Invariance is one of the most important notions in applications of mathematics. It is one of the key concepts in modern physics, is a computational tool that helps in solving complex equations, etc. In view of its importance, it is desirable to come up with a definition of invariance which is as general as possible. In this paper, we describe how to formulate a general notion of invariance in c...

The Meta-Schr\"odinger algebra arises as the dynamical symmetry in transport processes which are ballistic a chosen `parallel' direction and diffusive all other `transverse' directions. time-space transformations of this Lie its infinite-dimensional extension, meta-Schr\"odinger-Virasoro algebra, constructed. We also find representation suitable for non-stationary systems by proposing generalis...

We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with admit scale-free formulation of the functional integral and effective action in terms invariant fields. They correspond to exact scaling solutions renormalization flow equations. Such are highly predictive since all relevant parameters for deviations from solution vanish....

While it is often assumed that objects can be recognized irrespective of where they fall on the retina, little is known about the mechanisms underlying this ability. By exposing human subjects to an altered world where some objects systematically changed identity during the transient blindness that accompanies eye movements, we induced predictable object confusions across retinal positions, eff...

Factor mixture models (FMM's) are latent variable models with categorical and continuous latent variables which can be used as a model-based approach to clustering. A previous paper covered the results of a simulation study showing that in the absence of model violations, it is usually possible to choose the correct model when fitting a series of models with different numbers of classes and fac...

While it is often assumed that objects can be recognized irrespective of where they fall on the retina, little is known about the mechanisms underlying this ability. By exposing human subjects to an altered world where some objects systematically changed identity during the transient blindness that accompanies eye movements, we induced predictable object confusions across retinal positions, eff...