Differential analysis of matrix convex functions

We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix convexity which are necessary and locally sufficient, and they allow us to prove the existence of gaps between classes of matrix convex functions of successive orders, and to give explicit examples of the type of functions contained in each of these gaps. The given conditions are shown to be also globally sufficient for matrix convexity of order two. We finally introduce a fractional transformation which connects the set of matrix monotone functions of each order n with the set of matrix convex functions of order n+1

Testing for Food market integration: A study of the Vietnamese paddy market

With its increasing integration into the world economy, agricultural exports and rural incomes in Vietnam have increased substantially in recent years. At the sub-national level, however, there are concerns that not all regions and categories of agricultural producers have and will benefit from the ongoing liberalization of agricultural markets. Vietnam's elongated geography and lack of spatial market integration pose special problems in this regard. Accordingly, this study aims to answer three interrelated questions: (a) whether there is spatial integration between paddy markets in the North and South of Vietnam; (b) whether there is spatial integration in paddy markets within the North and within the South; and, (c) if within-region integration is stronger and faster than between-region integration. The empirical model we develop to answer these questions, uses estimates of transfer costs to generalize the well known model of spatial market integration due to Ravallion to allow for the possibility of threshold effects. A sequential testing strategy is developed which progressively tests for market segmentation, the number of thresholds, long-run market integration, common dynamics/informational efficiency, and (a strict version of) the 'Law' of One Price within an error-correction framework. When the unrestricted version of this model is estimated using monthly paddy prices for eight markets between 1993 and 2006, we find weak evidence of market integration between paddy markets in the North and South of Vietnam with an absence of threshold effects. However, there is evidence of both threshold effects and stronger forms of spatial market integration for paddy markets within the North and within the South, with at least 60% percent of price changes being transmitted between markets within one month whenever price spreads exceeds their upper or lower thresholds. The extent and speed of price transmission within regional paddy markets is generally faster in the South than the North of Vietnam. However, the instantaneous version of the 'Law' of One Price, which requires full price adjustment to occur within a month, only holds for a few regimes and market pairs. Three main policy implications flow from these results. First, since there is limited evidence of integration between paddy markets in the North and South of Vietnam, national level policies cannot be relied upon to stabilize or support paddy prices.Second, since there is evidence of spatial market integration within the Red River and Mekong River deltas, paddy markets within these regions can be relied upon to transmit price signals between deficit and surplus areas relatively well. Third, since the speed and extent of price transmission is relatively rapid within the North and within the South of Vietnam, the private sector trade can be relied upon to transfer rice and paddy between markets in an efficient manner. Problems might, however, emerge if large demand-supply imbalances were to emerge between the North and South, as transfer costs would prevent private sector trade taking place. In these circumstances, the public sector might need to intervene, in a consistent and market friendly way, to ensure adequate food supplies in the short-term.Market integration; Paddy market; Error-correction; Spatial integration; Vietnam

Pooling problem: Alternate formulations and solution methods

Copyright @ 2004 INFORMSThe pooling problem, which is fundamental to the petroleum industry, describes a situation in which products possessing different attribute qualities are mixed in a series of pools in such a way that the attribute qualities of the blended products of the end pools must satisfy given requirements. It is well known that the pooling problem can be modeled through bilinear and nonconvex quadratic programming. In this paper, we investigate how best to apply a new branch-and-cut quadratic programming algorithm to solve the pooling problem. To this effect, we consider two standard models: One is based primarily on flow variables, and the other relies on the proportion. of flows entering pools. A hybrid of these two models is proposed for general pooling problems. Comparison of the computational properties of flow and proportion models is made on several problem instances taken from the literature. Moreover, a simple alternating procedure and a variable neighborhood search heuristic are developed to solve large instances and compared with the well-known method of successive linear programming. Solution of difficult test problems from the literature is substantially accelerated, and larger ones are solved exactly or approximately.This project was funded by Ultramar Canada and Luc Massé. The work of C. Audet was supported by NSERC (Natural Sciences and Engineering Research Council) fellowship PDF-207432-1998 and by CRPC (Center for Research on Parallel Computation). The work of J. Brimberg was supported by NSERC grant #OGP205041. The work of P. Hansen was supported by FCAR(Fonds pour la Formation des Chercheurs et l’Aide à la Recherche) grant #95ER1048, and NSERC grant #GP0105574

MPSLIB:A C++ class for sequential simulation of multiple-point statistical models

AbstractGeostatistical simulation methods allow simulation of spatial structures and patterns based on a choice of statistical model. In the last few decades multiple-point statistics (MPS) has been developed that allows inferring the statistical model from a training image. This allows for a simpler quantification of the statistical model, and simulation of more realistic (Earth) structures. A number of different algorithms for MPS based simulation have been proposed, each associated with a unique set of pros or cons. MPSLIB is a C++ class that provides a framework for implementing most of the currently proposed multiple-point simulation methods based on sequential simulation. A number of the most widely used methods are provided as an example. The single normal equation simulation (SNESIM) method is implemented using both a tree and a list structure. A new generalized ENESIM (GENESIM) algorithm is proposed that can act as (in one extreme) the ENESIM algorithm, and (in another extreme) similar to the direct sampling algorithm. MPSLIB aims to be easy to compile on most platforms (standard C++11 is the only requirement) and is released under the Open Source LGPLv3 License to encourage reuse and further development

Using geographic profiling to locate elusive nocturnal animals: A case study with spectral tarsiers

© 2015 The Zoological Society of London. Estimates of biodiversity, population size, population density and habitat use have important implications for management of both species and habitats, yet are based on census data that can be extremely difficult to collect. Traditional assessment techniques are often limited by time and money and by the difficulties of working in certain habitats, and species become more difficult to find as population size decreases. Particular difficulties arise when studying elusive species with cryptic behaviours. Here, we show how geographic profiling (GP) - a statistical tool originally developed in criminology to prioritize large lists of suspects in cases of serial crime - can be used to address these problems. We ask whether GP can be used to locate sleeping sites of spectral tarsiers Tarsius tarsier in Sulawesi, Southeast Asia, using as input the positions at which tarsier vocalizations were recorded in the field. This novel application of GP is potentially of value as tarsiers are cryptic and nocturnal and can easily be overlooked in habitat assessments (e.g. in dense rainforest). Our results show that GP provides a useful tool for locating sleeping sites of this species, and indeed analysis of a preliminary dataset during field work strongly suggested the presence of a sleeping tree at a previously unknown location; two sleeping trees were subsequently found within 5m of the predicted site. We believe that GP can be successfully applied to locating the nests, dens or roosts of elusive animals such as tarsiers, potentially improving estimates of population size with important implications for management of both species and habitats.We thank Operation Wallacea for supporting S.C.F. in thisproject and for providing logistical support for the fieldwork,and Aidan Kelsey for invaluable assistance in the field. Wethank the Indonesian Institute of Sciences (LIPI) andKementerian Riset dan Teknologi Republik Indonesia(RISTEK) for providing permission to undertake the work(RISTEK permit no. 211/SIP/FRP/SM/VI/2013, and BalaiKonservasi Sumber Daya Alam (BKSDA) for theirassistance