The Linearly Independent Non Orthogonal yet Energy Preserving (LINOEP) vectors

It is well known that, in any inner product space, a set of linearly independent (LI) vectors can be transformed to a set of orthogonal vectors, spanning the same space, by the Gram-Schmidt Orthogonalization Method (GSOM). In this paper, we propose a transformation from a set of LI vectors to a set of LI non orthogonal yet energy (square of the norm) preserving (LINOEP) vectors in an inner product space and we refer it as LINOEP method. We also show that there are various solutions to preserve the square of the norm.Comment: 6 pages, 2 figure

Digital Filters Using Identical Blocks

Improved response of non-recursive digital filters is achieved using Amplitude Change Functions (ACFs) on a prototype filter. A generalized ACF with interesting properties is suggested. Methods for achieving variable cut-off frequency and frequency transformation are explained. A modular hardware implementation is also presented

Amplification of HER2 is a marker for global genomic instability

<p>Abstract</p> <p>Background</p> <p>Genomic alterations of the proto-oncogene c-erbB-2 (HER-2/neu) are associated with aggressive behavior and poor prognosis in patients with breast cancer. The variable clinical outcomes seen in patients with similar HER2 status, given similar treatments, suggests that the effects of amplification of HER2 can be influenced by other genetic changes. To assess the broader genomic implications of structural changes at the HER2 locus, we investigated relationships between genomic instability and HER2 status in patients with invasive breast cancer.</p> <p>Methods</p> <p>HER2 status was determined using the PathVysion^®assay. DNA was extracted after laser microdissection from the 181 paraffin-embedded HER2 amplified (n = 39) or HER2 negative (n = 142) tumor specimens with sufficient tumor available to perform molecular analysis. Allelic imbalance (AI) was assessed using a panel of microsatellite markers representing 26 chromosomal regions commonly altered in breast cancer. Student t-tests and partial correlations were used to investigate relationships between genomic instability and HER2 status.</p> <p>Results</p> <p>The frequency of AI was significantly higher (<it>P </it>< 0.005) in HER2 amplified (27%) compared to HER2 negative tumors (19%). Samples with HER2 amplification showed significantly higher levels of AI (<it>P </it>< 0.05) at chromosomes 11q23, 16q22-q24 and 18q21. Partial correlations including ER status and tumor grade supported associations between HER2 status and alterations at 11q13.1, 16q22-q24 and 18q21.</p> <p>Conclusion</p> <p>The poor prognosis associated with HER2 amplification may be attributed to global genomic instability as cells with high frequencies of chromosomal alterations have been associated with increased cellular proliferation and aggressive behavior. In addition, high levels of DNA damage may render tumor cells refractory to treatment. In addition, specific alterations at chromosomes 11q13, 16q22-q24, and 18q21, all of which have been associated with aggressive tumor behavior, may serve as genetic modifiers to HER2 amplification. These data not only improve our understanding of HER in breast pathogenesis but may allow more accurate risk profiles and better treatment options to be developed.</p

Poles of maximally flat sharp cutoff low-pass filters'

The poles of a recently discussed [2] maximally flat sharp-cutoff low-pass filter are tabulated for various orders of the filter and various values of the parameters. Loci of these poles are also sketched for some representative orders

Single-parameter controlled-variable amplitude change function for digital filtering

A single-parameter controlled-variable amplitude change function has been constructed for digital filtering using multiple units of a prototype filter. The limits of variation are discussed. The technique is shown to be useful not only for the reduction of errors in either the pass band or the stop band of the overall filter, but also for varying the cutoff frequency of the overall filter over a wide range. Hardware implementation problems resulting from a wide variation are shown to be overcome by a modular approach

New amplitude change functions for improving the filter response

A method is suggested for improving the response of a symmetric nonrecursive digital filter using several copies of that filter. This is based on shifting and/or scaling the amplitude change function (ACF). A new generalized ACF has been derived which has similar characteristics as that of the Kaiser-Hamming--Chebyshev ACF, but does not require additional correction filters for its implementation. Shifting and scaling of the new ACF are shown to result in further improvement of the response

Improving the response of a symmetric nonrecursive digital filter by multiple use of the same filter through ACF shifting/scaling

A method is suggested for improving the response of a symmetric nonrecursive digital filter using identical blocks. This is based on shifting and/ or scaling of the Amplitude Change Function (ACF). A new generalized ACF has been derived which has similar characteristics to that of the Kaiser-Hamming Chebyshev ACF but does not require additional correction filters for its implementation. Shifting and scaling of the new ACF are shown to result in further improvement of the response. A method is suggested for varying the cut-off frequency of a digital filter without modifying the coefficients of the prototype filter. This is achieved by interconnecting several copies of the prototype filter and adjusting a few gain factors. A modular hardware implementation scheme and its advantages are illustrated with the help of an example. The concept of ACF is also used for the frequency transformation of digital filters, viz transforming a lowpass filter into a high pass, bandpass or a bandstop filter. The method is extended to obtain variable cut-off and variable centre frequency bandpass/bandstop filters

Second order active RC filters with a single operational amplifier

The paper deals with economic realizations of second order active RC filters employing a single differential input operational amplifier as the active element. All the basic types of filters are considered and the sensitivities of Q arid undamped natural frequency with respect to various parameters are evaluated. Further, it is shown that one circuit configuration can lead to several types of filter realizations having the same Q simply by short circuiting or open circuiting certain elements, thereby reducing the manufacturing cost