Rotation invariant moments and transforms for geometrically invariant image watermarking
NASA Astrophysics Data System (ADS)
Singh, Chandan; Ranade, Sukhjeet K.
2013-01-01
We present invariant image watermarking based on a recently introduced set of polar harmonic transforms and angular radial transforms and their comparative analysis with state-of-art approaches based on Zernike moments and pseudo-Zernike moments (ZMs/PZMs). Similar to ZMs/PZMs, these transforms provide rotation invariance and resilience to noise while mitigating inherent limitations like numerical instability and computational cost at high order of moments. These characteristics motivate us to design invariant transform-based invariant image watermarking schemes that can withstand various intentional or unintentional attacks, handle large bitcarriers, and work in a limited computing environment. A comparative performance evaluation of watermarking systems regarding critical parameters like visual imperceptibility, embedding capacity, and watermark robustness against geometric transformations, common signal processing distortions, and Stirmark attacks is performed along with the empirical analysis of various inherent properties of transforms and moments such as magnitude invariance, reconstruction capabilities, and computational complexity to investigate relationships between the performance of watermarking schemes and inherent properties of transforms.
The use of force histograms for affine-invariant relative position description.
Matsakis, Pascal; Keller, James M; Sjahputera, Ozy; Marjamaa, Jonathon
2004-01-01
Affine invariant descriptors have been widely used for recognition of objects regardless of their position, size, and orientation in space. Examples of color, texture, and shape descriptors abound in the literature. However, many tasks in computer vision require looking not only at single objects or regions in images but also at their spatial relationships. In an earlier work, we showed that the relative position of two objects can be quantitatively described by a histogram of forces. Here, we study how affine transformations affect this descriptor. The position of an object with respect to another changes when the objects are affine transformed. We analyze the link between 1) the applied affinity, 2) the relative position before transformation (described through a force histogram), and 3) the relative position after transformation. We show that any two of these elements allow the third one to be recovered. Moreover, it is possible to determine whether (or how well) two relative positions are actually related through an affine transformation. If they are not, the affinity that best approximates the unknown transformation can be retrieved, and the quality of the approximation assessed. PMID:15382682
A new affine-invariant image matching method based on SIFT
NASA Astrophysics Data System (ADS)
Wang, Peng-cheng; Chen, Qian; Chen, Hai-xin; Cheng, Hong-chang; Gong, Zhen-fei
2013-09-01
Local invariant feature extraction, as one of the main problems in the field of computer vision, has been widely applied to image matching, splicing and target recognition etc. Lowe's scale invariant feature transform (known as SIFT) algorithm has attracted much attention due to its invariance to scale, rotation and illumination. However, SIFT is not robust to affine deformations, because it is based on the DoG detector which extracts keypoints in a circle region. Besides, the feature descriptor is represented by a 128-dimensional vector, which means that the algorithm complexity is extremely large especially when there is a great quantity of keypoints in the image. In this paper, a new feature descriptor, which is robust to affine deformations, is proposed. Considering that circles turn to be ellipses after affine deformations, some improvements have been made. Firstly, the Gaussian image pyramids are constructed by convoluting the source image and the elliptical Gaussian kernel with two volatile parameters, orientation and eccentricity. In addition, the two parameters are discretely selected in order to imitate the possibilities of the affine deformation, which can make sure that anisotropic regions are transformed into isotropic ones. Next, all extreme points can be extracted as the candidates for the affine-invariant keypoints in the image pyramids. After accurate keypoints localization is performed, the secondary moment of the keypoints' neighborhood is calculated to identify the elliptical region which is affineinvariant, the same as SIFT, the main orientation of the keypoints can be determined and the feature descriptor is generated based on the histogram constructed in this region. At last, the PCA method for the 128-dimensional descriptor's reduction is used to improve the computer calculating efficiency. The experiments show that this new algorithm inherits all SIFT's original advantages, and has a good resistance to affine deformations; what's more, it
Affine Legendre moment invariants for image watermarking robust to geometric distortions
Zhang, Hui; Shu, Huazhong; Coatrieux, Gouenou; Zhu, Jie; Wu, Jonathan Q. M.; Zhang, Yue; Zhu, Hongqing; Luo, Limin
2011-01-01
Geometric distortions are generally simple and effective attacks for many watermarking methods. They can make detection and extraction of the embedded watermark difficult or even impossible by destroying the synchronization between the watermark reader and the embedded watermark. In this paper, we propose a new watermarking approach which allows watermark detection and extraction under affine transformation attacks. The novelty of our approach stands on a set of affine invariants we derived from Legendre moments. Watermark embedding and detection are directly performed on this set of invariants. We also show how these moments can be exploited for estimating the geometric distortion parameters in order to permit watermark extraction. Experimental results show that the proposed watermarking scheme is robust to a wide range of attacks: geometric distortion, filtering, compression, and additive noise. PMID:21342852
Reflection symmetry detection using locally affine invariant edge correspondence.
Wang, Zhaozhong; Tang, Zesheng; Zhang, Xiao
2015-04-01
Reflection symmetry detection receives increasing attentions in recent years. The state-of-the-art algorithms mainly use the matching of intensity-based features (such as the SIFT) within a single image to find symmetry axes. This paper proposes a novel approach by establishing the correspondence of locally affine invariant edge-based features, which are superior to the intensity based in the aspects that it is insensitive to illumination variations, and applicable to textureless objects. The locally affine invariance is achieved by simple linear algebra for efficient and robust computations, making the algorithm suitable for detections under object distortions like perspective projection. Commonly used edge detectors and a voting process are, respectively, used before and after the edge description and matching steps to form a complete reflection detection pipeline. Experiments are performed using synthetic and real-world images with both multiple and single reflection symmetry axis. The test results are compared with existing algorithms to validate the proposed method. PMID:25608306
Transformation invariant on-line target recognition.
Iftekharuddin, Khan M
2011-06-01
Transformation invariant automatic target recognition (ATR) has been an active research area due to its widespread applications in defense, robotics, medical imaging and geographic scene analysis. The primary goal for this paper is to obtain an on-line ATR system for targets in presence of image transformations, such as rotation, translation, scale and occlusion as well as resolution changes. We investigate biologically inspired adaptive critic design (ACD) neural network (NN) models for on-line learning of such transformations. We further exploit reinforcement learning (RL) in ACD framework to obtain transformation invariant ATR. We exploit two ACD designs, such as heuristic dynamic programming (HDP) and dual heuristic dynamic programming (DHP) to obtain transformation invariant ATR. We obtain extensive statistical evaluations of proposed on-line ATR networks using both simulated image transformations and real benchmark facial image database, UMIST, with pose variations. Our simulations show promising results for learning transformations in simulated images and authenticating out-of plane rotated face images. Comparing the two on-line ATR designs, HDP outperforms DHP in learning capability and robustness and is more tolerant to noise. The computational time involved in HDP is also less than that of DHP. On the other hand, DHP achieves a 100% success rate more frequently than HDP for individual targets, and the residual critic error in DHP is generally smaller than that of HDP. Mathematical analyses of both our RL-based on-line ATR designs are also obtained to provide a sufficient condition for asymptotic convergence in a statistical average sense. PMID:21571610
Invariant relationships deriving from classical scaling transformations
Bludman, Sidney; Kennedy, Dallas C.
2011-04-15
Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to evolutionary laws that prove useful, even if the transformations are not symmetries of the equations of motion. In the case of scaling, symmetry leads to a scaling evolutionary law, a first-order equation in terms of scale invariants, linearly relating kinematic and dynamic degrees of freedom. This scaling evolutionary law appears in dynamical and in static systems. Applied to dynamical central-force systems, the scaling evolutionary equation leads to generalized virial laws, which linearly connect the kinetic and potential energies. Applied to barotropic hydrostatic spheres, the scaling evolutionary equation linearly connects the gravitational and internal energy densities. This implies well-known properties of polytropes, describing degenerate stars and chemically homogeneous nondegenerate stellar cores.
The classical Korteweg capillarity system: geometry and invariant transformations
NASA Astrophysics Data System (ADS)
Rogers, C.; Schief, W. K.
2014-08-01
A class of invariant transformations is presented for the classical Korteweg capillarity system. The invariance is an extension of a kind originally introduced in an anisentropic gasdynamics context. In a particular instance, application of the invariant transformation leads to a deformed one-parameter class of Kármán-Tsien-type capillarity laws associated with a deformation of an integrable nonlinear Schrödinger-type equation which incorporates a de Broglie-Bohm potential. The latter and another integrable case associated with the classical Boussinesq equation may be linked to the motion of curves in Euclidean and projective space so that both the invariant transformation and the Galilean invariance of the capillarity system may be interpreted in a geometric and soliton-theoretic manner. The work is set in the broader context of other connections of invariant transformations in gasdynamics with soliton theory.
Automated transformation-invariant shape recognition through wavelet multiresolution
NASA Astrophysics Data System (ADS)
Brault, Patrice; Mounier, Hugues
2001-12-01
We present here new results in Wavelet Multi-Resolution Analysis (W-MRA) applied to shape recognition in automatic vehicle driving applications. Different types of shapes have to be recognized in this framework. They pertain to most of the objects entering the sensors field of a car. These objects can be road signs, lane separation lines, moving or static obstacles, other automotive vehicles, or visual beacons. The recognition process must be invariant to global, affine or not, transformations which are : rotation, translation and scaling. It also has to be invariant to more local, elastic, deformations like the perspective (in particular with wide angle camera lenses), and also like deformations due to environmental conditions (weather : rain, mist, light reverberation) or optical and electrical signal noises. To demonstrate our method, an initial shape, with a known contour, is compared to the same contour altered by rotation, translation, scaling and perspective. The curvature computed for each contour point is used as a main criterion in the shape matching process. The original part of this work is to use wavelet descriptors, generated with a fast orthonormal W-MRA, rather than Fourier descriptors, in order to provide a multi-resolution description of the contour to be analyzed. In such way, the intrinsic spatial localization property of wavelet descriptors can be used and the recognition process can be speeded up. The most important part of this work is to demonstrate the potential performance of Wavelet-MRA in this application of shape recognition.
Real-time affine invariant gesture recognition for LED smart lighting control
NASA Astrophysics Data System (ADS)
Chen, Xu; Liao, Miao; Feng, Xiao-Fan
2015-03-01
Gesture recognition has attracted extensive research interest in the field of human computer interaction. Realtime affine invariant gesture recognition is an important and challenging problem. This paper presents a robust affine view invariant gesture recognition system for realtime LED smart light control. As far as we know, this is the first time that gesture recognition has been applied for control LED smart light in realtime. Employing skin detection, hand blobs captured from a top view camera are first localized and aligned. Subsequently, SVM classifiers trained on HOG features and robust shape features are then utilized for gesture recognition. By accurately recognizing two types of gestures ("gesture 8" and a "5 finger gesture"), a user is enabled to toggle lighting on/off efficiently and control light intensity on a continuous scale. In each case, gesture recognition is rotation- and translation-invariant. Extensive evaluations in an office setting demonstrate the effectiveness and robustness of the proposed gesture recognition algorithm.
Registration algorithm research for work-pieces based on affine invariant
NASA Astrophysics Data System (ADS)
Chen, Meng; Yan, Bixi
2011-11-01
Work-pieces registration is a crucial item in flexible manufacture assembly. In order to finish work-pieces registration, a method is proposed based on affine invariant. After the CAD model data and actual measurement data of a work-piece are acquired, the method consists of the following five steps: sampling point clouds data, extracting characteristic four-points set, searching characteristic congruent four-points set, computing transformation congruent matrix and the last, further precise point clouds data registration. Point clouds data of CAD and measuring model are sampled respectively through calculating the curvature of the two sets of data and selecting the obvious curvature points as their reduced characteristic points. Based on this, the characteristic four-points set from the reduced ones of CAD model and the corresponding matching congruent four-points set of the measuring model are extracted according to RANSAC algorithm. The rotation matrix R and translation vector T of any two matching four-points are then calculated through the algorithm of quaternion. After that, the measuring model is rotated and translated and then compared with the CAD model data, the most congruent transformation matrix is selected as the coarse registration result. Furthermore, Iterative Closest Point (ICP) algorithm is applied to the congruent transformation to improve registration precision. The experiment shows that the run time of the algorithm is 129.56s and mean-error of point-to-point distance is 0.062mm when accessing measuring model data more than 80000 points. Compared with the traditional curvature registration, the experiment also shows that the algorithm is more efficient and robust when the volume of point clouds data is larger.
Affine calibration based on invariable extrinsic parameters for stereo light microscope
NASA Astrophysics Data System (ADS)
Li, Weixian; Wei, Zhenzhong; Zhang, Guangjun
2014-10-01
The stereo light microscope (SLM) plays an important role in the measurement of three-dimensional geometry on the microscopic scale. We propose a fast and precise affine calibration algorithm based on the invariable extrinsic parameters for the SLM. This calibration algorithm with a free planar reference consists of three steps: first, derive the extrinsic parameters based on their invariable definition in the pinhole and affine models; second, calculate the intrinsic parameters through homography matrix; finally, refine all the model parameters by global optimization with the previous closed-form solutions as the initial values. The effectiveness of assuming a noncoaxial optical system as an affine camera is also verified to affinely model all types of SLMs. The calibration experiments show that the affine calibration is preferable for multicriteria including running time, relative positioning precision, and absolute positioning precision. With PlanApo S 1.5× and a total magnification of 3.024×, the proposed affine calibration algorithm achieves a distance error of 0.423 μm and a positioning error of 0.195 mm within 10.6 s.
Bidirectional Elastic Image Registration Using B-Spline Affine Transformation
Gu, Suicheng; Meng, Xin; Sciurba, Frank C.; Wang, Chen; Kaminski, Naftali; Pu, Jiantao
2014-01-01
A registration scheme termed as B-spline affine transformation (BSAT) is presented in this study to elastically align two images. We define an affine transformation instead of the traditional translation at each control point. Mathematically, BSAT is a generalized form of the affine transformation and the traditional B-Spline transformation (BST). In order to improve the performance of the iterative closest point (ICP) method in registering two homologous shapes but with large deformation, a bi-directional instead of the traditional unidirectional objective / cost function is proposed. In implementation, the objective function is formulated as a sparse linear equation problem, and a sub-division strategy is used to achieve a reasonable efficiency in registration. The performance of the developed scheme was assessed using both two-dimensional (2D) synthesized dataset and three-dimensional (3D) volumetric computed tomography (CT) data. Our experiments showed that the proposed B-spline affine model could obtain reasonable registration accuracy. PMID:24530210
Bidirectional elastic image registration using B-spline affine transformation.
Gu, Suicheng; Meng, Xin; Sciurba, Frank C; Ma, Hongxia; Leader, Joseph; Kaminski, Naftali; Gur, David; Pu, Jiantao
2014-06-01
A registration scheme termed as B-spline affine transformation (BSAT) is presented in this study to elastically align two images. We define an affine transformation instead of the traditional translation at each control point. Mathematically, BSAT is a generalized form of the affine transformation and the traditional B-spline transformation (BST). In order to improve the performance of the iterative closest point (ICP) method in registering two homologous shapes but with large deformation, a bidirectional instead of the traditional unidirectional objective/cost function is proposed. In implementation, the objective function is formulated as a sparse linear equation problem, and a sub-division strategy is used to achieve a reasonable efficiency in registration. The performance of the developed scheme was assessed using both two-dimensional (2D) synthesized dataset and three-dimensional (3D) volumetric computed tomography (CT) data. Our experiments showed that the proposed B-spline affine model could obtain reasonable registration accuracy. PMID:24530210
Dresner, L.
1987-08-01
Problems of technological interest can very often be described by partial differential equations (PDEs) with one dependent and two independent variables (call them c, z, and t, respectively). Many such PDEs are invariant to one-parameter families of one-parameter affine groups. Similarity solutions are solutions of the PDE that are invariant to one group of the family. The great utility of similarity solutions is that they may be calculated by solving an ODE rather than a PDE and are thus much more easily accessible than other solutions. The form of the principal ODE depends, of course, on the form of the PDE, but it can be proved quite generally that the principal ODE is itself invarient to the one-parameter affine group or associated group. because of the invariance of the principal ODE to the associated group, the dependence on the boundary and initial conditions of certain special values of the function y(x), e.g., y(O), y(infinity), y(O), ets., may be predicted a priori without solving the principal ODE. The nonlinear PDE of heat transport in superfluid He-II, is used as an illustration of these ideas in this review.
An affine point-set and line invariant algorithm for photo-identification of gray whales
NASA Astrophysics Data System (ADS)
Chandan, Chandan; Kehtarnavaz, Nasser; Hillman, Gilbert; Wursig, Bernd
2004-05-01
This paper presents an affine point-set and line invariant algorithm within a statistical framework, and its application to photo-identification of gray whales (Eschrichtius robustus). White patches (blotches) appearing on a gray whale's left and right flukes (the flattened broad paddle-like tail) constitute unique identifying features and have been used here for individual identification. The fluke area is extracted from a fluke image via the live-wire edge detection algorithm, followed by optimal thresholding of the fluke area to obtain the blotches. Affine point-set and line invariants of the blotch points are extracted based on three reference points, namely the left and right tips and the middle notch-like point on the fluke. A set of statistics is derived from the invariant values and used as the feature vector representing a database image. The database images are then ranked depending on the degree of similarity between a query and database feature vectors. The results show that the use of this algorithm leads to a reduction in the amount of manual search that is normally done by marine biologists.
Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2015-05-01
This paper focuses on a class of reinforcement learning (RL) algorithms, named integral RL (I-RL), that solve continuous-time (CT) nonlinear optimal control problems with input-affine system dynamics. First, we extend the concepts of exploration, integral temporal difference, and invariant admissibility to the target CT nonlinear system that is governed by a control policy plus a probing signal called an exploration. Then, we show input-to-state stability (ISS) and invariant admissibility of the closed-loop systems with the policies generated by integral policy iteration (I-PI) or invariantly admissible PI (IA-PI) method. Based on these, three online I-RL algorithms named explorized I-PI and integral Q -learning I, II are proposed, all of which generate the same convergent sequences as I-PI and IA-PI under the required excitation condition on the exploration. All the proposed methods are partially or completely model free, and can simultaneously explore the state space in a stable manner during the online learning processes. ISS, invariant admissibility, and convergence properties of the proposed methods are also investigated, and related with these, we show the design principles of the exploration for safe learning. Neural-network-based implementation methods for the proposed schemes are also presented in this paper. Finally, several numerical simulations are carried out to verify the effectiveness of the proposed methods. PMID:25163070
AN AFFINE-INVARIANT SAMPLER FOR EXOPLANET FITTING AND DISCOVERY IN RADIAL VELOCITY DATA
Hou Fengji; Hogg, David W.; Goodman, Jonathan; Weare, Jonathan; Schwab, Christian
2012-02-01
Markov chain Monte Carlo (MCMC) proves to be powerful for Bayesian inference and in particular for exoplanet radial velocity fitting because MCMC provides more statistical information and makes better use of data than common approaches like chi-square fitting. However, the nonlinear density functions encountered in these problems can make MCMC time-consuming. In this paper, we apply an ensemble sampler respecting affine invariance to orbital parameter extraction from radial velocity data. This new sampler has only one free parameter, and does not require much tuning for good performance, which is important for automatization. The autocorrelation time of this sampler is approximately the same for all parameters and far smaller than Metropolis-Hastings, which means it requires many fewer function calls to produce the same number of independent samples. The affine-invariant sampler speeds up MCMC by hundreds of times compared with Metropolis-Hastings in the same computing situation. This novel sampler would be ideal for projects involving large data sets such as statistical investigations of planet distribution. The biggest obstacle to ensemble samplers is the existence of multiple local optima; we present a clustering technique to deal with local optima by clustering based on the likelihood of the walkers in the ensemble. We demonstrate the effectiveness of the sampler on real radial velocity data.
An Invariant of Topologically Ordered States Under Local Unitary Transformations
NASA Astrophysics Data System (ADS)
Haah, Jeongwan
2016-03-01
For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can compute the S-matrix from a single ground state wave function. Here, we define a class of Hamiltonians consisting of local commuting projectors and an associated matrix that is invariant under local unitary transformations. We argue that the invariant is equivalent to the topological S-matrix. The definition does not require degeneracy of the ground state. We prove that the invariant depends on the state only, in the sense that it can be computed by any Hamiltonian in the class of which the state is a ground state. As a corollary, we prove that any local quantum circuit that connects two ground states of quantum double models (discrete gauge theories) with non-isomorphic abelian groups must have depth that is at least linear in the system's diameter. As a tool for the proof, a manifestly Hamiltonian-independent notion of locally invisible operators is introduced. This gives a sufficient condition for a many-body state not to be generated from a product state by any small depth quantum circuit; this is a many-body entanglement witness.
NASA Astrophysics Data System (ADS)
Possieri, Corrado; Tornambè, Antonio
2015-05-01
The main goal of this paper is to compute a class of polynomial vector fields, whose associated dynamical system has a given affine variety as attractive and invariant set, a given point in such an affine variety as invariant and attractive and another given affine variety as invariant set, solving the application of this technique in the robotic area. This objective is reached by using some tools taken from algebraic geometry. Practical examples of how these vector fields can be computed are reported. Moreover, by using these techniques, two feedback control laws, respectively, for a unicycle-like mobile robot and for a car-like mobile robot, which make them move, within the workspace, approaching to a selected algebraic curve, are given.
Bi-invariant functions on the group of transformations leaving a measure quasi-invariant
Neretin, Yu A
2014-09-30
Let Gms be the group of transformations of a Lebesgue space leaving the measure quasi-invariant. Let Ams be a subgroup of it consisting of transformations preserving the measure. We describe canonical forms of double cosets of Gms by the subgroup Ams and show that all continuous Ams-bi-invariant functions on Gms are functionals of the distribution of a Radon-Nikodym derivative. Bibliography: 14 titles.
Qualitative cues in the discrimination of affine-transformed minimal patterns.
Kukkonen, H T; Foster, D H; Wood, J R; Wagemans, J; Van Gool, L
1996-01-01
An important factor in judging whether two retinal images arise from the same object viewed from different positions may be the presence of certain properties or cues that are 'qualitative invariants' with respect to the natural transformations, particularly affine transformations, associated with changes in viewpoint. To test whether observers use certain affine qualitative cues such as concavity, convexity, collinearity, and parallelism of the image elements, a 'same-different' discrimination experiment was carried out with planar patterns that were defined by four points either connected by straight line segments (line patterns) or marked by dots (dot patterns). The first three points of each pattern were generated randomly; the fourth point fell on their diagonal bisector. According to the position of that point, the patterns were concave, triangular (three points being collinear), convex, or parallel sided. In a 'same' trial, an affine transformation was applied to one of two identical patterns; in a 'different' trial, the affine transformation was applied after the point lying on the diagonal bisector was perturbed a short, fixed distance along the bisector, inwards for one pattern and outwards for the other. Observers' ability to discriminate 'same' from 'different' pairs of patterns depended strongly on the position of the fourth, displaced, point: performance varied rapidly when the position of the displaced point was such that the patterns were nearly triangular or nearly parallel sided, consistent with observers using the hypothesised qualitative cues. The experimental data were fitted with a simple probabilistic model of discrimination performance that used a combination of these qualitative cues and a single quantitative cue. PMID:8733148
Invariant properties and rotation transformations of the GPR scattering matrix
NASA Astrophysics Data System (ADS)
Villela, Almendra; Romo, José M.
