Second order and third order statistics with application to EEG [finger movements]

In an earlier study by Julesz (1962) pairs of random textures were generated side-by-side using a Markov process with different third-order joint-probability distributions but identical first- and second-order distributions. Such texture pairs could not be discriminated from each other by the human visual system without scrutiny. Unfortunately, Markov processes are inherently one-dimensional while the general processes underlying visual texture discrimination are two-dimensional. Here three new methods are introduced that generate two-dimensional non-Markovian textures with different third-order but identical first- and second-order statistics. All three methods generate texture pairs that cannot be discriminated from each other. The lack of texture discrimination is the more astonishing since the individual elements that form the texture pair are clearly perceived as being very different. However, a counterexample was found that yields discrimination although the texture pair has approximately identical second-order statistics. This case can be explained by assuming that early feature extractors do some preprocessing. These new demonstrations give support to a model of texture discrimination in which the stimulus is first analyzed by local feature extractors that can detect only simple features such as dots and edges of given sizes and orientations. Then the outputs of these simple extractors are evaluated by a global processor that can compute only second- or first-order statistics (that is can compare at most two such outputs).

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Bulk Contributions Modulate the Sum-Frequency Generation Spectra of Interfacial Water on Model Sea-Spray Aerosols

10.26434/chemrxiv.5743638 ◽

2018 ◽

Author(s):

Sandeep K. Reddy ◽

Raphael Thiraux ◽

Bethany A. Wellen Rudd ◽

Lu Lin ◽

Tehseen Adel ◽

...

Keyword(s):

Single Layer ◽

Sum Frequency Generation ◽

Second Order ◽

Interfacial Structure ◽

Sea Spray ◽

Third Order ◽

Systematic Analysis ◽

Sum Frequency ◽

Structure Of Water ◽

Frequency Generation

Vibrational sum-frequency generation (vSFG) spectroscopy is used to determine the molecular structure of water at the interface of palmitic acid monolayers. Both measured and calculated spectra display speci c features due to third-order contributions to the vSFG response which are associated with nite interfacial electric potentials. We demonstrate that theoretical modeling enables to separate the third-order contributions, thus allowing for a systematic analysis of the strictly surface-sensitive, second-order component of the vSFG response. This study provides fundamental, molecular-level insights into the interfacial structure of water in a neutral surfactant system with relevance to single layer bio-membranes and environmentally relevant sea-spray aerosols. These results emphasize the key role that computer simulations can play in interpreting vSFG spectra and revealing microscopic details of water at complex interfaces, which can be difficult to extract from experiments due to the mixing of second-order, surface-sensitive and third-order, bulk-dependent contributions to the vSFG response.

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Second-Order Statistics of Spectral and Correlation Estimates Obtained by Means of Weighted Overlapped FFT Processing

10.21236/ada439705 ◽

2005 ◽

Author(s):

Albert H. Nuttall

Keyword(s):

Order Statistics ◽

Second Order ◽

Second Order Statistics ◽

Overlapped Fft

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Evidence for general base catalysis by protic solvents in a kinetic study of alcoholyses and hydrolyses of 1-(phenoxycarbonyl)pyridinium ions under both solvolytic and non-solvolytic conditions

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc2008164 ◽

2009 ◽

Vol 74 (1) ◽

pp. 43-55 ◽

Cited By ~ 1

Author(s):

Dennis N. Kevill ◽

Byoung-Chun Park ◽

Jin Burm Kyong

Keyword(s):

Second Order ◽

Base Catalysis ◽

Substitution Reactions ◽

Third Order ◽

Methoxy Derivative ◽

First Order ◽

General Base ◽

Protic Solvents ◽

Kinetics Of ◽

Pyridinium Ions

The kinetics of nucleophilic substitution reactions of 1-(phenoxycarbonyl)pyridinium ions, prepared with the essentially non-nucleophilic/non-basic fluoroborate as the counterion, have been studied using up to 1.60 M methanol in acetonitrile as solvent and under solvolytic conditions in 2,2,2-trifluoroethan-1-ol (TFE) and its mixtures with water. Under the non- solvolytic conditions, the parent and three pyridine-ring-substituted derivatives were studied. Both second-order (first-order in methanol) and third-order (second-order in methanol) kinetic contributions were observed. In the solvolysis studies, since solvent ionizing power values were almost constant over the range of aqueous TFE studied, a Grunwald–Winstein equation treatment of the specific rates of solvolysis for the parent and the 4-methoxy derivative could be carried out in terms of variations in solvent nucleophilicity, and an appreciable sensitivity to changes in solvent nucleophilicity was found.

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