Belief Propagation for Linear Programming

Belief Propagation (BP) is a popular, distributed heuristic for performing MAP computations in Graphical Models. BP can be interpreted, from a variational perspective, as minimizing the Bethe Free Energy (BFE). BP can also be used to solve a special class of Linear Programming (LP) problems. For this class of problems, MAP inference can be stated as an integer LP with an LP relaxation that coincides with minimization of the BFE at ``zero temperature". We generalize these prior results and establish a tight characterization of the LP problems that can be formulated as an equivalent LP relaxation of MAP inference. Moreover, we suggest an efficient, iterative annealing BP algorithm for solving this broader class of LP problems. We demonstrate the algorithm's performance on a set of weighted matching problems by using it as a cutting plane method to solve a sequence of LPs tightened by adding ``blossom'' inequalities.Comment: To appear in ISIT 201

The Somerset tradition

No Abstract

A Model of the Production of Spontaneous Otoacoustic Emissions in the Tokay Gecko

The role of the ear is to detect sound. Many ears, however, can also generate sounds and transmit them into the environment. These sounds, known as spontaneous otoacoustic emissions, are the most striking proof of the existence of an active process within the ear. This active process originates in hair cells, the sensory receptors of the inner ear; by augmenting the energy contained in sound, it improves both the sensitivity and the frequency selectivity of hearing. Under certain conditions, the active process generates spontaneous oscillations, which then produce spontaneous emissions. Little is known about the process by which the spontaneous oscillations of a collection of hair cells within the ear are transformed into a particular sound that can be measured externally. Here, we suggest that interactions between tonotopically arranged hair cells play a critical role in the formation of spontaneous otoacoustic emissions. We have created a model based on the basilar papilla of the tokay gecko, a species notable both for the unusual anatomy of its inner ear and for the prominence of its spontaneous emissions. In this model, the papilla is represented by a tonotopic array of nonlinear van der Pol oscillators, with connections along the array mediated by either viscous or elastic elements. We find that a model incorporating elastic interactions, but not one incorporating viscous interactions, reproduces the appearance of spontaneous emissions. The model also suggests a prominent role for disorder along the length of the papilla. Finally, the model explains what may be the most distinctive feature of spontaneous emissions: the repulsion of spectral peaks within the emission by pure-tone external stimuli. To test our model, we also recorded spontaneous otoacoustic emissions from the tokay gecko. Previous recordings of emissions have primarily focused on the behavior of single peaks within the emission spectrum. We chose instead to focus on the relationships between multiple emission peaks. Upon applying single-frequency tones at a range of amplitudes and frequencies into the ears of geckos we have observed novel behaviors previously predicted by our model. We conclude that interactions along the basilar papilla, mediated by elastic elements, play an important role in the formation of spontaneous otoacoustic emissions

Effects of certain diseases on population

A CAJM article on the effects of some tropical African diseases, in the 1950's, on the health of the population.Although for long now we have been acquainted with the many diseases occurring in Africa, yet, as our experience grows, we find the subject by no means easy. For instance, one might think that by now we should know all about the clinical effects of malaria on this continent, yet, when the experiences of the different workers in tropical Africa are pooled, one finds so many conflicting opinions that one begins to wonder if our knowledge is really much further advanced than it was some 70 years ago, when we first began to study the disease microscopically. But in spite of this we have advanced considerably. The mistake made in the past, and still being made in some quarters to-day, when assessing the effects of the diseases, was to look upon them as separate entities instead of viewing the picture as a whole, since the majority of African subjects suffer from more than one ailment at a time