2013-03-01
We analyze the properties of the scattering matrix associated with the incident and scattered electric fields used in GPR. The elements of the scattering matrix provide information produced by different polarizations of the incident wave field. Rotationally invariant quantities such as trace, determinant and Frobenius norm lead to images that combine the information contained in the four elements of the scattering matrix in a mathematically simple and sound manner. The invariant quantities remove the directional properties implicit in the dipolar field used in GPR allowing the application of standard processing techniques designed for scalar fields, such as those used in seismic data processing. We illustrate the non-directional properties of the invariants using a 3D simulation of the wavefield produced by a point scatterer. The estimation of the azimuth angle of elongated targets is also explored using rotation transformations that maximize alternatively the co-polarized or the cross-polarized responses. The angle estimation is essentially an unstable process, particularly if low amplitudes or noisy data are involved. We apply the Frobenius norm ‖S‖F as a criterion for selection of the best amplitudes to use for a more stable and significant angle estimation. The performance of our formulation was tested with synthetic data produced by a 3D model of an air-filled metal pipe buried in a homogeneous halfspace. The images resulting from the invariants show a clear diffraction hyperbola suitable for a scalar wavefield migration, while the azimuth of the pipe is neatly resolved for amplitudes selected with ‖S‖F ≥ 0.4. A field experiment conducted above an aqueduct pipe illustrates the proposed methods with real data. The images obtained from the invariants are better than those from the individual elements of the scattering matrix. The azimuth estimated using our formulation is in agreement with the probable orientation of the aqueduct. Finally, a field
Deformation of supersymmetric and conformal quantum mechanics through affine transformations
NASA Technical Reports Server (NTRS)
Spiridonov, Vyacheslav
1993-01-01
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.
NASA Technical Reports Server (NTRS)
Norbury, John W.
1989-01-01
The invariance of classical electromagnetism under charge-conjugation, parity, and time-reversal (CPT) is studied by considering the motion of a charged particle in electric and magnetic fields. Upon applying CPT transformations to various physical quantities and noting that the motion still behaves physically demonstrates invariance.
Perception of Invariance Over Perspective Transformations in Five Month Old Infants.
ERIC Educational Resources Information Center
Gibson, Eleanor; And Others
This experiment asked whether infants at 5 months perceived an invariant over four types of rigid motion (perspective transformations), and thereby differentiated rigid motion from deformation. Four perspective transformations of a sponge rubber object (rotation around the vertical axis, rotation around the horizontal axis, rotation in the frontal…
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.
Helicity is the only integral invariant of volume-preserving transformations.
Enciso, Alberto; Peralta-Salas, Daniel; de Lizaur, Francisco Torres
2016-02-23
We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional I defined on exact divergence-free vector fields of class C(1) on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that I is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity. PMID:26864201
Helicity is the only integral invariant of volume-preserving transformations
Enciso, Alberto; Peralta-Salas, Daniel; de Lizaur, Francisco Torres
2016-01-01
We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional ℐ defined on exact divergence-free vector fields of class C1 on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that ℐ is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity. PMID:26864201
Quantum image encryption based on generalized affine transform and logistic map
NASA Astrophysics Data System (ADS)
Liang, Hao-Ran; Tao, Xiang-Yang; Zhou, Nan-Run
2016-03-01
Quantum circuits of the generalized affine transform are devised based on the novel enhanced quantum representation of digital images. A novel quantum image encryption algorithm combining the generalized affine transform with logistic map is suggested. The gray-level information of the quantum image is encrypted by the XOR operation with a key generator controlled by the logistic map, while the position information of the quantum image is encoded by the generalized affine transform. The encryption keys include the independent control parameters used in the generalized affine transform and the logistic map. Thus, the key space is large enough to frustrate the possible brute-force attack. Numerical simulations and analyses indicate that the proposed algorithm is realizable, robust and has a better performance than its classical counterpart in terms of computational complexity.
Quantum image encryption based on generalized affine transform and logistic map
NASA Astrophysics Data System (ADS)
Liang, Hao-Ran; Tao, Xiang-Yang; Zhou, Nan-Run
2016-07-01
Quantum circuits of the generalized affine transform are devised based on the novel enhanced quantum representation of digital images. A novel quantum image encryption algorithm combining the generalized affine transform with logistic map is suggested. The gray-level information of the quantum image is encrypted by the XOR operation with a key generator controlled by the logistic map, while the position information of the quantum image is encoded by the generalized affine transform. The encryption keys include the independent control parameters used in the generalized affine transform and the logistic map. Thus, the key space is large enough to frustrate the possible brute-force attack. Numerical simulations and analyses indicate that the proposed algorithm is realizable, robust and has a better performance than its classical counterpart in terms of computational complexity.
Geometrically invariant and high capacity image watermarking scheme using accurate radial transform
NASA Astrophysics Data System (ADS)
Singh, Chandan; Ranade, Sukhjeet K.
2013-12-01
Angular radial transform (ART) is a region based descriptor and possesses many attractive features such as rotation invariance, low computational complexity and resilience to noise which make them more suitable for invariant image watermarking than that of many transform domain based image watermarking techniques. In this paper, we introduce ART for fast and geometrically invariant image watermarking scheme with high embedding capacity. We also develop an accurate and fast framework for the computation of ART coefficients based on Gaussian quadrature numerical integration, 8-way symmetry/anti-symmetry properties and recursive relations for the calculation of sinusoidal kernel functions. ART coefficients so computed are then used for embedding the binary watermark using dither modulation. Experimental studies reveal that the proposed watermarking scheme not only provides better robustness against geometric transformations and other signal processing distortions, but also has superior advantages over the existing ones in terms of embedding capacity, speed and visual imperceptibility.
Transform-invariant feature based functional MR image registration and neural activity modelling.
Gong, Jiaqi; Hao, Qi; Hu, Fei
2013-01-01
In this paper, a set of non-rigid image registration and neural activity modelling methods using functional MR Images (fMRI) are proposed based on transform-invariant feature representations. Our work made two contributions. First, we propose to use a transform-invariant feature to improve image registration performance of Iterative Closest Point (ICP) based methods. The proposed feature utilises Gaussian Mixture Models (GMM) to describe the local topological structure of fMRI data. Second, we propose to use a 3-dimensional Scale-Invariant Feature Transform (SIFT) based descriptor to represent neural activities related to drinking behaviour. As a result, neural activities patterns of different subjects drinking water or intaking glucose can be recognised, with strong robustness against various artefacts. PMID:23900434
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.
Einstein-aether theory, violation of Lorentz invariance, and metric-affine gravity
Heinicke, Christian; Baekler, Peter; Hehl, Friedrich W.
2005-07-15
We show that the Einstein-aether theory of Jacobson and Mattingly (J and M) can be understood in the framework of the metric-affine (gauge theory of) gravity (MAG). We achieve this by relating the aether vector field of J and M to certain post-Riemannian nonmetricity pieces contained in an independent linear connection of spacetime. Then, for the aether, a corresponding geometrical curvature-square Lagrangian with a massive piece can be formulated straightforwardly. We find an exact spherically symmetric solution of our model.
Source-position transformation: an approximate invariance in strong gravitational lensing
NASA Astrophysics Data System (ADS)
Schneider, Peter; Sluse, Dominique
2014-04-01
The main obstacle that gravitational lensing has in determining accurate masses of deflectors, or in determining precise estimates for the Hubble constant, is the degeneracy of lensing observables with respect to the mass-sheet transformation (MST). The MST is a global modification of the mass distribution which leaves all image positions, shapes, and flux ratios invariant, but which changes the time delay. Here we show that another global transformation of lensing mass distributions exists which leaves image positions and flux ratios almost invariant, and of which the MST is a special case. As is the case for the MST, this new transformation only applies if one considers only those source components that are at the same distance from us. Whereas for axi-symmetric lenses this source position transformation exactly reproduces all strong lensing observables, it does so only approximately for more general lens situations. We provide crude estimates for the accuracy with which the transformed mass distribution can reproduce the same image positions as the original lens model, and present an illustrative example of its performance. This new invariance transformation is most likely the reason why the same strong lensing information can be accounted for with rather different mass models.
Li, Junning; Shi, Yonggang; Toga, Arthur W.
2015-01-01
Thresholding statistical maps with appropriate correction of multiple testing remains a critical and challenging problem in brain mapping. Since the false discovery rate (FDR) criterion was introduced to the neuroimaging community a decade ago, various improvements have been proposed. However, a highly desirable feature, transformation invariance, has not been adequately addressed, especially for voxel-based FDR. Thresholding applied after spatial transformation is not necessarily equivalent to transformation applied after thresholding in the original space. We find this problem closely related to another important issue: spatial correlation of signals. A Gaussian random vector-valued image after normalization is a random map from a Euclidean space to a high-dimension unit-sphere. Instead of defining the FDR measure in the image’s Euclidean space, we define it in the signals’ hyper-spherical space whose measure not only reflects the intrinsic “volume” of signals’ randomness but also keeps invariant under images’ spatial transformation. Experiments with synthetic and real images demonstrate that our method achieves transformation invariance and significantly minimizes the bias introduced by the choice of template images. PMID:26213450
The shift-invariant discrete wavelet transform and application to speech waveform analysis
NASA Astrophysics Data System (ADS)
Enders, Jörg; Geng, Weihua; Li, Peijun; Frazier, Michael W.; Scholl, David J.
2005-04-01
The discrete wavelet transform may be used as a signal-processing tool for visualization and analysis of nonstationary, time-sampled waveforms. The highly desirable property of shift invariance can be obtained at the cost of a moderate increase in computational complexity, and accepting a least-squares inverse (pseudoinverse) in place of a true inverse. A new algorithm for the pseudoinverse of the shift-invariant transform that is easier to implement in array-oriented scripting languages than existing algorithms is presented together with self-contained proofs. Representing only one of the many and varied potential applications, a recorded speech waveform illustrates the benefits of shift invariance with pseudoinvertibility. Visualization shows the glottal modulation of vowel formants and frication noise, revealing secondary glottal pulses and other waveform irregularities. Additionally, performing sound waveform editing operations (i.e., cutting and pasting sections) on the shift-invariant wavelet representation automatically produces quiet, click-free section boundaries in the resulting sound. The capabilities of this wavelet-domain editing technique are demonstrated by changing the rate of a recorded spoken word. Individual pitch periods are repeated to obtain a half-speed result, and alternate individual pitch periods are removed to obtain a double-speed result. The original pitch and formant frequencies are preserved. In informal listening tests, the results are clear and understandable. .
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
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
Fast computation of rotation-invariant image features by an approximate radial gradient transform.
Takacs, Gabriel; Chandrasekhar, Vijay; Tsai, Sam S; Chen, David; Grzeszczuk, Radek; Girod, Bernd
2013-08-01
We present the radial gradient transform (RGT) and a fast approximation, the approximate RGT (ARGT). We analyze the effects of the approximation on gradient quantization and histogramming. The ARGT is incorporated into the rotation-invariant fast feature (RIFF) algorithm. We demonstrate that, using the ARGT, RIFF extracts features 16× faster than SURF while achieving a similar performance for image matching and retrieval. PMID:23204286
A biologically inspired neural network model to transformation invariant object recognition
NASA Astrophysics Data System (ADS)
Iftekharuddin, Khan M.; Li, Yaqin; Siddiqui, Faraz
2007-09-01
Transformation invariant image recognition has been an active research area due to its widespread applications in a variety of fields such as military operations, robotics, medical practices, geographic scene analysis, and many others. The primary goal for this research is detection of objects in the presence of image transformations such as changes in resolution, rotation, translation, scale and occlusion. We investigate a biologically-inspired neural network (NN) model for such transformation-invariant object recognition. In a classical training-testing setup for NN, the performance is largely dependent on the range of transformation or orientation involved in training. However, an even more serious dilemma is that there may not be enough training data available for successful learning or even no training data at all. To alleviate this problem, a biologically inspired reinforcement learning (RL) approach is proposed. In this paper, the RL approach is explored for object recognition with different types of transformations such as changes in scale, size, resolution and rotation. The RL is implemented in an adaptive critic design (ACD) framework, which approximates the neuro-dynamic programming of an action network and a critic network, respectively. Two ACD algorithms such as Heuristic Dynamic Programming (HDP) and Dual Heuristic dynamic Programming (DHP) are investigated to obtain transformation invariant object recognition. The two learning algorithms are evaluated statistically using simulated transformations in images as well as with a large-scale UMIST face database with pose variations. In the face database authentication case, the 90° out-of-plane rotation of faces from 20 different subjects in the UMIST database is used. Our simulations show promising results for both designs for transformation-invariant object recognition and authentication of faces. Comparing the two algorithms, DHP outperforms HDP in learning capability, as DHP takes fewer steps to
Scope and applications of translation invariant wavelets to image registration
NASA Technical Reports Server (NTRS)
Chettri, Samir; LeMoigne, Jacqueline; Campbell, William
1997-01-01
The first part of this article introduces the notion of translation invariance in wavelets and discusses several wavelets that have this property. The second part discusses the possible applications of such wavelets to image registration. In the case of registration of affinely transformed images, we would conclude that the notion of translation invariance is not really necessary. What is needed is affine invariance and one way to do this is via the method of moment invariants. Wavelets or, in general, pyramid processing can then be combined with the method of moment invariants to reduce the computational load.
HONTIOR - HIGHER-ORDER NEURAL NETWORK FOR TRANSFORMATION INVARIANT OBJECT RECOGNITION
NASA Technical Reports Server (NTRS)
Spirkovska, L.
1994-01-01
Neural networks have been applied in numerous fields, including transformation invariant object recognition, wherein an object is recognized despite changes in the object's position in the input field, size, or rotation. One of the more successful neural network methods used in invariant object recognition is the higher-order neural network (HONN) method. With a HONN, known relationships are exploited and the desired invariances are built directly into the architecture of the network, eliminating the need for the network to learn invariance to transformations. This results in a significant reduction in the training time required, since the network needs to be trained on only one view of each object, not on numerous transformed views. Moreover, one hundred percent accuracy is guaranteed for images characterized by the built-in distortions, providing noise is not introduced through pixelation. The program HONTIOR implements a third-order neural network having invariance to translation, scale, and in-plane rotation built directly into the architecture, Thus, for 2-D transformation invariance, the network needs only to be trained on just one view of each object. HONTIOR can also be used for 3-D transformation invariant object recognition by training the network only on a set of out-of-plane rotated views. Historically, the major drawback of HONNs has been that the size of the input field was limited to the memory required for the large number of interconnections in a fully connected network. HONTIOR solves this problem by coarse coding the input images (coding an image as a set of overlapping but offset coarser images). Using this scheme, large input fields (4096 x 4096 pixels) can easily be represented using very little virtual memory (30Mb). The HONTIOR distribution consists of three main programs. The first program contains the training and testing routines for a third-order neural network. The second program contains the same training and testing procedures as the
Shi, Yan; Yang, Xiaoyuan; Guo, Yuhua
2014-01-01
This paper is devoted to the study of a directional lifting transform for wavelet frames. A nonsubsampled lifting structure is developed to maintain the translation invariance as it is an important property in image denoising. Then, the directionality of the lifting-based tight frame is explicitly discussed, followed by a specific translation invariant directional framelet transform (TIDFT). The TIDFT has two framelets ψ1, ψ2 with vanishing moments of order two and one respectively, which are able to detect singularities in a given direction set. It provides an efficient and sparse representation for images containing rich textures along with properties of fast implementation and perfect reconstruction. In addition, an adaptive block-wise orientation estimation method based on Gabor filters is presented instead of the conventional minimization of residuals. Furthermore, the TIDFT is utilized to exploit the capability of image denoising, incorporating the MAP estimator for multivariate exponential distribution. Consequently, the TIDFT is able to eliminate the noise effectively while preserving the textures simultaneously. Experimental results show that the TIDFT outperforms some other frame-based denoising methods, such as contourlet and shearlet, and is competitive to the state-of-the-art denoising approaches. PMID:24215934
NASA Astrophysics Data System (ADS)
Gundreddy, Rohith Reddy; Tan, Maxine; Qui, Yuchen; Zheng, Bin
2015-03-01
The purpose of this study is to develop and test a new content-based image retrieval (CBIR) scheme that enables to achieve higher reproducibility when it is implemented in an interactive computer-aided diagnosis (CAD) system without significantly reducing lesion classification performance. This is a new Fourier transform based CBIR algorithm that determines image similarity of two regions of interest (ROI) based on the difference of average regional image pixel value distribution in two Fourier transform mapped images under comparison. A reference image database involving 227 ROIs depicting the verified soft-tissue breast lesions was used. For each testing ROI, the queried lesion center was systematically shifted from 10 to 50 pixels to simulate inter-user variation of querying suspicious lesion center when using an interactive CAD system. The lesion classification performance and reproducibility as the queried lesion center shift were assessed and compared among the three CBIR schemes based on Fourier transform, mutual information and Pearson correlation. Each CBIR scheme retrieved 10 most similar reference ROIs and computed a likelihood score of the queried ROI depicting a malignant lesion. The experimental results shown that three CBIR schemes yielded very comparable lesion classification performance as measured by the areas under ROC curves with the p-value greater than 0.498. However, the CBIR scheme using Fourier transform yielded the highest invariance to both queried lesion center shift and lesion size change. This study demonstrated the feasibility of improving robustness of the interactive CAD systems by adding a new Fourier transform based image feature to CBIR schemes.
Pan, W; Coatrieux, G; Cuppens, N; Cuppens, F; Roux, Ch
2010-01-01
In this article, we propose a new additive lossless watermarking scheme which identifies parts of the image that can be reversibly watermarked and conducts message embedding in the conventional Haar wavelet transform coefficients. Our approach makes use of an approximation of the image signal that is invariant to the watermark addition for classifying the image in order to avoid over/underflows. The method has been tested on different sets of medical images and some usual natural test images as Lena. Experimental result analysis conducted with respect to several aspects including data hiding capacity and image quality preservation, shows that our method is one of the most competitive existing lossless watermarking schemes in terms of high capacity and low distortion. PMID:21096246
CT image noise reduction using rotational-invariant feature in Stockwell transform
NASA Astrophysics Data System (ADS)
Su, Jian; Li, Zhoubo; Yu, Lifeng; Warner, Joshua; Blezek, Daniel; Erickson, Bradley
2014-03-01
Iterative reconstruction and other noise reduction methods have been employed in CT to improve image quality and to reduce radiation dose. The non-local means (NLM) filter emerges as a popular choice for image-based noise reduction in CT. However, the original NLM method cannot incorporate similar structures if they are in a rotational format, resulting in ineffective denoising in some locations of the image and non-uniform noise reduction across the image. We have developed a novel rotational-invariant image texture feature derived from the multiresolutional Stockwell-transform (ST), and applied it to CT image noise reduction so that similar structures can be identified and fully utilized even when they are in different orientations. We performed a computer simulation study in CT to demonstrate better efficiency in terms of utilizing redundant information in the image and more uniform noise reduction achieved by ST than by NLM.
Promoting rotational-invariance in object recognition despite experience with only a single view.
Soto, Fabian A; Wasserman, Edward A
2016-02-01
Different processes are assumed to underlie invariant object recognition across affine transformations, such as changes in size, and non-affine transformations, such as rotations in depth. From this perspective, promoting invariant object recognition across rotations in depth requires visual experience with the object from multiple viewpoints. One learning mechanism potentially contributing to invariant recognition is the error-driven learning of associations between relatively view-invariant visual properties and motor responses or object labels. This account uniquely predicts that experience with affine transformations of a single object view may also promote view-invariance, if view-invariant properties are also invariant across such affine transformations. We empirically confirmed this prediction in both people and pigeons, thereby suggesting that: (a) the hypothesized mechanism participates in view-invariance learning, (b) this mechanism is present across distantly-related vertebrates, and (c) the distinction between affine and non-affine transformations may not be fundamental for biological visual systems, as previously assumed. PMID:26608549
Lemeshewsky, G.P.
2002-01-01
Enhanced false color images from mid-IR, near-IR (NIR), and visible bands of the Landsat thematic mapper (TM) are commonly used for visually interpreting land cover type. Described here is a technique for sharpening or fusion of NIR with higher resolution panchromatic (Pan) that uses a shift-invariant implementation of the discrete wavelet transform (SIDWT) and a reported pixel-based selection rule to combine coefficients. There can be contrast reversals (e.g., at soil-vegetation boundaries between NIR and visible band images) and consequently degraded sharpening and edge artifacts. To improve performance for these conditions, I used a local area-based correlation technique originally reported for comparing image-pyramid-derived edges for the adaptive processing of wavelet-derived edge data. Also, using the redundant data of the SIDWT improves edge data generation. There is additional improvement because sharpened subband imagery is used with the edge-correlation process. A reported technique for sharpening three-band spectral imagery used forward and inverse intensity, hue, and saturation transforms and wavelet-based sharpening of intensity. This technique had limitations with opposite contrast data, and in this study sharpening was applied to single-band multispectral-Pan image pairs. Sharpening used simulated 30-m NIR imagery produced by degrading the spatial resolution of a higher resolution reference. Performance, evaluated by comparison between sharpened and reference image, was improved when sharpened subband data were used with the edge correlation.
NASA Astrophysics Data System (ADS)
Ayatollahi, Fazael; Raie, Abolghasem A.; Hajati, Farshid
2015-03-01
A new multimodal expression-invariant face recognition method is proposed by extracting features of rigid and semirigid regions of the face which are less affected by facial expressions. Dual-tree complex wavelet transform is applied in one decomposition level to extract the desired feature from range and intensity images by transforming the regions into eight subimages, consisting of six band-pass subimages to represent face details and two low-pass subimages to represent face approximates. The support vector machine has been used to classify both feature fusion and score fusion modes. To test the algorithm, BU-3DFE and FRGC v2.0 datasets have been selected. The BU-3DFE dataset was tested by low intensity versus high intensity and high intensity versus low intensity strategies using all expressions in both training and testing stages in different levels. Findings include the best rank-1 identification rate of 99.8% and verification rate of 100% at a 0.1% false acceptance rate. The FRGC v2.0 was tested by the neutral versus non-neutral strategy, which applies images without expression in training and with expression in the testing stage, thereby achieving the best rank-1 identification rate of 93.5% and verification rate of 97.4% at a 0.1% false acceptance rate.
