Search results for "Calculus"
showing 10 items of 617 documents
Monadic Second-Order Logic over Rectangular Pictures and Recognizability by Tiling Systems
1996
Abstract It is shown that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system iff it is definable in existential monadic second-order logic. As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and also matches a natural logic. The proof is based on the Ehrenfeucht–Fraisse technique for first-order logic and an implementation of “threshold counting” within tiling systems.
On Using the Theory of Regular Functions to Prove the ε-Optimality of the Continuous Pursuit Learning Automaton
2013
Published version of a chapter in the book: Recent Trends in Applied Artificial Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-38577-3_27 There are various families of Learning Automata (LA) such as Fixed Structure, Variable Structure, Discretized etc. Informally, if the environment is stationary, their ε-optimality is defined as their ability to converge to the optimal action with an arbitrarily large probability, if the learning parameter is sufficiently small/large. Of these LA families, Estimator Algorithms (EAs) are certainly the fastest, and within this family, the set of Pursuit algorithms have been considered to be the pioneering schemes. The…
Pathogens and host immunity in the ancient human oral cavity.
2014
Calcified dental plaque (dental calculus) preserves for millennia and entraps biomolecules from all domains of life and viruses. We report the first high-resolution taxonomic and protein functional characterization of the ancient oral microbiome and demonstrate that the oral cavity has long served as a reservoir for bacteria implicated in both local and systemic disease. We characterize: (i) the ancient oral microbiome in a diseased state, (ii) 40 opportunistic pathogens, (iii) the first evidence of ancient human-associated putative antibiotic resistance genes, (iv) a genome reconstruction of the periodontal pathogen Tannerella forsythia, (v) 239 bacterial and 43 human proteins, allowing co…
Exploring Students’ Metacognitive Knowledge: The Case of Integral Calculus
2020
Previous studies of integral calculus have mainly explored students&rsquo
Calculus Self-Efficacy Inventory : Its Development and Relationship with Approaches to Learning
2019
This study was framed within a quantitative research methodology to develop a concise measure of calculus self-efficacy with high psychometric properties. A survey research design was adopted in which 234 engineering and economics students rated their confidence in solving year-one calculus tasks on a 15-item inventory. The results of a series of exploratory factor analyses using minimum rank factor analysis for factor extraction, oblique promin rotation, and parallel analysis for retaining extracted factors revealed a one-factor solution of the model. The final 13-item inventory was unidimensional with all eigenvalues greater than 0.42, an average communality of 0.74, and a 62.55% variance…
Bismut’s Way of the Malliavin Calculus for Non-Markovian Semi-groups: An Introduction
2019
We give a review of our recent works related to the Malliavin calculus of Bismut type for non-Markovian generators. Part IV is new and relates the Malliavin calculus and the general theory of elliptic pseudo-differential operators.
Finite type invariants of knots in homology 3-spheres with respect to null LP-surgeries
2017
We study a theory of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries. It is an analogue in the setting of the rational homology of the Goussarov-Rozansky theory for knots in integral homology 3-spheres. We give a partial combinatorial description of the graded space associated with our theory and determine some cases when this description is complete. For null-homologous knots in rational homology 3-spheres with a trivial Alexander polynomial, we show that the Kricker lift of the Kontsevich integral and the Lescop equivariant invariant built from integrals in configuration spaces are universal finite type i…
A note on the isoperimetric inequality
2003
We show that the sharp integral form on the isoperimetric inequality holds for those orientation-preserving mappings f ∈ W l o c n 2 n + 1 ( Ω , R n ) f\in W^\frac {n^2}{n+1}_{loc}(\Omega , \mathbb {R}^n) whose Jacobians obey the rule of integration by parts.
HOLOMORPHIC SUPERPOSITION OPERATORS BETWEEN BANACH FUNCTION SPACES
2013
AbstractWe prove that for a large class of Banach function spaces continuity and holomorphy of superposition operators are equivalent and that bounded superposition operators are continuous. We also use techniques from infinite dimensional holomorphy to establish the boundedness of certain superposition operators. Finally, we apply our results to the study of superposition operators on weighted spaces of holomorphic functions and the$F(p, \alpha , \beta )$spaces of Zhao. Some independent properties on these spaces are also obtained.
Malliavin Calculus of Bismut Type for Fractional Powers of Laplacians in Semi-Group Theory
2011
We translate into the language of semi-group theory Bismut's Calculus on boundary processes (Bismut (1983), Lèandre (1989)) which gives regularity result on the heat kernel associated with fractional powers of degenerated Laplacian. We translate into the language of semi-group theory the marriage of Bismut (1983) between the Malliavin Calculus of Bismut type on the underlying diffusion process and the Malliavin Calculus of Bismut type on the subordinator which is a jump process.