CONSTANS and the evolutionary origin of photoperiodic timing of flowering

A network of promoting and inhibiting pathways that respond to environmental and internal signals controls the flowering transition. The outcome of this regulatory network establishes, for any particular plant, the correct time of the year to flower. The photoperiod pathway channels inputs from light, day length, and the circadian clock to promote the floral transition. CONSTANS (CO) is a central regulator of this pathway, triggering the production of the mobile florigen hormone FT (FLOWERING LOCUS T) that induces flower differentiation. Because plant reproductive fitness is directly related to its capacity to flower at a precise time, the photoperiod pathway is present in all known plant species. Recent findings have stretched the evolutionary span of this photophase signal to unicellular algae, which show unexpected conserved characteristics with modern plant photoperiodic responses. In this review, a comparative description of the photoperiodic systems in algae and plants will be presented and a general role for the CO family of transcriptional activators proposed.Gobierno de Andalucía P08‐AGR‐03582Ministerio de Ciencia e Innovación CSIC‐200920I181, BIO2007‐6183

Galois Connections between Semimodules and Applications in Data Mining

In [1] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the standard Boolean carrier set. A fundamental result was missing there, namely the second half of the equivalent of the main theorem of Formal Concept Analysis. In this continuation we introduce the structural lattice of such generalised contexts, providing a limited equivalent to the main theorem of K-Formal Concept Analysis which allows to interpret the standard version as a privileged case in yet another direction. We motivate our results by providing instances of their use to analyse the confusion matrices of multiple-input multiple-output classifiers

Towards the algebraization of Formal Concept Analysis over complete dioids

Actas de: XVII Congreso Español sobre Tecnologías y Lógica Fuzzy (ESTYLF 2014). Zaragoza, 5-7 de febrero de 2014.Complete dioids are already complete residuated lattices. Formal contexts with entries in them generate Concept Lattices with the help of the polar maps. Previous work has already established the spectral nature of some formal concepts for contexts over certain kinds of dioids. This paper tries to raise the awareness that linear algebra over exotic semirings should be one place to look to understand the properties of FCA over L-lattices.FJVA was partially supported by EU FP7 project LiMoSINe (contract 288024) for this research. CPM was partially supported by the Spanish Government-Comisión Interministerial de Ciencia y Tecnología project 2011-268007/TEC.Publicad

Two Information-Theoretic Tools to Assess the Performance of Multi-class Classifiers

We develop two tools to analyze the behavior of multiple-class, or multi-class, classifiers by means of entropic measures on their confusion matrix or contingency table. First we obtain a balance equation on the entropies that captures interesting properties of the classifier. Second, by normalizing this balance equation we first obtain a 2-simplex in a three-dimensional entropy space and then the de Finetti entropy diagram or entropy triangle. We also give examples of the assessment of classifiers with these tools.Spanish Government-Comisión Interministerial de Ciencia y Tecnología projects 2008-06382/TEC and 2008-02473/TEC and the regional projects S-505/TIC/0223 (DGUI-CM) and CCG08-UC3M/TIC-4457 (Comunidad Autónoma de Madrid – UC3M)Publicad

The evaluation of data sources using multivariate entropy tools

We introduce from first principles an analysis of the information content of multivariate distributions as information sources. Specifically, we generalize a balance equation and a visualization device, the Entropy Triangle, for multivariate distributions and find notable differences with similar analyses done on joint distributions as models of information channels. As an example application, we extend a framework for the analysis of classifiers to also encompass the analysis of data sets. With such tools we analyze a handful of UCI machine learning task to start addressing the question of how well do datasets convey the information they are supposed to capture about the phenomena they stand for

Spectral Lattices of reducible matrices over completed idempotent semifields

Proceedings of: 10th International Conference on Concept Lattices and Their Applications. (CLA 2013). La Rochelle, France, October 15-18, 2013.Previous work has shown a relation between L-valued extensions of FCA and the spectra of some matrices related to L-valued contexts. We investigate the spectra of reducible matrices over completed idempotent semifields in the framework of dioids, naturally-ordered semirings, that encompass several of those extensions. Considering special sets of eigenvectors also brings out complete lattices in the picture and we argue that such structure may be more important than standard eigenspace structure for matrices over completed idempotent semifields.FJVA is supported by EU FP7 project LiMoSINe (contract 288024). CPM has been partially supported by the Spanish Government-Comisión Interministerial de Ciencia y Tecnología project TEC2011-26807 for this paper.Publicad