Dermatitis Gangrenosa Infantum: a Report of a Case

A 1950's CAJM report on Dermatitis Gangrenosa in African infants at a Rhodesian African hospital.From time to time in African infants one meets a condition generally known to dermatologists as dermatitis gangrenosa infantum, in which a characteristic destruction of a large area of skin occurs. It may start with a small blister or it may begin de novo, being quickly followed by loss of skin and rapid spread. The affected skin assumes a blackened colour, is dull, opaque and usually sharply demarcated from the healthy surrounding skin. The dead skin is hard and the size of the lesion varies, but often it is extensive, measuring several inches across. Its shape too varies very much, although roughly circular, with many small projections and indentations. It usually has the appearance of an indented outline of a map, the normal skin representing the sea. The condition is said to be due to the Haemolytic streptococcus which can regularly be recovered from it. ft is believed that an initial scratch or boil starts off the process, which develops in an alarming manner. It frequently, but not always, occurs in marasmic or undernourished children, often when recovering from one of the common infectious diseases

Three cases of tetanus neonatorum

A research paper on tetanus neonatorum in the 1950's Southern Rhodesia

Coma The Common Causes In An African Medical Ward

A CAJM article on the prevalence of coma's African hospital patience,Coma is a common reason for a patient to be admitted to hospital. It has many causes and the physician attending a comatose patient must determine its etiology at an early stage so that the appropriate therapy can be instituted. The causes of coma are well known but, in a country like Rhodesia, where the pattern of disease differs from that of Europe, it seems that it would be a worthwhile procedure to find out the more usual causes of coma in African patients admitted to hospital. Most of the patients in this ward are adult but a few children (over the age of seven) are seen. The cases were studied consecutively in a prospective manner. Thus in this study, from 1963 to 1965 inclusive, only factors related to the cause of the coma were considered and not the outcome of the disease

Symmetrical Gangrene Occurring in a Female African Affected with Endomyocardial Fibrosis

A CAJM article on Endomyocardial Fibrosis as diagnosed in the then Southern Rhodesia of the 1950's.Endomyocardial fibrosis was first described in Africans in 1946 by Bedford and Konstam, who recognised it in West African soldiers, and two years later Davies gave a fuller account of it from Uganda. Since then several important and confirmatory papers from Uganda, the Union and elsewhere in Africa have appeared. We now possess a fairly good conception of its pathology and clinical course. Briefly, it is characterised by an endomyocardial fibrosis of varying extent, especially marked at the apex of the left ventricle. Almost always a thrombus is seen on the damaged endocardium or a large one forms in the appendage of one or other of the auricular appendages. The fibrosis may be patchy or diffuse, involving the whole of the ventricle. The layer may be several millimetres thick, extending on to the epicardium, and in rare instances may be so pronounced that an obliterative effect from the fibrosis is produced, reducing considerably the capacity of the right ventricle (Ball, Williams and Davies, 1954). The site of election is in the apex of the left ventricle

Cardiac Disease of Obscure Origin in Africa

A Central African Journal of Medicine (CAJM) article on heart disease in Africa.Within recent years a number of papers have emanated from East, West, Central and South Africa, all reporting a form or forms of congestive heart failure, the etiology of which remains obscure. Interest in this subject began in 1946, when Bedford and Konstam published a series of 40 cases of unexplained heart disease in African troops, mostly from West Africa, serving in the Middle East. There were earlier references in the literature to peculiar aspects of heart disease in Africans. Although the cause may have been incorrectly attributed, the fact remains that these men had the good sense and courage to publish their findings. For instance, Macfie and Ingram (1920) reported the occurrence of cardiac aneurysm of uncertain cause in the African of the West Coast, which occurred in either childhood or adult life. The aneurysm could be situated in an auricle, ventricle or in one of the heart valves. It not frequently ruptured with the supervention of sudden death. In other cases the heart failed gradually

North American Blastomycosis in Rhodesia

A CAJM article on the prevalence of American blastomycosis in Zimbabwe (formerly Rhodesia.)The clinical and pathological features of North American Blastomycosis in the United States of America have been well documented by Abernathy (1959) and by Witorsch & Utz (1968) who showed that blastomycosis is a chronic mycosis generally believed to begin in the lungs and which then spreads to other organs giving rise to secondary lesions, especially in the skin and bones