Search results for "functional"

Teaching types with a cognitively effective worked example format

2015

AbstractTeaching functional programming as a second programming paradigm is often difficult as students can have strong preconceptions about programming. When most of these preconceived ideas fail to be confirmed, functional programming may be seen as an unnecessarily difficult topic. A typical topic that causes such difficulties is the language of types employed by many modern functional languages. In this paper, we focus on addressing this difficulty through the use of step-by-step calculations of type expressions. The outcome of the study is an elaboration of a worked example format and a methodical approach for teaching types to beginner functional programmers.

A Functional Near-Infrared Spectroscopy Examination of the Neural Correlates of Cognitive Shifting in Dimensional Change Card Sort Task

2020

This study aims to examine the neural correlates of cognitive shifting during the Dimensional Change Card Sort Task (DCCS) task with functional near-infrared spectroscopy. Altogether 49 children completed the DCCS tasks, and 25 children (Mage = 68.66, SD = 5.3) passing all items were classified into the Switch group. Twenty children (Mage = 62.05, SD = 8.13) committing more than one perseverative errors were grouped into the Perseverate group. The Switch group had Brodmann Area (BA) 9 and 10 activated in the pre-switch period and BA 6, 9, 10, 40, and 44 in the post-switch period. In contrast, the Perseverate group had BA 9 and 10 activated in the pre-switch period and BA 8, 9, 10 in the pos…

Data from: Functional structure of European forest beetle communities is enhanced by rare species

2022

From article abstract: https://doi.org/10.1016/j.biocon.2022.109491 ABSTRACT Biodiverse communities have been shown to sustain high levels of multifunctionality and thus a loss of species likely negatively impacts ecosystem functions. For most taxa, however, the roles of individual species are poorly known. Rare species, often the most likely to go extinct, may have unique traits leading to unique functional roles. Alternatively, rare species may be functionally redundant, such that their loss would not disrupt ecosystem functions. We quantified the functional role of rare species by using capture records of wood-living (saproxylic) beetle species, combined with recent databases of their mo…

Toward an Understanding of Molecular Mechanism of Domino Cycloadditions. Density Functional Theory Study of the Reaction between Hexafluorobut-2-yne …

1998

Thermodynamic stability of non-stoichiometric SrFeO 3−δ : a hybrid DFT study

2019

SrFeO3-δ is mixed ionic-electronic conductor with complex magnetic structure which reveals also colossal magnetoresistance effect. This material and its solid solutions are attractive for various spintronic, catalytic and electrochemical applications, including cathodes for solid oxide fuel cells and permeation membranes. Its properties strongly depend on oxygen non-stoichiometry. Ab initio hybrid functional approach was applied here for a study of thermodynamic stability of a series of SrFeO3-δ compositions with several non-stoichiometries δ, ranging from 0 to 0.5 (SrFeO3 - SrFeO2.875 - SrFeO2.75 - SrFeO2.5) as the function of temperature and oxygen pressure. The results obtained by consid…

A complete characterization of all weakly additive measures and of all valuations on the canonical extension of any finite MV-chain

2010

We consider extensions of the unique additive measure on a finite MV-chain to uncertainty measures on its canonical Girard algebra extension. If the underlying MV-chain has more than two non-trivial elements, in a previous paper we have proved the non-existence of strongly additive measure extensions, where strong additivity is defined as additivity not for all disjoint unions but only restricted to the so-called divisible disjoint unions. This negative result motivates to look for weakly additive measure extensions which are defined to be additive only on all MV-subalgebras of the canonical Girard algebra extension. We obtain a characterization of all such MV-subalgebras which are in fact …

Stochastic Processes on Ends of Tree and Dirichlet Forms

2016

We present main ideas and compare two constructions of stochastic processes on the ends (leaves) of the trees with varying numbers of edges at the nods. In one of them the trees are represented by spaces of numerical sequences and the processes are obtained by solving a class of Chapman-Kolmogorov Equations. In the other the trees are described by the set of nodes and edges. To each node there is naturally associated a finite dimensional function space and the Dirichlet form on it. Having a class of Dirichlet forms at the nodes one can under certain conditions build a Dirichlet form on L2 space of funcions on the ends of the trees. We show that the state spaces of two approaches are homeomo…

On the spectrum of linear combinations of two projections inC*-algebras

2010

In this note, we study the spectrum and give estimations for the spectral radius of linear combinations of two projections in C*-algebras. We also study the commutator of two projections.

Integer Complexity: Experimental and Analytical Results II

2015

We consider representing natural numbers by expressions using only 1’s, addition, multiplication and parentheses. Let \( \left\| n \right\| \) denote the minimum number of 1’s in the expressions representing \(n\). The logarithmic complexity \( \left\| n \right\| _{\log } \) is defined to be \({ \left\| n \right\| }/{\log _3 n}\). The values of \( \left\| n \right\| _{\log } \) are located in the segment \([3, 4.755]\), but almost nothing is known with certainty about the structure of this “spectrum” (are the values dense somewhere in the segment?, etc.). We establish a connection between this problem and another difficult problem: the seemingly “almost random” behaviour of digits in the ba…

Summing multi-norms defined by Orlicz spaces and symmetric sequence space

2016

We develop the notion of the \((X_1,X_2)\)-summing power-norm based on a~Banach space \(E\), where \(X_1\) and \(X_2\) are symmetric sequence spaces. We study the particular case when \(X_1\) and \(X_2\) are Orlicz spaces \(\ell_\Phi\) and \(\ell_\Psi\) respectively and analyze under which conditions the \((\Phi, \Psi)\)-summing power-norm becomes a~multinorm. In the case when \(E\) is also a~symmetric sequence space \(L\), we compute the precise value of \(\|(\delta_1,\cdots,\delta_n)\|_n^{(X_1,X_2)}\) where \((\delta_k)\) stands for the canonical basis of \(L\), extending known results for the \((p,q)\)-summing power-norm based on the space \(\ell_r\) which corresponds to \(X_1=\ell_p\), …