functional representations
Recently Published Documents

Mechanisms for retrieving basic knowledge in the human mind are still unknown. Exploration is usually represented by cognitive units, i.e., concepts, linked together by associative relationships forming semantic networks. However, understanding how humans navigate such networks remains elusive, because the underlying topology of concepts cannot be observed directly, and only functional representations are accessible. Here, we overcome those limitations and show that the hypothesis of an underlying, latent geometry characterizing the human mind is plausible. We characterize this geometry by means of adequate descriptors for exploring and navigating dynamics, demonstrating that they can capture the differences between healthy subjects and patients at different stages of dementia. Our results provide the first fundamental step to develop a new unifying conceptual and computational framework that can be used to support the assessment of neurodegenerative diseases from language and semantic memory retrieval tasks, as well as helping develop targeted nonpharmacological therapies to maintain residual cognitive capacity.

Which part of the brain contributes to our complex cognitive processes? Studies have revealed contributions of the cerebellum and subcortex to higher-order cognitive functions; however it is unclear whether such functional representations are preserved across the cortex, cerebellum, and subcortex. In this study, we used functional magnetic resonance imaging data with 103 cognitive tasks and constructed three voxel-wise encoding and decoding models independently using cortical, cerebellar, and subcortical voxels. Representational similarity analysis revealed that the structure of task representations is preserved across the three brain parts. Principal component analysis visualized distinct organizations of abstract cognitive functions in each part of the cerebellum and subcortex. More than 90% of the cognitive tasks were decodable from the cerebellum and subcortical activities, even for the novel tasks not included in model training. Furthermore, we discovered that the cerebellum and subcortex have sufficient information to reconstruct activity in the cerebral cortex.

Motivated by mapping adverse artifactual events caused by body movements in electroencephalographic (EEG) signals, we present a functional independent component analysis based on the spectral decomposition of the kurtosis operator of a smoothed principal component expansion. A discrete roughness penalty is introduced in the orthonormality constraint of the covariance eigenfunctions in order to obtain the smoothed basis for the proposed independent component model. To select the tuning parameters, a cross-validation method that incorporates shrinkage is used to enhance the performance on functional representations with a large basis dimension. This method provides an estimation strategy to determine the penalty parameter and the optimal number of components. Our independent component approach is applied to real EEG data to estimate genuine brain potentials from a contaminated signal. As a result, it is possible to control high-frequency remnants of neural origin overlapping artifactual sources to optimize their removal from the signal. An R package implementing our methods is available at CRAN.

Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly establish asymptotic laws of records value, not necessarily as limits in type and their rates of convergences. Results beyond the extreme value value domain are provided. Explicit asymptotic laws concerning very usual laws and related rates of convergence are listed as well. Some of these laws are expected to be used in fitting distribution.

This chapter develops dynamic production analysis within the context of the adjustment cost model of the firm, where adjustment costs are associated with changes in the level of the quasi-fixed factors, also known as internal adjustment costs. The chapter characterizes axiomatically several primal representations of the adjustment cost production technology. The axiomatic approach is a cornerstone to model production technology both in theoretical and empirical work. The existence of several representations of the adjustment cost production technology is essential in the analysis of the firm’s decisions and its adjustment path that are conditioned by the technology. Three set representations of the adjustment cost production technology are discussed and characterized axiomatically. Two functional representations of the technology are also addressed using an axiomatic approach.

Abstract Biomimetic practice requires a diverse set of knowledge from both biology and engineering. Several researchers have been supporting the integration of biologists within biomimetic design teams in order to meet those biological requirements and improve the effectiveness of biomimetic processes. However, interdisciplinarity practices create well-known communication challenges. Based on functional representations (like SAPPhIRE or function behavior structure (FBS)), several approaches to model biological information have been investigated in the literature. Nonetheless, actual communication processes within interdisciplinary biomimetic design teams are yet to be studied. Following this research axis, this publication focuses on communication noises and wonders if a shared framework of reference can be defined to improve communication between biologists and engineers? Through the comparison of processes and graphic representations between biology and engineering design, a set of guidelines is defined to structure a shared framework of reference. Within this framework, a new tool referred to as LINKAGE is then proposed to assist interdisciplinary communication during the biomimetic process.