We study the cohomology and hence K-theory of the aperiodic tilings formed by the so called ‘cut and project’ method, i.e., patterns in d dimensional Euclidean space which arise as sections of higher dimensional, periodic structures. They form one of the key families of patterns used in quasicrystal physics, where their topological invariants carry quantum mechanical information. Our work devel...

The paper presents a method for uncertainty propagation in Bayesian networks in symbolic, as opposed to numeric, form. The algebraic structure of probabilities is characterized. The prior probabilities of instantiations and the marginal probabilities are shown to be rational functions of the parameters, where the polynomials appearing in the numerator and the denominator are at the most first d...

All rational parametric curves with prescribed polynomial tangent direction form a vector space. Via directions norm, this includes the important case of Pythagorean hodograph curves. We study subspaces defined by fixing denominator and describe construction canonical bases for them. also show (as an analogy to fraction decomposition functions) that any element space can be obtained as finite s...

A canonical form for circuit diagrams with a designated start state is presented. The form is based upon nite automata minimization and Shannon's canonical form for boolean expressions.

Given a linear time-invariant control system, it is well known that the transmission zeroes are the generalized eigenvalues of a matrix pencil. Adding outputs to place additional zeroes is equivalent to appending rows to this pencil to place new generalized eigenvalues. Adding inputs is likewise equivalent to appending columns. Since both problems are dual to each other, we only show in this pa...

The canonical inflation specification in sticky-price rational expectations models (the new-Keynesian Phillips curve) is often criticized on the grounds that it fails to account for the dependence of inflation on its own lags. In response, many recent studies have employed a “hybrid” sticky-price specification in which inflation depends on a weighted average of lagged and expected future values...

act on the upper half-plane by linear fractional transformations. We may form the quotient Y0(N) = Γ0(N)\H, a Riemann surface with finitely many cusps. Compactifying gives a curve X0(N) which is in fact defined over Q; the map z → (j(z), j(Nz)) ∈ AC realizes Y0(N) as a (highly singular) plane curve with Q-coefficients. Over a general field k of characteristic zero, the k-points of the curve X0(...

Some elementary facts on canonical representations of small rational integers are listed and a reformulation of a characterization of a certain class of CNS polynomials is presented. Furthermore, several examples in support of a conjecture of S. Akiyama on the canonical representative of −1 are provided.

We discuss the uniruledness of various base loci of linear systems related to the canonical divisor. In particular we prove that the stable base locus of the canonical divisor of a smooth projective variety of general type is covered by rational curves.