On the monoids of transformations that preserve the order and a uniform partition

In this article we consider the monoid O(mxn) of all order-preserving full transformations on a chain with mn elements that preserve a uniformm-partition and its submonoids O(mxn)(+) and O(mxn)(-) of all extensive transformations and of all co-extensive transformations, respectively. We determine their ranks and construct a bilateral semidirect product decomposition of O(mxn) in terms of O(mxn)(-) and O(mxn)(+).

Cork industry wastewater partition by ultra/nanofiltration: A biodegradation and valorisation study

Wastewater from cork processing industry present high levels of organic and phenolic compounds, such as tannins, with a low biodegradability and a significant toxicity. These compounds are not readily removed by conventional municipal wastewater treatment, which is largely based on primary sedimentation followed by biological treatment. The purpose of this work is to study the biodegradability of different cork wastewater fractions, obtained through membrane separation, in order to assess its potential for biological treatment and having in view its valorisation through tannins recovery, which could be applied in other industries. Various ultrafiltration and nanofiltration membranes where used, with molecular weight cut-offs (MWCO) ranging from 0.125 to 91 kDa. The wastewater and the different permeated fractions were analyzed in terms of Total Organic Carbon (TOC), Chemical Oxygen Demand (COD), Biochemical Oxygen Demand (BOD), Total Phenols (TP), Tannins, Color, pH and Conductivity. Results for the wastewater shown that it is characterized by a high organic content (670.5-1056.8 mg TOC/L, 2285-2604 mg COD/L, 1000-1225 mg BOD/L), a relatively low biodegradability (0.35-0.38 for BODs/COD and 0.44-0.47 for BOD20/COD) and a high content of phenols (360-410 mg tannic acid/L) and tannins (250-270 mg tannic acid/L). The results for the wastewater fractions shown a general decrease on the pollutant content of permeates, and an increase of its biodegradability, with the decrease of the membrane MWCO applied. Particularly, the permeated fraction from the membrane MWCO of 3.8 kDa, presented a favourable index of biodegradability (0.8) and a minimized phenols toxicity that enables it to undergo a biological treatment and so, to be treated in a municipal wastewater treatment plant. Also, within the perspective of valorisation, the rejected fraction obtained through this membrane MWCO may have a significant potential for tannins recovery. Permeated fractions from membranes with MWCO lower than 3.8 kDa, presented a particularly significant decline of organic matter and phenols, enabling this permeates to be reused in the cork processing and so, representing an interesting perspective of zero discharge for the cork industry, with evident environmental and economic advantages. (C) 2010 Elsevier Ltd. All rights reserved.

On the ranks of certain monoids of transformations that preserve a uniform partition

The rank of a semigroup, an important and relevant concept in Semigroup Theory, is the cardinality of a least-size generating set. Semigroups of transformations that preserve or reverse the order or the orientation as well as semigroups of transformations preserving an equivalence relation have been widely studied over the past decades by many authors. The purpose of this article is to compute the ranks of the monoid

The cardinal of various monoids of transformations that preserve a uniform partition

In this paper we give formulas for the number of elements of the monoids ORm x n of all full transformations on it finite chain with tun elements that preserve it uniform m-partition and preserve or reverse the orientation and for its submonoids ODm x n of all order-preserving or order-reversing elements, OPm x n of all orientation-preserving elements, O-m x n of all order-preserving elements, O-m x n(+) of all extensive order-preserving elements and O-m x n(-) of all co-extensive order-preserving elements.

Short-term Feature Space and Music Genre Classification

In music genre classification, most approaches rely on statistical characteristics of low-level features computed on short audio frames. In these methods, it is implicitly considered that frames carry equally relevant information loads and that either individual frames, or distributions thereof, somehow capture the specificities of each genre. In this paper we study the representation space defined by short-term audio features with respect to class boundaries, and compare different processing techniques to partition this space. These partitions are evaluated in terms of accuracy on two genre classification tasks, with several types of classifiers. Experiments show that a randomized and unsupervised partition of the space, used in conjunction with a Markov Model classifier lead to accuracies comparable to the state of the art. We also show that unsupervised partitions of the space tend to create less hubs.

