Search

INTRODUCTION: Deep brain stimulation (DBS) is widely used to alleviate symptoms of movement disorders. During intraoperative stimulation the influence of active or passive movements on the neuronal activity is often evaluated but the evaluation remains mostly subjective. The objective of this paper is to investigate the potential of a previously developed Weighted-frequency Fourier Linear combiner and Kalman filter-based recursive algorithm to identify tremor phases and types. METHODS: Ten accelerometer recordings from eight patients were acquired during DBS from which 186 phases were manually annotated into: rest, postural and kinetic phase without tremor, and rest, postural and kinetic phase with tremor. The method first estimates the instantaneous tremor frequency and then decomposes the motion signal into voluntary and tremorous parts. The tremorous part is used to quantify tremor and the voluntary part to differentiate rest, postural and kinetic phases. RESULTS: Instantaneous tremor frequency and amplitude are successfully tracked online. The overall accuracy for tremorous phases only is 89.1% and 76.3% when also non-tremorous phases are considered. Two main misclassification cases are identified and further discussed. CONCLUSION: The results demonstrate the potential of the developed algorithm as an online tremorous movement classifier. It would benefit from a more advanced tremor detector but nevertheless the obtained digital biomarkers offer an evidence-based analysis and could optimize the efficacy of DBS treatment.

We present three equivalent definitions of S¹-equivariant symplectic homology. We show that, using rational coefficients, the positive part of S¹-equivariant symplectic homology is isomorphic to linearized contact homology when the latter is defined. We present several computations and applications, and introduce a substitute for cylindrical/linearized contact homology based on an S¹-equivariant construction. [ABSTRACT FROM AUTHOR]

When a voltage is applied across the electrodes of a flat piezoelectric transducer attached to a thin plate structure, the transducer acts as equivalent loads applied to the host plate structure. In this paper, analytical expressions of these equivalent loads are derived for the general case of an orthotropic piezoelectric actuator using Hamilton's principle and two different mathematical approaches leading to the same results: Green's theorem and derivation using the theory of distributions. The equivalent loads are a function of the material properties as well as the normal to the contour of the transducer. Examples of applications to simple geometric shapes (triangle, rectangle, and circle) are given. [ABSTRACT FROM AUTHOR]

We study the parametrized Hamiltonian action functional for finite-dimensional families of Hamiltonians. We show that the linearized operator for the L²-gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and almost complex structure. We also establish the Fredholm property and transversality for generic S¹-invariant families of Hamiltonians and almost complex structures, parametrized by odd-dimensional spheres. This is a foundational result used to define S¹-equivariant Floer homology. As an intermediate result of independent interest, we generalize Aronszajn's unique continuation theorem to a class of elliptic integro-differential inequalities of order two. [ABSTRACT FROM AUTHOR]

We show that on any closed contact manifold of dimension greater than 1 a contact structure with vanishing contact homology can be constructed. The basic idea for the construction comes from Giroux. We use a special open book decomposition for spheres. The page is the cotangent bundle of a sphere and the monodromy is given by a left-handed Dehn twist. In the resulting contact manifold, we exhibit a closed Reeb orbit that bounds a single finite energy plane like in the computation for the overtwisted case. As a result, the unit element of the contact homology algebra is exact and so the contact homology vanishes. This result can be extended to other contact manifolds by using connected sums. The latter is related to the plumbing or 2-Murasugi sum of contact open books. We shall give a possible description of this construction and some conjectures about the plumbing operation. [ABSTRACT FROM AUTHOR]

We show that, for every contact manifold M and for every Riemann surface Σ of genus at least 1, the manifold Σ × M admits a contact structure. In particular, the tori T2n+1 are contact manifolds. [ABSTRACT FROM AUTHOR]