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
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
Construction of panoramic image mosaics based on affine transform and graph cut
NASA Astrophysics Data System (ADS)
Wang, Haiying; Qin, Kaihuai
2010-08-01
Image-based rendering has been a popular technique to simulate a visually rich telepresence and virtual reality experience. The construction of panoramic image mosaics is an indispensable step in image-based rendering systems like QuickTime VR and Surround Video. The conventional methods for creating panoramic image mosaics with regular photographic or video images use geometrical feature points and optimization to the overlapped areas of the two consecutive images, and then align and mosaic the corresponding areas using the blending or stitching algorithm. This paper introduces a novel and efficient method to build panoramic image mosaics. The proposed method divides the overlapped areas of the consecutive images into several sub-areas. The feature point, whose gradient value of intensity is the maximum in the sub-area can be found easily. After selecting these feature points, we warp the images using an affine transformation based on point set matching. Then the graph cut algorithm is used to build the seamless image mosaic which makes the overlapped areas containing no visible ghosting or blurred details. It is shown by the experiments that the new method can obtain mosaics of high quality and reduce the computing time.
Rusydi, Muhammad Ilhamdi; Sasaki, Minoru; Ito, Satoshi
2014-01-01
Biosignals will play an important role in building communication between machines and humans. One of the types of biosignals that is widely used in neuroscience are electrooculography (EOG) signals. An EOG has a linear relationship with eye movement displacement. Experiments were performed to construct a gaze motion tracking method indicated by robot manipulator movements. Three operators looked at 24 target points displayed on a monitor that was 40 cm in front of them. Two channels (Ch1 and Ch2) produced EOG signals for every single eye movement. These signals were converted to pixel units by using the linear relationship between EOG signals and gaze motion distances. The conversion outcomes were actual pixel locations. An affine transform method is proposed to determine the shift of actual pixels to target pixels. This method consisted of sequences of five geometry processes, which are translation-1, rotation, translation-2, shear and dilatation. The accuracy was approximately 0.86° ± 0.67° in the horizontal direction and 0.54° ± 0.34° in the vertical. This system successfully tracked the gaze motions not only in direction, but also in distance. Using this system, three operators could operate a robot manipulator to point at some targets. This result shows that the method is reliable in building communication between humans and machines using EOGs. PMID:24919013
A tale of two paralogs: human Transformer2 proteins with differential RNA-binding affinities.
Ghosh, Pritha; Grellscheid, Sushma Nagaraja; Sowdhamini, R
2016-09-01
The Transformer2 (Tra2) proteins in humans are homologues of the Drosophila Tra2 protein. One of the two RNA-binding paralogs, Tra2β, has been very well-studied over the past decade, but not much is known about Tra2α. It was very recently shown that the two proteins demonstrate the phenomenon of paralog compensation. Here, we provide a structural basis for this genetic backup circuit, using molecular modelling and dynamics studies. We show that the two proteins display similar binding specificities, but differential affinities to a short GAA-rich RNA stretch. Starting from the 6-nucleotide RNA in the solution structure, close to 4000 virtual mutations were modelled on RNA and the domain-RNA interactions were studied after energy minimisation to convergence. Separately, another known 13-nucleotide stretch was docked and the domain-RNA interactions were observed through a 100-ns dynamics trajectory. We have also demonstrated the 'compensatory' mechanism at the level of domains in one of the domain repeat-containing RNA-binding proteins. PMID:26414300
Action as an invariant of Bäcklund transformations for Lagrangian systems
NASA Astrophysics Data System (ADS)
Marikhin, V. G.
2015-07-01
We construct a general theory of Bäcklund transformations for Lagrangian systems under the condition that the action is preserved by these transformations. We discuss the known Bäcklund transformations for classical soliton equations from the standpoint of this approach and obtain a new Bäcklund transformation for the Tzitzéica equation.
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.
Pejler, G; David, G
1987-01-01
Basement-membrane proteoglycans, biosynthetically labelled with [35S]sulphate, were isolated from normal and transformed mouse mammary epithelial cells. Proteoglycans synthesized by normal cells contained mainly heparan sulphate and, in addition, small amounts of chondroitin sulphate chains, whereas transformed cells synthesized a relatively higher proportion of chondroitin sulphate. Polysaccharide chains from transformed cells were of lower average Mr and of lower anionic charge density compared with chains isolated from the untransformed counterparts, confirming results reported previously [David & Van den Berghe (1983) J. Biol. Chem. 258, 7338-7344]. A large proportion of the chains isolated from normal cells bound with high affinity to immobilized antithrombin, and the presence of 3-O-sulphated glucosamine residues, previously identified as unique markers for the antithrombin-binding region of heparin [Lindahl, Bäckström, Thunberg & Leder (1980) Proc. Natl. Acad. Sci. U.S.A. 77, 6551-6555], could be demonstrated. A significantly lower proportion of the chains derived from transformed cells bound with high affinity to antithrombin, and a corresponding decrease in the amount of incorporated 3-O-sulphate was observed. PMID:2963617
Minimal information to determine affine shape equivalence.
Wagemans, J; Van Gool, L; Lamote, C; Foster, D H
2000-04-01
Participants judged the affine equivalence of 2 simultaneously presented 4-point patterns. Performance level (d') varied between 1.5 and 2.7, depending on the information available for solving the correspondence problem (insufficient in Experiment 1a, superfluous in Experiment 1b, and minimal in Experiments 1c, 2a, 2b) and on the exposure time (unlimited in Experiments 1 and 2a and 500 ms in Experiment 2b), but it did not vary much with the complexity of the affine transformation (rotation and slant in Experiment 1 and same plus tilt in Experiment 2). Performance in Experiment 3 was lower with 3-point patterns than with 4-point patterns, whereas blocking the trials according to the affine transformation parameters had little effect. Determining affine shape equivalence with minimal-information displays is based on a fast assessment of qualitatively or quasi-invariant properties such as convexity/ concavity, parallelism, and collinearity. PMID:10811156
Parker, Sarah M.; Serre, Thomas
2015-01-01
Non-accidental properties (NAPs) correspond to image properties that are invariant to changes in viewpoint (e.g., straight vs. curved contours) and are distinguished from metric properties (MPs) that can change continuously with in-depth object rotation (e.g., aspect ratio, degree of curvature, etc.). Behavioral and electrophysiological studies of shape processing have demonstrated greater sensitivity to differences in NAPs than in MPs. However, previous work has shown that such sensitivity is lacking in multiple-views models of object recognition such as Hmax. These models typically assume that object processing is based on populations of view-tuned neurons with distributed symmetrical bell-shaped tuning that are modulated at least as much by differences in MPs as in NAPs. Here, we test the hypothesis that unsupervised learning of invariances to object transformations may increase the sensitivity to differences in NAPs vs. MPs in Hmax. We collected a database of video sequences with objects slowly rotating in-depth in an attempt to mimic sequences viewed during object manipulation by young children during early developmental stages. We show that unsupervised learning yields shape-tuning in higher stages with greater sensitivity to differences in NAPs vs. MPs in agreement with monkey IT data. Together, these results suggest that greater NAP sensitivity may arise from experiencing different in-depth rotations of objects. PMID:26500528
Adetiba, Emmanuel; Olugbara, Oludayo O.
2015-01-01
Lung cancer is one of the diseases responsible for a large number of cancer related death cases worldwide. The recommended standard for screening and early detection of lung cancer is the low dose computed tomography. However, many patients diagnosed die within one year, which makes it essential to find alternative approaches for screening and early detection of lung cancer. We present computational methods that can be implemented in a functional multi-genomic system for classification, screening and early detection of lung cancer victims. Samples of top ten biomarker genes previously reported to have the highest frequency of lung cancer mutations and sequences of normal biomarker genes were respectively collected from the COSMIC and NCBI databases to validate the computational methods. Experiments were performed based on the combinations of Z-curve and tetrahedron affine transforms, Histogram of Oriented Gradient (HOG), Multilayer perceptron and Gaussian Radial Basis Function (RBF) neural networks to obtain an appropriate combination of computational methods to achieve improved classification of lung cancer biomarker genes. Results show that a combination of affine transforms of Voss representation, HOG genomic features and Gaussian RBF neural network perceptibly improves classification accuracy, specificity and sensitivity of lung cancer biomarker genes as well as achieving low mean square error. PMID:26625358
Radon transform, bispectra, and principal component analysis for RTS invariant image retrieval
NASA Astrophysics Data System (ADS)
Shao, Yuan; Celenk, Mehmet
1999-08-01
An image retrieval method is presented based on shape similarity measure for multimedia and imaging database system. In the proposed algorithm, the spatial and spectral properties of images are combined using the Radon transform, bispectra, and principal components analysis. For each model image in the database, the original 2D image data are reduced to a set of 1D projections via the Radon transform, and then a feature vector is calculated from the bispectra of the resultant 1D functions. The principal component analysis is applied to further reduce the dimension of the feature vector so that it can be stored along with the original image in the database at a small cost of memory. The derived feature vector is considered as the index or key of the corresponding image, which uniquely identifies the image independent of rotation, translation, and scaling. For image retrieval, the data feature vector is computed for a query image, and matched against the feature vectors of all the model images in the database using the Tanimoto similarity measure. The closely matching images are brought out as the searching results. The proposed technique has been tested on a large image database. The experimental results show that the retrieval accuracy is very high even for query images with low signal-to-noise ratio.
Hazarika, P.; Pardue, R.L.; Earls, R.; Dedman, J.R.
1987-04-07
Monospecific antibodies were generated against each of six different peptide sequences derived from rat and human ..cap alpha..-transforming growth factor (..cap alpha..-TGF). The affinity-purified antibody to the 17 amino acid carboxyl-terminal portion of the molecule proved most useful in detecting ..cap alpha..-TGF. When used in a peptide-based radioimmunoassay, it was possible to measure nanogram quantities of native ..cap alpha..-TGF in conditioned cell culture media. When used to analyze cell lysate, these antibodies specifically recognized a 21-kilodalton protein species. Indirect immunofluorescence localization procedures revealed a high concentration of ..cap alpha..-TCF in a perinuclear ring with a diffuse cytoplasmic distribution. These results suggest that a precursor form of ..cap alpha..-TGF has a cellular role beyond that of an autocrine growth factor.
Sang-Aroon, Wichien; Ruangpornvisuti, Vithaya; Amornkitbamrung, Vittaya
2016-05-01
The gas-phase geometry optimizations of bare, mono- and dihydrated complexes of temozolomide isomers were carried out using density functional calculation at the M06-2X/6-31+G(d,p) level of the theory. The structures and protonation energies of protonated species of temozolomide are reported. Chemical indices of all isomers and protonated species are also reported. Energies, thermodynamic quantities, rate constants and equilibrium constants of tautomeric and rotameric transformations of all isomers I1↔TZM↔HIa↔HIb↔I2↔I3 in bare and hydrated systems were obtained. PMID:27041447
NASA Astrophysics Data System (ADS)
Mishra, D. C.; Sharma, R. K.; Dawar, Mayank; Hanmandlu, M.
2015-09-01
In this cryptosystem, we have presented a novel technique for security of video data by using matrix affine cipher (MAC) combined with two-dimensional discrete wavelet transform (2D-DWT). Existing schemes for security of video data provides only one layer of security, but the presented technique provides two layers of security for video data. In this cryptosystem, keys and arrangement of MAC parameters are imperative for decryption process. In this cryptosystem, if the attacker knows about all the exact keys, but has no information about the specific arrangement of MAC parameters, then the information of original video cannot be recovered from the encrypted video. Experimental results on standard examples support to the robustness and appropriateness of the presented cryptosystem of video encryption and decryption. The statistical analysis of the experimental results based on standard examples critically examine the behavior of the proposed technique. Comparison between existing schemes for security of video with the presented cryptosystem is also provided for the robustness of the proposed cryptosystem.
Bengtsson, Henrik; Hössjer, Ola
2006-01-01
Background Low-level processing and normalization of microarray data are most important steps in microarray analysis, which have profound impact on downstream analysis. Multiple methods have been suggested to date, but it is not clear which is the best. It is therefore important to further study the different normalization methods in detail and the nature of microarray data in general. Results A methodological study of affine models for gene expression data is carried out. Focus is on two-channel comparative studies, but the findings generalize also to single- and multi-channel data. The discussion applies to spotted as well as in-situ synthesized microarray data. Existing normalization methods such as curve-fit ("lowess") normalization, parallel and perpendicular translation normalization, and quantile normalization, but also dye-swap normalization are revisited in the light of the affine model and their strengths and weaknesses are investigated in this context. As a direct result from this study, we propose a robust non-parametric multi-dimensional affine normalization method, which can be applied to any number of microarrays with any number of channels either individually or all at once. A high-quality cDNA microarray data set with spike-in controls is used to demonstrate the power of the affine model and the proposed normalization method. Conclusion We find that an affine model can explain non-linear intensity-dependent systematic effects in observed log-ratios. Affine normalization removes such artifacts for non-differentially expressed genes and assures that symmetry between negative and positive log-ratios is obtained, which is fundamental when identifying differentially expressed genes. In addition, affine normalization makes the empirical distributions in different channels more equal, which is the purpose of quantile normalization, and may also explain why dye-swap normalization works or fails. All methods are made available in the aroma package, which is
Invariance of visual operations at the level of receptive fields.
Lindeberg, Tony
2013-01-01
The brain is able to maintain a stable perception although the visual stimuli vary substantially on the retina due to geometric transformations and lighting variations in the environment. This paper presents a theory for achieving basic invariance properties already at the level of receptive fields. Specifically, the presented framework comprises (i) local scaling transformations caused by objects of different size and at different distances to the observer, (ii) locally linearized image deformations caused by variations in the viewing direction in relation to the object, (iii) locally linearized relative motions between the object and the observer and (iv) local multiplicative intensity transformations caused by illumination variations. The receptive field model can be derived by necessity from symmetry properties of the environment and leads to predictions about receptive field profiles in good agreement with receptive field profiles measured by cell recordings in mammalian vision. Indeed, the receptive field profiles in the retina, LGN and V1 are close to ideal to what is motivated by the idealized requirements. By complementing receptive field measurements with selection mechanisms over the parameters in the receptive field families, it is shown how true invariance of receptive field responses can be obtained under scaling transformations, affine transformations and Galilean transformations. Thereby, the framework provides a mathematically well-founded and biologically plausible model for how basic invariance properties can be achieved already at the level of receptive fields and support invariant recognition of objects and events under variations in viewpoint, retinal size, object motion and illumination. The theory can explain the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, from a requirement that the
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.
Measuring polynomial invariants of multiparty quantum states
Leifer, M.S.; Linden, N.; Winter, A.
2004-05-01
We present networks for directly estimating the polynomial invariants of multiparty quantum states under local transformations. The structure of these networks is closely related to the structure of the invariants themselves and this lends a physical interpretation to these otherwise abstract mathematical quantities. Specifically, our networks estimate the invariants under local unitary (LU) transformations and under stochastic local operations and classical communication (SLOCC). Our networks can estimate the LU invariants for multiparty states, where each party can have a Hilbert space of arbitrary dimension and the SLOCC invariants for multiqubit states. We analyze the statistical efficiency of our networks compared to methods based on estimating the state coefficients and calculating the invariants.
A novel image compression algorithm based on the biorthogonal invariant set multiwavelet
NASA Astrophysics Data System (ADS)
Li, Yongjun; Li, Yunsong; Liu, Weijia
2015-05-01
On the basis of the theory of the biorthogonal invariant set multiwavelets (BISM) which is established by Micchelli and Xu, a biorthogonal invariant set multi-wavelets (BISM) filter is designed and the algorithms of decomposition and reconstruction of this filter are given in this paper, and it has many characteristics, such as symmetry, compact support, orthogonality and low complexity. In this filter, the self-affine triangle domain is as support interval, and constant function is as scaling function. Advantages such as low algorithm complexity, the energy and entropy in high concentration after transformation, no blocking effect to facilitate parallel computing are analyzed when the biorthogonal invariant sets multiwavelet (BISM) filters are used image compression. Finally, the validity of image compression algorithm based on biorthogonal invariant set multiwavelet is verified by the approximate JPEG2000 framework.
NASA Astrophysics Data System (ADS)
Fan, X.; Liang, M.; Yeap, T.
2009-08-01
In-line oil debris sensors are important devices for the detection of machinery failures. However, two key issues remain to be addressed to more effectively make use of the existing oil debris sensors: the responsiveness to early machine failures and false alarms. The responsiveness level depends on the size of the debris that can be detected by an oil debris sensor. The detectable particle size in turn is mainly limited by the background noise. The false alarms are often caused by spurious impulses such as vibration-like signals. The challenge of improving the responsiveness and reducing false alarms lies in the very weak particle signals and their similarity to spurious signals. In this paper, a joint time-invariant wavelet transform and kurtosis analysis method is proposed to address the two issues simultaneously. The proposed method has been tested by extracting signatures of ultra-small metal particles from background noise and a wide range of simulated vibration-like and real vibration signals. Our test results have demonstrated that the proposed method can effectively detect very weak particle signals buried in strong background noise and eliminate vibration-like spurious signals. The implementation of the proposed method will substantially enhance many existing oil debris sensors. Patent pending (application number: 12/235,008, Countries: US and Canada).
ERIC Educational Resources Information Center
Gray, Gary R.
1980-01-01
Presents selected recent advances in immobilization chemistry which have important connections to affinity chromatography. Discusses ligand immobilization and support modification. Cites 51 references. (CS)
Avoiding degenerate coframes in an affine gauge approach to quantum gravity
Mielke, E.W.; McCrea, J.D.; Ne`eman, Y.; Hehl, F.W.
1993-04-01
This report discusses the following concepts on quantum gravity: The affine gauge approach; affine gauge transformations versus active differomorphisms; affine gauge approach to quantum gravity with topology change.
Tractors, mass, and Weyl invariance
NASA Astrophysics Data System (ADS)
Gover, A. R.; Shaukat, A.; Waldron, A.
2009-05-01
Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describe massive and gauge invariant theories using Weyl invariance. The key idea is to introduce a new scalar field which is constant when evaluated at the scale corresponding to the metric of physical interest. This technique relies on being able to efficiently construct Weyl invariant theories. This is achieved using tractor calculus—a mathematical machinery designed for the study of conformal geometry. From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws. Our approach gives a mechanism for generating masses from Weyl weights. Breitenlohner-Freedman stability bounds for Anti-de Sitter theories arise naturally as do direct derivations of the novel Weyl invariant theories given by Deser and Nepomechie. In constant curvature spaces, partially massless theories—which rely on the interplay between mass and gauge invariance—are also generated by our method. Another simple consequence is conformal invariance of the maximal depth partially massless theories. Detailed examples for spins s⩽2 are given including tractor and component actions, on-shell and off-shell approaches and gauge invariances. For all spins s⩾2 we give tractor equations of motion unifying massive, massless, and partially massless theories.
NASA Astrophysics Data System (ADS)
Kobayashi, Tatsuo; Nitta, Daisuke; Urakawa, Yuko
2016-08-01
Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field T whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by T. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential Vht, but it also has a non-negligible deviation from Vht. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still possible to falsify this model by combining the information in the reheating process which can be determined self-completely in this setup.
Rotation Invariant Vortices for Flow Visualization.
Günther, Tobias; Schulze, Maik; Theisel, Holger
2016-01-01
We propose a new class of vortex definitions for flows that are induced by rotating mechanical parts, such as stirring devices, helicopters, hydrocyclones, centrifugal pumps, or ventilators. Instead of a Galilean invariance, we enforce a rotation invariance, i.e., the invariance of a vortex under a uniform-speed rotation of the underlying coordinate system around a fixed axis. We provide a general approach to transform a Galilean invariant vortex concept to a rotation invariant one by simply adding a closed form matrix to the Jacobian. In particular, we present rotation invariant versions of the well-known Sujudi-Haimes, Lambda-2, and Q vortex criteria. We apply them to a number of artificial and real rotating flows, showing that for these cases rotation invariant vortices give better results than their Galilean invariant counterparts. PMID:26390472
Affine hypersurfaces with parallel difference tensor relative to affine α-connection
NASA Astrophysics Data System (ADS)
Li, Cece
2014-12-01
Li and Zhang (2014) studied affine hypersurfaces of R n + 1 with parallel difference tensor relative to the affine α-connection ∇ (α), and characterized the generalized Cayley hypersurfaces by K n - 1 ≠ 0 and ∇ (α) K = 0 for some nonzero constant α, where the affine α-connection ∇ (α) of information geometry was introduced on affine hypersurface. In this paper, by a slightly different method we continue to study affine hypersurfaces with ∇ (α) K = 0, if α = 0 we further assume that the Pick invariant vanishes and affine metric is of constant sectional curvature. It is proved that they are either hyperquadrics or improper affine hypersphere with flat indefinite affine metric, the latter can be locally given as a graph of a polynomial of at most degree n + 1 with constant Hessian determinant. In particular, if the affine metric is definite, Lorentzian, or its negative index is 2, we complete the classification of such hypersurfaces.
Shape invariant potentials in higher dimensions
Sandhya, R.; Sree Ranjani, S.; Kapoor, A.K.
2015-08-15
In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended to arrive at a large class of new shape invariant potentials in arbitrary dimensions. A reformulation of the shape invariance property and possible generalizations are proposed. These may lead to an important extension of the shape invariance property to Hamiltonians that are related to standard potential problems via space time transformations, which are found useful in path integral formulation of quantum mechanics.
Modular invariant partition functions for the doubly extended N = 4 superconformal algebras
NASA Astrophysics Data System (ADS)
Ooguri, Hirosi; Petersen, Jens Lyng; Taormina, Anne
1992-01-01
Non-trivial modular properties of characters of the doubly extended N = 4 superconformal algebras Aγ, Ãγ are derived from two different points of view. First, we use realizations on Wolf spaces, in particular when one of the levels of the two commuting affine SU(2) subalgebras takes the value 2. We emphasize how these realizations involve rational torus theories, and how some specific combinations of massless characters transform under the modular group as affine SU(2) characters. Second, we show how these combinations, and generalizations thereof, emerge from a study of the explicit form of the characters when angular variables are partly restricted, but the levels are not. The two results are then combined to give stringent constraints on the modular invariant Ãγ partition functions and they give rise to a partial classification of the latter, closely related to that of affine SU(2).
Compact noncontraction semigroups of affine operators
NASA Astrophysics Data System (ADS)
Voynov, A. S.; Protasov, V. Yu
2015-07-01
We analyze compact multiplicative semigroups of affine operators acting in a finite-dimensional space. The main result states that every such semigroup is either contracting, that is, contains elements of arbitrarily small operator norm, or all its operators share a common invariant affine subspace on which this semigroup is contracting. The proof uses functional difference equations with contraction of the argument. We look at applications to self-affine partitions of convex sets, the investigation of finite affine semigroups and the proof of a criterion of primitivity for nonnegative matrix families. Bibliography: 32 titles.
Renormalization for breakup of invariant tori
NASA Astrophysics Data System (ADS)
Apte, A.; Wurm, A.; Morrison, P. J.
2005-01-01
We present renormalization group operators for the breakup of invariant tori with winding numbers that are quadratic irrationals. We find the simple fixed points of these operators and interpret the map pairs with critical invariant tori as critical fixed points. Coordinate transformations on the space of maps relate these fixed points, and also induce conjugacies between the corresponding operators.
LACKS,S.A.
