14859195
Solving for Set Variables in Higher-Order Theorem Proving
In higher-order logic, we must consider literals with flexible (set variable) heads. Set variables may be instantiated with logical formulas of arbitrary complexity. An alternative to guessing the logical structures of instantiations for set variables is to solve for sets satisfying constraints. Using the Knaster-Tarski Fixed Point Theorem [15], constraints whose solutions require recursive definitions can be solved as fixed points of monotone set functions. In this paper, we consider an approach to higher-order theorem proving which intertwines conventional theorem proving in the form of mating search with generating and solving set constraints.
13531439
Combining Type Theory and Untyped Set Theory
We describe a dependent type theory with proof irrelevance. Within this framework, we give a representation of a form of Mac Lane set theory and discuss automated support for constructing proofs within this set theory. One of the novel aspects of the representation is that one is allowed to use any class (in the set theory) as a type (in the type theory). Such class types allow a natural way of representing partial functions (e.g., the first and second operators on the class of Kuratowski ordered pairs). We also discuss how automated search can be used to construct proofs. In particular, the first-order prover Vampire can be called to solve a challenge problem (the injective Cantor Theorem) which is notoriously difficult for higher-order automated provers.
14987889
Optimal Camera Parameter Selection for State Estimation with Applications in Object Recognition
In this paper we introduce a formalism for optimal camera parameter selection for iterative state estimation. We consider a framework based on Shannon's information theory and select the camera parameters that maximize the mutual information, i.e. the information that the captured image conveys about the true state of the system. The technique explicitly takes into account the a priori probability governing the computation of the mutual information. Thus, a sequential decision process can be formed by treating the a posteriori probability at the current time step in the decision process as the a priori probability for the next time step. The convergence of the decision process can be proven. 
 
We demonstrate the benefits of our approach using an active object recognition scenario. The results show that the sequential decision process outperforms a random strategy, both in the sense of recognition rate and number of views necessary to return a decision.
829668
Prediction of Boundaries Between Intrinsically Ordered and Disordered Protein Regions
Using proteins with both disordered and ordered regions collected through literature searches and database scanning, we assembled a set of 24-residue long segments centered on their order/disorder boundaries as well as a larger set of non-boundary segments consisting of either order or disorder. We analyzed position-specific amino acid compositions around the order/disorder boundaries and found more than thirty significant (p < 0.05) compositional differences between boundary and non-boundary data. From this analysis, we constructed several logistic regression predictors of order/disorder boundaries using slightly different data modeling approaches. Exact boundary prediction accuracies were estimated to be in the range from 74% to 80% for the different predictors.
7808447
Optimizing Long Intrinsic Disorder Predictors with Protein Evolutionary Information
Protein existing as an ensemble of structures, called intrinsically disordered, has been shown to be responsible for a wide variety of biological functions and to be common in nature. Here we focus on improving sequence-based predictions of long (>30 amino acid residues) regions lacking specific 3-D structure by means of four new neural-network-based Predictors Of Natural Disordered Regions (PONDRs): VL3, VL3H, VL3P, and VL3E. PONDR VL3 used several features from a previously introduced PONDR VL2, but benefitted from optimized predictor models and a slightly larger (152 vs. 145) set of disordered proteins that were cleaned of mislabeling errors found in the smaller set. PONDR VL3H utilized homologues of the disordered proteins in the training stage, while PONDR VL3P used attributes derived from sequence profiles obtained by PSI-BLAST searches. The measure of accuracy was the average between accuracies on disordered and ordered protein regions. By this measure, the 30-fold cross-validation accuracies of VL3, VL3H, and VL3P were, respectively, 83.6 +/- 1.4%, 85.3 +/- 1.4%, and 85.2 +/- 1.5%. By combining VL3H and VL3P, the resulting PONDR VL3E achieved an accuracy of 86.7 +/- 1.4%. This is a significant improvement over our previous PONDRs VLXT (71.6 +/- 1.3%) and VL2 (80.9 +/- 1.4%). The new disorder predictors with the corresponding datasets are freely accessible through the web server at http://www.ist.temple.edu/disprot.
8482892
Improving Sequence Alignments For Intrinsically Disordered Proteins
Here we analyze sequence alignments for intrinsically disordered proteins. For 55 disordered protein families we measure the performance of different scoring matrices and propose one adjusted to disordered regions. An iterative algorithm of realigning sequences and recalculating matrices is designed and tested. For each matrix we also test a wide range of gap penalties. Results show an improvement in the ability to detect and discriminate related disordered proteins whose average sequence identity with the other family members is below 50%.
15122204
Action Representation and Purpose: Re-evaluating the Foundations of Computational Vision
The traditional goal of computer vision, to reconstruct, or recover properties of, the scene has recently been challenged by advocates of a new purposive approach in which the vision problem is defined in terms of the goals of an active agent. In the starkest light the debate can be characterized as one about the role of explicit representations. The extreme traditionalists strive for a detailed representation of the 3D world while the other extreme adopts a strict behaviorist stance which eschews representations in favor of “direct sensing.” This panel will explore the roles of action, representation, and purpose in computer vision and, in doing so, will hopefully discover areas of agreement.