Gibonacci Optimization : duality (Mathematical Decision Making Under Uncertainty and Related Topics)

We show that a parametric linear system of equations plays a fundamental part in establishing a mutual relation between minimization problem (primal) and maximization problem (dual). The system is of 2n-equation on 2n-variable, called zero-minimum condition. It yields a couple of second-order finite (n-) linear difference equation on n-variable, which constitute the respective optimal conditions. The respective equations have a mimimum solution for primal and a maximum one for dual. Both the optimal solutions are expressed in terms of Gibonacci sequence, which is a parametric generalization of the Fibonacci one. Either solution is characterized by the backward Gibonacci sequence and its complementary --Hibonacci sequence--

Identical Duals : Gap Function (Study on Nonlinear Analysis and Convex Analysis)

We consider identical duals of two pairs of minimization (primal) problems and maximization (dual) problems from a view point of gap function. The identical dual means that both optimum points of a primal problem and its dual one are identical. An identity (Cl) n-1 Σ k-1 [(xk-1 - Xk)μk + Xk(μk - μk+1)] + (xn-1 - Xn)μn + Xnμn = x0μ1 is called complementary [17]. The complementary identity leads to a gap function. We show that the complementary identity and the gap function play a fundamental part in analyzing an identical duality between primal and dual

Triplet of Fibonacci Duals : with or without constraint (New Developments on Mathematical Decision Making Under Uncertainty)

We consider a dual relation between minimization (primal) problem and maximization (dual) problem from a view point of complementarity. An identity (CI) [n-1]Σ[k=1][(xk-1 - xk)μk + xk(μk - μk+1)] + (xn-1 - xn)μn + xnμn = x0μ1 is called complementary [20, 22]. We present three types of complementary identities, which take a fundamental role in analyzing respective pairs of primal and dual. Moreover, we show that a primal and its dual satisfy Fibonacci Complementary Duality [18, 19, 21, 22]

Two Distinct Pathways to Development of Squamous Cell Carcinoma of the Vulva

Squamous cell carcinoma (SCC) accounts for approximately 95% of the malignant tumors of the vaginal vulva and is mostly found in elderly women. The future numbers of patients with vulvar SCC is expected to rise, mainly because of the proportional increase in the average age of the general population. Two different pathways for vulvar SCC have been put forth. The first pathway is triggered by infection with a high-risk-type Human Papillomavirus (HPV). Integration of the HPV DNA into the host genome leads to the development of a typical vulvar intraepithelial neoplasia (VIN), accompanied with overexpression of p14ARF and p16INK4A. This lesion subsequently forms a warty- or basaloid-type SCC. The HPV vaccine is a promising new tool for prevention of this HPV related SCC of the vulva. The second pathway is HPV-independent. Keratinizing SCC develops within a background of lichen sclerosus (LS) through a differentiated VIN. It has a different set of genetic alterations than those in the first pathway, including p53 mutations, allelic imbalances (AI), and microsatellite instability (MSI). Further clinical and basic research is still required to understand and prevent vulvar SCC. Capsule. Two pathway for pathogenesis of squamous cell carcinoma of the value are reviewed