Multi-dimensional Boltzmann Sampling of Languages

This paper addresses the uniform random generation of words from a context-free language (over an alphabet of size $k$), while constraining every letter to a targeted frequency of occurrence. Our approach consists in a multidimensional extension of Boltzmann samplers \cite{Duchon2004}. We show that, under mostly \emph{strong-connectivity} hypotheses, our samplers return a word of size in $[(1-\varepsilon)n, (1+\varepsilon)n]$ and exact frequency in $\mathcal{O}(n^{1+k/2})$ expected time. Moreover, if we accept tolerance intervals of width in $\Omega(\sqrt{n})$ for the number of occurrences of each letters, our samplers perform an approximate-size generation of words in expected $\mathcal{O}(n)$ time. We illustrate these techniques on the generation of Tetris tessellations with uniform statistics in the different types of tetraminoes.Comment: 12p

Organic farming values in Switzerland – results of a focus group study

Eight focus group discussions, conducted in 2004 and 2005, about ethical values among established and recently converted organic producers (mountain and lowland area) and other stakeholders in Switzerland are summarised. The aim was to contrib-ute to the elaboration of principles for the new EU regulation for organic food and farming as part of the EU Organic-Revision project. The participants’ values were contrasted with the four new principles of organic production of IFOAM (International Federation of Organic Agriculture Movements). Health and ecological sustainability were key issues. The producers saw secure livelihood, the maintenance of their family farm, authenticity, animal welfare and farming with nature as major issues. The sys-tem approach was important for other stakeholders. The major value conflicts were seen to arise from conventionalization and globalisation of the organic agriculture sector. Another central discussion point was the overregulation and inspection. Ethical values and principles should play a more important role in standard setting and trade

Polynomial tuning of multiparametric combinatorial samplers

Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like structures. In their multiparametric variants, these samplers allow to control the profile of expected values corresponding to multiple combinatorial parameters. One can control, for instance, the number of leaves, profile of node degrees in trees or the number of certain subpatterns in strings. However, such a flexible control requires an additional non-trivial tuning procedure. In this paper, we propose an efficient polynomial-time, with respect to the number of tuned parameters, tuning algorithm based on convex optimisation techniques. Finally, we illustrate the efficiency of our approach using several applications of rational, algebraic and P\'olya structures including polyomino tilings with prescribed tile frequencies, planar trees with a given specific node degree distribution, and weighted partitions.Comment: Extended abstract, accepted to ANALCO2018. 20 pages, 6 figures, colours. Implementation and examples are available at [1] https://github.com/maciej-bendkowski/boltzmann-brain [2] https://github.com/maciej-bendkowski/multiparametric-combinatorial-sampler

A Quantitative Study of Pure Parallel Processes

In this paper, we study the interleaving -- or pure merge -- operator that most often characterizes parallelism in concurrency theory. This operator is a principal cause of the so-called combinatorial explosion that makes very hard - at least from the point of view of computational complexity - the analysis of process behaviours e.g. by model-checking. The originality of our approach is to study this combinatorial explosion phenomenon on average, relying on advanced analytic combinatorics techniques. We study various measures that contribute to a better understanding of the process behaviours represented as plane rooted trees: the number of runs (corresponding to the width of the trees), the expected total size of the trees as well as their overall shape. Two practical outcomes of our quantitative study are also presented: (1) a linear-time algorithm to compute the probability of a concurrent run prefix, and (2) an efficient algorithm for uniform random sampling of concurrent runs. These provide interesting responses to the combinatorial explosion problem

Random sampling of plane partitions

This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are slightly superlinear: the complexity is $O(n (\ln n)^3)$ in approximate-size sampling and $O(n^{4/3})$ in exact-size sampling (under a real-arithmetic computation model). To our knowledge, these are the first polynomial-time samplers for plane partitions according to the size (there exist polynomial-time samplers of another type, which draw plane partitions that fit inside a fixed bounding box). The same principles yield efficient samplers for $(a\times b)$-boxed plane partitions (plane partitions with two dimensions bounded), and for skew plane partitions. The random samplers allow us to perform simulations and observe limit shapes and frozen boundaries, which have been analysed recently by Cerf and Kenyon for plane partitions, and by Okounkov and Reshetikhin for skew plane partitions.Comment: 23 page

Stochastic Flips on Two-letter Words

This paper introduces a simple Markov process inspired by the problem of quasicrystal growth. It acts over two-letter words by randomly performing \emph{flips}, a local transformation which exchanges two consecutive different letters. More precisely, only the flips which do not increase the number of pairs of consecutive identical letters are allowed. Fixed-points of such a process thus perfectly alternate different letters. We show that the expected number of flips to converge towards a fixed-point is bounded by $O(n^3)$ in the worst-case and by $O(n^{5/2}\ln{n})$ in the average-case, where $n$ denotes the length of the initial word.Comment: ANALCO'1

Focus groups of value concepts of producers: National Report Switzerland

The Organic Revision project was funded by the EU with the aim of supporting the further development of the EU Regulation 2092/91 on organic production. As part of the project focus groups were run in five European countries on value concepts of organic producers and other stakeholders, during 2004-2005. The project aims to provide an overview of values held among organic stakeholders, and of similarities and differences among the various national and private organic standards. In Switzerland, three group sessions were held with established organic farmers, two groups with newly converted organic farmers, one group involved experts from BIO SUISSE and one group was conducted with students from Agronomy, Environmental Sciences and Geography faculties of Zurich. The following conclusions were reached: Almost all participants were engaged in organic agriculture based on a certain believe or because they just like organic farming. Not only farmers had strong concerns with regard to the current development. The discussion about the basic values and the over-arching principles of organic agriculture were seen as very positive and a move in the right direction. The health of the ecosystem were in the discussions several times a fundamental value. Fair trading conditions were seen for many participants as a core issue. The producers did see the maintenance of their family farm and the farm succession as major issue. Many farmers were against an industrialisation of agriculture and against a too strong commercialisation of their products. Several farmers and several groups mentioned the problem of the lack of solidarity between farmers. Solidarity should get more importance in the future. Several farmers wished that there will be better cooperation between farmers and market actors as well as a better common strategy with a clear concept. Another issue was a truthful and careful processing, which is also for farmers very relevant. The farmers as well as the experts found that the added value of the production, the ideologic content of the products, and as well as the special intrinsic quality of the products are very important. Furthermore farmers and experts were in favour of “100 % entirely supply and market chains with only organic product, where not only the producers but also the trader and sales staff is convinced of organic agriculture. Many producers found that the communication with costumers, in particular public relation, will be important to survive on a competitive market and must be improved. A secure livelihood, surviving on he market and the strong workload were for many producers a major issues. Another central discussion point was the overregulation and inspection. Not only the producers but all main actors wished that the standard/rules are more comprehensive and the inspection work less bureaucratic. This issue is highly relevant not only for organic farmers. Experts saw a potential for an adaptation of the standards. In particular the health of the Ecosystem and the regionality are seen as key topics