invariance in Two-Dimensional Fermi Gases
NASA Astrophysics Data System (ADS)
Taylor, Edward
2013-05-01
Strongly-interacting systems in two dimensions have occupied a central position in the study of quantum materials. From high temperature superconductors to the Hall effect in two-dimensional electron gases, strong quantum and thermal fluctuations conspire to make this an extremely rich yet poorly-understood regime to work in. Several remarkable and surprising recent experiments in ultracold atomic gases show us that there are puzzles to be understood even in the simplest nontrivial two-dimensional system: a dilute quantum gas with strong s-wave interactions. Amongst these is an experiment that finds an undamped breathing mode oscillating at twice the trap frequency over a wide range of parameters, behaviour nominally associated with scale invariance, even though scale invariance is strictly broken in this system by a finite s-wave scattering length. This apparent scale symmetry is all the more remarkable given that the mean-field BCS theory for the 2D gas predicts an exact low-energy scale invariance, relevant to the low-energy breathing mode, meaning that only quantum and thermal fluctuations can break this low-energy scale symmetry. Understanding why the symmetry breaking is so weak may give insight into how to make reliable theoretical predictions in systems with strong fluctuation effects, where there is no obvious small parameter from which a perturbation expansion can be formulated. Supported by NSF Grant No. DMR-1006532 (Mohit Randeria), NSERC, and the Canadian Institute for Advanced Research.
Generating scale-invariant perturbations from rapidly-evolving equation of state
NASA Astrophysics Data System (ADS)
Khoury, Justin; Steinhardt, Paul J.
2011-06-01
Recently, we introduced an ekpyrotic model based on a single, canonical scalar field that generates nearly scale-invariant curvature fluctuations through a purely “adiabatic mechanism” in which the background evolution is a dynamical attractor. Despite the starkly different physical mechanism for generating fluctuations, the two-point function is identical to inflation. In this paper, we further explore this concept, focusing in particular on issues of non-Gaussianity and quantum corrections. We find that the degeneracy with inflation is broken at three-point level: for the simplest case of an exponential potential, the three-point amplitude is strongly scale dependent, resulting in a breakdown of perturbation theory on small scales. However, we show that the perturbative breakdown can be circumvented—and all issues raised in Linde et al. (arXiv:0912.0944) can be addressed—by altering the potential such that power is suppressed on small scales. The resulting range of nearly scale-invariant, Gaussian modes can be as much as 12 e-folds, enough to span the scales probed by microwave background and large-scale structure observations. On smaller scales, the spectrum is not scale invariant but is observationally acceptable.
ERIC Educational Resources Information Center
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
NASA Astrophysics Data System (ADS)
Schlager, Wolfgang
2015-04-01
In contrast to the realms of magmatism and metamorphism, most depositional processes can be observed directly at the earth's surface. Observation of sediment patterns advanced significantly with the advent of remote sensing and 3D reflection seismics. Remote sensing is particularly relevant for the present topic because it documents mainly Holocene sediments - the best objects to link depositional processes to products. Classic examples of scale-invariant geometry are channel-fan systems, i.e. river-delta and canyon-fan complexes. The underlying control in both instances is the energy-dispersion of a channeled stream of water that discharges in a body of still water. The resulting fan-shaped sediment accumulations are scale-invariant over 7 orders of magnitude in linear size. The Mesozoic-Cenozoic record shows comparable trends and patterns. Further examples of depositional scale-invariance include foresets of non-cohesive sediments and braided-channel deposits. Reefs and carbonate platforms offer an example of scale-invariance related to biotic growth. Shallow-water carbonate platforms rimmed by reefs or reef-rimmed atolls with deep lagoons are characteristic morphologies of tropical carbonate deposits. The structure has been compared to a bucket where stiff reef rims hold a pile of loose sediment. Remote sensing data from the Maldive, Chagos and Laccadive archipelagos of the Indian Ocean show that bucket structures are the dominant depositional pattern from meter-size reefs to archipelagos of hundreds of kilometers in diameter, i.e. over more than 4 orders of magnitude in linear size. Over 2.5 orders of magnitude, the bucket structures qualify as statistical fractals. Ecologic and hydrodynamic studies on modern reefs suggest that the bucket structure is a form of biotic self-organization: The edge position in a reef is favored over the center position because bottom shear is higher and the diffusive boundary layer between reef and water thinner. Thus, the reef
Scale-Invariant Sparse PCA on High Dimensional Meta-elliptical Data
Han, Fang; Liu, Han
2014-01-01
We propose a semiparametric method for conducting scale-invariant sparse principal component analysis (PCA) on high dimensional non-Gaussian data. Compared with sparse PCA, our method has weaker modeling assumption and is more robust to possible data contamination. Theoretically, the proposed method achieves a parametric rate of convergence in estimating the parameter of interests under a flexible semiparametric distribution family; Computationally, the proposed method exploits a rank-based procedure and is as efficient as sparse PCA; Empirically, our method outperforms most competing methods on both synthetic and real-world datasets. PMID:24932056
Scale-invariance underlying the logistic equation and its social applications
NASA Astrophysics Data System (ADS)
Hernando, A.; Plastino, A.
2013-01-01
On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie a large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way.
Learning How to Extract Rotation-Invariant and Scale-Invariant Features from Texture Images
NASA Astrophysics Data System (ADS)
Montoya-Zegarra, Javier A.; Papa, João Paulo; Leite, Neucimar J.; da Silva Torres, Ricardo; Falcão, Alexandre
2008-12-01
Learning how to extract texture features from noncontrolled environments characterized by distorted images is a still-open task. By using a new rotation-invariant and scale-invariant image descriptor based on steerable pyramid decomposition, and a novel multiclass recognition method based on optimum-path forest, a new texture recognition system is proposed. By combining the discriminating power of our image descriptor and classifier, our system uses small-size feature vectors to characterize texture images without compromising overall classification rates. State-of-the-art recognition results are further presented on the Brodatz data set. High classification rates demonstrate the superiority of the proposed system.
Scale-invariant behavior in a spatial game of prisoners' dilemma
NASA Astrophysics Data System (ADS)
Lim, Y. F.; Chen, Kan; Jayaprakash, C.
2002-02-01
A spatially extended version of the game of prisoner's dilemma, originally proposed by Nowak and May, is modified to include stochastic updating and found to exhibit scale-invariant behavior. Two critical regimes with different scaling behaviors are found; the corresponding exponents have been determined numerically. Spatially, the critical states are characterized by the existence of delicately balanced networks of defectors separating domains of cooperators; temporally, the evolution of the critical states following local perturbations is characterized by avalanches of various magnitudes, which cause restructuring of the networks of defectors on all scales.
Nearly scale invariant spectrum of gravitational radiation from global phase transitions.
Jones-Smith, Katherine; Krauss, Lawrence M; Mathur, Harsh
2008-04-01
Using a large N sigma model approximation we explicitly calculate the power spectrum of gravitational waves arising from a global phase transition in the early Universe and we confirm that it is scale invariant, implying an observation of such a spectrum may not be a unique feature of inflation. Moreover, the predicted amplitude can be over 3 orders of magnitude larger than the naive dimensional estimate, implying that even a transition that occurs after inflation may dominate in cosmic microwave background polarization or other gravity wave signals. PMID:18517931
NASA Astrophysics Data System (ADS)
Wang, Sai; Chang, Zhe
2015-06-01
We propose the gravity's rainbow scenario as a possible alternative of the inflation paradigm to account for the flatness and horizon problems. We focus on studying the cosmological scalar perturbations which are seeded by the quantum fluctuations in the very early universe. The scalar power spectrum is expected to be nearly scale-invariant. We estimate the rainbow index and energy scale M in the gravity's rainbow scenario by analyzing the Planck temperature and WMAP polarization datasets. The constraints on them are given by and at the confidence level.
An Anisotropic Scale-Invariant Unstructured Mesh Generator Auitable for Volumetric Imaging Data
Kuprat, Andrew P.; Einstein, Daniel R.
2009-02-20
Mesh generation algorithms must consider the computational physics schemes to be adopted insomuch as tessellation should attempt to minimize discretization error metrics a priori, while placing elements judiciously yet economically. Basing local element size and shape on local geometric feature size is a promising approach, as the underlying physics may either be scale-invariant or may vary with scale in a predictable way. We present a boundary-fitted scale-invariant unstructured tetrahedral mesh generation algorithm that enables registration of element size to local geometric scale, given a triangulated mesh surface. The resulting tetrahedra are well-shaped and nearly orthogonal to the boundary. Unlike previous feature-based approaches, our algorithm does not require a background mesh, nor does it rely on the medial-axis. In contrast, as a first step, our algorithm produces a gradientlimited feature-size field over the input surface based on efficient ray casting. We illustrate how this field can be used to produce quality grids for computational fluid dynamics based simulations of challenging, topologically complex surfaces derived from magnetic resonance images. The algorithm is implemented in the Pacific Northwest National Laboratory (PNNL) version of the Los Alamos grid toolbox LaGriT[6].
An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data.
Kuprat, Andrew P; Einstein, Daniel R
2009-02-20
We present a boundary-fitted, scale-invariant unstructured tetrahedral mesh generation algorithm that enables registration of element size to local feature size. Given an input triangulated surface mesh, a feature size field is determined by casting rays normal to the surface and into the geometry and then performing gradient-limiting operations to enforce continuity of the resulting field. Surface mesh density is adjusted to be proportional to the feature size field and then a layered anisotropic volume mesh is generated. This mesh is "scale-invariant" in that roughly the same number of layers of mesh exist in mesh cross-sections, between a minimum scale size L(min) and a maximum scale size L(max). We illustrate how this field can be used to produce quality grids for computational fluid dynamics based simulations of challenging, topologically complex biological surfaces derived from magnetic resonance images. The algorithm is implemented in the Pacific Northwest National Laboratory (PNNL) version of the Los Alamos grid toolbox LaGriT[14]. Research funded by the National Heart and Blood Institute Award 1RO1HL073598-01A1. PMID:19784397
Generating scale-invariant tensor perturbations in the non-inflationary universe
NASA Astrophysics Data System (ADS)
Li, Mingzhe
2014-09-01
It is believed that the recent detection of large tensor perturbations strongly favors the inflation scenario in the early universe. This common sense depends on the assumption that Einstein's general relativity is valid at the early universe. In this paper we show that nearly scale-invariant primordial tensor perturbations can be generated during a contracting phase before the radiation dominated epoch if the theory of gravity is modified by the scalar-tensor theory at that time. The scale-invariance protects the tensor perturbations from suppressing at large scales and they may have significant amplitudes to fit BICEP2's result. We construct a model to achieve this purpose and show that the universe can bounce to the hot big bang after long time contraction, and at almost the same time the theory of gravity approaches to general relativity through stabilizing the scalar field. Theoretically, such models are dual to inflation models if we change to the frame in which the theory of gravity is general relativity. Dual models are related by the conformal transformations. With this study we reinforce the point that only the conformal invariant quantities such as the scalar and tensor perturbations are physical. How did the background evolve before the radiation time depends on the frame and has no physical meaning. It is impossible to distinguish different pictures by later time cosmological probes.
The pseudo-conformal universe: scale invariance from spontaneous breaking of conformal symmetry
Hinterbichler, Kurt; Khoury, Justin E-mail: jkhoury@sas.upenn.edu
2012-04-01
We present a novel theory of the very early universe which addresses the traditional horizon and flatness problems of big bang cosmology and predicts a scale invariant spectrum of perturbations. Unlike inflation, this scenario requires no exponential accelerated expansion of space-time. Instead, the early universe is described by a conformal field theory minimally coupled to gravity. The conformal fields develop a time-dependent expectation value which breaks the flat space so(4,2) conformal symmetry down to so(4,1), the symmetries of de Sitter, giving perturbations a scale invariant spectrum. The solution is an attractor, at least in the case of a single time-dependent field. Meanwhile, the metric background remains approximately flat but slowly contracts, which makes the universe increasingly flat, homogeneous and isotropic, akin to the smoothing mechanism of ekpyrotic cosmology. Our scenario is very general, requiring only a conformal field theory capable of developing the appropriate time-dependent expectation values, and encompasses existing incarnations of this idea, specifically the U(1) model of Rubakov and the Galileon Genesis scenario. Its essential features depend only on the symmetry breaking pattern and not on the details of the underlying lagrangian. It makes generic observational predictions that make it potentially distinguishable from standard inflation, in particular significant non-gaussianities and the absence of primordial gravitational waves.
Derivative-based scale invariant image feature detector with error resilience.
Mainali, Pradip; Lafruit, Gauthier; Tack, Klaas; Van Gool, Luc; Lauwereins, Rudy
2014-05-01
We present a novel scale-invariant image feature detection algorithm (D-SIFER) using a newly proposed scale-space optimal 10th-order Gaussian derivative (GDO-10) filter, which reaches the jointly optimal Heisenberg's uncertainty of its impulse response in scale and space simultaneously (i.e., we minimize the maximum of the two moments). The D-SIFER algorithm using this filter leads to an outstanding quality of image feature detection, with a factor of three quality improvement over state-of-the-art scale-invariant feature transform (SIFT) and speeded up robust features (SURF) methods that use the second-order Gaussian derivative filters. To reach low computational complexity, we also present a technique approximating the GDO-10 filters with a fixed-length implementation, which is independent of the scale. The final approximation error remains far below the noise margin, providing constant time, low cost, but nevertheless high-quality feature detection and registration capabilities. D-SIFER is validated on a real-life hyperspectral image registration application, precisely aligning up to hundreds of successive narrowband color images, despite their strong artifacts (blurring, low-light noise) typically occurring in such delicate optical system setups. PMID:24723627
A regional GEV scale-invariant framework for Intensity-Duration-Frequency analysis
NASA Astrophysics Data System (ADS)
Blanchet, J.; Ceresetti, D.; Molinié, G.; Creutin, J.-D.
2016-09-01
We propose in this paper a regional formulation of Intensity-Duration-Frequency curves of point-rainfall maxima in a scale-invariant Generalized Extreme Value (GEV) framework. The two assumptions we make is that extreme daily rainfall is GEV-distributed - which is justified by Extreme Value Theory (EVT) - and that extremes of aggregated daily rainfall follow simple-scaling relationships. Following these assumptions, we develop in a unified way a GEV simple-scaling model for extremes of aggregated daily rainfall over the range of durations where scaling applies. Then we propose a way of correcting this model for measurement frequency, giving a new GEV-scaling model for extremes of aggregated hourly rainfall. This model deviates from the simple-scaling assumption. This framework is applied to the Mediterranean region of Cévennes-Vivarais, France. A network of about 300 daily raingage stations covering the last 50 years and accumulated to span the range 1 day-1 week is used to fit the scale invariant GEV-model locally. By means of spatial interpolation of the model parameters, and correction for measurement frequency, we are able to build a regional model with good performances down to 1 h duration, even though only one hourly station is used to build the model. Finally we produce mean and return level maps within the region in the range 1 h-1 week and comment on the potential rain storms leading to these maps.
Dimensionless, Scale Invariant, Edge Weight Metric for the Study of Complex Structural Networks
Colon-Perez, Luis M.; Spindler, Caitlin; Goicochea, Shelby; Triplett, William; Parekh, Mansi; Montie, Eric; Carney, Paul R.; Price, Catherine; Mareci, Thomas H.
2015-01-01
High spatial and angular resolution diffusion weighted imaging (DWI) with network analysis provides a unique framework for the study of brain structure in vivo. DWI-derived brain connectivity patterns are best characterized with graph theory using an edge weight to quantify the strength of white matter connections between gray matter nodes. Here a dimensionless, scale-invariant edge weight is introduced to measure node connectivity. This edge weight metric provides reasonable and consistent values over any size scale (e.g. rodents to humans) used to quantify the strength of connection. Firstly, simulations were used to assess the effects of tractography seed point density and random errors in the estimated fiber orientations; with sufficient signal-to-noise ratio (SNR), edge weight estimates improve as the seed density increases. Secondly to evaluate the application of the edge weight in the human brain, ten repeated measures of DWI in the same healthy human subject were analyzed. Mean edge weight values within the cingulum and corpus callosum were consistent and showed low variability. Thirdly, using excised rat brains to study the effects of spatial resolution, the weight of edges connecting major structures in the temporal lobe were used to characterize connectivity in this local network. The results indicate that with adequate resolution and SNR, connections between network nodes are characterized well by this edge weight metric. Therefore this new dimensionless, scale-invariant edge weight metric provides a robust measure of network connectivity that can be applied in any size regime. PMID:26173147
NASA Astrophysics Data System (ADS)
Ijjas, Anna; Lehners, Jean-Luc; Steinhardt, Paul J.
