A New Method for Extraction of Signals with Higher Order Temporal Structure

2012 ◽  
pp. 372-379
Author(s):  
Lei Hu ◽  
Bowen Chen ◽  
Zhen Huang
Keyword(s):  
Temporal Structure ◽  
Higher Order ◽  
New Method

A New Method for High-Degree Spline Interpolation: Proof of Continuity for Piecewise Polynomials

2019 ◽  
Vol 63 (3) ◽  
pp. 655-669
Author(s):  
A. Pepin ◽  
S. S. Beauchemin ◽  
S. Léger ◽  
N. Beaudoin
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Spline Interpolation ◽  
Higher Order ◽  
New Method ◽  
System Of Equations ◽  
Piecewise Polynomials ◽  
Odd Degree ◽  
High Degree

AbstractEffective and accurate high-degree spline interpolation is still a challenging task in today’s applications. Higher degree spline interpolation is not so commonly used, because it requires the knowledge of higher order derivatives at the nodes of a function on a given mesh.In this article, our goal is to demonstrate the continuity of the piecewise polynomials and their derivatives at the connecting points, obtained with a method initially developed by Beaudoin (1998, 2003) and Beauchemin (2003). This new method, involving the discrete Fourier transform (DFT/FFT), leads to higher degree spline interpolation for equally spaced data on an interval $[0,T]$. To do this, we analyze the singularities that may occur when solving the system of equations that enables the construction of splines of any degree. We also note an important difference between the odd-degree splines and even-degree splines. These results prove that Beaudoin and Beauchemin’s method leads to spline interpolation of any degree and that this new method could eventually be used to improve the accuracy of spline interpolation in traditional problems.

scholarly journals On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 891 ◽  
Author(s):  
Janak Raj Sharma ◽  
Deepak Kumar ◽  
Lorentz Jäntschi
Keyword(s):  
Order Of Convergence ◽  
Higher Order ◽  
New Method ◽  
Systems Of Nonlinear Equations ◽  
Third Order ◽  
Type Method ◽  
Cpu Time ◽  
Chebyshev’S Method ◽  
Derivative Free ◽  
Fifth Order

We propose a derivative-free iterative method with fifth order of convergence for solving systems of nonlinear equations. The scheme is composed of three steps, of which the first two steps are that of third order Traub-Steffensen-type method and the last is derivative-free modification of Chebyshev’s method. Computational efficiency is examined and comparison between the efficiencies of presented technique with existing techniques is performed. It is proved that, in general, the new method is more efficient. Numerical problems, including those resulting from practical problems viz. integral equations and boundary value problems, are considered to compare the performance of the proposed method with existing methods. Calculation of computational order of convergence shows that the order of convergence of the new method is preserved in all the numerical examples, which is not so in the case of some of the existing higher order methods. Moreover, the numerical results, including the CPU-time consumed in the execution of program, confirm the accurate and efficient behavior of the new technique.

scholarly journals The stability of collocation methods for higher-order Volterra integro-differential equations

2005 ◽  
Vol 2005 (19) ◽  
pp. 3075-3089 ◽  
Author(s):  
Edris Rawashdeh ◽  
Dave McDowell ◽  
Leela Rakesh
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Numerical Stability ◽  
Polynomial Spline ◽  
Higher Order ◽  
Collocation Methods ◽  
New Method ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
The Stability

The numerical stability of the polynomial spline collocation method for general Volterra integro-differential equation is being considered. The convergence and stability of the new method are given and the efficiency of the new method is illustrated by examples. We also proved the conjecture suggested by Danciu in 1997 on the stability of the polynomial spline collocation method for the higher-order integro-differential equations.

The completeness of the first-order functional calculus

1949 ◽  
Vol 14 (3) ◽  
pp. 159-166 ◽  
Author(s):  
Leon Henkin
Keyword(s):  
Functional Calculus ◽  
Propositional Calculus ◽  
Higher Order ◽  
New Method ◽  
Completeness Proof ◽  
New Approach ◽  
First Order ◽  
Formal Systems ◽  
The Subject ◽  
Image Position

Although several proofs have been published showing the completeness of the propositional calculus (cf. Quine (1)), for the first-order functional calculus only the original completeness proof of Gödel (2) and a variant due to Hilbert and Bernays have appeared. Aside from novelty and the fact that it requires less formal development of the system from the axioms, the new method of proof which is the subject of this paper possesses two advantages. In the first place an important property of formal systems which is associated with completeness can now be generalized to systems containing a non-denumerable infinity of primitive symbols. While this is not of especial interest when formal systems are considered as logics—i.e., as means for analyzing the structure of languages—it leads to interesting applications in the field of abstract algebra. In the second place the proof suggests a new approach to the problem of completeness for functional calculi of higher order. Both of these matters will be taken up in future papers.The system with which we shall deal here will contain as primitive symbolsand certain sets of symbols as follows:(i) propositional symbols (some of which may be classed as variables, others as constants), and among which the symbol “f” above is to be included as a constant;(ii) for each number n = 1, 2, … a set of functional symbols of degree n (which again may be separated into variables and constants); and(iii) individual symbols among which variables must be distinguished from constants. The set of variables must be infinite.

scholarly journals A High-Order Iterate Method for ComputingAT,S(2)

