Structured total least norm and approximate GCDs of inexact polynomials

The determination of an approximate greatest common divisor (GCD) of two inexact polynomials f=f(y) and g=g(y) arises in several applications, including signal processing and control. This approximate GCD can be obtained by computing a structured low rank approximation S*(f,g) of the Sylvester resultant matrix S(f,g). In this paper, the method of structured total least norm (STLN) is used to compute a low rank approximation of S(f,g), and it is shown that important issues that have a considerable effect on the approximate GCD have not been considered. For example, the established works only yield one matrix S*(f,g), and therefore one approximate GCD, but it is shown in this paper that a family of structured low rank approximations can be computed, each member of which yields a different approximate GCD. Examples that illustrate the importance of these and other issues are presented

A non-linear structure preserving matrix method for the low rank approximation of the Sylvester resultant matrix

A non-linear structure preserving matrix method for the computation of a structured low rank approximation S((f) over bar , (g) over bar) of the Sylvester resultant matrix S(f , g) of two inexact polynomials f = f(y) and g = g(y) is considered in this paper. It is shown that considerably improved results are obtained when f (y) and g(y) are processed prior to the computation of S((f) over bar , (g) over bar), and that these preprocessing operations introduce two parameters. These parameters can either be held constant during the computation of S((f) over bar , (g) over bar), which leads to a linear structure preserving matrix method, or they can be incremented during the computation of S((f) over bar, (g) over bar), which leads to a non-linear structure preserving matrix method. It is shown that the non-linear method yields a better structured low rank approximation of S((f) over bar , (g) over bar) and that the assignment of f (y) and g(y) is important because S((f) over bar , (g) over bar) may be a good structured low rank approximation of S(f, g), but S((f) over bar , (g) over bar) may be a poor structured low rank approximation of S (g f) because its numerical rank is not defined. Examples that illustrate the differences between the linear and non-linear structure preserving matrix methods, and the importance of the assignment off (y) and g(y), are shown. (C) 2010 Elsevier B.V. All rights reserved

Electrical vestibular stimulation in humans. A narrative review

Background: In patients with bilateral vestibulopathy, the regular treatment options, such as medication, surgery, and/ or vestibular rehabilitation, do not always suffice. Therefore, the focus in this field of vestibular research shifted to electri- cal vestibular stimulation (EVS) and the development of a system capable of artificially restoring the vestibular func- tion. Key Message: Currently, three approaches are being investigated: vestibular co-stimulation with a cochlear im- plant (CI), EVS with a vestibular implant (VI), and galvanic vestibular stimulation (GVS). All three applications show promising results but due to conceptual differences and the experimental state, a consensus on which application is the most ideal for which type of patient is still missing. Summa- ry: Vestibular co-stimulation with a CI is based on “spread of excitation,” which is a phenomenon that occurs when the currents from the CI spread to the surrounding structures and stimulate them. It has been shown that CI activation can indeed result in stimulation of the vestibular structures. Therefore, the question was raised whether vestibular co- stimulation can be functionally used in patients with bilat- eral vestibulopathy. A more direct vestibular stimulation method can be accomplished by implantation and activa- tion of a VI. The concept of the VI is based on the technology and principles of the CI. Different VI prototypes are currently being evaluated regarding feasibility and functionality. So far, all of them were capable of activating different types of vestibular reflexes. A third stimulation method is GVS, which requires the use of surface electrodes instead of an implant- ed electrode array. However, as the currents are sent through the skull from one mastoid to the other, GVS is rather unspe- cific. It should be mentioned though, that the reported spread of excitation in both CI and VI use also seems to in- duce a more unspecific stimulation. Although all three ap- plications of EVS were shown to be effective, it has yet to be defined which option is more desirable based on applicabil- ity and efficiency. It is possible and even likely that there is a place for all three approaches, given the diversity of the pa- tient population who serves to gain from such technologies

GPGCD: An iterative method for calculating approximate GCD of univariate polynomials

We present an iterative algorithm for calculating approximate greatest common divisor (GCD) of univariate polynomials with the real or the complex coefficients. For a given pair of polynomials and a degree, our algorithm finds a pair of polynomials which has a GCD of the given degree and whose coefficients are perturbed from those in the original inputs, making the perturbations as small as possible, along with the GCD. The problem of approximate GCD is transfered to a constrained minimization problem, then solved with the so-called modified Newton method, which is a generalization of the gradient-projection method, by searching the solution iteratively. We demonstrate that, in some test cases, our algorithm calculates approximate GCD with perturbations as small as those calculated by a method based on the structured total least norm (STLN) method and the UVGCD method, while our method runs significantly faster than theirs by approximately up to 30 or 10 times, respectively, compared with their implementation. We also show that our algorithm properly handles some ill-conditioned polynomials which have a GCD with small or large leading coefficient.Comment: Preliminary versions have been presented as doi:10.1145/1576702.1576750 and arXiv:1007.183

Dupuytren's disease in bosnia and herzegovina. An epidemiological study

BACKGROUND: It is generally held that Dupuytren's disease is more common in northern than in southern Europe, but there are very few studies from southern European countries. METHODS: We examined the hands of 1207 men and women over the age of 50 years in Bosnia and Herzegovina. RESULTS: The prevalence of Dupuytren's disease was highly age-dependent, ranging from 17% for men between 50–59 years to 60% in the oldest men. The prevalence among women was lower. The great majority only had palmar changes without contracture of the digit. The prevalence was significantly lower among Bosnian Muslim men than among Bosnian Croat and Serbian men and significantly increased among diabetics. No association could be detected between Dupuytren's disease and smoking, alcohol consumption or living in rural or urban areas. CONCLUSION: We conclude that, contrary to previous opinion, Dupuytren's disease is common in Bosnia and Herzegovina

