Bessel processes, the Brownian snake and super-Brownian motion

We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of dimension -5. We also discuss a spine decomposition for the Brownian snake conditioned on the minimizing path.Comment: Submitted to the special volume of S\'eminaire de Probabilit\'es in memory of Marc Yo

Feller property and infinitesimal generator of the exploration process

We consider the exploration process associated to the continuous random tree (CRT) built using a Levy process with no negative jumps. This process has been studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is a useful tool to study CRT as well as super-Brownian motion with general branching mechanism. In this paper we prove this process is Feller, and we compute its infinitesimal generator on exponential functionals and give the corresponding martingale

The topological structure of scaling limits of large planar maps

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.Comment: 45 pages Second version with minor modification

Apraxia: a gestural or a cognitive disorder?

François Osiurak1,2 and Didier Le Gall31 Laboratoire d’Etude des Mécanismes Cognitifs (EA 3082), Université de Lyon, France2 Institut Universitaire de France, Paris, France3 Laboratoire de Psychologie des Pays de la Loire (EA 4638), Université d’Angers, FranceCorrespondence to: François Osiurak, Laboratoire d’Etude des Mécanismes Cognitifs (EA 3082), Institut de Psychologie, 5, avenue Pierre Mendès-France, 69676 Bron Cedex, France E-mail: Francois.Osiurak{at}univ-lyon2.frSir,We read with great interest the article by Buxbaum et al. (2014) about the critical brain regions for tool-related and imitative actions. The authors performed voxel-based lesion–symptom mapping with data from 71 left brain-damaged patients. Three types of actions were examined: (i) pantomime to sight of tools (GestTool); (ii) pantomime on imitation (ImTool); and (iii) imitation of meaningless gestures (ImNov). Impairments in all three of the gesture tasks were associated with lesions in left middle and inferior temporal and inferior parietal regions. Moreover, tool-related actions (both GestTool and ImTool) were dependent on left middle and inferior temporal lobe, whereas imitation of meaningless gestures (ImNov) was dependent on left inferior parietal regions. From these findings, the authors drew two conclusions. First, the left inferior parietal lobe might be the basis for the kinematic component of the praxis system, useful for planning movement trajectories in terms of extent, direction and timing. Second, middle and inferior temporal regions might support representational components of the praxis system (e.g. the arm and hand posture associated with the use of a hammer). Note that these conclusions lead to a profound revision of Buxbaum’s initial (2001) model. In this model, the left inferior parietal lobe was viewed

Magnetization reversal and spin dynamics exchange in biased F/AF bilayers probed with complex permeability spectra

The spin dynamics of the ferromagnetic pinned layer of ferro-antiferromagnetic coupled NiFe/MnNi bilayers is investigated in a broad frequency range (30 MHz-6 GHz). A phenomenological model based on the Landau-Lifshitz equation for the complex permeability of the F/AF bilayer is proposed. The experimental results are compared to theoretical predictions. We show that the resonance frequencies, measured during the magnetization, are likewise hysteretic.Comment: 4 pages, 4 figure

NP-hardness of decoding quantum error-correction codes

Though the theory of quantum error correction is intimately related to the classical coding theory, in particular, one can construct quantum error correction codes (QECCs) from classical codes with the dual containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expect degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or non-degenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems, and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.Comment: 5 pages, no figure. Final version for publicatio