391 research outputs found
Tensor products and regularity properties of Cuntz semigroups
The Cuntz semigroup of a C*-algebra is an important invariant in the
structure and classification theory of C*-algebras. It captures more
information than K-theory but is often more delicate to handle. We
systematically study the lattice and category theoretic aspects of Cuntz
semigroups.
Given a C*-algebra , its (concrete) Cuntz semigroup is an object
in the category of (abstract) Cuntz semigroups, as introduced by Coward,
Elliott and Ivanescu. To clarify the distinction between concrete and abstract
Cuntz semigroups, we will call the latter -semigroups.
We establish the existence of tensor products in the category and study
the basic properties of this construction. We show that is a symmetric,
monoidal category and relate with for
certain classes of C*-algebras.
As a main tool for our approach we introduce the category of
pre-completed Cuntz semigroups. We show that is a full, reflective
subcategory of . One can then easily deduce properties of from
respective properties of , e.g. the existence of tensor products and
inductive limits. The advantage is that constructions in are much easier
since the objects are purely algebraic.
We also develop a theory of -semirings and their semimodules. The Cuntz
semigroup of a strongly self-absorbing C*-algebra has a natural product giving
it the structure of a -semiring. We give explicit characterizations of
-semimodules over such -semirings. For instance, we show that a
-semigroup tensorially absorbs the -semiring of the Jiang-Su
algebra if and only if is almost unperforated and almost divisible, thus
establishing a semigroup version of the Toms-Winter conjecture.Comment: 195 pages; revised version; several proofs streamlined; some results
corrected, in particular added 5.2.3-5.2.
Computation of biochemical pathway fluctuations beyond the linear noise approximation using iNA
The linear noise approximation is commonly used to obtain intrinsic noise
statistics for biochemical networks. These estimates are accurate for networks
with large numbers of molecules. However it is well known that many biochemical
networks are characterized by at least one species with a small number of
molecules. We here describe version 0.3 of the software intrinsic Noise
Analyzer (iNA) which allows for accurate computation of noise statistics over
wide ranges of molecule numbers. This is achieved by calculating the next order
corrections to the linear noise approximation's estimates of variance and
covariance of concentration fluctuations. The efficiency of the methods is
significantly improved by automated just-in-time compilation using the LLVM
framework leading to a fluctuation analysis which typically outperforms that
obtained by means of exact stochastic simulations. iNA is hence particularly
well suited for the needs of the computational biology community.Comment: 5 pages, 2 figures, conference proceeding IEEE International
Conference on Bioinformatics and Biomedicine (BIBM) 201
Abstract bivariant Cuntz semigroups
We show that abstract Cuntz semigroups form a closed symmetric
monoidal category. Thus, given Cuntz semigroups S and T, there is another
Cuntz semigroup JS, TK playing the role of morphisms from S to T. Applied to
C*-algebras A and B, the semigroup JCu(A),Cu(B)K should be considered as
the target in analogues of the UCT for bivariant theories of Cuntz semigroups.
Abstract bivariant Cuntz semigroups are computable in a number of interesting
cases. We explore its behaviour under the tensor product with the Cuntz
semigroup of strongly self-absorbing C*-algebras and the Jacelon-Razak algebra.
We also show that order-zero maps between C*-algebras naturally define
elements in the respective bivariant Cuntz semigroup
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Abstract bivariant Cuntz semigroups
We show that abstract Cuntz semigroups form a closed symmetric
monoidal category. Thus, given Cuntz semigroups S and T, there is another
Cuntz semigroup JS, TK playing the role of morphisms from S to T. Applied to
C*-algebras A and B, the semigroup JCu(A),Cu(B)K should be considered as
the target in analogues of the UCT for bivariant theories of Cuntz semigroups.
Abstract bivariant Cuntz semigroups are computable in a number of interesting
cases. We explore its behaviour under the tensor product with the Cuntz
semigroup of strongly self-absorbing C*-algebras and the Jacelon-Razak algebra.
We also show that order-zero maps between C*-algebras naturally define
elements in the respective bivariant Cuntz semigroup
Traces on ultrapowers of C*-algebras
Using Cuntz semigroup techniques, we characterize when limit traces are dense
in the space of all traces on a free ultrapower of a C*-algebra. More
generally, we consider density of limit quasitraces on ultraproducts of
C*-algebras.
Quite unexpectedly, we obtain as an application that every simple C*-algebra
that is (m,n)-pure in the sense of Winter is already pure. As another
application, we provide a partial verification of the first Blackadar-Handelman
conjecture on dimension functions.
Crucial ingredients in our proof are new Hahn-Banach type separation theorems
for noncancellative cones, which in particular apply to the cone of
extended-valued traces on a C*-algebra.Comment: 47 pages; minor changes, included further reference
Efficient parallelization of polyphase arbitrary resampling FIR filters for high-speed applications
This article describes a method for increasing the sampling rate of efficient polyphase arbitrary resampling FIR filters. An FPGA proof of concept prototype of this architecture has been implemented in a Xilinx Kintex-7 FPGA which is able to convert the sampling rate of a signal from 500 MHz to 600 MHz. This article compares this new architecture with other best known efficient resampling architectures implemented on the same FPGA. The area usage on the FPGA shows that our proposed implementation is very proficient in high bandwidth applications without requiring significantly more resources on the FPGA. A theoretical calculation of the resampling error introduced on a modulated data stream is provided to evaluate the new architecture against other existing resampling architectures
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