2014-06-01
We explore a new type of entropic mechanism for generating density perturbations in a contracting phase in which there are two scalar fields but only one has a steep negative potential. This first field dominates the energy density and is the source of the ekpyrotic equation of state. The second field has a negligible potential, but its kinetic energy density is coupled to the first field with a nonlinear sigma-model type interaction. We show that for any ekpyrotic equation of state it is possible to choose the potential and the kinetic coupling such that exactly scale-invariant (or nearly scale-invariant) entropy perturbations are produced. The corresponding background solutions are stable, and the bispectrum of the entropy perturbations vanishes as no non-Gaussianity is produced during the ekpyrotic phase. Hence, the only contribution to non-Gaussianity comes from the nonlinearity of the conversion process during which entropic perturbations are turned into adiabatic ones, resulting in a local non-Gaussianity parameter, fNL˜5.
A scale-invariant cellular-automata model for distributed seismicity
NASA Technical Reports Server (NTRS)
Barriere, Benoit; Turcotte, Donald L.
1991-01-01
In the standard cellular-automata model for a fault an element of stress is randomly added to a grid of boxes until a box has four elements, these are then redistributed to the adjacent boxes on the grid. The redistribution can result in one or more of these boxes having four or more elements in which case further redistributions are required. On the average added elements are lost from the edges of the grid. The model is modified so that the boxes have a scale-invariant distribution of sizes. The objective is to model a scale-invariant distribution of fault sizes. When a redistribution from a box occurs it is equivalent to a characteristic earthquake on the fault. A redistribution from a small box (a foreshock) can trigger an instability in a large box (the main shock). A redistribution from a large box always triggers many instabilities in the smaller boxes (aftershocks). The frequency-size statistics for both main shocks and aftershocks satisfy the Gutenberg-Richter relation with b = 0.835 for main shocks and b = 0.635 for aftershocks. Model foreshocks occur 28 percent of the time.
Scale-invariant Perturbations: Model-independent Analysis of Alternatives to Cosmic inflation
NASA Astrophysics Data System (ADS)
Moradinezhad Dizgah, Azadeh
The focus of this thesis is to study generation of scale-invariant perturbation in non-inflationary backgrounds. Throughout we assume that the universe is dominated by a single scalar degree of freedom at early times when the perturbations are generated. The first three chapters consist of review materials needed for the follow up discussion in the last three chapters which present our findings. We probe the parameter space of scalar field models first by using the dualities that preserve the form of the horizons relevant for generation of perturbations. For canonical scalar field models, we use a known duality between expanding and contracting cosmologies to construct a dual of the inflationary flow hierarchy applicable to contracting cosmologies such as ekpyrotic and cyclic models. We show that the inflationary flow equations are invariant under the duality and therefore apply equally well to inflation or to cyclic cosmology. We then generalize the cosmological duality between inflation and cyclic contraction to the case of non-canonical scalar field theories with varying speed of sound. The single duality in the canonical case generalizes to a family of three dualities constructed to leave the cosmological acoustic horizon invariant. We find three classes of models: (I) DBI inflation, (II) the non-canonical generalization of cyclic contraction, and (III) a new cosmological solution with rapidly decreasing speed of sound and relatively slowly growing scale factor, which we dub stalled cosmology. We construct dual analogs to the inflationary slow roll approximation, and solve for the curvature perturbation in all three cases. Both cyclic contraction and stalled cosmology predict a strongly blue spectrum for the curvature perturbations inconsistent with observations. Taking a more phenomenological approach, in the last chapter, we investigate the general properties of expanding cosmological models which generate scale-invariant curvature perturbations in the
Scale invariance of continuum size distribution upon irreversible growth of surface islands
NASA Astrophysics Data System (ADS)
Dubrovskii, V. G.; Sokolova, Zh. V.
2015-06-01
The continuum kinetic equation for irreversible heterogeneous growth of a surface island is ana-lyzed given a special form of the dependence of capture coefficient σ on size s and coverage of the surface Θ. It is shown that, if σ( s, Θ) = α(Θ)( a + s)β, the function α(Θ) is arbitrary, and 0 ≤ β ≤ 1, then the solutions of the continuum equation of the first order satisfy the hypothesis about the scale invariance of the size distribu-tion (scaling) in a single exceptional case—at ≤ = 1. The obtained results testify about the presence of a fun-damental relation of the scaling and linearity of the dependence σ( s). Problems about associations of distri-bution functions in continuum and discrete growth models and about application of the obtained solutions for modeling and interpretation of experimental data in different systems are discussed.
Discretization of Continuous Time Discrete Scale Invariant Processes: Estimation and Spectra
NASA Astrophysics Data System (ADS)
Rezakhah, Saeid; Maleki, Yasaman
2016-07-01
Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a second continuous time DSI process which provides a proper approximation of the first one. This enables us to provide a bilateral relation between covariance functions of the subsidiary process and the new continuous time processes. The time varying spectral representation of such continuous time DSI process is characterized, and its spectrum is estimated. Also, a new method for estimation time dependent Hurst parameter of such processes is provided which gives a more accurate estimation. The performance of this estimation method is studied via simulation. Finally this method is applied to the real data of S & P500 and Dow Jones indices for some special periods.
Hidden scale invariance in molecular van der Waals liquids: A simulation study
NASA Astrophysics Data System (ADS)
Schrøder, Thomas B.; Pedersen, Ulf R.; Bailey, Nicholas P.; Toxvaerd, Søren; Dyre, Jeppe C.
2009-10-01
Results from molecular dynamics simulations of two viscous molecular model liquids—the Lewis-Wahnström model of orthoterphenyl and an asymmetric dumbbell model—are reported. We demonstrate that the liquids have a “hidden” approximate scale invariance: equilibrium potential energy fluctuations are accurately described by inverse power-law (IPL) potentials, the radial distribution functions are accurately reproduced by the IPL’s, and the radial distribution functions obey the IPL predicted scaling properties to a good approximation. IPL scaling of the dynamics also applies—with the scaling exponent predicted by the equilibrium fluctuations. In contrast, the equation of state does not obey the IPL scaling. We argue that our results are general for van der Waals liquids, but do not apply, e.g., for hydrogen-bonded liquids.
Shadow Higgs boson from a scale-invariant hidden U(1){sub s} model
Chang, W.-F.; Ng, John N.; Wu, Jackson M. S.
2007-06-01
We study a scale-invariant SU(2)xU(1){sub Y}xU(1){sub s} model which has only dimensionless couplings. The shadow U(1){sub s} is hidden, and it interacts with the standard model (SM) solely through mixing in the scalar sector and kinetic mixing of the U(1) gauge bosons. The gauge symmetries are broken radiatively by the Coleman-Weinberg mechanism. Lifting of the flat direction in the scalar potential gives rise to a light scalar, the scalon, or the shadow Higgs, and a heavier scalar which we identify as the SM Higgs boson. The phenomenology of this model is discussed. In particular, the constraints on the shadow Higgs in different mass ranges, and the possibility of discovering a shadow Higgs with a mass a few tens of GeV in precision t-quark studies at the LHC, are investigated.
Adiabatic perturbations in pre-big bang models: Matching conditions and scale invariance
NASA Astrophysics Data System (ADS)
Durrer, Ruth; Vernizzi, Filippo
2002-10-01
At low energy, the four-dimensional effective action of the ekpyrotic model of the universe is equivalent to a slightly modified version of the pre-big bang model. We discuss cosmological perturbations in these models. In particular we address the issue of matching the perturbations from a collapsing to an expanding phase. We show that, under certain physically motivated and quite generic assumptions on the high energy corrections, one obtains n=0 for the spectrum of scalar perturbations in the original pre-big bang model (with a vanishing potential). With the same assumptions, when an exponential potential for the dilaton is included, a scale invariant spectrum (n=1) of adiabatic scalar perturbations is produced under very generic matching conditions, both in a modified pre-big bang and ekpyrotic scenario. We also derive the resulting spectrum for arbitrary power law scale factors matched to a radiation-dominated era.
Real-time object tracking based on scale-invariant features employing bio-inspired hardware.
Yasukawa, Shinsuke; Okuno, Hirotsugu; Ishii, Kazuo; Yagi, Tetsuya
2016-09-01
We developed a vision sensor system that performs a scale-invariant feature transform (SIFT) in real time. To apply the SIFT algorithm efficiently, we focus on a two-fold process performed by the visual system: whole-image parallel filtering and frequency-band parallel processing. The vision sensor system comprises an active pixel sensor, a metal-oxide semiconductor (MOS)-based resistive network, a field-programmable gate array (FPGA), and a digital computer. We employed the MOS-based resistive network for instantaneous spatial filtering and a configurable filter size. The FPGA is used to pipeline process the frequency-band signals. The proposed system was evaluated by tracking the feature points detected on an object in a video. PMID:27268260
Towards anisotropy-free and nonsingular bounce cosmology with scale-invariant perturbations
NASA Astrophysics Data System (ADS)
Qiu, Taotao; Gao, Xian; Saridakis, Emmanuel N.
2013-08-01
We investigate nonsingular bounce realizations in the framework of ghost-free generalized Galileon cosmology, which furthermore can be free of the anisotropy problem. Considering an ekpyroticlike potential we can obtain a total equation of state larger than 1 in the contracting phase, which is necessary for the evolution to be stable against small anisotropic fluctuations. Since such a large equation of state forbids the Galileon field to generate the desired form of perturbations, we additionally introduce the curvaton field which can in general produce the observed nearly scale-invariant spectrum. In particular, we provide approximate analytical and exact semianalytical expressions under which the bouncing scenario is consistent with observations. Finally, the combined Galileon-curvaton system is free of the big rip after the bounce.
Automated Image Retrieval of Chest CT Images Based on Local Grey Scale Invariant Features.
Arrais Porto, Marcelo; Cordeiro d'Ornellas, Marcos
2015-01-01
Textual-based tools are regularly employed to retrieve medical images for reading and interpretation using current retrieval Picture Archiving and Communication Systems (PACS) but pose some drawbacks. All-purpose content-based image retrieval (CBIR) systems are limited when dealing with medical images and do not fit well into PACS workflow and clinical practice. This paper presents an automated image retrieval approach for chest CT images based local grey scale invariant features from a local database. Performance was measured in terms of precision and recall, average retrieval precision (ARP), and average retrieval rate (ARR). Preliminary results have shown the effectiveness of the proposed approach. The prototype is also a useful tool for radiology research and education, providing valuable information to the medical and broader healthcare community. PMID:26262345
A position, rotation, and scale invariant image descriptor based on rays and circular paths
NASA Astrophysics Data System (ADS)
Solorza-Calderón, Selene
2015-09-01
In this paper a rotation, scale and translation (RST) invariant image descriptor based on 1D signatures is presented. The position invariant is obtained using the amplitude spectrum of the Fourier transform of the image. That spectrum is introduced in the analytical Fourier-Mellin transform (AFMT) to obtain the scale invariance. From the normalized AFMT amplitude spectrum two 1D signatures are constructed. To build a 1D circular signature, circular path binary masks are used to filter the spectrum image. On the other hand, ray path binary filters are utilized in the construction of the 1D ray signature. These 1D signatures are RST invariant image descriptors. The Latin alphabet letters in Arial font style were used to test the descriptor efficiency. According with the statistical analysis of bootstrap with a constant replacement B = 1000 and normal distribution, the descriptor has a confidence level at least of 95%.
Scale invariant extension of the standard model with a strongly interacting hidden sector.
Hur, Taeil; Ko, P
2011-04-01
We present a scale invariant extension of the standard model with a new QCD-like strong interaction in the hidden sector. A scale Λ(H) is dynamically generated in the hidden sector by dimensional transmutation, and chiral symmetry breaking occurs in the hidden sector. This scale is transmitted to the SM sector by a real singlet scalar messenger S and can trigger electroweak symmetry breaking. Thus all the mass scales in this model arise from the hidden sector scale Λ(H), which has quantum mechanical origin. Furthermore, the lightest hadrons in the hidden sector are stable by the flavor conservation of the hidden sector strong interaction, and could be the cold dark matter (CDM). We study collider phenomenology, relic density, and direct detection rates of the CDM of this model. PMID:21561182
Meng, Xianjing; Yin, Yilong; Yang, Gongping; Xi, Xiaoming
2013-01-01
Retinal identification based on retinal vasculatures in the retina provides the most secure and accurate means of authentication among biometrics and has primarily been used in combination with access control systems at high security facilities. Recently, there has been much interest in retina identification. As digital retina images always suffer from deformations, the Scale Invariant Feature Transform (SIFT), which is known for its distinctiveness and invariance for scale and rotation, has been introduced to retinal based identification. However, some shortcomings like the difficulty of feature extraction and mismatching exist in SIFT-based identification. To solve these problems, a novel preprocessing method based on the Improved Circular Gabor Transform (ICGF) is proposed. After further processing by the iterated spatial anisotropic smooth method, the number of uninformative SIFT keypoints is decreased dramatically. Tested on the VARIA and eight simulated retina databases combining rotation and scaling, the developed method presents promising results and shows robustness to rotations and scale changes. PMID:23873409
Scale-invariant cellular automata and self-similar Petri nets
NASA Astrophysics Data System (ADS)
Schaller, M.; Svozil, K.
2009-05-01
Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, “solve” the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior, whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.
Meng, Xianjing; Yin, Yilong; Yang, Gongping; Xi, Xiaoming
2013-01-01
Retinal identification based on retinal vasculatures in the retina provides the most secure and accurate means of authentication among biometrics and has primarily been used in combination with access control systems at high security facilities. Recently, there has been much interest in retina identification. As digital retina images always suffer from deformations, the Scale Invariant Feature Transform (SIFT), which is known for its distinctiveness and invariance for scale and rotation, has been introduced to retinal based identification. However, some shortcomings like the difficulty of feature extraction and mismatching exist in SIFT-based identification. To solve these problems, a novel preprocessing method based on the Improved Circular Gabor Transform (ICGF) is proposed. After further processing by the iterated spatial anisotropic smooth method, the number of uninformative SIFT keypoints is decreased dramatically. Tested on the VARIA and eight simulated retina databases combining rotation and scaling, the developed method presents promising results and shows robustness to rotations and scale changes. PMID:23873409
NASA Astrophysics Data System (ADS)
Schertzer, D. J.; Tchiguirinskaia, I.; Lovejoy, S.; Tuck, A.
2010-12-01
We discuss the claim of Lindborg et al (2009) that the spectrum power law E(k)≈k-3 on scales ≥600 km obtained with the help of commercial jetliner trajectory deviations (GASP and Mozaic databases) could not be brought into question by Lovejoy et al (2009), because this spectrum corresponds to a “well known theory of quasi-geostrophic turbulence developed by Charney (1971)”. Lindborg, et al (2009) also argued that “earlier limitations [of this theory] would have been relaxed in many of the modern models of atmospheric turbulence”. We show that both these statements are irrelevant and that generalized scale invariance (GSI, Schertzer and Lovejoy 1985) is rather indispensable to go beyond the quasi-geostrophic limitations, to go in fact from scale analysis to scaling analysis. This enables us to derive dynamical equations for the vorticity in an embedding space of (fractional) dimension D=2+Hz (0≤ Hz ≤1, 1- Hz measures the scaling stratification of atmospheric turbulence). These equations correspond to an interesting dynamical alternative to quasi-geostrophic approximation and turbulence. References: Charney, J. G. (1971). "Geostrophic Turbulence." J. Atmos. Sci 28: 1087. Lindborg, E., K. K. Tung, G. D. Nastrom, J. Y. N. Cho and K. S. Gage (2009). "Comment on "Reinterpreting aircraft measurements in anisotropic scaling turbulence" by lovejoy et al. (2009)." Atmos. Chem. Phys. Discuss. 9: 22331-22336. Lovejoy, S., A. F. Tuck, D. Schertzer and S. J. Hovde (2009). "Rinterpreting aircraft measurements in anisotropic scaling turbulence." Atmos. Chem. Phys. 9: 5007-5025. Schertzer, D. and S. Lovejoy (1985). "Generalised scale invariance in turbulent phenomena." Physico-Chemical Hydrodynamics Journal 6: 623-635.
SUPERFLUID VORTEX UNPINNING AS A COHERENT NOISE PROCESS, AND THE SCALE INVARIANCE OF PULSAR GLITCHES
Melatos, A.; Warszawski, L.
2009-08-01
The scale-invariant glitch statistics observed in individual pulsars (exponential waiting-time and power-law size distributions) are consistent with a critical self-organization process, wherein superfluid vortices pin metastably in macroscopic domains and unpin collectively via nearest-neighbor avalanches. Macroscopic inhomogeneity emerges naturally if pinning occurs at crustal faults. If, instead, pinning occurs at lattice sites and defects, which are macroscopically homogeneous, we show that an alternative, noncritical self-organization process operates, termed coherent noise, wherein the global Magnus force acts uniformly on vortices trapped in a range of pinning potentials and undergoing thermal creep. It is found that vortices again unpin collectively, but not via nearest-neighbor avalanches, and that, counterintuitively, the resulting glitch sizes are scale invariant, in accord with observational data. A mean-field analytic theory of the coherent noise process, supported by Monte Carlo simulations, yields a power-law size distribution, between the smallest and largest glitch, with exponent a in the range -2 {<=} a {<=} 0. When the theory is fitted to data from the nine most active pulsars, including the two quasi-periodic glitchers PSR J0537-6910 and PSR J0835-4510, it directly constrains the distribution of pinning potentials in the star, leading to two conclusions: (1) the potentials are broadly distributed, with the mean comparable to the standard deviation; and (2) the mean potential decreases with characteristic age. Fitting the theory to the data also constrains the pinned vortex fraction and the rate of thermal creep. An observational test is proposed to discriminate between nearest-neighbor avalanches and coherent noise: the latter process predicts a statistical excess of large glitches ('aftershocks') following a large glitch, whereas the former process does not. Its discriminatory power is discussed under various microphysical scenarios.
