This chapter introduces some concentration inequalities for discrete-time martingales with bounded increments, and it exemplifies some of their potential applications in information theory and related topics. The first part of this chapter introduces briefly discrete-time martingales and the Azuma-Hoeffding & McDiardmid’s inequalities which are widely used in this context. It then derives these...

The far-field response of a bi-axially pre-stressed incompressible elastic plate, subjected to an instantaneous edge impulse loading, is studied using a refined long-wave low-frequency theory. The second order correction introduced by the refined theory is demonstrated to smooth the discontinuity associated with one of the wave fronts predicted by the leading order hyperbolic theory. The charac...

This chapter introduces some concentration inequalities for discrete-time martingales with bounded increments, and it exemplifies some of their potential applications in information theory and related topics. The first part of this chapter introduces briefly discrete-time martingales and the Azuma-Hoeffding & McDiardmid’s inequalities which are widely used in this context. It then derives these...

The groupoid interpretation of Martin-Löf type theory not only shows the independence of uniqueness of identity proofs from the axioms of intensional type theory but is also constructive and validates the computation rules as definitional equalities. The groupoid semantics are very clear when interpreting dependent types and in particular the identity types but less so when defining equality pr...