‎In this paper we consider the special classes of Sonnenschein matrices‎, ‎namely the Karamata matrices $K[alpha,beta]=left(a_{n,k}right)$ with the entries‎ ‎[{a_{n,k}} = sumlimits_{v = 0}^k {left( begin{array}{l}‎ ‎n\‎ ‎v‎ ‎end{array} right){{left( {1‎ - ‎alpha‎ - ‎beta } right)}^v}{alpha ^{n‎ - ‎v}}left( begin{array}{l}‎ ‎n‎ + ‎k‎ - ‎v‎ - ‎1\‎ ‎,,,,,,,,,,k...

In the present work, we discuss a procedure for constructing sparse binary and ternary matrices from existing two binary sensing matrices. The matrices that we construct have several attractive properties such as smaller density, which supports algorithms with low computational complexity. As an application of our method, we show that a CS matrix of general row size different from p, p, pq (for...

The structures called organ-matrix and cell-matrix are introduced. Organ-matrices contain data and operators as data, which can be stored in database tables and reflect business logic in particular business domain. An algorithm can be presented by one row of an organ-matrix. A set of algorithms in a particular business domain can be represented by an entire organ-matrix. It’s shown that an orga...

Two-Player (Normal-Form) Games. A two-player normal-form game is specified via a pair (R,C) of m × n payoff matrices. The two players of the game, called the row player and the column player, have respectively m and n pure strategies. As the players’ names imply, the pure strategies of the row player are in one-to-one correspondence with the rows of the payoff matrices, while the strategies of ...

Today’s focus on sustainability within industry presents a modeling challenge that may be dealt with using dynamic programming over an infinite time horizon. However, the curse of dimensionality often results in a large number of states in these models. These large-scale models require numerically stable solution methods. The best method for infinite-horizon dynamic programming depends on both ...

Two-Player (Normal-Form) Games. A two-player normal-form game is specified via a pair (R,C) of m × n payoff matrices. The two players of the game, called the row player and the column player, have respectively m and n pure strategies. As the players’ names imply, the pure strategies of the row player are in one-to-one correspondence with the rows of the payoff matrices, while the strategies of ...

Minimally nonideal matrices are a key to understanding when the set covering problem can be solved using linear programming. The complete classification of minimally nonideal matrices is an open problem. One of the most important results on these matrices comes from a theorem of Lehman, which gives a property of the core of a minimally nonideal matrix. Cornuéjols and Novick gave a conjecture on...

Let Amx„, Bmxn, Xnxl, and Ymxl be matrices whose entries are nonnegative real numbers and suppose that no row of A and no column of B consists entirely of zeroes. Define the operators U, T and T by (UX)t-X? [or (UY),= Y;1], T=UB'UA and T' = UAUB'. Tis called irreducible if for no nonempty proper subset S of (1, • ■ ■ , n} it is true that X,=0, ieS; X,^0, i$ S, implies (TX),=0, ieS; (TX)i^O, i $...

We study the problem of sampling contingency tables (nonnegative integer matrices with specified row and column sums) uniformly at random. We give an algorithm which runs in polynomial time provided that the row sums ri and the column sums cj satisfy ri (n 3/ m log m), and cj (m 3/ n log n). This algorithm is based on a reduction to continuous sampling from a convex set. The same approach was t...

The spectrum of branching-time relations for probabilistic systems has been investigated thoroughly by Baier, Hermanns, Katoen and Wolf (2003, 2005), including weak simulation for systems involving substochastic distributions. Weak simulation was proven to be sound w. r. t. the liveness fragment of the logic PCTL\X , and its completeness was conjectured. We revisit this result and show that sou...