Academic literature on the topic 'Cross Resolvable Designs'

Triallel crosses can be readily exploited as breeding tool for developing commercial hybrids with traits of genetical and commercial importance by acquiring information on specific combining ability effects along with general combining ability effects if the experimentation size is reduced to an economical extent. In this paper, methods of constructing designs involving partial triallel crosses in smaller blocks using different types of lattice designs have been introduced. The designs have low degree of fractionation, which suggests their utility when there is a resource crunch. Canonical efficiency factor of these designs relative to an orthogonal design with same number of lines, assuming constant error variance for both situations, is high indicating that adoption of these designs for the trials could bring about improvement as the recommendations from the experiment will be associated with a high precision.

Rhizoctonia solani is a soilborne fungal pathogen of many economically important crops Thirteen closely related anastomosis groups (AGs) of this pathogen have been identified each of which affects different plant species Previous studies have suggested that R solani AG3 is the main cause of disease in potato Rhizoctonia solani infection of potato plants can result in stem canker and tubers with black scurf Affected plants give a reduced yield while affected tubers are considered to have reduced quality resulting in economic loss The current study investigated the response of different potato cultivars and lines to R solani AG3 Thirtytwo potato cultivars/lines many actively used in the Plant Food Research potato breeding programme were screened in a shadehouse pot trial The trial was laid out in an adapted resolvable block design to ensure uniform exposure to environmental factors Each cultivar had six replicates four with and two without AG3 inoculum Plants were grown to maturity and the resulting tubers were assessed for disease (black scurf) Preliminary results show that none of the lines/cultivars tested were resistant but degrees of susceptibility varied In this experiment stem canker was not observed in any of the lines/cultivars

Caching is a promising technique that can reduce the amount of data transmitted over latency-prone links, effectively trading affordable memory for expensive bandwidth resources. The frequently demanded content is stored in the caches (which the users can access) during the non-peak hours so that during the peak hours, the rate can be significantly reduced by using coded transmissions from the server. As opposed to conventional caching, coded caching differs in the sense that it uses coded transmissions allowing multiple users to benefit from the same transmission. In the past years, coded caching techniques have been explored in various network scenarios like Device to Device (D2D) networks, combination networks, etc. In all these settings, users have been associated with a dedicated cache. An exciting setting that has been explored is that of shared caches where multiple users can access the same cache, which is more practical than the ideal scenario when users have dedicated caches. Another interesting real-life scenario is that of a multi-access setting where users can conceivably connect to multiple caches whose coverage areas may overlap. This was motivated by the upcoming heterogeneous cellular architecture, which will contain a dense deployment of wireless access points with small coverage and relatively large data rates, in addition to sparse cellular base stations with large coverage area and small data rates. Placing cache at local access points could then significantly reduce the base station transmission rate, with each user being able to access the content at multiple access points along with the base station broadcast. Most of the attention in multi-access networks has been centered around the setup with cyclic wraparound, where all the users connect to the same number of caches cyclically with a wraparound at the end. In our work, we deviate from the assumption of multi-access setups with cyclic wraparound and consider general multi-access setups where a very large number of users can be supported through a relatively small number of caches. Our first scheme is obtained from a class of resolvable designs satisfying certain properties, which we will refer to as cross resolvable designs. We specify the placement of contents in the caches, the user to cache association, and the content delivery through the cross resolvable design. The resulting multi-access coded caching scheme can support a large number of users compared to the number of caches. We then introduce the metric per-user rate or rate per user, which is basically the rate normalized by the number of users, to compare multi-access networks with different user to cache associations. In this work, we also focus on the metric subpacketization and that cross resolvable designs in multi-access networks can, in fact, yield sublinear subpacketization levels with respect to the number of users. Based on the metric per user rate, we show that our scheme performs better than the well-known Maddah-Ali Niesen (MaN) scheme in high memory regimes and some multi-access schemes that have been traditionally associated with cyclic wraparound. We identify certain well-studied block designs called Affine Resolvable BIBDs from affine geometry and Hadamard matrices to be cross resolvable designs and use them for detailed performance comparison. An improvised class of multi-access schemes using cross resolvable designs that can provide better per-user rates and support different user to cache associations is also presented. The class of schemes proposed absorbs the first scheme as a special case and shows the variation of number of users, rate per user and rate with respect to the number of caches that a user has access to. We also propose a new construction of cross resolvable design that can perform better than the MaN scheme in terms of per-user rate in the entire memory regime and even provide better rates in certain memory points, motivating the necessity to study cross resolvable designs for multi-access networks. The new construction does not place any restriction on the number of caches a user can access, as opposed to the cross-resolvable designs from Affine Resolvable BIBDs. We then give another construction of CRDs from linear block codes over fields whose generator matrix satisfies certain properties. The advantage of this construction is that it can result in multi-access schemes with low subpacketization levels at the same per-user rate as given by the first construction. Lastly, we consider another multi-access coded caching setup, where all possible user to cache associations exist, resulting in a larger number of users than the schemes from cross resolvable designs and better per-user rates. This scheme does not perform as well as schemes from cross resolvable designs in terms of subpacketization levels but is better than the multi-access schemes from cross resolvable designs and most other multi-access schemes with cyclic wraparound in terms of per-user rate for certain parameter ranges.