Probabilistic Latent Semantic Analysis (PLSA) is a popular technique to analyze non-negative data where multinomial distributions underlying every data vector are expressed as linear combinations of a set of basis distributions. These learned basis distributions that characterize the dataset lie on the standard simplex and themselves represent corners of a simplex within which all data approxim...

This case is reported to raise awareness of herpes simplex encephalitis as a persisting brain disorder. A 66 year old immunocompetent man developed status epilepticus and died of pneumonia in the course of progressive hemiparesis, cognitive decline, and atrophy of the brain over a five year period after herpes simplex encephalitis. In addition to a completely destroyed left temporal lobe, necro...

The fuzzy primal simplex method [15] and the fuzzy dual simplex method [17] have been proposed to solve a kind of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers. The fuzzy simplex method starts with a primal fuzzy basic feasible solution (FBFS) for FLP problem and moves to an optimal basis by walking truth sequence of exception of the optimal basis obtaine...

where r denotes the cross-ratio. In this note we show that the Bloch-Wigner function can be naturally extended to the (infinite dimensional) variety of all algebraic curves in CP 3 which are in sufficiently general position with respect to a given simplex L. (By definition a simplex in CP 3 is a collection of 4 hyperplanes in generic position). We call the corresponding function the Chow diloga...

The simplex algorithm requires artificial variables for solving linear programs, which lack primal feasibility at the origin point. We present a new general-purpose solution algorithm, called Push-and-Pull, which obviates the use of artificial variables. The algorithm consists of preliminaries for setting up the initialization followed by two main phases. The Push Phase develops a basic variabl...

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. ...