Valid inequalities and complete characterizations of the 2-domination and P3-hull number polytope

Given a graph G = (V;E), a subset S V is 2-dominating if every vertex in S has at least two neighbors in S. The minimum cardinality of such a set is called the 2-domination number of G. Consider a process in discrete time that, starting with an initial set of marked vertices S, at each step marks all unmarked vertices having two marked neighbors. In such a process, the minimum number of initial vertices in S such that eventually all vertices are marked is called the P3-hull number of G. In this work, we explore a polyhedral relation between these two parameters and, in addition, we provide new families of valid inequalities for the associated polytopes. Finally, we give explicit descriptions of the polytopes associated to these problems when G is a path, a cycle, a complete graph, or a tree

An integer programming approach for the 2-class single-group classification problem

Two sets XB, XR ⊆ Rd are linearly separable if their convex hulls are disjoint, implying that a hyperplane separating XB from XR exists. Such a hyperplane provides a method for classifying new points, according to the side of the hyperplane in which the new points lie. In this work we consider a particular case of the 2-class classification problem, which asks to select the maximum number of points from XB and XR in such a way that the selected points are linearly separable. We present an integer programming formulation for this problem, explore valid inequalities for the associated polytope, and develop a cutting plane approach coupled with a lazy-constraints scheme.Fil: Corrêa, Ricardo C.. Universidade Federal Rural Do Rio de Janeiro; BrasilFil: Blaum, Manuela. Universidad Nacional de General Sarmiento; ArgentinaFil: Marenco, Javier Leonardo. Universidad Nacional de General Sarmiento; ArgentinaFil: Koch, Ivo Valerio. Universidad Nacional de General Sarmiento; ArgentinaFil: Mydlarz, Marcelo. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaLatin-American Algorithms, Graphs and Optimization Symposium (LAGOS 2019)Belo HorizonteBrasilCoordenação de Aperfeiçoamento de Pessoal de Nivel SuperiorConselho Nacional de Desenvolvimento Científico e Técnologico do BrasilUniversidade Federal de Minas Gerai

Un estudio poliedral del problema de cálculo del P3-hull number de un grafo

En este trabajo comenzamos un estudio poliedral de este problema, a partir de una formulación natural del problema como un modelo de programación lineal entera. Estudiamos la dimensión del poliedro asociado y determinamos bajo qué condiciones las restricciones del modelo definen facetas de este poliedro. Además, estudiamos familias de desigualdades válidas y analizamos bajo qué condiciones estas desigualdades definen facetas de este poliedro.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Un estudio poliedral del problema de cálculo del P3-hull number de un grafo

En este trabajo comenzamos un estudio poliedral de este problema, a partir de una formulación natural del problema como un modelo de programación lineal entera. Estudiamos la dimensión del poliedro asociado y determinamos bajo qué condiciones las restricciones del modelo definen facetas de este poliedro. Además, estudiamos familias de desigualdades válidas y analizamos bajo qué condiciones estas desigualdades definen facetas de este poliedro.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Avances en el estudio poliedral del cálculo del P₃-hull number de un grafo

Calcular el hull number de un grafo es un problema NP-hard, y ha sido objeto de interés recientemente por parte de la comunidad de optimización combinatoriaSociedad Argentina de Informática e Investigación Operativa (SADIO

Avances en el estudio poliedral del cálculo del P₃-hull number de un grafo

Calcular el hull number de un grafo es un problema NP-hard, y ha sido objeto de interés recientemente por parte de la comunidad de optimización combinatoriaSociedad Argentina de Informática e Investigación Operativa (SADIO

Chemical and Physical Characterisation of Macroaggregated Human Serum Albumin: Strength and Specificity of Bonds with 99mTc and 68Ga

Background: Macroaggregated human serum albumin (MAA) properties are widely used in nuclear medicine, labelled with 99mTc. The aim of this study is to improve the knowledge about the morphology, size, dimension and physical–chemical characteristics of MAA and their bond with 99mTc and 68Ga. Methods: Commercial kits of MAA (Pulmocis®) were used. Characterisation through experiments based on SEM, DLS and Stokes’ Law were carried out. In vitro experiments for Langmuir isotherms and pH studies on radiolabelling were performed and the stability of the radiometal complex was verified through competition reactions. Results: The study settles the MAA dimension within the range 43–51 μm. The Langmuir isotherm reveals for [99mTc]MAA: Bmax (46.32), h (2.36); for [68Ga]MAA: Bmax (44.54), h (0.893). Dual labelling reveals that MAA does not discriminate different radioisotopes. Experiments on pH placed the optimal pH for labelling with 99mTc at 6. Conclusion: Radiolabelling of MAA is possible with high efficiency. The nondiscriminatory MAA bonds make this drug suitable for radiolabelling with different radioisotopes or for dual labelling. This finding illustrates the need to continue investigating MAA chemical and physical characteristics to allow for secure labelling with different isotopes

99mTc-68Ga-ICG-Labelled Macroaggregates and Nanocolloids of Human Serum Albumin: Synthesis Procedures of a Trimodal Imaging Agent Using Commercial Kits

Recent developments in sentinel lymph node (SLN) and radio occult lesion localization (ROLL) highlight the need for a multimodal contrast agent, providing better presurgical PET imaging and improved intraoperative mapping thanks to fluorescence detection. For this reason, we have studied a trimodal SLN/ROLL targeting agent (99mTc-68Ga-ICG) with commercially available kits of macroaggregated or nanocolloidal albumin (MA/NC-HSA). 68Ga PET imaging does provide better spatial resolution and makes it possible to predict signal intensity during surgery. The presence of 99mTc assesses the efficacy of these compounds in vitro and also during the surgery procedure. The aim of this study was to optimise the labelling and tagging of these two radiopharmaceuticals and assess their yields and stability. Kits of MA/NC-HSA particles (Pulmocis® and NanoAlbumon®) were used for sequential radiolabelling with 99mTc and 68Ga. Fluorescent tagging was performed using indocyanine green, a tricarbocyanine dye. The ITLC radiochemical purity of the trilabelled MA/NC-HSA was >95%. Fluorescent purity was measured by scanning the strips with a PhotoDynamicEye probe. Finally, in vitro stability tests, performed with DTPA and human serum solutions, assessed the efficacy of fluorescent tagging and radiolabelling