1. Write-up Wish List 2 2. To Do List 2 3. History 3 4. Basic definitions and notation 4 5. Codimension One Finite Length [Sarah] 5 6. Codimension Two Finite Length [Sarah] 5 7. Codimension Three Finite Length 7 8. Attempts at Codimension Four 8 9. Betti Death 8 10. Alternative diagram decompostions for complete intersections 9 11. Decomposition Via Separating the Betti Diagram 13 11.1. Heurist...

In this paper, we investigate the application of a new method, the Finite Difference and Stochastic Gradient (Hybrid method), for history matching in reservoir models. History matching is one of the processes of solving an inverse problem by calibrating reservoir models to dynamic behaviour of the reservoir in which an objective function is formulated based on a Bayesian approach for optimizati...

In this article we present the realization of a generic finite-state system. The system has been used to create concrete lexical tools for word form analysis, word form generation, creation and derivation history, and spenchecking. It will also be used to create a finite-state transducer for the recognition of phrases. Producing a finitestate component with the generic system requires little e~...

In every finite-state leavable gambling problem and in every finite-state Markov decision process with discounted, negative or positive reward criteria there exists a Markov strategy which is monotonically improving and optimal in the limit along every history. An example is given to show that for the positive and gambling cases such strategies cannot be constructed by simply switching to a "be...

We consider deterministic and nondeterministic finite automata with acceptance conditions that rely on the whole history of a computation on a given word and not only on the last state of the computation under consideration. Formally, these conditions can be seen as the natural analogies of the Büchi and Muller acceptance for finite automata on infinite words. We study the computational power o...

An infinite-horizon, stochastic model of entry and exit with sunk costs and imperfect competition is constructed. A subgame perfect Nash equilibrium for the general dynamic stochastic game is shown to exist as a limit of finite-horizon equilibria. This equilibrium has a relatively simple structure characterized by two numbers per finite history. Under very general conditions, it tends to exhibi...

We survey in this paper some variants of the notion of determinism, refining the spectrum between non-determinism and determinism. We present unambiguous automata, strongly unambiguous automata, prophetic automata, guidable automata, and history-deterministic automata. We instantiate these various notions for finite words, infinite words, finite trees, infinite trees, data languages, and cost f...

Finite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems, and also the application to 4d problems has been addressed. However, due to the enormous increase of the computational costs, different strategie...