NASA Astrophysics Data System (ADS)
Tavares, Gustavo Marques
The Standard Model of particle physics describes all known elementary particles and their interactions. Despite its great experimental success, we know that the Standard Model is not a complete description of Nature and therefore new phenomena should be observed at higher energies. In the coming years the Large Hadron Collider will test the Standard Model by colliding protons with center of mass energies of up to 14 TeV providing some of the most stringent tests on the Standard Model. Experimental searches for Dark Matter provide a complementary program to test physics at the weak scale. In the near future new experimental data coming from direct detection experiments, and from satellites and telescopes will drastically improve our sensitivity to weak scale dark matter. This could lead to the first direct observation of dark matter, and thus of physics beyond the Standard Model. In this thesis I propose different extensions of the Standard Model and discuss their experimental consequences. I first discuss models for Axigluons, which are spin one particles in the adjoint representation of the SU(3) color gauge group. These models were motivated by the measurement of higher than predicted forward-backward asymmetry in top quark pair production at the Tevatron. I study different scenarios for Axigluon models that can explain the Tevatron result and explore their signatures at the Large Hadron Collider. Second I discuss the implications of ultraviolet scale invariance for the Standard Model, which has been advocated as a solution to the hierarchy problem. I show that in order to solve the hierarchy problem with scale invariance, new physics is required not far from the weak scale. In the last part of this thesis I propose a new model for dark matter, in which dark matter is charged under a hidden non-Abelian gauge group. This leads to modifications in the sensitivity of the usual experimental searches for dark matter in addition to distinct signatures in the Cosmic
NASA Astrophysics Data System (ADS)
Blanes, Sergio; Budd, Chris J.
2004-05-01
We present a generalisation of the Levi-Civita and Kustaanheimo-Stiefel regularisation. This allows the use of more general time rescalings. In particular, it is possible to find a regularisation which removes the singularity of the equations and preserves scaling invariance. In addition, these equations can, in certain cases, be integrated with explicit symplectic Runge-Kutta-Nyström methods. The combination of both techniques gives an explicit adaptive symplectic (EASY) integrator. We apply those methods to some perturbations of the Kepler problem and illustrate, by means of some numerical examples, when scaling invariant regularisations are more efficient that the LC/KS regularisation.
NASA Astrophysics Data System (ADS)
Anabitarte, M.; Bellini, M.; Aguilar, José Edgar Madriz
2010-01-01
We extend to 5D an approach of a 4D non-perturbative formalism to study scalar metric fluctuations of a 5D Riemann-flat de Sitter background metric. In contrast with the results obtained in 4D, the spectrum of cosmological scalar metric fluctuations during inflation can be scale invariant and the background inflaton field can take sub-Planckian values.
Model-Independent Phenotyping of C. elegans Locomotion Using Scale-Invariant Feature Transform
Koren, Yelena; Sznitman, Raphael; Arratia, Paulo E.; Carls, Christopher; Krajacic, Predrag; Brown, André E. X.; Sznitman, Josué
2015-01-01
To uncover the genetic basis of behavioral traits in the model organism C. elegans, a common strategy is to study locomotion defects in mutants. Despite efforts to introduce (semi-)automated phenotyping strategies, current methods overwhelmingly depend on worm-specific features that must be hand-crafted and as such are not generalizable for phenotyping motility in other animal models. Hence, there is an ongoing need for robust algorithms that can automatically analyze and classify motility phenotypes quantitatively. To this end, we have developed a fully-automated approach to characterize C. elegans’ phenotypes that does not require the definition of nematode-specific features. Rather, we make use of the popular computer vision Scale-Invariant Feature Transform (SIFT) from which we construct histograms of commonly-observed SIFT features to represent nematode motility. We first evaluated our method on a synthetic dataset simulating a range of nematode crawling gaits. Next, we evaluated our algorithm on two distinct datasets of crawling C. elegans with mutants affecting neuromuscular structure and function. Not only is our algorithm able to detect differences between strains, results capture similarities in locomotory phenotypes that lead to clustering that is consistent with expectations based on genetic relationships. Our proposed approach generalizes directly and should be applicable to other animal models. Such applicability holds promise for computational ethology as more groups collect high-resolution image data of animal behavior. PMID:25816290
Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply
NASA Astrophysics Data System (ADS)
Schertzer, D.; Tchiguirinskaia, I.; Lovejoy, S.; Tuck, A. F.
2012-01-01
Lindborg et al. (2010) claim that the apparent spectrum power law E(k) ≈ k-3 on scales ≥600 km obtained with the help of commercial jetliner trajectory deviations (GASP and Mozaic databases) could not be brought into question (Lovejoy et al., 2009a), because this spectrum corresponds to "a well known theory of quasi-geostrophic turbulence developed by Charney (1971)". Lindborg et al. (2010) also claim that "limitations [of this theory] have been relaxed in many of the modern models of atmospheric turbulence". We show that both claims are irrelevant and that generalized scale invariance (GSI) is indispensable to go beyond the quasi-geostrophic limitations, to go in fact from scale analysis to scaling analysis in order to derive better analytical models. In this direction, we derive vorticity equations in a space of (fractal) dimension D=2+Hz (0 ≤ Hz ≤ 1), which corresponds to a first step in the derivation of a dynamical alternative to the quasi-geostrophic approximation and turbulence. The corresponding precise definition of fractional dimensional turbulence already demonstrates that the classical 2-D and 3-D turbulence are not the main options to understand atmospheric dynamics. Although (2 + Hz)-D turbulence (with 0 < Hz < 1) has more common features with 3-D turbulence than with 2-D turbulence, it has nevertheless very distinctive features: its scaling anisotropy is in agreement with the layered pancake structure, which is typical of rotating and stratified turbulence but not of the classical 3-D turbulence.
Lee, Dong-Hoon; Lee, Do-Wan; Han, Bong-Soo
2016-01-01
The purpose of this study is an application of scale invariant feature transform (SIFT) algorithm to stitch the cervical-thoracic-lumbar (C-T-L) spine magnetic resonance (MR) images to provide a view of the entire spine in a single image. All MR images were acquired with fast spin echo (FSE) pulse sequence using two MR scanners (1.5 T and 3.0 T). The stitching procedures for each part of spine MR image were performed and implemented on a graphic user interface (GUI) configuration. Moreover, the stitching process is performed in two categories; manual point-to-point (mPTP) selection that performed by user specified corresponding matching points, and automated point-to-point (aPTP) selection that performed by SIFT algorithm. The stitched images using SIFT algorithm showed fine registered results and quantitatively acquired values also indicated little errors compared with commercially mounted stitching algorithm in MRI systems. Our study presented a preliminary validation of the SIFT algorithm application to MRI spine images, and the results indicated that the proposed approach can be performed well for the improvement of diagnosis. We believe that our approach can be helpful for the clinical application and extension of other medical imaging modalities for image stitching. PMID:27064404
An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data
Kuprat, Andrew P.; Einstein, Daniel R.
2009-01-01
We present a boundary-fitted, scale-invariant unstructured tetrahedral mesh generation algorithm that enables registration of element size to local feature size. Given an input triangulated surface mesh, a feature size field is determined by casting rays normal to the surface and into the geometry and then performing gradient-limiting operations to enforce continuity of the resulting field. Surface mesh density is adjusted to be proportional to the feature size field and then a layered anisotropic volume mesh is generated. This mesh is “scale-invariant” in that roughly the same number of layers of mesh exist in mesh cross-sections, between a minimum scale size Lmin and a maximum scale size Lmax. We illustrate how this field can be used to produce quality grids for computational fluid dynamics based simulations of challenging, topologically complex biological surfaces derived from magnetic resonance images. The algorithm is implemented in the Pacific Northwest National Laboratory (PNNL) version of the Los Alamos grid toolbox LaGriT[14]. Research funded by the National Heart and Blood Institute Award 1RO1HL073598-01A1. PMID:19784397
View FImP miracle (by scale invariance) à la self-interaction
NASA Astrophysics Data System (ADS)
Kang, Zhaofeng
2015-12-01
Combining feebly interacting massive particle (FIMP) dark matter (DM) with scale invariance (SI) leads to extremely light FIMP (thus the FImP) with FImP miracle, i.e., the mass and relic generations of FImP DM share the same dynamics. In this paper we show that due to the lightness of FImP, it, especially for a scalar FImP, can easily accommodate large DM self-interaction. For a fermionic FImP, such as the sterile neutrino, self-interaction additionally requires a mediator which is another FImP, a scalar boson with mass either much lighter or heavier than the FImP DM. DM self-interaction opens a new window to observe FImP (miracle), which does not leave traces in the conventional DM searches. As an example, FImP can account for the offsets between the centroid of DM halo and stars of galaxies recently observed in the galaxy cluster Abel 3827.
Self-organization of developing embryo using scale-invariant approach
2011-01-01
Background Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos. Methods In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing C. elegans during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method. Results and conclusion The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2. PMID:21635789
Robust FFT-based scale-invariant image registration with image gradients.
Tzimiropoulos, Georgios; Argyriou, Vasileios; Zafeiriou, Stefanos; Stathaki, Tania
2010-10-01
We present a robust FFT-based approach to scale-invariant image registration. Our method relies on FFT-based correlation twice: once in the log-polar Fourier domain to estimate the scaling and rotation and once in the spatial domain to recover the residual translation. Previous methods based on the same principles are not robust. To equip our scheme with robustness and accuracy, we introduce modifications which tailor the method to the nature of images. First, we derive efficient log-polar Fourier representations by replacing image functions with complex gray-level edge maps. We show that this representation both captures the structure of salient image features and circumvents problems related to the low-pass nature of images, interpolation errors, border effects, and aliasing. Second, to recover the unknown parameters, we introduce the normalized gradient correlation. We show that, using image gradients to perform correlation, the errors induced by outliers are mapped to a uniform distribution for which our normalized gradient correlation features robust performance. Exhaustive experimentation with real images showed that, unlike any other Fourier-based correlation techniques, the proposed method was able to estimate translations, arbitrary rotations, and scale factors up to 6. PMID:20479492
Scale invariance and universality of force networks in static granular matter
NASA Astrophysics Data System (ADS)
Ostojic, Srdjan; Somfai, Ellák; Nienhuis, Bernard
2006-02-01
Force networks form the skeleton of static granular matter. They are the key factor that determines mechanical properties such as stability, elasticity and sound transmission, which are important for civil engineering and industrial processing. Previous studies have focused on investigations of the global structure of external forces (the boundary condition) and on the probability distribution of individual contact forces. So far, however, precise knowledge of the disordered spatial structure of the force network has remained elusive. Here we report that molecular dynamics simulations of realistic granular packings reveal scale invariance of clusters of particles interacting by means of relatively strong forces. Despite visual variation, force networks for various values of the confining pressure and other parameters have identical scaling exponents and scaling function, thereby determining a universality class. Unexpectedly, the flat ensemble of force configurations (a simple generalization of equilibrium statistical mechanics) belongs to this universality class, whereas some widely studied simplified models do not. This implies that the elasticity of the grains and their geometrical disorder do not affect the universal mechanical properties.
Shortcuts to adiabaticity in classical and quantum processes for scale-invariant driving
NASA Astrophysics Data System (ADS)
Deffner, Sebastian; Jarzynski, Christopher; Del Campo, Adolfo
2014-03-01
All real physical processes in classical as well as in quantum devices operate in finite-time. For most applications, however, adiabatic, i.e. infinitely-slow processes, are more favorable, as these do not cause unwanted, parasitic excitations. A shortcut to adiabaticity is a driving protocol which reproduces in a short time the same final state that would result from an adiabatic process. A particular powerful technique to engineer such shortcuts is transitionless quantum driving by means of counterdiabatic fields. However, determining closed form expressions for the counterdiabatic field has generally proven to be a daunting task. In this paper, we introduce a novel approach, with which we find the explicit form of the counterdiabatic driving field in arbitrary scale-invariant dynamical processes, encompassing expansions and transport. Our approach originates in the formalism of generating functions, and unifies previous approaches independently developed for classical and quantum systems. We show how this new approach allows to design shortcuts to adiabaticity for a large class of classical and quantum, single-particle, non-linear, and many-body systems. SD and CJ acknowledge support from the National Science Foundation (USA) under grant DMR-1206971. This research is further supported by the U.S Department of Energy through the LANL/LDRD Program and a LANL J. Robert Oppenheimer fellowship (AdC).
Are galaxy distributions scale invariant? A perspective from dynamical systems theory
NASA Astrophysics Data System (ADS)
McCauley, J. L.
2002-06-01
Unless there is an evidence for fractal scaling with a single exponent over distances 0.1<=r<=100h-1Mpc, then the widely accepted notion of scale invariance of the correlation integral for 0.1<=r<=10h-1Mpc must be questioned. The attempt to extract a scaling exponent /ν from the correlation integral /n(r) by plotting /log(n(r)) vs. /log(r) is unreliable unless the underlying point set is approximately monofractal. The extraction of a spectrum of generalized dimensions νq from a plot of the correlation integral generating function Gn(q) by a similar procedure is probably an indication that Gn(q) does not scale at all. We explain these assertions after defining the term multifractal, mutually inconsistent definitions having been confused together in the cosmology literature. Part of this confusion is traced to the confusion in interpreting a measure-theoretic formula written down by Hentschel and Procaccia in the dynamical systems theory literature, while other errors follow from confusing together entirely different definitions of multifractal from two different schools of thought. Most important are serious errors in data analysis that follow from taking for granted a largest term approximation that is inevitably advertised in the literature on both fractals and dynamical systems theory.
NASA Technical Reports Server (NTRS)
Thompson, P. M.; Stein, G.
1980-01-01
The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain, feedback decouples into single input, single output systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.
Traffic sign recognition based on a context-aware scale-invariant feature transform approach
NASA Astrophysics Data System (ADS)
Yuan, Xue; Hao, Xiaoli; Chen, Houjin; Wei, Xueye
2013-10-01
A new context-aware scale-invariant feature transform (CASIFT) approach is proposed, which is designed for the use in traffic sign recognition (TSR) systems. The following issues remain in previous works in which SIFT is used for matching or recognition: (1) SIFT is unable to provide color information; (2) SIFT only focuses on local features while ignoring the distribution of global shapes; (3) the template with the maximum number of matching points selected as the final result is instable, especially for images with simple patterns; and (4) SIFT is liable to result in errors when different images share the same local features. In order to resolve these problems, a new CASIFT approach is proposed. The contributions of the work are as follows: (1) color angular patterns are used to provide the color distinguishing information; (2) a CASIFT which effectively combines local and global information is proposed; and (3) a method for computing the similarity between two images is proposed, which focuses on the distribution of the matching points, rather than using the traditional SIFT approach of selecting the template with maximum number of matching points as the final result. The proposed approach is particularly effective in dealing with traffic signs which have rich colors and varied global shape distribution. Experiments are performed to validate the effectiveness of the proposed approach in TSR systems, and the experimental results are satisfying even for images containing traffic signs that have been rotated, damaged, altered in color, have undergone affine transformations, or images which were photographed under different weather or illumination conditions.
