We discuss local mirror symmetry for higher-genus curves. Specifically, we consider the topological string partition function from higher genus curves contained in a Fano surface within a Calabi-Yau. Our main example is the local P case. The Kodaira-Spencer theory of gravity, tailored to this local geometry, can be solved to compute this partition function. Then, using the results of Gopakumar ...

Let N be a large parameter, C a constant, and let ΓN (C) denote the C-neighborhood of the cone segment {ξ : 2−CN ≤ |ξ| ≤ 2N}. For fixed N , we take a partition of unity subordinate to a covering of Sd−1 by caps Θ of diameter about N− 1 2 , and use this to form a (smooth) partition of unity yΘ on ΓN(C) in the natural way. We will write ΓN,Θ(C) = supp yΘ. Let ΞΘ be a function whose Fourier transf...

The basic Schema Theorem for genetic algorithms is modiied for a grammatically-based learning system. A context-free grammar is used to deene a language in which each sentence is mapped to a tness value. The derivation trees associated with these sentences are used to deene the structure of schemata. The eeect of crossover and mutation on schemata is described. A schema theorem is developed whi...

Cellular adhesion provides one of the fundamental forms of biological interaction between cells and their surroundings, yet the continuum modelling of cellular adhesion has remained mathematically challenging. In 2006, Armstrong et al. proposed a mathematical model in the form of an integro-partial differential equation. Although successful in applications, a derivation from an underlying stoch...

To completely address database integration problems in the context of multidatabase and data warehousing systems, one has to examine various integration and query requirements. In this paper, we identify three phases of database integration, i.e. analysis, derivation, and evolution. Due to poor data quality in local databases and local database updates, some unresolved instance connicts have to...

It has been shown that the Einstein equation can be derived from the requirement that the First Law δQ = TdS holds for all local Rindler causal horizons through each spacetime point. Here δQ and T are the energy flux and Unruh temperature seen by an accelerating observer just inside the horizon, and the entropy S is one quarter the horizon area in Planck units. In this paper we show that there ...

We prove that in a ring Rwith an identity there exists an element a ∈ R and a nonzero derivation d ∈ Der R such that ad(a) 6= 0. A ring R is said to be a d-rigid ring for some derivation d ∈ Der R if d(a) = 0 or ad(a) 6= 0 for all a ∈ R. We study rings with rigid derivations and establish that a commutative Artinian ring R either has a non-rigid derivation or R = R1 ⊕ · · · ⊕ Rn is a ring direc...

Features such as Local Binary Patterns (LBP) and Local Ternary Patterns (LTP) have been very successful in a number of areas including texture analysis, face recognition and object detection. They are based on the idea that small patterns of qualitative local gray-level differences contain a great deal of information about higher-level image content. Existing local pattern features use hand-spe...

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.