Optimization of strip-layout using graph-theoretic methodology for stamping operations on progressive die: a case study

The design of the progressive die stamping process is optimized through minimizing the number of die stamping stations in the strip layout to reduce the die cost. In order to accomplish such end, in this study, a graph-theoretic based method is implemented to model and optimize the strip layout design. This method starts with mapping stamping features into stamping operations. This step is followed by constructing two graphs to model the precedence and adjacency constraints among stamping operations based on a set of manufacturing rules. These two graphs are called: operation precedence graph and operation adjacency graph. In the next step, a topological sorting algorithm clusters the operations into partially ordered sets. Then, a graph coloring algorithm clusters the partially ordered operations sets into final sequence of operations. The graph-theoretic technique has been implemented on a part currently manufactured by laser cutting process technology in some Egyptian factory in Cairo. This study indicated that the graph-theoretic technique offers several advantages including the ease of programming and transparency in understanding the obtained strip layout design. This is besides being a systematic and logically approach to obtain an optimized strip layout design. In general, the progressive die manufacturing can increase productivity of sheet metal works in Egypt, only in situations of mass production. The limitation is that it requires considerable skill level and training for labor to conduct die strip layout design.

Entrack: Probabilistic Spherical Regression with Entropy Regularization for Fiber Tractography

White matter tractography, based on diffusion-weighted magnetic resonance images, is currently the only available in vivo method to gather information on the structural brain connectivity. The low resolution of diffusion MRI data suggests to employ probabilistic methods for streamline reconstruction, i.e., for fiber crossings. We propose a general probabilistic model for spherical regression based on the Fisher-von-Mises distribution, which efficiently estimates maximum entropy posteriors of local streamline directions with machine learning methods. The optimal precision of posteriors for streamlines is determined by an information-theoretic technique, the expected log-posterior agreement concept. It relies on the requirement that the posterior distributions of streamlines, inferred on retest measurements of the same subject, should yield stable results within the precision determined by the noise level of the data source.

Optimal Recovery of Missing Values for Non-negative Matrix Factorization

We extend the approximation-theoretic technique of optimal recovery to the setting of imputing missing values in clustered data, specifically for non-negative matrix factorization (NMF), and develop an implementable algorithm. Under certain geometric conditions, we prove tight upper bounds on NMF relative error, which is the first bound of this type for missing values. We also give probabilistic bounds for the same geometric assumptions. Experiments on image data and biological data show that this theoretically-grounded technique performs as well as or better than other imputation techniques that account for local structure.

Spurious Ambiguity and Focalization

Spurious ambiguity is the phenomenon whereby distinct derivations in grammar may assign the same structural reading, resulting in redundancy in the parse search space and inefficiency in parsing. Understanding the problem depends on identifying the essential mathematical structure of derivations. This is trivial in the case of context free grammar, where the parse structures are ordered trees; in the case of type logical categorial grammar, the parse structures are proof nets. However, with respect to multiplicatives, intrinsic proof nets have not yet been given for displacement calculus, and proof nets for additives, which have applications to polymorphism, are not easy to characterize. In this context we approach here multiplicative-additive spurious ambiguity by means of the proof-theoretic technique of focalization.

Computing Nash Equilibria of Unbounded Games

Using techniques from higher-type computability theory and proof theory we extend the well-known game-theoretic technique of backward induction to finite games of unbounded length. The main application is a closed formula for calculating strategy profiles in Nash equilibrium and subgame perfect equilibrium even in the case of games where the length of play is not a-priori fixed.