This paper proposes a fast algorithm, called the SpiralFFT, that computes samples of the 3-D discrete Fourier transform of an object of interest along spiral contours in frequency space. This type of sampling geometry is prevalent in 3-D magnetic resonance imaging, as spiral sampling patterns allow for rapid, uninterrupted scanning over a large range of frequencies. We show that parameterizing ...

Given a normal proper and geometrically connected curve C over the function field K(S) of S, we seek “good” models over S. For instance, if we choose a projective embedding of C into some PK(S) then its Zariski closure in PS is an arithmetic surface (where the S-flatness uses that S is Dedekind). Hence, we can always find an arithmetic surface with generic fiber C. Since S is normal and C is re...

For [contemporary] social anthropologists, the important conclusion, always worth repeating, is that the observation and the labelling of 'behaviour' are inseparable from the importation of socially derived meanings even when observing monkeys. How much more so when the process is reflexive, when the observers and the observed are both 'meaning-makers' ... Edwin Ardener, 1977: Comprehending Oth...

The classical Kummer construction attaches to an abelian surface a K3 surface. As Shioda and Katsura showed, this construction breaks down for supersingular abelian surfaces in characteristic two. Replacing supersingular abelian surfaces by the selfproduct of the rational cuspidal curve, and the sign involution by suitable infinitesimal group scheme actions, I give the correct Kummer-type const...

In America’s visually-oriented, quantitatively illiterate culture, images have a great deal of power, so if a picture is today worth a thousand words, it must be worth a least a billion numbers. This power of the image is a hallmark of the postmodern era, in which the critical role of the observer has come to be recognized, and an understanding of the viewpoint has become inseparable from that ...

The attention mechanism plays a pivotal role in designing advanced super-resolution (SR) networks. In this work, we design an efficient SR network by improving the mechanism. We start from simple pixel module and gradually modify it to achieve better performance with reduced parameters. specific approaches include: (1) increasing receptive field of branch, (2) replacing large dense convolution ...

Even linear operators on infinite-dimensional spaces can display interesting dynamical properties and yield important links among functional analysis, differential and global geometry and dynamical systems, with a wide range of applications. In particular, hypercyclicity is an essentially infinite-dimensional property, when iterations of the operator generate a dense subspace. A Fréchet space a...

In this note I am writing out some of the material from Paul Halmos, Hilbert Space Problem Book, on shift operators. The reason I’m doing this is because shift operators are standard objects in operator theory and every analyst should know their properties and their spectra. A reference to Problem n of Halmos is a reference to Problem n in this book. An orthonormal basis for a Hilbert space is ...

Deep learning (DL)-based object detection algorithms have gained impressive achievements in natural images and gradually matured recent years. However, compared with images, remote sensing are faced severe challenges due to the complex backgrounds difficult of small objects dense scenes. To address these problems, a novel one-stage model named MDCT is proposed based on multi-kernel dilated conv...

We investigate existence and permanence properties of invariant measures for abstract stochastic Cauchy problems of the form dU(t) = (AU(t) + f) dt+B dWH(t), t > 0, governed by the generator A of an asymptotically unstable C0-semigroup on a Banach space E. Here f ∈ E is fixed, WH is a cylindrical Brownian motion over a separable real Hilbert space H, and B : H → E is a bounded operator. We show...