We consider Volterra Gaussian processes on [0, T ], where T > 0 is a fixed time horizon. These are processes of type Xt = R t 0 zX(t, s)dWs, t ∈ [0, T ], where zX is a square-integrable kernel, and W is a standard Brownian motion. An example is fractional Brownian motion. By using classical techniques from operator theory, we derive measure-preserving transformations of X, and their inherently ...

We study the dynamics of metrics generated by measure-preserving transformations. We consider sequences of average metrics and entropies of the measure with respect to these metrics. The main result, which gives a criterion for checking that the spectrum of a transformation if purely point, is that the scaling sequence for the -entropies with respect to the averages of an admissible metric is b...

We analyze the canonical structure of a continuum model of ferromagnets and clarify known difficulties in defining a momentum density. The moments of the momentum density corresponding to volume-preserving coordinate transformations can be defined, but a non-singular definition of the other moments requires an enlargement of the phase space which illuminates a close relation to fluid mechanics....

In this note, we present a method for flattening anatomical surfaces such as branched vessels and intestinal tracts in an areapreserving way. This method is based on the theory of optimal mass transport and conformal mapping of surfaces. The flattened representations differ minimally from conformality in a certain precise sense. Potential applications include the detection and visualization of ...

We calculate the Riemann curvature tensor and sectional curvature for the Lie group of volume-preserving diffeomorphisms of the Klein bottle and projective plane. In particular, we investigate the sign of the sectional curvature, and find a possible disagreement with a theorem of Lukatskii. We suggest an amendment to this theorem.

As modeling details can have a large impact on planner performance, domain transformation has been a traditional subject of interest in the planning community not only between languages, but also within languages. Herein, we automate an intra-language transformation method that has as yet been applied only manually, and that has never been formally described: action schema splitting, which tran...

Consider the configuration space Q for some physical system, and a continuous group of transformations G whose action on the configurations is declared to be physically irrelevant. G is to be implemented indirectly by adjoining 1 auxiliary g per independent generator to Q, by writing the action for the system in an arbitrary G-frame, and then passing to the quotient Q/G thanks to the constraint...

Given a divergence operator δ on a probability space such that the law of δ(h) is infinitely divisible with characteristic exponent h 7→ − 2 ∫ ∞ 0 htdt, or ∫ ∞ 0 (e − ih(t)− 1)dt, h ∈ L(R+), (0.1) we derive a family of Laplace transform identities for the derivative ∂E[eλδ(u)]/∂λ when u is a non-necessarily adapted process. These expressions are based on intrinsic geometric tools such as the Ca...

With growing shares of the market of mobile microelectronic systems the reduction of energy consumption is becoming a prominent design goal. We present a method to reduce the energy consumed in processor and memory elements. The basic idea of the approach is to apply parallelizing transformations , a method known from compiler construction. In order to be sure that the transformed system still ...