Two New Proofs of Afriat's Theorem

We provide two, new simple proofs of Afriat's celebrated theorem..Afriat's theorem, SARP, GARP

Bayesian estimation for selective trace gas detection

We present a Bayesian estimation analysis for a particular trace gas detection technique with species separation provided by differential diffusion. The proposed method collects a sample containing multiple gas species into a common volume, and then allows it to diffuse across a linear array of optical absorption detectors, using, for example, high-finesse Fabry-Perot cavities. The estimation procedure assumes that all gas parameters (e.g. diffusion constants, optical cross sections) are known except for the number population of each species, which are determined from the time-of-flight absorption profiles in each detector

Sums of hermitian squares and the BMV conjecture

Recently Lieb and Seiringer showed that the Bessis-Moussa-Villani conjecture from quantum physics can be restated in the following purely algebraic way: The sum of all words in two positive semidefinite matrices where the number of each of the two letters is fixed is always a matrix with nonnegative trace. We show that this statement holds if the words are of length at most 13. This has previously been known only up to length 7. In our proof, we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming. As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric matrices of the same size, yet not being a sum of hermitian squares and commutators.Comment: 21 pages; minor changes; a companion Mathematica notebook is now available in the source fil

Smart Focal Plane Technologies for VLT Instruments

As we move towards the era of ELTs, it is timely to think about the future role of the 8-m class telescopes. Under the OPTICON programme, novel technologies have been developed that are intended for use in multi-object and integral-field spectrographs. To date, these have been targeted at instrument concepts for the European ELT, but there are also significant possibilities for their inclusion in new VLT instruments, ensuring the continued success and productivity of these unique telescopes.Comment: 5 pages, to appear in the proceedings of the ESO Workshop "Science with the VLT in the ELT era

Polyhedral Analysis using Parametric Objectives

The abstract domain of polyhedra lies at the heart of many program analysis techniques. However, its operations can be expensive, precluding their application to polyhedra that involve many variables. This paper describes a new approach to computing polyhedral domain operations. The core of this approach is an algorithm to calculate variable elimination (projection) based on parametric linear programming. The algorithm enumerates only non-redundant inequalities of the projection space, hence permits anytime approximation of the output

Strong duality in conic linear programming: facial reduction and extended duals

The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$(P) \sup {<c, x> | Ax \leq_K b}$$ in the absence of any constraint qualification. The facial reduction algorithm solves a sequence of auxiliary optimization problems to obtain such a dual. Ramana's dual is applicable when (P) is a semidefinite program (SDP) and is an explicit SDP itself. Ramana, Tuncel, and Wolkowicz showed that these approaches are closely related; in particular, they proved the correctness of Ramana's dual using certificates from a facial reduction algorithm. Here we give a clear and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual: -- we state a simple facial reduction algorithm and prove its correctness; and -- building on this algorithm we construct a family of extended duals when $K$ is a {\em nice} cone. This class of cones includes the semidefinite cone and other important cones.Comment: A previous version of this paper appeared as "A simple derivation of a facial reduction algorithm and extended dual systems", technical report, Columbia University, 2000, available from http://www.unc.edu/~pataki/papers/fr.pdf Jonfest, a conference in honor of Jonathan Borwein's 60th birthday, 201

Structural, item, and test generalizability of the psychopathology checklist - revised to offenders with intellectual disabilities

The Psychopathy Checklist–Revised (PCL-R) is the most widely used measure of psychopathy in forensic clinical practice, but the generalizability of the measure to offenders with intellectual disabilities (ID) has not been clearly established. This study examined the structural equivalence and scalar equivalence of the PCL-R in a sample of 185 male offenders with ID in forensic mental health settings, as compared with a sample of 1,212 male prisoners without ID. Three models of the PCL-R’s factor structure were evaluated with confirmatory factor analysis. The 3-factor hierarchical model of psychopathy was found to be a good fit to the ID PCL-R data, whereas neither the 4-factor model nor the traditional 2-factor model fitted. There were no cross-group differences in the factor structure, providing evidence of structural equivalence. However, item response theory analyses indicated metric differences in the ratings of psychopathy symptoms between the ID group and the comparison prisoner group. This finding has potential implications for the interpretation of PCL-R scores obtained with people with ID in forensic psychiatric settings