Le Bec, Jimmy; Courbaud, Benoit; Le Moguédec, Gilles; Pélissier, Raphaël
2015-01-01
Understanding how tropical tree species differ in their growth strategies is critical to predict forest dynamics and assess species coexistence. Although tree growth is highly variable in tropical forests, species maximum growth is often considered as a major axis synthesizing species strategies, with fast-growing pioneer and slow-growing shade tolerant species as emblematic representatives. We used a hierarchical linear mixed model and 21-years long tree diameter increment series in a monsoon forest of the Western Ghats, India, to characterize species growth strategies and question whether maximum growth summarizes these strategies. We quantified both species responses to biotic and abiotic factors and individual tree effects unexplained by these factors. Growth responses to competition and tree size appeared highly variable among species which led to reversals in performance ranking along those two gradients. However, species-specific responses largely overlapped due to large unexplained variability resulting mostly from inter-individual growth differences consistent over time. On average one-third of the variability captured by our model was explained by covariates. This emphasizes the high dimensionality of the tree growth process, i.e. the fact that trees differ in many dimensions (genetics, life history) influencing their growth response to environmental gradients, some being unmeasured or unmeasurable. In addition, intraspecific variability increased as a power function of species maximum growth partly as a result of higher absolute responses of fast-growing species to competition and tree size. However, covariates explained on average the same proportion of intraspecific variability for slow- and fast-growing species, which showed the same range of relative responses to competition and tree size. These results reflect a scale invariance of the growth process, underlining that slow- and fast-growing species exhibit the same range of growth strategies. PMID
Scale-Invariant Neuronal Avalanche Dynamics and the Cut-Off in Size Distributions
Yang, Hongdian; Plenz, Dietmar
2014-01-01
Identification of cortical dynamics strongly benefits from the simultaneous recording of as many neurons as possible. Yet current technologies provide only incomplete access to the mammalian cortex from which adequate conclusions about dynamics need to be derived. Here, we identify constraints introduced by sub-sampling with a limited number of electrodes, i.e. spatial ‘windowing’, for well-characterized critical dynamics―neuronal avalanches. The local field potential (LFP) was recorded from premotor and prefrontal cortices in two awake macaque monkeys during rest using chronically implanted 96-microelectrode arrays. Negative deflections in the LFP (nLFP) were identified on the full as well as compact sub-regions of the array quantified by the number of electrodes N (10–95), i.e., the window size. Spatiotemporal nLFP clusters organized as neuronal avalanches, i.e., the probability in cluster size, p(s), invariably followed a power law with exponent −1.5 up to N, beyond which p(s) declined more steeply producing a ‘cut-off’ that varied with N and the LFP filter parameters. Clusters of size s≤N consisted mainly of nLFPs from unique, non-repeated cortical sites, emerged from local propagation between nearby sites, and carried spatial information about cluster organization. In contrast, clusters of size s>N were dominated by repeated site activations and carried little spatial information, reflecting greatly distorted sampling conditions. Our findings were confirmed in a neuron-electrode network model. Thus, avalanche analysis needs to be constrained to the size of the observation window to reveal the underlying scale-invariant organization produced by locally unfolding, predominantly feed-forward neuronal cascades. PMID:24927158
Le Bec, Jimmy; Courbaud, Benoit; Le Moguédec, Gilles; Pélissier, Raphaël
2015-01-01
Understanding how tropical tree species differ in their growth strategies is critical to predict forest dynamics and assess species coexistence. Although tree growth is highly variable in tropical forests, species maximum growth is often considered as a major axis synthesizing species strategies, with fast-growing pioneer and slow-growing shade tolerant species as emblematic representatives. We used a hierarchical linear mixed model and 21-years long tree diameter increment series in a monsoon forest of the Western Ghats, India, to characterize species growth strategies and question whether maximum growth summarizes these strategies. We quantified both species responses to biotic and abiotic factors and individual tree effects unexplained by these factors. Growth responses to competition and tree size appeared highly variable among species which led to reversals in performance ranking along those two gradients. However, species-specific responses largely overlapped due to large unexplained variability resulting mostly from inter-individual growth differences consistent over time. On average one-third of the variability captured by our model was explained by covariates. This emphasizes the high dimensionality of the tree growth process, i.e. the fact that trees differ in many dimensions (genetics, life history) influencing their growth response to environmental gradients, some being unmeasured or unmeasurable. In addition, intraspecific variability increased as a power function of species maximum growth partly as a result of higher absolute responses of fast-growing species to competition and tree size. However, covariates explained on average the same proportion of intraspecific variability for slow- and fast-growing species, which showed the same range of relative responses to competition and tree size. These results reflect a scale invariance of the growth process, underlining that slow- and fast-growing species exhibit the same range of growth strategies. PMID
Time-Scale Invariance As an Emergent Property in Water Balance
NASA Astrophysics Data System (ADS)
Wang, D.; Tang, Y.
2014-12-01
The Darwinian modeling approach seeks to explain the behavior of a hydrologic system as a whole by identifying simple and robust temporal or spatial patterns that capture the relevant processes. Darwinian-based hydrologic models include the Soil Conservation Service (SCS) curve number model, the "abcd" model, and the Budyko-type models. However, these models were developed based on widely differing principles and assumptions and applied to distinct time scales. Here, we derive a one-parameter Budyko-type model for mean annual water balance which is based on a generalization of the proportionality hypothesis of the SCS model and therefore is independent of temporal scale. Furthermore, we show that the new model is equivalent to the key equation of the "abcd" model. Theoretical lower and upper bounds of the new model are identified and validated based on previous observations. Thus, we illustrate a time-scale invariance property in water balance, which allows for synthesis with the Newtonian approach and offers opportunities for progress in hydrologic modeling. In the derivation of Budyko equation, total evaporation is divided into initial evaporation (E0) and continuing evaporation. Runoff does not compete with initial evaporation for water storage by interception and top soils. The assumption behind the derived equation is that the ratio of continuing evaporation to its potential value is equal to the ratio of runoff to the maximum possible value of runoff. The derived equation satisfies the boundary conditions of Budyko hypothesis, and includes one parameter (ɛ). From the perspective of evaporation, is the ratio between initial evaporation and total evaporation; from the soil wetting (W) perspective, e can be interpreted as the ratio between initial evaporation ratio (λ =E0/W) and Horton index (H=E/W), i.e. ɛ =λ/H. H is dominantly controlled by vegetation represented by NDVI; l is found to increase with decreasing product between NDVI and the fraction of rainy
From elasticity to inelasticity in cancer cell mechanics: A loss of scale-invariance
NASA Astrophysics Data System (ADS)
Laperrousaz, B.; Drillon, G.; Berguiga, L.; Nicolini, F.; Audit, B.; Satta, V. Maguer; Arneodo, A.; Argoul, F.
2016-08-01
Soft materials such as polymer gels, synthetic biomaterials and living biological tissues are generally classified as viscoelastic or viscoplastic materials, because they behave neither as pure elastic solids, nor as pure viscous fluids. When stressed beyond their linear viscoelastic regime, cross-linked biopolymer gels can behave nonlinearly (inelastically) up to failure. In living cells, this type of behavior is more frequent because their cytoskeleton is basically made of cross-linked biopolymer chains with very different structural and flexibility properties. These networks have high sensitivity to stress and great propensity to local failure. But in contrast to synthetic passive gels, they can "afford" these failures because they have ATP driven reparation mechanisms which often allow the recovery of the original texture. A cell pressed in between two plates for a long period of time may recover its original shape if the culture medium brings all the nutrients for keeping it alive. When the failure events are too frequent or too strong, the reparation mechanisms may abort, leading to an irreversible loss of mechanical homeostasis and paving the way for chronic diseases such as cancer. To illustrate this discussion, we consider a model of immature cell transformation during cancer progression, the chronic myelogenous leukemia (CML), where the formation of the BCR-ABL oncogene results from a single chromosomal translocation t(9; 22). Within the assumption that the cell response to stress is scale invariant, we show that the power-law exponent that characterizes their mechanosensitivity can be retrieved from AFM force indentation curves. Comparing control and BCR-ABL transduced cells, we observe that in the later case, one month after transduction, a small percentage the cancer cells no longer follows the control cell power law, as an indication of disruption of the initial cytoskeleton network structure.
Natural islands for a 125 GeV Higgs in the scale-invariant NMSSM
NASA Astrophysics Data System (ADS)
Agashe, Kaustubh; Cui, Yanou; Franceschini, Roberto
2013-02-01
We study whether a 125 GeV standard model-like Higgs boson can be accommodated within the scale-invariant NMSSM in a way that is natural in all respects, i.e., not only is the stop mass and hence its loop contribution to Higgs mass of natural size, but we do not allow significant tuning of NMSSM parameters as well. We pursue as much as possible an analytic approach which gives clear insights on various ways to accommodate such a Higgs mass, while conducting complementary numerical analyses. We consider both scenarios with singlet-like state being heavier and lighter than SM-like Higgs. With A-terms being small, we find for the NMSSM to be perturbative up to GUT scale, it is not possible to get 125 GeV Higgs mass, which is true even if we tune parameters of NMSSM. If we allow some of the couplings to become non-perturbative below the GUT scale, then the non-tuned option implies that the singlet self-coupling, κ, is larger than the singlet-Higgs coupling, λ, which itself is order 1. This leads to a Landau pole for these couplings close to the weak scale, in particular below ~ 104 TeV. In both the perturbative and non-perturbative NMSSM, allowing large A λ , A κ gives "more room" to accommodate a 125 GeV Higgs, but a tuning of these A-terms may be needed. In our analysis we also conduct a careful study of the constraints on the parameter space from requiring global stability of the desired vacuum fitting a 125 GeV Higgs, which is complementary to existing literature. In particular, as the singlet-higgs coupling λ increases, vacuum stability becomes more serious of an issue.
Scale-Invariance in the Spatial Development of Landslides in the Umbria Region (Italy)
NASA Astrophysics Data System (ADS)
Liucci, Luisa; Melelli, Laura; Suteanu, Cristian
2015-07-01
Understanding the spatial distribution of mass movements is a major issue in the management and forecasting of landslide risk. In this context, the present study examines the most widespread types of landslide in the Umbria region (central Italy), that is, slides and flows, in order to establish if it is possible to identify a well-defined structure in their spatial pattern. By using the landslide inventory map available for the area and by resorting to the principles of fractal theory, the scaling properties of the landslide sample were investigated. The application of the box-counting algorithm to the maps of landslide triggering points and landslide areas allowed for the identification of a clear scale-invariant structure. Two distinct types of fractal behaviour were recognized, separated by a scale value of 1 km and characterized by capacity dimensions of 1.35 and 1.76, in the ranges of 25 m-1 km and 1-16 km, respectively. The comparison between the scaling exponents obtained from a map of points and one of areas, and the elaboration of the cumulative frequency distributions of landslide areas supported the interpretation of this result: the higher capacity dimension describes the spatial distribution of landslides in the Umbria region, while the lower contains additional information about their geometries, suggesting that the latter also possess scaling properties. Based on the finding of two different types of behaviour of landslides in space, the hypothesis is discussed that the contribution of each causal factor (i.e., predisposing and triggering factors) to the occurrence of landslide events and to their spatial development could be different in the two scale ranges identified, depending on its spatial variability at local and regional scale. According to this hypothesis, factors with high local variability (i.e., topographic attributes) would mainly affect the assortment of landslide geometries, while those with high regional variability (e.g., rainfalls
NASA Astrophysics Data System (ADS)
Berry, M. V.
2005-01-01
By applying the technique of uniform asymptotic approximation to the oscillatory integrals representing tsunami wave profiles, the form of the travelling wave far from the source is calculated for arbitrary initial disturbances. The approximations reproduce the entire profiles very accurately, from the front to the tail, and their numerical computation is much faster than that of the oscillatory integrals. For one-dimensional propagation, the uniform asymptotics involve Airy functions and their derivatives; for two-dimensional propagation, the uniform asymptotics involve products of these functions. Separate analyses are required when the initial disturbance is specified as surface elevation or surface velocity as functions of position, and when these functions are even or odd. 'There was an awful rainbow once in heaven' (John Keats, 1820)
NASA Technical Reports Server (NTRS)
Elizalde, E.; Gaztanaga, E.
1992-01-01
The dependence of counts in cells on the shape of the cell for the large scale galaxy distribution is studied. A very concrete prediction can be done concerning the void distribution for scale invariant models. The prediction is tested on a sample of the CfA catalog, and good agreement is found. It is observed that the probability of a cell to be occupied is bigger for some elongated cells. A phenomenological scale invariant model for the observed distribution of the counts in cells, an extension of the negative binomial distribution, is presented in order to illustrate how this dependence can be quantitatively determined. An original, intuitive derivation of this model is presented.
Spontaneous breaking of scale invariance in a D = 3 U(N ) model with Chern-Simons gauge fields
Bardeen, William A.; Moshe, Moshe
2014-06-18
We study spontaneous breaking of scale invariance in the large N limit of three dimensional U(N )_{κ} Chern-Simons theories coupled to a scalar field in the fundamental representation. When a λ_{6} ( Ø^{† }· Ø)^{3 }self interaction term is added to the action we find a massive phase at a certain critical value for a combination of the λ(6) and ’t Hooft’s λ = N/κ couplings. This model attracted recent attention since at finite κ it contains a singlet sector which is conjectured to be dual to Vasiliev’s higher spin gravity on AdS_{4}. Our paper concentrates on the massive phase of the 3d boundary theory. We discuss the advantage of introducing masses in the boundary theory through spontaneous breaking of scale invariance.
Spontaneous breaking of scale invariance in a D = 3 U(N ) model with Chern-Simons gauge fields
Bardeen, William A.; Moshe, Moshe
2014-06-18
We study spontaneous breaking of scale invariance in the large N limit of three dimensional U(N )κ Chern-Simons theories coupled to a scalar field in the fundamental representation. When a λ6 ( Ø† · Ø)3 self interaction term is added to the action we find a massive phase at a certain critical value for a combination of the λ(6) and ’t Hooft’s λ = N/κ couplings. This model attracted recent attention since at finite κ it contains a singlet sector which is conjectured to be dual to Vasiliev’s higher spin gravity on AdS4. Our paper concentrates on the massive phasemore » of the 3d boundary theory. We discuss the advantage of introducing masses in the boundary theory through spontaneous breaking of scale invariance.« less
Li, Changhong; Cheung, Yeuk-Kwan E. E-mail: cheung@nju.edu.cn
2014-07-01
We investigate the spectrum of cosmological perturbations in a bounce cosmos modeled by a scalar field coupled to the string tachyon field (CSTB cosmos). By explicit computation of its primordial spectral index we show the power spectrum of curvature perturbations, generated during the tachyon matter dominated contraction phase, to be nearly scale invariant. We propose a unified parameter space for a systematic study of inflationary and bounce cosmologies. The CSTB cosmos is dual-in Wands's sense-to slow-roll inflation as can be visualized with the aid of this parameter space. Guaranteed by the dynamical attractor behavior of the CSTB Cosmos, the scale invariance of its power spectrum is free of the fine-tuning problem, in contrast to the slow-roll inflation model.
Quantification of organ motion based on an adaptive image-based scale invariant feature method
Paganelli, Chiara; Peroni, Marta
2013-11-15
Purpose: The availability of corresponding landmarks in IGRT image series allows quantifying the inter and intrafractional motion of internal organs. In this study, an approach for the automatic localization of anatomical landmarks is presented, with the aim of describing the nonrigid motion of anatomo-pathological structures in radiotherapy treatments according to local image contrast.Methods: An adaptive scale invariant feature transform (SIFT) was developed from the integration of a standard 3D SIFT approach with a local image-based contrast definition. The robustness and invariance of the proposed method to shape-preserving and deformable transforms were analyzed in a CT phantom study. The application of contrast transforms to the phantom images was also tested, in order to verify the variation of the local adaptive measure in relation to the modification of image contrast. The method was also applied to a lung 4D CT dataset, relying on manual feature identification by an expert user as ground truth. The 3D residual distance between matches obtained in adaptive-SIFT was then computed to verify the internal motion quantification with respect to the expert user. Extracted corresponding features in the lungs were used as regularization landmarks in a multistage deformable image registration (DIR) mapping the inhale vs exhale phase. The residual distances between the warped manual landmarks and their reference position in the inhale phase were evaluated, in order to provide a quantitative indication of the registration performed with the three different point sets.Results: The phantom study confirmed the method invariance and robustness properties to shape-preserving and deformable transforms, showing residual matching errors below the voxel dimension. The adapted SIFT algorithm on the 4D CT dataset provided automated and accurate motion detection of peak to peak breathing motion. The proposed method resulted in reduced residual errors with respect to standard SIFT
Strongly first-order electroweak phase transition and classical scale invariance
NASA Astrophysics Data System (ADS)
Farzinnia, Arsham; Ren, Jing
2014-10-01
In this work, we examine the possibility of realizing a strongly first-order electroweak phase transition within the minimal classically scale-invariant extension of the standard model (SM), previously proposed and analyzed as a potential solution to the hierarchy problem. By introducing one complex gauge-singlet scalar and three (weak scale) right-handed Majorana neutrinos, the scenario was successfully rendered capable of achieving a radiative breaking of the electroweak symmetry (by means of the Coleman-Weinberg mechanism), inducing nonzero masses for the SM neutrinos (via the seesaw mechanism), presenting a pseudoscalar dark matter candidate (protected by the CP symmetry of the potential), and predicting the existence of a second CP-even boson (with suppressed couplings to the SM content) in addition to the 125 GeV scalar. In the present treatment, we construct the full finite-temperature one-loop effective potential of the model, including the resummed thermal daisy loops, and demonstrate that finite-temperature effects induce a first-order electroweak phase transition. Requiring the thermally driven first-order phase transition to be sufficiently strong at the onset of the bubble nucleation (corresponding to nucleation temperatures TN˜100-200 GeV) further constrains the model's parameter space; in particular, an O(0.01) fraction of the dark matter in the Universe may be simultaneously accommodated with a strongly first-order electroweak phase transition. Moreover, such a phase transition disfavors right-handed Majorana neutrino masses above several hundreds of GeV, confines the pseudoscalar dark matter masses to ˜1-2 TeV, predicts the mass of the second CP-even scalar to be ˜100-300 GeV, and requires the mixing angle between the CP-even components of the SM doublet and the complex singlet to lie within the range 0.2≲sinω ≲0.4. The obtained results are displayed in comprehensive exclusion plots, identifying the viable regions of the parameter space
NASA Astrophysics Data System (ADS)
Murase, M.
