The paper deals with a filter design for nonlinear continuous stochastic systems with discrete-time measurements. The general recursive solution is given by the Fokker–Planck equation (FPE) and by the Bayesian rule. The stress is laid on the computation of the predictive conditional probability density function from the FPE. The solution of the FPE and its integration into the estimation algori...

Small-angle x-ray scattering (SAXS) is an experimental biophysical method used for gaining insight into the structure of large biomolecular complexes. Under appropriate chemical conditions, the information obtained from a SAXS experiment can be equated to the pair distribution function, which is the distribution of distances between every pair of points in the complex. Here we develop a mathema...

The objective of the Theory of Computing course is to introduce and study abstract, mathematical models of computation (such as Turing machines, formal grammars, recursive functions), and to use the abstract computation models to study the ability to solve computational problems, by identifying both the intrinsic limitations of computing devices, and the practical limitations due to limited ava...

We present a procedure for computing the coeecients of the expansion of a bivariate polynomial into Bernstein polynomials over subtriangles. These triangles are generated by partitioning the standard simplex of IR 2. The coeecients are computed directly from the coeecients on the subdivided triangle from the preceding subdivision level. This allows a recursive computation of the coeecients and ...

The sometimes so-called Main Theorem of Recursive Analysis implies that any computable real function is necessarily continuous. We consider three relaxations of this common notion of real computability for the purpose of treating also discontinuous functions f : R → R: – non-deterministic computation; – relativized computation, specifically given access to oracles like ∅′ or ∅′′; – encoding inp...

One of the key problems when extending relational database query languages to include deductive capabilities, is to provide them with efficient methods for answering recursive queries. During the last few years many algorithms have been proposed to deal with transitive closure computation of a relation. In this paper, we discuss some important criteria for developing transitive closure algorith...

In this paper, we show how the framework of von Neumann algebras can be applied to model the dynamics of computational processes. Namely, our aim is to gain an understanding of classical computation in terms of the hyperfinite factor, starting from the class of Kalmar recursive functions. Our model fits within a vast project of reshaping the unified theory of semantics of computation called geo...

We report a computation of the exact output rate of recently-discovered generalization of Peres algorithm for generating random bits from loaded dice. Instead of resorting to brute-force computation for all possible inputs, which becomes quickly impractical as the input size increases, we compute the total output length on equiprobable sets of inputs by dynamic programming using a recursive for...

In this article we present a strong support to real recursive function theory as a branch of computability theory rooted in mathematical analysis. This new paradigm connects computation on reals with differential equations and infinite limits in a robust and smooth way. The results presented here are taken mainly from the article (4) of the same authors. Key–Words: Computation on Reals, Differe...

It is common practice to compare the computational power of different models of computation. For example, the recursive functions are strictly more powerful than the primitive recursive functions, because the latter are a proper subset of the former (which includes Ackermann’s function). Side-by-side with this “containment” method of measuring power, it is also standard to base comparisons on “...