2003-10-09
Transformation, which alters the genetic makeup of an individual, is a concept that intrigues the human imagination. In Streptococcus pneumoniae such transformation was first demonstrated. Perhaps our fascination with genetics derived from our ancestors observing their own progeny, with its retention and assortment of parental traits, but such interest must have been accelerated after the dawn of agriculture. It was in pea plants that Gregor Mendel in the late 1800s examined inherited traits and found them to be determined by physical elements, or genes, passed from parents to progeny. In our day, the material basis of these genetic determinants was revealed to be DNA by the lowly bacteria, in particular, the pneumococcus. For this species, transformation by free DNA is a sexual process that enables cells to sport new combinations of genes and traits. Genetic transformation of the type found in S. pneumoniae occurs naturally in many species of bacteria (70), but, initially only a few other transformable species were found, namely, Haemophilus influenzae, Neisseria meningitides, Neisseria gonorrheae, and Bacillus subtilis (96). Natural transformation, which requires a set of genes evolved for the purpose, contrasts with artificial transformation, which is accomplished by shocking cells either electrically, as in electroporation, or by ionic and temperature shifts. Although such artificial treatments can introduce very small amounts of DNA into virtually any type of cell, the amounts introduced by natural transformation are a million-fold greater, and S. pneumoniae can take up as much as 10% of its cellular DNA content (40).
Homotopy invariance of η-invariants
Weinberger, Shmuel
1988-01-01
Intersection homology and results related to the higher signature problem are applied to show that certain combinations of η-invariants of the signature operator are homotopy invariant in various circumstances. PMID:16593961
Topological invariants and renormalization of Lorenz maps
NASA Astrophysics Data System (ADS)
Silva, Luis; Sousa Ramos, J.
2002-02-01
We prove that the invariants of the topological semiconjugation of Lorenz maps with β-transformations remains constant on the renormalization archipelagoes and analyze how the dynamics on the archipelagoes depends on its structure.
Baker, W.R.
1959-08-25
Transformers of a type adapted for use with extreme high power vacuum tubes where current requirements may be of the order of 2,000 to 200,000 amperes are described. The transformer casing has the form of a re-entrant section being extended through an opening in one end of the cylinder to form a coaxial terminal arrangement. A toroidal multi-turn primary winding is disposed within the casing in coaxial relationship therein. In a second embodiment, means are provided for forming the casing as a multi-turn secondary. The transformer is characterized by minimized resistance heating, minimized external magnetic flux, and an economical construction.
Invariant length of a cosmic string
NASA Astrophysics Data System (ADS)
Anderson, Malcolm R.
1990-06-01
The world sheet of a cosmic string is characterized by a function l, invariant under both coordinate and gauge transformations, which can be interpreted as the ``invariant length'' of the string. In flat space, l reduces to the invariant length of Vachaspati and Vilenkin, and gives an upper bound for the actual length of the string, and a lower bound for its energy, as measured by any inertial observer. In curved spacetime, time variations in the invariant length divide naturally into two parts: one due to the tidal tensor at points exterior to the world sheet and one due to the tidal tensor at points on the world sheet itself.
NASA Astrophysics Data System (ADS)
Gonçalves, Bruno; Dias Júnior, Mário M.; Ribeiro, Baltazar J.
2014-10-01
The exact Foldy-Wouthuysen transformation is performed in order to study the Dirac field interacting with many possible external fields associated with C P T -Lorentz violation. We also derived the calculation of equations of motion as well as the generalized Lorentz force corrected by the mentioned external fields. The main point is the interaction between the Dirac particle and the terms that have the multiplication of the electromagnetic field and the terms that break C P T -Lorentz. Finally, with the transformed Hamiltonian we were able to write an expression for the bound state of the theory and analyze it in the atomic experiments context. This result is an analytical expression that gives the possibility of the weakness of C P T -Lorentz terms to be compensated by the presence of a strong magnetic field.
Invariance of the Noether charge
NASA Astrophysics Data System (ADS)
Silagadze, Z. K.
2016-01-01
Surprisingly, an interesting property of the Noether charge that it is by itself invariant under the corresponding symmetry transformation is never discussed in quantum field theory or classical mechanics textbooks we have checked. This property is also almost never mentioned in articles devoted to Noether’s theorem. Nevertheless, to prove this property in the context of Lagrangian formalism is not quite trivial and the proof, outlined in this article, can constitute an useful and interesting exercise for students.
Affine Contractions on the Plane
ERIC Educational Resources Information Center
Celik, D.; Ozdemir, Y.; Ureyen, M.
2007-01-01
Contractions play a considerable role in the theory of fractals. However, it is not easy to find contractions which are not similitudes. In this study, it is shown by counter examples that an affine transformation of the plane carrying a given triangle onto another triangle may not be a contraction even if it contracts edges, heights or medians.…
Relativistic chaos is coordinate invariant.
Motter, Adilson E
2003-12-01
The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion regarding the noninvariance of chaos in cosmology, a major claim about chaos in general relativity, necessarily involves the violation of hypotheses required for a proper definition of the Lyapunov exponents. PMID:14683170
Geometric invariance of compressible turbulent boundary layers
NASA Astrophysics Data System (ADS)
Bi, Wei-Tao; Wu, Bin; She, Zhen-Su; Hussain, Fazle
2015-11-01
A symmetry based approach is applied to analyze the mean velocity and temperature fields of compressible, flat plate turbulent boundary layers (CTBL). A Reynolds stress length scale and a turbulent heat flux length scale are identified to possess the same defect scaling law in the CTBL bulk, which is solely owing to the constraint of the wall to the geometry of the wall-attached eddies, but invariant to compressibility and wall heat transfer. This invariance is called the geometric invariance of CTBL eddies and is likely the origin of the Mach number invariance of Morkovin's hypothesis, as well as the similarity of energy and momentum transports. A closure for the turbulent transport by using the invariant lengths is attainted to predict the mean velocity and temperature profiles in the CTBL bulk- superior to the van Driest transformation and the Reynolds analogy based relations for its sound physics and higher accuracy. Additionally, our approach offers a new understanding of turbulent Prandtl number.
Generalizing twisted gauge invariance
Duenas-Vidal, Alvaro; Vazquez-Mozo, Miguel A.
2009-05-01
We discuss the twisting of gauge symmetry in noncommutative gauge theories and show how this can be generalized to a whole continuous family of twisted gauge invariances. The physical relevance of these twisted invariances is discussed.
NASA Astrophysics Data System (ADS)
Bihlo, Alexander; Dos Santos Cardoso-Bihlo, Elsa Maria; Nave, Jean-Christophe; Popovych, Roman
2012-11-01
Various subgrid-scale closure models break the invariance of the Euler or Navier-Stokes equations and thus violate the geometric structure of these equations. A method is shown which allows one to systematically derive invariant turbulence models starting from non-invariant turbulence models and thus to correct artificial symmetry-breaking. The method is illustrated by finding invariant hyperdiffusion schemes to be applied in the two-dimensional turbulence problem.
Report: Affinity Chromatography.
ERIC Educational Resources Information Center
Walters, Rodney R.
1985-01-01
Supports, affinity ligands, immobilization, elution methods, and a number of applications are among the topics considered in this discussion of affinity chromatography. An outline of the basic principles of affinity chromatography is included. (JN)
Fermions in gravity with local spin-base invariance
NASA Astrophysics Data System (ADS)
Gies, Holger; Lippoldt, Stefan
2014-03-01
We study a formulation of Dirac fermions in curved spacetime that respects general coordinate invariance as well as invariance under local spin-base transformations. The natural variables for this formulation are spacetime-dependent Dirac matrices subject to the Clifford-algebra constraint. In particular, a coframe, i.e. vierbein field is not required. The corresponding affine spin connection consists of a canonical part that is completely fixed in terms of the Dirac matrices and a free part that can be interpreted as spin torsion. A general variation of the Dirac matrices naturally induces a spinorial Lie derivative which coincides with the known Kosmann-Lie derivative in the absence of torsion. Using this formulation for building a field theory of quantized gravity and matter fields, we show that it suffices to quantize the metric and the matter fields. This observation is of particular relevance for field theory approaches to quantum gravity, as it can serve for a purely metric-based quantization scheme for gravity even in the presence of fermions.
A Partial Intensity Invariant Feature Descriptor for Multimodal Retinal Image Registration
Chen, Jian; Tian, Jie; Lee, Noah; Zheng, Jian; Smith, R. Theodore; Laine, Andrew F.
2011-01-01
Detection of vascular bifurcations is a challenging task in multimodal retinal image registration. Existing algorithms based on bifurcations usually fail in correctly aligning poor quality retinal image pairs. To solve this problem, we propose a novel highly distinctive local feature descriptor named partial intensity invariant feature descriptor (PIIFD) and describe a robust automatic retinal image registration framework named Harris-PIIFD. PIIFD is invariant to image rotation, partially invariant to image intensity, affine transformation, and viewpoint/perspective change. Our Harris-PIIFD framework consists of four steps. First, corner points are used as control point candidates instead of bifurcations since corner points are sufficient and uniformly distributed across the image domain. Second, PIIFDs are extracted for all corner points, and a bilateral matching technique is applied to identify corresponding PIIFDs matches between image pairs. Third, incorrect matches are removed and inaccurate matches are refined. Finally, an adaptive transformation is used to register the image pairs. PIIFD is so distinctive that it can be correctly identified even in nonvascular areas. When tested on 168 pairs of multimodal retinal images, the Harris-PIIFD far outperforms existing algorithms in terms of robustness, accuracy, and computational efficiency. PMID:20176538
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
Anisotropic invariance in minisuperspace models
NASA Astrophysics Data System (ADS)
Chagoya, Javier; Sabido, Miguel
2016-06-01
In this paper we introduce invariance under anisotropic transformations to cosmology. This invariance is one of the key ingredients of the theory of quantum gravity at a Lifshitz point put forward by Hořava. We find that this new symmetry in the minisuperspace introduces characteristics to the model that can be relevant in the ultraviolet regime. For example, by canonical quantization we find a Schrödinger-type equation which avoids the problem of frozen time in quantum cosmology. For simple cases we obtain solutions to this quantum equation in a Kantowski–Sachs (KS) minisuperspace. At the classical level, we study KS and Friedmann–Robertson–Walker cosmologies, obtaining modifications to the solutions of general relativity that can be relevant in the early Universe.
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…
Combining local affine frames and SIFT for remote sensing image registration
NASA Astrophysics Data System (ADS)
Sun, Hao; Wang, Cheng; Hao, Shengyong
2009-10-01
Local invariant features such as scale invariant feature transform (SIFT) have received considerable attention in recent years. Despite its tremendous success in computer vision applications, SIFT matching alone is not sufficient for remote sensing image registration because of low detection repeatablility and nonlinear intensity changes. In this paper, we introduce a remote sensing image registration algorithm that combines local affine frames (LAF) together with SIFT matching. Firstly, distinctive SIFT keypoints and maximally stable extremal regions (MSER) are detected independently in the reference image and the sensed image. Contrast reversal invariant SIFT descriptor is constructed for describing texture patches around SIFT keypoints and shape descriptor defined in LAF is constructed for describing MSER contour. Nearest neighbor distance ratio matching with confidence measurement is then adopted to match both descriptors. Tentative correspondences are ranked according to their confidence measurements. Finally, random sample consensus (RANSAC) is performed in the top ranked matched features to obtain a global set of transform parameters. Experimental results demonstrate the robustness and accuracy of the proposed method.
Feature-based affine-Invariant localization of faces.
Hamouz, M; Kittler, J; Kamarainen, J K; Paalanen, P; Kälviäinen, H; Matas, J
2005-09-01
We present a novel method for localizing faces in person identification scenarios. Such scenarios involve high resolution images of frontal faces. The proposed algorithm does not require color, copes well in cluttered backgrounds, and accurately localizes faces including eye centers. An extensive analysis and a performance evaluation on the XM2VTS database and on the realistic BioID and BANCA face databases is presented. We show that the algorithm has precision superior to reference methods. PMID:16173191
Geometric local invariants and pure three-qubit states
Williamson, Mark S.; Ericsson, Marie; Johansson, Markus; Sjoeqvist, Erik; Sudbery, Anthony; Vedral, Vlatko; Wootters, William K.
2011-06-15
We explore a geometric approach to generating local SU(2) and SL(2,C) invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or ''gauge'' invariant is associated with a distinct closed path (or plaquette) joining some or all of the qubits. In lattice gauge theory, the lattice points are the discrete space-time points, the transformations between the points of the lattice are defined by parallel transporters, and the gauge invariant observable associated with a particular closed path is given by the Wilson loop. In our approach the points of the lattice are qubits, the link transformations between the qubits are defined by the correlations between them, and the gauge invariant observable, the local invariants associated with a particular closed path, are also given by a Wilson looplike construction. The link transformations share many of the properties of parallel transporters, although they are not undone when one retraces one's steps through the lattice. This feature is used to generate many of the invariants. We consider a pure three-qubit state as a test case and find we can generate a complete set of algebraically independent local invariants in this way; however, the framework given here is applicable to generating local unitary invariants for mixed states composed of any number of d-level quantum systems. We give an operational interpretation of these invariants in terms of observables.
Geometric local invariants and pure three-qubit states
NASA Astrophysics Data System (ADS)
Williamson, Mark S.; Ericsson, Marie; Johansson, Markus; Sjöqvist, Erik; Sudbery, Anthony; Vedral, Vlatko; Wootters, William K.
2011-06-01
We explore a geometric approach to generating local SU(2) and SL(2,C) invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or “gauge” invariant is associated with a distinct closed path (or plaquette) joining some or all of the qubits. In lattice gauge theory, the lattice points are the discrete space-time points, the transformations between the points of the lattice are defined by parallel transporters, and the gauge invariant observable associated with a particular closed path is given by the Wilson loop. In our approach the points of the lattice are qubits, the link transformations between the qubits are defined by the correlations between them, and the gauge invariant observable, the local invariants associated with a particular closed path, are also given by a Wilson looplike construction. The link transformations share many of the properties of parallel transporters, although they are not undone when one retraces one’s steps through the lattice. This feature is used to generate many of the invariants. We consider a pure three-qubit state as a test case and find we can generate a complete set of algebraically independent local invariants in this way; however, the framework given here is applicable to generating local unitary invariants for mixed states composed of any number of d-level quantum systems. We give an operational interpretation of these invariants in terms of observables.
Stereo matching using epipolar distance transform.
Yang, Qingxiong; Ahuja, Narendra
2012-10-01
In this paper, we propose a simple but effective image transform, called the epipolar distance transform, for matching low-texture regions. It converts image intensity values to a relative location inside a planar segment along the epipolar line, such that pixels in the low-texture regions become distinguishable. We theoretically prove that the transform is affine invariant, thus the transformed images can be directly used for stereo matching. Any existing stereo algorithms can be directly used with the transformed images to improve reconstruction accuracy for low-texture regions. Results on real indoor and outdoor images demonstrate the effectiveness of the proposed transform for matching low-texture regions, keypoint detection, and description for low-texture scenes. Our experimental results on Middlebury images also demonstrate the robustness of our transform for highly textured scenes. The proposed transform has a great advantage, its low computational complexity. It was tested on a MacBook Air laptop computer with a 1.8 GHz Core i7 processor, with a speed of about 9 frames per second for a video graphics array-sized image. PMID:22801509
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.
The dynamics of metric-affine gravity
Vitagliano, Vincenzo; Sotiriou, Thomas P.; Liberati, Stefano
2011-05-15
Highlights: > The role and the dynamics of the connection in metric-affine theories is explored. > The most general second order action does not lead to a dynamical connection. > Including higher order invariants excites new degrees of freedom in the connection. > f(R) actions are also discussed and shown to be a non- representative class. - Abstract: Metric-affine theories of gravity provide an interesting alternative to general relativity: in such an approach, the metric and the affine (not necessarily symmetric) connection are independent quantities. Furthermore, the action should include covariant derivatives of the matter fields, with the covariant derivative naturally defined using the independent connection. As a result, in metric-affine theories a direct coupling involving matter and connection is also present. The role and the dynamics of the connection in such theories is explored. We employ power counting in order to construct the action and search for the minimal requirements it should satisfy for the connection to be dynamical. We find that for the most general action containing lower order invariants of the curvature and the torsion the independent connection does not carry any dynamics. It actually reduces to the role of an auxiliary field and can be completely eliminated algebraically in favour of the metric and the matter field, introducing extra interactions with respect to general relativity. However, we also show that including higher order terms in the action radically changes this picture and excites new degrees of freedom in the connection, making it (or parts of it) dynamical. Constructing actions that constitute exceptions to this rule requires significant fine tuned and/or extra a priori constraints on the connection. We also consider f(R) actions as a particular example in order to show that they constitute a distinct class of metric-affine theories with special properties, and as such they cannot be used as representative toy theories to
Lorentz invariance with an invariant energy scale.
Magueijo, João; Smolin, Lee
2002-05-13
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity. PMID:12005620
Global surpluses of spin-base invariant fermions
NASA Astrophysics Data System (ADS)
Gies, Holger; Lippoldt, Stefan
2015-04-01
The spin-base invariant formalism of Dirac fermions in curved space maintains the essential symmetries of general covariance as well as similarity transformations of the Clifford algebra. We emphasize the advantages of the spin-base invariant formalism both from a conceptual as well as from a practical viewpoint. This suggests that local spin-base invariance should be added to the list of (effective) properties of (quantum) gravity theories. We find support for this viewpoint by the explicit construction of a global realization of the Clifford algebra on a 2-sphere which is impossible in the spin-base non-invariant vielbein formalism.
Perceptual information for the age level of faces as a higher order invariant of growth.
Pittenger, J B; Shaw, R E; Mark, L S
1979-08-01
Previous work supports the hypothesis that cardioidal strain, a nonlinear topological transformation, offers a plausible mathematical model for the perceived global changes in human craniofacial morphology due to growth. Experiment 1 examined the generality of the effect of this growth transformation on relative age judgments by applying it to profiles of a dog, bird, and monkey. Experiment 2 investigated the abstractness of this transformation by looking at its effect on perceived age level of a Volkswagen "Beetle." In both experiments, cardioidal strain resulted in changes in the perceived age of the nonhuman profiles that were similar to those produced on human faces in earlier work. A second transformation, affine shear, failed to produce as significant an effect on perceived age as cardioidal strain when applied to the same structures. Because cardioidal strain produces changes in structures that do not share an isomorphism of rigid (Euclidian) local features or rigid feature configurations, this transformation seems both sufficiently general and abstract to specify what J.J. Gibson has called a "higher-order invariant of perceptual information. PMID:528953
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-12-15
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Forward-looking recognition based on convex hull invariants of oil depot region
NASA Astrophysics Data System (ADS)
He, Fangfang; Sun, Jiyin; Han, Bing; Xia, Jing
2007-11-01
Forward-looking navigation system is a fire-new technique for terminal guidance of intending precision-guided weapons and research on oil depot recognition of forward-looking imaging is an essential task for this control and guide system. As conventional matching methods could not overcome perspective transmutation, a new method to identify the forward-looking area of oil depot was advanced in this paper. First, constructed three statistics of regions based on convex hull, which were invariant to affine transform. Then, number of inside oilcans could easily be achieved by adding a decision step. Finally the area of oil depot could be located according to the comparison between the computed number and the foreknowable number under a given threshold. Experiments applied to optical images in different areas show that the proposed method is accurate and has wider application in identifying such small objects as oilcans, and it realizes automatically recognizing area of oil depot from forward-looking imaging.
Fast Traffic Sign Recognition with a Rotation Invariant Binary Pattern Based Feature
Yin, Shouyi; Ouyang, Peng; Liu, Leibo; Guo, Yike; Wei, Shaojun
2015-01-01
Robust and fast traffic sign recognition is very important but difficult for safe driving assistance systems. This study addresses fast and robust traffic sign recognition to enhance driving safety. The proposed method includes three stages. First, a typical Hough transformation is adopted to implement coarse-grained location of the candidate regions of traffic signs. Second, a RIBP (Rotation Invariant Binary Pattern) based feature in the affine and Gaussian space is proposed to reduce the time of traffic sign detection and achieve robust traffic sign detection in terms of scale, rotation, and illumination. Third, the techniques of ANN (Artificial Neutral Network) based feature dimension reduction and classification are designed to reduce the traffic sign recognition time. Compared with the current work, the experimental results in the public datasets show that this work achieves robustness in traffic sign recognition with comparable recognition accuracy and faster processing speed, including training speed and recognition speed. PMID:25608217
Lorentz invariance in shape dynamics
NASA Astrophysics Data System (ADS)
Carlip, S.; Gomes, Henrique
2015-01-01
Shape dynamics is a reframing of canonical general relativity in which time reparametrization invariance is ‘traded’ for a local conformal invariance. We explore the emergence of Lorentz invariance in this model in three contexts: as a maximal symmetry, an asymptotic symmetry and a local invariance.
Tests of Lorentz invariance: a 2013 update
NASA Astrophysics Data System (ADS)
Liberati, S.
2013-07-01
We present an updated review of Lorentz invariance tests in effective field theories (EFTs) in the matter as well as in the gravity sector. After a general discussion of the role of Lorentz invariance and a derivation of its transformations along the so-called von Ignatovski theorem, we present the dynamical frameworks developed within local EFT and the available constraints on the parameters governing the Lorentz breaking effects. In the end, we discuss two specific examples: the OPERA ‘affaire’ and the case of Hořava-Lifshitz gravity. The first case will serve as an example, and a caveat, of the practical application of the general techniques developed for constraining Lorentz invariance violation to a direct observation potentially showing these effects. The second case will show how the application of the same techniques to a specific quantum gravity scenario has far-reaching implications not foreseeable in a purely phenomenological EFT approach.
Extensive Adiabatic Invariants for Nonlinear Chains
NASA Astrophysics Data System (ADS)
Giorgilli, Antonio; Paleari, Simone; Penati, Tiziano
2012-09-01
We look for extensive adiabatic invariants in nonlinear chains in the thermodynamic limit. Considering the quadratic part of the Klein-Gordon Hamiltonian, by a linear change of variables we transform it into a sum of two parts in involution. At variance with the usual method of introducing normal modes, our constructive procedure allows us to exploit the complete resonance, while keeping the extensive nature of the system. Next we construct a nonlinear approximation of an extensive adiabatic invariant for a perturbation of the discrete nonlinear Schrödinger model. The fluctuations of this quantity are controlled via Gibbs measure estimates independent of the system size, for a large set of initial data at low specific energy. Finally, by numerical calculations we show that our adiabatic invariant is well conserved for times much longer than predicted by our first order theory, with fluctuation much smaller than expected according to standard statistical estimates.
Lorentz invariance in chiral kinetic theory.
