Metric foundations of continuous transformations

Rapid on-site cytopathology evaluation (ROSE) has been considered an effective method to increase the diagnostic ability of endoscopic ultrasound-guided fine needle aspiration (EUS-FNA); however, ROSE is unavailable in most institutes worldwide due to the shortage of cytopathologists. To overcome this situation, we created an artificial intelligence (AI)-based system (the ROSE-AI system), which was trained with the augmented data to evaluate the slide images acquired by EUS-FNA. This study aimed to clarify the effects of such data-augmentation on establishing an effective ROSE-AI system by comparing the efficacy of various data-augmentation techniques. The ROSE-AI system was trained with increased data obtained by the various data-augmentation techniques, including geometric transformation, color space transformation, and kernel filtering. By performing five-fold cross-validation, we compared the efficacy of each data-augmentation technique on the increasing diagnostic abilities of the ROSE-AI system. We collected 4059 divided EUS-FNA slide images from 36 patients with pancreatic cancer and nine patients with non-pancreatic cancer. The diagnostic ability of the ROSE-AI system without data augmentation had a sensitivity, specificity, and accuracy of 87.5%, 79.7%, and 83.7%, respectively. While, some data-augmentation techniques decreased diagnostic ability, the ROSE-AI system trained only with the augmented data using the geometric transformation technique had the highest diagnostic accuracy (88.2%). We successfully developed a prototype ROSE-AI system with high diagnostic ability. Each data-augmentation technique may have various compatibilities with AI-mediated diagnostics, and the geometric transformation was the most effective for the ROSE-AI system.

This paper proposes a method for solving fractional partial difference equations using discrete Sumudu transformation. Some properties of discrete Sumudu transformation were used. The applications of the test examples for the initial value problems of fractional partial difference equations were tested using two methods: the successive approximation method. The second, homotopy perturbation, was proven efficient with the proposed method.

It is sometimes necessary to determine the optimal value for a direction dependent quantity. Using a search technique based on Powell's quadratic convergent method such an optimal direction can be approximated. The necessary geometric transformations in n-dimensional space are introduced. As an example we consider the approximation of the minimum bounding box of a set of three-dimensional points. Minimum bounding boxes can significantly improve accuracy and efficiency of the calculations in modern brachytherapy treatment planning of the volumes of objects or the dose distribution inside an object. A covariance matrix based approximation method for the minimum bounding box is compared with the results of the search method. The benefits of the use of optimal oriented bounding boxes in brachytherapy treatment planning systems are demonstrated and discussed.

MGAug: Multimodal Geometric Augmentation in Latent Spaces of Image Deformations.

This paper presents a novel predictive model, MetaMorph, for metamorphic registration of images with appearance changes (i.e., caused by brain tumors). In contrast to previous learning-based registration methods that have little or no control over appearance-changes, our model introduces a new regularization that can effectively suppress the negative effects of appearance changing areas. In particular, we develop a piecewise regularization on the tangent space of diffeomorphic transformations (also known as initial velocity fields) via learned segmentation maps of abnormal regions. The geometric transformation and appearance changes are treated as joint tasks that are mutually beneficial. Our model MetaMorph is more robust and accurate when searching for an optimal registration solution under the guidance of segmentation, which in turn improves the segmentation performance by providing appropriately augmented training labels. We validate MetaMorph on real 3D human brain tumor magnetic resonance imaging (MRI) scans. Experimental results show that our model outperforms the state-of-the-art learning-based registration models. The proposed MetaMorph has great potential in various image-guided clinical interventions, e.g., real-time image-guided navigation systems for tumor removal surgery.

§1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually calledPolish spaces. Typical examples are ℝn, ℂn, (separable) Hilbert space and more generally all separable Banach spaces, theCantor space2ℕ, theBaire spaceℕℕ, the infinite symmetric groupS∞, the unitary group (of the Hilbert space), the group of measure preserving transformations of the unit interval, etc.In this theory sets are classified in hierarchies according to the complexity of their definitions and the structure of sets in each level of these hierarchies is systematically analyzed. In the beginning we have theBorelsets in Polish spaces, obtained by starting with the open sets and closing under the operations of complementation and countable unions, and the correspondingBorel hierarchy(sets). After this come theprojective sets, obtained by starting with the Borel sets and closing under the operations of complementation and projection, and the correspondingprojective hierarchy(sets).There are also transfinite extensions of the projective hierarchy and even much more complex definable sets studied in descriptive set theory, but I will restrict myself here to Borel and projective sets, in fact just those at the first level of the projective hierarchy, i.e., theBorel(),analytic() andcoanalytic() sets.

