Current taxonomic composition of European genebank material documented in EURISCO

Taxonomy plays an essential role in genebank documentation. It is often the first level at which users search material, and it determines the protocols used in the management of collections. Especially, when plant genetic resources information is pooled in systems such as EURISCO, the European catalogue of ex situ plant genetic resources, problems regarding technical handling of taxonomic nomenclature, such as lack of standardization and low quality of data, become apparent. These problems were studied by analysing the content of EURISCO and mapping the taxon names in EURISCO on those used in the United States Department of Agriculture genebank system GRIN-Tax. Thus, the number of spelling errors and the level of standardization could be quantified and improved. An analysis of the content of EURISCO was made, showing a highly unbalanced distribution over crops: 50% of the accessions belong to ten genera only. Mapping EURISCO on the crops listed in Annex 1 of the International Treaty on Plant Genetic Resources for Food and Agriculture showed that 67% of the accessions in EURISCO belong to crops in that list

The European ex situ PGR Information Landscape

In this paper the authors try to describe the current situation regarding the documentation of Plant Genetic Resources (PGR) maintained in ex situ collections in Europe. It will tackle the systems that are used to manage the information involved, the mechanisms and systems that exist to exchange this information, and we will discuss the developments and challenges in this area. Apart from this technical description, the authors also try to give a functional description of the changing role of these systems in the light of international, technical and legal developments

Optimization of the composition of crop collections for ex situ conservation

Many crop genetic resources collections have been established without a clearly defined conservation goal or mandate, which has resulted in collections of considerable size, unbalanced composition and high levels of duplication. Attempts to improve the composition of collections are hampered by the fact that conceptual views to optimize collection composition are very rare. An optimization strategy is proposed herein, which largely builds on the concepts of core collection and core selection. The proposed strategy relies on hierarchically structuring the crop gene pool and assigning a relative importance to each of its different components. Comparison of the resulting optimized distribution of the number of accessions with the actual distribution allows identification of under- and over-representation within a collection. Application of this strategy is illustrated by an example using potato. The proposed optimization strategy is applicable not only to individual genebanks, but also to consortia of cooperating genebanks, which makes it relevant for ongoing activities within projects that aim at sharing responsibilities among institutions on the basis of rational conservation, such as a European genebank integrated system and the global cacao genetic resources network CacaoNet

