Characteristic Function Research Papers - Academia.edu (original) (raw)

A unified, analysis is presented for the spatial and the spectral sensitivity of speckle (the rapid spatial variations which occur in an image when illumination of narrow spectral width is used) in a space-invariant linear system. In... more

A unified, analysis is presented for the spatial and the spectral sensitivity of speckle (the rapid spatial variations which occur in an image when illumination of narrow spectral width is used) in a space-invariant linear system. In prior work considering speckle size, others have shown that its spatial variation is functionally dependent primarily on the autocorrelation function of the system's impulse response, but effects of varying the wavelength were largely ignored. In the present paper we treat the general problem in which a diffuse object, illuminated by a collimated, monochromatic beam, is imaged by a system whose amplitude impulse response isz(x, η), wherex and η are space and normalized (temporal) frequency coordinates, respectively. An expression is derived for the multidimensional autocorrelation functionR u (Δx,η 1,η 2) of the intensityu(x,η) in the image plane. Functionally, it depends upon a convolution of the system autocorrelation functionR u (Δx,η 1,η 2) with the characteristic function of the distribution function for heights, which is used to model the input object's surface. Examples are presented; and, it is shown that one can infer valuable information about the variation of heights for points on the surface of the input diffuse object, which are separated by much less than the classical resolution limit.

This paper presents an artificial intelligence based solution, proposed to solve electromagnetic interference problems between high voltage power lines and nearby metallic pipelines, for different construction geometries. The presented... more

This paper presents an artificial intelligence based solution, proposed to solve electromagnetic interference problems between high voltage power lines and nearby metallic pipelines, for different construction geometries. The presented artificial intelligence method is a neural network one. Results gained with neural networks are compared to the finite element solutions considered as standard ones.

This paper extends the Integrated Conditional Moment (ICM) test for the functional form of nonlinear regression models to tests for para- metric conditional distributions. This test is formed on the basis of the integrated squared... more

This paper extends the Integrated Conditional Moment (ICM) test for the functional form of nonlinear regression models to tests for para- metric conditional distributions. This test is formed on the basis of the integrated squared difference between the empirical characteristic function of the actual data and the characteristic function implied by the model. This test is consistent, and has nontrivial

The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the... more

The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit formulae for the distribution of the sum of n non-identically distributed uniform random variables in both the continuous and the discrete case. The results, though involved, have a certain elegance. As examples, we derive from our general formulae some special cases which have appeared in the literature.

Molten salt technology is a catchall phrase that includes some very diverse technologies; electrochemistry, heat transfer, chemical oxidation/reduction baths, and nuclear reactors. All of these technologies are linked by the general... more

Molten salt technology is a catchall phrase that includes some very diverse technologies; electrochemistry, heat transfer, chemical oxidation/reduction baths, and nuclear reactors. All of these technologies are linked by the general characteristics of molten salts that can function as solvents, have good heat-transfer characteristics, function like a fluid, can attain very high temperatures, can conduct electricity, and also may have chemical catalytic properties. The Janz molten salt database is the most comprehensive compilation of property data about molten salts available today and is widely used for both fundamental and applied purposes. Databases are traditionally viewed as “static” documents that are used in a “search and retrieval” mode. These static data can be transformed by informatics and data mining tools into a dynamic dataset for analysis of the properties of the, materials and for making predictions. While this approch has been successful in the chemical and biochemical sciences in searching for and establishing structure-property relationships, it is not widely used in the materials science community. Because the design of the original molten salt database was not oriented toward this informatics goal, it was essential to evaluate this dataset in terms of data mining standards. Two techniques were used—a projection (principal components analysis (PCA)) and a predictive method (partial least squares (PLS))—in conjunction with fundamental knowledge acquired from the long-term practice of molten salt chemistry.

