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In recent years, magnetic particle imaging (MPI) has emerged as a promising imaging technique depicting high sensitivity and spatial resolution. It originated in the early 2000s where it proposed a new approach to challenge the low spatial resolution achieved by using relaxometry in order to measure the magnetic fields. MPI presents 2D and 3D images with high temporal resolution, non‐ionizing radiation, and optimal visual contrast due to its lack of background tissue signal. Traditionally, the images were reconstructed by the conversion of signal from the induced voltage by generating system matrix and X‐space based methods. Because image reconstruction and analyses play an integral role in obtaining precise information from MPI signals, newer artificial intelligence‐based methods are continuously being researched and developed upon. In this work, we summarize and review the significance and employment of machine learning and deep learning models for applications with MPI and the potential they hold for the future. Level of Evidence5 Technical EfficacyStage 1 

The cone penetration test (CPT) is one of the most popular in situ soil characterization tools. However, the test is often difficult to conduct in soils with high penetration resistance. To resolve the problem, a rotary CPT device has recently been adopted in practice by rotating the rod to increase the penetrability, particularly in deep dense sand. This study investigates the underlying mechanism of the rotation effects from a micromechanical perspective using models based on the discrete element method. With rotation, the cone penetration resistance ( q_c) decreases by up to 50%, while the cone torque resistance ( t_c) increases gradually. These results are also used to successfully assess existing theoretical solutions. The mechanical work required during penetration is observed to keep rising as the rotational velocity increases. Microscopic variables including particle displacement and velocity field show that rotation reduces the volume of disturbed soil during penetration and drives particles to rotate horizontally, while contact force chain and contact fabric indicate that rotation increases the number of radial and tangential contacts and the corresponding contact forces, forming a lateral stable structure around the shaft, which can reduce the force transmitted to the particles below the cone, thus decreasing the vertical penetration resistance. 

Regularized learning problems in Banach spaces, which often minimize the sum of a data fidelity term in one Banach norm and a regularization term in another Banach norm, is challenging to solve. We construct a direct sum space based on the Banach spaces for the fidelity term and the regularization term and recast the objective function as the norm of a quotient space of the direct sum space. We then express the original regularized problem as an optimization problem in the dual space of the direct sum space. It is to find the maximum of a linear function on a convex polytope, which may be solved by linear programming. A solution of the original problem is then obtained by using related extremal properties of norming functionals from a solution of the dual problem. Numerical experiments demonstrate that the proposed duality approach is effective for solving the regularization learning problems. 

Sparsity of a learning solution is a desirable feature in machine learning. Certain reproducing kernel Banach spaces (RKBSs) are appropriate hypothesis spaces for sparse learning methods. The goal of this paper is to understand what kind of RKBSs can promote sparsity for learning solutions. We consider two typical learning models in an RKBS: the minimum norm interpolation (MNI) problem and the regularization problem. We first establish an explicit representer theorem for solutions of these problems, which represents the extreme points of the solution set by a linear combination of the extreme points of the subdifferential set, of the norm function, which is data-dependent. We then propose sufficient conditions on the RKBS that can transform the explicit representation of the solutions to a sparse kernel representation having fewer terms than the number of the observed data. Under the proposed sufficient conditions, we investigate the role of the regularization parameter on sparsity of the regularized solutions. We further show that two specific RKBSs, the sequence space l_1(N) and the measure space, can have sparse representer theorems for both MNI and regularization models.