383 research outputs found
On the Utility of Representation Learning Algorithms for Myoelectric Interfacing
Electrical activity produced by muscles during voluntary movement is a reflection of the firing patterns of relevant motor neurons and, by extension, the latent motor intent driving the movement. Once transduced via electromyography (EMG) and converted into digital form, this activity can be processed to provide an estimate of the original motor intent and is as such a feasible basis for non-invasive efferent neural interfacing. EMG-based motor intent decoding has so far received the most attention in the field of upper-limb prosthetics, where alternative means of interfacing are scarce and the utility of better control apparent. Whereas myoelectric prostheses have been available since the 1960s, available EMG control interfaces still lag behind the mechanical capabilities of the artificial limbs they are intended to steer—a gap at least partially due to limitations in current methods for translating EMG into appropriate motion commands. As the relationship between EMG signals and concurrent effector kinematics is highly non-linear and apparently stochastic, finding ways to accurately extract and combine relevant information from across electrode sites is still an active area of inquiry.This dissertation comprises an introduction and eight papers that explore issues afflicting the status quo of myoelectric decoding and possible solutions, all related through their use of learning algorithms and deep Artificial Neural Network (ANN) models. Paper I presents a Convolutional Neural Network (CNN) for multi-label movement decoding of high-density surface EMG (HD-sEMG) signals. Inspired by the successful use of CNNs in Paper I and the work of others, Paper II presents a method for automatic design of CNN architectures for use in myocontrol. Paper III introduces an ANN architecture with an appertaining training framework from which simultaneous and proportional control emerges. Paper Iv introduce a dataset of HD-sEMG signals for use with learning algorithms. Paper v applies a Recurrent Neural Network (RNN) model to decode finger forces from intramuscular EMG. Paper vI introduces a Transformer model for myoelectric interfacing that do not need additional training data to function with previously unseen users. Paper vII compares the performance of a Long Short-Term Memory (LSTM) network to that of classical pattern recognition algorithms. Lastly, paper vIII describes a framework for synthesizing EMG from multi-articulate gestures intended to reduce training burden
Beam scanning by liquid-crystal biasing in a modified SIW structure
A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium
Nonperturbative Aspects of Quantum Field Theory in Curved Spacetime
Quantum field theory in curved spacetime is perhaps the most reliable
framework in which one can investigate quantum effects in the presence of
strong gravitational fields. Nevertheless, it is often studied by means of
perturbative treatments. In this thesis, we aim at using the functional
renormalization group -- a nonperturbative realization of the renormalization
group -- as a technique to describe nonperturbative quantum phenomena in curved
spacetimes. The chosen system is an Unruh--DeWitt particle detector coupled to
a scalar quantum field. We discuss how to formulate such a system in terms of
an action and how one can compute its renormalization group flow in the case of
an inertial detector in flat spacetime, for simplicity. We learn, however, that
the results are divergent in the limit in which the detector's energy gap
vanishes. Possible workarounds are discussed at the end.
This thesis also presents a review of quantum field theory in curved
spacetimes by means of the algebraic approach, although it assumes no previous
experience with functional analysis. Hence, it fills a pedagogical gap in the
literature. Furthermore, we also review the functional renormalization group
and derive the Wetterich equation assuming a general field content that might
include both bosonic and fermionic fields. Such a derivation is also hardly
found in pedagogical introductions available in the high energy physics
literature.Comment: MSc thesis defended at the Federal University of ABC (Brazil) on 28
April 2023. xxiv + 152 pages, 22 figure
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Complexes from Complexes: Finite Element Complexes in Three Dimensions
In the realm of solving partial differential equations (PDEs), Hilbert
complexes have gained paramount importance, and recent progress revolves around
devising new complexes using the Bernstein-Gelfand-Gelfand (BGG) framework, as
demonstrated by Arnold and Hu [Complexes from complexes. {\em Found. Comput.