Chen, Jing-Yuan; Son, Dam T; Stephanov, Mikhail A; Yee, Ho-Ung; Yin, Yi
2014-10-31
We show that Lorentz invariance is realized nontrivially in the classical action of a massless spin-1/2 particle with definite helicity. We find that the ordinary Lorentz transformation is modified by a shift orthogonal to the boost vector and the particle momentum. The shift ensures angular momentum conservation in particle collisions and implies a nonlocality of the collision term in the Lorentz-invariant kinetic theory due to side jumps. We show that 2/3 of the chiral-vortical effect for a uniformly rotating particle distribution can be attributed to the magnetic moment coupling required by the Lorentz invariance. We also show how the classical action can be obtained by taking the classical limit of the path integral for a Weyl particle. PMID:25396362
Breaking of de Sitter invariance in quantum cosmological gravity
NASA Astrophysics Data System (ADS)
Kleppe, Gary
1993-11-01
The effects of de Sitter transformations on linearized quantum gravity in a de Sitter space background are worked out explicitly. It is shown that the linearized solutions are closed under the transformations of the de Sitter group. To do this it is necessary to use a compensating gauge transformation to return the transformed solution to the original gauge. It is then shown that the form of the graviton propagator in this background, as found by Tsamis and Woodard, is not de Sitter invariant, and no suitable invariant propagator exists, even when gauge transformations which compensate for the noninvariant gauge choice are introduced. This leads us to conclude that the vacuum is not invariant. Address after 1 August 1993: Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA.
Janse Van Rensburg, E.J.
1996-12-31
The geometry of polygonal knots in the cubic lattice may be used to define some knot invariants. One such invariant is the minimal edge number, which is the minimum number of edges necessary (and sufficient) to construct a lattice knot of given type. In addition, one may also define the minimal (unfolded) surface number, and the minimal (unfolded) boundary number; these are the minimum number of 2-cells necessary to construct an unfolded lattice Seifert surface of a given knot type in the lattice, and the minimum number of edges necessary in a lattice knot to guarantee the existence of an unfolded lattice Seifert surface. In addition, I derive some relations amongst these invariants. 8 refs., 5 figs., 2 tabs.
Reparametrization invariant collinear operators
Marcantonini, Claudio; Stewart, Iain W.
2009-03-15
In constructing collinear operators, which describe the production of energetic jets or energetic hadrons, important constraints are provided by reparametrization invariance (RPI). RPI encodes Lorentz invariance in a power expansion about a collinear direction, and connects the Wilson coefficients of operators at different orders in this expansion to all orders in {alpha}{sub s}. We construct reparametrization invariant collinear objects. The expansion of operators built from these objects provides an efficient way of deriving RPI relations and finding a minimal basis of operators, particularly when one has an observable with multiple collinear directions and/or soft particles. Complete basis of operators is constructed for pure glue currents at twist-4, and for operators with multiple collinear directions, including those appearing in e{sup +}e{sup -}{yields}3 jets, and for pp{yields}2 jets initiated via gluon fusion.
Funabashi, Masatoshi
2015-05-01
This study applies information geometry of normal distribution to model Japanese vowels on the basis of the first and second formants. The distribution of Kullback-Leibler (KL) divergence and its decomposed components were investigated to reveal the statistical invariance in the vowel system. The results suggest that although significant variability exists in individual KL divergence distributions, the population distribution tends to converge into a specific log-normal distribution. This distribution can be considered as an invariant distribution for the standard-Japanese speaking population. Furthermore, it was revealed that the mean and variance components of KL divergence are linearly related in the population distribution. The significance of these invariant features is discussed. PMID:25994716
Invariants of DNA genomic signals
NASA Astrophysics Data System (ADS)
Cristea, Paul Dan A.
2005-02-01
For large scale analysis purposes, the conversion of genomic sequences into digital signals opens the possibility to use powerful signal processing methods for handling genomic information. The study of complex genomic signals reveals large scale features, maintained over the scale of whole chromosomes, that would be difficult to find by using only the symbolic representation. Based on genomic signal methods and on statistical techniques, the paper defines parameters of DNA sequences which are invariant to transformations induced by SNPs, splicing or crossover. Re-orienting concatenated coding regions in the same direction, regularities shared by the genomic material in all exons are revealed, pointing towards the hypothesis of a regular ancestral structure from which the current chromosome structures have evolved. This property is not found in non-nuclear genomic material, e.g., plasmids.
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.
Rotation invariant features for wear particle classification
NASA Astrophysics Data System (ADS)
Arof, Hamzah; Deravi, Farzin
1997-09-01
This paper investigates the ability of a set of rotation invariant features to classify images of wear particles found in used lubricating oil of machinery. The rotation invariant attribute of the features is derived from the property of the magnitudes of Fourier transform coefficients that do not change with spatial shift of the input elements. By analyzing individual circular neighborhoods centered at every pixel in an image, local and global texture characteristics of an image can be described. A number of input sequences are formed by the intensities of pixels on concentric rings of various radii measured from the center of each neighborhood. Fourier transforming the sequences would generate coefficients whose magnitudes are invariant to rotation. Rotation invariant features extracted from these coefficients were utilized to classify wear particle images that were obtained from a number of different particles captured at different orientations. In an experiment involving images of 6 classes, the circular neighborhood features obtained a 91% recognition rate which compares favorably to a 76% rate achieved by features of a 6 by 6 co-occurrence matrix.
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. .
Gauge invariants and bosonization
NASA Astrophysics Data System (ADS)
Kijowski, J.; Rudolph, G.; Rudolph, M.
1998-12-01
We present some results, which are part of our program of analyzing gauge theories with fermions in terms of local gauge invariant fields. In a first part the classical Dirac-Maxwell system is discussed. Next we develop a procedure which leads to a reduction of the functional integral to an integral over (bosonic) gauge invariant fields. We apply this procedure to the case of QED and the Schwinger model. In a third part we go some steps towards an analysis of the considered models. We construct effective (quantum) field theories which can be used to calculate vacuum expectation values of physical quantities.
Early-time particle dynamics and non-affine deformations during microstructure selection in solids
NASA Astrophysics Data System (ADS)
Sengupta, Surajit; Rao, Madan; Bhattacharya, Jayee
2011-07-01
Solid-solid transitions are invariably associated with groups of particles whose deformations cannot be expressed as an affine strain about a reference configuration. The dynamics of these non-affine zones (NAZ) determine the subsequent microstructure, i.e. the mesoscale patterning resulting from the structural transition. Here, we focus on early-time dynamics of individual particles within an NAZ associated with a nucleation event. We show that the early-time behavior of these particles have distinctive characteristics depending on the transition temperature. The dynamics is heterogeneous, consisting of a few active particles exhibiting complex intermittent jamming and flow in response to internal stresses generated during the transformation. At low temperatures, the dynamics of these active particles is ballistic and the structural transformation proceeds via string-like correlated movement of active particles, along ridges in the potential energy topography set up by inactive particles. On increasing temperature, the dynamics of active particles show an abrupt transition from ballistic to diffusive behavior with a diffusion coefficient which appears to be independent of temperature. This dynamical transition in the nature of the trajectories of particles is coincident with a discontinuous transition in the microstructure of the solid. Finally, we characterize this transition in terms of a dynamical order parameter in the space of trajectories and discuss its connection with the glass transition and rheology of soft and granular matter.
Symmetry classification and joint invariants for the scalar linear (1 + 1) elliptic equation
NASA Astrophysics Data System (ADS)
Mahomed, F. M.; Johnpillai, A. G.; Aslam, A.
2015-08-01
The equations for the classification of symmetries of the scalar linear (1 + 1) elliptic partial differential equation (PDE) are obtained in terms of Cotton's invariants. New joint differential invariants of the scalar linear elliptic (1 + 1) PDE in two independent variables are derived in terms of Cotton's invariants by application of the infinitesimal method. Joint differential invariants of the scalar linear elliptic equation are also deduced from the basis of the joint differential invariants of the scalar linear (1 + 1) hyperbolic equation under the application of the complex linear transformation. We also find a basis of joint differential invariants for such type of equations by utilization of the operators of invariant differentiation. The other invariants are functions of the basis elements and their invariant derivatives. Examples are given to illustrate our results.
Idiographic Measurement Invariance?
ERIC Educational Resources Information Center
Willoughby, Michael T.; Sideris, John
2007-01-01
In this article, the authors comment on Nesselroade, Gerstorf, Hardy, and Ram's efforts (this issue) to grapple with the challenge of accommodating idiographic assessment as it pertains to measurement invariance (MI). Although the authors are in complete agreement with the motivation for Nesselroade et al.'s work, the authors have concerns about…
Pokhozhaev, Stanislav I
2011-06-30
The notion of Riemann quasi-invariants is introduced and their applications to several conservation laws are considered. The case of nonisentropic flow of an ideal polytropic gas is analysed in detail. Sufficient conditions for gradient catastrophes are obtained. Bibliography: 16 titles.
Conformally invariant wave equations for massless particles
NASA Astrophysics Data System (ADS)
McLennan, James A.
1984-07-01
The invariance of wave equations for massless particles under conformal transformations of space-time is briefly summarized. Particular attention is given to a recent paper by Bracken and Jessup in which it is claimed that results obtained by the author are in error. Their paper contains several misleading statements based on a misreading of the author's paper, and in addition an argument of theirs, intended to show error, is itself invalid. Their claims of error on the author's part are therefore unfounded.
Shiftable multiscale transforms
NASA Technical Reports Server (NTRS)
Simoncelli, Eero P.; Freeman, William T.; Adelson, Edward H.; Heeger, David J.
1992-01-01
A type of translational invariance, referred to as shiftability, is defined for wavelet transforms. The property of shiftability is first discussed with respect to individual parameters: spatial position, orientation, and scale. The discussion then focuses on transformations that are simultaneously shiftable with respect to subsets of these parameters. It is shown that the critical sampling condition on the wavelet transforms must be relaxed to achieve shiftability. Two example transforms are implemented and applied to several signal and image processing problems.
Invariant quantities of a nondepolarizing Mueller matrix
NASA Astrophysics Data System (ADS)
Gil, José J.; José, Ignacio San
2016-07-01
Orthogonal Mueller matrices can be considered either as corresponding to retarders or to generalized transformations of the polarization basis for the representation of Stokes vectors, so that they constitute the only type of Mueller matrices that preserve the degree of polarization and the intensity of any partially-polarized input Stokes vector. The physical quantities which remain invariant when a nondepolarizing Mueller matrix is transformed through its product by different types of orthogonal Mueller matrices are identified and interpreted, providing a better knowledge of the information contained in a nondepolarizing Mueller matrix.
Special Report: Affinity Chromatography.
ERIC Educational Resources Information Center
Parikh, Indu; Cuatrecasas, Pedro
1985-01-01
Describes the nature of affinity chromatography and its use in purifying enzymes, studying cell interactions, exploring hormone receptors, and other areas. The potential the technique may have in treating disease is also considered. (JN)
FAST TRACK COMMUNICATION: Symmetry breaking, conformal geometry and gauge invariance
NASA Astrophysics Data System (ADS)
Ilderton, Anton; Lavelle, Martin; McMullan, David
2010-08-01
When the electroweak action is rewritten in terms of SU(2) gauge-invariant variables, the Higgs can be interpreted as a conformal metric factor. We show that asymptotic flatness of the metric is required to avoid a Gribov problem: without it, the new variables fail to be nonperturbatively gauge invariant. We also clarify the relations between this approach and unitary gauge fixing, and the existence of similar transformations in other gauge theories.
Gauge invariance and non-Gaussianity in inflation
NASA Astrophysics Data System (ADS)
Rigopoulos, Gerasimos
2011-07-01
We clarify the role of gauge invariance for the computation of quantum non-Gaussian correlators in inflation. A gauge invariant generating functional for n-point functions is given and the special status of the spatially flat gauge is pointed out. We also comment on the relation between gauge transformations, field redefinitions, the choice of t=const hypersurfaces and the use of boundary terms in computations of non-Gaussianity.
View Invariant Gait Recognition
NASA Astrophysics Data System (ADS)
Seely, Richard D.; Goffredo, Michela; Carter, John N.; Nixon, Mark S.
Recognition by gait is of particular interest since it is the biometric that is available at the lowest resolution, or when other biometrics are (intentionally) obscured. Gait as a biometric has now shown increasing recognition capability. There are many approaches and these show that recognition can achieve excellent performance on current large databases. The majority of these approaches are planar 2D, largely since the early large databases featured subjects walking in a plane normal to the camera view. To extend deployment capability, we need viewpoint invariant gait biometrics. We describe approaches where viewpoint invariance is achieved by 3D approaches or in 2D. In the first group, the identification relies on parameters extracted from the 3D body deformation during walking. These methods use several video cameras and the 3D reconstruction is achieved after a camera calibration process. On the other hand, the 2D gait biometric approaches use a single camera, usually positioned perpendicular to the subject’s walking direction. Because in real surveillance scenarios a system that operates in an unconstrained environment is necessary, many of the recent gait analysis approaches are orientated toward view-invariant gait recognition.
Universality for the breakup of invariant tori in Hamiltonian flows
NASA Astrophysics Data System (ADS)
Chandre, C.; Govin, M.; Jauslin, H. R.; Koch, H.
1998-06-01
In this article, we describe a new renormalization-group scheme for analyzing the breakup of invariant tori for Hamiltonian systems with two degrees of freedom. The transformation, which acts on Hamiltonians that are quadratic in the action variables, combines a rescaling of phase space and a partial elimination of irrelevant (nonresonant) frequencies. It is implemented numerically for the case applying to golden invariant tori. We find a nontrivial fixed point and compute the corresponding scaling and critical indices. If one compares flows to maps in the canonical way, our results are consistent with existing data on the breakup of golden invariant circles for area-preserving maps.
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.
NASA Astrophysics Data System (ADS)
Green, Larry Herschel
1982-03-01
This dissertation provides an investigation of certain fundamental invariance and symmetry properties of field theories and their structures at the classical level. Our results provide insight into the physical roles of invariance properties and symmetry demands in the context of various field theoretical models. We stress the role of the conformal and projective properties of the space -time structure. However, more generally, we are concerned with transformations which leave the trace of the Ricci tensor invariant. These objectives are approached by first considering particular types of symmetry conditions that can be characterized by point mappings on a given space-time. After considering the symmetry conditions, invariance properties are examined as free transformations in the context of particular physical models. Symmetry properties which are members of the Family of Contracted Ricci Collineations (FCRC) are considered. Several theorems are given concerning FCRC symmetry properties. While the major part of the investigation is restricted to Einstein's theory, the extension of these results to ECSK theory is discussed. A symmetry property which cannot, in general, be characterized in terms of Lie deformations is the existence of a Killing tensor. The form of all metric tensors which admit Killing tensors with a Segre characteristic {1(111) } which have non-constant eigenvalues is found. The role of conformal invariance in various field theoretical models is examined. Particular attention is given to conformal invariance in theories which have a variable "gravitational constant". While most previous investigations in this area have been restricted to considering symmetric connections, we are chiefly concerned with space -times with a general metric connection. A new type of conformal invariance, which couples conformal transformations on the metric tensor to projective transformations on the torsion tensor and preserves metricity, is discussed. We show that
Gauge invariant quantum cosmology
NASA Technical Reports Server (NTRS)
Berger, Beverly K.
1987-01-01
The study of boundary conditions, the Hamiltonian constraint, reparameterization-invariance, and quantum dynamics, is presently approached by means of the path-integral quantization of minisuperspace models. The separation of the wave functions for expansion and contraction by the Feynman boundary conditions is such that there can be no interference between them. This is implemented by the choice of a contour in the complex plane, in order to define the phase of the square-root Arnowitt, Deser, and Misner (1960) Hamiltonian for expansion, collapse, and the classically forbidden region.
Invariant visual object recognition: biologically plausible approaches.
Robinson, Leigh; Rolls, Edmund T
2015-10-01
Key properties of inferior temporal cortex neurons are described, and then, the biological plausibility of two leading approaches to invariant visual object recognition in the ventral visual system is assessed to investigate whether they account for these properties. Experiment 1 shows that VisNet performs object classification with random exemplars comparably to HMAX, except that the final layer C neurons of HMAX have a very non-sparse representation (unlike that in the brain) that provides little information in the single-neuron responses about the object class. Experiment 2 shows that VisNet forms invariant representations when trained with different views of each object, whereas HMAX performs poorly when assessed with a biologically plausible pattern association network, as HMAX has no mechanism to learn view invariance. Experiment 3 shows that VisNet neurons do not respond to scrambled images of faces, and thus encode shape information. HMAX neurons responded with similarly high rates to the unscrambled and scrambled faces, indicating that low-level features including texture may be relevant to HMAX performance. Experiment 4 shows that VisNet can learn to recognize objects even when the view provided by the object changes catastrophically as it transforms, whereas HMAX has no learning mechanism in its S-C hierarchy that provides for view-invariant learning. This highlights some requirements for the neurobiological mechanisms of high-level vision, and how some different approaches perform, in order to help understand the fundamental underlying principles of invariant visual object recognition in the ventral visual stream. PMID:26335743
Nonclassicality Invariant of General Two-Mode Gaussian States
NASA Astrophysics Data System (ADS)
Arkhipov, Ievgen I.; Peřina, Jan, Jr.; Svozilík, Jiří; Miranowicz, Adam
2016-05-01
We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given.
Nonclassicality Invariant of General Two-Mode Gaussian States.
Arkhipov, Ievgen I; Peřina, Jan; Svozilík, Jiří; Miranowicz, Adam
2016-01-01
We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given. PMID:27210547
Nonclassicality Invariant of General Two-Mode Gaussian States
Arkhipov, Ievgen I.; Peřina Jr., Jan; Svozilík, Jiří; Miranowicz, Adam
2016-01-01
We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given. PMID:27210547
The relation between the waveguide invariant and array invariant.
Song, H C; Cho, Chomgun
2015-08-01
The waveguide invariant β is based on the dependence of group speed on phase speed and summarizes the robust interference phenomenon in the range-frequency plane. Over the last decade the elegant approach has been utilized for various applications including passive source ranging. Separately, the array invariant approach [Lee and Makris, J. Acoust. Soc. Am. 119, 336-351 (2006)] has been proposed for a robust source-range estimator from beam-time intensity data using either a horizontal or vertical array. In this paper, it is shown that the array invariant can be derived from the waveguide invariant theory assuming β=1. PMID:26328705
Entanglement, Invariants, and Phylogenetics
NASA Astrophysics Data System (ADS)
Sumner, J. G.
2007-10-01
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units from biomolecular sequence data. The techniques of mathematical physics are plethora and have been developed for some time. The Markov model of phylogenetics and its analysis is a relatively new technique where most progress to date has been achieved by using discrete mathematics. This thesis takes a group theoretical approach to the problem by beginning with a remarkable mathematical parallel to the process of scattering in particle physics. This is shown to equate to branching events in the evolutionary history of molecular units. The major technical result of this thesis is the derivation of existence proofs and computational techniques for calculating polynomial group invariant functions on a multi-linear space where the group action is that relevant to a Markovian time evolution. The practical results of this thesis are an extended analysis of the use of invariant functions in distance based methods and the presentation of a new reconstruction technique for quartet trees which is consistent with the most general Markov model of sequence evolution.
Invariants from classical field theory
Diaz, Rafael; Leal, Lorenzo
2008-06-15
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.
Wall-crossing invariants: from quantum mechanics to knots
NASA Astrophysics Data System (ADS)
Galakhov, D.; Mironov, A.; Morozov, A.
2015-03-01
We offer a pedestrian-level review of the wall-crossing invariants. The story begins from the scattering theory in quantum mechanics where the spectrum reshuffling can be related to permutations of S-matrices. In nontrivial situations, starting from spin chains and matrix models, the S-matrices are operatorvalued and their algebra is described in terms of R- and mixing (Racah) U-matrices. Then the Kontsevich-Soibelman (KS) invariants are nothing but the standard knot invariants made out of these data within the Reshetikhin-Turaev-Witten approach. The R and Racah matrices acquire a relatively universal form in the semiclassical limit, where the basic reshufflings with the change of moduli are those of the Stokes line. Natural from this standpoint are matrices provided by the modular transformations of conformal blocks (with the usual identification R = T and U = S), and in the simplest case of the first degenerate field (2, 1), when the conformal blocks satisfy a second-order Shrödinger-like equation, the invariants coincide with the Jones ( N = 2) invariants of the associated knots. Another possibility to construct knot invariants is to realize the cluster coordinates associated with reshufflings of the Stokes lines immediately in terms of check-operators acting on solutions of the Knizhnik-Zamolodchikov equations. Then the R-matrices are realized as products of successive mutations in the cluster algebra and are manifestly described in terms of quantum dilogarithms, ultimately leading to the Hikami construction of knot invariants.
Wall-crossing invariants: from quantum mechanics to knots
Galakhov, D. E-mail: galakhov@physics.rutgers.edu; Mironov, A. Morozov, A.
2015-03-15
We offer a pedestrian-level review of the wall-crossing invariants. The story begins from the scattering theory in quantum mechanics where the spectrum reshuffling can be related to permutations of S-matrices. In nontrivial situations, starting from spin chains and matrix models, the S-matrices are operatorvalued and their algebra is described in terms of R- and mixing (Racah) U-matrices. Then the Kontsevich-Soibelman (KS) invariants are nothing but the standard knot invariants made out of these data within the Reshetikhin-Turaev-Witten approach. The R and Racah matrices acquire a relatively universal form in the semiclassical limit, where the basic reshufflings with the change of moduli are those of the Stokes line. Natural from this standpoint are matrices provided by the modular transformations of conformal blocks (with the usual identification R = T and U = S), and in the simplest case of the first degenerate field (2, 1), when the conformal blocks satisfy a second-order Shrödinger-like equation, the invariants coincide with the Jones (N = 2) invariants of the associated knots. Another possibility to construct knot invariants is to realize the cluster coordinates associated with reshufflings of the Stokes lines immediately in terms of check-operators acting on solutions of the Knizhnik-Zamolodchikov equations. Then the R-matrices are realized as products of successive mutations in the cluster algebra and are manifestly described in terms of quantum dilogarithms, ultimately leading to the Hikami construction of knot invariants.
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.
Gauge-invariant Green function dynamics: A unified approach
Swiecicki, Sylvia D. Sipe, J.E.
2013-11-15
We present a gauge-invariant description of Green function dynamics introduced by means of a generalized Peirels phase involving an arbitrary differentiable path in space–time. Two other approaches to formulating a gauge-invariant description of systems, the Green function treatment of Levanda and Fleurov [M. Levanda, V. Fleurov, J. Phys.: Condens. Matter 6 (1994) 7889] and the usual multipolar expansion for an atom, are shown to arise as special cases of our formalism. We argue that the consideration of paths in the generalized Peirels phase that do not lead to introduction of an effective gauge-invariant Hamiltonian with polarization and magnetization fields may prove useful for the treatment of the response of materials with short electron correlation lengths. -- Highlights: •Peirels phase for an arbitrary path in space–time established. •Gauge-invariant Green functions and the Power–Zienau–Wooley transformation connected. •Limitations on possible polarization and magnetization fields established.
Invariant approach to CP in unbroken Δ (27)
NASA Astrophysics Data System (ADS)
Branco, Gustavo C.; de Medeiros Varzielas, Ivo; King, Stephen F.
2015-10-01
The invariant approach is a powerful method for studying CP violation for specific Lagrangians. The method is particularly useful for dealing with discrete family symmetries. We focus on the CP properties of unbroken Δ (27) invariant Lagrangians with Yukawa-like terms, which proves to be a rich framework, with distinct aspects of CP, making it an ideal group to investigate with the invariant approach. We classify Lagrangians depending on the number of fields transforming as irreducible triplet representations of Δ (27). For each case, we construct CP-odd weak basis invariants and use them to discuss the respective CP properties. We find that CP violation is sensitive to the number and type of Δ (27) representations.
