arXiv subjects

Fernando Guevara Vasquez

Publications and source records attributed to Fernando Guevara Vasquez.

At least 19 recordsLinked to original sources

arXiv2026

A wearable electrical hemodynamic imaging ring

Continuous ambulatory monitoring of peripheral vascular perfusion could enable earlier detection of vascular dysfunction in individuals with diabetes mellitus and more timely management of cardiovascular disease. Clinical imaging modalities provide high-fidelity vascular information but are impractical for ambulatory use, whereas most wearable devices are limited to single-modality sensing and do not provide imaging. Electrical bioimpedance has the potential to bridge this gap by enabling rapid spatial and temporal imaging while remaining sensitive to hemodynamic changes. Here, we introduce a wearable ring with 8 electrodes and 32-channel bioimpedance sensing for finger blood flow imaging. In 96 healthy participants measured at rest and during autonomic maneuvers, we resolve conductivity images in the digital arteries associated with pulsatile blood flow and train neural network models for continuous cuffless blood pressure waveform estimation. We demonstrate the feasibility of bioimpedance imaging in a ring form factor, supporting its potential for ambulatory cuffless hemodynamic monitoring.

physics.med-ph↗

arXiv2025

A potential theory on weighted graphs

We present an analog to classic potential theory on weighted graphs. With nodes partitioned into exterior, boundary and interior nodes and an appropriate decomposition of the Laplacian, we define discrete analogues to the trace operators, the single and double layer potential operators, and the boundary layer operators. As in the continuum, these operators can represent exterior or interior harmonic functions with different boundary conditions. The formalism we introduce includes a discrete Calderón calculus and brings some well known results from potential theory to weighted graphs, e.g. on the spectrum of the Neumann-Poincaré operator. We illustrate the formalism with a cloaking strategy on weighted graphs which allows to hide an anomaly from the perspective of electrical measurements made away from the anomaly.

math.PR↗

arXiv2024

Design and control of quasiperiodic patterns of particles with standing acoustic waves

We develop a method to design tunable quasiperiodic structures of particles suspended in a fluid by controlling standing acoustic waves. One application of our results is to ultrasound directed self-assembly, which allows fabricating composite materials with desired microstructures. Our approach is based on identifying the minima of a functional, termed the acoustic radiation potential, determining the locations of the particle clusters. This functional can be viewed as a two- or three-dimensional slice of a similar functional in higher dimensions as in the cut-and-project method of constructing quasiperiodic patterns. The higher dimensional representation allows for translations, rotations, and reflections of the patterns. Constrained optimization theory is used to characterize the quasiperiodic designs based on local minima of the acoustic radiation potential and to understand how changes to the controls affect particle patterns. We also show how to transition smoothly between different controls, producing smooth transformations of the quasiperiodic patterns. The developed approach unlocks a route to creating tunable quasiperiodic and moiré structures known for their unconventional superconductivity and other extraordinary properties. Several examples of constructing quasiperiodic structures, including in two and three dimensions, are given.

math.AP↗

arXiv2024

Discrete inverse problems with internal functionals

We study the problem of finding the resistors in a resistor network from measurements of the power dissipated by the resistors under different loads. We give sufficient conditions for local uniqueness, i.e. conditions that guarantee that the linearization of this non-linear inverse problem admits a unique solution. Our method is inspired by a method to study local uniqueness of inverse problems with internal functionals in the continuum, where the inverse problem is reformulated as a redundant system of differential equations. We use our method to derive local uniqueness conditions for other discrete inverse problems with internal functionals including a discrete analogue of the inverse Schrödinger problem and problems where the resistors are replaced by impedances and dissipated power at the zero and a positive frequency are available. Moreover, we show that the dissipated power measurements can be obtained from measurements of thermal noise induced currents.

math.AP↗

arXiv2023

Imaging with thermal noise induced currents

We use thermal noise induced currents to image the real and imaginary parts of the conductivity of a body. Covariances of the thermal noise currents measured at a few electrodes are shown to be related to a deterministic problem. We use the covariances obtained while selectively heating the body to recover the real power density in the body under known boundary conditions and at a known frequency. The resulting inverse problem is related to acousto-electric tomography, but where the conductivity is complex and only the real power is measured. We study the local solvability of this problem by determining where its linearization is elliptic. Numerical experiments illustrating this inverse problem are included.

math.NA↗

arXiv2022

Active exterior cloaking for the 2D Helmholtz equation with complex wavenumbers and application to thermal cloaking

We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive wavenumbers, the sources are also determined by the Green identities. The novelty is that we prove that the same approach works for complex wavenumbers which makes it applicable to a variety of media, including media with dispersion, loss and gain. Furthermore, by deriving bounds on Graf's addition formulas with complex arguments, we obtain new estimates that allow to quantify the quality of the cloaking effect. We illustrate our results by applying them to achieve active exterior cloaking for the heat equation.