Combinatorics and Metric Geometry

This thesis consists of an introduction and seven chapters, each devoted to a different combinatorial problem. In Chapters 1 and 2, we consider the main subject of this thesis; the sharp stability of the Brunn-Minkowski inequality (BM). This celebrated theorem from the 19th century asserts that for bodies A,B $\subset$ $\mathbb{R}$$^{k}$, we have |A + B|$^{1/k}$ $\geq$ |A|$^{1/k}$ + |B|$^{1/k}$, where |$\cdot$| is the Lebesgue measure and A + B := {a + b : a $\in$ A, b $\in$ B} is the Minkowski sum. Moreover, we have equality if and only if A,B are homothetic convex sets. The stability question, studied in many papers, asks how the distance to equality in BM relates to the distance from A,B to homothetic convex sets. In particular, given Brunn-Minkowsi deficit $\delta$ := |A+B|$^{1/k}$ / |A|$^{1/k}$ + |B|$^{1/k}$ -1, and normalized volume ratio $\textit{t}$ := |A|$^{1/k}$ / |A|$^{1/k}$ + |B|$^{1/k}$, what is the best bound one can find on $\omega$ := |K$_{A}$ \ A| / |A| + |K$_{B}$ \ B| / |B|, where K$_{A}$ $\supset$ A, and K$_{B}$ $\supset$ B are homothetic convex sets of minimal size? In Chapter 2, we prove a conjecture by Figalli and Jerison establishing the sharp stability for homothetic sets. In particular, we show that for homothetic sets, we have $\omega$ = O$_{k}$($\delta$t$^{-1}$), for $\delta$ sufficiently small. In Chapter 3, we establish the sharp stability for planar sets, i.e. we show that for planar sets and $\delta$ sufficiently small, we have $\omega$ = O($\delta$$^{1/2}$t$^{-1/2}$). A crucial result in Chapter 3 shows that for any $\epsilon$ > 0, if $\delta$ is sufficiently small, then we have |co(A + B) \ (A + B)| $\leq$ (1 + $\epsilon$)(|co(A) \ A| + |co(B) \ B|). In Chapter 4, we consider a reconstruction problem for functions on graphs. Given a function $\textit{f}$:V(G) $\rightarrow$ [k] on the vertices of a graph G and a random walk (U$_{i}$)$^{{\infty}}_{i = 1}$ on that graph, can we reconstruct $\textit{f}$ (up to automorphisms) based on just ($\textit{f}$(U$_{i}$)$^{{\infty}}_{i = 1}$? Gross and Grupel showed this was not generally possible on the hypercube, by constructing non-isomorphic $\textit{locally p-biased}$ sets $\textit{X}$, so that for each vertex $\textit{v}$ the fraction of neighbours which is in $\textit{X}$ is exactly $\textit{p}$. Answering a question of Gross and Grupel, we construct uncountably many non-isomorphic partitions of $\mathbb{Z}$$^{k}$ into 2k parts such that every element of $\mathbb{Z}$$^{k}$ has exactly one neighbour in each part. As a result, we find $\textit{locally p-biased}$ sets for all $\textit{p = c/2n}$ with $\textit{c}$ $\in$ {0, ... , 2n}. In Chapter 5, we prove the complete graph case of the bunkbed conjecture. Given a graph G, let the bunkbed graph BB(G) be the graph G$\Box$K$_{2}$, i.e. the graph obtained from considering two copies of G and connecting equivalent vertices with an edge. The bunkbed conjecture posed by Kasteleyn in 1985 asserts the very intuitive statement that when considering percolation with uniform parameter p, we have $\mathbb{P}$(u$_{1}$ $\leftrightarrow$ v$_{1}$) $\geq$ $\mathbb{P}$(u$_{1}$ $\leftrightarrow$ v$_{2}$), i.e. a vertex has a higher probability of being connected to a vertex in the same copy of G than being connected to the equivalent vertex in the other copy of G. In Chapter 6, we consider the (t,r) broadcast domination number, a generalisation of the domination number in graphs. In this form of domination, we consider a set T $\subset$ V(G) of towers which broadcast at strength t, where broadcast strength decays linearly with distance in the graph. A set of towers is (t,r) broadcast dominating if every vertex in the graph receives at least r signal from all towers combined. More formally, the (t,r) broadcast domination number of a graph G is the minimal cardinality of a set T $\subset$ V(G) such that for every vertex v $\in$ V(G), we have $^{{\Sigma}}_{u {{\in}} T}$ max{t - d(u,v),0} $\geq$ r. Proving a conjecture by Drews, Harris, and Randolph, we establish that the minimal asymptotical density of (t,3) broadcasting subset of $\mathbb{Z}$$^{2}$ is the same as the minimal asymptotical density of a (t-1,1) broadcasting subset of $\mathbb{Z}$$^{2}$. In Chapter 7, we consider the eternal game chromatic number, a version of the game chromatic number in which the game continues after all vertices have been coloured. We show that with high probability $\chi$$^\infty_g$ (G$_{n,p}$) = (p/2 + o(1))n for odd n, and also for even n when p = 1/k for some k $\in$ $\mathbb{N}$. The upper bound applies for even n and any other value of p as well, but we conjecture in this case this upper bound is not sharp. Finally, we answer a question posed by Klostermeyer and Mendoza. In Chapter 8, we consider the bridge-burning cops and robbers game, a version of the game where after a robber moves over an edge, the edge is removed from the graph. Proving a generalization of a conjecture by Kinnersley and Peterson, we establish the asymptotically maximal capture time in this game for graphs with bridge-burning cops number at least three. In particular, we show that this maximal capture time grows as k$^{-O(k)}$n$^{k+2}$, where k $\geq$ 3 is the bridge burning cop number and n is the number of vertices of the graph

