Search results for "Discrete"
showing 10 items of 2205 documents
On the arithmetic and geometry of binary Hamiltonian forms
2011
Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most $s$ by $f$, as $s$ tends to $+\infty$. We compute the volumes of hyperbolic 5-manifolds constructed by quaternions using Eisenstein series. In the Appendix, V. Emery computes these volumes using Prasad's general formula. We use hyperbolic geometry in dimension 5 to describe the reduction theory of both definite and indefinite binary quaternionic Hermitian forms.
A note on higher order Melnikov functions
2005
We present several classes of planar polynomial Hamilton systems and their polynomial perturbations leading to vanishing of the first Melnikov integral. We discuss the form of higher order Melnikov integrals. In particular, we present new examples where the second order Melnikov integral is not an Abelian integral.
Automorphisms of hyperelliptic GAG-codes
2009
Abstract We determine the n –automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field.
Instantaneous transfer entropy for the study of cardio-respiratory dynamics
2015
Measures of transfer entropy have been proposed to quantify the directional coupling and strength between two complex physiological variables. Particular attention has been given to nonlinear interactions within cardiovascular and respiratory dynamics as influenced by the autonomic nervous system. However, standard transfer entropy estimates have shown major limitations in dealing with issues concerning stochastic system modeling, limited observations in time, and the assumption of stationarity of the considered physiological variables. Moreover, standard estimates are unable to track time-varying changes in nonlinear coupling with high resolution in time. Here, we propose a novel definitio…
Instantaneous Transfer Entropy for the Study of Cardiovascular and Cardio-Respiratory Nonstationary Dynamics
2017
Objective: Measures of transfer entropy (TE) quantify the direction and strength of coupling between two complex systems. Standard approaches assume stationarity of the observations, and therefore are unable to track time-varying changes in nonlinear information transfer with high temporal resolution. In this study, we aim to define and validate novel instantaneous measures of TE to provide an improved assessment of complex nonstationary cardiorespiratory interactions. Methods: We here propose a novel instantaneous point-process TE (ipTE) and validate its assessment as applied to cardiovascular and cardiorespiratory dynamics. In particular, heartbeat and respiratory dynamics are characteriz…
A discrete-choice experiment to assess patients’ preferences for osteoarthritis treatment: An ESCEO working group
2020
Objective: To evaluate the preferences of patients with osteoarthritis for treatment.Methods: A discrete-choice experiment was conducted among adult OA patients who were presented with 12 choice sets of two treatment options and asked in each to select the treatment they would prefer. Based on literature reviews, expert consultation, patient survey and expert meeting, treatment options were characterized by seven attributes: improvement in pain, improvement in walking, ability to manage domestic activities, ability to manage social activities, improvement in overall energy and well-being, risk of moderate/severe side effects and impact on disease progression. Random parameters logit model w…
Darstellung von Hyperebenen in verallgemeinerten affinen Räumen durch Moduln
1994
The starting point of this article is a generalized concept of affine space which includes all affine spaces over unitary modules. Our main result is a representation theorem for hyperplanes of affine spaces: Every hyperplane which satisfies a weak richness condition is induced by a module. 1
Affine Kettengeometrien �ber Jordanalgebren
1996
It is shown that an affine chain geometry over a Jordan algebra can be constructed in a nearly classical manner. Conversely, such chain geometries are characterized as systems of rational normal curves having a group of automorphisms with certain properties.
On the algebraic representation of projectively embeddable affine geometries
1995
The main result of this article is an application of [1] and [2] which yields that an at least 2-dimensional affine geometry is module-induced if and only if it is projectively embeddable into an Arguesian projective lattice geometry.
Products of snowflaked Euclidean lines are not minimal for looking down
2017
We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance $d$ such that the product of snowflaked Euclidean lines looks down on $(\mathbb R^N,d)$, but not vice versa.