1996-01-01
with self-organization, has been thought to underlie `creative' aspects of biological phenomena such as the origin of life, adaptive evolution of viruses, immune recognition and brain function. It therefore must be surprising to find that the same principles will also underlie `non-creative' aspects, for example, the development of cancer and the aging of complex organisms. Although self-organization has extensively been studied in nonliving things such as chemical reactions and laser physics, it is undoubtedly true that the similar sources of the order are available to living things at different levels and scales. Several paradigm shifts are, however, required to realize how the general principles of natural selection can be extensible to non-DNA molecules which do not possess the intrinsic nature of self-reproduction. One of them is, from the traditional, genetic inheritance view that DNA (or RNA) molecules are the ultimate unit of heritable variations and natural selection at any organization level, to the epigenetic (nongenetic) inheritance view that any non-DNA molecule can be the target of heritable variations and molecular selection to accumulate in certain biochemical environment. Because they are all enriched with a β-sheet content, ready to mostly interact with one another, different denatured proteins like β-amyloid, PHF and prions can individually undergo self-templating or self-aggregating processes out of gene control. Other paradigm shifts requisite for a break-through in the etiology of neurodegenerative disorders will be discussed. As it is based on the scale-invariant principles, the present theory also predicts plausible mechanisms underlying quite different classes of disorders such as amyotrophic lateral sclerosis (ALS), atherosclerosis, senile cataract and many other symptoms of aging. The present theory, thus, provides the consistent and comprehensive account to the origin of aging by means of natural selection and self-organization.
NASA Astrophysics Data System (ADS)
Deidda, Roberto; Mascaro, Giuseppe; Hellies, Matteo; Baldini, Luca; Roberto, Nicoletta
2013-04-01
COSMO Sky-Med (CSK) is an important programme of the Italian Space Agency aiming at supporting environmental monitoring and management of exogenous, endogenous and anthropogenic risks through X-band Synthetic Aperture Radar (X-SAR) on board of 4 satellites forming a constellation. Most of typical SAR applications are focused on land or ocean observation. However, X-band SAR can be detect precipitation that results in a specific signature caused by the combination of attenuation of surface returns induced by precipitation and enhancement of backscattering determined by the hydrometeors in the SAR resolution volume. Within CSK programme, we conducted an intercomparison between the statistical properties of precipitation fields derived by CSK SARs and those derived by the CNR Polar 55C (C-band) ground based weather radar located in Rome (Italy). This contribution presents main results of this research which was aimed at the robust characterisation of rainfall statistical properties across different scales by means of scale-invariance analysis and multifractal theory. The analysis was performed on a dataset of more two years of precipitation observations collected by the CNR Polar 55C radar and rainfall fields derived from available images collected by the CSK satellites during intense rainfall events. Scale-invariance laws and multifractal properties were detected on the most intense rainfall events derived from the CNR Polar 55C radar for spatial scales from 4 km to 64 km. The analysis on X-SAR retrieved rainfall fields, although based on few images, leaded to similar results and confirmed the existence of scale-invariance and multifractal properties for scales larger than 4 km. These outcomes encourage investigating SAR methodologies for future development of meteo-hydrological forecasting models based on multifractal theory.
NASA Astrophysics Data System (ADS)
Yu, Yongtao; Guan, Haiyan; Zai, Dawei; Ji, Zheng
2016-02-01
This paper proposes a rotation-and-scale-invariant method for detecting airplanes from high-resolution satellite images. To improve feature representation capability, a multi-layer feature generation model is created to produce high-order feature representations for local image patches through deep learning techniques. To effectively estimate airplane centroids, a Hough forest model is trained to learn mappings from high-order patch features to the probabilities of an airplane being present at specific locations. To handle airplanes with varying orientations, patch orientation is defined and integrated into the Hough forest to augment Hough voting. The scale invariance is achieved by using a set of scale factors embedded in the Hough forest. Quantitative evaluations on the images collected from Google Earth service show that the proposed method achieves a completeness, correctness, quality, and F1-measure of 0.968, 0.972, 0.942, and 0.970, respectively, in detecting airplanes with arbitrary orientations and sizes. Comparative studies also demonstrate that the proposed method outperforms the other three existing methods in accurately and completely detecting airplanes in high-resolution remotely sensed images.
NASA Astrophysics Data System (ADS)
Cao, L.; Cheng, Q.
2004-12-01
The scale invariant generator technique (SIG) and spectrum-area analysis technique (S-A) were developed independently relevant to the concept of the generalized scale invariance (GSI). The former was developed for characterizing the parameters involved in the GSI for characterizing and simulating multifractal measures whereas the latter was for identifying scaling breaks for decomposition of superimposed multifractal measures caused by multiple geophysical processes. A natural integration of these two techniques may yield a new technique to serve two purposes, on the one hand, that can enrich the power of S-A by increasing the interpretability of decomposed patterns in some applications of S-A and, on the other hand, that can provide a mean to test the uniqueness of multifractality of measures which is essential for application of SIG technique in more complicated environment. The implementation of the proposed technique has been done as a Dynamic Link Library (DLL) in Visual C++. The program can be friendly used for method validation and application in different fields.
Constructions for scale-invariant and kink-free vortex stretching
NASA Astrophysics Data System (ADS)
Dijkhuis, Geert C.
1996-10-01
Models for turbulent vortex stretching are presented as differentiable fractal curve constructions with circle arcs and screw segments replacing line elements in the usual definitions of non-analytic Koch- and Peano curves. Examples pf kink-free fractal curves are shown as self-intersecting, self-avoiding or (asymptotically) self-tangent loops, with flat versions partially or fully filling the plane, and spatial versions likewise for three dimensions. One set of kink-free fractal curves analytically models growing horseshoe vortices in Hinześ conceptual model for turbulence near a wall. From random walk analysis of transition layer vorticity on a defective lattice for intermittency, the inverse Von Karman constant emerges as fractal dimension threshold for escape of turbulence to infinity. A second curve sequence analytically models a vortex ring in superfluid helium stretching into a homogeneous vortex tangle moving between flat walls in a square channel. The deformation rule employs Hilbert's cube-filling loop construction with line segments bent into circle arcs with end points meeting at zero angle. Dynamically, the deformation geometry demands unequal skin friction on adjacent channel walls as boundary condition. The stretching process accelerates circulation velocities exponentially by conservation of angular momentum in vortex tubes with constant core volume. A third class of curves models deformation of a plasma vortex ring formed by (high-voltage or laser) discharge impact on a flat electrode surface, and carried sideways by turbulent shear flow. The construction rule now uses circle arcs twisted into Hopf-invariant screw segments for the streamlines, with mirror-symmetric halves preserving zero topoligical charge in the loop structure. Dynamically, skin friction from no-slip boundary conditions here exerts parallel torques on leading and trailing ring sections, twisting its right and left halves into mirror images with equal amounts of opposite helicity.
Creasing, point-bifurcations, and the spontaneous breakdown of scale-invariance
NASA Astrophysics Data System (ADS)
Hohlfeld, Evan Benjamin
Symmetry and symmetry breaking are important in condensed matter theory; they explain how continuum phases of matter emerge from molecular-scale chaos and lead directly to the classes of Partial Differential Equations (PDEs) that describe them. Here I suggest a new kind of symmetry breaking, the spontaneous breaking of scale symmetry, which is an asymptotic symmetry of all continuum models at small scales, and explains why things like fracture and first order phase transitions have macroscopic robustness. I formalize this idea with the notions of a point-instability and a point-bifurcation, which are sudden changes in the state of a system that develop from a point manifesting as a kind of topological change. As a non-trivial example of an equilibrium point-bifurcation, I discuss creasing in the surfaces of soft rubber-like materials. A crease is a singular, self-contacting fold, such as in the cup of the hand. Numerical methods (which rely on a novel kind of pseudo arc-length continuation for variational inequalities, called rough continuation) agree with experiments that show that creases in bent PDMS blocks form suddenly, but vanish continuously to a point, showing an effect called perfect hysteresis. Like a phase transition, creasing is characterized by intensive criterion---critical stresses---but the "phases" are a smooth surface and an intrinsically localized crease. Indeed I prove that for a wide class of PDEs of any differential and in any dimension, the only kinds of instabilities are ordinary linear instabilities and point-instabilities. I show that while linear stability is almost never sufficient to prove actual stability, linear stability (linear hyperbolicity) and a condition called a point-Lipshitz condition (or metastability) are necessary and sufficient conditions. I show this constructively: generically, when an equilibrium system loses metastability but retains linear stability, a bifurcation occurs where the bifurcating branch develops as a
Rundle, J.B. )
1989-09-10
The purpose of this paper is to show that the various observational parameters characterizing the statistical properties of earthquakes can be related to each other. The fundamental postulate which is used to obtain quantitative results is the idea that the physics of earthquake occurrence scales as a power law, similar to properties one often sees in critical phenomena. When the physics of earthquake occurrence is exactly scale invariant, {ital b}=1, and it can be shown as a consequence that earthquakes in any magnitude band {Delta}m cover the same area in unit time. This result therefore implies the existence of a universal'' covering interval {tau}{sub {ital T}}, which is here called the cycle interval.'' Using this idea, the complete Gutenberg-Richter relation is derived in terms of the fault area {ital S}{sub {ital T}}, which is available to events of any given size, the average stress drop {Delta}{sigma}{sub {ital T}} for events occurring on {ital S}{sub {tau}}, the interval {tau}{sub {ital T}} for events of stress drop {Delta}{sigma}{sub {ital T}} to cover an area {ital S}{sub {ital T}}, and the scaling exponent {alpha}, which is proportional to the {ital b} value. Observationally, the average recurrence time interval for great earthquakes, or perhaps equivalently, the recurrence interval for characteristic earthquakes on a fault segment, is a measure of the cycle interval {tau}{sub {ital T}}. The exponent {alpha} may depend on time, but scale invariance (self similarity) demands that {alpha}=1. It is shown in the appendix that the {ital A} value in the Gutenberg-Richter relation can be written in terms of {ital S}{sub {ital T}}, {tau}{sub {ital T}}, {Delta}{sigma}{sub {ital T}}, and the parameter {alpha}. The {ital b} value is either 1 or 1.5 (depending on the geometry of the fault zone) multiplied by {alpha}. {copyright} American Geophysical Union 1989
Masotti, Matteo; Lanconelli, Nico; Campanini, Renato
2009-02-15
In this work, gray-scale invariant ranklet texture features are proposed for false positive reduction (FPR) in computer-aided detection (CAD) of breast masses. Two main considerations are at the basis of this proposal. First, false positive (FP) marks surviving our previous CAD system seem to be characterized by specific texture properties that can be used to discriminate them from masses. Second, our previous CAD system achieves invariance to linear/nonlinear monotonic gray-scale transformations by encoding regions of interest into ranklet images through the ranklet transform, an image transformation similar to the wavelet transform, yet dealing with pixels' ranks rather than with their gray-scale values. Therefore, the new FPR approach proposed herein defines a set of texture features which are calculated directly from the ranklet images corresponding to the regions of interest surviving our previous CAD system, hence, ranklet texture features; then, a support vector machine (SVM) classifier is used for discrimination. As a result of this approach, texture-based information is used to discriminate FP marks surviving our previous CAD system; at the same time, invariance to linear/nonlinear monotonic gray-scale transformations of the new CAD system is guaranteed, as ranklet texture features are calculated from ranklet images that have this property themselves by construction. To emphasize the gray-scale invariance of both the previous and new CAD systems, training and testing are carried out without any in-between parameters' adjustment on mammograms having different gray-scale dynamics; in particular, training is carried out on analog digitized mammograms taken from a publicly available digital database, whereas testing is performed on full-field digital mammograms taken from an in-house database. Free-response receiver operating characteristic (FROC) curve analysis of the two CAD systems demonstrates that the new approach achieves a higher reduction of FP marks
NASA Technical Reports Server (NTRS)
Sohrab, Siavash H.; Pitch, Nancy (Technical Monitor)
1999-01-01
A scale-invariant statistical theory of fields is presented that leads to invariant definition of density, velocity, temperature, and pressure, The definition of Boltzmann constant is introduced as k(sub k) = m(sub k)v(sub k)c = 1.381 x 10(exp -23) J x K(exp -1), suggesting that the Kelvin absolute temperature scale is equivalent to a length scale. Two new state variables called the reversible heat Q(sub rev) = TS and the reversible work W(sub rev) = PV are introduced. The modified forms of the first and second law of thermodynamics are presented. The microscopic definition of heat (work) is presented as the kinetic energy due to the random (peculiar) translational, rotational, and pulsational motions. The Gibbs free energy of an element at scale Beta is identified as the total system energy at scale (Beta-1), thus leading to an invariant form of the first law of thermodynamics U(sub Beta) = Q(sub Beta) - W(sub Beta) +N(e3)U(sub Beta-1).
NASA Astrophysics Data System (ADS)
Rodríguez, A.; Tsallis, C.
2014-12-01
We show that the N → ∞ limiting probability distributions of a recently introduced family of d-dimensional scale-invariant probabilistic models based on Leibniz-like (d + 1)-dimensional hyperpyramids (Rodríguez and Tsallis 2012 J. Math. Phys. 53 023302) are given by Dirichlet distributions for d = 1, 2, …. It was formerly proved by Rodríguez et al that, for the one-dimensional case (d = 1), the corresponding limiting distributions are q-Gaussians (\\propto e_q- β x^2 , with e_1-β x^2=e-β x^2) . The Dirichlet distributions generalize the so-called Beta distributions to higher dimensions. Consistently, we make a connection between one-dimensional q-Gaussians and Beta distributions via a linear transformation. In addition, we discuss the probabilistically admissible region of parameters q and β defining a normalizable q-Gaussian, focusing particularly on the possibility of having both bell-shaped and U-shaped q-Gaussians, the latter corresponding, in an appropriate physical interpretation, to negative temperatures.
Zorick, Todd; Mandelkern, Mark A
2015-01-01
Electroencephalography (EEG) is typically viewed through the lens of spectral analysis. Recently, multiple lines of evidence have demonstrated that the underlying neuronal dynamics are characterized by scale-free avalanches. These results suggest that techniques from statistical physics may be used to analyze EEG signals. We utilized a publicly available database of fourteen subjects with waking and sleep stage 2 EEG tracings per subject, and observe that power-law dynamics of critical-state neuronal avalanches are not sufficient to fully describe essential features of EEG signals. We hypothesized that this could reflect the phenomenon of discrete scale invariance (DSI) in EEG large voltage deflections (LVDs) as being more prominent in waking consciousness. We isolated LVDs, and analyzed logarithmically transformed LVD size probability density functions (PDF) to assess for DSI. We find evidence of increased DSI in waking, as opposed to sleep stage 2 consciousness. We also show that the signatures of DSI are specific for EEG LVDs, and not a general feature of fractal simulations with similar statistical properties to EEG. Removing only LVDs from waking EEG produces a reduction in power in the alpha and beta frequency bands. These findings may represent a new insight into the understanding of the cortical dynamics underlying consciousness. PMID:26696860
Zorick, Todd; Mandelkern, Mark A.
2015-01-01
Electroencephalography (EEG) is typically viewed through the lens of spectral analysis. Recently, multiple lines of evidence have demonstrated that the underlying neuronal dynamics are characterized by scale-free avalanches. These results suggest that techniques from statistical physics may be used to analyze EEG signals. We utilized a publicly available database of fourteen subjects with waking and sleep stage 2 EEG tracings per subject, and observe that power-law dynamics of critical-state neuronal avalanches are not sufficient to fully describe essential features of EEG signals. We hypothesized that this could reflect the phenomenon of discrete scale invariance (DSI) in EEG large voltage deflections (LVDs) as being more prominent in waking consciousness. We isolated LVDs, and analyzed logarithmically transformed LVD size probability density functions (PDF) to assess for DSI. We find evidence of increased DSI in waking, as opposed to sleep stage 2 consciousness. We also show that the signatures of DSI are specific for EEG LVDs, and not a general feature of fractal simulations with similar statistical properties to EEG. Removing only LVDs from waking EEG produces a reduction in power in the alpha and beta frequency bands. These findings may represent a new insight into the understanding of the cortical dynamics underlying consciousness. PMID:26696860
NASA Astrophysics Data System (ADS)
Soundrapandiyan, Rajkumar; Chandra Mouli, P. V. S. S. R.
2016-09-01
In this paper, a novel and robust rotation and scale invariant structuring elements based descriptor (RSSED) for pedestrian classification in infrared (IR) images is proposed. In addition, a segmentation method using difference of Gaussian (DoG) and horizontal intensity projection is proposed. The three major steps are moving object segmentation, feature extraction and classification of objects as pedestrian or non-pedestrian. The segmentation result is used to extract the RSSED feature descriptor. To extract features, the segmentation result is encoded using local directional pattern (LDP). This helps in the identification of local textural patterns. The LDP encoded image is further quantized adaptively to four levels. Finally the proposed RSSED is used to formalize the descriptor from the quantized image. Support vector machine is employed for classification of the moving objects in a given IR image into pedestrian and non-pedestrian classes. The segmentation results shows the robustness in extracting the moving objects. The classification results obtained from SVM classifier shows the efficacy of the proposed method.