A Note on Invariant Temporal Functions
NASA Astrophysics Data System (ADS)
Müller, Olaf
2016-07-01
The purpose of this article is to present a result on the existence of Cauchy temporal functions invariant by the action of a compact group of conformal transformations in arbitrary globally hyperbolic manifolds. Moreover, the previous results about the existence of Cauchy temporal functions with additional properties on arbitrary globally hyperbolic manifolds are unified in a very general theorem. To make the article more accessible for non-experts, and in the lack of an appropriate single reference for the Lorentzian geometry background of the result, the latter is provided in an introductory section.
A Note on Invariant Temporal Functions
NASA Astrophysics Data System (ADS)
Müller, Olaf
2016-05-01
The purpose of this article is to present a result on the existence of Cauchy temporal functions invariant by the action of a compact group of conformal transformations in arbitrary globally hyperbolic manifolds. Moreover, the previous results about the existence of Cauchy temporal functions with additional properties on arbitrary globally hyperbolic manifolds are unified in a very general theorem. To make the article more accessible for non-experts, and in the lack of an appropriate single reference for the Lorentzian geometry background of the result, the latter is provided in an introductory section.
Origin of gauge invariance in string theory
NASA Technical Reports Server (NTRS)
Horowitz, G. T.; Strominger, A.
1986-01-01
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
NASA Astrophysics Data System (ADS)
De Maio, Antonio; Orlando, Danilo
2016-04-01
This paper deals with adaptive radar detection of a subspace signal competing with two sources of interference. The former is Gaussian with unknown covariance matrix and accounts for the joint presence of clutter plus thermal noise. The latter is structured as a subspace signal and models coherent pulsed jammers impinging on the radar antenna. The problem is solved via the Principle of Invariance which is based on the identification of a suitable group of transformations leaving the considered hypothesis testing problem invariant. A maximal invariant statistic, which completely characterizes the class of invariant decision rules and significantly compresses the original data domain, as well as its statistical characterization are determined. Thus, the existence of the optimum invariant detector is addressed together with the design of practically implementable invariant decision rules. At the analysis stage, the performance of some receivers belonging to the new invariant class is established through the use of analytic expressions.
A Discussion of Population Invariance
ERIC Educational Resources Information Center
Brennan, Robert L.
2008-01-01
The discussion here covers five articles that are linked in the sense that they all treat population invariance. This discussion of population invariance is a somewhat broader treatment of the subject than simply a discussion of these five articles. In particular, occasional reference is made to publications other than those in this issue. The…
Invariant Measures for Cherry Flows
NASA Astrophysics Data System (ADS)
Saghin, Radu; Vargas, Edson
2013-01-01
We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we prove that there exists also an invariant probability measure supported on the quasi-minimal set, we discuss some situations when this other invariant measure is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.
Knot invariants from Virasoro related representation and pretzel knots
NASA Astrophysics Data System (ADS)
Galakhov, D.; Melnikov, D.; Mironov, A.; Morozov, A.
2015-10-01
We remind the method to calculate colored Jones polynomials for the plat representations of knot diagrams from the knowledge of modular transformation (monodromies) of Virasoro conformal blocks with insertions of degenerate fields. As an illustration we use a rich family of pretzel knots, lying on a surface of arbitrary genus g, which was recently analyzed by the evolution method. Further generalizations can be to generic Virasoro modular transformations, provided by integral kernels, which can lead to the Hikami invariants.
Physical Invariants of Intelligence
NASA Technical Reports Server (NTRS)
Zak, Michail
2010-01-01
A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective
Bias Coefficients for Lack of Invariance in Unidimensional IRT Models.
ERIC Educational Resources Information Center
Rupp, Andre A.; Zumbo, Bruno D.
The feature that makes item response theory (IRT) models the models of choice for many psychometric data analysts is parameter invariance, the equality of item and examinee parameters from different populations. Using the well-known fact that item and examinee parameters are identical only up to a set of linear transformations specific to the…
NASA Astrophysics Data System (ADS)
Goncharovskii, M. M.; Shirokov, I. V.
2015-05-01
We describe the relation between operators of invariant differentiation and invariant operators on orbits of Lie group actions. We propose a new effective method for finding differential invariants and operators of invariant differentiation and present examples.
NASA Astrophysics Data System (ADS)
Cerba Diaconescu, Oxana; Schlomiuk, Dana; Vulpe, Nicolae
In this article, we consider the class QSL4{u +vc+w^c, ∞ } of all real quadratic differential systems (dx)/(dt) = p(x, y), (dy)/(dt) = q(x, y) with gcd(p, q) = 1, having invariant lines of total multiplicity four and two complex and one real infinite singularities. We first construct compactified canonical forms for the class QSL4{u +vc+w^c, ∞ } so as to include limit points in the 12-dimensional parameter space of this class. We next construct the bifurcation diagrams for these compactified canonical forms. These diagrams contain many repetitions of phase portraits and we show that these are due to many symmetries under the group action. To retain the essence of the dynamics we finally construct the quotient spaces under the action of the group G = Aff(2, R) × R* of affine transformations and time homotheties and we place the phase portraits in these quotient spaces. The final diagrams retain only the necessary information to capture the dynamics under the motion in the parameter space as well as under this group action. We also present here necessary and sufficient conditions for an affine line to be invariant of multiplicity k for a quadratic system.
Casimir invariants for systems undergoing collective motion
Bishop, C. Allen; Byrd, Mark S.; Wu Lianao
2011-06-15
Dicke states are an important class of states which exhibit collective behavior in many-body systems. They are interesting because (1) the decay rates of these states can be quite different from a set of independently evolving particles and (2) a particular class of these states are decoherence-free or noiseless with respect to a set of errors. These noiseless states, or more generally subsystems, avoid certain types of errors in quantum-information-processing devices. Here we provide a method for determining a set of transformations of these states which leave the states in their subsystems but still enable them to evolve in particular ways. For subsystems of particles undergoing collective motions, these transformations can be calculated by using essentially the same construction which is used to determine the famous Casimir invariants for quantum systems. Such invariants can be used to determine a complete set of commuting observables for a class of Dicke states as well as to identify possible logical operations for decoherence-free-noiseless subsystems. Our method is quite general and provides results for cases where the constituent particles have more than two internal states.
Shaping propagation invariant laser beams
NASA Astrophysics Data System (ADS)
Soskind, Michael; Soskind, Rose; Soskind, Yakov
2015-11-01
Propagation-invariant structured laser beams possess several unique properties and play an important role in various photonics applications. The majority of propagation invariant beams are produced in the form of laser modes emanating from stable laser cavities. Therefore, their spatial structure is limited by the intracavity mode formation. We show that several types of anamorphic optical systems (AOSs) can be effectively employed to shape laser beams into a variety of propagation invariant structured fields with different shapes and phase distributions. We present a propagation matrix approach for designing AOSs and defining mode-matching conditions required for preserving propagation invariance of the output shaped fields. The propagation matrix approach was selected, as it provides a more straightforward approach in designing AOSs for shaping propagation-invariant laser beams than the alternative technique based on the Gouy phase evolution, especially in the case of multielement AOSs. Several practical configurations of optical systems that are suitable for shaping input laser beams into a diverse variety of structured propagation invariant laser beams are also presented. The laser beam shaping approach was applied by modeling propagation characteristics of several input laser beam types, including Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian structured field distributions. The influence of the Ince-Gaussian beam semifocal separation parameter and the azimuthal orientation between the input laser beams and the AOSs onto the resulting shape of the propagation invariant laser beams is presented as well.
Delplace, Vianney; Obermeyer, Jaclyn; Shoichet, Molly S
2016-07-26
The use of hydrogels for therapeutic delivery is a burgeoning area of investigation. These water-swollen polymer matrices are ideal platforms for localized drug delivery that can be further combined with specific ligands or nanotechnologies to advance the controlled release of small-molecule drugs and proteins. Due to the advantage of hydrophobic, electrostatic, or specific extracellular matrix interactions, affinity-based strategies can overcome burst release and challenges associated with encapsulation. Future studies will provide innovative binding tools, truly stimuli-responsive systems, and original combinations of emerging technologies to control the release of therapeutics spatially and temporally. Local drug delivery can be achieved by directly injecting a therapeutic to its site of action and is advantageous because off-target effects associated with systemic delivery can be minimized. For prolonged benefit, a vehicle that provides sustained drug release is required. Hydrogels are versatile platforms for localized drug release, owing to the large library of biocompatible building blocks from which they can be formed. Injectable hydrogel formulations that gel quickly in situ and provide sustained release of therapeutics are particularly advantageous to minimize invasiveness. The incorporation of polymers, ligands or nanoparticles that have an affinity for the therapeutic of interest improve control over the release of small-molecule drugs and proteins from hydrogels, enabling spatial and temporal control over the delivery. Such affinity-based strategies can overcome drug burst release and challenges associated with protein instability, allowing more effective therapeutic molecule delivery for a range of applications from therapeutic contact lenses to ischemic tissue regeneration. PMID:27403513
Berube, D.; Kroeger, H.; Lafrance, R.; Marleau, L. )
1991-02-15
We discuss properties of a noncompact formulation of gauge theories with fermions on a momentum ({ital k}) lattice. (a) This formulation is suitable to build in Fourier acceleration in a direct way. (b) The numerical effort to compute the action (by fast Fourier transform) goes essentially like log{ital V} with the lattice volume {ital V}. (c) For the Yang-Mills theory we find that the action conserves gauge symmetry and chiral symmetry in a weak sense: On a finite lattice the action is invariant under infinitesimal transformations with compact support. Under finite transformations these symmetries are approximately conserved and they are restored on an infinite lattice and in the continuum limit. Moreover, these symmetries also hold on a finite lattice under finite transformations, if the classical fields, instead of being {ital c}-number valued, take values from a finite Galois field. (d) There is no fermion doubling. (e) For the {phi}{sup 4} model we investigate the transition towards the continuum limit in lattice perturbation theory up to second order. We compute the two- and four-point functions and find local and Lorentz-invariant results. (f) In QED we compute a one-loop vacuum polarization and find in the continuum limit the standard result. (g) As a numerical application, we compute the propagator {l angle}{phi}({ital k}){phi}({ital k}{prime}){r angle} in the {phi}{sup 4} model, investigate Euclidean invariance, and extract {ital m}{sub {ital R}} as well as {ital Z}{sub {ital R}}. Moreover we compute {l angle}{ital F}{sub {mu}{nu}}({ital k}){ital F}{sub {mu}{nu}}({ital k}{prime}){r angle} in the SU(2) model.
ODE/IM correspondence and modified affine Toda field equations
NASA Astrophysics Data System (ADS)
Ito, Katsushi; Locke, Christopher
2014-08-01
We study the two-dimensional affine Toda field equations for affine Lie algebra gˆ modified by a conformal transformation and the associated linear equations. In the conformal limit, the associated linear problem reduces to a (pseudo-)differential equation. For classical affine Lie algebra gˆ, we obtain a (pseudo-)differential equation corresponding to the Bethe equations for the Langlands dual of the Lie algebra g, which were found by Dorey et al. in study of the ODE/IM correspondence.
Invariant manifolds and global bifurcations.
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn
2015-09-01
Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems. PMID:26428557
Lee, S; Young, N L; Whetstone, P A; Cheal, S M; Benner, W H; Lebrilla, C B; Meares, C F
2005-08-25
Protein oxidation is linked to cellular stress, aging, and disease. Protein oxidations that result in reactive species are of particular interest, since these reactive oxidation products may react with other proteins or biomolecules in an unmediated and irreversible fashion, providing a potential marker for a variety of disease mechanisms. We have developed a novel system to identify and quantitate, relative to other states, the sites of oxidation on a given protein. A specially designed Oxidation-dependent carbonyl-specific Element-Coded Affinity Mass Tag (O-ECAT), AOD, ((S)-2-(4-(2-aminooxy)-acetamido)-benzyl)-1, 4, 7, 10-tetraazacyclododecane-N, N', N'', N'''-tetraacetic acid, is used to covalently tag the residues of a protein oxidized to aldehyde or keto end products. After proteolysis, the resulting AOD-tagged peptides are affinity purified, and analyzed by nanoLC-FTICR-MS, which provides high specificity in extracting co-eluting AOD mass pairs with a unique mass difference and affords relative quantitation based on isotopic ratios. Using this methodology, we have mapped the surface oxidation sites on a model protein, recombinant human serum albumin (rHSA) in its native form (as purchased) and after FeEDTA oxidation. A variety of modified amino acid residues including lysine, arginine, proline, histidine, threonine, aspartic and glutamic acids, were found to be oxidized to aldehyde and keto end products. The sensitivity of this methodology is shown by the number of peptides identified, twenty peptides on the native protein and twenty-nine after surface oxidation using FeEDTA and ascorbate. All identified peptides map to the surface of the HSA crystal structure validating this method for identifying oxidized amino acids on protein surfaces. In relative quantitation experiments between FeEDTA oxidation and native protein oxidation, identified sites showed different relative propensities towards oxidation independent of amino acid residue. We expect to extend
Wavelet-based moment invariants for pattern recognition
NASA Astrophysics Data System (ADS)
Chen, Guangyi; Xie, Wenfang
2011-07-01
Moment invariants have received a lot of attention as features for identification and inspection of two-dimensional shapes. In this paper, two sets of novel moments are proposed by using the auto-correlation of wavelet functions and the dual-tree complex wavelet functions. It is well known that the wavelet transform lacks the property of shift invariance. A little shift in the input signal will cause very different output wavelet coefficients. The autocorrelation of wavelet functions and the dual-tree complex wavelet functions, on the other hand, are shift-invariant, which is very important in pattern recognition. Rotation invariance is the major concern in this paper, while translation invariance and scale invariance can be achieved by standard normalization techniques. The Gaussian white noise is added to the noise-free images and the noise levels vary with different signal-to-noise ratios. Experimental results conducted in this paper show that the proposed wavelet-based moments outperform Zernike's moments and the Fourier-wavelet descriptor for pattern recognition under different rotation angles and different noise levels. It can be seen that the proposed wavelet-based moments can do an excellent job even when the noise levels are very high.
Movement Timing and Invariance Arise from Several Geometries
Bennequin, Daniel; Fuchs, Ronit; Berthoz, Alain; Flash, Tamar
2009-01-01
Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain
Morphometric affinities of gigantopithecus.
Gelvin, B R
1980-11-01
Multivariate analyses, supplemented by univariate statistical methods, of measurements from mandibular tooth crown dimensions and the mandible of Gigantopithecus blacki, G. bilaspurensis, Plio-Plelstocene hominids, Homo erectus, and seven Neogene ape species from the genera Proconsul, Sivapithecus, Ouranopithecus, and Dryopithecus were used to assess the morphometric affinities of Gigantopithecus. The results show that Gigantopithecus displays affinities to Ouranopithecus and to the hominids, particularly the Plio-Plelstocene hominids, rather than to the apes. Ouranopithecus demonstrated dental resemblances to G. bilaspurensis and the Plio-Pleistocene hominids but mandibular similarities to the apes. Results of analyses of tooth and mandibular shape indices, combined with multivariate distance and temporal relationships, suggest that Ouranopithecus is a more likely candidate for Gigantopithecus ancestry than is Silvapithecus indicus. Shape and allometric differences between G. bilaspurensis and the robust australopithecines weaken the argument for an ancestral-descendant relationship between these groups. The results support the hypothesis that Gigantopithecus is an extinct side branch of the Hominidae. PMID:7468790
Orthosymplectically invariant functions in superspace
Coulembier, K.; De Bie, H.; Sommen, F.
2010-08-15
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically symmetric functions can be used to solve orthosymplectically invariant Schroedinger equations in superspace, such as the (an)harmonic oscillator or the Kepler problem. Finally, the obtained machinery is used to prove the Funk-Hecke theorem and Bochner's relations in superspace.
Form Invariance Symmetry Generates a Large Set of FRW Cosmologies
NASA Astrophysics Data System (ADS)
Chimento, Luis P.; Richarte, Martín G.; Sánchez, Iván E.
2013-02-01
We show that Einstein's field equations for spatially flat Friedmann-Robertson-Walker (FRW) spacetimes have a form invariance symmetry (FIS) realized by the form invariance transformations (FIT) which are indeed generated by an invertible function of the source energy density. These transformations act on the Hubble expansion rate, the energy density and pressure of the cosmic fluid; likewise such transformations are endowed with a Lie group structure. Each representation of this group is associated with a particular fluid and consequently a determined cosmology, so that, the FIS defines a set of equivalent cosmological models. We focus our seek in the FIT generated by a linear function because it provides a natural framework to express the duality and also produces large sets of cosmologies, starting from a seed one, in several contexts as for instance in the cases of a perfect fluid source and a scalar field driven by a potential depending linearly on the scalar field kinetic energy density.
On the disformal invariance of the Dirac equation
NASA Astrophysics Data System (ADS)
Bittencourt, Eduardo; Lobo, Iarley P.; Carvalho, Gabriel G.
2015-09-01
We analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field acting on the metric tensor. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric tensors, respecting the order of differentiability of the Dirac operator and satisfying the Clifford algebra in both metrics. We split the analysis in some cases according to the spinor mass and the norm of the Dirac current, exhibiting sufficient conditions to find classes of solutions which keep the Dirac operator invariant under the action of the disformal group.
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.
Affine and deformable registration based on polynomial expansion.
Farnebäck, Gunnar; Westin, Carl-Fredrik
2006-01-01
This paper presents a registration framework based on the polynomial expansion transform. The idea of polynomial expansion is that the image is locally approximated by polynomials at each pixel. Starting with observations of how the coefficients of ideal linear and quadratic polynomials change under translation and affine transformation, algorithms are developed to estimate translation and compute affine and deformable registration between a fixed and a moving image, from the polynomial expansion coefficients. All algorithms can be used for signals of any dimensionality. The algorithms are evaluated on medical data. PMID:17354971
Adjoint affine fusion and tadpoles
NASA Astrophysics Data System (ADS)
Urichuk, Andrew; Walton, Mark A.
2016-06-01
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.
Lorentz-invariant three-vectors and alternative formulation of relativistic dynamics
NASA Astrophysics Data System (ADS)
RÈ©bilas, Krzysztof
2010-03-01
Besides the well-known scalar invariants, there also exist vectorial invariants in special relativity. It is shown that the three-vector (dp⃗/dt)∥+γv(dp⃗/dt)⊥ is invariant under the Lorentz transformation. The subscripts ∥ and ⊥ denote the respective components with respect to the direction of the velocity of the body v⃗, and p⃗ is the relativistic momentum. We show that this vector is equal to a force F⃗R, which satisfies the classical Newtonian law F⃗R=ma⃗R in the instantaneous inertial rest frame of an accelerating body. Therefore, the relation F⃗R=(dp⃗/dt)∥+γv(dp⃗/dt)⊥, based on the Lorentz-invariant vectors, may be used as an invariant (not merely a covariant) relativistic equation of motion in any inertial system of reference. An alternative approach to classical electrodynamics based on the invariant three-vectors is proposed.
CPT violation implies violation of Lorentz invariance.
Greenberg, O W
2002-12-01
A interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal. PMID:12484997
Invariant facial feature extraction using biologically inspired strategies
NASA Astrophysics Data System (ADS)
Du, Xing; Gong, Weiguo
2011-12-01
In this paper, a feature extraction model for face recognition is proposed. This model is constructed by implementing three biologically inspired strategies, namely a hierarchical network, a learning mechanism of the V1 simple cells, and a data-driven attention mechanism. The hierarchical network emulates the functions of the V1 cortex to progressively extract facial features invariant to illumination, expression, slight pose change, and variations caused by local transformation of facial parts. In the network, filters that account for the local structures of the face are derived through the learning mechanism and used for the invariant feature extraction. The attention mechanism computes a saliency map for the face, and enhances the salient regions of the invariant features to further improve the performance. Experiments on the FERET and AR face databases show that the proposed model boosts the recognition accuracy effectively.
Machine learning strategies for systems with invariance properties
Ling, Julia; Jones, Reese E.; Templeton, Jeremy Alan
2016-01-01
Here, in many scientific fields, empirical models are employed to facilitate computational simulations of engineering systems. For example, in fluid mechanics, empirical Reynolds stress closures enable computationally-efficient Reynolds-Averaged Navier-Stokes simulations. Likewise, in solid mechanics, constitutive relations between the stress and strain in a material are required in deformation analysis. Traditional methods for developing and tuning empirical models usually combine physical intuition with simple regression techniques on limited data sets. The rise of high-performance computing has led to a growing availability of high-fidelity simulation data, which open up the possibility of using machine learning algorithms, such as random forests or neural networks, to develop more accurate and general empirical models. A key question when using data-driven algorithms to develop these models is how domain knowledge should be incorporated into the machine learning process. This paper will specifically address physical systems that possess symmetry or invariance properties. Two different methods for teaching a machine learning model an invariance property are compared. In the first , a basis of invariant inputs is constructed, and the machine learning model is trained upon this basis, thereby embedding the invariance into the model. In the second method, the algorithm is trained on multiple transformations of the raw input data until the model learns invariance to that transformation. Results are discussed for two case studies: one in turbulence modeling and one in crystal elasticity. It is shown that in both cases embedding the invariance property into the input features yields higher performance with significantly reduced computational training costs.
Machine learning strategies for systems with invariance properties
NASA Astrophysics Data System (ADS)
Ling, Julia; Jones, Reese; Templeton, Jeremy
2016-08-01
In many scientific fields, empirical models are employed to facilitate computational simulations of engineering systems. For example, in fluid mechanics, empirical Reynolds stress closures enable computationally-efficient Reynolds Averaged Navier Stokes simulations. Likewise, in solid mechanics, constitutive relations between the stress and strain in a material are required in deformation analysis. Traditional methods for developing and tuning empirical models usually combine physical intuition with simple regression techniques on limited data sets. The rise of high performance computing has led to a growing availability of high fidelity simulation data. These data open up the possibility of using machine learning algorithms, such as random forests or neural networks, to develop more accurate and general empirical models. A key question when using data-driven algorithms to develop these empirical models is how domain knowledge should be incorporated into the machine learning process. This paper will specifically address physical systems that possess symmetry or invariance properties. Two different methods for teaching a machine learning model an invariance property are compared. In the first method, a basis of invariant inputs is constructed, and the machine learning model is trained upon this basis, thereby embedding the invariance into the model. In the second method, the algorithm is trained on multiple transformations of the raw input data until the model learns invariance to that transformation. Results are discussed for two case studies: one in turbulence modeling and one in crystal elasticity. It is shown that in both cases embedding the invariance property into the input features yields higher performance at significantly reduced computational training costs.
