Search results for "Linear"
showing 10 items of 7165 documents
Computing the Cell
2015
Here I call for the need to revisit cell theory. The idea that the cell is the basic unit of life is well-known and foundational to Biology, but it has not received sufficient attention. We have increasingly detailed knowledge of the intracellular world and all its components, but these are often considered independently. On the other hand, there is excessive theorising about the cell on the basis of its being a black box. The time is ripe to formulate an integrative cell theory .
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…
A nonlinear electronic circuit mimicking the neuronal activity in presence of noise
2013
We propose a nonlinear electronic circuit simulating the neuronal activity in a noisy environment. This electronic circuit is ruled by the set of Bonhaeffer-Van der Pol equations and is excited with a white gaussian noise, that is without external deterministic stimuli. Under these conditions, our circuits reveals the Coherence Resonance signature, that is an optimum of regularity in the system response for a given noise intensity.
Integrable systems, Frobenius manifolds and cohomological field theories
2022
In this dissertation, we study the underlying geometry of integrable systems, in particular tausymmetric bi-Hamiltonian hierarchies of evolutionary PDEs and differential-difference equations.First, we explore the close connection between the realms of integrable systems and algebraic geometry by giving a new proof of the Witten conjecture, which constructs the string taufunction of the Korteweg-de Vries hierarchy via intersection theory of the moduli spaces of stable curves with marked points. This novel proof is based on the geometry of double ramification cycles, tautological classes whose behavior under pullbacks of the forgetful and gluing maps facilitate the computation of intersection…
A numerical study of attraction/repulsion collective behavior models: 3D particle analyses and 1D kinetic simulations
2013
39p; International audience; We study at particle and kinetic level a collective behavior model based on three phenomena: self-propulsion, friction (Rayleigh effect) and an attractive/repulsive (Morse) potential rescaled so that the total mass of the system remains constant independently of the number of particles N . In the first part of the paper, we introduce the particle model: the agents are numbered and described by their position and velocity. We iden- tify five parameters that govern the possible asymptotic states for this system (clumps, spheres, dispersion, mills, rigid-body rotation, flocks) and perform a numerical analysis on the 3D setting. Then, in the second part of the paper…
Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations
2011
In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we discuss the relationships between necessary conditions for blow-up of collocation solutions and exact solutions.
A Generalised RBF Finite Difference Approach to Solve Nonlinear Heat Conduction Problems on Unstructured Datasets
2011
Radial Basis Functions have traditionally been used to provide a continuous interpolation of scattered data sets. However, this interpolation also allows for the reconstruction of partial derivatives throughout the solution field, which can then be used to drive the solution of a partial differential equation. Since the interpolation takes place on a scattered dataset with no local connectivity, the solution is essentially meshless. RBF-based methods have been successfully used to solve a wide variety of PDEs in this fashion. Such full-domain RBF methods are highly flexible and can exhibit spectral convergence rates Madych & Nelson (1990). However, in their traditional implementation the fu…
Shape indices to identify regional differences in otolith morphology of comber, Serranus cabrilla (L., 1758)
2003
Summary Sagittal otoliths from the Atlantic and Mediterranean regions of Serranus cabrilla L. were compared using shape indices (form-factor, roundness, circularity, rectangularity, ellipticity and eccentricity). Regional differences were best described by form-factor, circularity and eccentricity variables. The canonical discriminant functions were built with form-factor or rectangularity indices. The results indicated slight regional variations. The G-test was the criterion more useful to identify the otolith origin in the discriminant analysis.
On complexity and motion planning for co-rank one sub-Riemannian metrics
2004
In this paper, we study the motion planning problem for generic sub-Riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean (10,11)), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic C ∞ case, we study some non-generic generalizations in the analytic case.
Baer cones in finite projective spaces
1987
Let R and V be two skew subspaces with dimensions r and v of P=PG(d,q). If q is a square, then there is a Baer subspace V* of V, i.e. a subspace of dimension v and order √q. We call the set C(R,V*)=\(\mathop \cup \limits_p \), where the union is taken over all PeV*, aBaer cone oftype (r,v).