Shear-induced lamellar phase of an ionic liquid crystal at room temperature

The phase behaviour of a number of N-alkylimidazolium salts was studied using polarizing optical microscopy, differential scanning calorimetry and X-ray diffraction. Two of these compounds exhibit lamellar mesophases at temperatures above 50 degrees C. In these systems, the liquid crystalline behaviour may be induced at room temperature by shear. Sheared films of these materials, observed between crossed polarisers, have a morphology that is typical of (wet) liquid foams: they partition into dark domains separated by brighter (birefringent) walls, which are approximately arcs of circle and meet at "Plateau borders" with three or more sides. Where walls meet three at a time, they do so at approximately 120 degrees angles. These patterns coarsen with time and both T1 and T2 processes have been observed, as in foams. The time evolution of domains is also consistent with von Neumann's law. We conjecture that the bright walls are regions of high concentration of defects produced by shear, and that the system is dominated by the interfacial tension between these walls and the uniform domains. The control of self-organised monodomains, as observed in these systems, is expected to play an important role in potential applications.

How foam-like is the shear-induced lamellar phase of an ionic liquid crystal?

Philosophical Magazine Letters Volume 88, Issue 9-10, 2008 Special Issue: Solid and Liquid Foams. In commemoration of Manuel Amaral Fortes

Enhancing the selection of a model-based clustering with external categorical variables

In cluster analysis, it can be useful to interpret the partition built from the data in the light of external categorical variables which are not directly involved to cluster the data. An approach is proposed in the model-based clustering context to select a number of clusters which both fits the data well and takes advantage of the potential illustrative ability of the external variables. This approach makes use of the integrated joint likelihood of the data and the partitions at hand, namely the model-based partition and the partitions associated to the external variables. It is noteworthy that each mixture model is fitted by the maximum likelihood methodology to the data, excluding the external variables which are used to select a relevant mixture model only. Numerical experiments illustrate the promising behaviour of the derived criterion. © 2014 Springer-Verlag Berlin Heidelberg.

Probabilistic consensus clustering using evidence accumulation

Clustering ensemble methods produce a consensus partition of a set of data points by combining the results of a collection of base clustering algorithms. In the evidence accumulation clustering (EAC) paradigm, the clustering ensemble is transformed into a pairwise co-association matrix, thus avoiding the label correspondence problem, which is intrinsic to other clustering ensemble schemes. In this paper, we propose a consensus clustering approach based on the EAC paradigm, which is not limited to crisp partitions and fully exploits the nature of the co-association matrix. Our solution determines probabilistic assignments of data points to clusters by minimizing a Bregman divergence between the observed co-association frequencies and the corresponding co-occurrence probabilities expressed as functions of the unknown assignments. We additionally propose an optimization algorithm to find a solution under any double-convex Bregman divergence. Experiments on both synthetic and real benchmark data show the effectiveness of the proposed approach.

Enhancing the selection of a model-based clustering with external categorical variables

In cluster analysis, it can be useful to interpret the partition built from the data in the light of external categorical variables which are not directly involved to cluster the data. An approach is proposed in the model-based clustering context to select a number of clusters which both fits the data well and takes advantage of the potential illustrative ability of the external variables. This approach makes use of the integrated joint likelihood of the data and the partitions at hand, namely the model-based partition and the partitions associated to the external variables. It is noteworthy that each mixture model is fitted by the maximum likelihood methodology to the data, excluding the external variables which are used to select a relevant mixture model only. Numerical experiments illustrate the promising behaviour of the derived criterion.

A MAP approach to evidence accumulation clustering

The Evidence Accumulation Clustering (EAC) paradigm is a clustering ensemble method which derives a consensus partition from a collection of base clusterings obtained using different algorithms. It collects from the partitions in the ensemble a set of pairwise observations about the co-occurrence of objects in a same cluster and it uses these co-occurrence statistics to derive a similarity matrix, referred to as co-association matrix. The Probabilistic Evidence Accumulation for Clustering Ensembles (PEACE) algorithm is a principled approach for the extraction of a consensus clustering from the observations encoded in the co-association matrix based on a probabilistic model for the co-association matrix parameterized by the unknown assignments of objects to clusters. In this paper we extend the PEACE algorithm by deriving a consensus solution according to a MAP approach with Dirichlet priors defined for the unknown probabilistic cluster assignments. In particular, we study the positive regularization effect of Dirichlet priors on the final consensus solution with both synthetic and real benchmark data.