In this paper, we give a probabilistic counterpart of  Mazur-Ulam theorem  in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.

This paper presents a probabilistic framework for robust recovery of dense 3D shape, motion, texture and lighting from monocular image streams. We assume that the object is smooth, Lambertian, illuminated by one distant light source, and subject to smoothly-varying rigid motion. The problem is formulated as a MAP estimation problem in which all shape, motion, noise variances and outlier probabi...

Some new concepts of generating spaces of quasi-norm family are introduced and their linear topological structures are studied. These spaces are not necessarily locally convex. By virtue of some properties in these spaces, several Schauder-type fixed point theorems are proved, which include the corresponding theorems in locally convex spaces as their special cases. As applications, some new fix...

Two extensions of the Shapley value are given. First we consider a probabilistic framework in which certain consistent allocation rules such as the Shapley value are characterized. The second generalization of the Shapley value is an extension to the structure of posets by means of a recursive form. In the latter setting, the Shapley value for quasi-concave games is shown to be a core-allocation.

Bound states generated by the K coupled PT −symmetric square wells are studied in a series of models where the Hamiltonians are assumed R−pseudo-Hermitian and R2−symmetric. Specific rotation-like generalized parities R are considered such that RN = I at some integers N . We show that and how our assumptions make the models exactly solvable and quasi-Hermitian. This means that they possess the r...

We present a powerful quasi-probabilistic default formalism for graded defaults based on a well-motivated canonical ranking construction procedure, System JLZ. It implements the minimal construction paradigm and verifies the major inference principles and inheritance desiderata, including rational monotony for propositions and structured cumulativity for default conditionals. With help from a s...

We attempt to dissolve the measurement problem using a quasi-anthropic principle which allows us to invoke rational observers. We argue that the key feature of such observers is that they are rational (we need not care whether they are ‘classical’ or ‘macroscopic’ for example) and thus, since quantum theory can be expressed as a rational theory of probabilistic inference, the measurement proble...

Limitations of one-hidden-layer perceptron networks to represent efficiently finite mappings is investigated. It is shown that almost any uniformly randomly chosen mapping on a sufficiently large finite domain cannot be tractably represented by a one-hidden-layer perceptron network. This existential probabilistic result is complemented by a concrete example of a class of functions constructed u...

In this paper, we consider new and general models for imperfect sources of randomness, and show how to obtain quasi-random sequences from such sources. Intuitively, quasi-random sequences are sequences of almost unbiased elements over a finite set. Our model is as follows: Let A be a finite set whose number of elements is a power of 2. Let 1/|A| ≤ δ < 1 be a constant. The source outputs an elem...

Let X be an algebraic variety over the algebraically closed field K and Ξ ⊆ X(K) a set of K-rational points on X. We say that a subvariety Y ⊆ Xn of some Cartesian power of X is Ξ-special if Ξn ∩ Y (K) is Zariski dense in Y . We show under certain hypotheses on Ξ, for instance, that the class of Ξ-special varieties is closed under intersections, that when subvarieties of X vary in an algebraic ...