Ganea conjectured that for any finite CW complex and any k > 0, cat(X×Sk) = cat(X) + 1. In this paper we prove two special cases of this conjecture. The main result is the following. Let X be a (p − 1) connected n dimensional CW complex (not necessarily finite). We show that if cat(X) = ⌊ n p ⌋ + 1 and n 6≡ −1 mod p (which implies p > 1), then cat(X×Sk) = cat(X) + 1. This is proved by showing t...

In this paper we consider the online scheduling of jobs, which require processing on a number of machines simultaneously. These jobs are presented to a decision maker one by one, where the next job becomes known as soon as the current job is scheduled. The objective is to minimize the makespan. For the problem with three machines we give a 2.8-competitive algorithm, improving upon the 3-competi...

Logistic regression is a classical linear model for logit-transformed conditional probabilities of a binary target variable. It recovers the true conditional probabilities if the joint distribution of predictors and the target is of log-linear form. Weights-of-evidence is an ordinary logistic regression with parameters equal to the differences of the weights of evidence if all predictor variabl...

Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are typically entangled. In contrast, here, we study the problem of performing coding in a high-dimensional Hilbert space, where the classes are expected to be m...

Except for well-studied special cases in which bidders have single-unit demand or bidders are risk-neutral with independent private values, equilibria of uniform-price auctions with private values need not possess familiar monotonicity properties. In particular, equilibria in weakly undominated strategies may exist in which some bidders bid strictly less on some units when they have strictly hi...

An endeavour was made to examine the female contacts of all new male N.G.U. patients attending three special treatment centres. 63-6 per cent. of the women were referred by their husbands and the remainder by other sex contacts (Table I). The 250 cases dealt with in this series were unselected except that the contacts of men who developed N.G.U. while under surveillance for gonorrhoea were excl...

The dual risk model is a popular in finance and insurance, which often used to the wealth process of venture capital or high tech company. Optimal dividends have been extensively studied literature for model. It well known that value function this optimal control problem does not yield closed-form solutions except some special cases. In paper, we study asymptotics dividend when parameters go ei...

The field equations are obtained in Sen–Dunn theory of gravitation with the help of LRS Bainchi type-I in the context of cosmic strings. We have solved the field equations when the shear σ is proportional to the scalar expansion θ. It is found that the cosmic do not exist with the scalar field except for some special cases and hence vacuum solutions are presented and discussed. c © Electronic J...