Abstract. We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic codes are ideals in the group ring over a cyclic group. The fresh focus is on the encodings themselves, which only under very limited conditions result in ideals.We use the result that a group ring is isomorphic to a certain well-defined ring of matrices, and thus every group ring element has an associated matrix. This allows matrix algebra to be used as needed in the study and production of codes, enabling the creation of standard generator and check matrices.Group rings are a fruitful source of units and zero-divisors from which new codes result. Many code properties, such as being LDPC or self-dual, may be expressed as properties within the group ring thus enabling the construction of codes with these properties. The methods are general enabling the construction of codes with many types of group rings. There is no restriction on the ring and thus codes over the integers, over matrix rings or even over group rings themselves are possible and fruitful.

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Abstract. One of the challenges in unsupervised machine learning is finding the number of clusters in a dataset. Clustering Validity Indices (CVI) are popular tools used to address this problem. A large number of CVIs have been proposed, and reports that compare different CVIs suggest that no single CVI can always outperform others. Following suggestions found in prior art, in this paper we formalize the concept of using multiple CVIs for cluster number estimation in the framework of multi-classifier fusion. Using a large number of datasets, we show that decision-level fusion of multiple CVIs can lead to significant gains in accuracy in estimating the number of clusters, in particular for highdimensional datasets with large number of clusters.

e present an enhancement to the IP best effort service, alternative best effort (ABE), which relies on the idea of providing low delay at the expense of maybe less throughput. The motivation for such a service is twofold. First, there now exist interactive multimedia applications that perform well across a wide range of loss and throughput conditions [1,2], but for which delay often remains the major impediment [3]. Second, unlike differentiated services, we would like to design a service where it is not required to police how much traffic uses the low delay capability, in order to retain the operational simplicity of a single-class network.The article is organized as follows. We define the ABE service and analyze its implications. In particular, we identify and discuss the central issue, called green does not hurt blue. We also discuss migration issues from the traditional IP service (flat best effort) to ABE. As a proof of concept, a router implementation is described; it is based on the combination of a scheduler called duplicate scheduling with deadlines (DSD) and a traditional control loop. Implementations were done in the Linux kernel, in the Dummynet network emulator, and in the ns-2 simulator [4]. Simulation results of the ns-2 implementation are shown. We review related work and position ABE with respect to other proposals in differentiated services. The ABE Service Definition of the ServiceABE is defined as follows:• ABE packets are marked either green or blue. 1 • Green packets receive a low bounded delay at every hop.Realistic values of the per-hop delay bound are discussed later in this section.• Green does not hurt blue: If some source decides to mark some of its packets green rather than blue, the quality of the service(delay and throughput) received by sources that mark all their packets blue remains the same or becomes better. This definition is made more specific later.• All ABE packets belong to one single best effort class. If the total load is high, every source may receive little throughput. However, entirely blue sources experience more throughput than entirely green sources sharing the same network resources. AbstractWe propose alternative best effort (ABE), a novel service for IP networks, which relies on the idea of providing low delay at the expense of maybe less throughput. The objective is to retain the simplicity of the original Internet single-class best-effort service while providing low delay to interactive adaptive applications. With ABE, every best effort packet is marked as either green or blue. Green packets are guaranteed a low bounded delay in every router. In exchange, green packets are more likely to be dropped (or marked using congestion notification) during periods of congestion than blue packets. For every packet, the choice of color is made by the application based on the nature of its traffic and on global traffic conditions. Typically, an interactive application with real-time deadlines, such as audio, will mark most of its packets as green, as long as the network ...