Cochlear erosion due to a facial nerve schwannoma

Facial nerve schwannomas are rare benign neoplasms. We report a case of a 60-year-old woman who initially presented with vestibular complaints. Magnetic resonance imaging (MRI) revealed a facial nerve schwannoma centered on the right geniculate ganglion extending in the labyrinthine segment. The patient consulted again after 2 months because she developed a sudden and severe right-sided sensorineural hearing loss. MRI showed no progression or pathological enhancement in the membranous labyrinth. A cone beam computed tomography (CT) of the temporal bone was performed and revealed a large erosion at the region of the geniculate ganglion in open communication with the middle turn of the cochlea. This case report demonstrates the importance of CT in facial nerve schwannomas for evaluating the impact on the surrounding structures

The computation of the degree of an approximate greatest common divisor of two Bernstein polynomials

This paper considers the computation of the degree t of an approximate greatest common divisor d(y) of two Bernstein polynomials f(y) and g(y), which are of degrees m and n respectively. The value of t is computed from the QR decomposition of the Sylvester resultant matrix S(f, g) and its subresultant matrices Sk(f, g), k = 2, . . . , min(m, n), where S1(f, g) = S(f, g). It is shown that the computation of t is significantly more complicated than its equivalent for two power basis polynomials because (a) Sk(f, g) can be written in several forms that differ in the complexity of the computation of their entries, (b) different forms of Sk(f, g) may yield different values of t, and (c) the binomial terms in the entries of Sk(f, g) may cause the ratio of its entry of maximum magnitude to its entry of minimum magnitude to be large, which may lead to numerical problems. It is shown that the QR decomposition and singular value decomposition (SVD) of the Sylvester matrix and its subresultant matrices yield better results than the SVD of the B´ezout matrix, and that f(y) and g(y) must be processed before computations are performed on these resultant and subresultant matrices in order to obtain good results

Electrical vestibular stimulation in humans: a narrative review

Background: In patients with bilateral vestibulopathy, the regular treatment options, such as medication, surgery, and/ or vestibular rehabilitation, do not always suffice. Therefore, the focus in this field of vestibular research shifted to electrical vestibular stimulation (EVS) and the development of a system capable of artificially restoring the vestibular function. Key Message: Currently, three approaches are being investigated: vestibular co-stimulation with a cochlear implant (CI), EVS with a vestibular implant (VI), and galvanic vestibular stimulation (GVS). All three applications show promising results but due to conceptual differences and the experimental state, a consensus on which application is the most ideal for which type of patient is still missing. Summary: Vestibular co-stimulation with a CI is based on “spread of excitation,” which is a phenomenon that occurs when the currents from the CI spread to the surrounding structures and stimulate them. It has been shown that CI activation can indeed result in stimulation of the vestibular structures. Therefore, the question was raised whether vestibular costimulation can be functionally used in patients with bilateral vestibulopathy. A more direct vestibular stimulation method can be accomplished by implantation and activation of a VI. The concept of the VI is based on the technology and principles of the CI. Different VI prototypes are currently being evaluated regarding feasibility and functionality. So far, all of them were capable of activating different types of vestibular reflexes. A third stimulation method is GVS, which requires the use of surface electrodes instead of an implanted electrode array. However, as the currents are sent through the skull from one mastoid to the other, GVS is rather unspecific. It should be mentioned though, that the reported spread of excitation in both CI and VI use also seems to induce a more unspecific stimulation. Although all three applications of EVS were shown to be effective, it has yet to be defined which option is more desirable based on applicability and efficiency. It is possible and even likely that there is a place for all three approaches, given the diversity of the patient population who serves to gain from such technologies

Polynomial computations for blind image deconvolution

This paper considers the problem of blind image deconvolution (BID) when the blur arises from a spatially invariant point spread function (PSF) H, which implies that a blurred image G is formed by the convolution of H and the exact form F of G. Since the multiplication of two bivariate polynomials is performed by convolving their coefficient matrices, the equivalence of the formation of a blurred image and the product of two bivariate polynomials implies that BID can be performed by considering F, G and H to be bivariate polynomials on which polynomial operations are performed. These operations allow the PSF to be computed, which is then deconvolved from the blurred image G, thereby obtaining a deblurred image that is a good approximation of the exact image F. Computational results show that the deblurred image obtained using polynomial computations is better than the deblurred image obtained using other methods for blind image deconvolution

Magnetic resonance imaging in patients with meningitis induced hearing loss

The aim of this multicentre study was to compare T1 with T2 weighted MRI scans of the labyrinth after meningitis and to investigate whether waiting with scanning improved the reliability of diagnosing an ongoing process such as cochlear osteogenesis. Forty-five patients were included who suffered from meningitis induced hearing loss (radiological imaging <1 year after meningitis). Twenty-one gadolinium enhanced T1 and 45 T2 weighted MRI scans were scored by two radiologists regarding the condition of the labyrinth. These radiological observations were compared with the condition of the cochlea as described during cochlear implantation. A higher percentage of agreement with surgery was found for T2 (both radiologists 73%) than for T1 weighted MRI scans (radiologist 1: 62%, radiologist 2: 67%), but this difference is not significant. There was no significant difference between early (0–3 months) and late (>3 months) scanning, showing that radiological imaging soon after meningitis allows early diagnosis without suffering from a lower agreement with surgical findings