NASA Astrophysics Data System (ADS)
Paganelli, Chiara; Peroni, Marta; Riboldi, Marco; Sharp, Gregory C.; Ciardo, Delia; Alterio, Daniela; Orecchia, Roberto; Baroni, Guido
2013-01-01
Adaptive radiation therapy (ART) aims at compensating for anatomic and pathological changes to improve delivery along a treatment fraction sequence. Current ART protocols require time-consuming manual updating of all volumes of interest on the images acquired during treatment. Deformable image registration (DIR) and contour propagation stand as a state of the ART method to automate the process, but the lack of DIR quality control methods hinder an introduction into clinical practice. We investigated the scale invariant feature transform (SIFT) method as a quantitative automated tool (1) for DIR evaluation and (2) for re-planning decision-making in the framework of ART treatments. As a preliminary test, SIFT invariance properties at shape-preserving and deformable transformations were studied on a computational phantom, granting residual matching errors below the voxel dimension. Then a clinical dataset composed of 19 head and neck ART patients was used to quantify the performance in ART treatments. For the goal (1) results demonstrated SIFT potential as an operator-independent DIR quality assessment metric. We measured DIR group systematic residual errors up to 0.66 mm against 1.35 mm provided by rigid registration. The group systematic errors of both bony and all other structures were also analyzed, attesting the presence of anatomical deformations. The correct automated identification of 18 patients who might benefit from ART out of the total 22 cases using SIFT demonstrated its capabilities toward goal (2) achievement.
NASA Astrophysics Data System (ADS)
Sohrab, Siavash
2016-03-01
A scale-invariant model of statistical mechanics is applied to described modified forms of four laws of classical thermodynamics. Following de Broglie formula λrk = h /mkvrk , frequency of matter waves is defined as νrk = k /mkvrk leading to stochastic definitions of (Planck, Boltzmann) universal constants (h =mk <λrk > c , k =mk <νrk > c), λrkνrk = c , relating to spatiotemporal Casimir vacuum fluctuations. Invariant Mach number Maβ = v /vrβ is introduced leading to hierarchy of ``supersonic'' flow separated by shock front, viewed as ``event-horizon'' EHβ, from subsonic flow that terminates at surface of stagnant condensate of ``atoms'' defined as ``black-hole'' BHβ at scale β thus resulting in hierarchy of embedded ``black holes'' at molecular- atomic-, electron-, photon-, tachyon-. . . scales, ad infinitum. Classical black hole will correspond to solid phase photon or solid-light. It is argued that Bardeen-Carter-Hawking (1973) first law of black hole mechanics δM = (κ / 8 π) δA +ΩH δJ +ΦH δQ , instead of dE = TdS - PdV suggested by Bekenstein (1973), is analogous to first law of thermodynamics expressed as TdS = PdV + dE such that entropy of black hole, rather than to its horizon surface area, will be related to its total energy hence enthalpy H = TS leading to SBH = 4 kN in exact agreement with prediction of Major and Setter.
Galactic rotation curves, the baryon-to-dark-halo-mass relation and space-time scale invariance
NASA Astrophysics Data System (ADS)
Wu, Xufen; Kroupa, Pavel
2015-01-01
Low-acceleration space-time scale invariant dynamics (SID) predicts two fundamental correlations known from observational galactic dynamics: the baryonic Tully-Fisher relation and a correlation between the observed mass discrepancy and acceleration (MDA) in the low-acceleration regime for disc galaxies. SID corresponds to the deep Modified Newtonian Dynamics limit. The MDA data emerging in cold/warm dark matter (C/WDM) cosmological simulations disagree significantly with the tight MDA correlation of the observed galaxies. Therefore, the most modern simulated disc galaxies, which are delicately selected to have a quiet merging history in a standard dark matter cosmological model, still do not represent the correct rotation curves. Also, the observed tight correlation contradicts the postulated stochastic formation of galaxies in low-mass dark matter haloes. Moreover, we find that SID predicts a baryonic to apparent virial halo (dark matter) mass relation which agrees well with the correlation deduced observationally assuming Newtonian dynamics to be valid, while the baryonic to halo mass relation predicted from CDM models does not. The distribution of the observed ratios of dark matter halo masses to baryonic masses may be empirical evidence for the external field effect, which is predicted in SID as a consequence of the forces acting between two galaxies depending on the position and mass of a third galaxy. Applying the external field effect, we predict the masses of galaxies in the proximity of the dwarf galaxies in the Miller et al. sample. Classical non-relativistic gravitational dynamics is thus best described as being Milgromian, rather than Newtonian.
NASA Astrophysics Data System (ADS)
Kiyani, K. H.; Chapman, S. C.; Khotyaintsev, Y. V.; Dunlop, M. W.; Sahraoui, F.
2009-12-01
Spacecraft measurements of magnetic fluctuations of collisionless plasma turbulence in the solar wind typically show an ‘inertial range’ of MHD turbulence with a power-law power spectra. At higher frequencies a spectral break is seen around the ion-gyroscale with a subsequent steeper power-law, indicating a cross-over to spatial-temporal scales where kinetic effects become important. Theories for this second scaling range, also known as the “dissipation/dispersion” range focus on the spectral slope and the associated scaling exponents. We will present some results from very high-frequency magnetic field data from the four Cluster II spacecraft in intervals where the spacecraft were in quasi-stationary ambient solar wind and where the instruments were operating in burst mode. The magnetic field data are from the fluxgate and search-coil magnetometers from the Cluster FGM experiment (~67Hz), and the STAFF experiment (~450 Hz). These data sets provide observations of this dissipation/dispersion range over approximately two decades in frequency. This high cadence allows a better determination of the statistics at these small scales; especially the estimation of scaling exponents. We present a robust multiscale statistical analysis focusing on power spectra, PDFs of field fluctuations and higher-order statistics to quantify the scaling of fluctuations; as well as describing the degree of anisotropy in the fluctuations parallel and perpendicular to the average magnetic field. Both neutral fluid and MHD turbulence share a ‘‘classic’’ statistical signature - namely an intermittent multifractal scaling seen in the higher-order statistics. We test the statistical properties of the dissipation range and find in contrast monoscaling behavior, i.e., a global scale invariance. This provides a strong discriminator for the physics and phenomenology of the dissipation range in collisionless plasmas. Reference article: K. H. Kiyani, S. C. Chapman, Yu. V. Khotyaintsev
Schmitt, Daniel T.; Stein, Phyllis K.; Ivanov, Plamen Ch.
2010-01-01
Cardiac dynamics exhibit complex variability characterized by scale-invariant and nonlinear temporal organization related to the mechanism of neuroautonomic control, which changes with physiologic states and pathologic conditions. Changes in sleep regulation during sleep stages are also related to fluctuations in autonomic nervous activity. However, the interaction between sleep regulation and cardiac autonomic control remains not well understood. Even less is known how this interaction changes with age, as aspects of both cardiac dynamics and sleep regulation differ in healthy elderly compared to young subjects. We hypothesize that because of the neuroautonomic responsiveness in young subjects, fractal and nonlinear features of cardiac dynamics exhibit a pronounced stratification pattern across sleep stages, while in elderly these features will remain unchanged due to age-related loss of cardiac variability and decline of neuroautonomic responsiveness. We analyze the variability and the temporal fractal organization of heartbeat fluctuations across sleep stages in both young and elderly. We find that independent linear and nonlinear measures of cardiac control consistently exhibit the same ordering in their values across sleep stages, forming a robust stratification pattern. Despite changes in sleep architecture and reduced heart rate variability in elderly subjects, this stratification surprisingly does not break down with advanced age. Moreover, the difference between sleep stages for some linear, fractal, and nonlinear measures exceeds the difference between young and elderly, suggesting that the effect of sleep regulation on cardiac dynamics is significantly stronger than the effect of healthy aging. Quantifying changes in this stratification pattern may provide insights into how alterations in sleep regulation contribute to increased cardiac risk. PMID:19203874
The social brain: scale-invariant layering of Erdős-Rényi networks in small-scale human societies.
Harré, Michael S; Prokopenko, Mikhail
2016-05-01
The cognitive ability to form social links that can bind individuals together into large cooperative groups for safety and resource sharing was a key development in human evolutionary and social history. The 'social brain hypothesis' argues that the size of these social groups is based on a neurologically constrained capacity for maintaining long-term stable relationships. No model to date has been able to combine a specific socio-cognitive mechanism with the discrete scale invariance observed in ethnographic studies. We show that these properties result in nested layers of self-organizing Erdős-Rényi networks formed by each individual's ability to maintain only a small number of social links. Each set of links plays a specific role in the formation of different social groups. The scale invariance in our model is distinct from previous 'scale-free networks' studied using much larger social groups; here, the scale invariance is in the relationship between group sizes, rather than in the link degree distribution. We also compare our model with a dominance-based hierarchy and conclude that humans were probably egalitarian in hunter-gatherer-like societies, maintaining an average maximum of four or five social links connecting all members in a largest social network of around 132 people. PMID:27194482
Asymptotes in Polar Coordinates.
ERIC Educational Resources Information Center
Fay, Temple H.
1986-01-01
An old way to determine asymptotes for curves described in polar coordinates is presented. Practice in solving trigonometric equations, in differentiation, and in calculating limits is involved. (MNS)
Scale invariance of the η-deformed AdS5 × S5 superstring, T-duality and modified type II equations
NASA Astrophysics Data System (ADS)
Arutyunov, G.; Frolov, S.; Hoare, B.; Roiban, R.; Tseytlin, A. A.
2016-02-01
We consider the ABF background underlying the η-deformed AdS5 ×S5 sigma model. This background fails to satisfy the standard IIB supergravity equations which indicates that the corresponding sigma model is not Weyl invariant, i.e. does not define a critical string theory in the usual sense. We argue that the ABF background should still define a UV finite theory on a flat 2d world-sheet implying that the η-deformed model is scale invariant. This property follows from the formal relation via T-duality between the η-deformed model and the one defined by an exact type IIB supergravity solution that has 6 isometries albeit broken by a linear dilaton. We find that the ABF background satisfies candidate type IIB scale invariance conditions which for the R-R field strengths are of the second order in derivatives. Surprisingly, we also find that the ABF background obeys an interesting modification of the standard IIB supergravity equations that are first order in derivatives of R-R fields. These modified equations explicitly depend on Killing vectors of the ABF background and, although not universal, they imply the universal scale invariance conditions. Moreover, we show that it is precisely the non-isometric dilaton of the T-dual solution that leads, after T-duality, to modification of type II equations from their standard form. We conjecture that the modified equations should follow from κ-symmetry of the η-deformed model. All our observations apply also to η-deformations of AdS3 ×S3 ×T4and AdS2 ×S2 ×T6models.
NASA Astrophysics Data System (ADS)
Bousso, Raphael
2016-07-01
We show that known entropy bounds constrain the information carried off by radiation to null infinity. We consider distant, planar null hypersurfaces in asymptotically flat spacetime. Their focusing and area loss can be computed perturbatively on a Minkowski background, yielding entropy bounds in terms of the energy flux of the outgoing radiation. In the asymptotic limit, we obtain boundary versions of the quantum null energy condition, of the generalized Second Law, and of the quantum Bousso bound.
ERIC Educational Resources Information Center
Pottawattamie County School System, Council Bluffs, IA.
The 15 occupational clusters (transportation, fine arts and humanities, communications and media, personal service occupations, construction, hospitality and recreation, health occupations, marine science occupations, consumer and homemaking-related occupations, agribusiness and natural resources, environment, public service, business and office…
Asymptotics for spherical needlets
NASA Astrophysics Data System (ADS)
Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.
We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT convergence results for polynomial functionals of the needlet coefficients: here the asymptotic theory is considered in the high-frequency sense. Our proposals emerge from strong empirical motivations, especially in connection with the analysis of cosmological data sets.
Asymptotically safe Higgs inflation
Xianyu, Zhong-Zhi; He, Hong-Jian E-mail: hjhe@tsinghua.edu.cn
2014-10-01
We construct a new inflation model in which the standard model Higgs boson couples minimally to gravity and acts as the inflaton. Our construction of Higgs inflation incorporates the standard model with Einstein gravity which exhibits asymptotic safety in the ultraviolet region. The slow roll condition is satisfied at large field value due to the asymptotically safe behavior of Higgs self-coupling at high energies. We find that this minimal construction is highly predictive, and is consistent with both cosmological observations and collider experiments.
NASA Astrophysics Data System (ADS)
Cristallini, Achille
2016-07-01
A new and intriguing machine may be obtained replacing the moving pulley of a gun tackle with a fixed point in the rope. Its most important feature is the asymptotic efficiency. Here we obtain a satisfactory description of this machine by means of vector calculus and elementary trigonometry. The mathematical model has been compared with experimental data and briefly discussed.
NASA Astrophysics Data System (ADS)
Wan, Jun; Ruan, Qiuqi; Li, Wei; An, Gaoyun; Zhao, Ruizhen
2014-03-01
Human activity recognition based on RGB-D data has received more attention in recent years. We propose a spatiotemporal feature named three-dimensional (3D) sparse motion scale-invariant feature transform (SIFT) from RGB-D data for activity recognition. First, we build pyramids as scale space for each RGB and depth frame, and then use Shi-Tomasi corner detector and sparse optical flow to quickly detect and track robust keypoints around the motion pattern in the scale space. Subsequently, local patches around keypoints, which are extracted from RGB-D data, are used to build 3D gradient and motion spaces. Then SIFT-like descriptors are calculated on both 3D spaces, respectively. The proposed feature is invariant to scale, transition, and partial occlusions. More importantly, the running time of the proposed feature is fast so that it is well-suited for real-time applications. We have evaluated the proposed feature under a bag of words model on three public RGB-D datasets: one-shot learning Chalearn Gesture Dataset, Cornell Activity Dataset-60, and MSR Daily Activity 3D dataset. Experimental results show that the proposed feature outperforms other spatiotemporal features and are comparative to other state-of-the-art approaches, even though there is only one training sample for each class.
Kawakami, Hayato; Mitsuda, Eiji; Nambu, Yasusada; Tomimatsu, Akira
2009-07-15
In considering the gravitational collapse of matter, it is an important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla et al. to the spherically symmetric gravitational collapse of a perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecture that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.
Asymptotic symmetries from finite boxes
NASA Astrophysics Data System (ADS)
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Asthma - occupational exposure; Irritant-induced reactive airways disease ... the workplace can trigger asthma symptoms, leading to occupational asthma. The most common triggers are wood dust, grain ...
Dynamics of Dollard asymptotic variables. Asymptotic fields in Coulomb scattering
NASA Astrophysics Data System (ADS)
Morchio, G.; Strocchi, F.
2016-03-01
Generalizing Dollard’s strategy, we investigate the structure of the scattering theory associated to any large time reference dynamics UD(t) allowing for the existence of Møller operators. We show that (for each scattering channel) UD(t) uniquely identifies, for t →±∞, asymptotic dynamics U±(t); they are unitary groups acting on the scattering spaces, satisfy the Møller interpolation formulas and are interpolated by the S-matrix. In view of the application to field theory models, we extend the result to the adiabatic procedure. In the Heisenberg picture, asymptotic variables are obtained as LSZ-like limits of Heisenberg variables; their time evolution is induced by U±(t), which replace the usual free asymptotic dynamics. On the asymptotic states, (for each channel) the Hamiltonian can by written in terms of the asymptotic variables as H = H±(qout/in,pout/in), H±(q,p) the generator of the asymptotic dynamics. As an application, we obtain the asymptotic fields ψout/in in repulsive Coulomb scattering by an LSZ modified formula; in this case, U±(t) = U0(t), so that ψout/in are free canonical fields and H = H0(ψout/in).
Asymptotic entropic uncertainty relations
NASA Astrophysics Data System (ADS)
Adamczak, Radosław; Latała, Rafał; Puchała, Zbigniew; Życzkowski, Karol
2016-03-01
We analyze entropic uncertainty relations for two orthogonal measurements on a N-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix U relating both bases is distributed according to the Haar measure on the unitary group. We provide lower bounds on the average Shannon entropy of probability distributions related to both measurements. The bounds are stronger than those obtained with use of the entropic uncertainty relation by Maassen and Uffink, and they are optimal up to additive constants. We also analyze the case of a large number of measurements and obtain strong entropic uncertainty relations, which hold with high probability with respect to the random choice of bases. The lower bounds we obtain are optimal up to additive constants and allow us to prove a conjecture by Wehner and Winter on the asymptotic behavior of constants in entropic uncertainty relations as the dimension tends to infinity. As a tool we develop estimates on the maximum operator norm of a submatrix of a fixed size of a random unitary matrix distributed according to the Haar measure, which are of independent interest.
