Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multiscale entanglement renormalization Ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually states with finite correlations, i.e., projected entangled pair states (PEPS) with a bond dimension independent of ...

We study a class of lattices called weak* complemented lattices which are shown to have the property that the order complex of any interval of the lattice is either contractible or homotopy equivalent to a sphere. The two main examples are lattices generated by intervals in a total order and the lattices of partitions of integers under dominance order. The proofs are done mainly using homotopy ...

A brief proof of the existence of an equilibrium in incomplete markets is given for regular economies (Theorem 1) ; a robust example of such economies is provided . Theorem 2 establishes that the manifold fl of global pseudo-equilibria is a fiber bundle with the topological structure of a oneor two-fold covering space of G k . ", the space of k planes in R", where k is the number of assets in t...

We obtain exact densities of contractible and non-contractible loops in the O(1) model on a strip square lattice rolled into an infinite cylinder finite even circumference $L$. They are also equal to critical percolation clusters forty five degree rotated cylinder, which do not or wrap around respectively. The results presented as explicit rational functions $L$ taking values for any Their asym...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

We study differently framed incentives in dynamic laboratory buyerseller relationships with multi-tasking and endogenous matching. The experimental design tries to mitigate the role of social preferences and intrinsic motivation. Absent explicit incentives, effort is low in both tasks. Their introduction boosts efficiency substantially increasing effort in the contractible task, mildly crowding...

Given a compact and connected metric space (continuum) X, we study topological and dynamical properties of the hyperspace of normal fuzzy sets F1(X) equipped with the Hausdorff, endograph or sendograph metric. Among the many results we show that it is contractible, path connected, locally contractible, locally path connected, locally simply connected and locally connected. For the endograph met...

We investigate the combinatorics of a topological space that is generated by the set of edgeweighted finite trees. This space arises by multiplying the weights of edges on paths in trees and is closely connected to tree reconstruction problems involving finite state Markov processes. We show that this space is a contractible finite CW-complex whose face poset can be described via a partial orde...

We analyze explicit and implicit contracts in a repeated principal-agent model with observable but only partially contractible actions of the agent. It is shown that the set of implementable actions may increase or decrease if additional actions become contractible. We would like to thank Bengt Holmstrr om who stimulated this research several years ago by telling an anecdote about the insuucien...