Discrete Convex Functions on Graphs and Their Algorithmic Applications

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems

Palindromic Decompositions with Gaps and Errors

Identifying palindromes in sequences has been an interesting line of research in combinatorics on words and also in computational biology, after the discovery of the relation of palindromes in the DNA sequence with the HIV virus. Efficient algorithms for the factorization of sequences into palindromes and maximal palindromes have been devised in recent years. We extend these studies by allowing gaps in decompositions and errors in palindromes, and also imposing a lower bound to the length of acceptable palindromes. We first present an algorithm for obtaining a palindromic decomposition of a string of length n with the minimal total gap length in time O(n log n * g) and space O(n g), where g is the number of allowed gaps in the decomposition. We then consider a decomposition of the string in maximal \delta-palindromes (i.e. palindromes with \delta errors under the edit or Hamming distance) and g allowed gaps. We present an algorithm to obtain such a decomposition with the minimal total gap length in time O(n (g + \delta)) and space O(n g).Comment: accepted to CSR 201

Model for the hydration of non-polar compounds and polymers

We introduce an exactly solvable statistical-mechanical model of the hydration of non-polar compounds, based on grouping water molecules in clusters where hydrogen bonds and isotropic interactions occur; interactions between clusters are neglected. Analytical results show that an effective strengthening of hydrogen bonds in the presence of the solute, together with a geometric reorganization of water molecules, are enough to yield hydrophobic behavior. We extend our model to describe a non-polar homopolymer in aqueous solution, obtaining a clear evidence of both ``cold'' and ``warm'' swelling transitions. This suggests that our model could be relevant to describe some features of protein folding.Comment: REVTeX, 6 pages, 3 figure

Structured Sparsity: Discrete and Convex approaches

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional space. However, many solutions proposed nowadays do not leverage the true underlying structure. Recent results in CS extend the simple sparsity idea to more sophisticated {\em structured} sparsity models, which describe the interdependency between the nonzero components of a signal, allowing to increase the interpretability of the results and lead to better recovery performance. In order to better understand the impact of structured sparsity, in this chapter we analyze the connections between the discrete models and their convex relaxations, highlighting their relative advantages. We start with the general group sparse model and then elaborate on two important special cases: the dispersive and the hierarchical models. For each, we present the models in their discrete nature, discuss how to solve the ensuing discrete problems and then describe convex relaxations. We also consider more general structures as defined by set functions and present their convex proxies. Further, we discuss efficient optimization solutions for structured sparsity problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure

Rhizobium Promotes Non-Legumes Growth and Quality in Several Production Steps: Towards a Biofertilization of Edible Raw Vegetables Healthy for Humans

The biofertilization of crops with plant-growth-promoting microorganisms is currently considered as a healthy alternative to chemical fertilization. However, only microorganisms safe for humans can be used as biofertilizers, particularly in vegetables that are raw consumed, in order to avoid sanitary problems derived from the presence of pathogenic bacteria in the final products. In the present work we showed that Rhizobium strains colonize the roots of tomato and pepper plants promoting their growth in different production stages increasing yield and quality of seedlings and fruits. Our results confirmed those obtained in cereals and alimentary oil producing plants extending the number of non-legumes susceptible to be biofertilized with rhizobia to those whose fruits are raw consumed. This is a relevant conclusion since safety of rhizobia for human health has been demonstrated after several decades of legume inoculation ensuring that they are optimal bacteria for biofertilization

Inter- and intrachromosomal asynchrony of cell division cycle events in root meristem cells of Allium cepa: possible connection with gradient of cyclin B-like proteins

Alternate treatments of Allium cepa root meristems with hydroxyurea (HU) and caffeine give rise to extremely large and highly elongated cells with atypical images of mitotic divisions, including internuclear asynchrony and an unknown type of interchromosomal asynchrony observed during metaphase-to-anaphase transition. Another type of asynchrony that cannot depend solely on the increased length of cells was observed following long-term incubation of roots with HU. This kind of treatment revealed both cell nuclei entering premature mitosis and, for the first time, an uncommon form of mitotic abnormality manifested in a gradual condensation of chromatin (spanning from interphase to prometaphase). Immunocytochemical study of polykaryotic cells using anti-β tubulin antibodies revealed severe perturbations in the microtubular organization of preprophase bands. Quantitative immunofluorescence measurements of the control cells indicate that the level of cyclin B-like proteins reaches the maximum at the G2 to metaphase transition and then becomes reduced during later stages of mitosis. After long-term incubation with low doses of HU, the amount of cyclin B-like proteins considerably increases, and a significant number of elongated cells show gradients of these proteins spread along successive regions of the perinuclear cytoplasm. It is suggested that there may be a direct link between the effects of HU-mediated deceleration of S- and G2-phases and an enhanced concentration of cyclin B-like proteins. In consequence, the activation of cyclin B-CDK complexes gives rise to an abnormal pattern of premature mitotic chromosome condensation with biphasic nuclear structures having one part of chromatin decondensed, and the other part condensed

Selective phosphodiesterase inhibitors: a promising target for cognition enhancement

# The Author(s) 2008. This article is published with open access at Springerlink.com Rationale One of the major complaints most people face during aging is an impairment in cognitive functioning. This has a negative impact on the quality of daily life and is even more prominent in patients suffering from neurodegenerative and psychiatric disorders including Alzheimer’s disease, schizophrenia, and depression. So far, the majority of cognition enhancers are generally targeting one particular neurotransmitter system. However, recently phosphodiesterases (PDEs) have gained increased attention as a potential new target for cognition enhancement. Inhibition of PDEs increases the intracellular availability of the second messengers cGMP and/or cAMP. Objective The aim of this review was to provide an overvie

Combinatorial integer labeling theorems on finite sets with applications

Tucker’s well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {±1, ±2, · · · , ±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits a 1-dimensional simplex whose two vertices have opposite labels. In this paper, we are concerned with an arbitrary finite set D of integral vectors in the n-dimensional Euclidean space and an integer labeling that assigns to each element of D a label from the set {±1, ±2, · · · , ±n}. Using a constructive approach, we prove two combinatorial theorems of Tucker type. The theorems state that, under some mild conditions, there exists two integral vectors in D having opposite labels and being cell-connected in the sense that both belong to the set {0, 1} n +q for some integral vector q. These theorems are used to show in a constructive way the existence of an integral solution to a system of nonlinear equations under certain natural conditions. An economic application is provided