Planet of the cavendish - understanding the domination

Those seeking to bring change to cultivars sold in the banana markets of the world have encountered major difficulties over the years. Change has been sought because of production difficulties caused by banana diseases such as Fusarium wilt or a desire to invigorate a stagnant market and obtain a competitive advantage by the introduction of diversity of product. Currently the world banana scene is dominated by cultivars from the Cavendish subgroup with their production in excess of 40% of total world production of banana and plantain combined, and in most western countries Cavendish is synonymous with banana. But Cavendish production usually necessitates very regular applications of pesticides, particularly fungicides for Mycosphaerella leaf spots control. So genetic resistance to these and other diseases would be very beneficial to minimizing costs of production, as well as reducing health risks to banana workers and the general population and minimizing impacts on the environment. In recent years, the overall market sales of some crops, such as tomatoes, have increased by providing diversity of cultivars to consumers. Can the same be done for banana? Perhaps a better understanding of how we have arrived at our current situation and the forces that have shaped our preference for Cavendish will allow us to plan more strategic crop improvement research which has enhanced chances of adoption by the banana industries of the world. A scoping study was recently undertaken in Australia to determine the current market opportunity for alternative cultivars and provide a roadmap for the industry to successfully develop this market. A multidisciplinary team reviewed the literature, surveyed the supply chain, analyzed gross margins and conducted consumer and sensory evaluations of 'new' cultivars. This has provided insight on why Cavendish dominates the market, which is the focus of this paper, and we believe will provide a solid foundation for future progress.

Efficient algorithms for domination and Hamilton circuit problems on permutation graphs

The domination and Hamilton circuit problems are of interest both in algorithm design and complexity theory. The domination problem has applications in facility location and the Hamilton circuit problem has applications in routing problems in communications and operations research.The problem of deciding if G has a dominating set of cardinality at most k, and the problem of determining if G has a Hamilton circuit are NP-Complete. Polynomial time algorithms are, however, available for a large number of restricted classes. A motivation for the study of these algorithms is that they not only give insight into the characterization of these classes but also require a variety of algorithmic techniques and data structures. So the search for efficient algorithms, for these problems in many classes still continues.A class of perfect graphs which is practically important and mathematically interesting is the class of permutation graphs. The domination problem is polynomial time solvable on permutation graphs. Algorithms that are already available are of time complexity O(n2) or more, and space complexity O(n2) on these graphs. The Hamilton circuit problem is open for this class.We present a simple O(n) time and O(n) space algorithm for the domination problem on permutation graphs. Unlike the existing algorithms, we use the concept of geometric representation of permutation graphs. Further, exploiting this geometric notion, we develop an O(n2) time and O(n) space algorithm for the Hamilton circuit problem.

Algorithmic aspects of k-tuple total domination in graphs

For a fixed positive integer k, a k-tuple total dominating set of a graph G = (V. E) is a subset T D-k of V such that every vertex in V is adjacent to at least k vertices of T Dk. In minimum k-tuple total dominating set problem (MIN k-TUPLE TOTAL DOM SET), it is required to find a k-tuple total dominating set of minimum cardinality and DECIDE MIN k-TUPLE TOTAL DOM SET is the decision version of MIN k-TUPLE TOTAL DOM SET problem. In this paper, we show that DECIDE MIN k-TUPLE TOTAL DOM SET is NP-complete for split graphs, doubly chordal graphs and bipartite graphs. For chordal bipartite graphs, we show that MIN k-TUPLE TOTAL DOM SET can be solved in polynomial time. We also propose some hardness results and approximation algorithms for MIN k-TUPLE TOTAL DOM SET problem. (c) 2012 Elsevier B.V. All rights reserved.

Complexity of distance paired-domination problem in graphs

Suppose G = (V, E) is a simple graph and k is a fixed positive integer. A subset D subset of V is a distance k-dominating set of G if for every u is an element of V. there exists a vertex v is an element of D such that d(G)(u, v) <= k, where d(G)(u, v) is the distance between u and v in G. A set D subset of V is a distance k-paired-dominating set of G if D is a distance k-dominating set and the induced subgraph GD] contains a perfect matching. Given a graph G = (V, E) and a fixed integer k > 0, the MIN DISTANCE k-PAIRED-DOM SET problem is to find a minimum cardinality distance k-paired-dominating set of G. In this paper, we show that the decision version of MIN DISTANCE k-PAIRED-DOM SET iS NP-complete for undirected path graphs. This strengthens the complexity of decision version Of MIN DISTANCE k-PAIRED-DOM SET problem in chordal graphs. We show that for a given graph G, unless NP subset of DTIME (n(0)((log) (log) (n)) MIN DISTANCE k-PAIRED-Dom SET problem cannot be approximated within a factor of (1 -epsilon ) In n for any epsilon > 0, where n is the number of vertices in G. We also show that MIN DISTANCE k-PAIRED-DOM SET problem is APX-complete for graphs with degree bounded by 3. On the positive side, we present a linear time algorithm to compute the minimum cardinality of a distance k-paired-dominating set of a strongly chordal graph G if a strong elimination ordering of G is provided. We show that for a given graph G, MIN DISTANCE k-PAIRED-DOM SET problem can be approximated with an approximation factor of 1 + In 2 + k . In(Delta(G)), where Delta(G) denotes the maximum degree of G. (C) 2012 Elsevier B.V All rights reserved.

