Above are papers related to the following paper: [Paper_ID] Paper #102061. 	[Title] Simulating Quadratic Dynamical Systems is PSPACE-complete (preliminary version) [Abstract] Quadratic Dynamical Systems (QDS), whose definition extends that of Markov chains, are used to model phenomena in a variety of fields like statistical physics and natural evolution. Such systems also play a role in genetic algorithms, a widely-used class of heuristics that are notoriously hard to analyze. Recently Rabinovich et al. took an important step in the study of QDS's by showing, under some technical assumptions, that such systems converge to a stationary distribution (similar theorems for Markov Chains are well-known). We show, however, that the following sampling problem for QDS's is PSPACE-hard: Given an initial distribution, produce a random sample from the t'th generation. The hardness result continues to hold for very restricted classes of QDS's with very simple initial distributions, thus suggesting that QDS's are intrinsically more complicated than Markov chains. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #509315. 	[Title] A Computational View of Population Genetics (preliminary version) [Abstract] This paper contributes to the study of nonlinear dynamical systems from a computational perspective. These systems are inherently more powerful than their linear counterparts (such as Markov chains), which have had a wide impact in Computer Science, and they seem likely to play an increasing role in future. However, there are as yet no general techniques available for handling the computational aspects of discrete nonlinear systems, and even the simplest examples seem very hard to analyze. We focus in this paper on a class of quadratic systems that are widely used as a model in population genetics and also in genetic algorithms. These systems describe a process where random matings occur between parental chromosomes via a mechanism known as "crossover": i.e., children inherit pieces of genetic material from different parents according to some random rule. Our results concern two fundamental quantitative properties of crossover systems: 1. We develop a general technique for computing the Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66805. 	[Title] Where Genetic Algorithms Excel [Abstract] We analyze the performance of a Genetic Algorithm (GA) we call Culling and a variety of other algorithms on a problem we refer to as Additive Search Problem (ASP). ASP is closely related to several previously well studied problems, such as the game of Mastermind and additive fitness functions. We show that the problem of learning the Ising perceptron is reducible to a noisy version of ASP. Culling is efficient on ASP, highly noise tolerant, and the best known approach in some regimes. Noisy ASP is the first problem we are aware of where a Genetic Type Algorithm bests all known competitors. Standard GA's, by contrast, perform much more poorly on ASP than hillclimbing and other approaches even though the Schema theorem holds for ASP. We generalize ASP to k-ASP to study whether GA's will achieve `implicit parallelism' in a problem with many more schemata. GA's fail to achieve this implicit parallelism, but we describe an algorithm we call Explicitly Parallel Search that succeeds. We also compute the optimal culling point for selective breeding, which turns out to be independent of the fitness function or the population distribution. We also analyze a Mean Field Theoretic algorithm performing similarly to Culling on many problems. These results provide insight into when and how GA's can beat competing methods. Please summarise all the given information.

Paper #102061 has the title `Simulating Quadratic Dynamical Systems is PSPACE-complete (preliminary version)  
` and the abstract `Quadratic Dynamical Systems (QDS), whose definition extends that of Markov chains, are used to model phenomena in a variety of fields like statistical physics and natural evolution. Such systems also play a role in genetic algorithms, a widely-used class of heuristics that are notoriously hard to analyze. Recently Rabinovich et al. took an important step in the study of QDS's by showing, under some technical assumptions, that such systems converge to a stationary distribution (similar theorems for Markov Chains are well-known). We show, however, that the following sampling problem for QDS's is PSPACE-hard: Given an initial distribution, produce a random sample from the t'th generation. The hardness result continues to hold for very restricted classes of QDS's with very simple initial distributions, thus suggesting that QDS's are intrinsically more complicated than Markov chains. 
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Question: Which category should Paper #102061 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #102061 has the title `Simulating Quadratic Dynamical Systems is PSPACE-complete (preliminary version)  
` and the abstract `Quadratic Dynamical Systems (QDS), whose definition extends that of Markov chains, are used to model phenomena in a variety of fields like statistical physics and natural evolution. Such systems also play a role in genetic algorithms, a widely-used class of heuristics that are notoriously hard to analyze. Recently Rabinovich et al. took an important step in the study of QDS's by showing, under some technical assumptions, that such systems converge to a stationary distribution (similar theorems for Markov Chains are well-known). We show, however, that the following sampling problem for QDS's is PSPACE-hard: Given an initial distribution, produce a random sample from the t'th generation. The hardness result continues to hold for very restricted classes of QDS's with very simple initial distributions, thus suggesting that QDS's are intrinsically more complicated than Markov chains. 
`.
Question: Which category should Paper #102061 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Genetic_Algorithms