Algorithms for Linearly Recurrent Sequences of Truncated Polynomials

Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements are vectors over the ring A = K[x]/ of truncated polynomials. Finding the ideal of their recurrence relations has applications such as the computation of minimal polynomials and determinants of sparse matrices over A. We present three methods for finding this ideal: a Berlekamp-Massey-like approach due to Kurakin, one which computes the kernel of some block-Hankel matrix over A via a minimal approximant basis, and one based on bivariate Pade approximation. We propose complexity improvements for the first two methods, respectively by avoiding the computation of redundant relations and by exploiting the Hankel structure to compress the approximation problem. Then we confirm these improvements empirically through a C++ implementation, and we discuss the above-mentioned applications

Change of basis for m-primary ideals in one and two variables

Following recent work by van der Hoeven and Lecerf (ISSAC 2017), we discuss the complexity of linear mappings, called untangling and tangling by those authors, that arise in the context of computations with univariate polynomials. We give a slightly faster tangling algorithm and discuss new applications of these techniques. We show how to extend these ideas to bivariate settings, and use them to give bounds on the arithmetic complexity of certain algebras.Comment: In Proceedings ISSAC'19, ACM, New York, USA. See proceedings version for final formattin

Prediction of severe accident occurrence time using support vector machines

AbstractIf a transient occurs in a nuclear power plant (NPP), operators will try to protect the NPP by estimating the kind of abnormality and mitigating it based on recommended procedures. Similarly, operators take actions based on severe accident management guidelines when there is the possibility of a severe accident occurrence in an NPP. In any such situation, information about the occurrence time of severe accident-related events can be very important to operators to set up severe accident management strategies. Therefore, support systems that can quickly provide this kind of information will be very useful when operators try to manage severe accidents. In this research, the occurrence times of several events that could happen during a severe accident were predicted using support vector machines with short time variations of plant status variables inputs. For the preliminary step, the break location and size of a loss of coolant accident (LOCA) were identified. Training and testing data sets were obtained using the MAAP5 code. The results show that the proposed algorithm can correctly classify the break location of the LOCA and can estimate the break size of the LOCA very accurately. In addition, the occurrence times of severe accident major events were predicted under various severe accident paths, with reasonable error. With these results, it is expected that it will be possible to apply the proposed algorithm to real NPPs because the algorithm uses only the early phase data after the reactor SCRAM, which can be obtained accurately for accident simulations

A Novel Magnetic Resonance Quality Assurance Phantom (KMRP-4): Multi-Site Comparison With the American College of Radiology Phantom

Purpose: To propose a novel standard magnetic resonance imaging (MRI) phantom, hereafter called the Korea Magnetic Resonance Phantom-4th edition (KMRP-4). Its related quality control (QC) assessment protocols and its comparison with the American College of Radiology (ACR) phantom and its QC assessment protocols. / Materials and Methods: Internally, the KMRP-4 phantom is composed of cubic and triangular vessels, brain tissue structures, and a uniform region designed to facilitate a variety of QC protocols. Using magnetic resonance (MR) images of these structures, we quantitatively evaluated a total of 10 parameters, seven from those of existing ACR protocols (i.e., geometric accuracy, high-contrast spatial resolution, slice thickness accuracy, slice position accuracy, image intensity uniformity, percent signal ghosting, and low-contrast object detectability) and three additional parameters for evaluating vessel conspicuity, brain tissue contrast, and signal-to-noise ratio (SNR) introduced in the KMRP-4 protocols. Twentyt-wo MRI systems of 0.32–3.0 T static magnetic field strength were tested using both ACR and KMRP-4 phantoms. Mann–Whitney U-tests were performed on the seven evaluation items of the ACR method to compare KMRP-4 and ACR methods. / Results: The results of Mann–Whitney U-test demonstrated that p-values were more than 0.05 for all seven items that could be assessed with both ACR and KMRP-4, indicating similar results between the two methods. Additionally, assessments of vessel conspicuity, brain tissue contrast, and SNR using the KMRP-4 method demonstrated utility of the KMRP-4 phantom. / Conclusion: A novel standard phantom and related QC methods were developed to perform objective, observer-independent, and semi-automatic QC tests. Quantitative comparisons of MR images with KMPR-4 and ACR phantoms were performed. Results demonstrated the utility of the newly proposed KMRP-4 phantom and its related QC methods

Observation of First-Order Metal-Insulator Transition without Structural Phase Transition in VO_2

An abrupt first-order metal-insulator transition (MIT) without structural phase transition is first observed by current-voltage measurements and micro-Raman scattering experiments, when a DC electric field is applied to a Mott insulator VO_2 based two-terminal device. An abrupt current jump is measured at a critical electric field. The Raman-shift frequency and the bandwidth of the most predominant Raman-active A_g mode, excited by the electric field, do not change through the abrupt MIT, while, they, excited by temperature, pronouncedly soften and damp (structural MIT), respectively. This structural MIT is found to occur secondarily.Comment: 4 pages, 4 figure