Asymptotic probabilities of existential second-order Gödel sentences

1991 ◽  
Vol 56 (2) ◽  
pp. 427-438 ◽  
Author(s):  
Leszek Pacholski ◽  
WiesŁaw Szwast
Keyword(s):  
Second Order ◽  
First Order ◽  
Existential Sentences ◽  
Order Part

In [9] and [10] P. Kolaitis and M. Vardi proved that the 0-1 law holds for the second-order existential sentences whose first-order parts are formulas of Bernays-Schonfinkel or Ackermann prefix classes. They also provided several examples of second-order formulas for which the 0-1 law does not hold, and noticed that the classification of second-order sentences for which the 0-1 law holds resembles the classification of decidable cases of first-order prenex sentences. The only cases they have not settled are the cases of Gödel classes with and without equality.In this paper we confirm the conjecture of Kolaitis and Vardi that the 0-1 law does not hold for the existential second-order sentences whose first-order part is in Gödel prenex form with equality. The proof we give is based on a modification of the example employed by W. Goldfarb [5] in his proof that, contrary to the Gödel claim [6], the class of Gödel prenex formulas with equality is undecidable.

scholarly journals First order normalization in the generalized photo gravitational non-planar restricted three body problems

2015 ◽  
Vol 3 (2) ◽  
pp. 46
Author(s):  
Nirbhay Kumar Sinha
Keyword(s):  
Oblate Spheroid ◽  
Second Order ◽  
Elliptic Motion ◽  
First Order ◽  
Short Period ◽  
Order Part ◽  
Three Body

<p>In this paper, we normalised the second-order part of the Hamiltonian of the problem. The problem is generalised in the sense that fewer massive primary is supposed to be an oblate spheroid. By photogravitational we mean that both primaries are radiating. With the help of Mathematica, H<sub>2</sub> is normalised to H<sub>2</sub> = a<sub>1</sub>b<sub>1</sub>w<sub>1</sub> + a<sub>2</sub>b<sub>2</sub>w<sub>2</sub>. The resulting motion is composed of elliptic motion with a short period (2p/w<sub>1</sub>), completed by an oscillation along the z-axis with a short period (2p/w<sub>2</sub>).</p>

A NOTE ON THE ASYMPTOTIC PROBABILITIES OF EXISTENTIAL SECOND-ORDER MINIMAL GÖDEL SENTENCES WITH EQUALITY

1995 ◽  
Vol 06 (04) ◽  
pp. 339-351
Author(s):  
WIESŁAW SZWAST
Keyword(s):  
Dense Subset ◽  
Unit Interval ◽  
Second Order ◽  
Existential Quantifier ◽  
First Order ◽  
Order Part ◽  
Universal Quantifiers

The minimal Gödel class is the class of first-order prenex sentences whose quantifier prefix consists of two universal quantifiers followed by just one existential quantifier. We prove that asymptotic probabilities of existential second-order sentences, whose first-order part is in the minimal Gödel class, form a dense subset of the unit interval.

3D Interlock Composite Preforming Simulation

2012 ◽  
Vol 504-506 ◽  
pp. 261-266 ◽  
Author(s):  
Jean Guillaume Orliac ◽  
Adrien Charmetant ◽  
Fabrice Morestin ◽  
Philippe Boisse ◽  
Stephane Otin
Keyword(s):  
Virtual Work ◽  
Experimental Testing ◽  
Second Order ◽  
Beam Model ◽  
Forming Simulation ◽  
First Order ◽  
Material Stiffness ◽  
Material Formulation ◽  
Order Part ◽  
Continuous Material

In order to simulate 3D interlock composite reinforcement behavior in forming processes like Resin Transfer Molding (RTM), it is necessary to predict yarns positions in the fabric during the preforming stage of the process. The present paper deals about thick 3D interlock fabric forming simulation using a specific hexahedral semi-discrete finite elements simulation tool : Plast4. Using the virtual work principle, we distinguish the virtual internal work due to tensions in yarns from other internal virtual works. The part of material stiffness relative to yarns tension is described as "first order stiffness" by a 3D discrete beam model. The rest of the rigidities - like transverse compression, shear strains or friction between yarns - are depicted by a continuous quad-based discretization designated in our work as "second order stiffness". A combination of this "first order" discrete model and a continuous orthotropic hyperelastic "second order" material formulation will enables us to simulate interlock preforming process. Jointly to the simulation work, we also had to specify and perform experimental testing identification of material's parameters. Thoses parameters concern both parts of the model. A bilinear tension approach for the yarns discrete modelization and an orthotropic continuous material for the "second order" part.

scholarly journals Detection of degenerate points on the surface

2018 ◽  
Author(s):  
Marián Jenčo
Keyword(s):  
Automatic Recognition ◽  
Second Order ◽  
Ridge Line ◽  
Partial Derivatives ◽  
First Order ◽  
Convex Section ◽  
Pass Through ◽  
Derivatives Of

Landslides, bifurcations, multi-saddles and remnants of terraces are distinctive landforms. Some points on the surfaces of these objects are degenerate points. This may help us with their automatic recognition and identification. All first-order and second-order partial derivatives of analyzed function are necessary for detection of degenerate points. Terrain slope, curvatures and Hessian are required for classification of degenerate points. The paper is aimed at detection of fossil landslides. A point of landslide surface where the concave section of thalweg is turning into convex section of ridge line is a degenerate point. Two zero isolines of Hessian and zero isoline of profile, streamline and plan or tangential curvatures pass through this point. Final result of the detection procedure depends to a great extent on the quality of DEM and accuracy of derivatives.

