I would first like to acknowledge your kindness in asking me to come and speak to you. I am afraid that you may find much of what I have to say is obvious. This, I think, is inevitable, since you have actually experienced what I can, for the most part, only talk about. You have felt the tensions that arise in the family with the advent and the upbringing of a backward child : I can only see the...

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to...

To make sure that existing client software applications are not broken after a library update, backward compatibility has always been one of the most important requirements during the evolution of software libraries. However, due to various reasons, backward compatibility is seldom fully achieved in practice, so it is important to understand the status, major reasons, and impact of backward inc...

Central pressure augmentation is associated with greater backward wave amplitude and shorter transit time and is higher in women for reasons only partially elucidated. Augmentation also is affected by left ventricular function and shapes of the forward and backward waves. The goal of this study was to examine the relative contributions of forward and backward wave morphology to central pressure...

One-third of the people with an age over twenty have some signs of degenerated discs. However, in most of the patients the mere presence of degenerative discs is not a problem leading to pain, neurological compression, or other symptoms. This paper presents an interval type-2 fuzzy hybrid rule-based system to diagnose the abnormal degenerated discs where pain variables are represented by interv...

This work is devoted to the study of the existence and smoothness of the marginal densities of the solution of one dimensional backward stochastic differential equations. Under monotonicity conditions of a function of the coefficients, we obtain that the smoothness properties of the forward process influencing the backward equation, transfer to the densities of the solution. Once established th...

It has been shown (Hart [2002]) that the backward induction (or subgame-perfect) equilibrium of a perfect information game is the unique stable outcome for dynamic models consisting of selection and mutation, when the mutation rate is low and the populations are large, under the assumption that the expected number of mutations per generation is bounded away from zero. Here it is shown that one ...

The equilibrium concepts that we now think of as various forms of backwards induction, namely subgame perfect equilibrium (Selten, 1965), perfect equilibrium (Selten, 1975), sequential equilibrium (Kreps and Wilson, 1982), and quasi-perfect equilibrium (van Damme, 1984), are explicitly restricted their analysis to games with perfect recall. In spite of this the concepts are well defined, exactl...

We formulate and study a general finite-horizon bargaining game with simultaneous moves and a disagreement outcome that need not be the worst possible result for the agents. Conditions are identified under which the game is dominance solvable in the sense that iterative deletion of weakly dominated strategies selects a unique outcome. Our analysis uses a backward induction procedure to pinpoint...

In this paper we present a model for games with perfect information in which the players, upon observing an unexpected move, may revise their beliefs about the opponents’ preferences over outcomes. For a given profile P of preference relations over outcomes, we impose the following three principles: (1) players initially believe that opponents have preference relations as specified by P ; (2) p...