Sharpened lower bounds for cut elimination

We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our new lower bounds remove the constant of proportionality, giving an exponential stack of height equal to d − O(1). The proof method is based on more efficiently expressing the Gentzen-Solovay cut formulas as low depth formulas.

Miguel de Unamuno and Heraclitus: from ‘The Eternal Elegy’ (‘La elegía eterna’) to ‘The Cut Flower’(‘La flor tronchada’)

The aim of this brief article is to demonstrate and analyze the influence of Heraclitus’s thought on some of the poems written by Miguel de Unamuno, in particular ‘La elegía eterna’ and ‘La flor tronchada’. At times –as in ‘La elegía eterna’– Heraclitus merely serves as a sort of a walking stick, an aid to his efforts to poetically reveal his anxieties. On other occasions –as in ‘La flor tronchada’– he genuinely needs Heraclitus’s philosophy to illustrate his view of human life and its relation to God as unending warfare.

Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model.

Interior crises are understood as discontinuous changes of the size of a chaotic attractor that occur when an unstable periodic orbit collides with the chaotic attractor. We present here numerical evidence and theoretical reasoning which prove the existence of a chaos-chaos transition in which the change of the attractor size is sudden but continuous. This occurs in the Hindmarsh¿Rose model of a neuron, at the transition point between the bursting and spiking dynamics, which are two different dynamic behaviors that this system is able to present. Moreover, besides the change in attractor size, other significant properties of the system undergoing the transitions do change in a relevant qualitative way. The mechanism for such transition is understood in terms of a simple one-dimensional map whose dynamics undergoes a crossover between two different universal behaviors

The Rose Bengal test in human brucellosis: a neglected test for the diagnosis of a neglected disease

Brucellosis is a highly contagious zoonosis affecting livestock and human beings. The human disease lacks pathognomonic symptoms and laboratory tests are essential for its diagnosis. However, most tests are difficult to implement in the areas and countries were brucellosis is endemic. Here, we compared the simple and cheap Rose Bengal Test (RBT) with serum agglutination, Coombs, competitive ELISA, Brucellacapt, lateral flow immunochromatography for IgM and IgG detection and immunoprecipitation with Brucella proteins. We tested 208 sera from patients with brucellosis proved by bacteriological isolation, 20 contacts with no brucellosis, and 1559 sera of persons with no recent contact or brucellosis symptoms. RBT was highly sensitive in acute and long evolution brucellosis cases and this related to its ability to detect IgM, IgG and IgA, to the absence of prozones, and to the agglutinating activity of blocking IgA at the pH of the test. RBT was also highly specific in the sera of persons with no contact with Brucella. No test in this study outperformed RBT, and none was fully satisfactory in distinguishing contacts from infected patients. When modified to test serum dilutions, a diagnostic titer >4 in RBT resulted in 87.4% sensitivity (infected patients) and 100% specificity (contacts). We discuss the limitations of serological tests in the diagnosis of human brucellosis, particularly in the more chronic forms, and conclude that simplicity and affordability of RBT make it close to the ideal test for small and understaffed hospitals and laboratories.