We develop a unifying framework for the treatment of various persistent homology architectures using notion correspondence modules. In this formulation, morphisms between vector spaces are given by partial linear relations, as opposed to mappings. one-dimensional case, among other things, allows us to: (i) treat persistence modules and zigzag algebraic objects same type; (ii) give categorical f...

Motivated by the Landau-Ginzburg model, we study Witten deformation on a noncompact manifold with bounded geometry, together some tameness condition growth of Morse function $f$ near infinity. We prove that cohomology $d_{Tf}$ acting complex smooth $L^2$ forms is isomorphic to Thom-Smale as well relative certain pair $(M, U)$ for sufficiently large $T$. establish an Agmon estimate eigenforms La...

This work gives a new approach to the construction of implicit operations. By considering “higher-dimensional” spaces of implicit operations and implicit operators between them, the projection of idempotents back to one-dimensional spaces produces implicit operations with interesting properties. Besides providing a wealth of examples of implicit operations which can be obtained by these means, ...

For first-order expansions of the field of real numbers, nondefinability of the set of natural numbers is equivalent to equality of topological and Assouad dimension on images of closed definable sets under definable continuous maps.

One of Darwin's most widely known conjectures is that prey are tame on remote islands, where mammalian predators are absent. Many species appear to permit close approach on such islands, but no comparative studies have demonstrated reduced wariness quantified as flight initiation distance (FID; i.e. predator-prey distance when the prey begins to flee) in comparison with mainland relatives. We u...

An ordered structure is called o-minimalistic if it has all the first-order features of an o-minimal structure. In this paper, we concentrate on a well-known fragment DCTC (Definable Completeness/Type Completeness) and generalize o-minimal properties to this more general situation (dimension theory, monotonicity, Hardy structures, quasi-cell decomposition) upon replacing finiteness by discreten...

The influence of neonatal handling on behavior and immune function was assessed in Orange-winged Amazon parrots (Amazona amazonica). Chicks (n=11) were gently handled daily from 25 days of age until 38 days post-fledging, while control chicks (n=9) were not handled. At 10 days post-fledging ( approximately 66 days of age), chicks were given tests to evaluate tameness (e.g., willingness to perch...