math.AP↗

arXiv2020

Active Thermal Cloaking and Mimicking

We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active we mean that it relies on designing monopole and dipole heat source distributions on the boundary of the region to be cloaked. The same technique can be used to make a source or an object look like a different one to an observer outside the cloaked region, from the perspective of thermal measurements. Our results assume a homogeneous isotropic bulk medium and require knowledge of the source to cloak or mimic, but are in most cases independent of the object to cloak.

math.AP↗

arXiv2020

Wave-driven assembly of quasi periodic patterns of particles

We theoretically show that a superposition of plane waves causes small (compared to the wavelength) particles dispersed in a fluid to assemble in quasiperiodic two or three dimensional patterns. We experimentally demonstrate this theory by using ultrasound waves to assemble quasiperiodic patterns of carbon nanoparticles in water using an octagonal arrangement of ultrasound transducers, and we document good agreement between theory and experiments. The theory also applies to obtaining quasiperiodic patterns in other situations where particles move with linear waves, such as optical lattices.

math-ph↗

arXiv2019

Periodic particle arrangements using standing acoustic waves

We determine crystal-like materials that can be fabricated by using a standing acoustic wave to arrange small particles in a non-viscous liquid resin, which is cured afterwards to keep the particles in the desired locations. For identical spherical particles with the same physical properties and small compared to the wavelength, the locations where the particles are trapped correspond to the minima of an acoustic radiation potential which describes the net forces that a particle is subject to. We show that the global minima of spatially periodic acoustic radiation potentials can be predicted by the eigenspace of a small real symmetric matrix corresponding to its smallest eigenvalue. We relate symmetries of this eigenspace to particle arrangements composed of points, lines or planes. Since waves are used to generate the particle arrangements, the arrangement's periodicity is limited to certain Bravais lattice classes that we enumerate in two and three dimensions.

math.NA↗

arXiv2019

Broadband lightweight flat lenses for longwave-infrared imaging

We experimentally demonstrate imaging in the longwave-infrared (LWIR) spectral band (8um to 12um) using a single polymer flat lens based upon multi-level diffractive optics. The device thickness is only 10μm, and chromatic aberrations are corrected over the entire LWIR band with one surface. Due to the drastic reduction in device thickness, we are able to utilize polymers with absorption in the LWIR, allowing for inexpensive manufacturing via imprint lithography. The weight of our lens is less than 100 times those of comparable refractive lenses. We fabricated and characterized two different flat lenses. Even with about 25% absorption losses, experiments show that our flat polymer lenses obtain good imaging with field of view of ~35degrees and angular resolution less than 0.013 degrees. The flat lenses were characterized with two different commercial LWIR image sensors. Finally, we show that by using lossless, higher-refractive-index materials like silicon, focusing efficiencies in excess of 70% can be achieved over the entire LWIR band. Our results firmly establish the potential for lightweight, ultra-thin, broadband lenses for high-quality imaging in the LWIR band.

physics.optics↗

arXiv2018

Matrix valued inverse problems on graphs with application to elastodynamic networks

We consider the inverse problem of finding matrix valued edge or nodal quantities in a graph from measurements made at a few boundary nodes. This is a generalization of the problem of finding resistors in a resistor network from voltage and current measurements at a few nodes, but where the voltages and currents are vector valued. The measurements come from solving a series of Dirichlet problems, i.e. finding vector valued voltages at some interior nodes from voltages prescribed at the boundary nodes. We give conditions under which the Dirichlet problem admits a unique solution and study the degenerate case where the edge weights are rank deficient. Under mild conditions, the map that associates the matrix valued parameters to boundary data is analytic. This has practical consequences to iterative methods for solving the inverse problem numerically and to local uniqueness of the inverse problem. Our results allow for complex valued weights and give also explicit formulas for the Jacobian of the parameter to data map in terms of certain products of Dirichlet problem solutions. An application to inverse problems arising in elastodynamic networks (networks of springs, masses and dampers) is presented.

math.CO↗

arXiv2018

Imaging small polarizable scatterers with polarization data

We present a method for imaging small scatterers in a homogeneous medium from polarization measurements of the electric field at an array. The electric field comes from illuminating the scatterers with a point source with known location and polarization. We view this problem as a generalized phase retrieval problem with data being the coherency matrix or Stokes parameters of the electric field at the array. We introduce a simple preprocessing of the coherency matrix data that partially recovers the ideal data where all the components of the electric field are known for different source dipole moments. We prove that the images obtained using an electromagnetic version of Kirchhoff migration applied to the partial data are, for high frequencies, asymptotically identical to the images obtained from ideal data. We analyze the image resolution and show that polarizability tensor components in an appropriate basis can be recovered from the Kirchhoff images, which are tensor fields. A time domain interpretation of this imaging problem is provided and numerical experiments are used to illustrate the theory.

