Limit Theorems for Some Occupancy and Sequential Occupancy Problems

Occupancy problems and random algebras

For k randomly chosen subsets of [n] = {1,2, ,n} we consider the probability that the Boolean algebra, distributive lattice, and meet semilattice which they generate are respectively free, or all of 2*. In each case we describe a threshold function for the occurrence of these events. The threshold functions for freeness are close to their theoretical maximum values. 1 §

Lexicon acquisition algorithms and random occupancy problems

Lexicon acquisition algorithms involve the repeated interaction between at least two agents who must reach a consensus on how to name N objects using H words. Here we consider minimal models of two types of learning algorithms: cross-situational learning in which the learner determines the meaning of a word by looking for something in common across all observed uses of that word, and operant co...

The Occupancy and Coupon Collector problems

Home Occupancy Agent: Occupancy and Sleep Detection

Smart homes of the future will have a number of different types of sensors. What types of sensors and how they will be used depends on the behaviour needed from the smart home. Using the sensors to automatically determine if a home is occupied can lead to a wide range of benefits. For example, it could trigger a change in the thermostat setting to save money, or even a change in security monito...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...