On the classification of simple amenable C∗C*-algebras with finite decomposition rank, II

We prove that every unital stably finite simple amenable $C^*$-algebra $A$ with finite nuclear dimension and with UCT such that every trace is quasi-diagonal has the property that $A\otimes Q$ has generalized tracial rank at most one, where $Q$ is the universal UHF-algebra. Consequently, $A$ is classifiable in the sense of Elliott.Comment: submitted. Some minor upda

The Sorting Index and Permutation Codes

In the combinatorial study of the coefficients of a bivariate polynomial that generalizes both the length and the reflection length generating functions for finite Coxeter groups, Petersen introduced a new Mahonian statistic $sor$, called the sorting index. Petersen proved that the pairs of statistics $(sor,cyc)$ and $(inv,rl\textrm{-}min)$ have the same joint distribution over the symmetric group, and asked for a combinatorial proof of this fact. In answer to the question of Petersen, we observe a connection between the sorting index and the B-code of a permutation defined by Foata and Han, and we show that the bijection of Foata and Han serves the purpose of mapping $(inv,rl\textrm{-}min)$ to $(sor,cyc)$. We also give a type $B$ analogue of the Foata-Han bijection, and we derive the quidistribution of $(inv_B,{\rm Lmap_B},{\rm Rmil_B})$ and $(sor_B,{\rm Lmap_B},{\rm Cyc_B})$ over signed permutations. So we get a combinatorial interpretation of Petersen's equidistribution of $(inv_B,nmin_B)$ and $(sor_B,l_B')$. Moreover, we show that the six pairs of set-valued statistics $\rm (Cyc_B,Rmil_B)$, $\rm(Cyc_B,Lmap_B)$, $\rm(Rmil_B,Lmap_B)$, $\rm(Lmap_B,Rmil_B)$, $\rm(Lmap_B,Cyc_B)$ and $\rm(Rmil_B,Cyc_B)$ are equidistributed over signed permutations. For Coxeter groups of type $D$, Petersen showed that the two statistics $inv_D$ and $sor_D$ are equidistributed. We introduce two statistics $nmin_D$ and $\tilde{l}_D'$ for elements of $D_n$ and we prove that the two pairs of statistics $(inv_D,nmin_D)$ and $(sor_D,\tilde{l}_D')$ are equidistributed.Comment: 25 page

Extracting particle freeze-out phase-space densities and entropies from sources imaged in heavy-ion reactions

The space-averaged phase-space density and entropy per particle are both fundamental observables which can be extracted from the two-particle correlation functions measured in heavy-ion collisions. Two techniques have been proposed to extract the densities from correlation data: either by using the radius parameters from Gaussian fits to meson correlations or by using source imaging, which may be applied to any like pair correlation. We show that the imaging and Gaussian fits give the same result in the case of meson interferometry. We discuss the concept of an equivalent instantaneous source on which both techniques rely. We also discuss the phase-space occupancy and entropy per particle. Finally, we propose an improved formula for the phase-space occupancy that has a more controlled dependence on the uncertainty of the experimentally measured source functions.Comment: 14 pages, final version, to appear PRC. Fixed typos, added refs. for last section, added discussions of imaging and d/p ratio

Secure Multiple Amplify-and-Forward Relaying Over Correlated Fading Channels

This paper quantifies the impact of correlated fading on secure communication of multiple amplify-and-forward (AF) relaying networks. In such a network, the base station (BS) is equipped with multiple antennas and communicates with the destination through multiple AF relays, while the message from the relays can be overheard by an eavesdropper. We focus on the practical communication scenario, where the main and eavesdropper’s channels are correlated. In order to enhance the transmission security, transmit antenna selection (TAS) is performed at the BS, and the best relay is chosen according to the full or partial relay selection criterion, which relies on the dualhop relay channels or the second-hop relay channels, respectively. For these criteria, we study the impact of correlated fading on the network secrecy performance, by deriving an analytical approximation for the secrecy outage probability (SOP) and an asymptotic expression for the high main-to-eavesdropper ratio (MER). From these results, it is concluded that the channel correlation is always beneficial to the secrecy performance of full relay selection. However, it deteriorates the secrecy performance if partial relay selection is used, when the number of antennas at the BS is less than the number of relays.ARC Discovery Projects Grant DP150103905