Kenyon, Nicholas J; Morrissey, Brian M; Schivo, Michael; Albertson, Timothy E
2012-08-01
Occupational asthma is the most common occupational lung disease. Work-aggravated asthma and occupational asthma are two forms of asthma causally related to the workplace, while reactive airways dysfunction syndrome is a separate entity and a subtype of occupational asthma. The diagnosis of occupational asthma is most often made on clinical grounds. The gold standard test, specific inhalation challenge, is rarely used. Low molecular weight isocyanates are the most common compounds that cause occupational asthma. Workers with occupational asthma secondary to low molecular weight agents may not have elevated specific IgE levels. The mechanisms of occupational asthma associated with these compounds are partially described. Not all patients with occupational asthma will improve after removal from the workplace. PMID:21573916
Asymptotic Parachute Performance Sensitivity
NASA Technical Reports Server (NTRS)
Way, David W.; Powell, Richard W.; Chen, Allen; Steltzner, Adam D.
2006-01-01
In 2010, the Mars Science Laboratory mission will pioneer the next generation of robotic Entry, Descent, and Landing systems by delivering the largest and most capable rover to date to the surface of Mars. In addition to landing more mass than any other mission to Mars, Mars Science Laboratory will also provide scientists with unprecedented access to regions of Mars that have been previously unreachable. By providing an Entry, Descent, and Landing system capable of landing at altitudes as high as 2 km above the reference gravitational equipotential surface, or areoid, as defined by the Mars Orbiting Laser Altimeter program, Mars Science Laboratory will demonstrate sufficient performance to land on 83% of the planet s surface. By contrast, the highest altitude landing to date on Mars has been the Mars Exploration Rover at 1.3 km below the areoid. The coupling of this improved altitude performance with latitude limits as large as 60 degrees off of the equator and a precise delivery to within 10 km of a surface target, will allow the science community to select the Mars Science Laboratory landing site from thousands of scientifically interesting possibilities. In meeting these requirements, Mars Science Laboratory is extending the limits of the Entry, Descent, and Landing technologies qualified by the Mars Viking, Mars Pathfinder, and Mars Exploration Rover missions. Specifically, the drag deceleration provided by a Viking-heritage 16.15 m supersonic Disk-Gap-Band parachute in the thin atmosphere of Mars is insufficient, at the altitudes and ballistic coefficients under consideration by the Mars Science Laboratory project, to maintain necessary altitude performance and timeline margin. This paper defines and discusses the asymptotic parachute performance observed in Monte Carlo simulation and performance analysis and its effect on the Mars Science Laboratory Entry, Descent, and Landing architecture.
Exponential tilting in Bayesian asymptotics
Kharroubi, S. A.; Sweeting, T. J.
2016-01-01
We use exponential tilting to obtain versions of asymptotic formulae for Bayesian computation that do not involve conditional maxima of the likelihood function, yielding a more stable computational procedure and significantly reducing computational time. In particular we present an alternative version of the Laplace approximation for a marginal posterior density. Implementation of the asymptotic formulae and a modified signed root based importance sampler are illustrated with an example. PMID:27279661
Asymptotic dynamics of monopole walls
NASA Astrophysics Data System (ADS)
Cross, R.
2015-08-01
We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole wall splits into subwalls when any of its moduli become large. The long-distance gauge and Higgs field interactions of these subwalls are Abelian, allowing us to derive an asymptotic metric for the monopole wall moduli space.
Polynomial Asymptotes of the Second Kind
ERIC Educational Resources Information Center
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
ERIC Educational Resources Information Center
Occupational Outlook Quarterly, 2012
2012-01-01
When choosing a career, jobseekers often want to know which occupations offer the best prospects. Generally, occupations that have rapid job growth, many new jobs, or many job openings--and good wages--promise better opportunities. This paper shows how employment in particular occupations is projected to change from 2010 to 2020. It presents…
ERIC Educational Resources Information Center
Occupational Outlook Quarterly, 2010
2010-01-01
When choosing a career, jobseekers often want to know which occupations offer the best prospects. Generally, occupations that have rapid job growth, many new jobs, or many job openings--and good wages--promise better opportunities. This article shows how employment in particular occupations is projected to change over the 2008-2018 decade. The…
Asymptotic vacua with higher derivatives
NASA Astrophysics Data System (ADS)
Cotsakis, Spiros; Kadry, Seifedine; Kolionis, Georgios; Tsokaros, Antonios
2016-04-01
We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Asymptotic Rayleigh instantaneous unit hydrograph
Troutman, B.M.; Karlinger, M.R.
1988-01-01
The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.
Ramugondo, Elelwani L.
2015-01-01
Occupational consciousness refers to ongoing awareness of the dynamics of hegemony and recognition that dominant practices are sustained through what people do every day, with implications for personal and collective health. The emergence of the construct in post-apartheid South Africa signifies the country’s ongoing struggle with negotiating long-standing dynamics of power that were laid down during colonialism, and maintained under black majority rule. Consciousness, a key component of the new terminology, is framed from post-colonial perspectives – notably work by Biko and Fanon – and grounded in the philosophy of liberation, in order to draw attention to continuing unequal intersubjective relations that play out through human occupation. The paper also draws important links between occupational consciousness and other related constructs, namely occupational possibilities, occupational choice, occupational apartheid, and collective occupation. The use of the term ‘consciousness’ in sociology, with related or different meanings, is also explored. Occupational consciousness is then advanced as a critical notion that frames everyday doing as a potentially liberating response to oppressive social structures. This paper advances theorizing as a scholarly practice in occupational science, and could potentially expand inter or transdisciplinary work for critical conceptualizations of human occupation. PMID:26549984
Asymptotic Safety in quantum gravity
NASA Astrophysics Data System (ADS)
Nink, Andreas; Reuter, Martin; Saueressig, Frank
2013-06-01
Asymptotic Safety (sometimes also referred to as nonperturbative renormalizability) is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravitational field. Its key ingredient is a nontrivial fixed point of the theory's renormalization group flow which controls the behavior of the coupling constants in the ultraviolet (UV) regime and renders physical quantities safe from divergences. Although originally proposed by Steven Weinberg to find a theory of quantum gravity the idea of a nontrivial fixed point providing a possible UV completion can be applied also to other field theories, in particular to perturbatively nonrenormalizable ones. The essence of Asymptotic Safety is the observation that nontrivial renormalization group fixed points can be used to generalize the procedure of perturbative renormalization. In an asymptotically safe theory the couplings do not need to be small or tend to zero in the high energy limit but rather tend to finite values: they approach a nontrivial UV fixed point. The running of the coupling constants, i.e. their scale dependence described by the renormalization group (RG), is thus special in its UV limit in the sense that all their dimensionless combinations remain finite. This suffices to avoid unphysical divergences, e.g. in scattering amplitudes. The requirement of a UV fixed point restricts the form of the bare action and the values of the bare coupling constants, which become predictions of the Asymptotic Safety program rather than inputs. As for gravity, the standard procedure of perturbative renormalization fails since Newton's constant, the relevant expansion parameter, has negative mass dimension rendering general relativity perturbatively nonrenormalizable. This has driven the search for nonperturbative frameworks describing quantum gravity, including Asymptotic Safety which -- in contrast to other approaches -- is characterized by its use of quantum field theory
Asymptotic safety goes on shell
NASA Astrophysics Data System (ADS)
Benedetti, Dario
2012-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
Higher dimensional nonclassical eigenvalue asymptotics
NASA Astrophysics Data System (ADS)
Camus, Brice; Rautenberg, Nils
2015-02-01
In this article, we extend Simon's construction and results [B. Simon, J. Funct. Anal. 53(1), 84-98 (1983)] for leading order eigenvalue asymptotics to n-dimensional Schrödinger operators with non-confining potentials given by Hn α = - Δ + ∏ i = 1 n |x i| α i on ℝn (n > 2), α ≔ ( α 1 , … , α n ) ∈ ( R+ ∗ ) n . We apply the results to also derive the leading order spectral asymptotics in the case of the Dirichlet Laplacian -ΔD on domains Ωn α = { x ∈ R n : ∏ j = 1 n }x j| /α j α n < 1 } .
Asymptotic safety: A simple example
Braun, Jens; Gies, Holger; Scherer, Daniel D.
2011-04-15
We use the Gross-Neveu model in 2
Supersymmetric asymptotic safety is not guaranteed
NASA Astrophysics Data System (ADS)
Intriligator, Kenneth; Sannino, Francesco
2015-11-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.
Grammer, Leslie C
2016-05-01
Occupational rhinitis (OR) involves nasal congestion, rhinorrhea, nasal itching, and/or sneezing resulting from workplace exposures. OR can have a significant negative effect on quality of life and productivity. OR can be divided into allergic or nonallergic subgroups based on the underlying pathogenesis. Certain occupational exposures place employees at greater risk for developing disease. Primary treatment is avoidance of implicated exposures. Antihistamines, saline rinses, and nasal steroids may be useful. OR can coexist with occupational asthma, and rhinitis symptoms have been reported to precede those of the lower respiratory tract. OR is has both medical and socioeconomic implications. PMID:27083106
Occupational health problems occur at work or because of the kind of work you do. These problems can include ... by exposure to radiation Exposure to germs in health care settings Good job safety and prevention practices ...
The maximum drag reduction asymptote
NASA Astrophysics Data System (ADS)
Choueiri, George H.; Hof, Bjorn
2015-11-01
Addition of long chain polymers is one of the most efficient ways to reduce the drag of turbulent flows. Already very low concentration of polymers can lead to a substantial drag and upon further increase of the concentration the drag reduces until it reaches an empirically found limit, the so called maximum drag reduction (MDR) asymptote, which is independent of the type of polymer used. We here carry out a detailed experimental study of the approach to this asymptote for pipe flow. Particular attention is paid to the recently observed state of elasto-inertial turbulence (EIT) which has been reported to occur in polymer solutions at sufficiently high shear. Our results show that upon the approach to MDR Newtonian turbulence becomes marginalized (hibernation) and eventually completely disappears and is replaced by EIT. In particular, spectra of high Reynolds number MDR flows are compared to flows at high shear rates in small diameter tubes where EIT is found at Re < 100. The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° [291734].
Asymptotically Free Gauge Theories. I
DOE R&D Accomplishments Database
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Ahrens, W; Behrens, T; Mester, B; Schmeisser, N
2008-03-01
The aim of occupational epidemiology is to describe workplace-related diseases and to identify their underlying causes. Its primary goal is to protect workers from hazardous effects of the working process by applying work-related primary and secondary prevention measures. To assess health risks different study designs and a wide array of complex study instruments and methods are frequently employed that cannot be replaced by toxicological investigations. This paper primarily addresses health risks by agent exposures. In this context a central task of occupational epidemiology is careful assessment of exposure. Different data sources, such as work site measurements, register data, archive material, experts' opinion, and the workers' personal estimates of exposure may be used during this process. In addition, biological markers can complement exposure assessment. Since thorough occupational epidemiologic studies allow assessment of disease risks under realistic exposure conditions, their results should be more frequently used to derive workplace-related threshold limit values. PMID:18311483
Lachapelle, J M
1998-05-01
Cases of occupational allergic contact dermatitis are less frequent nowadays than in the past: for instance the prevalence of allergic contact dermatitis to cement chromates is decreasing steadily among building workers. On the other hand, new haptens do occur in our environment, due to the diversification of industrial techniques; e.g. methylchloro- and methylisothiazolinone (MCI/MI) present as a preservative in paints or varnishes, acrylates and methacrylates, or, at the hospital, glutaraldehyde, propacetamol or various antibiotics. A new entity has been clinically characterized: protein contact dermatitis. The prevention of occupational allergic contact dermatitis is multidisciplinary. It includes all aspects of prevention: primary, secondary and tertiary. PMID:11767354
Numerical Asymptotic Solutions Of Differential Equations
NASA Technical Reports Server (NTRS)
Thurston, Gaylen A.
1992-01-01
Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.
ERIC Educational Resources Information Center
Morris, William R.
Although fiscal support for occupational programs in California Community Colleges is provided primarily by state and local district taxes, about ten percent of the total support is provided through federal sources. Federal regulations under the Vocational Education Act (VEA) require the recipients of federal funds to provide consultative,…
Pauli, G; Bessot, J C; Gourdon, C
1992-12-01
The diagnosis of occupational asthma requires the integration of a multiplicity of data; the history, cutaneous skin tests, biological tests, respiratory function tests and non-specific tests of bronchial hyperreactivity and specific bronchial provocation test. The history search for the presence of an atopic state, the occurrence of similar disorders in members of the same firm and also the timing of symptoms in relation to the occupational activities. Cutaneous tests are particularly helpful in IgE-mediated asthma in relation to the inhalation of animal or vegetable materials of glycoprotein origin. For haptens, the need for their prior coupling to a protein carrier causes problems which have not been entirely resolved. Laboratory tests run into the same snags. Respiratory function and non-specific bronchial provocation tests, confirm the diagnosis of asthma and enable the medium and long term prognostic to be assessed. Specific bronchial provocation tests are the most appropriate tests to establish an aetiological diagnosis in occupational asthma. Different technical methods are possible: quantitative administration of allergen aerosols, realistic tests, and tests using exposure chambers to achieve true test doses. The products responsible for occupational asthma are multiple. The different substances are characterised in a simplified manner: first animal matter (mammalian and arthropod allergens), secondly substances of vegetable origin (roots, leaves, flowers, grain and flour, wood and its derivates) and finally chemical products. The chemical products are primarily from the pharmaceutical and metal industries and above all from the plastics industry. PMID:1296320
... care industry is one of largest providers of jobs in the United States. Many health jobs are in hospitals. Others are in nursing homes, ... clinics and laboratories. To work in a health occupation, you often must have special training. Some, like ...
Asymptotically optimal topological quantum compiling.
Kliuchnikov, Vadym; Bocharov, Alex; Svore, Krysta M
2014-04-11
We address the problem of compiling quantum operations into braid representations for non-Abelian quasiparticles described by the Fibonacci anyon model. We classify the single-qubit unitaries that can be represented exactly by Fibonacci anyon braids and use the classification to develop a probabilistically polynomial algorithm that approximates any given single-qubit unitary to a desired precision by an asymptotically depth-optimal braid pattern. We extend our algorithm in two directions: to produce braids that allow only single-strand movement, called weaves, and to produce depth-optimal approximations of two-qubit gates. Our compiled braid patterns have depths that are 20 to 1000 times shorter than those output by prior state-of-the-art methods, for precisions ranging between 10(-10) and 10(-30). PMID:24765934
Plane Wave and Coulomb Asymptotics
NASA Astrophysics Data System (ADS)
Mulligan, P. G.; Crothers, D. S. F.
2004-01-01
A simple plane wave solution of the Schrödinger Helmholtz equation is a quantum eigenfunction obeying both energy and linear momentum correspondence principles. Inclusion of the outgoing wave with scattering amplitude f obeys unitarity and the optical theorem. By closely considering the standard asymptotic development of the plane wave, we show that there is a problem with angular momentum when we consider forward scattering at the point of closest approach and at large impact parameter given semiclassically by (l + 1/2)/k where l is the azimuthal quantum number and may be large (J Leech et al, Phys. Rev. Lett. 88 257901 (2002)). The problem is resolved via non-uniform, non-standard analysis involving the Heaviside step function, unifying classical, semiclassical and quantum mechanics, and the treatment is extended to the case of pure Coulomb scattering.
8. Asymptotically Flat and Regular Cauchy Data
NASA Astrophysics Data System (ADS)
Dain, Sergio
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
Einstein-Yang-Mills theory: Asymptotic symmetries
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Lambert, Pierre-Henry
2013-11-01
Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four-dimensional asymptotically flat case.
An asymptotic model of the F layer
NASA Astrophysics Data System (ADS)
Oliver, W. L.
2012-01-01
A model of the F layer of the ionosphere is presented that consists of a bottomside asymptote that ignores transport and a topside asymptote that ignores chemistry. The asymptotes connect at the balance height dividing the chemistry and transport regimes. A combination of these two asymptotes produces a good approximation to the true F layer. Analogously, a model of F layer response to an applied vertical drift is presented that consists of two asymptotic responses, one that ignores transport and one that ignores chemistry. The combination of these asymptotic responses produces a good approximation to the response of the true F layer. This latter response is identical to the “servo” response of Rishbeth et al. (1978), derived from the continuity equation. The asymptotic approach bypasses the continuity equation in favor of “force balance” arguments and so replaces a differential equation with simpler algebraic equations. This new approach provides a convenient and intuitive mean for first-order estimates of the change in F layer peak height and density in terms of changes in neutral density, composition, temperature, winds, and electric fields. It is applicable at midlatitudes and at magnetically quiet times at high latitudes. Forensic inverse relations are possible but are not unique. The validity of the asymptotic relations is shown through numerical simulation.
Chan-Yeung, M.; Grzybowski, S.
