Not much has been known about these spaces except for some special cases. It was known since 1953 that every operator A ∈ B(H) is the sum of two commutators of bounded linear operators [35], [16] while the commutator spaces of Schatten ideals Lp , p > 0, were the subject of several studies over the last 30 years, notably [49], [66], [3], [68], [67], [4], [38] and [18]. Aside from these efforts,...

For any countable discrete group Γ (without further assumptions on it) we first construct an explicit morphism from the Left-Hand side of Baum-Connes assembly map, Ktop⁎(Γ), to periodic cyclic homology algebra, HP⁎(CΓ). This morphism, called Chern-Baum-Connes allows in particular give a proper and formulation for Chern-Connes pairingKtop⁎(Γ)×HP⁎(CΓ)⟶C. Several theorems are needed formulate map....

We study the problem of applying statistical methods for approximate model checking of probabilistic systems against properties encoded as PCTL formulas. Such approximate methods have been proposed primarily to deal with state-space explosion that makes the exact model checking by numerical methods practically infeasible for large systems. However, the existing statistical methods either consid...

The paper investigates parameterized approximate message-passing schemes that are based on bounded inference and are inspired by Pearl's belief propagation algorithm (BP). We start with the bounded inference mini-clustering algorithm and then move to the iterative scheme called Iterative Join-Graph Propagation (IJGP), that combines both iteration and bounded inference. Algorithm IJGP belongs to...

We construct small cancellation labellings for some infinite sequences of finite graphs of bounded degree. We use them to define infinite graphical small cancellation presentations of groups. This technique allows us to provide examples of groups with exotic properties: • We construct the first examples of finitely generated coarsely nonamenable groups (that is, groups without Guoliang Yu’s Pro...

We consider L1-isotonic regression and L∞ isotonic and unimodal regression. For L1isotonic regression, we present a linear time algorithm when the number of outputs are bounded. We extend the algorithm to construct an approximate isotonic regression in linear time when the output range is bounded. We present linear time algorithms for L∞ isotonic and unimodal regression.

An online adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem for continuous-time uncertain nonlinear systems. A novel actor–critic–identifier (ACI) is proposed to approximate the Hamilton–Jacobi–Bellman equation using three neural network (NN) structures—actor and critic NNs approximate the optimal control and the optimal value function,...

The behavioral theory of dynamical system is used to address a deterministic system identification problem with a newly defined measure of misfit between data and linear time-invariant systems. An approximate model identification problem is formalized using this misfit criterium. In particular, Pareto optimal models are defined as feasible trade-offs between low complexity and low misfit models...

In this paper we propose a novel algorithm that provides bounded approximate solutions for decentralised coordination problems. Our approach removes cycles in any general constraint network by eliminating dependencies between functions and variables which have the least impact on the solution quality. It uses the max-sum algorithm to optimally solve the resulting tree structured constraint netw...