We study the topological structure of the symmetry group of the standard model, GSM=U(1)timesSU(2)timesSU(3)G_{SM}=U(1)\times SU(2)\times SU(3)GSM=U(1)timesSU(2)timesSU(3). Locally, GSMcongS1times(S3)2timesS5G_{SM}\cong S^1\times (S^3)^2\times S^5GSMcongS1times(S3)2timesS5. For SU(3), which is an S3S^3S3 bundle over S5S^5S5 (and therefore a... more

We study the topological structure of the symmetry group of the standard model, GSM=U(1)timesSU(2)timesSU(3)G_{SM}=U(1)\times SU(2)\times SU(3)GSM=U(1)timesSU(2)timesSU(3). Locally, GSMcongS1times(S3)2timesS5G_{SM}\cong S^1\times (S^3)^2\times S^5GSMcongS1times(S3)2timesS5. For SU(3), which is an S3S^3S3 bundle over S5S^5S5 (and therefore a local product of these spheres) we give a canonical gauge i.e. a canonical set of local trivializations. These formulae give the matrices of SU(3) in terms of points of spheres. Globally, we prove that the characteristic function of SU(3) is the suspension of the Hopf map h:S3toS2h: S^3 \to S^2h:S3toS2. We also study the case of SU(n) for arbitrary nnn, in particular the cases of SU(4), a flavour group, and of SU(5), a candidate group for grand unification. We show that the 2-sphere is also related to the fundamental symmetries of nature due to its relation to SO0(3,1)SO^0(3,1)SO0(3,1), the identity component of the Lorentz group, a subgroup of the symmetry group of several gauge theories of gravity.

In this article we investigate a way in which quantum computing can be used to extend the class of fuzzy sets. The core idea is to see states of a quantum register as characteristic functions of quantum fuzzy subsets of a given set. As... more

In this article we investigate a way in which quantum computing can be used to extend the class of fuzzy sets. The core idea is to see states of a quantum register as characteristic functions of quantum fuzzy subsets of a given set. As the real unit interval is embedded in the Bloch sphere, every fuzzy set is automatically a quantum fuzzy set. However, a generic quantum fuzzy set can be seen as a (possibly entangled) superposition of many fuzzy sets at once, offering new opportunities for modeling uncertainty. After introducing the main framework of quantum fuzzy set theory, we analyze the standard operations of fuzzification and defuzzification from our viewpoint. We conclude this preliminary paper with a list of possible applications of quantum fuzzy sets to pattern recognition, as well as future directions of pure research in quantum fuzzy set theory.

We investigate statistically the characteristics, functioning and incidence of pre-emptive patenting, defined as patent filings whose main effect is to hamper the grant of other patents. Patent applications can be used defensively to... more

We investigate statistically the characteristics, functioning and incidence of pre-emptive patenting, defined as patent filings whose main effect is to hamper the grant of other patents. Patent applications can be used defensively to prevent the grant of exclusive rights over markets and technologies, in order to ensure freedom of operation or keep competitors out of a given technological field. Combining data from examination outcomes and prior art at the European Patent Office, we develop a methodology to identify pre-emptive patent applications. We find evidence of pre-emption associated with patent applications cited as compromising patentability while not being deemed relevant to the state of the art. We also find that, among them, those which are withdrawn have the strongest pre-emptive power. The coincidence of low inventiveness and high pre-emptive impact supports the idea that some of these patents may be strategically designed by their applicants to block patenting by others.

Triassic tracks and trackways assigned to dinosaur trackmakers or closest relatives have been mentioned from several Middle to the latest Triassic successions from both northern and southern Pangea. At present, the earliest gondwanan... more

Triassic tracks and trackways assigned to dinosaur trackmakers or closest relatives have been mentioned from several Middle to the latest Triassic successions from both northern and southern Pangea. At present, the earliest gondwanan records are those from the Middle Triassic Los Rastros Formation in west-central Argentina. A reanalysis of Los Rastros ichnites at the Ischichuca area, including new material, has

ABSTRACT With respect to Rosenblatt linear perceptron, two classical limitation theorems demonstrated by M. Minsky and S. Papert are discussed. These two theorems, `(Psi) One-in-a-box' and `(Psi) Parity,' ultimately... more

ABSTRACT With respect to Rosenblatt linear perceptron, two classical limitation theorems demonstrated by M. Minsky and S. Papert are discussed. These two theorems, `(Psi) One-in-a-box' and `(Psi) Parity,' ultimately concern the intrinsic limitations of parallel calculations in pattern recognition problems. We demonstrate a possible solution of these limitation problems by substituting the static definition of characteristic functions and of their domains in the `geometrical' perceptron, with their dynamic definition. This dynamic consists in the mutual redefinition of the characteristic function and of its domain depending on the matching with the input.