Modern regularization techniques for inverse modelling: a comparative study

Regularization techniques are used for computing stable solutions to ill-posed problems. The well-known form of regularization is that of Tikhonov in which the regularized solution is searched as a minimiser of the weighted combination of the residual norm and a side constraint-controlled by the regularization parameter. For the practical choice of regularization parameter we can use the L-curve approach, U-curve criterion introduced by us [1] and empirical risk method [2]. We present a comparative study of different strategies for the regularization parameter choice on examples of function approximation by radial basis neural networks. Such networks are universal approximators and can learn any nonlinear mapping. e.g. representing an magnetic inverse problem. Some integral equations of the first kind are considered as well

The importance of preoperative elevated serum levels of CEA and CA15-3 in patients with breast cancer in predicting its histological type.

It is not known whether in patients with breast cancer the occurrence of elevated serum tumour markers depends on its histological type. The aim of the study was to assess relationship between breast cancer histological type and the presence of increased serum levels of CEA and CA 15-3. The study population was 428 patients (all women, mean age 52.5 years), treated at The Department of Surgery of Wroclaw Medical University from 2005 to 2008 due to breast cancer. All of them had their preoperative CA 15-3 and CEA serum concentrations measured. According to the TNM system, 21% of patients were in stage I, 32.5% in stage II, 46.5% in stage III of the disease. In patients with ductal type of the cancer the elevated serum levels of CEA and CA 15-3 were observed in 48.7% and 42.2%, in lobular type in 42.4% and 52.5%, and in non-ductal/tubular types in 48.1% and 40.4% (p=N/S). Stepwise logistic regression analyses showed that ductal breast cancer is related to elevated CEA and normal CA 15-3 serum levels. The histological types of breast cancer are not significantly related to elevated serum levels of CEA and/or CA 15-3

Prognostic value of CA 19-9 level in resectable pancreatic adenocarcinoma.

The prognosis in patients with pancreatic cancer is poor and some authors describe it as a lethal disease. At the time of diagnosis only 14% of patients could be surgically treated and up to 30% of them die within 12 months. Therefore, further clinical investigations on preoperative patient qualification are needed. A total of 81 patients were included into the study. The CA 19-9 concentration was measured before surgery by an automated, commercially available enzyme immunoassay in Axsym analyzer (Abott Diagnostics Laboratory). A value of 37 U/ml was used as the upper limit of normal levels. Tumors were staged according to the Union Against Cancer (UICC) of 2004 and graded during the histological evaluation according to the G0-G4 scale. All patients were monitored every three month via outpatient clinic visits. In the case of missing visit we contacted the families to establish the cause. We assessed perioperative, 12 month, 2 year and 5 year survival. Twelve moth, 2 year and 5 year survival were assessed in the whole studied population and in the group of patients with the exception of these who died during the perioperative period. The total five year survival was 6%. The median time of survival was 467 days (range: 163 - 586 days). The perioperative period was survived by 91.4% patients, 12 months were survived by 71.6% patients, 2 years were survived by 35.8% patients, 5 years were survived by 6.2% patients. The serum Ca 19-9 level was above the normal limit in 80.5% patients. ROC curve analysis revealed that CA 19-9 level of more than 106 U/ml was linked to 2 year survival with 79.3% sensitivity and 74.5% specificity. Preoperative level of CA 19-9 below 106U/ml represents a predictive factor of 2- and 5-year survival, independent of other factors, such as lower size of the tumor, absence of metastases to lymph nodes, female gender of patients. After exclusion of the patients who died in the perioperative period, no relationship could have been disclosed between preoperative CA 19-9 levels and one year survival. The observation points to the chance that patients with higher levels of CA 19-9 harbour micrometastases, the development of which is sufficiently slow to allow for a one-year survival of the patients but which increase the risk of death after two and five years

Optimization and inverse problems in electromagnetism

From 12 to 14 September 2002, the Academy of Humanities and Economics (AHE) hosted the workshop "Optimization and Inverse Problems in Electromagnetism". After this bi-annual event, a large number of papers were assembled and combined in this book. During the workshop recent developments and applications in optimization and inverse methodologies for electromagnetic fields were discussed. The contributions selected for the present volume cover a wide spectrum of inverse and optimal electromagnetic methodologies, ranging from theoretical to practical applications. A number of new optimal and inverse methodologies were proposed. There are contributions related to dedicated software. Optimization and Inverse Problems in Electromagnetism consists of three thematic chapters, covering: -General papers (survey of specific aspects of optimization and inverse problems in electromagnetism), -Methodologies, -Industrial Applications. The book can be useful to students of electrical and electronics engineering, computer science, applied mathematics (PhD level) and to researchers interested in the topic

REGULARIZATION PARAMETER SELECTION IN DISCRETE ILL–POSED PROBLEMS — THE USE OF THE U–CURVE

To obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This paper proposes a new criterion for choosing the regularization parameter α, based on the so-called U-curve. A comparison of the two methods made on numerical examples is additionally included. Keywords: ill-posed problems, Tikhonov regularization, regularization parameter, L-curve, U-curve 1

Salivary catecholamines in examinational stress and cognitive effort

By ustalić przydatność katecholamin w ślinie do badania stresu, pobrano próbki od 30 studentów przed egzaminem oraz w dniu pozbawionym stresorów. Następnie aby zbadać wpływ wysiłku poznawczego na poziomy katecholamin, przebadano 31 ochotników, którzy uczestniczyli w dwóch spotkaniach poświęconych realizacji różnych testów poznawczych. Za pomocą HPLC-ED zmierzono poziomy noradrenaliny, dopaminy i adrenaliny w ślinie. W grupie przed egzaminem zaobserwowano wyłącznie obniżony poziom dopaminy w porównaniu do dnia nieobciążonego stresorami. W drugiej grupie wysiłek poznawczy wywołał podwyższenie poziomów wszystkich trzech katecholamin. Zważywszy na niejednoznaczne wyniki z dotychczasowych badań wydaje się, iż adrenalina i noradrenalina w ślinie mogą być stosowane jako markery aktywności współczulnej w badaniach psychologicznych.In order to determine utility of salivary catecholamines in stress studies, samples were collected from 30 students before an exam and on an ordinary day. Subsequently, to examine the effect of cognitive effort on catecholamines, 31 volunteers, on two days, performed two sets of different cognitive tasks. Noradrenaline, adrenaline and dopamine levels were examined with HPLC-ED. Stressed group shown alleviated levels of dopamine, while levels of other substances remained unchanged. In the second group cognitive effort elicited elevated excretion of all three catecholamines. Given conflicting results from previous literature it appears that salivary adrenaline and noradrenaline might be useful as non-invasive markers of sympathetic activity in psychological research