18741005
Reasoning in Extensional Type Theory with Equality
We describe methods for automated theorem proving in extensional type theory with primitive equality. We discuss a complete, cut-free sequent calculus as well as a compact representation of cut-free (ground) proofs as extensional expansion dags. Automated proof search can be realized using a few operations to manipulate extensional expansion dags with variables. These search operations form a basis for complete search procedures. Procedures based on these ideas are implemented in the higher-order theorem prover Tps.
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.
27008190
Tutorial: Using TPS for Higher-Order Theorem Proving and ETPS for Teaching Logic
TPS is an automated theorem proving system which can be used to prove theorems of first- or higher-order logic automatically, interactively, or in a combination of these modes of operation. Proofs in TPS are presented in natural deduction style. ETPS is a program which was obtained from TPS by deleting all the facilities for proving theorems automatically. ETPS can be used by students to learn how to prove theorems interactively. The objective of the tutorial is to teach participants how to make effective use of TPS and ETPS.
16390848
A Fully Projective Formulation to Improve the Accuracy of Lowe's Pose-Estimation Algorithm
Both the original version of David Lowe's influential and classic algorithm for tracking known objects and a reformulation of it implemented by Ishiiet al. rely on (different) approximated imaging models. Removing their simplifying assumptions yields a fully projective solution with significantly improved accuracy and convergence, and arguably better computation-time properties.
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.
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%.
3260299
The Protein Non-Folding Problem: Amino Acid Determinants of Intrinsic Order and Disorder
To investigate the determinants of protein order and disorder, three primary and one derivative database of intrinsically disordered proteins were compiled. The segments in each primary database were characterized by one of the following: X-ray crystallography, nuclear magnetic resonance (NMR), or circular dichroism (CD). The derivative database was based on homology. The three primary disordered databases have a combined total of 157 proteins or segments of length.30 with 18,010 residues, while the derivative database contains 572 proteins from 32 families with 52,688 putatively disordered residues. For the four disordered databases, the amino acid compositions were compared with those from a database of ordered structure. Relative to the ordered protein, the intrinsically disordered segments in all four databases were significantly depleted in W, C, F, I, Y, V, L and N, significantly enriched in A, R, G, Q, S, P, E and K, and inconsistently different in H, M, T, and D, suggesting that the first set be called order-promoting and the second set disorder-promoting. Also, 265 amino acid properties were ranked by their ability to discriminate order and disorder and then pruned to remove the most highly correlated pairs. The 10 highest-ranking properties after pruning consisted of 2 residue contact scales, 4 hydrophobicity scales, 3 scales associated with.-sheets and one polarity scale. Using these 10 properties for comparisons of the 3 primary databases suggests that disorder in all 3 databases is very similar, but with those characterized by NMR and CD being the most similar, those by CD and X-ray being next, and those by NMR and X-ray being the least similar.
31238264
The populated web: Browsing, searching and inhabiting the WWW using collaborative virtual environments
This paper presents new approaches for accessing the World Wide Web using multi-user three dimensional spaces, or collaborative virtual environments (CVEs.) The major sections of the paper deal with the aspects of browsing and navigating, searching, populating and displaying information within, and about the WWW. The methods described are illustrated with examples of working applications developed by the authors which together present an image of a possible future for Web access and collaboration based around the Web and its contents.