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoji Liu ◽  
Zemeng Zuo
Keyword(s):  
Iterative Method ◽  
Generalized Inverse ◽  
Higher Order ◽  
High Order ◽  
New Method ◽  
Order Convergence ◽  
Approximate Inverses

We investigate a new higher order iterative method for computing the generalized inverseAT,S(2)for a given matrixA. We also discuss how the new method could be applied for finding approximate inverses of nonsingular square matrices. Analysis of convergence is included to show that the proposed scheme has at least fifteenth-order convergence. Some tests are also presented to show the superiority of the new method.

scholarly journals Detecting Transient Trapping from a Single Trajectory: A Structural Approach

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1044
Author(s):  
Yann Lanoiselée ◽  
Jak Grimes ◽  
Zsombor Koszegi ◽  
Davide Calebiro
Keyword(s):  
Plasma Membrane ◽  
Single Particle ◽  
Adrenergic Receptors ◽  
Particle Trajectory ◽  
Temporal Structure ◽  
Structural Approach ◽  
New Method ◽  
Trajectory Data ◽  
Receptor Stimulation ◽  
Over Time

In this article, we introduce a new method to detect transient trapping events within a single particle trajectory, thus allowing the explicit accounting of changes in the particle’s dynamics over time. Our method is based on new measures of a smoothed recurrence matrix. The newly introduced set of measures takes into account both the spatial and temporal structure of the trajectory. Therefore, it is adapted to study short-lived trapping domains that are not visited by multiple trajectories. Contrary to most existing methods, it does not rely on using a window, sliding along the trajectory, but rather investigates the trajectory as a whole. This method provides useful information to study intracellular and plasma membrane compartmentalisation. Additionally, this method is applied to single particle trajectory data of β2-adrenergic receptors, revealing that receptor stimulation results in increased trapping of receptors in defined domains, without changing the diffusion of free receptors.

scholarly journals Higher-Order Conditioning With Simultaneous and Backward Conditioned Stimulus: Implications for Models of Pavlovian Conditioning

2021 ◽  
Vol 15 ◽  
Author(s):  
Arthur Prével ◽  
Ruth M. Krebs
Keyword(s):  
Conditioned Stimulus ◽  
Pavlovian Conditioning ◽  
Temporal Structure ◽  
Higher Order ◽  
Prediction Errors ◽  
Temporal Difference ◽  
Conditioned Stimuli ◽  
Form Complex ◽  
Reward Prediction ◽  
Order Conditioning

In a new environment, humans and animals can detect and learn that cues predict meaningful outcomes, and use this information to adapt their responses. This process is termed Pavlovian conditioning. Pavlovian conditioning is also observed for stimuli that predict outcome-associated cues; a second type of conditioning is termed higher-order Pavlovian conditioning. In this review, we will focus on higher-order conditioning studies with simultaneous and backward conditioned stimuli. We will examine how the results from these experiments pose a challenge to models of Pavlovian conditioning like the Temporal Difference (TD) models, in which learning is mainly driven by reward prediction errors. Contrasting with this view, the results suggest that humans and animals can form complex representations of the (temporal) structure of the task, and use this information to guide behavior, which seems consistent with model-based reinforcement learning. Future investigations involving these procedures could result in important new insights on the mechanisms that underlie Pavlovian conditioning.

scholarly journals EVENT GRAPHS: ADVANCES AND APPLICATIONS OF SECOND-ORDER TIME-UNFOLDED TEMPORAL NETWORK MODELS

2019 ◽  
Vol 22 (03) ◽  
pp. 1950006
Author(s):  
ANDREW MELLOR
Keyword(s):  
Protein Interactions ◽  
Temporal Structure ◽  
Network Models ◽  
Higher Order ◽  
Temporal Network ◽  
Temporal Networks ◽  
Protein Protein Interactions ◽  
Temporal Features ◽  
Aggregated Model ◽  
Temporal Interaction

Recent advances in data collection and storage have allowed both researchers and industry alike to collect data in real time. Much of this data comes in the form of ‘events’, or timestamped interactions, such as email and social media posts, website clickstreams, or protein–protein interactions. This type of data poses new challenges for modeling, especially if we wish to preserve all temporal features and structure. We highlight several recent approaches in modeling higher-order temporal interaction and bring them together under the umbrella of event graphs. Through examples, we demonstrate how event graphs can be used to understand the higher-order topological-temporal structure of temporal networks and capture properties of the network that are unobservable when considering either a static (or time-aggregated) model. We introduce new algorithms for temporal motif enumeration and provide a novel analysis of the communicability centrality for temporal networks. Furthermore, we show that by modeling a temporal network as an event graph our analysis extends easily to non-dyadic interactions, known as hyper-events.

Two-Scale Algorithm for Computing the Approximation of the Displacement in Periodic Perforated Structure of Composites

2011 ◽  
Vol 374-377 ◽  
pp. 1226-1229
Author(s):  
Ming Xiang Deng ◽  
Yong Ping Feng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Higher Order ◽  
New Method ◽  
Approximation Solution ◽  
Scale Method ◽  
Small Periodic ◽  
Element Method

By means of two-scale method, the approximation solution of the displacement for structure of composites with small periodic perforated configuration is built, and the algorithm corresponding to two-scale finite element method is presented. One new method of higher order for computing approximate solution of the displacement in periodic perforated composites is given.

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