Layer-by-layer films for tunable and rewritable control of contact electrification

Charges generated by contact of solid surfaces (contact electrification) can be hazardous or useful depending on the circumstance. This paper describes a process to design a solid surface rationally to either induce or prevent charging during contact electrification; this process coats the surface with polyelectrolytes. It is observed experimentally that a surface coated with a layer of a polymer having multiple, covalently attached positive charges (a “polycation”) develops a positive charge after contacting another surface; a surface coated with a layer of polymer having negative charges (a “polyanion”) develops a negative charge. By coating the surface using layer-by-layer (LBL) deposition, the tendency of the surface to charge either positively or negatively can be switched: adding a layer of polyelectrolyte with charge opposite to the charge on the surface switches the polarity of the surface. Through microcontact printing (μCP), the surface can be stamped to create a mosaic pattern of polycation and polyanion — and importantly, the fraction of the surface area covered with polycation and polyanion can be tuned by using stamps of different patterns. Using poly(diallyldimethylammonium chloride) (PDDA) as the polycation and poly(sodium 4-styrenesulfonate) (PSS) as the polyanion, it is found that for a surface with >75% PSS, the surface charges negatively; with <75% PSS, the surface charges positively. At [similar]75% PSS, the surface becomes non-charging. The patterns on the surface can, subsequently, be erased through coating the surface with a uniform layer of polyelectrolyte. After erasing, the surface is rewritable by depositing or patterning the surface with a desired polyelectrolyte.Chemistry and Chemical Biolog

ESTIMA, a tool for EST management in a multi-project environment

BACKGROUND: Single-pass, partial sequencing of complementary DNA (cDNA) libraries generates thousands of chromatograms that are processed into high quality expressed sequence tags (ESTs), and then assembled into contigs representative of putative genes. Usually, to be of value, ESTs and contigs must be associated with meaningful annotations, and made available to end-users. RESULTS: A web application, Expressed Sequence Tag Information Management and Annotation (ESTIMA), has been created to meet the EST annotation and data management requirements of multiple high-throughput EST sequencing projects. It is anchored on individual ESTs and organized around different properties of ESTs including chromatograms, base-calling quality scores, structure of assembled transcripts, and multiple sources of comparison to infer functional annotation, Gene Ontology associations, and cDNA library information. ESTIMA consists of a relational database schema and a set of interactive query interfaces. These are integrated with a suite of web-based tools that allow a user to query and retrieve information. Further, query results are interconnected among the various EST properties. ESTIMA has several unique features. Users may run their own EST processing pipeline, search against preferred reference genomes, and use any clustering and assembly algorithm. The ESTIMA database schema is very flexible and accepts output from any EST processing and assembly pipeline. ESTIMA has been used for the management of EST projects of many species, including honeybee (Apis mellifera), cattle (Bos taurus), songbird (Taeniopygia guttata), corn rootworm (Diabrotica vergifera), catfish (Ictalurus punctatus, Ictalurus furcatus), and apple (Malus x domestica). The entire resource may be downloaded and used as is, or readily adapted to fit the unique needs of other cDNA sequencing projects. CONCLUSIONS: The scripts used to create the ESTIMA interface are freely available to academic users in an archived format from . The entity-relationship (E-R) diagrams and the programs used to generate the Oracle database tables are also available. We have also provided detailed installation instructions and a tutorial at the same website. Presently the chromatograms, EST databases and their annotations have been made available for cattle and honeybee brain EST projects. Non-academic users need to contact the W.M. Keck Center for Functional and Comparative Genomics, University of Illinois at Urbana-Champaign, Urbana, IL, for licensing information