math.NA↗

arXiv2017

Approximation by Herglotz wave functions

We consider the problem of approximating a function using Herglotz wave functions, which are a superposition of plane waves. When the discrepancy is measured in a ball, we show that the problem can essentially be solved by considering the function we wish to approximate as a source distribution and time reversing the resulting field. Unfortunately this gives generally poor approximations. Intuitively, this is because Herglotz wave functions are determined by a two-dimensional field and the function to approximate is three-dimensional. If the discrepancy is measured on a plane, we show that the best approximation corresponds to a low-pass filter, where only the spatial frequencies with length less than the wavenumber are kept. The corresponding Herglotz wave density can be found explicitly. Our results have application to designing standing acoustic waves for self-assembly of micro-particles in a fluid.

math.NA↗

arXiv2017

Imaging polarizable dipoles

We present a method for imaging the polarization vector of an electric dipole distribution in a homogeneous medium from measurements of the electric field made at a passive array. We study an electromagnetic version of Kirchhoff imaging and prove, in the Fraunhofer asymptotic regime, that range and cross-range resolution estimates are identical to those in acoustics. Our asymptotic analysis provides error estimates for the cross-range dipole orientation reconstruction and shows that the range component of the dipole orientation is lost in this regime. A naive generalization of the Kirchhoff imaging function is afflicted by oscillatory artifacts in range, that we characterize and correct. We also consider the active imaging problem which consists in imaging both the position and polarizability tensors of small scatterers in the medium using an array of collocated sources and receivers. As in the passive array case, we provide resolution estimates that are consistent with the acoustic case and give error estimates for the cross-range entries of the polarizability tensor. Our theoretical results are illustrated by numerical experiments.

math.NA↗

arXiv2016

A discrete Liouville identity for numerical reconstruction of Schrödinger potentials

We propose a discrete approach for solving an inverse problem for Schrödinger's equation in two dimensions, where the unknown potential is to be determined from boundary measurements of the Dirichlet to Neumann map. For absorptive potentials, and in the continuum, it is known that by using the Liouville identity we obtain an inverse conductivity problem. Its discrete analogue is to find a resistor network that matches the measurements, and is well understood. Here we show how to use a discrete Liouville identity to transform its solution to that of Schrödinger's problem. The discrete Schrödinger potential given by the discrete Liouville identity can be used to reconstruct the potential in the continuum in two ways. First, we can obtain a direct but coarse reconstruction by interpreting the values of the discrete Schrödinger potential as averages of the continuum Schrödinger potential on a special sensitivity grid. Second, the discrete Schrödinger potential may be used to reformulate the conventional nonlinear output least squares optimization formulation of the inverse Schrödinger problem. Instead of minimizing the boundary measurement misfit, we minimize the misfit between the discrete Schrödinger potentials. This results in a better behaved optimization problem that converges in a single Gauss-Newton iteration, and gives good quality reconstructions of the potential, as illustrated by the numerical results.

math.NA↗

arXiv2016

Kirchhoff migration without phases

We present a simple, frequency domain, preprocessing step to Kirchhoff migration that allows the method to image scatterers when the wave field phase information is lost at the receivers, and only intensities are measured. The resulting imaging method does not require knowing the phases of the probing field or manipulating the phase of the wave field at the receivers. In a regime where the scattered field is small compared to the probing field, the problem of recovering the full-waveform scattered field from intensity data can be formulated as an embarrassingly simple least-squares problem. Although this only recovers the projection (on a known subspace) of the full-waveform scattered field, we show that, for high frequencies, this projection gives Kirchhoff images asymptotically identical to the images obtained with full waveform data. Our method can also be used when the source is modulated by a Gaussian process and autocorrelations are measured at an array of receivers.

math.NA↗

arXiv2015

On the solvability of the discrete conductivity and Schrödinger inverse problems

We study the uniqueness question for two inverse problems on graphs. Both problems consist in finding (possibly complex) edge or nodal based quantities from boundary measurements of solutions to the Dirichlet problem associated with a weighted graph Laplacian plus a diagonal perturbation. The weights can be thought of as a discrete conductivity and the diagonal perturbation as a discrete Schrödinger potential. We use a discrete analogue to the complex geometric optics approach to show that if the linearized problem is solvable about some conductivity (or Schrödinger potential) then the linearized problem is solvable for almost all conductivities (or Schrödinger potentials) in a suitable set. We show that the conductivities (or Schrödinger potentials) in a certain set are determined uniquely by boundary data, except on a zero measure set. This criterion for solvability is used in a statistical study of graphs where the conductivity or Schrödinger inverse problem is solvable.

math.CO↗

arXiv2015

Imaging with power controlled source pairs

Scatterers in a homogeneous medium are imaged by probing the medium with two point sources of waves modulated by correlated signals and by measuring only intensities at one single receiver. For appropriately chosen source pairs, we show that full waveform array measurements can be recovered from such intensity measurements by solving a linear least squares problem. The least squares solution can be used to image with Kirchhoff migration, even if the solution is determined only up to a known one-dimensional nullspace. The same imaging strategy can be used when the medium is probed with point sources driven by correlated Gaussian processes and autocorrelations are measured at a single location. Since autocorrelations are robust to noise, this can be used for imaging when the probing wave is drowned in background noise.

physics.optics↗