Marker-assisted optimization of an expert-based strategy for the acquisition of modern lettuce varieties to improve a genebank collection

To regularly improve the composition of the lettuce collection of the Centre for Genetic Resources, the Netherlands (CGN) with modern varieties, feedback from crop experts is used to select approximately 10% of the new material for incorporation in the collection. In the present study, assessments of six experts were compared to microsatellite data of 414 new varieties and 1408 existing accessions. Based on the microsatellite data, the extent to which the genetic diversity of the collection would be enriched (added value) was calculated for specific sets of new varieties. When individual assessments of experts were evaluated, the total added value of expert-based selections was not significantly higher compared to randomly chosen groups, except for a single expert. Unfamiliarity with new varieties was shown to be a crucial factor in the assessment of crop experts. According to the current acquisition protocol that seeks for consensus among experts, varieties are selected based on recommendations from at least three experts. This protocol also did not perform better than randomly chosen groups of new varieties. However, significantly better results were obtained with alternative protocols. It was concluded that breeding value was a more decisive criterion in the current acquisition protocol than maximal extension of the genetic diversity within the collection. A modified protocol addressing both commercial and diversity aspects was suggested in order to meet the demands of plant breeders as well as conservationist

To Serve and Conserve: strengthening germplasm evaluation to focus on users' needs

Powerpointpresentatie over het gebruik van genenbanken: focus op wat de gebruiker nodig heeft

Locality in Sumsets

Motivated by the Polynomial Freiman-Ruzsa (PFR) Conjecture, we develop a theory of locality in sumsets, with applications to John-type approximation and sets with small doubling. First we show that if $A \subset \mathbb{Z}$ with $|A+A| \le (1-\epsilon) 2^d |A|$ is non-degenerate then $A$ is covered by $O(2^d)$ translates of a $d$-dimensional generalised arithmetic progression ($d$-GAP) $P$ with $|P| \le O_{d,\epsilon}(|A|)$; thus we obtain one of the polynomial bounds required by PFR, under the non-degeneracy assumption that $A$ is not efficiently covered by $O_{d,\epsilon}(1)$ translates of a $(d-1)$-GAP. We also prove a stability result showing for any $\epsilon,\alpha>0$ that if $A \subset \mathbb{Z}$ with $|A+A| \le (2-\epsilon)2^d|A|$ is non-degenerate then some $A' \subset A$ with $|A'|>(1-\alpha)|A|$ is efficiently covered by either a $(d+1)$-GAP or $O_{\alpha}(1)$ translates of a $d$-GAP. This `dimension-free' bound for approximate covering makes for a stark contrast with exact covering, where the required number of translates grows exponentially with $d$. We further show that if $A \subset \mathbb{Z}$ is non-degenerate with $|A+A| \le (2^d + \ell)|A|$ and $\ell \le 0.1 \cdot 2^d$ then $A$ is covered by $\ell+1$ translates of a $d$-GAP $P$ with $|P| \le O_d(|A|)$; this is tight, in that $\ell+1$ cannot be replaced by any smaller number. The above results also hold for $A \subset \mathbb{R}^d$, replacing GAPs by a suitable common generalisation of GAPs and convex bodies. In this setting the non-degeneracy condition holds automatically, so we obtain essentially optimal bounds with no additional assumption on $A$. These results are all deduced from a unifying theory, in which we introduce a new intrinsic structural approximation of any set, which we call the `additive hull', and develop its theory via a refinement of Freiman's theorem with additional separation properties.Comment: 36 pages, comments welcom