Lower and Upper Bounds for Misclassification Probability Based on Renyi's Information

Fano's inequality has proven to be one important result in Shannon's information theory having found applications in numerous proofs of convergence. It also provides us with a lower bound on the symbol error probability in a communication channel, in terms of Shannon's definitions of entropy and mutual information. This result is also significant in that it suggests insights on how the classification performance is influenced by the amount of information transferred through the classifier. We have previously extended Fano's lower bound on the probability of error to a family of lower and upper bounds based on Renyi's definitions of entropy and mutual information. These new bounds however, despite their theoretical appeal, were practically incomputable. In this paper, we present some modifications to these bounds that will allow us to utilize them in practical situations. The significance of these new bounds is threefold: Illustrating a theoretical use of Renyi's definition of information, extending Fano's result to include an upper bound for probability of classification error, and providing insights on how the information transfer through a classifier affects its performance. The performance of the modified bounds is investigated in various numerical examples, including applications to digital communication channels that are designed to point out the major conclusions.     

A new algorithm for the detection of tool breakage in milling

In this paper a novel signal processing algorithm is presented for the detection of tool breakage using the displacement signal (RORPA). The algorithm extracts information from consecutive revolutions to decrease dependencies on runout conditions and idle noise, creating a much more robust signal for the automatic determination of tool breakage conditions. The algorithm is explained as well as the determination of dynamic thresholds. The thresholds are set using the information regarding the cutting conditions (mean displacement signal and its slope during transient milling). Examples with real data are also presented. A critique of the overall performance and future work incorporating information from x and y channels completes the discussion.     

Extended Kernel Recursive Least Squares Algorithm

This paper presents a kernelized version of the extended recursive least squares (EX-KRLS) algorithm which implements for the first time a general linear state model in reproducing kernel Hilbert spaces (RKHS), or equivalently a general nonlinear state model in the input space. The center piece of this development is a reformulation of the well known extended recursive least squares (EX-RLS) algorithm in RKHS which only requires inner product operations between input vectors, thus enabling the application of the kernel property (commonly known as the kernel trick). The first part of the paper presents a set of theorems that shows the generality of the approach. The EX-KRLS is preferable to 1) a standard kernel recursive least squares (KRLS) in applications that require tracking the state-vector of general linear state-space models in the kernel space, or 2) an EX-RLS when the application requires a nonlinear observation and state models. The second part of the paper compares the EX-KRLS in nonlinear Rayleigh multipath channel tracking and in Lorenz system modeling problem. We show that the proposed algorithm is able to outperform the standard KRLS and EX-RLS in both simulations.     

The separation and concentration of iron from zinc process solutions

In order for solvent-extraction technology to be acceptable in the zinc industry as an alternative to existing jarosite precipitation circuits, iron must be cleanly separated and concentrated into a feed stream suitable for downstream iron by-product recovery. In this article, the use of OPAP, a mixed extractant consisting of mono- and di-octylphenyl phosphoric acids, is described as a potentially suitable extractant to selectively extract Fe(III) from concentrated ZnSO₄(90 g/l zinc)/H₂SO₄(50 g/l) solutions, followed by stripping of Fe(III) with 4–6 N HCl. OPAP was found to exhibit very low solubility/degradation characteristics (similar to D2EHPA) and excellent loading characteristics with minimal zinc and sulfate co-extraction. OPAP seems to have the lowest sulfate carryover than any other extractant previously proposed for iron extraction from strong acidic solutions. In terms of stripping, a 70 g/l Fe(II) (as FeCl₂)/6 N HCl solution was found to be effective in producting 100 g/l total iron in the strip solution. For more information, contact G.P. Demopoulos, McGill University, Department of Mining and Metallurgical Engineering, 3610 University Street, Montreal, QC, Canada H3A 2B2; (514) 398-2046; fax (514) 398-4492; e-mail george@minmet.lan.mcgill.ca.     

A Monaural Cue Sound Localizer

We describe the first single microphone sound localization system and its inspiration from theories of human monaural sound localization. Reflections and diffractions caused by the external ear (pinna) allow humans to estimate sound source elevations using only one ear. Our single microphone localization model relies on a specially shaped reflecting structure that serves the role of the pinna. Specially designed analog VLSI circuitry uses echo-time processing to localize the sound. A CMOS integrated circuit has been designed, fabricated, and successfully demonstrated on actual sounds.