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Aberration-corrected Scanning Transmission Electron Microscopy (STEM) has become an essential tool in understanding materials at the atomic scale. However, tuning the aberration corrector to produce a sub-{\AA}ngstr\"om probe is a complex…
Boosting is a popular algorithm in supervised machine learning with wide applications in regression and classification problems. It combines weak learners, such as regression trees, to obtain accurate predictions. However, in the presence…
The Doppler effect is a shift in the frequency of waves emitted from an object moving relative to the observer. By observing and analysing the Doppler shift in electromagnetic waves from astronomical objects, astronomers gain greater…
In this paper we extend the traditional framework of noncommutative geometry in order to deal with spectral truncations of geometric spaces (i.e. imposing an ultraviolet cutoff in momentum space) and with tolerance relations which provide a…
The observed dipole anisotropy of the cosmic microwave background (CMB) temperature is much larger than the fluctuations observed on smaller scales and is dominated by the kinematic contribution from the Doppler shifting of the monopole due…
Convolutional neural networks (CNNs) and transformers, which are composed of multiple processing layers and blocks to learn the representations of data with multiple abstract levels, are the most successful machine learning models in recent…
Image subtraction in astronomy is a tool for transient object discovery and characterization, particularly useful in wide fields, and is well suited for moving or photometrically varying objects such as asteroids, extra-solar planets and…
This paper constructs a kinematic basis for spin networks with planar or cylindrical symmetry, by exploiting the fact that the basis elements are representations of an O(3) subgroup of O(4). The action of the volume operator on this basis…
Discrete circular convolution over $\mathbb{Z}/N\mathbb{Z}$ is a linear operator and can be implemented on quantum hardware within the linear-combination-of-unitaries (LCU) framework. In this work, we make this connection explicit through…
In this work we examine the impact of our motion with respect to the CMB rest frame on statistics of CMB maps by examining the one-, two-, three- and four- point statistics of simulated maps of the CMB and Sunyaev-Zeldovich (SZ) effects. We…
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure.…
The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…
State-of-the art neutron spectrometers enable simultaneous measurements of high-dimensional datasets, allowing for a large collection rate of dynamic material properties. In this paper, we present the Algorithm for Multiplexing spectrometer…
This work analyzes centered binary Restricted Boltzmann Machines (RBMs) and binary Deep Boltzmann Machines (DBMs), where centering is done by subtracting offset values from visible and hidden variables. We show analytically that (i)…
The success of many computer vision tasks lies in the ability to exploit the interdependency between different image modalities such as intensity and depth. Fusing corresponding information can be achieved on several levels, and one…
Sparse representation systems that encode signal architecture have had a profound impact on sampling and compression paradigms. Remarkable examples are multi-scale directional systems, which, similar to our vision system, encode the…
Recently the general linear transformation for point rotation coordinate frames was considered. A distinguishing feature of the frame, in contrast to the Cartesian one, is the existence of the rotation axis at every point. The frame…
Constructing effective representations is a critical but challenging problem in multimedia understanding. The traditional handcraft features often rely on domain knowledge, limiting the performances of exiting methods. This paper discusses…
This thesis develops a general theoretical and numerical framework for achieving high-contrast atom interferometry based on double Bragg diffraction (DBD). While DBD offers intrinsic symmetry, reduced sensitivity to internal-state…
Doppler effect is a fundamental phenomenon that appears in wave propagation, where a moving observer experiences dilation or contraction of wavelength of a wave. It also appears in radio frequency (RF) wireless communication when there…