Four-fold Formal Concept Analysis based on Complete Idempotent Semifields

Formal Concept Analysis (FCA) is a well-known supervised boolean data-mining technique rooted in Lattice and Order Theory, that has several extensions to, e.g., fuzzy and idempotent semirings. At the heart of FCA lies a Galois connection between two powersets. In this paper we extend the FCA formalism to include all four Galois connections between four different semivectors spaces over idempotent semifields, at the same time. The result is K¯¯¯¯-four-fold Formal Concept Analysis (K¯¯¯¯-4FCA) where K¯¯¯¯ is the idempotent semifield biasing the analysis. Since complete idempotent semifields come in dually-ordered pairs—e.g., the complete max-plus and min-plus semirings—the basic construction shows dual-order-, row–column- and Galois-connection-induced dualities that appear simultaneously a number of times to provide the full spectrum of variability. Our results lead to a fundamental theorem of K¯¯¯¯-four-fold Formal Concept Analysis that properly defines quadrilattices as 4-tuples of (order-dually) isomorphic lattices of vectors and discuss its relevance vis-à-vis previous formal conceptual analyses and some affordances of their results

The Singular Value Decomposition over Completed Idempotent Semifields

In this paper, we provide a basic technique for Lattice Computing: an analogue of the Singular Value Decomposition for rectangular matrices over complete idempotent semifields (i-SVD). These algebras are already complete lattices and many of their instances—the complete schedule algebra or completed max-plus semifield, the tropical algebra, and the max-times algebra—are useful in a range of applications, e.g., morphological processing. We further the task of eliciting the relation between i-SVD and the extension of Formal Concept Analysis to complete idempotent semifields (K-FCA) started in a prior work. We find out that for a matrix with entries considered in a complete idempotent semifield, the Galois connection at the heart of K-FCA provides two basis of left- and right-singular vectors to choose from, for reconstructing the matrix. These are join-dense or meet-dense sets of object or attribute concepts of the concept lattice created by the connection, and they are almost surely not pairwise orthogonal. We conclude with an attempt analogue of the fundamental theorem of linear algebra that gathers all results and discuss it in the wider setting of matrix factorization.This research was funded by the Spanish Government-MinECo project TEC2017-84395-P and the Dept. of Research and Innovation of Madrid Regional Authority project EMPATIA-CM (Y2018/TCS-5046)

100% classification accuracy considered harmful: The normalized information transfer factor explains the accuracy paradox

The most widely spread measure of performance, accuracy, suffers from a paradox: predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy. Despite optimizing classification error rate, high accuracy models may fail to capture crucial information transfer in the classification task. We present evidence of this behavior by means of a combinatorial analysis where every possible contingency matrix of 2, 3 and 4 classes classifiers are depicted on the entropy triangle, a more reliable information-theoretic tool for classification assessment. Motivated by this, we develop from first principles a measure of classification performance that takes into consideration the information learned by classifiers. We are then able to obtain the entropy-modulated accuracy (EMA), a pessimistic estimate of the expected accuracy with the influence of the input distribution factored out, and the normalized information transfer factor (NIT), a measure of how efficient is the transmission of information from the input to the output set of classes. The EMA is a more natural measure of classification performance than accuracy when the heuristic to maximize is the transfer of information through the classifier instead of classification error count. The NIT factor measures the effectiveness of the learning process in classifiers and also makes it harder for them to "cheat" using techniques like specialization, while also promoting the interpretability of results. Their use is demonstrated in a mind reading task competition that aims at decoding the identity of a video stimulus based on magnetoencephalography recordings. We show how the EMA and the NIT factor reject rankings based in accuracy, choosing more meaningful and interpretable classifiers.Francisco José Valverde-Albacete has been partially supported by EU FP7 project LiMoSINe (contract 288024): www.limosine-project.eu Carmen Peláez Moreno has been partially supported by the Spanish Government-Comisión Interministerial de Ciencia y Tecnología project TEC2011–26807