Machine learning strategies for systems with invariance properties
Ling, Julia; Jones, Reese E.; Templeton, Jeremy Alan
2016-05-06
Here, in many scientific fields, empirical models are employed to facilitate computational simulations of engineering systems. For example, in fluid mechanics, empirical Reynolds stress closures enable computationally-efficient Reynolds-Averaged Navier-Stokes simulations. Likewise, in solid mechanics, constitutive relations between the stress and strain in a material are required in deformation analysis. Traditional methods for developing and tuning empirical models usually combine physical intuition with simple regression techniques on limited data sets. The rise of high-performance computing has led to a growing availability of high-fidelity simulation data, which open up the possibility of using machine learning algorithms, such as random forests or neuralmore » networks, to develop more accurate and general empirical models. A key question when using data-driven algorithms to develop these models is how domain knowledge should be incorporated into the machine learning process. This paper will specifically address physical systems that possess symmetry or invariance properties. Two different methods for teaching a machine learning model an invariance property are compared. In the first , a basis of invariant inputs is constructed, and the machine learning model is trained upon this basis, thereby embedding the invariance into the model. In the second method, the algorithm is trained on multiple transformations of the raw input data until the model learns invariance to that transformation. Results are discussed for two case studies: one in turbulence modeling and one in crystal elasticity. It is shown that in both cases embedding the invariance property into the input features yields higher performance with significantly reduced computational training costs.« less
Invariants of triangular Lie algebras
NASA Astrophysics Data System (ADS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-07-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated.
Abelian link invariants and homology
Guadagnini, Enore; Mancarella, Francesco
2010-06-15
We consider the link invariants defined by the quantum Chern-Simons field theory with compact gauge group U(1) in a closed oriented 3-manifold M. The relation of the Abelian link invariants with the homology group of the complement of the links is discussed. We prove that, when M is a homology sphere or when a link--in a generic manifold M--is homologically trivial, the associated observables coincide with the observables of the sphere S{sup 3}. Finally, we show that the U(1) Reshetikhin-Turaev surgery invariant of the manifold M is not a function of the homology group only, nor a function of the homotopy type of M alone.
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.
Experimental observations of active invariance striations in a tank environment.
Quijano, Jorge E; Campbell, Richard L; Oesterlein, Tobias G; Zurk, Lisa M
2010-08-01
The waveguide invariant in shallow water environments has been widely studied in the context of passive sonar. The invariant provides a relationship between the frequency content of a moving broadband source and the distance to the receiver, and this relationship is not strongly affected by small perturbations in environment parameters such as sound speed or bottom features. Recent experiments in shallow water suggest that a similar range-frequency structure manifested as striations in the spectrogram exists for active sonar, and this property has the potential to enhance the performance of target tracking algorithms. Nevertheless, field experiments with active sonar have not been conclusive on how the invariant is affected by the scattering kernel of the target and the sonar configuration (monostatic vs bistatic). The experimental work presented in this paper addresses those issues by showing the active invariance for known scatterers under controlled conditions of bathymetry, sound speed profile and high SNR. Quantification of the results is achieved by introducing an automatic image processing approach inspired on the Hough transform for extraction of the invariant from spectrograms. Normal mode simulations are shown to be in agreement with the experimental results. PMID:20707430
Onboard Image Registration from Invariant Features
NASA Technical Reports Server (NTRS)
Wang, Yi; Ng, Justin; Garay, Michael J.; Burl, Michael C
2008-01-01
This paper describes a feature-based image registration technique that is potentially well-suited for onboard deployment. The overall goal is to provide a fast, robust method for dynamically combining observations from multiple platforms into sensors webs that respond quickly to short-lived events and provide rich observations of objects that evolve in space and time. The approach, which has enjoyed considerable success in mainstream computer vision applications, uses invariant SIFT descriptors extracted at image interest points together with the RANSAC algorithm to robustly estimate transformation parameters that relate one image to another. Experimental results for two satellite image registration tasks are presented: (1) automatic registration of images from the MODIS instrument on Terra to the MODIS instrument on Aqua and (2) automatic stabilization of a multi-day sequence of GOES-West images collected during the October 2007 Southern California wildfires.
Invariant conserved currents in generalized gravity
NASA Astrophysics Data System (ADS)
Obukhov, Yuri N.; Portales-Oliva, Felipe; Puetzfeld, Dirk; Rubilar, Guillermo F.
2015-11-01
We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to non-Riemannian spacetime geometry and nonminimal coupling. We demonstrate that an arbitrary vector field on the spacetime manifold generates a current density that is conserved under certain conditions, and find the expression of the corresponding superpotential. For a family of models including nonminimal coupling between geometry and matter, we discuss in detail the differential conservation laws and the conserved quantities defined in terms of covariant multipole moments. We show that the equations of motion for the multipole moments of extended microstructured test bodies lead to conserved quantities that are closely related to the conserved currents derived in the field-theoretic framework.
Affinity chromatography: a historical perspective.
Hage, David S; Matsuda, Ryan
2015-01-01
Affinity chromatography is one of the most selective and versatile forms of liquid chromatography for the separation or analysis of chemicals in complex mixtures. This method makes use of a biologically related agent as the stationary phase, which provides an affinity column with the ability to bind selectively and reversibly to a given target in a sample. This review examines the early work in this method and various developments that have lead to the current status of this technique. The general principles of affinity chromatography are briefly described as part of this discussion. Past and recent efforts in the generation of new binding agents, supports, and immobilization methods for this method are considered. Various applications of affinity chromatography are also summarized, as well as the influence this field has played in the creation of other affinity-based separation or analysis methods. PMID:25749941
Dark coupling and gauge invariance
Gavela, M.B.; Honorez, L. Lopez; Rigolin, S. E-mail: llopezho@ulb.ac.be E-mail: stefano.rigolin@pd.infn.it
2010-11-01
We study a coupled dark energy-dark matter model in which the energy-momentum exchange is proportional to the Hubble expansion rate. The inclusion of its perturbation is required by gauge invariance. We derive the linear perturbation equations for the gauge invariant energy density contrast and velocity of the coupled fluids, and we determine the initial conditions. The latter turn out to be adiabatic for dark energy, when assuming adiabatic initial conditions for all the standard fluids. We perform a full Monte Carlo Markov Chain likelihood analysis of the model, using WMAP 7-year data.
Affinity Inequality among Serum Antibodies That Originate in Lymphoid Germinal Centers
Eisen, Ellen A.; Chakraborty, Arup K.
2015-01-01
Upon natural infection with pathogens or vaccination, antibodies are produced by a process called affinity maturation. As affinity maturation ensues, average affinity values between an antibody and ligand increase with time. Purified antibodies isolated from serum are invariably heterogeneous with respect to their affinity for the ligands they bind, whether macromolecular antigens or haptens (low molecular weight approximations of epitopes on antigens). However, less is known about how the extent of this heterogeneity evolves with time during affinity maturation. To shed light on this issue, we have taken advantage of previously published data from Eisen and Siskind (1964). Using the ratio of the strongest to the weakest binding subsets as a metric of heterogeneity (or affinity inequality), we analyzed antibodies isolated from individual serum samples. The ratios were initially as high as 50-fold, and decreased over a few weeks after a single injection of small antigen doses to around unity. This decrease in the effective heterogeneity of antibody affinities with time is consistent with Darwinian evolution in the strong selection limit. By contrast, neither the average affinity nor the heterogeneity evolves much with time for high doses of antigen, as competition between clones of the same affinity is minimal. PMID:26444899
Thomas, Anthony W.
2008-10-13
We discuss recent theoretical progress in understanding the distribution of spin and orbital angular momentum in the proton. Particular attention is devoted to the effect of QCD evolution and to the distinction between 'chiral' and 'invariant' spin. This is particularly significant with respect to the possible presence of polarized strange quarks.
Link invariants of electromagnetic fields.
von Bodecker, Hanno; Hornig, Gunnar
2004-01-23
The cross-helicity integral is known in fluid dynamics and plasma physics as a topological invariant which measures the mutual linkage of two divergence-free vector fields, e.g., magnetic fields, on a three-dimensional domain. Generalizing this concept, a new topological invariant is found which measures the mutual linkage of three closed two-forms, e.g., electromagnetic fields, on a four-dimensional domain. The integral is shown to detect a separation of the cross helicity between two of the fields with the help of the third field. It can be related to the triple linking number known in knot theory. Furthermore, it is shown that the well-known three-dimensional cross helicity and the new four-dimensional invariant are the first two examples of a series of topological invariants which are defined by n-1 field strengths F=dA on a simply connected n-dimensional manifold M(n). PMID:14753856
Thomas, Anthony
2008-11-01
We discuss recent theoretical progress in understanding the distribution of spin and orbital angular momentum in the proton. Particular attention is devoted to the effect of QCD evolution and to the distinction between "chiral" and "invariant" spin. This is particularly significant with respect to the possible presence of polarized strange quarks.
Gauge-invariant masses through Schwinger-Dyson equations
Bashir, A.; Raya, A.
2007-02-27
Schwinger-Dyson equations (SDEs) are an ideal framework to study non-perturbative phenomena such as dynamical chiral symmetry breaking (DCSB). A reliable truncation of these equations leading to gauge invariant results is a challenging problem. Constraints imposed by Landau-Khalatnikov-Fradkin transformations (LKFT) can play an important role in the hunt for physically acceptable truncations. We present these constrains in the context of dynamical mass generation in QED in 2 + 1-dimensions.
Local unitary invariants for N-qubit pure states
Sharma, S. Shelly; Sharma, N. K.
2010-11-15
The concept of negativity font, a basic unit of multipartite entanglement, is introduced. Transformation properties of determinants of negativity fonts under local unitary (LU) transformations are exploited to obtain relevant N-qubit polynomial invariants and construct entanglement monotones from first principles. It is shown that entanglement monotones that detect the entanglement of specific parts of the composite system may be constructed to distinguish between states with distinct types of entanglement. The structural difference between entanglement monotones for an odd and even number of qubits is brought out.
The solar system's invariable plane
NASA Astrophysics Data System (ADS)
Souami, D.; Souchay, J.
2012-07-01
Context. The dynamics of solar system objects, such as dwarf planets and asteroids, has become a well-established field of celestial mechanics in the past thirty years, owing to the improvements that have been made in observational techniques and numerical studies. In general, the ecliptic is taken as the reference plane in these studies, although there is no dynamical reason for doing so. In contrast, the invariable plane as originally defined by Laplace, seems to be a far more natural choice. In this context, the latest study of this plane dates back to Burkhardt. Aims: We define and determine the orientation of the invariable plane of the solar system with respect to both the ICRF and the equinox-ecliptic of J2000.0, and evaluate the accuracy of our determination. Methods: Using the long-term numerical ephemerides DE405, DE406, and INPOP10a over their entire available time span, we computed the total angular momentum of the solar system, as well as the individual contribution to it made by each of the planets, the dwarf planets Pluto and Ceres, and the two asteroids Pallas and Vesta. We then deduced the orientation of the invariable plane from these ephemerides. Results: We update the previous results on the determination of the orientation of the invariable plane with more accurate data, and a more complete analysis of the problem, taking into account the effect of the dwarf planet (1) Ceres as well as two of the biggest asteroids, (4) Vesta and (2) Pallas. We show that the inclusion of these last three bodies significantly improves the accuracy of determination of the invariable plane, whose orientation over a 100 y interval does not vary more than 0.1 mas in inclination, and 0.3 mas in longitude of the ascending node. Moreover, we determine the individual contributions of each body to the total angular momentum of the solar system, as well as the inclination and longitude of the node with respect to this latter plane. Conclusions: Owing to the high accuracy
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%.
SLOCC invariants for multipartite mixed states
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Li, Ming; Li-Jost, Xianqing; Zhang, Tinggui; Fei, Shao-Ming
2014-05-01
We construct a nontrivial set of invariants for any multipartite mixed states under the stochastic local operations and classical communication symmetry. These invariants are given by hyperdeterminants and independent of basis change. In particular, a family of d2 invariants for arbitrary d-dimensional even partite mixed states are explicitly given.
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…
Supergravity with broken Lorentz invariance
NASA Astrophysics Data System (ADS)
Marakulin, A. O.; Sibiryakov, S. M.
Incompatibility of the principles of quantum field theory with general relativity is one of the most important problems in modern theoretical physics. A potential way out of this situation consists in restricting the domain of validity of some basic postulates of general relativity and abandoning them at high energy scales. A promising approach to quantization of gravity based on abandoning the Lorentz invariance has been proposed by Horava. The low-energy limit of the Horava theory, called khrono-metric model, presents a special case of the Einstein-aether gravity. In the latter model violation of the Lorentz invariance is described by the time-like vector field um with unit norm (umum = -1) called aether that minimally couples to the Einstein-Hilbert action for gravity.
Quantum mechanics from invariance principles
NASA Astrophysics Data System (ADS)
Moldoveanu, Florin
2015-07-01
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.
Geometry-invariant resonant cavities
NASA Astrophysics Data System (ADS)
Liberal, I.; Mahmoud, A. M.; Engheta, N.
2016-03-01
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices.
Geometry-invariant resonant cavities
Liberal, I.; Mahmoud, A. M.; Engheta, N.
2016-01-01
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices. PMID:27010103
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.
Permutation-invariant quantum codes
NASA Astrophysics Data System (ADS)
Ouyang, Yingkai
2014-12-01
A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded. Ideally, the quantum code lies within the ground space of the physical system. When the physical model is the Heisenberg ferromagnet in the absence of an external magnetic field, the corresponding ground space contains all permutation-invariant states. We use techniques from combinatorics and operator theory to construct families of permutation-invariant quantum codes. These codes have length proportional to t2; one family of codes perfectly corrects arbitrary weight t errors, while the other family of codes approximately correct t spontaneous decay errors. The analysis of our codes' performance with respect to spontaneous decay errors utilizes elementary matrix analysis, where we revisit and extend the quantum error correction criterion of Knill and Laflamme, and Leung, Chuang, Nielsen and Yamamoto.
Holographic multiverse and conformal invariance
Garriga, Jaume; Vilenkin, Alexander E-mail: vilenkin@cosmos.phy.tufts.edu
2009-11-01
We consider a holographic description of the inflationary multiverse, according to which the wave function of the universe is interpreted as the generating functional for a lower dimensional Euclidean theory. We analyze a simple model where transitions between inflationary vacua occur through bubble nucleation, and the inflating part of spacetime consists of de Sitter regions separated by thin bubble walls. In this model, we present some evidence that the dual theory is conformally invariant in the UV.
Conformal Invariance of Graphene Sheets
Giordanelli, I.; Posé, N.; Mendoza, M.; Herrmann, H. J.
2016-01-01
Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent 0.72 ± 0.01. Here, we show that, independent of the temperature, the iso-height lines at the percolation threshold have a well-defined fractal dimension and are conformally invariant, sharing the same statistical properties as Schramm-Loewner evolution (SLEκ) curves with κ = 2.24 ± 0.07. Interestingly, iso-height lines of other rough surfaces are not necessarily conformally invariant even if they have the same Hurst exponent, e.g. random Gaussian surfaces. We have found that the distribution of the modulus of the Fourier coefficients plays an important role on this property. Our results not only introduce a new universality class and place the study of suspended graphene membranes within the theory of critical phenomena, but also provide hints on the long-standing question about the origin of conformal invariance in iso-height lines of rough surfaces. PMID:26961723
Inflationary quasiscale-invariant attractors
NASA Astrophysics Data System (ADS)
Rinaldi, Massimiliano; Vanzo, Luciano; Zerbini, Sergio; Venturi, Giovanni
2016-01-01
In a series of recent papers Kallosh, Linde, and collaborators provide a unified description of single-field inflation with several types of potentials ranging from power law to supergravity, in terms of just one parameter α . These so-called α attractors predict a spectral index ns and a tensor-to-scalar ratio r , which are fully compatible with the latest Planck data. The only common feature of all α attractors is a noncanonical kinetic term with a pole, and a potential analytic around the pole. In this paper, starting from the same Einstein frame with a noncanonical scalar kinetic energy, we explore the case of nonanalytic potentials. We find the functional form that corresponds to quasiscale-invariant gravitational models in the Jordan frame characterized by a universal relation between r and ns that fits the observational data but is clearly distinct from the one of the α attractors. It is known that the breaking of the exact classical scale invariance in the Jordan frame can be attributed to one-loop corrections. Therefore we conclude that there exists a class of nonanalytic potentials in the noncanonical Einstein frame that is physically equivalent to a class of models in the Jordan frame, with scale invariance softly broken by one-loop quantum corrections.
Conformal Invariance of Graphene Sheets.
Giordanelli, I; Posé, N; Mendoza, M; Herrmann, H J
2016-01-01
Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent 0.72 ± 0.01. Here, we show that, independent of the temperature, the iso-height lines at the percolation threshold have a well-defined fractal dimension and are conformally invariant, sharing the same statistical properties as Schramm-Loewner evolution (SLEκ) curves with κ = 2.24 ± 0.07. Interestingly, iso-height lines of other rough surfaces are not necessarily conformally invariant even if they have the same Hurst exponent, e.g. random Gaussian surfaces. We have found that the distribution of the modulus of the Fourier coefficients plays an important role on this property. Our results not only introduce a new universality class and place the study of suspended graphene membranes within the theory of critical phenomena, but also provide hints on the long-standing question about the origin of conformal invariance in iso-height lines of rough surfaces. PMID:26961723
Benacquista, M.J.
1988-01-01
The gravitational many-body parameterized post-Newtonian (PNN) Lagrangian for compact celestial bodies is extended to second post-Newtonian order and is constrained to exhibit the invariances observed in nature-generalized Lorentz invariance, the strong equivalence principle, and the isotropy of the gravitational potential. These invariances are imposed on the Lagrangian using an empirical approach which is based on calculated observables rather than through formal procedures involving post-Newtonian approximations of transformations. When restricted in this way, the Lagrangian possesses two free parameters which can be related to light-deflection experiments and the effect of an environment of proximate matter on such experiments.
IGES transformer and NURBS in grid generation
NASA Technical Reports Server (NTRS)
Yu, Tzu-Yi; Soni, Bharat K.
1993-01-01
In the field of Grid Generation and the CAD/CAM, there are numerous geometry output formats which require the designer to spend a great deal of time manipulating geometrical entities in order to achieve a useful sculptured geometrical description for grid generation. Also in this process, there is a danger of losing fidelity of the geometry under consideration. This stresses the importance of a standard geometry definition for the communication link between varying CAD/CAM and grid system. The IGES (Initial Graphics Exchange Specification) file is a widely used communication between CAD/CAM and the analysis tools. The scientists at NASA Research Centers - including NASA Ames, NASA Langley, NASA Lewis, NASA Marshall - have recognized this importance and, therefore, in 1992 they formed the committee of the 'NASA-IGES' which is the subset of the standard IGES. This committee stresses the importance and encourages the CFD community to use the standard IGES file for the interface between the CAD/CAM and CFD analysis. Also, two of the IGES entities -- the NURBS Curve (Entity 126) and NURBS Surface (Entity 128) -- which have many useful geometric properties -- like the convex hull property, local control property and affine invariance, also widely utilized analytical geometries can be accurately represented using NURBS. This is important in today grid generation tools because of the emphasis of the interactive design. To satisfy the geometry transformation between the CAD/CAM system and Grid Generation field, the CAGI (Computer Aided Geometry Design) developed, which include the Geometry Transformation, Geometry Manipulation and Geometry Generation as well as the user interface. This paper will present the successful development IGES file transformer and application of NURBS definition in the grid generation.
Einstein gravity as a 3D conformally invariant theory
NASA Astrophysics Data System (ADS)
Gomes, Henrique; Gryb, Sean; Koslowski, Tim
2011-02-01
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is irrelevant. The dual theory is invariant under foliation-preserving 3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume (for the spatially compact case). Locally, this symmetry is identical to that of Hořava-Lifshitz gravity in the high energy limit but our theory is equivalent to Einstein gravity. Specifically, we find that the solutions of general relativity, in a gauge where the spatial hypersurfaces have constant mean extrinsic curvature, can be mapped to solutions of a particular gauge fixing of the dual theory. Moreover, this duality is not accidental. We provide a general geometric picture for our procedure that allows us to trade foliation invariance for conformal invariance. The dual theory provides a new proposal for the theory space of quantum gravity.
NASA Astrophysics Data System (ADS)
Ma, Jianwei; Jiang, Xiangqian; Scott, Paul
2005-09-01
A complex ridgelet transform, which provides shift invariance and good performance for line singularities, is proposed to solve the problems with existing wavelet-based methods in surface metrology by taking a dual-tree complex wavelet transform on the projections of the finite Radon transform. Numerical experiments show the efficiency of this methodology in approximation, denoising, and characterization of engineering and bioengineering surfaces with straight scratches.
Super-Weyl invariance in 5D supergravity
NASA Astrophysics Data System (ADS)
Kuzenko, Sergei M.; Tartaglino-Mazzucchelli, Gabriele
2008-04-01
We propose a superspace formulation for the Weyl multiplet of Script N = 1 conformal supergravity in five dimensions. The corresponding superspace constraints are invariant under super-Weyl transformations generated by a real scalar parameter. The minimal supergravity multiplet, which was introduced by Howe in 1981, emerges if one couples the Weyl multiplet to an Abelian vector multiplet and then breaks the super-Weyl invariance by imposing the gauge condition W = 1, with W the field strength of the vector multiplet. The geometry of superspace is shown to allow the existence of a large family of off-shell supermultiplets that possess uniquely determined super-Weyl transformation laws and can be used to describe supersymmetric matter. Many of these supermultiplets have not appeared within the superconformal tensor calculus. We formulate a manifestly locally supersymmetric and super-Weyl invariant action principle. In the super-Weyl gauge W = 1, this action reduces to that constructed in arXiv:0712.3102. We also present a superspace formulation for the dilaton Weyl multiplet.
Wilson lines and gauge invariant off-shell amplitudes
NASA Astrophysics Data System (ADS)
Kotko, Piotr
2014-07-01
We study matrix elements of Fourier-transformed straight infinite Wilson lines as a way to calculate gauge invariant tree-level amplitudes with off-shell gluons. The off-shell gluons are assigned "polarization vectors" which (in the Feynman gauge) are transverse to their off-shell momenta and define the direction of the corresponding Wilson line operators. The infinite Wilson lines are first regularized to prove the correctness of the method. We have implemented the method in a computer FORM program that can calculate gluonic matrix elements of Wilson line operators automatically. In addition we formulate the Feynman rules that are convenient in certain applications, e.g. proving the Ward identities. Using both the program and the Feynman rules we calculate a few examples, in particular the matrix elements corresponding to gauge invariant g * g * g * g and g * g * g * g * g processes. An immediate application of the approach is in the high energy scattering, as in a special kinematic setup our results reduce to the form directly related to Lipatov's vertices. Thus the results we present can be directly transformed into Lipatov's vertices, in particular into RRRP and RRRRP vertices with arbitrary "orientation" of reggeized gluons. Since the formulation itself is not restricted to high-energy scattering, we also apply the method to a decomposition of an ordinary on-shell amplitude into a set of gauge invariant objects.
Invariant recognition of polychromatic images of Vibrio cholerae 01
NASA Astrophysics Data System (ADS)
Alvarez-Borrego, Josue; Mourino-Perez, Rosa R.; Cristobal, Gabriel; Pech-Pacheco, Jose L.
