Suppose that to every non-degenerate simplex ∆ ⊂ Rn a ‘center’ C(∆) is assigned so that the following assumptions hold: (i) The map ∆ → C(∆) commutes with similarities and is invariant under the permutations of the vertices of the simplex; (ii) The map ∆ → Vol(∆)C(∆) is polynomial in the coordinates of the vertices of the simplex. Then C(∆) is an affine combination of the center of mass CM(∆) a...

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007...

We introduce a new network simplex pivot rule for the shortest path simplex algorithm. This new pivot rule chooses a subset of non-basic arcs to enter into the basis simultaneously. We call to this operation multiple pivot. We show that a shortest path simplex algorithm with this pivot rule makes O(n) multiple pivots and runs in O(nm) time. This new pivot rule is based on the new concept of pse...

Sphere close packed (SCP) lattice arrangements of points are well-suited for formulating symmetric quadrature rules on simplexes, as they are symmetric under affine transformations of the simplex unto itself in 2D and 3D. As a result, SCP lattice arrangements have been utilized to formulate symmetric quadrature rules with Np = 1, 4, 10, 20, 35, and 56 points on the 3-simplex (Shunn andHam, 2012...

Immunodeficient patients are at risk of developing extended or atypical herpes simplex virus infections, which can be easily misdiagnosed. We present the case of a 79-year-old, treatment-induced (oral corticosteroid), immunocompromised female with an extensive atypical herpes simplex virus infection. This patient presented with multiple erosions and vesicles on the trunk with a subacute onset. ...

A rat cell line, RE1, oncogenically transformed by a herpes simplex virus type 2 ts mutant (ts 1), has been demonstrated to contain herpes simplex virus type 2-specific thymidine kinase activity, as have two of four tumors induced in rats by inoculation of these transformed cells. A high proportion of sera from tumor-bearing rats (5 of 11) have detectable antibody against herpes simplex virus t...

Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differentialgeometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining ...

We review complexity results for minimizing polynomials over the standard simplex and unit hypercube. In addition, we derive new results on the computational complexity of approximating the minimum of some classes of functions (including Lipschitz continuous functions) on the standard simplex. The main tools used in the analysis are Bernstein approximation and Lagrange interpolation on the simp...

An avidin-biotin complex system was compared with three commercially available immunofluorescence kits for serotyping herpes simplex virus isolates from clinical specimens. Sensitivity values showed that the Electro-Nucleonics and Immulok reagents were useful in detecting the presence of virus, whereas the predictive values showed that the Syva and Immulok reagents possessed adequate discrimina...

In this paper, we describe the Simplex architecture, a real-time software technology which supports the safe, reliable introduction of control system upgrades while the system is running. We present the Simplex architecture from a control application point of view. In particular, we discuss the fault-tolerance feature of the technology, introduce its basic structure in control systems, and inve...