We improve Kleinberg’s original greedy routing algorithm, and show that if each node can look ahead logk log n depth of its long-range contacts, the routing path can be found with expected length of O(log n logk log n), where n is the size of the network and k is the number of long-range contacts per node. To our knowledge, this is presently the best result for routing messages in Kleinberg’s s...

Abstract Over the recent years deep learning has found successful applications in mathematical reasoning. Today, we can predict fine-grained proof steps, relevant premises, and even useful conjectures using neural networks. This extended abstract summarizes developments of machine reasoning vision N2Formal group at Google Research to create an automatic mathematician. The second part discusses ...

The paper considers two types of models for forecasting seasonally adjusted Russian GDP under the structural breaks. Models that allow breaks in a deterministic trend, which dates are set exogenously, and more flexible class – with stochastic trend considered. It is shown modeling break or adding significantly improves quality 3–4 steps ahead forecasts, sometimes even on shorter horizons, compa...

Mexico faces important demographic and epidemiological transitions with significant implications to patterns of disease, disability, and death. On the one hand, there are problems of underdevelopment and, on the other, the emerging challenges of the chronic and degenerative diseases of the industrialized world. For these diseases, prevention becomes a key strategy for alleviating a major burden...

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. We present an implementation of a look-ahead version of the Lanczos algorithm that|except for the very special situation of an in...

Research on vehicle longitudinal control with a stop and go system is presently one of the most important topics in the field of intelligent transportation systems. The purpose of stop and go systems is to assist drivers for repeatedly accelerate and stop their vehicles in traffic jams. This system can improve the driving comfort, safety and reduce the danger of collisions and fuel consumption....

The major breast cancer story of 2005 was trastuzumab, a monoclonal antibody directed against the Her-2 oncoprotein, and how it greatly improves outcomes for women with HER2-positive early-stage breast cancer. With early results showing that use of the drug can prevent roughly one half of relapses, adjuvant trastuzumab has been approved, funded, and accepted as the standard of care in many Cana...