Medians of discrete sets according to a linear distance

l'URL de l'article publié est http://www.springerlink.com/link.asp?id=9rukhuabxp8abkweIn this paper, we present some results concerning the median points of a discrete set according to a distance defined by means of two directions p and q. We describe a local characterization of the median points and show how these points can be determined from the projections of the discrete set along directions p and q. We prove that the discrete sets having some connectivity properties have at most four median points according to a linear distance, and if there are four median points they form a parallelogram. Finally, we show that the 4-connected sets which are convex along the diagonal directions contain their median points along these directions

Approximate X-rays reconstruction of special lattice sets

Sometimes the inaccuracy of the measurements of the X-rays can give rise to an inconsistent reconstruction problem. In this paper we address the problem of reconstructing special lattice sets in Z2 from their approximate X-rays in a finite number of prescribed lattice directions. The class of "strongly Q-convex sets" is taken into consideration and a polynomial time algorithm for reconstructing members of that class with line sums having possibly some bounded differences with the given X-ray values is provided. In particular, when these differences are zero, the algorithm exactly reconstructs any set. As a result, this algorithm can also be used to reconstruct convex subsets of Z2 from their exact X-rays in a finite set of suitable prescribed lattice directions

The number of convex polyominoes reconstructible from their orthogonal projections

AbstractMany problems of computer-aided tomography, pattern recognition, image processing and data compression involve a reconstruction of bidimensional discrete sets from their projections. [3–5,10,12,16,17]. The main difficulty involved in reconstructing a set Λ starting out from its orthogonal projections (V,H) is the ‘ambiguity’ arising from the fact that, in some cases, many different sets have the same projections (V,H). In this paper, we study this problem of ambiguity with respect to convex polyominoes, a class of bidimensional discrete sets that satisfy some connection properties similar to those used by some reconstruction algorithms. We determine an upper and lower bound to the maximum number of convex polyominoes having the same orthogonal projections (V,H), with V ∈ Nn and H ∈ Nm. We prove that under these connection conditions, the ambiguity is sometimes exponential. We also define a construction in order to obtain some convex polyominoes having the same orthogonal projections

Permutations avoiding an increasing number of length-increasing forbidden subsequences

A permutation π is said to be τ -avoiding if it does not contain any subsequence having all the same pairwise comparisons as τ . This paper concerns the characterization and enumeration of permutations which avoid a set F^j of subsequences increasing both in number and in length at the same time. Let F^j be the set of subsequences of the form σ (j+1)(j+2), σ being any permutation on \1,...,j\. For j=1 the only subsequence in F^1 is 123 and the 123-avoiding permutations are enumerated by the Catalan numbers; for j=2 the subsequences in F^2 are 1234 2134 and the (1234,2134)avoiding permutations are enumerated by the Schröder numbers; for each other value of j greater than 2 the subsequences in F^j are j! and their length is (j+2) the permutations avoiding these j! subsequences are enumerated by a number sequence \a_n\ such that C_n ≤ a_n ≤ n!, C_n being the nth Catalan number. For each j we determine the generating function of permutations avoiding the subsequences in F^j according to the length, to the number of left minima and of non-inversions

Re-use of wastewater for a sustainable forest production and climate change mitigation under arid environments

Over the last decades biotic and abiotic constrains together with human actions are determining a substantial environmental pressure, particularly in dry lands as the south of the Mediterranean region. From very long time, indeed, simultaneous drivers such as demographic growth, climate change and socio-economic factors are weakening the previous homeostasis between human needs and natural resources on the regional scale.Resulting pressures are determining environmental degradation and increase of desertification risk for the arid and semiarid lands. Water quality and availability are both crucial points limiting people well-being and livelihoods in the same context. Scarcity of fresh water and heavy and mismanaged production of wastewater are the main factors affecting water resources. Increasing pollution of soil and ground waters reduces the possibility of sustainable development of local communities with relevant social consequences. The FAO's supporting program in north Africa aims to: a) develop new and cheaper phytotechnologies (e.g. constructed wetland system; innovative treatment system for reuse of waste water for fertigation); b) treat wastewater for water quality protection; c) promote land recovery by means of sustainable multipurpose forestry; d) adopt bioengineering interventions to stop slopes erosion and protect urban, and semi-urban infrastructures; e) create pilot demonstrative areas to test multi-purpose sustainable agroforestry systems. Within this frame, an integrated approach was designed to promote innovative sustainable water management and multipurpose forestry, in order to mitigate the effects of climate change, promote land recovery, and improve the livelihoods of local population. The present paper aims to provide an overview of the FAO project GCP/RAB/013/ITA. Particularly, two pilot studies are shown and discussed

Tomografia discreta: ricostruzione di figure digitali dalle loro proiezioni

Dottorato di ricerca in informatica. 8. cicloConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro,7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Discrete Mathematics and Theoretical Computer Science Proceedings AA (DM-CCG), 2001, 133–144 A Bijection for Directed-Convex Polyominoes

In this paper we consider two classes of lattice paths on the plane which use north, east, south, and west unitary steps, beginning and ending at 0¡0¢. We enumerate them according to the number of steps by means of bijective arguments; in particular, we apply the cycle lemma. Then, using these results, we provide a bijective proof for the number of directed-convex polyominoes having a fixed number of rows and columns