1976-01-01
Occupational asthma is probably much more common than is generally realized. Though many causes have been described, undoubtedly many more are yet to be recognized. One of the diagnostic difficulties lies in the fact that in most forms of this disease a late asthmatic reaction occurs in the evening rather than at work. The pathogenetic mechanisms differ in various forms of occupational asthma. In some, an immunologic mechanism is likely; in others, a "pharmacologic" action of the offending agent is implicated. Asthma due to inhalation of dusts of western red cedar, isocyanates, detergent enzymes and textiles is considered in detail. Periodic examination of workers at risk is of value for early diagnosis and prevention of irrversible airway obstruction. PMID:766943
Scale Invariant Fluctuations of Proteins Native States
NASA Astrophysics Data System (ADS)
Tang, Qian-Yuan; Zhang, Yang-Yang; Wang, Jun; Wang, Wei; Chialvo, Dante R.
Long-range correlations in biological systems often hints for the presence of universal mechanism at work. Here we study protein native dynamics by analyzing a large set of structure ensembles determined by solution NMR. For proteins of diverse sizes, the average distance-dependent cross-correlation functions ϕ (r) and its correlation length ξϕ are analyzed. The analysis uncovered the presence of nontrivial scaling in the proteins' equilibrium dynamics around native states. We show that the correlation length is proportional to the gyration radius of the molecule, implying that the motion of any residue could influence all the others, up to the entire molecule. In addition, it is found that certain shapes are favored, such that for any given protein size the folding process ``chooses'' the shape with the maximum susceptibility. These results suggest that the proteins native state is critical in the same sense with other slowly built self-organized critical systems, which once posed near the minimum of the energy landscape, preserve their dynamic flexibility. Supported by Natural Science Foundation of China (Grants 11334004, 11174133, 81421091) and National Basic Research Program of China (Grant 2013CB834100).
Scale invariance and universality in economic phenomena
NASA Astrophysics Data System (ADS)
Stanley, H. E.; Amaral, L. A. N.; Gopikrishnan, P.; Plerou, V.; Salinger, M. A.
2002-03-01
This paper discusses some of the similarities between work being done by economists and by computational physicists seeking to contribute to economics. We also mention some of the differences in the approaches taken and seek to justify these different approaches by developing the argument that by approaching the same problem from different points of view, new results might emerge. In particular, we review two such new results. Specifically, we discuss the two newly discovered scaling results that appear to be `universal', in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function, which is a simple power law with exponent -4 extending over 102 standard deviations (a factor of 108 on the y-axis); this result is analogous to the Gutenberg-Richter power law describing the histogram of earthquakes of a given strength; (ii) for a wide range of economic organizations, the histogram that shows how size of organization is inversely correlated to fluctuations in size with an exponent ≈0.2. Neither of these two new empirical laws has a firm theoretical foundation. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behaviour of the response function at the critical point (zero magnetic field) leads to large fluctuations. We discuss a curious `symmetry breaking' for values of Σ above a certain threshold value Σc here Σ is defined to be the local first moment of the probability distribution of demand Ω - the difference between the number of shares traded in buyer-initiated and seller-initiated trades. This feature is qualitatively identical to the behaviour of the probability density of the magnetization for fixed values of the inverse temperature.
Scale-invariant breaking of conformal symmetry
NASA Astrophysics Data System (ADS)
Dymarsky, Anatoly; Zhiboedov, Alexander
2015-10-01
Known examples of unitary relativistic scale but not conformal-invariant field theories (SFTs) can be embedded into conventional conformal field theories (CFTs). We show that any SFT which is a subsector of a unitary CFT is a free theory. Our discussion applies to an arbitrary number of spacetime dimensions and explains triviality of known SFTs in four spacetime dimensions. We comment on examples of unitary SFTs which are not captured by our construction.
Snow Avalanche Release, Scale Invariance and Criticallity
NASA Astrophysics Data System (ADS)
Dendievel, R.; Faillettaz, J.; Daudon, D.; Louchet, F.
It is widely recognised that a number of geophysical phenomena as volcanic eruptions, landslides, etc, obey the so-called Gutenberg-Richter relation, first established for the frequency-magnitude statistics of earthquakes, where is the occurence frequency of earthquakes with a magnitude greater than m. This power law behaviour, character- istic of critical phenomena, is usually evidenced in the form of a linear distribution in a double logarithmic plot, in a way similar to the self organised criticality of a sand pile (2). We have shown very recently and for the first time that snow avalanche release exhibited such a behaviour (3). The only reliable parameter we had at that time was the amplitude of the acoustic emission associated with the avalanche release. Since it was not possible to record several events in the same gully, data were taken in sev- eral gullys of the same mountain range. Yet, the data aligned quite well on a unique straight line, with a critical exponent of about 1.6. This observation suggests that the very nature of the release mechanism is independent of the average slope and mor- phology of the gully. In order to understand the origin of this critical behaviour and to further investigate the mechanisms responsible for avalanche release, the avalanche release is studied in the present paper both by discrete elements simulations and cel- lular automata, and compared to further field data. The discrete elements simulations deal with a population of spheres on a slope, experiencing both a gravitational stress, interactions with the substrate, and mutual contact interactions. A gradual increase of the slope or a gradual change in contact forces (accounting for thermal snow mi- crostructure evolution) eventually result in avalanche release. The conditions are ad- justed until the frequency-magnitude of avalanches exhibit a critical behaviour. The cellular automaton is more or less similar to a game of life: a 2-d grid of boxes repre- sents the interface between the substrate and the snow slab, loaded in shear by the slab weight. Each box can be in one of two states labelled 0 and 1, according whether the slab/substrate interface is locally cracked or not. The state of a box can be changed ac- cording whether a given number of neighbours are in a 0 state or in a 1 state. A group of adjacent boxes in the 0 state represents a crack. The automaton is run from vari- ous randomly generated initial populations. Avalanches of various sizes are recorded. The local rules are adjusted until the avalanche frequency- size distribution aligns on a critical line. In both cases, the critical slopes are compared to field data. 1 (1) B. Gutenberg and C.F. Richter, seismicity of the earth and associated phenomenon, 2d edition, Princeton University Press, Princeton (1954) (2) P. Bak, How Nature Works, Springer Verlag (1996) (3) F. Louchet, J. Faillettaz, D. Daudon, N. Bédouin, E. Collet, J. Lhuissier and A-M. Portal XXVI General Assembly of the European Geophysical Society, Nice (F), 25-30 mars 2001 2
Occupational Sex Roles and Occupational Prestige.
ERIC Educational Resources Information Center
Simerly, D. Emily; Ruback, R. Barry
Past studies on the sex-typing of occupations have used a single bipolar scale, ranging from masculinity to femininity. An empirical examination of both occupational sex roles and occupational prestige was conducted using two unipolar scales to assess masculinity and femininity. College students (N=183) rated 94 occupations, which were then…
Detecting communities using asymptotical surprise
NASA Astrophysics Data System (ADS)
Traag, V. A.; Aldecoa, R.; Delvenne, J.-C.
2015-08-01
Nodes in real-world networks are repeatedly observed to form dense clusters, often referred to as communities. Methods to detect these groups of nodes usually maximize an objective function, which implicitly contains the definition of a community. We here analyze a recently proposed measure called surprise, which assesses the quality of the partition of a network into communities. In its current form, the formulation of surprise is rather difficult to analyze. We here therefore develop an accurate asymptotic approximation. This allows for the development of an efficient algorithm for optimizing surprise. Incidentally, this leads to a straightforward extension of surprise to weighted graphs. Additionally, the approximation makes it possible to analyze surprise more closely and compare it to other methods, especially modularity. We show that surprise is (nearly) unaffected by the well-known resolution limit, a particular problem for modularity. However, surprise may tend to overestimate the number of communities, whereas they may be underestimated by modularity. In short, surprise works well in the limit of many small communities, whereas modularity works better in the limit of few large communities. In this sense, surprise is more discriminative than modularity and may find communities where modularity fails to discern any structure.
Endre, László
2010-06-01
Occupational rhinitis (OR) is an inflammatory disease of the nose, which is characterized by intermittent or persistent symptoms, arising out of causes and conditions attributable to a particular work environment and not to stimuli encountered outside the workplace. Its clinical symptoms (nasal congestion, sneezing, rhinorrhea, itching, nasal airflow limitation) are very similar with the symptoms of the allergic rhinitis caused by other (classical) agents. According to the 27/1996 NM Departmental Order, OR in Hungary is a notifiable disease. Despite, between year 1997 and 2009, not even a single case was reported in Hungary. In the last 20 years the only Hungarian reference in this field was published in 2004, in the Textbook of Occupational Medicine, edited by Ungváry. This disease is not unknown in other European countries. It can be produced by both high and low molecular weight agents. For example, according to the publications, its prevalence among bakers can be 18-29%, and among workers with diisocyanates (painters, urethane mould workers) 36-42%. Risk factors are atopy, high concentration and multiple irritant agents in the air of workplace. Atopy has been associated with an increased risk of specific sensitization to a variety of HMW agents. Beside of the clinical and occupational history, objective investigations have to be used as well, for the diagnosis of OR. The gold standard for confirming the diagnosis of OR is the nasal provocation test. Objective methods that can be used for assessing nasal patency during the investigation of OR include rhinomanometry, acoustic rhinometry, peak nasal inspiratory flow, and gravimetry of the nasal secret. The management of the OR needs environmental interventions. These are: increasing the ventilation, decreasing the time of exposure, substitution of the irritant agent, investigation of possible asthma in all workers with OR. Medical treatments are: oral antihistamines, local (nasal) corticosteroids, combined
EMC effect: asymptotic freedom with nuclear targets
West, G.B.
1984-01-01
General features of the EMC effect are discussed within the framework of quantum chromodynamics as expressed via the operator product expansion and asymptotic freedom. These techniques are reviewed with emphasis on the target dependence. 22 references.
Hermite polynomials and quasi-classical asymptotics
Ali, S. Twareque; Engliš, Miroslav
2014-04-15
We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.
Chan-Yeung, M
1995-01-01
Many toxic compounds found in air emissions may induce bronchoconstriction. In the workplace, workers are exposed to these compounds, often in much higher concentrations. Some of these compounds act as sensitizers. Of these, some compounds induce asthma by producing specific IgE antibodies to the compound or its protein conjugate, while others induce asthma through yet unidentified immunologic mechanisms. Some compounds, when inhaled in high concentrations, act as irritants and produce bronchoconstriction probably by inducing acute airway inflammation. The latter condition is called Reactive Airways Dysfunction Syndrome (RADS) or irritant-induced asthma. Occupational asthma is an excellent model to study the pathogenesis and the natural history of adult onset asthma because the responsible agent can be identified, complete avoidance is possible, and exposure can be measured or estimated. PMID:8549481
Maximal hypersurfaces in asymptotically stationary spacetimes
NASA Astrophysics Data System (ADS)
Chrusciel, Piotr T.; Wald, Robert M.
1992-12-01
The purpose of the work is to extend the results on the existence of maximal hypersurfaces to encompass some situations considered by other authors. The existence of maximal hypersurface in asymptotically stationary spacetimes is proven. Existence of maximal surface and of foliations by maximal hypersurfaces is proven in two classes of asymptotically flat spacetimes which possess a one parameter group of isometries whose orbits are timelike 'near infinity'. The first class consists of strongly causal asymptotically flat spacetimes which contain no 'blackhole or white hole' (but may contain 'ergoregions' where the Killing orbits fail to be timelike). The second class of space times possess a black hole and a white hole, with the black and white hole horizon intersecting in a compact 2-surface S.
Dispersive shock wave interactions and asymptotics.
Ablowitz, Mark J; Baldwin, Douglas E
2013-02-01
Dispersive shock waves (DSWs) are physically important phenomena that occur in systems dominated by weak dispersion and weak nonlinearity. The Korteweg-de Vries (KdV) equation is the universal model for systems with weak dispersion and weak, quadratic nonlinearity. Here we show that the long-time-asymptotic solution of the KdV equation for general, steplike data is a single-phase DSW; this DSW is the "largest" possible DSW based on the boundary data. We find this asymptotic solution using the inverse scattering transform and matched-asymptotic expansions. So while multistep data evolve to have multiphase dynamics at intermediate times, these interacting DSWs eventually merge to form a single-phase DSW at large time. PMID:23496590
Asymptotic structure of hydromagnetically driven relativistic winds
NASA Technical Reports Server (NTRS)
Chiueh, Tzihong; Li, Zhi-Yun; Begelman, Mitchell C.
1991-01-01
A fully relativistic analysis has been performed of the asymptotic structure of stationary axisymmetric hydromagnetic winds. If a flow fills the region containing the rotation axis, then the flux surfaces in the flow must collimate to a set of current-carrying cylindrical surface extending to infinite transverse radius, collimate to a set of cylindrical surfaces extending to a finite radius, or collimate to a current-free paraboloidal field configuration which fills up the entire space. If an asymptotically cylindrical flow carries a finite current at radii well beyond the light cylinder, then the Lorentz factor of the terminal flow speed on a given flux surface is proportional to the total current enclosed within this flux surface. If a flow is of type II paraboloidal, then its asymptotic energy flux is carried entirely by the gas motion rather than the electromagnetic fields.
Asymptotic behavior of degenerate logistic equations
NASA Astrophysics Data System (ADS)
Arrieta, José M.; Pardo, Rosa; Rodríguez-Bernal, Aníbal
2015-12-01
We analyze the asymptotic behavior of positive solutions of parabolic equations with a class of degenerate logistic nonlinearities of the type λu - n (x)uρ. An important characteristic of this work is that the region where the logistic term n (ṡ) vanishes, that is K0 = { x : n (x) = 0 }, may be non-smooth. We analyze conditions on λ, ρ, n (ṡ) and K0 guaranteeing that the solution starting at a positive initial condition remains bounded or blows up as time goes to infinity. The asymptotic behavior may not be the same in different parts of K0.
Asymptotics of a horizontal liquid bridge
NASA Astrophysics Data System (ADS)
Haynes, M.; O'Brien, S. B. G.; Benilov, E. S.
2016-04-01
This paper uses asymptotic techniques to find the shape of a two dimensional liquid bridge suspended between two vertical walls. We model the equilibrium bridge shape using the Laplace-Young equation. We use the Bond number as a small parameter to deduce an asymptotic solution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibrium is only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this interval to the Bond number. This result is verified by comparison with a global force balance. In addition, we examine the quasi-static evolution of such a two dimensional bridge.
Selected Health Service Occupations.
ERIC Educational Resources Information Center
Coleman, Arthur D.
Prepared by an occupational analyst of the Utah Department of Employment Security, this manual provides job guides for 39 health service occupations concerned mainly with doctors, nurses, and related hospital-medical-health consultants and services. Classified according to "The Dictionary of Occupational Titles," each occupational description…
ERIC Educational Resources Information Center
Willett, Lynn H.
A survey was conducted to determine the need for health occupations personnel in the Moraine Valley Community College district, specifically to: (1) describe present employment for selected health occupations; (2) project health occupation employment to 1974; (3) identify the supply of applicants for the selected occupations; and (4) identify…
NASA Technical Reports Server (NTRS)
Bopp, Genie; Somers, Jeff; Granderson, Brad; Gernhardt, Mike; Currie, Nancy; Lawrence, Chuck
2010-01-01
Topics include occupant protection overview with a focus on crew protection during dynamic phases of flight; occupant protection collaboration; modeling occupant protection; occupant protection considerations; project approach encompassing analysis tools, injury criteria, and testing program development; injury criteria update methodology, unique effects of pressure suits and other factors; and a summary.
Occupational Therapy Assistant.
ERIC Educational Resources Information Center
Ohio State Univ., Columbus. Center on Education and Training for Employment.
This document, which is designed for use in developing a tech prep competency profile for the occupation of occupational therapy assistant, lists technical competencies and competency builders for 16 units pertinent to the health technologies cluster in general as well as those specific to the occupation of occupational therapy assistant. The…
Asymptotic behaviour of backward elastic scattering
NASA Astrophysics Data System (ADS)
Germond, J. F.; Lombard, R. J.
1988-05-01
We discuss a compact formula proposed by Dias de Deus and Pimenta for the asymptotic value of the elastic scattering amplitude at backward angles. Improvements and generalization are obtained by means of the saddle-point method which corroborate old calculations by Serber.
Asymptotic theory of relativistic, magnetized jets
Lyubarsky, Yuri
2011-01-15
The structure of a relativistically hot, strongly magnetized jet is investigated at large distances from the source. Asymptotic equations are derived describing collimation and acceleration of the externally confined jet. Conditions are found for the transformation of the thermal energy into the fluid kinetic energy or into the Poynting flux. Simple scalings are presented for the jet collimation angle and Lorentz factors.
Exponential asymptotics of the Voigt functions
NASA Astrophysics Data System (ADS)
Paris, R. B.
2015-06-01
We obtain the asymptotic expansion of the Voigt functionss K( x, y) and L( x, y) for large (real) values of the variables x and y, paying particular attention to the exponentially small contributions. A Stokes phenomenon is encountered as with x > 0 fixed. Numerical examples are presented to demonstrate the accuracy of these new expansions.
Lectures on renormalization and asymptotic safety
Nagy, Sandor
2014-11-15
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method.