Finite domination and Novikov rings. Iterative approach

Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,x -1]. Then C is R-finitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules if and only if the two chain complexes C ? L R((x)) and C ? L R((x -1)) are acyclic, as has been proved by Ranicki (A. Ranicki, Finite domination and Novikov rings, Topology 34(3) (1995), 619–632). Here R((x)) = R[[x]][x -1] and R((x -1)) = R[[x -1]][x] are rings of the formal Laurent series, also known as Novikov rings. In this paper, we prove a generalisation of this criterion which allows us to detect finite domination of bounded below chain complexes of projective modules over Laurent rings in several indeterminates.

Discursive Control, Non-Domination and Hegelian Recognition Theory: Marrying Pettit’s Account(s) of Freedom with a Pippinian/Brandomian Reading of Hegelian Agency

The aim of this article is to combine Pettit’s account(s) of freedom, both his work on discursive control and on non-domination, with Pippin’s and Brandom’s reinterpretation of Hegelian rational agency and the role of recognition theory within it. The benefits of combining these two theories lie, as the article hopes to show, in three findings: first, re-examining Hegelian agency in the spirit of Brandom and Pippin in combination with Pettit’s views on freedom shows clearly why and in which way a Hegelian account of rational agency can ground an attractive socio-political account of freedom; second, the reconciling of discursive control and non-domination with Hegelian agency shows how the force and scope of recognition become finally tangible, without either falling into the trap of overburdening the concept, or merely reducing it to the idea of simple respect; third, the arguments from this article also highlight the importance of freedom as non-domination and how this notion is, indeed, as Pettit himself claims, an agency-freedom which aims at successfully securing the social, political, economic and even (some) psychological conditions for free and autonomous agency.

Finite domination and Novikov rings: Laurent polynomial rings in two variables

Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called R-finitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.

Vector bundles on the projective line and finite domination of chain complexes

We present an algebro-geometric approach to a theorem on finite domination of chain complexes over a Laurent polynomial ring. The approach uses extension of chain complexes to sheaves on the projective line, which is governed by a K-theoretical obstruction.

Non-domination, non-alienation and social equality: towards a republican understanding of equality

The republican idea of non-domination stresses the importance of certain social relationships for a person’s freedom, showing that freedom is a social-relational state. While the idea of freedom as non-domination receives a lot of attention in the literature, republican theorists say surprisingly little about equality. Therefore, the aim of this paper is to carve out the contours of a republican conception of equality.. In so doing, I will argue that republican accounts of equality share a significant normative overlap with the idea of social equality. However, closer analysis of Philip Pettit’s account of ‘expressive egalitarianism’ (which Pettit sees as inherently connected to non-domination) and recent theories of social equality shows that republican non-domination – in contrast to what Pettit seems to claim – is not sufficient for securing (republican) social equality. In order to secure social equality for all, republicans would have to go beyond non-domination.

Freedom as non-domination: radicalisation or retreat?

Key challenges for contemporary neorepublicans are identified and explored. Firstly, the attempt to maintain a sharp line between neorepublicanism and the wider family of liberal–egalitarian political theories is questioned. Secondly, in response to challenges from democratic theorists, it is argued that republicanism needs to effect an appropriate rapprochement with the ideal of collective political autonomy, on which it appears to rely. Thirdly, it is argued that freedom as non-domination draws so heavily on the idea of equal respect that it is hard to maintain that freedom is the sole value grounding the theory. Finally, it is suggested that the consequentialist framework of Pettit’s theory imposes significant limitations on republican social justice. How republican political theorists respond to these challenges will determine whether the neorepublican revival will be seen as enriching contemporary debates about democracy and social justice or as a retreat from more ambitious accounts of freedom and justice.

Finite domination and Novikov rings. Laurent polynomial rings in several variables

We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely generated free modules). The main tools, which we develop in the paper, are a non-standard totalisation construction for multi-complexes based on truncated products, and a high-dimensional mapping torus construction employing a theory of cubical diagrams that commute up to specified coherent homotopies.