On generalized Cauchy and Pexider functional equations over a field

Let K be a commutative field and (P,+) be a uniquely 2-divisible group (not necessarily abelian). We characterize all functions T : K → P such that the Cauchy difference T(s+t) - T(t) - T(s) depends only on the product st for all s, t ∈ K. Further, we apply this result to describe solutions of the functional equation F(s+t) = K(st) ◦ H(s) ◦ G(t), where the unknown functions F, K, H, G map the field K into some function spaces arranged so that the compositions make sense. Conditions are established under which the equation can be reduced to a corresponding generalized Cauchy equation, and the general solution is given. Finally, we solve the equation F(s+t) = K(st) + H(s) + G(t) for functions F, K, H, G mapping K into P

Automatic tuning of a graph-based image segmentation method for digital mammography applications

Los Alamitos, C

Minimum spanning trees and active contours for identification of the pectoral muscle in screening mamograms

Danvers, US

Mammographic Mass Detection with Statistical Region Merging

An automatic method for detection of mammographic masses is presented which utilizes statistical region merging for segmentation (SRM) and linear discriminant analysis (LDA) for classification. The performance of the scheme was evaluated on 36 images selected from the local database of mammograms and on 48 images taken from the Digital Database for Screening Mammography (DDSM). The Az value (area under the ROC curve) for classifying each region was 0.90 for the local dataset and 0.96 for the images from DDSM. Results indicate that SRM segmentation can form part of an robust and efficient basis for analysis of mammograms

3D Segmentation for Multi-Organs in CT Images

The study addresses the challenging problem of automatic segmentation of the human anatomy needed for radiation dose calculations.Three-dimensional extensions of two well-known state-of-the art segmentation techniques are proposed and tested for usefulness on a set of clinical CT images.The new techniques are 3D Statistical Region Merging (3D-SRM) and 3D Efficient Graph-based Segmentation (3D-EGS). Segmentations of eight representative tissues (lungs, stomach, liver, heart, kidneys, spleen, bones and the spinal cord)were tested for accuracy using the Dice index, the Hausdorff distance and the $H_t$ index. The 3D-SRM outperformed 3D-EGS producing the average(across the 8 tissues) Dice index, the Hausdorff distance, and the $H_2$ of $0.89$, $12.5$~mm and $0.93$, respectively

On the composite Pexider equation modulo a subgroup

MATEMATIKAI INTEZET NAGYERDEIKORUT, DEBRECEN, HUNGARY, 1

Hvilke utfordringer ligger i behandlingen for dobbeltdiagnose-pasienter, og hvordan skal man legge til rette for en god behandling?

A method based on sublevel sets is presented for refining segmentation of screening mammograms. Initial segmentation is provided by an adaptive pyramid (AP) scheme which is viewed as seeding of the final segmentation by sublevel sets. Performance is tested with and without prior anisotropic smoothing and is compared to refinement based on component merging. The combination of anisotropic smoothing, AP segmentation and sublevel refinement is found to outperform other combinations

Mathematical model of endothelial cell proliferation and maturation

Angiogeneza jest jedna z cech charakterystycznych raka. Lepsze ilosciowe zrozumienie tego procesu pozwoliłoby na opracowanie skuteczniejszych terapii antyangiogennych. Postawiono hipoteze, ze nie tylko liczba komórek sródbłonka, ale takze jakosc układu naczyniowego, odgrywa wazna role w sposobie, w jaki chemio- iradioterapie sa dostarczane do guza. W zwiazku z tym rozwazamy minimalnie sparametryzowany matematyczny model proliferacji i dojrzewania komórek sródbłonka. Komórki sródbłonka dziela sie na dwa rodzaje - dojrzałe i niedojrzałe (lub proliferujace). Zakłada sie, ze komórki ulegaja samoistnemu dojrzewaniu, podczas gdy utracie jakosci naczyn krwionosnych posredniczy zewnetrzny czynnik wzrostu (tutaj VEGF). Rozwazany model został dopasowany do danych eksperymentalnych. Pokazuje on, w jaki sposób hamowanie VEGF prowadzi do lepszej jakosci układu naczyniowego i wolniejszej proliferacji.Blood vessel sprouting (angiogenesis) is one of the hallmarks of cancer. Better quantitative understanding of this process would allow more effective antiangiogenic therapies to be developed. It has been hypothesised that not only the number of endothelial cells, but also the quality of the vasculature play an important role in how chemo- and radiotherapies are delivered to tumour site. Hence in this study a minimally-parametrised mathematical model of endothelial cell proliferation and maturation is developed. Endothelial cells are subdivided into two compartments -- mature and immature (or proliferating). The cells are assumed to undergo a self-mediated maturation, while loss of blood vessel quality is mediated by an external growth factor (here VEGF). The model is fitted to experimental data. The model shows how inhibition of VEGF results in better quality vasculature and slower proliferation