Math.}, 2021]. This paper significantly extends this methodology to
three-dimensional finite element complexes, surmounting challenges posed by
disparate degrees of smoothness and continuity mismatches. By incorporating
techniques such as smooth finite element de Rham complexes, the
decomposition, and trace complexes with corresponding two-dimensional finite
element analogs, we systematically derive finite element Hessian, elasticity,
and divdiv complexes. Notably, the construction entails the incorporation of
reduction operators to handle continuity disparities in the BGG diagram at the
continuous level, ultimately culminating in a comprehensive and robust
framework for constructing finite element complexes with diverse applications
in PDE solving.Comment: 46 pages, 6 figure
1-D broadside-radiating leaky-wave antenna based on a numerically synthesized impedance surface
A newly-developed deterministic numerical technique for the automated design of metasurface antennas is applied here for the first time to the design of a 1-D printed Leaky-Wave Antenna (LWA) for broadside radiation. The surface impedance synthesis process does not require any a priori knowledge on the impedance pattern, and starts from a mask constraint on the desired far-field and practical bounds on the unit cell impedance values. The designed reactance surface for broadside radiation exhibits a non conventional patterning; this highlights the merit of using an automated design process for a design well known to be challenging for analytical methods. The antenna is physically implemented with an array of metal strips with varying gap widths and simulation results show very good agreement with the predicted performance
Unification of the Fundamental Forces in Higher-Order Differential Geometry
Riemannian geometry is generalized to allow infinitesimals to any order. In
the differential calculus, it is shown how to extend the affine connection to
enable parallel transport in the direction of a higher tangent vector, while on
the integral side, a theory of integration adapted to integrands possibly of
higher than first order in the differentials is developed. The curvature tensor
generalizes naturally in order to describe how space can curve along higher
tangents. These elegant ideas stand on their own as a discovery in pure
mathematics, independent of whatever fate they may encounter when applied to
physics, where one expects novel phenomena rooted in interactions among
infinitesimals differing in order (never before studied). Free fall must now be
described by geodesics in a higher sense and Einstein's field equations acquire
a hierarchy of higher sectors. As soon as one goes to second order, a profound
revision of the concept of inertia is called for which manifests itself on the
phenomenological level as a modified Newtonian dynamics obeyed by spacecraft in
the solar system (thereby explaining the flyby anomaly). A second major
implication is to open a path to field-theoretical unification on the classical
level in the spirit of Einstein. The present theory leads immediately to
another fundamental force arising at each successive order in the jets. The
1-jet case reduces to gravity as known in the conventional general theory of
relativity, of course. It is striking that, at the 2-jet level, one recovers
the electroweak forces including spontaneous symmetry breaking from a single
postulate, the proper generalization of the equivalence principle. At the 3-jet
level, following the same procedure we obtain chromodynamics without any ad hoc
modifications. In future work, we hope to analyze the 4-jet level and its
implications for the anomalous magnetic moment of the muon.Comment: 222 pages, 1 figur
Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides
In a time-harmonic setting, we show for heterogeneous acoustic and
homogeneous electromagnetic wavesguides stability estimates with the stability
constant depending linearly on the length of the waveguide. These stability
estimates are used for the analysis of the (ideal) ultraweak (UW) variant of
the Discontinuous Petrov Galerkin (DPG) method. For this UW DPG, we show that
the stability deterioration with can be countered by suitably scaling the
test norm of the method. We present the ``full envelope approximation'', a UW
DPG method based on non-polynomial ansatz functions that allows for treating
long waveguides
Numerical homogenization: multi-resolution and super-localization approaches
Multi-scale problems arise in many scientific and engineering applications, where the effective behavior of a system is determined by the interaction of effects at multiple scales. To accurately simulate such problems without globally resolving all microscopic features, numerical homogenization techniques have been developed. One such technique is the Localized Orthogonal Decomposition (LOD). It provides reliable approximations at coarse discretization levels using problem-adapted basis functions obtained by solving local sub-scale correction problems. This allows the treatment of problems with heterogeneous coefficients without structural assumptions such as periodicity or scale separation.
This thesis presents recent achievements in the field of LOD-based numerical homogenization. As a starting point, we introduce a variant of the LOD and provide a rigorous error analysis. This LOD variant is then extended to the multi-resolution setting using the Helmholtz problem as a model problem. The multi-resolution approach allows to improve the accuracy of an existing LOD approximation by adding more discretization levels. All discretization levels are decoupled, resulting in a block-diagonal coarse system matrix. We provide a wavenumber-explicit error analysis that shows convergence under mild assumptions. The fast numerical solution of the block-diagonal coarse system matrix with a standard iterative solver is demonstrated.
We further present a novel LOD-based numerical homogenization method named Super-Localized Orthogonal Decomposition (SLOD). The method identifies basis functions that are significantly more local than those of the LOD, resulting in reduced computational cost for the basis computation and improved sparsity of the coarse system matrix. We provide a rigorous error analysis in which the stability of the basis is quantified a posteriori.
However, for challenging problems, basis stability issues may arise degrading the approximation quality of the SLOD. To overcome these issues, we combine the SLOD with a partition of unity approach. The resulting method is conceptually simple and easy to implement. Higher order versions of this method, which achieve higher order convergence rates using only the regularity of the source term, are derived.
Finally, a local reduced basis (RB) technique is introduced to address the challenges of parameter-dependent multi-scale problems. This method integrates a RB approach into the SLOD framework, enabling an efficient generation of reliable coarse-scale models of the problem. Due to the unique localization properties of the SLOD, the RB snapshot computation can be performed on particularly small patches, reducing the offline and online complexity of the method. All theoretical results of this thesis are supported by numerical experiments
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