Related papers: $\lambda$-Scale, a lambda calculus for spaces with…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we prove a…
We introduce weighted cb maps and $\Lambda_\mu$-cb maps on operator spaces which are generalizations of completely bounded maps and a certain class of bilinear maps on operator spaces which we call $\lambda_\mu$-cb bilinear maps. Some basic…
A new kind of numbers called Hyper Space Complex Numbers and its algebras are defined and proved. It is with good properties as the classic Complex Numbers, such as expressed in coordinates, triangular and exponent forms and following the…
We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…
In this paper we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras, and describe…
This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus…
Operationally, index functions of variable Hilbert scales can be viewed as generators for families of spaces and norms. Using a one parameter family of index functions based on the dilations of a given index function, a new class of scales…
It is formulated conditions on functions $Q(x)$ and boundaries of domains under which every $Q$-homeomorphism admits continuous or homeomorphic extension to the boundary in metric spaces with measures.
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
Pointwise estimates for the gradient of solutions to the $p$-Laplace system with right-hand side in divergence form are established. They enable us to develop a nonlinear counterpart of the classical Calder\'on-Zygmund theory in terms of…
We construct a deformed $C_{\lambda}$-extended Heisenberg algebra in two-dimensional space using non-commuting coordinates which close an algebra depends on statistical parameter characterizing exotic particles. The obtained symmetry is…
In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but…
The formal system $\lambda\delta$ is a typed lambda calculus derived from $\Lambda_\infty$, aiming to support the foundations of Mathematics that require an underlying theory of expressions (for example the Minimal Type Theory). The system…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…
We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as…
It is shown using experimental and numerical data that within the traditional inertial subrange defined by where the third order structure function is linear that the higher order structure function scaling exponents for longitudinal and…