Different structures of master-equation used for the description of decoherence of a microsystem interacting through collisions with a surrounding environment are considered and compared. These results are connected to the general expression of the generator of a quantum dynamical semigroup in presence of translation invariance recently found by Holevo.

Different structures of master-equation used for the description of decoherence of a microsystem interacting through collisions with a surrounding environment are considered and compared. These results are connected to the general expression of the generator of a quantum dynamical semigroup in presence of translation invariance recently found by Holevo.

Rényi entropies are compared to generalized log-Fisher information and variational entropies in the context of translation, scale and concentration invariance. It is proved that the Rényi entropies occupy a special place amongst these entropies. It is also shown that Shannon entropy is centrally positioned amidst the Rényi entropies.

The Earth Mover's Distance (EMD) between two nite distributions of weight is proportional to the minimum amount of work required to transform one distribution into the other. Current content-based retrieval work in the Stanford Vision Laboratory uses the EMD as a common framework for measuring image similarity with respect to color, texture, and shape content. In this report, we present some fa...

We study the structural stability of coupled map lattice models of hyperbolic type under certain metrics. We prove the existence of equilibrium states for continuous functions on lattice models under the conditions of weak interaction and translation invariance. We also study the uniqueness and ergodic properties of these equilibrium states for HH older continuous functions.

Many signal categories in vision and auditory problems are invariant to the action of transformation groups, such as translations, rotations or frequency transpositions. This property motivates the study of signal representations which are also invariant to the action of these transformation groups. For instance, translation invariance can be achieved with a registration or with auto-correlatio...

One of the important features of the human visual system is that it is able to recognize objects in a scale and translational invariant manner. However, achieving this desirable behavior through biologically realistic networks is a challenge. Neurons may be modeled as oscillatory dynamical units. It is possible for a network of these units to exhibit synchronized oscillations under the right co...

We reconsider the problem of absence of continuous symmetry breaking for systems of point particles in R. Assuming smoothness and suitable decay of the interaction, we show that each tempered Gibbs measure is invariant under translations. If the particles exhibit internal degrees of freedom with continuous symmetries, the latter are also preserved. The proof is elementary and avoids the use of ...

Inferotemporal (IT) neurons in monkeys can respond to visual stimuli in a translation-and scale-invariant manner. In a neural circuit model based on a recently reported form of gain modulation by attention in area V4, the modulated visual responses of model V4 neurons produce object-centered receptive elds further down the visual processing stream, accounting for invariances exhibited by IT neu...

Quasi-invariance under translation is established for the σ-finite measure unifying Brownian penalisations, which has been introduced by Najnudel, Roynette and Yor ([10]). For this purpose, the theory of Wiener integrals for centered Bessel processes, due to Funaki, Hariya and Yor ([5]), plays a key role.