For Y a closed normal subvariety of codimension c of a smooth C–variety X, Brylinski and Kashiwara showed in [BK81] that the local cohomology module HcY (X,OX) contains a unique simple DX– submodule, denoted by L(Y, X). In this paper the analogous result is shown for X and Y defined over a perfect field of finite characteristic. Moreover, a local construction of L(Y,X) is given, relating it to ...

This paper proposes and examines a semiotic framework to inform the use of technology in mathematics education. Semiotics asserts that all cognition is irreducibly triadic, of the nature of a sign, fallible, and thoroughly immersed in a continuing process of interpretation (Halton, 1992). Mathematical meaning-making or meaningful knowledge construction is a continuing process of interpretation ...

Building on existing stochastic actor-oriented models for panel data, we employ a conditional logistic framework to explore growth mechanisms for tie creation in continuously-observed networks. This framework models the likelihood of tie formation distinguishing it from hazard models that consider time to tie formation. It enables multiple growth mechanisms for network evolution (homophily, foc...

Networks that learn to make familiar activity patterns into stable attractors have proven useful in accounting for many aspects of normal and impaired cognition. However, their ability to generalize is questionable, particularly in quasiregular tasks that involve both regularities and exceptions, such as word reading. We trained an attractor network to pronounce virtually all of a large corpus ...

It can be difficult for people to perform the behaviors necessary address sustainability challenges because selfish actions are often more appealing than choices that benefit nature and future generations. Although many useful approaches pro-environmentalism focus on strengthening relatively simple bivariate relations (e.g., connectedness community-based conservation), we propose effective outc...

One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose a unique self-consistent experimental and numerical set up that models a cascade of triadic interactions transferring energy from large-scale monochromatic input to multiscale internal wave motion. We also provide, for the first ...

In our previous work an efficient one-pass online algorithm for triclustering of binary data (triadic formal contexts) was proposed. This algorithm is a modified version of the basic algorithm for OACtriclustering approach; it has linear time and memory complexities. In this paper we parallelise it via map-reduce framework in order to make it suitable for big datasets. The results of computer e...

Formal Concept Analysis offers a simple formalization for representing knowledge structures extracted from various data. Lately, the triadic case has become increasingly popular, given that data can often be interpreted in a triadic setting for further processing and analysis. However, visualization and navigation in triadic conceptual landscapes is not trivial and, so far, there are no tools i...

Later-born siblings of children with autism spectrum disorder (Sibs-ASD) are at elevated risk for social impairments. Two putative predictors of later social impairment-measures of responding to joint attention and weighted triadic communication-were examined in a sample of 43 Sibs-ASD who were followed from 15 to 34 months of age. Results revealed that initial level of responding to joint atte...