Counterexamples of the 0-1 Law for Fragments of Existential Second-Order Logic: an Overview

2000 ◽  
Vol 6 (1) ◽  
pp. 67-82 ◽  
Author(s):  
Jean-Marie Le Bars
Keyword(s):  
Graph Theory ◽  
Random Graph ◽  
Second Order ◽  
Order Logic ◽  
First Order ◽  
Random Graph Theory ◽  
Asymptotic Probability ◽  
Second Order Logic

AbstractWe propose an original use of techniques from random graph theory to find a Monadic(Minimal Scott without equality) sentence without an asymptotic probability. Our result implies that the 0-1 law fails for the logics(FO2) and](Minimal Gödel without equality). Therefore we complete the classification of first-order prefix classes with or without equality, according to the existence of the 0-1 law for the correspondingfragment. In addition, our counterexample can be viewed as a single explanation of the failure of the 0-1 law of all the fragments of existential second-order logic for which the failure is already known.

scholarly journals Toward Measuring Target Perception: First-Order and Second-Order Deep Network Pipeline for Classification of Fixation-Related Potentials

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Hong Zeng ◽  
Junjie Shen ◽  
Wenming Zheng ◽  
Aiguo Song ◽  
Jia Liu
Keyword(s):  
Order Statistics ◽  
Object Perception ◽  
Representation Learning ◽  
Second Order ◽  
Visual Object ◽  
Second Order Statistics ◽  
First Order ◽  
Related Potentials ◽  
Perceptual Ability

The topdown determined visual object perception refers to the ability of a person to identify a prespecified visual target. This paper studies the technical foundation for measuring the target-perceptual ability in a guided visual search task, using the EEG-based brain imaging technique. Specifically, it focuses on the feature representation learning problem for single-trial classification of fixation-related potentials (FRPs). The existing methods either capture only first-order statistics while ignoring second-order statistics in data, or directly extract second-order statistics with covariance matrices estimated with raw FRPs that suffer from low signal-to-noise ratio. In this paper, we propose a new representation learning pipeline involving a low-level convolution subnetwork followed by a high-level Riemannian manifold subnetwork, with a novel midlevel pooling layer bridging them. In this way, the discriminative power of the first-order features can be increased by the convolution subnetwork, while the second-order information in the convolutional features could further be deeply learned with the subsequent Riemannian subnetwork. In particular, the temporal ordering of FRPs is well preserved for the components in our pipeline, which is considered to be a valuable source of discriminant information. The experimental results show that proposed approach leads to improved classification performance and robustness to lack of data over the state-of-the-art ones, thus making it appealing for practical applications in measuring the target-perceptual ability of cognitively impaired patients with the FRP technique.

scholarly journals Detection of degenerate points on the surface

2018 ◽  
Author(s):  
Marián Jenčo
Keyword(s):  
Automatic Recognition ◽  
Second Order ◽  
Ridge Line ◽  
Partial Derivatives ◽  
First Order ◽  
Convex Section ◽  
Pass Through ◽  
Derivatives Of

Landslides, bifurcations, multi-saddles and remnants of terraces are distinctive landforms. Some points on the surfaces of these objects are degenerate points. This may help us with their automatic recognition and identification. All first-order and second-order partial derivatives of analyzed function are necessary for detection of degenerate points. Terrain slope, curvatures and Hessian are required for classification of degenerate points. The paper is aimed at detection of fossil landslides. A point of landslide surface where the concave section of thalweg is turning into convex section of ridge line is a degenerate point. Two zero isolines of Hessian and zero isoline of profile, streamline and plan or tangential curvatures pass through this point. Final result of the detection procedure depends to a great extent on the quality of DEM and accuracy of derivatives.

Nonlinear initial value problems with a singular perturbation of hyperbolic type

1981 ◽  
Vol 89 (3-4) ◽  
pp. 333-345 ◽  
Author(s):  
R. Geel
Keyword(s):  
Initial Value Problems ◽  
A Priori ◽  
Second Order ◽  
Initial Value ◽  
Existence Of A Solution ◽  
Nonlinear Operators ◽  
First Order ◽  
Order Part ◽  
The Difference ◽  
Small Factor

SynopsisThis paper deals with initial value problems in ℝ2 which are governed by a hyperbolic differential equation consisting of a nonlinear first order part and a linear second order part. The second order part of the differential operator contains a small factor ε and can therefore be considered as a perturbation of the nonlinear first order part of the operator.The existence of a solution u together with pointwise a priori estimates for this solution are established by applying a fixed point theorem for nonlinear operators in a Banach space.It is shown that the difference between the solution u and the solution w of the unperturbed nonlinear initial value problem (which follows from the original problem by putting ε = 0) is of order ε, uniformly in compact subsets of ℝ2 where w is sufficiently smooth.

Nonlinear Analysis of Visual Evoked Potentials Elicited by Color Stimulation

1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama
Keyword(s):  
Visual System ◽  
Evoked Potentials ◽  
Visual Evoked Potentials ◽  
Normal Subjects ◽  
Second Order ◽  
First Order ◽  
The Relationship ◽  
Perceived Color ◽  
Second Order Nonlinearity ◽  
Visual Evoked

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

2002 ◽  
Vol 7 (1) ◽  
pp. 31-42
Author(s):  
J. Šaltytė ◽  
K. Dučinskas
Keyword(s):  
Spatial Correlation ◽  
Random Fields ◽  
Data Augmentation ◽  
Gaussian Random Fields ◽  
Classification Rule ◽  
Numerical Comparison ◽  
First Order ◽  
Bayesian Risk ◽  
Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

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