Martingale theory for housekeeping heat

Notes on Martingale Theory

Housekeeping for prefix coding

We consider the problem of constructing and transmitting the prelude for Huffman coding. With careful organization of the required operations and an appropriate representation for the prelude, it is possible to make semistatic coding efficient even when , the size of the source alphabet, is of the same magnitude as , the length of the message being coded. The proposed structures are of direct r...

Martingale Differences and the Metric Theory of Continued Fractions

Abstract. We investigate a collection of orthonormal functions that encodes information about the continued fraction expansion of real numbers. When suitably ordered these functions form a complete system of martingale differences and are a special case of a class of martingale differences considered by R. F. Gundy. By applying known results for martingales we obtain corresponding metric theore...

Probability Theory-related Fields Multiparameter Martingale Differential Forms

A substantial body of results on stochastic integration with respect to multiparameter martingales now exists. Yet, as it stands, the theory is not entirely satisfactory in a number of ways. In particular, the calculus for stochastic integration, already complicated in two dimension, becomes prohibitively so in higher dimensions. In retrospect, the source of the difficulty seems to be that inte...

Good Housekeeping

In this issue of Neuron, Tani et al. (2014) revisit a disputed issue where biochemical and physiological data have provided conflicting results. Using a novel stimulation protocol, the authors isolate the contribution of the glutamate-glutamine cycle to excitatory synaptic transmission.