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

Wiretapping a hidden network

We consider the problem of maximizing the probability of hitting a strategically chosen hidden virtual network by placing a wiretap on a single link of a communication network. This can be seen as a two-player win-lose (zero-sum) game that we call the wiretap game. The value of this game is the greatest probability that the wiretapper can secure for hitting the virtual network. The value is shown to equal the reciprocal of the strength of the underlying graph. We efficiently compute a unique partition of the edges of the graph, called the prime-partition, and find the set of pure strategies of the hider that are best responses against every maxmin strategy of the wiretapper. Using these special pure strategies of the hider, which we call omni-connected-spanning-subgraphs, we define a partial order on the elements of the prime-partition. From the partial order, we obtain a linear number of simple two-variable inequalities that define the maxmin-polytope, and a characterization of its extreme points. Our definition of the partial order allows us to find all equilibrium strategies of the wiretapper that minimize the number of pure best responses of the hider. Among these strategies, we efficiently compute the unique strategy that maximizes the least punishment that the hider incurs for playing a pure strategy that is not a best response. Finally, we show that this unique strategy is the nucleolus of the recently studied simple cooperative spanning connectivity game

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

Decomposition algorithms for submodular optimization with applications to parallel machine scheduling with controllable processing times

In this paper we present a decomposition algorithm for maximizing a linear function over a submodular polyhedron intersected with a box. Apart from this contribution to submodular optimization, our results extend the toolkit available in deterministic machine scheduling with controllable processing times. We demonstrate how this method can be applied to developing fast algorithms for minimizing total compression cost for preemptive schedules on parallel machines with respect to given release dates and a common deadline. Obtained scheduling algorithms are faster and easier to justify than those previously known in the scheduling literature

A Fluorescent Chromatophore Changes the Level of Fluorescence in a Reef Fish

Body coloration plays a major role in fish ecology and is predominantly generated using two principles: a) absorbance combined with reflection of the incoming light in pigment colors and b) scatter, refraction, diffraction and interference in structural colors. Poikilotherms, and especially fishes possess several cell types, so-called chromatophores, which employ either of these principles. Together, they generate the dynamic, multi-color patterns used in communication and camouflage. Several chromatophore types possess motile organelles, which enable rapid changes in coloration. Recently, we described red fluorescence in a number of marine fish and argued that it may be used for private communication in an environment devoid of red. Here, we describe the discovery of a chromatophore in fishes that regulates the distribution of fluorescent pigments in parts of the skin. These cells have a dendritic shape and contain motile fluorescent particles. We show experimentally that the fluorescent particles can be aggregated or dispersed through hormonal and nervous control. This is the first description of a stable and natural cytoskeleton-related fluorescence control mechanism in vertebrate cells. Its nervous control supports suggestions that fluorescence could act as a context-dependent signal in some marine fish species and encourages further research in this field. The fluorescent substance is stable under different chemical conditions and shows no discernible bleaching under strong, constant illumination

Phosphodiesterase 10A Upregulation Contributes to Pulmonary Vascular Remodeling

Phosphodiesterases (PDEs) modulate the cellular proliferation involved in the pathophysiology of pulmonary hypertension (PH) by hydrolyzing cAMP and cGMP. The present study was designed to determine whether any of the recently identified PDEs (PDE7-PDE11) contribute to progressive pulmonary vascular remodeling in PH. All in vitro experiments were performed with lung tissue or pulmonary arterial smooth muscle cells (PASMCs) obtained from control rats or monocrotaline (MCT)-induced pulmonary hypertensive (MCT-PH) rats, and we examined the effects of the PDE10 inhibitor papaverine (Pap) and specific small interfering RNA (siRNA). In addition, papaverine was administrated to MCT-induced PH rats from day 21 to day 35 by continuous intravenous infusion to examine the in vivo effects of PDE10A inhibition. We found that PDE10A was predominantly present in the lung vasculature, and the mRNA, protein, and activity levels of PDE10A were all significantly increased in MCT PASMCs compared with control PASMCs. Papaverine and PDE10A siRNA induced an accumulation of intracellular cAMP, activated cAMP response element binding protein and attenuated PASMC proliferation. Intravenous infusion of papaverine in MCT-PH rats resulted in a 40%–50% attenuation of the effects on pulmonary hypertensive hemodynamic parameters and pulmonary vascular remodeling. The present study is the first to demonstrate a central role of PDE10A in progressive pulmonary vascular remodeling, and the results suggest a novel therapeutic approach for the treatment of PH

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

Subcellular Location of PKA Controls Striatal Plasticity: Stochastic Simulations in Spiny Dendrites

Dopamine release in the striatum has been implicated in various forms of reward dependent learning. Dopamine leads to production of cAMP and activation of protein kinase A (PKA), which are involved in striatal synaptic plasticity and learning. PKA and its protein targets are not diffusely located throughout the neuron, but are confined to various subcellular compartments by anchoring molecules such as A-Kinase Anchoring Proteins (AKAPs). Experiments have shown that blocking the interaction of PKA with AKAPs disrupts its subcellular location and prevents LTP in the hippocampus and striatum; however, these experiments have not revealed whether the critical function of anchoring is to locate PKA near the cAMP that activates it or near its targets, such as AMPA receptors located in the post-synaptic density. We have developed a large scale stochastic reaction-diffusion model of signaling pathways in a medium spiny projection neuron dendrite with spines, based on published biochemical measurements, to investigate this question and to evaluate whether dopamine signaling exhibits spatial specificity post-synaptically. The model was stimulated with dopamine pulses mimicking those recorded in response to reward. Simulations show that PKA colocalization with adenylate cyclase, either in the spine head or in the dendrite, leads to greater phosphorylation of DARPP-32 Thr34 and AMPA receptor GluA1 Ser845 than when PKA is anchored away from adenylate cyclase. Simulations further demonstrate that though cAMP exhibits a strong spatial gradient, diffusible DARPP-32 facilitates the spread of PKA activity, suggesting that additional inactivation mechanisms are required to produce spatial specificity of PKA activity

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