This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Gröbner-type bases associated with polynomials of shift operators. The algorithm is used for calculating Feynman integrals and has proven itself efficient in several complicated cases. E-mail: [email protected] Supported in part by RFBR, grant 05-01-00988

Using standard calculus, explicit formulas for one-, twoand three-dimensional homotopy operators are presented. A derivation of the one-dimensional homotopy operator is given. A similar methodology can be used to derive the multi-dimensional versions. The calculus-based formulas for the homotopy operators are easy to implement in computer algebra systems such as Mathematica, Maple, and REDUCE. ...

In simple detection tasks, reaction times (RTs) are faster when stimuli are presented to the visual field or side of the body ipsilateral to the body part used to respond. This advantage, the crossed-uncrossed difference (CUD), is thought to reflect inter-hemispheric interactions needed for sensorimotor information to be integrated between the two cerebral hemispheres. However, it is unknown wh...

We establish an integration by parts formula based on jump times in an abstract framework in order to study the regularity of the law for processes solution of stochastic differential equations with jumps. 2010 MSC. Primary: 60H07, Secondary: 60G55, 60G57

We establish an integration by parts formula for the random functionals of a continuous-time Markov chain, based on partial differentiation with respect to jump times. In comparison with existing methods, our approach does not rely on the Girsanov theorem and it imposes less restrictions on the choice of directions of differentiation, while assuming additional continuity conditions on the consi...

The reduction of a large number of scalar integrals to a small set of master integrals via Laporta’s algorithm is common practice in multi-loop calculations. It is also a major bottleneck in terms of running time and memory consumption. It involves solving a large set of linear equations where many of the equations are linearly dependent. We propose a simple algorithm that eliminates all linear...

Dynamic emission computed tomographic imaging with compartment modeling can quantify in vivo physiologic processes, eliciting more information regarding underlying molecular disease processes than is obtained from static imaging. However, estimation of kinetic rate parameters for multi-compartment models can be computationally demanding and problematic due to local minima. A number of technique...

We develop a theory of BV and Sobolev Spaces via integration by parts formula in abstract metric spaces; the role of vector fields is played by Weaver’s metric derivations. The definition hereby given is shown to be equivalent to many others present in literature. Introduction In the last few years a great attention has been devoted to the theory of Sobolev spaces W 1,q on metric measure spaces...