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Frame multipliers are an abstract version of Toeplitz operators in frame theory and consist of a composition of a multiplication operator with the analysis and synthesis operators. Whereas the boundedness properties of frame multipliers on…
Spectral distortions of the cosmic microwave background (CMB) may become a powerful probe of primordial perturbations at small scales. Existing studies of spectral distortions focus almost exclusively on primordial scalar metric…
A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…
Capturing complex dependence structures between outcome variables (e.g., study endpoints) is of high relevance in contemporary biomedical data problems and medical research. Distributional copula regression provides a flexible tool to model…
In recent years, numerous ideas have emerged for designing a mutually reinforcing mechanism or extra stages for the image fusion task, ignoring the inevitable gaps between different vision tasks and the computational burden. We argue that…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
The convolution operator is the fundamental building block of modern convolutional neural networks (CNNs), owing to its simplicity, translational equivariance, and efficient implementation. However, its structure as a fixed, linear,…
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…
Bundle adjustment (BA) is a technique for refining sensor orientations of satellite images, while adjustment accuracy is correlated with feature matching results. Feature match-ing often contains high uncertainties in weak/repeat textures,…
In this thesis we investigate several aspects related to the theory of fluctuations in the Cosmic Microwave Background. We develop a new algorithm to calculate the angular power spectrum of the anisotropies which is two orders of magnitude…
The quantization of gauge fields and gravitation on manifolds with boundary makes it necessary to study boundary conditions which involve both normal and tangential derivatives of the quantized field. The resulting one-loop divergences can…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Light-pulse atom interferometers rely on the wave nature of matter and its manipulation with coherent laser pulses. They are used for precise gravimetry and inertial sensing as well as for accurate measurements of fundamental constants.…
The peculiar motion of an observer with respect to the CMB rest frame induces a deflection in the arrival direction of the observed photons (also known as CMB aberration) and a Doppler shift in the measured photon frequencies. As a…
Atom interferometers are sensitive to a wide range of forces by encoding their signals in interference patterns of matter waves. To estimate the magnitude of these forces, the underlying phase shifts they imprint on the atoms must be…
In celestial holography, scattering particles in four-dimensional asymptotically flat spacetimes are dual to conformal primary field operators on the celestial sphere. Multi-particle celestial operators can be formed from regularized…
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
We report the observation of two additional sub-natural line width quantum interference in the $D_2$ manifold of $^{39}K$ vapor, in addition to the usual single Electromagnetically induced transparency peak. The other two features appear…
A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…