Algorithm Studies on How to Obtain a Conditional Nonlinear Optimal Perturbation (CNOP)

The conditional nonlinear optimal perturbation (CNOP), which is a nonlinear generalization of the linear singular vector (LSV), is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming (SQP) algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, and the spectral projected gradients (SPG2) algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.

Summer diet of two sympatric species of raptors Upland Buzzard (Buteo hemilasius) and Eurasian Eagle Owl (Bubo bubo) in alpine meadow: problem of coexistence

Summer diets of two sympatric raptors Upland Buzzards (Buteo hemilasius Temminck et Schlegel) and Eurasian Eagle Owls (Bubo bubo L. subsp. Hemachalana Hume) were studied in an alpine meadow (3250 m a.s.l.) on Qinghai-Tibet Plateau, China. Root voles Microtus oeconomus Pallas, plateau pikas Ochotona curzoniae Hodgson, Gansu pikas O. cansus Lyon and plateau zokors Myospalax baileyi Thomas were the main diet components of Upland Buzzards as identified through the pellets analysis with the frequency of 57, 20, 19 and 4%, respectively. The four rodent species also were the main diet components of Eurasian Eagle Owls basing on the pellets and prey leftovers analysis with the frequency of 53, 26, 13 and 5%, respectively. The food niche breadth indexes of Upland Buzzards and Eurasian Eagle Owls were 1.60 and 1.77 respectively (higher value of the index means the food niche of the raptor is broader), and the diet overlap index of the two raptors was larger (C-ue = 0.90) (the index range from 0 - no overlap - to I - complete overlap). It means that the diets of Upland Buzzards and Eurasian Eagle Owls were similar (Two Related Samples Test, Z = -0.752, P = 0.452). The classical resource partitioning theory can not explain the coexistence of Upland Buzzards and Eurasian Eagle Owls in alpine meadows of Qinghai-Tibet Plateau. However, differences in body size, predation mode and activity rhythm between Upland Buzzards and Eurasian Eagle Owls may explain the coexistence of these two sympatric raptors.

心理旋转中的整体优先效应及其机制

In the history of psychology research, more attention had been focused on the relation between local processing and global processing. For the global information and the local information, which is processed earlier? And which is processed faster? Precedence of the global over the local level in visual perception has been well established by Navon with compound stimuli, and Navon’s original study gave rise to many publications, including replications, generalization to other kinds of stimuli (nonverbal material, digits), populations (infants, children, brain-damaged subjects), and tasks (lateral visual hemifield presentation, copy drawing, memory recognition, and recall), and triggered some debate about the conditions in which global precedence is and is not observed (number, size, sparsity, and goodness of the stimuli, exposure duration, etc.). However, whether there is a global advantage or precedence in other cognitive processes was less tested. Most researches had suggested that there was a functional equivalency between visual perception and visual image processing. However, it’s still unknown whether there will be a global advantage on mental rotation. In the present study, we combined the mental rotation task with the compound stimuli to explore whether the global or local advantage also existed at the mental imagery transformation stages. In two pilot studies, the perceptual global precedence was found to be present in a normal/mirror-image judgment task when the stimuli exposure time was short; while the stimuli exposure time was prolonged (stimuli kept available till subjects’ response) the perceptual global precedence was showed to be eliminated. In all of the subsequent experiments, stimili would be presented till subjects’ response. Then mental rotation was added in normal/mirror-image judgment (some of the stimuli were rotated to certain angles from upright) in normal experiments, experiment 1 and 2 observed a global advantage on mental rotation both with a focused-attention design (Experiment 1) and divided-attention design (Experiment 2). Subjects’ reaction times were increased with rotation angles, and the accuracy was decreased with rotation angles, suggesting that subject need a mental rotation to make a normal/mirror judgment. The most important results were that subjects’ response to global rotation was faster than that to local rotation. The analysis of slope of rotation further indicated that, to some extend, the speed of global rotation was faster than that of local rotation. These results suggest a global advantage on mental rotation. Experiment 3 took advantage of the high temporal resolution of event-related potentials to explore the temporal pattern of global advantage on mental rotation. Event-related potential results indicated the parietal P300 amplitude was inversely related to the character orientation, and the local rotation task delayed the onset of the mental-rotation-related negativity at parietal electrodes. None clear effect was found for occipital N150. All these results suggested that the global rotation was not only processed faster than local rotation, but also occurred earlier than local rotation. Experiments 4 and 5 took the effect size of global advantage as the main dependent variable, and visual angle and exposure duration of the stimuli as independent variables, to examine the relationship between perceptual global precedence and global advantage on mental rotation. Results indicated that visual angle and exposure duration did not influence the effect size of global advantage on mental rotation. The global advantage on mental rotation and the perceptual global advantage seemed to be independent but their effects could be accumulated at some condition. These findings not only contribute to revealing a new processing property of mental rotation, but also deepen our understanding of the problem of global/local processing and shed light on the debate on locus of global precedence.

Viewpoint-Specific Representations in Three-Dimensional Object Recognition

We report a series of psychophysical experiments that explore different aspects of the problem of object representation and recognition in human vision. Contrary to the paradigmatic view which holds that the representations are three-dimensional and object-centered, the results consistently support the notion of view-specific representations that include at most partial depth information. In simulated experiments that involved the same stimuli shown to the human subjects, computational models built around two-dimensional multiple-view representations replicated our main psychophysical results, including patterns of generalization errors and the time course of perceptual learning.

Multiple Resolution Image Classification

Binary image classifiction is a problem that has received much attention in recent years. In this paper we evaluate a selection of popular techniques in an effort to find a feature set/ classifier combination which generalizes well to full resolution image data. We then apply that system to images at one-half through one-sixteenth resolution, and consider the corresponding error rates. In addition, we further observe generalization performance as it depends on the number of training images, and lastly, compare the system's best error rates to that of a human performing an identical classification task given teh same set of test images.

