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K-frames, a new generalization of frames, were recently considered by L. Gavruta in connection with atomic systems and some problems arising in sampling theory. Also, fusion frames are an important generalization of frames, applied in a…

Functional Analysis · Mathematics 2017-05-02 Fahimeh Arabyani Neyshaburi , Ali Akbar Arefijamaal

In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data…

Medical Physics · Physics 2015-03-24 Vivek Athalye , Michael Lustig , Martin Uecker

Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…

Computational Geometry · Computer Science 2011-03-15 Sarang Joshi , Raj Varma Kommaraju , Jeff M. Phillips , Suresh Venkatasubramanian

Starting from the density-matrix equation of motion, we derive a semiclassical kinetic equation for a general two-band electronic Hamiltonian, systematically including quantum-mechanical corrections up to second order in space-time…

Mesoscale and Nanoscale Physics · Physics 2013-11-27 Clement H. Wong , Yaroslav Tserkovnyak

In this paper, we study the full asymptotic expansion of the partition functions of determinantal point processes defined on a polarized K\"ahler manifold. We show that the coefficients of the expansion are given by geometric functionals on…

Differential Geometry · Mathematics 2026-01-01 Kiyoon Eum

Streamflow, as a natural phenomenon, is continuous in time and so are the meteorological variables which influence its variability. In practice, it can be of interest to forecast the whole flow curve instead of points (daily or hourly). To…

Applications · Statistics 2016-10-20 Pierre Masselot , Sophie Dabo-Niang , Fateh Chebana , Taha B. M. J. Ouarda

Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…

Statistics Theory · Mathematics 2021-05-28 George Wynne , Stanislav Nagy

With an extremely high dimensionality, the spatial degree of freedom of entangled photons is a key tool for quantum foundation and applied quantum techniques. To fully utilize the feature, the essential task is to experimentally…

Motivated by the abundance of functional data such as time series and images, there has been a growing interest in integrating such data into neural networks and learning maps from function spaces to R (i.e., functionals). In this paper, we…

Machine Learning · Statistics 2024-03-20 Tian-Yi Zhou , Namjoon Suh , Guang Cheng , Xiaoming Huo

Micrograph quantification is an essential component of several materials science studies. Machine learning methods, in particular convolutional neural networks, have previously demonstrated performance in image recognition tasks across…

Applied Physics · Physics 2019-06-14 Elizabeth Kautz , Wufei Ma , Saumyadeep Jana , Arun Devaraj , Vineet Joshi , Bülent Yener , Daniel Lewis

Numerous powerful point process models have been developed to understand temporal patterns in sequential data from fields such as health-care, electronic commerce, social networks, and natural disaster forecasting. In this paper, we develop…

Computer Vision and Pattern Recognition · Computer Science 2018-08-15 Yatao Zhong , Bicheng Xu , Guang-Tong Zhou , Luke Bornn , Greg Mori

A novel representation is developed as a measure for multilinear fractional embedding. Corresponding extensions are given for the Bourgain-Brezis-Mironescu theorem and Pitt's inequality. New results are obtained for diagonal trace…

Analysis of PDEs · Mathematics 2014-06-06 William Beckner

This paper extends the recently developed framework of multilinear kernel regression and imputation via manifold learning (MultiL-KRIM) to impute time-varying edge flows in a graph. MultiL-KRIM uses simplicial-complex arguments and Hodge…

Machine Learning · Computer Science 2024-09-10 Duc Thien Nguyen , Konstantinos Slavakis , Dimitris Pados

We prove a finite-dimensional moment map property for certain canonical relatively K\"ahler metrics on holomorphic fibrations, called optimal symplectic connections. We then relate the existence of zeroes of this moment map to the stability…

Differential Geometry · Mathematics 2025-07-17 Annamaria Ortu

In statistical learning, identifying underlying structures of true target functions based on observed data plays a crucial role to facilitate subsequent modeling and analysis. Unlike most of those existing methods that focus on some…

Machine Learning · Statistics 2021-05-04 Xin He , Yeheng Ge , Xingdong Feng

Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an…

Mathematical Finance · Quantitative Finance 2014-04-22 A. Kushpel , J. Levesley

Advancing human induced pluripotent stem cell derived cardiomyocyte (hiPSC-CM) technology will lead to significant progress ranging from disease modeling, to drug discovery, to regenerative tissue engineering. Yet, alongside these potential…

Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…

Numerical Analysis · Mathematics 2025-11-11 Jianyu Hu , Juan-Pablo Ortega , Daiying Yin

We find necessary and sufficient conditions for a finite $K$-bi-invariant measure on a compact Gelfand pair $(G, K)$ to have a square-integrable density. For convolution semigroups, this is equivalent to having a continuous density in…

Probability · Mathematics 2017-06-05 David Applebaum , Trang Le Ngan

Research is taking place to find effective algorithms for content-based image representation and description. There is a substantial amount of algorithms available that use visual features (color, shape, texture). Shape feature has…

Computer Vision and Pattern Recognition · Computer Science 2012-03-23 Tranos Zuva , Oludayo O. Olugbara , Sunday O. Ojo , Seleman M. Ngwira