Message passing for the coloring problem: Gallager meets Alon and Kahale

Message passing algorithms are popular in many combinatorial optimization problems. For example, experimental results show that {\em survey propagation} (a certain message passing algorithm) is effective in finding proper $k$-colorings of random graphs in the near-threshold regime. In 1962 Gallager introduced the concept of Low Density Parity Check (LDPC) codes, and suggested a simple decoding algorithm based on message passing. In 1994 Alon and Kahale exhibited a coloring algorithm and proved its usefulness for finding a $k$-coloring of graphs drawn from a certain planted-solution distribution over $k$-colorable graphs. In this work we show an interpretation of Alon and Kahale's coloring algorithm in light of Gallager's decoding algorithm, thus showing a connection between the two problems - coloring and decoding. This also provides a rigorous evidence for the usefulness of the message passing paradigm for the graph coloring problem. Our techniques can be applied to several other combinatorial optimization problems and networking-related issues.Comment: 11 page

Hitting time results for Maker-Breaker games

We study Maker-Breaker games played on the edge set of a random graph. Specifically, we consider the random graph process and analyze the first time in a typical random graph process that Maker starts having a winning strategy for his final graph to admit some property \mP. We focus on three natural properties for Maker's graph, namely being $k$-vertex-connected, admitting a perfect matching, and being Hamiltonian. We prove the following optimal hitting time results: with high probability Maker wins the $k$-vertex connectivity game exactly at the time the random graph process first reaches minimum degree $2k$; with high probability Maker wins the perfect matching game exactly at the time the random graph process first reaches minimum degree $2$; with high probability Maker wins the Hamiltonicity game exactly at the time the random graph process first reaches minimum degree $4$. The latter two statements settle conjectures of Stojakovi\'{c} and Szab\'{o}.Comment: 24 page

Teorizando la inmunoinihibición y la inhibición del factor de necrosis tumoral (TNF) en la autoinmunidad

This article analyses the biochemical object of tnf inhibitors from the perspective of living with an autoimmune disease. The author tries to tease out how the concept of immune inhibition is used in tandem with the biochemical object of tnf inhibitors to dominate in defining and narrating what health and disease, normal and pathological, cure and healing can mean in the context of autoimmune bodies. Specifically, and within the ‘pathological’ framework of autoimmune diseases, the pharmacological treatment of tnf (tumour necrosis factor) inhibition is designed to suppress the ‘overly’ active immune system, thus acting as a negative or suppressing biochemical agent aimed at putting the ‘malfunctioning’ immune system back in balance. As can be seen in the current conjuncture, tnf inhibitors officially —and governmentally— place those taking them in a risk group, as they 'lower' their overall bodily immunity and make them more vulnerable to infectious diseases, while stabilizing their patho-logical, ‘over’-immune uninhibited condition. Part personal narrative of being diagnosed with an autoimmune condition, part speculative autoimmune theory inspired by such a diagnosis, the article ultimately calls for a different form of embodiment that is neither negative nor affirmative, and yet is resistant even to itself.En este artículo se analizan los inhibidores del factor de necrosis tumoral (tnf) como objeto bioquímico desde la perspectiva de la vivencia con una enfermedad autoinmune. El artículo trata de desentrañar cómo el concepto de inmunoinhibición se usa junto con los inhibidores de tnf como objeto bioquímico para definir y narrar lo que puede significar la salud y la enfermedad, lo normal y lo patológico, la curación y la sanación en el contexto de cuerpos autoinmunes. En concreto, y dentro del marco patológico de las enfermedades autoinmunes, el tratamiento farmacológico de inhibición del tnf (factor de necrosis tumoral) está diseñado para suprimir el sistema inmunitario demasiado activo, actuando así como un agente bioquímico negativo o supresor destinado a reequilibrar el mal funcionamiento del sistema inmunitario. Como puede verse en la coyuntura actual, los fármacos inhibidores del tnf sitúan oficial —y gubernamentalmente— a quienes los toman en un grupo de riesgo ya que rebajan su inmunidad corporal global y les hace más vulnerables a enfermedades infecciosas, mientras que estabilizan su condición patológica de sobreinmunidad desinhibida. En parte narración de la experiencia personal de ser diagnosticado con una condición autoinmune, en parte teoría autoinmune especulativa inspirada por tal diagnóstico, el artículo en última instancia explora una forma de encarnación diferente que no sea negativa ni afirmativa y, sin embargo, sea resistente incluso a sí misma

Image interpretation above and below the object level

Computational models of vision have advanced in recent years at a rapid rate, rivaling in some areas human- level performance. Much of the progress to date has focused on analyzing the visual scene at the object level – the recognition and localization of objects in the scene. Human understanding of images reaches a richer and deeper image understanding both ‘below’ the object level, such as identifying and localizing object parts and sub-parts, as well as ‘above’ the object levels, such as identifying object relations, and agents with their actions and interactions. In both cases, understanding depends on recovering meaningful structures in the image, their components, properties, and inter-relations, a process referred here as ‘image interpretation’. In this paper we describe recent directions, based on human and computer vision studies, towards human-like image interpretation, beyond the reach of current schemes, both below the object level, as well as some aspects of image interpretation at the level of meaningful configurations beyond the recognition of individual objects, in particular, interactions between two people in close contact. In both cases the recognition process depends on the detailed interpretation of so-called 'minimal images', and at both levels recognition depends on combining ‘bottom-up’ processing, proceeding from low to higher levels of a processing hierarchy, together with ‘top-down’ processing, proceeding from high to lower levels stages of visual analysis.This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF-1231216