The Grasping Problem: Toward Task-Level Programming for an Articulated Hand

This report presents a system for generating a stable, feasible, and reachable grasp of a polyhedral object. A set of contact points on the object is found that can result in a stable grasp; a feasible grasp is found in which the robot contacts the object at those contact points; and a path is constructed from the initial configuration of the robot to the stable, feasible final grasp configuration. The algorithm described in the report is designed for the Salisbury hand mounted on a Puma 560 arm, but a similar approach could be used to develop grasping systems for other robots.

Theories of Comparative Analysis

Comparative analysis is the problem of predicting how a system will react to perturbations in its parameters, and why. For example, comparative analysis could be asked to explain why the period of an oscillating spring/block system would increase if the mass of the block were larger. This thesis formalizes the task of comparative analysis and presents two solution techniques: differential qualitative (DQ) analysis and exaggeration. Both techniques solve many comparative analysis problems, providing explanations suitable for use by design systems, automated diagnosis, intelligent tutoring systems, and explanation based generalization. This thesis explains the theoretical basis for each technique, describes how they are implemented, and discusses the difference between the two. DQ analysis is sound; it never generates an incorrect answer to a comparative analysis question. Although exaggeration does occasionally produce misleading answers, it solves a larger class of problems than DQ analysis and frequently results in simpler explanations.

Natural Language Input for a Computer Problem Solving System

The STUDENT problem solving system, programmed in LISP, accepts as input a comfortable but restricted subset of English which can express a wide variety of algebra story problems. STUDENT finds the solution to a large class of these problems. STUDENT can utilize a store of global information not specific to any one problem, and may make assumptions about the interpretation of ambiguities in the wording of the problem being solved. If it uses such information or makes any assumptions, STUDENT communicates this fact to the user. The thesis includes a summary of other English language questions-answering systems. All these systems, and STUDENT, are evaluated according to four standard criteria. The linguistic analysis in STUDENT is a first approximation to the analytic portion of a semantic theory of discourse outlined in the thesis. STUDENT finds the set of kernel sentences which are the base of the input discourse, and transforms this sequence of kernel sentences into a set of simultaneous equations which form the semantic base of the STUDENT system. STUDENT then tries to solve this set of equations for the values of requested unknowns. If it is successful it gives the answers in English. If not, STUDENT asks the user for more information, and indicates the nature of the desired information. The STUDENT system is a first step toward natural language communication with computers. Further work on the semantic theory proposed should result in much more sophisticated systems.

Truth Maintenance Systems for Problem Solving

The thesis developed here is that reasoning programs which take care to record the logical justifications for program beliefs can apply several powerful, but simple, domain-independent algorithms to (1) maintain the consistency of program beliefs, (2) realize substantial search efficiencies, and (3) automatically summarize explanations of program beliefs. These algorithms are the recorded justifications to maintain the consistency and well founded basis of the set of beliefs. The set of beliefs can be efficiently updated in an incremental manner when hypotheses are retracted and when new information is discovered. The recorded justifications also enable the pinpointing of exactly whose assumptions which support any particular belief. The ability to pinpoint the underlying assumptions is the basis for an extremely powerful domain-independent backtracking method. This method, called Dependency-Directed Backtracking, offers vastly improved performance over traditional backtracking algorithms.

Justified Generalization: Acquiring Procedures from Examples

This thesis describes an implemented system called NODDY for acquiring procedures from examples presented by a teacher. Acquiring procedures form examples involves several different generalization tasks. Generalization is an underconstrained task, and the main issue of machine learning is how to deal with this underconstraint. The thesis presents two principles for constraining generalization on which NODDY is based. The first principle is to exploit domain based constraints. NODDY demonstrated how such constraints can be used both to reduce the space of possible generalizations to manageable size, and how to generate negative examples out of positive examples to further constrain the generalization. The second principle is to avoid spurious generalizations by requiring justification before adopting a generalization. NODDY demonstrates several different ways of justifying a generalization and proposes a way of ordering and searching a space of candidate generalizations based on how much evidence would be required to justify each generalization. Acquiring procedures also involves three types of constructive generalizations: inferring loops (a kind of group), inferring complex relations and state variables, and inferring predicates. NODDY demonstrates three constructive generalization methods for these kinds of generalization.

The Dirichlet problem in convex bounded domains for operators with L^\infty-coefficients

M.Hieber, I.Wood: The Dirichlet problem in convex bounded domains for operators with L^\infty-coefficients, Diff. Int. Eq., 20, 7 (2007),721-734.

James Joyce and the Problem of Psychoanalysis

Thurston, L. (2004). James Joyce and the Problem of Psychoanalysis. Cambridge: Cambridge University Press. RAE2008

Littered with meaning: The problem of sign pollution in postmodern, post-structuralist, and ecocritical thought

Slocombe, W. (2005). Littered with meaning: The problem of sign pollution in postmodern, post-structuralist, and ecocritical thought. Textual Practice. 19 (4), 493-508. RAE2008

Precise solutions of the one-dimensional Monge-Kantorovich problem

Plakhov, A.Y., (2004) 'Precise solutions of the one-dimensional Monge-Kantorovich problem', Sbornik: Mathematics 195(9) pp.1291-1307 RAE2008

Newton's aerodynamic problem in media of chaotically moving particles

Plakhov, A.Y.; Torres, D., (2005) 'Newton's aerodynamic problem in media of chaotically moving particles', Sbornik: Mathematics 196(6) pp.885-933 RAE2008