Search results for " algebra"

Non-archimedean hyperbolicity and applications

2018

Inspired by the work of Cherry, we introduce and study a new notion of Brody hyperbolicity for rigid analytic varieties over a non-archimedean field $K$ of characteristic zero. We use this notion of hyperbolicity to show the following algebraic statement: if a projective variety admits a non-constant morphism from an abelian variety, then so does any specialization of it. As an application of this result, we show that the moduli space of abelian varieties is $K$-analytically Brody hyperbolic in equal characteristic zero. These two results are predicted by the Green-Griffiths-Lang conjecture on hyperbolic varieties and its natural analogues for non-archimedean hyperbolicity. Finally, we use …

Probabilistic liver atlas construction

2017

Background Anatomical atlases are 3D volumes or shapes representing an organ or structure of the human body. They contain either the prototypical shape of the object of interest together with other shapes representing its statistical variations (statistical atlas) or a probability map of belonging to the object (probabilistic atlas). Probabilistic atlases are mostly built with simple estimations only involving the data at each spatial location. Results A new method for probabilistic atlas construction that uses a generalized linear model is proposed. This method aims to improve the estimation of the probability to be covered by the liver. Furthermore, all methods to build an atlas involve p…

Distributed BOLD-response in association cortex vector state space predicts reaction time during selective attention.

2006

Human cortical information processing is thought to be dominated by distributed activity in vector state space (Churchland, P.S., Sejnowski, T.J., 1992. The Computational Brain. MIT Press, Cambridge.). In principle, it should be possible to quantify distributed brain activation with independent component analysis (ICA) through vector-based decomposition, i.e., through a separation of a mixture of sources. Using event-related functional magnetic resonance imaging (fMRI) during a selective attention-requiring task (visual oddball), we explored how the number of independent components within activated cortical areas is related to reaction time. Prior to ICA, the activated cortical areas were d…

From algorithmic computing to direct retrieval: Evidence from number and alphabetic arithmetic in children and adults

1998

A number of theories of mental arithmetic suggest that the ability to solve simple addition and subtraction problems develops from an algorithmic strategy toward a strategy based on the direct retrieval of the result from memory. In the experiment presented here, 2nd and 12th graders were asked to solve two tasks of number and alphabet arithmetic. The subjects transformed series of 1 to 4 numbers or letters (item span) by adding or subtracting an operand varying from 1 to 4 (operation span). Although both the item and operation span were associated with major and identical effects in the case of both numbers and letters at 2nd grade, such effects were clearly observable only in the case of …

Affine Kettengeometrien �ber Jordanalgebren

1996

It is shown that an affine chain geometry over a Jordan algebra can be constructed in a nearly classical manner. Conversely, such chain geometries are characterized as systems of rational normal curves having a group of automorphisms with certain properties.

A SIMPLE CULTIVATION CHAMBER FOR THE STUDY OF AERIAL REPRODUCTIVE ELEMENTS OF FUNGI

1970

Finite-element design sensitivity analysis for non-linear potential problems

1990

Design sensitivity analysis is performed for the finite-element system arising from the discretization of non-linear potential problems using isoparametric Lagrangian elements. The calculated sensitivity formulae are given in a simple matrix form. Applications to the design of electromagnets and airfoils are given.

Bhabha Scattering and a special pencil of K3 surfaces

2018

We study a pencil of K3 surfaces that appeared in the $2$-loop diagrams in Bhabha scattering. By analysing in detail the Picard lattice of the general and special members of the pencil, we identify the pencil with the celebrated Ap\'ery--Fermi pencil, that was related to Ap\'ery's proof of the irrationality of $\zeta(3)$ through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.

On monadic quantale algebras: basic properties and representation theorems

2010

Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.

Symmetric and asymmetric cryptographic key exchange protocols in the octonion algebra

2019

AbstractWe propose three cryptographic key exchange protocols in the octonion algebra. Using the totient function, defined for integral octonions, we generalize the RSA public-key cryptosystem to the octonion arithmetics. The two proposed symmetric cryptographic key exchange protocols are based on the automorphism and the derivation of the octonion algebra.