Кратномасштабний аналіз дискретних функцій із заданою кількістю фільтрів

The method of discrete wavelet transforms at oriented basis that is constructed by use discrete spectral transform of the functions with modular argument is considered and generalized. Unlike traditional wavelet transforms (like classical Haar’s wavelet) this mathematical approach allows getting more information about the details and behavior of original signal due to more amount of discrete filters that are used for its decomposition. In Haar’s and other wavelet methods there are only two discrete filters are used to decompose initial signal – one low-frequency filter and one high-frequency filter. Low-frequency wavelet coefficients (marked as s-coefficients) give the compressed and approximated version of the initial signal (called trend), and high-frequency wavelet coefficients (marked as d-coefficients) give the high-frequency oscillations around the trend. Such decomposition and calculation of wavelet coefficients is realized at each level of wavelet analysis. While using wavelet transform at oriented basis, there are more than one type of high-frequency wavelet coefficients (marked as d(1)-, d(2)-,…, d(m)-coefficients) where m is defined by the type of spectral transform at oriented basis (dimension of the matrix of basic function). Number of decomposition levels is defined by the length of initial signal’s interval. In the case of Haar’s wavelet transform this length is determined as N=2n, and in the case of wavelet transform at oriented basis this length is determined as N=mn. While selecting the value m equal to three it gives some advantages in calculation volume and consequently, in the speed of wavelet analysis that could be very useful for the processing of the signals with large interval of definition and non-stationery signals. As an interesting example, time dependence of discrete function that describes electrical energy consumption in MicroGrid system could be considered as an object for compressing and removing of casual high-frequency oscillations with the help of wavelet analysis. The use of wavelet transforms with more than two high-frequency filters makes it possible to increase the quantity of data about signal fluctuations and to better localize its characteristic intervals compared with traditional discrete wavelets that operates with one low-frequency and one high-frequency filters. The principle of wavelet transform is based on a multiscale analysis. Basic functions are scaled and shifted along the time axis and by amplitude. A feature of the represented wavelet transform is the using of basic functions of new spectral transforms. These are functions of a symmetric transform on finite intervals and transform at oriented basis. The system of these functions is orthogonal and contains Np discrete functions of different shapes. One of these functions is a low-pass filter, and all the others are high-pass filters. Sphere of application of wavelet transforms with N basic functions is diagnostics of semiconductor converters, predictive energy-efficient control of energy consumption, analysis of bio-telemetric signals, processing and transmission of images and video signals.Ref. 7, fig. 1, tabl. 3.Рассмотрен и обобщен алгоритм построения вейвлет-преобразований на базе функций модульного аргумента, определенных на конечных интервалах. Использование предложенных вейвлет-преобразований с произвольным количеством высокочастотных фильтров позволяет увеличить объем данных о флуктуациях сигнала и лучше локализировать его характерные участки. Показаны сферы применения новых методов вейвлет-преобразований с N базисными функциями (диагностика полупроводниковых преобразователей, анализ, обработка, прогнозирование и передача сигналов) и преимущества в сравнении с традиционными.Библ. 7, рис. 1, табл. 3.Розглянуто та узагальнено алгоритм побудови вейвлет-перетворень на базі функцій модульного аргументу, визначених на кінцевих інтервалах. Використання запропонованих вейвлет-перетворень з довільною кількістю високочастотних фільтрів дозволяє збільшити об’єм даних про флуктуації сигналу та краще локалізувати його характерні ділянки. Показано сфери застосування нових методів вейвлет-перетворень з N базисними функціями (діагностика напівпровідникових перетворювачів, аналіз, обробка, прогнозування та передавання сигналів) та переваги в порівнянні з традиційними.Бібл. 7 , рис. 1, табл. 3

Discrimination between Complete versus Non-Complete Pathologic Response to Neoadjuvant Therapy Using Ultrasensitive Mutation Analysis: A Proof-of-Concept Study in <i>BRCA1</i>-Driven Breast Cancer Patients

Neoadjuvant chemotherapy (NACT) for breast cancer (BC) often results in pathologic complete response (pCR), i.e., the complete elimination of visible cancer cells. It is unclear whether the use of ultrasensitive genetic methods may still detect residual BC cells in complete responders. Breast carcinomas arising in BRCA1 mutation carriers almost always carry alterations of the TP53 gene thus providing an opportunity to address this question. The analysis of consecutive BC patients treated by NACT revealed a higher pCR rate in BRCA1-driven vs. BRCA1-wildtype BCs (13/24 (54%) vs. 29/192 (15%), p BRCA1 mutation carriers were available for the study. While TP53 mutation was identified in all chemonaive tumors, droplet digital PCR (ddPCR) analysis of the post-NACT tumor bed revealed the persistence of this alteration in all seven pCR-non-responders but in none of five pCR responders. Eleven patients provided to the study post-NACT tissue samples only; next-generation sequencing (NGS) analysis revealed mutated TP53 copies in all six cases without pCR but in none of five instances of pCR. In total, TP53 mutation was present in post-NACT tissues in all 13 cases without pCR, but in none of 10 patients with pCR (p < 0.000001). Therefore, the lack of visible tumor cells in the post-NACT tumor bed is indeed a reliable indicator of the complete elimination of transformed clones. Failure of ultrasensitive methods to identify patients with minimal residual disease among pCR responders suggests that the result of NACT is a categorical rather than continuous variable, where some patients are destined to be cured while others ultimately fail to experience tumor eradication

Effects of once-weekly exenatide on cardiovascular outcomes in type 2 diabetes

BACKGROUND: The cardiovascular effects of adding once-weekly treatment with exenatide to usual care in patients with type 2 diabetes are unknown. METHODS: We randomly assigned patients with type 2 diabetes, with or without previous cardiovascular disease, to receive subcutaneous injections of extended-release exenatide at a dose of 2 mg or matching placebo once weekly. The primary composite outcome was the first occurrence of death from cardiovascular causes, nonfatal myocardial infarction, or nonfatal stroke. The coprimary hypotheses were that exenatide, administered once weekly, would be noninferior to placebo with respect to safety and superior to placebo with respect to efficacy. RESULTS: In all, 14,752 patients (of whom 10,782 [73.1%] had previous cardiovascular disease) were followed for a median of 3.2 years (interquartile range, 2.2 to 4.4). A primary composite outcome event occurred in 839 of 7356 patients (11.4%; 3.7 events per 100 person-years) in the exenatide group and in 905 of 7396 patients (12.2%; 4.0 events per 100 person-years) in the placebo group (hazard ratio, 0.91; 95% confidence interval [CI], 0.83 to 1.00), with the intention-to-treat analysis indicating that exenatide, administered once weekly, was noninferior to placebo with respect to safety (P<0.001 for noninferiority) but was not superior to placebo with respect to efficacy (P=0.06 for superiority). The rates of death from cardiovascular causes, fatal or nonfatal myocardial infarction, fatal or nonfatal stroke, hospitalization for heart failure, and hospitalization for acute coronary syndrome, and the incidence of acute pancreatitis, pancreatic cancer, medullary thyroid carcinoma, and serious adverse events did not differ significantly between the two groups. CONCLUSIONS: Among patients with type 2 diabetes with or without previous cardiovascular disease, the incidence of major adverse cardiovascular events did not differ significantly between patients who received exenatide and those who received placebo