The extraction of remote sensing geological anomaly information is one of the important research methods in GARS.In this paper,taking Laos as an example and using such means as geometric rectification,image mosaicking,color composite,space transformation and image enhancement processing to the ETM+ image in the study area,the authors extracted the geological structural information.The interference information was removed by mask technique,and the iron staining and hydroxyl alteration information was extracted by using principal component analysis and threshold segmentation techniques.Five perspective areas for mineral exploration were delineated on the basis of a synthetic analysis of the multi-geoscience information.The results can provide a reference and effective means for accelerating the geological prospecting work in Laos.

On the maximum transform

Starting from the basic supersymmetry algebra of 2n-component Weyl spinors it is shown how this is enlarged to incorporate the discrete symmetries of parity and charge conjugation. The transformation properties of the superfield representations of the enlarged Dirac supersymmetry are found, and the particle content of a simple example examined.

A quantitative description of magnons in long-range ordered quantum antiferromagnets is presented which is consistent from low to high energies. It is illustrated for the generic S=1/2 Heisenberg model on the square lattice. The approach is based on a continuous similarity transformation in momentum space using the scaling dimension as the truncation criterion. Evidence is found for significant magnon-magnon attraction inducing a Higgs resonance. The high-energy roton minimum in the magnon dispersion appears to be induced by strong magnon-Higgs scattering.

Symmetrizable completely continuous linear transformations in Hilbert space

Discrete rigid registration: A local graph-search approach

Based on noncommutative relations and the Dirac canonical dequantization scheme, I generalize the canonical Poisson bracket to a deformed Poisson bracket and develop a non-canonical formulation of the Poisson, Hamilton, and Lagrange equations in the deformed Poisson and symplectic spaces. I find that both of these dynamical equations are the coupling systems of differential equations. The noncommutivity induces the velocity-dependent potential. These formulations give the Noether and Virial theorems in the deformed symplectic space. I find that the Lagrangian invariance and its corresponding conserved quantity depend on the deformed parameters and some points in the configuration space for a continuous infinitesimal coordinate transformation. These formulations provide a non-canonical framework of classical mechanics not only for insight into noncommutative quantum mechanics, but also for exploring some mysteries and phenomena beyond those in the canonical symplectic space.

In this paper, an integrated three-phase transformer is utilized in the partial parallel dual active bridge (PPDAB) converter. Due to the symmetrical structure, the flux generated by the primary windings is equally distributed to the three outer legs. Given the same number of turns of the windings in each parallel modules, the ac currents can inherently balance in the parallel modules. In order to enlarge the leakage inductor to serve as the interfacing ac inductor in the PPDAB converter, the coupling between the primary windings and secondary windings is weakened by placing the primary and secondary windings on the center and outer legs, respectively. Compared to the discrete three-phase transformers, the winding loss will also decrease with the proposed structure. A 1kW 400V/50V 500 kHz prototype with an efficiency of 96.72% is built and tested to verify the theoretical analysis.

In order to improve the performance of hyperspectral open set recognition processing with insufficient sample size, the authors propose a new supervised contrastive learning (SCL) framework (FSSCL‐OSC) that can achieve open‐set classification of hyperspectral images in scenarios with very few sample sizes, which consists of three steps. First, supervised contrastive learning (SCL) with geometric transformations is designed, which uses rotated labels as supervision to obtain lower‐level characteristics that more accurately capture various orientations and then makes use of a spectral‐spatial characteristic extraction network to maximize the utilization of HSI's spectrum and spatial information. Next, a class anchor open‐set classification module based on a twin clustering network is designed, which uses SCL and FSL to extract more specific personal information by mining the category‐invariant characteristics present in the known versus unknown class data. Finally, multiple convolution and open‐set recognition (OSC) is performed on the feature blocks. Experimental results on three classical HSI datasets show that FSSCL‐OSC provides a significant improvement over existing methods, under a sample size of only 10%, the overall accuracy reached 82.38%, 90.76% and 84.70%, respectively.