2002-04-01
Cholera is an acute intestinal infectious disease. It has claimed many lives throughout history, and it continues to be a global health threat. Cholera is considered one of the most important emergence diseases due its relation with global climate changes. Automated methods such as optical systems represent a new trend to make more accurate measurements of the presence and quantity of this microorganism in its natural environment. Automatic systems eliminate observer bias and reduce the analysis time. We evaluate the utility of coherent optical systems with invariant correlation for the recognition of Vibrio cholerae O1. Images of scenes are recorded with a CCD camera and decomposed in three RGB channels. A numeric simulation is developed to identify the bacteria in the different samples through an invariant correlation technique. There is no variation when we repeat the correlation and the variation between images correlation is minimum. The position-, scale-, and rotation-invariant recognition is made with a scale transform through the Mellin transform. The algorithm to recognize Vibrio cholerae O1 is the presence of correlation peaks in the green channel output and their absence in red and blue channels. The discrimination criterion is the presence of correlation peaks in red, green, and blue channels.
Affinities of the Swartkrans early Homo mandibles.
Curnoe, Darren
2008-01-01
The southern African early Homo assemblage continues to make important contributions to understanding the systematics, adaptations and evolutionary history of the human genus. However, the taxonomy of this sample is in a state of flux. This study examines the size and shape of the mandibular bodies of Swartkrans SK 15 and SK 45 comparing them with variation in two early Homo taxa (H. habilis sensu lato and H. sapiens erectus). The research aims to clarify their phenetic affinities and systematics through univariate statistics, inferential testing and multivariate analysis employing size (Log-transformed) and shape (Mosimann variables). Neither of them strongly resembles H. habilis sensu lato or H. sapiens erectus, rather, they probably sample a novel species of Homo not seen in East Africa. Moreover, there is considerable morphological variability within the Swartkrans sample and the possibility of more than one novel species being sampled at this site cannot be excluded. PMID:18402959
Recent advances in affinity capillary electrophoresis for binding studies.
Albishri, Hassan M; El Deeb, Sami; AlGarabli, Noura; AlAstal, Raghda; Alhazmi, Hassan A; Nachbar, Markus; El-Hady, Deia Abd; Wätzig, Hermann
2014-01-01
The present review covers recent advances and important applications of affinity capillary electrophoresis (ACE). It provides an overview about various ACE types, including ACE-MS, the multiple injection mode, the use of microchips and field-amplified sample injection-ACE. The most common scenarios of the studied affinity interactions are protein-drug, protein-metal ion, protein-protein, protein-DNA, protein-carbohydrate, carbohydrate-drug, peptide-peptide, DNA-drug and antigen-antibody. Approaches for the improvements of ACE in term of precision, rinsing protocols and sensitivity are discussed. The combined use of computer simulation programs to support data evaluation is presented. In conclusion, the performance of ACE is compared with other techniques such as equilibrium dialysis, parallel artificial membrane permeability assay, high-performance affinity chromatography as well as surface plasmon resonance, ultraviolet, circular dichroism, nuclear magnetic resonance, Fourier transform infrared, fluorescence, MS and isothermal titration calorimetry. PMID:25534793
NASA Astrophysics Data System (ADS)
Apte, Amit Shriram
This thesis presents numerical explorations of area-preserving nontwist maps, and a renormalization group framework for the destruction of invariant tori. We study the phenomena of bifurcation and reconnection, and the emergence of meandering tori which are non-KAM invariant curves. We also study the breakup of shearless invariant tori with noble winding numbers using improved numerical techniques to implement Greene's residue criterion. We interpret the breakup of invariant tori within a renormalization group framework by constructing renormalization group operators for the tori with winding numbers that are quadratic irrationals. We find the simple fixed points of these operators and interpret the map pairs with critical invariant tori as critical fixed points. We introduce coordinate transformations on the space of maps to relate these fixed points to each other. These transformations induce conjugacies between the corresponding operators, and provide a new perspective on the space of area-preserving maps.
NASA Astrophysics Data System (ADS)
Macsleyne, Jeremiah P.
The relation between microstructural features and a material's properties is central to materials science. Certain morphological features of a microstructure can only be determined by 3-D characterization techniques, e.g. the connectivity of precipitates, and the true precipitate shape; others require geometric assumptions for stereological estimates, e.g. precipitate size distribution and the number of precipitates. When these inherently 3-D features affect the properties of a specific material, experimental techniques are necessary to investigate the 3-D nature of the microstructure, and to provide a more complete microstructural characterization. The quantitative description of 2-D and 3-D shapes is of fundamental importance to microstructural characterization. One approach to describing a microstructure is to characterize the shapes of individual precipitates. This characterization has typically been limited to particle size, aspect-ratio, and other qualitative descriptors. In general, these are insufficient and do not provide an adequate characterization in a way that allows for a direct comparison between different microstructures. This is evident during microstructure evolution when changes in precipitate morphology occur or when precipitates exhibit complex shapes. In this thesis, we show how moment invariants (combinations of second order moments that are invariant w.r.t. affine or similarity transformations) can be used as sensitive shape discriminators in 2-D and 3-D. This work focuses on the characterization of the two phase microstructure of nickel base superalloys and specically the gamma-prime (Ni3Al) precipitate morphology. Experimental data is collected by means of automated Focused-Ion Beam (FIB) based serial sectioning. Techniques for automated image processing and segmentation are developed which allow for direct conversion of raw serial-sectioning data to 3-D microstructural data. The gamma-prime precipitate morphology is characterized using
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.
About Thinning Invariant Partition Structures
NASA Astrophysics Data System (ADS)
Starr, Shannon; Vermesi, Brigitta; Wei, Ang
2012-08-01
Bernoulli- p thinning has been well-studied for point processes. Here we consider three other cases: (1) sequences ( X 1, X 2,…); (2) gaps of such sequences ( X n+1- X 1) n∈ℕ; (3) partition structures. For the first case we characterize the distributions which are simultaneously invariant under Bernoulli- p thinning for all p∈(0,1]. Based on this, we make conjectures for the latter two cases, and provide a potential approach for proof. We explain the relation to spin glasses, which is complementary to important previous work of Aizenman and Ruzmaikina, Arguin, and Shkolnikov.
Quantum Weyl invariance and cosmology
NASA Astrophysics Data System (ADS)
Dabholkar, Atish
2016-09-01
Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.
Overview of affinity tags for protein purification.
Kimple, Michelle E; Sondek, John
2004-09-01
Addition of an affinity tag is a useful method for differentiating recombinant proteins expressed in bacterial and eukaryotic expression systems from the background of total cellular proteins, and for detecting protein-protein interactions. This overview describes the historical basis for the development of affinity tags, affinity tags that are commonly used today, how to choose an appropriate affinity tag for a particular purpose, and several recently developed affinity tag technologies that may prove useful in the near future. PMID:18429272
Overview of affinity tags for protein purification.
Kimple, Michelle E; Brill, Allison L; Pasker, Renee L
2013-01-01
Addition of an affinity tag is a useful method for differentiating recombinant proteins expressed in bacterial and eukaryotic expression systems from the background of total cellular proteins, as well as for detecting protein-protein interactions. This overview describes the historical basis for the development of affinity tags, affinity tags that are commonly used today, how to choose an appropriate affinity tag for a particular purpose, and several recently developed affinity tag technologies that may prove useful in the near future. PMID:24510596
Digital system of invariant correlation to position and rotation
NASA Astrophysics Data System (ADS)
Solorza, Selene; Álvarez-Borrego, Josué
2010-10-01
A new correlation digital system invariant to position and rotation is presented. This new algorithm requires low computational cost, because it uses uni-dimensional signatures (vectors). The signature of the target so like the signature of the object to be recognized in the problem image is obtained using a binary ring mask constructed based on the real positive values of the Fourier transform of the corresponding image. In this manner, each image will have one unique binary ring mask, avoiding in this form the relevant information leak. Using linear and non-linear correlations, this methodology is applied first in the identification of the alphabet letters in Arial font style and then in the classification of fossil diatoms images. Also, this system is tested using the diatom images with additive Gaussian noise. The non-linear correlation results were excellent, obtaining in this way a simple but efficient method to achieve rotation and translation invariance pattern recognition.
Invariant expansion for the trigonal band structure of graphene
NASA Astrophysics Data System (ADS)
Winkler, R.; Zülicke, U.
2010-12-01
We present a symmetry analysis of the trigonal band structure in graphene, elucidating the transformational properties of the underlying basis functions and the crucial role of time-reversal invariance. Group theory is used to derive an invariant expansion of the Hamiltonian for electron states near the K points of the graphene Brillouin zone. Besides yielding the characteristic k -linear dispersion and higher oder corrections to it, this approach enables the systematic incorporation of all terms arising from external electric and magnetic fields, strain, and spin-orbit coupling up to any desired order. Several new contributions are found, in addition to reproducing results obtained previously within tight-binding calculations. Physical ramifications of these new terms are discussed.
The path to cost transformation.
Hill-Mischel, Jody; Morrissey, Walter W; Neese, Kimberly; Shoger, Timothy R
2016-06-01
A healthcare organization's efforts to strategically transform its cost structure in preparation for value-based payment invariably must begin with a systemwide assessment of cost and quality. Such an assessment should focus on three categories of performance improvement activities: margin improvement, business restructuring, and clinical transformation. A work-team approach is recommended, where teams with multidisciplinary representation assume responsibility for assessing specific areas (e.g., acute care enterprise, physician enterprise, business restructuring). PMID:27451567
Quantifying Affinity among Chinese Dialects.
ERIC Educational Resources Information Center
Cheng, Chin-Chuan
A study of the relationships between Chinese dialects based on a quantitative measure of dialect affinity is summarized. First, tone values in all the dialect localities available in the early 1970s were used to calculate the dialectal differences in terms of tone height with respect to the "yin and yang" split. In the late 1970s, calculations of…
Effect of VSR invariant Chern-Simons Lagrangian on photon polarization
Nayak, Alekha C.; Verma, Ravindra K.; Jain, Pankaj
2015-07-21
We propose a generalization of the Chern-Simons (CS) Lagrangian which is invariant under the SIM(2) transformations but not under the full Lorentz group. The generalized lagrangian is also invariant under a SIM(2) gauge transformation. We study the effect of such a term on radiation propagating over cosmological distances. We find that the dominant effect of this term is to produce circular polarization as radiation propagates through space. We use the circular polarization data from distant radio sources in order to impose a limit on this term.
Size-dependent word frequencies and translational invariance of books
NASA Astrophysics Data System (ADS)
Bernhardsson, Sebastian; da Rocha, Luis Enrique Correa; Minnhagen, Petter
2010-01-01
It is shown that a real novel shares many characteristic features with a null model in which the words are randomly distributed throughout the text. Such a common feature is a certain translational invariance of the text. Another is that the functional form of the word-frequency distribution of a novel depends on the length of the text in the same way as the null model. This means that an approximate power-law tail ascribed to the data will have an exponent which changes with the size of the text-section which is analyzed. A further consequence is that a novel cannot be described by text-evolution models such as the Simon model. The size-transformation of a novel is found to be well described by a specific Random Book Transformation. This size transformation in addition enables a more precise determination of the functional form of the word-frequency distribution. The implications of the results are discussed.
Invariant imbedding in two dimensions
Faber, V.; Seth, D.L.; Wing, G.M.
1988-01-01
J. Corones has noted that the doubling and addition formulas of invariant imbedding can be extended conceptually to very general situations. All that is needed is a black box ''process'' with n ''ports.'' The /ital i/th port has vector input I/sub i/ and vector output J/sub i/. Addition formulas result when two or more of these processes are joined together to form a new process in some regular way. For example, four congruent squares can be juxtaposed to form a larger square. At each join, the output of one process becomes the input of the other and vice versa. (We always suppose the join to occur at one or more ports.) Addition formulas result from the combination of these shared quantities. Corones has thus pointed out that invariant imbedding is not, as is sometimes asserted, an inherently one-dimensional (1-D) method, but works conceptually in any number of dimensions; some previous work that is conceptually along these lines, with references to other such works, can be found in Refs. 2-4. The details can, of course, become very complicated. We shall show that the method is computationally feasible for certain two-dimensional (2-D) problems. To conform to the thrust of these proceedings, we shall usually phrase our discussions in terms of transport theory rather than speaking of more abstract processes. 7 refs., 13 figs.
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,.
Theoretical proton affinity and fluoride affinity of nerve agent VX.
Bera, Narayan C; Maeda, Satoshi; Morokuma, Keiji; Viggiano, Al A
2010-12-23
Proton affinity and fluoride affinity of nerve agent VX at all of its possible sites were calculated at the RI-MP2/cc-pVTZ//B3LYP/6-31G* and RI-MP2/aug-cc-pVTZ//B3LYP/6-31+G* levels, respectively. The protonation leads to various unique structures, with H(+) attached to oxygen, nitrogen, and sulfur atoms; among which the nitrogen site possesses the highest proton affinity of -ΔE ∼ 251 kcal/mol, suggesting that this is likely to be the major product. In addition some H(2), CH(4) dissociation as well as destruction channels have been found, among which the CH(4) + [Et-O-P(═O)(Me)-S-(CH(2))(2)-N(+)(iPr)═CHMe] product and the destruction product forming Et-O-P(═O)(Me)-SMe + CH(2)═N(+)(iPr)(2) are only 9 kcal/mol less stable than the most stable N-protonated product. For fluoridization, the S-P destruction channel to give Et-O-P(═O)(Me)(F) + [S-(CH(2))(2)-N-(iPr)(2)](-) is energetically the most favorable, with a fluoride affinity of -ΔE ∼ 44 kcal. Various F(-) ion-molecule complexes are also found, with the one having F(-) interacting with two hydrogen atoms in different alkyl groups to be only 9 kcal/mol higher than the above destruction product. These results suggest VX behaves quite differently from surrogate systems. PMID:21117653
Wilson loop invariants from WN conformal blocks
NASA Astrophysics Data System (ADS)
Alekseev, Oleg; Novaes, Fábio
2015-12-01
Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern-Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU (N), which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra.
NASA Astrophysics Data System (ADS)
Aizenberg, Evgeni; Bigio, Irving J.; Rodriguez-Diaz, Eladio
2012-03-01
The Fourier descriptors paradigm is a well-established approach for affine-invariant characterization of shape contours. In the work presented here, we extend this method to images, and obtain a 2D Fourier representation that is invariant to image rotation. The proposed technique retains phase uniqueness, and therefore structural image information is not lost. Rotation-invariant phase coefficients were used to train a single multi-valued neuron (MVN) to recognize satellite and human face images rotated by a wide range of angles. Experiments yielded 100% and 96.43% classification rate for each data set, respectively. Recognition performance was additionally evaluated under effects of lossy JPEG compression and additive Gaussian noise. Preliminary results show that the derived rotation-invariant features combined with the MVN provide a promising scheme for efficient recognition of rotated images.
Baker, W.M.
1980-01-01
We examine the scale-invariant Lagrangian densities in Riemannian and non-Riemannian spacetimes. We find that the most general scale-invariant Lagrangian density of a Riemann-Cartan spacetime can also be reduced in a manner similar to that demonstrated earlier by Lanczos for the Riemannian case. However, this type of reduction process is not possible in a non-metric spacetime. Duality transformations of the type defined in electromagnetic theory are discussed and classified in terms of those transformations having a direct relationship to an internal symmetry structure of a given gauge theory and those that do not. We show that to build a satisfactory generalized electromagnetic type theory with local duality invariance into a gauge theory, as at least a part of its internal symmetry structure, requires a group no smaller than SO/sub 3/ or (SU/sub 2/). By considering a special metric geometry with torsion (U/sub 4/) we can describe the duality vector field of a duality invariant Maxwell theory in terms of a special form of torsion. This result indicates that the special U/sub 4/ geometry could play a role in the already unified field theory of Rainich, Misner, and Wheeler (RMW). We show how one could express the RMW conditions, together with their immediate generalizations in terms of geometric objects of the special U/sub 4/ theory. Conformal and projective transformations on the U/sub 4/ connection are examined. It is shown that an appropriate combination of these transformations have the effect of producing a special type of projective transformation on a metric connection with torsion. In the context of a gauge theory based on a U/sub 4/ spacetime, this special type of projective invariance has been interpreted as the underlying invariance principle for baryon number conservation in the same way that gauge changes on the Maxwell vector potential relate to charge conservation.
Gao, Yun; Hu, Naihong; Zhang, Honglian
2015-01-15
In this paper, we define the two-parameter quantum affine algebra for type G{sub 2}{sup (1)} and give the (r, s)-Drinfeld realization of U{sub r,s}(G{sub 2}{sup (1)}), as well as establish and prove its Drinfeld isomorphism. We construct and verify explicitly the level-one vertex representation of two-parameter quantum affine algebra U{sub r,s}(G{sub 2}{sup (1)}), which also supports an evidence in nontwisted type G{sub 2}{sup (1)} for the uniform defining approach via the two-parameter τ-invariant generating functions proposed in Hu and Zhang [Generating functions with τ-invariance and vertex representations of two-parameter quantum affine algebras U{sub r,s}(g{sup ^}): Simply laced cases e-print http://arxiv.org/abs/1401.4925 ].
Extended Weyl invariance in a bimetric model and partial masslessness
NASA Astrophysics Data System (ADS)
Hassan, S. F.; Schmidt-May, Angnis; von Strauss, Mikael
2016-01-01
We revisit a particular ghost-free bimetric model which is related to both partial masslessness (PM) and conformal gravity. Linearly, the model propagates six instead of seven degrees of freedom not only around de Sitter but also around flat spacetime. Nonlinearly, the equations of motion can be recast in the form of expansions in powers of curvatures, and exhibit a remarkable amount of structure. In this form, the equations are shown to be invariant under scalar gauge transformations, at least up to six orders in derivatives, the lowest order term being a Weyl scaling of the metrics. The terms at two-derivative order reproduce the usual PM gauge transformations on de Sitter backgrounds. At the four-derivative order, a potential obstruction that could destroy the symmetry is shown to vanish. This in turn guarantees the gauge invariance to at least six-orders in derivatives. This is equivalent to adding up to ten-derivative corrections to conformal gravity. More generally, we outline a procedure for constructing the gauge transformations order by order as an expansion in derivatives and comment on the validity and limitations of the procedure. We also discuss recent arguments against the existence of a PM gauge symmetry in bimetric theory and show that, at least in their present form, they are evaded by the model considered here. Finally, we argue that a bimetric approach to PM theory is more promising than one based on the existence of a fundamental PM field.
Robust template matching for affine resistant image watermarks.
Pereira, S; Pun, T
2000-01-01
Digital watermarks have been proposed as a method for discouraging illicit copying and distribution of copyrighted material. This paper describes a method for the secure and robust copyright protection of digital images. We present an approach for embedding a digital watermark into an image using the Fourier transform. To this watermark is added a template in the Fourier transform domain to render the method robust against general linear transformations. We detail a new algorithm based on polar maps for the accurate and efficient recovery of the template in an image which has undergone a general affine transformation. We also present results which demonstrate the robustness of the method against some common image processing operations such as compression, rotation, scaling, and aspect ratio changes. PMID:18255481
Quaternion higher-order spectra and their invariants for color image recognition
NASA Astrophysics Data System (ADS)
Jia, Xiaoning; Yang, Hang; Ma, Siliang; Song, Dongzhe
2014-06-01
This paper describes an invariants generation method for color images, which could be a useful tool in color object recognition tasks. First, by using the algebra of quaternions, we introduce the definition of quaternion higher-order spectra (QHOS) in the spatial domain and derive its equivalent form in the frequency domain. Then, QHOS invariants with respect to rotation, translation, and scaling transformations for color images are constructed using the central slice theorem and quaternion bispectral analysis. The feature data are further reduced to a smaller set using quaternion principal component analysis. The proposed method can deal with color images in a holistic manner, and the constructed QHOS invariants are highly immune to background noise. Experimental results show that the extracted QHOS invariants form compact and isolated clusters, and that a simple minimum distance classifier can yield high recognition accuracy.
Sequence-invariant state machines
NASA Astrophysics Data System (ADS)
Whitaker, Sterling R.; Manjunath, Shamanna K.; Maki, Gary K.
1991-08-01
A synthesis method and an MOS VLSI architecture are presented to realize sequential circuits that have the ability to implement any state machine having N states and m inputs, regardless of the actual sequence specified in the flow table. The design method utilizes binary tree structured (BTS) logic to implement regular and dense circuits. The desired state sequence can be hardwired with power supply connections or can be dynamically reallocated if stored in a register. This allows programmable VLSI controllers to be designed with a compact size and performance approaching that of dedicated logic. Results of ICV implementations are reported and an example sequence-invariant state machine is contrasted with implementations based on traditional methods.
Moment Invariants for 2D Flow Fields via Normalization in Detail.
Bujack, Roxana; Hotz, Ingrid; Scheuermann, Gerik; Hitzer, Eckhard
2015-08-01
The analysis of 2D flow data is often guided by the search for characteristic structures with semantic meaning. One way to approach this question is to identify structures of interest by a human observer, with the goal of finding similar structures in the same or other datasets. The major challenges related to this task are to specify the notion of similarity and define respective pattern descriptors. While the descriptors should be invariant to certain transformations, such as rotation and scaling, they should provide a similarity measure with respect to other transformations, such as deformations. In this paper, we propose to use moment invariants as pattern descriptors for flow fields. Moment invariants are one of the most popular techniques for the description of objects in the field of image recognition. They have recently also been applied to identify 2D vector patterns limited to the directional properties of flow fields. Moreover, we discuss which transformations should be considered for the application to flow analysis. In contrast to previous work, we follow the intuitive approach of moment normalization, which results in a complete and independent set of translation, rotation, and scaling invariant flow field descriptors. They also allow to distinguish flow features with different velocity profiles. We apply the moment invariants in a pattern recognition algorithm to a real world dataset and show that the theoretical results can be extended to discrete functions in a robust way. PMID:26357255
f(T) gravity and local Lorentz invariance
Li Baojiu; Sotiriou, Thomas P.; Barrow, John D.
2011-03-15
We show that in theories of generalized teleparallel gravity, whose Lagrangians are algebraic functions of the usual teleparallel Lagrangian, the action and the field equations are not invariant under local Lorentz transformations. We also argue that these theories appear to have extra degrees of freedom with respect to general relativity. The usual teleparallel Lagrangian, which has been extensively studied and leads to a theory dynamically equivalent to general relativity, is an exception. Both of these facts appear to have been overlooked in the recent literature on f(T) gravity, but are crucial for assessing the viability of these theories as alternative explanations for the acceleration of the Universe.
The Yang-Baxter relation and gauge invariance
NASA Astrophysics Data System (ADS)
Kashaev, Rinat
2016-04-01
Starting from a quantum dilogarithm over a Pontryagin self-dual LCA group A, we construct an operator solution of the Yang-Baxter equation generalizing the solution of the Faddeev-Volkov model. Based on a specific choice of a subgroup B\\subset A and by using the Weil transformation, we also give a new non-operator interpretation of the Yang-Baxter relation. That allows us to construct a lattice QFT-model of IRF-type with gauge invariance under independent B-translations of local ‘spin’ variables. Dedicated to Professor Rodney Baxter on the occasion of his 75th birthday.