This paper deals with two related problems, namely distance-preserving binary embeddings and quantization for compressed sensing . First, we propose fast methods to replace points from a subset X ⊂ Rn, associated with the Euclidean metric, with points in the cube {±1}m and we associate the cube with a pseudo-metric that approximates Euclidean distance among points in X . Our methods rely on qua...

An operator on a complex Banach space is polynomially compact if a non-zero polynomial of the operator is compact, and power compact if a power of the operator is compact. Theorems on triangularizability of algebras (resp. semigroups) of compact operators are shown to be valid also for algebras (resp. semigroups) of polynomially (resp. power) compact operators, provided that pairs of operators ...

We present some formal systems in the language of linearly ordered rings with finite sets whose nonlogical axioms are strictly mathematical, which correspond to polynomially bounded arithmetic. With an additional strictly mathematical axiom, the systems correspond to exponentially bounded arithmetic. 1. T0 and IS0. In this section, we introduce the system T0, and show that it corresponds to the...

We give an abstract account of resource-bounded reducibilities as exemplified by the polynomially timeor logarithmically space-bounded reducibilities of Turing, truth-table, and many-one type. We introduce a small set of axioms that are satisfied for most of the specific resourcebounded reducibilities appearing in the literature. Some of the axioms are of a more algebraic nature, such as the re...

In [8] an algorithm has been presented that computes a maximal independent set (MIS) withinO(log n/F + log n polyloglogn) rounds in an n-node multichannel radio network with F commu-nication channels. The paper uses a multichannel variant of the standard graph-based radio networkmodel without collision detection and it assumes that the network graph is a polynomially bounded in-...

A natural term rewriting framework for the Bellantoni Cook schemata of predicative recursion, which yields a canonical definition of the polynomial time computable functions, is introduced. In terms of an exponential function both, an upper bound and a lower bound are proved for the resulting derivation lengths of the functions in question. It is proved that any natural reduction strategy yield...

The spin–network quantum simulator model, which essentially encodes the (quantum deformed) SU(2) Racah–Wigner tensor algebra, is particularly suitable to address problems arising in low dimensional topology and group theory. In this combinatorial framework we implement families of finite–states and discrete–time quantum automata capable of accepting the language generated by the braid group, an...

In this paper we study the growth of mild solutions of abstract Cauchy problems governed by a densely defined generator A of an o-times integrated semigroup {Sa(t)},>o. We prove the following results: (i) If lIsa( I Me wt for ime M > 0, w E W, and all t 2 0, then for all E > 0, o > 0 and zo E D((-Aw+o)a+E) a unique mild solution exists. Moreover, this solution is exponentially bounded, and its ...

In the framework of the spin-network simulator based on the SUq(2) tensor algebra, we implement families of finite state quantum automata capable of accepting the language generated by the braid group, and whose transition amplitudes are coloured Jones polynomials. The automaton calculation of the polynomial of a link L on n strands at any fixed root of unity q is bounded from above by a linear...

Let A generate a C0–semigroup T (·) on a Banach space X such that the resolvent R(iτ, A) exists and is uniformly bounded for τ ∈ R. We show that there exists a closed, possibly unbounded projection P on X commuting with T (t). Moreover, T (t)x decays exponentially as t → ∞ for x in the range of P and T (t)x exists and decays exponentially as t→ −∞ for x in kernel of P . The domain of P depends ...