Related papers: Non-Haar MRA on local fields of positive character…
We propose a method to construct Riesz MRA on local fields of positive characteristic and corresponding scaling step functions that generate it.
We present a new method for constructing an orthogonal step scaling function on local fields of positive characteristic, which generates multiresolution analysis.
A permanent magnet array (PMA) is a preferred source of magnetic field for body-part-dedicated low-field (<0.5 T) portable magnetic resonance imaging (MRI) because it has a small footprint, no power consumption, and no need for a cooling…
For each positive prime integer $p$ we construct a standard graded $F$-rational ring $R$, over a field $K$ of characteristic $p$, such that $R\otimes_K\overline{K}$ is not $F$-rational. By localizing we obtain a flat local homomorphism $(R,…
Many data-driven approaches exist to extract neural representations of functional magnetic resonance imaging (fMRI) data, but most of them lack a proper probabilistic formulation. We propose a group level scalable probabilistic sparse…
Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…
In this paper, the notion of {\em $p$-adic multiresolution analysis (MRA)} is introduced. We use a ``natural'' refinement equation whose solution (a refinable function) is the characteristic function of the unit disc. This equation reflects…
The concept of $p$-adic quincunx Haar MRA was introduced and studied in~\cite{KS10}. In contrast to the real setting, infinitely many different wavelet bases are generated by a $p$-adic MRA. We give an explicit description for all wavelet…
We propose a new method for constructing rational spatial Pythagorean Hodograph (PH) curves based on determining a suitable rational framing motion. While the spherical component of the framing motion is arbitrary, the translation part is…
We show that the double asymptotic scaling of the HERA structure function data is consistent with pre-HERA data at larger $x$, soft pomeron behaviour at small $x$ and a sensible starting scale $Q_0$. We can thus actually calculate $F_2^p$…
We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the…
Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
Multiresolution analysis (MRA) on compact abelian group $G$ has been constructed with epimorphism as a dilation operator. We show a characterization of scaling sequences of an MRA on $L^p(G)$, $1\le p<\infty$. With the help of this scaling…
We use the techniques developed in [1] to study the local average of random fields with spectral density $1/f^{\alpha}$. We study their scaling properties and show that the self-similarity of $1/f$ random fields is preserved under the local…
We demonstrate a convenient approach for simultaneously manipulating the amplitude and polarization of light beams by means of the modulation of the correlation structure. As an illustration, we constructed a periodic correlation structure…
Numerous algorithms are used for nonnegative matrix factorization under the assumption that the matrix is nearly separable. In this paper, we show how to make these algorithms efficient for data matrices that have many more rows than…
In tree based adaptive mesh refinement, elements are partitioned between processes using a space filling curve. The curve establishes an ordering between all elements that derive from the same root element, the tree. When representing more…
We consider a class of $(1,M)$-elementary step functions on the $p$-adic Vilenkin group. We prove that $(1,M)$-elementary step function generates a MRA on $p$-adic Vilenkin group iff it is generated by a rooted tree on the set of vertices…
The Highly Adaptive Lasso (HAL) is a nonparametric regression method that achieves almost dimension-free convergence rates under minimal smoothness assumptions, but its implementation can be computationally prohibitive in high dimensions…