An integer-valued data envelopment analysis model with bounded outputs

Integer-valued data envelopment analysis (DEA) with alternative returns to scale technology has been introduced and developed recently by Kuosmanen and Kazemi Matin. The proportionality assumption of their introduced "natural augmentability" axiom in constant and nondecreasing returns to scale technologies makes it possible to achieve feasible decision-making units (DMUs) of arbitrary large size. In many real world applications it is not possible to achieve such production plans since some of the input and output variables are bounded above. In this paper, we extend the axiomatic foundation of integer-valuedDEAmodels for including bounded output variables. Some model variants are achieved by introducing a new axiom of "boundedness" over the selected output variables. A mixed integer linear programming (MILP) formulation is also introduced for computing efficiency scores in the associated production set. �� 2011 The Authors. International Transactions in Operational Research �� 2011 International Federation of Operational Research Societies.

Branching Processes with Immigration and Integer-valued Time Series

In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ��� 1, are simple functionals of multitype branching processes with immigration. This allows the derivation of a simple criteria for the existence of a stationary distribution of the time series, thus proving and extending some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour [11]. One can then transfer results on estimation in subcritical multitype branching processes to stationary Ginar(d) and get consistency and asymptotic normality for the corresponding estimators. The technique covers autoregressive moving average time series as well.

Vertex splitting and connectivity augmentation in hypergraphs

We consider problems of splitting and connectivity augmentation in hypergraphs. In a hypergraph G = (V +s, E), to split two edges su, sv, is to replace them with a single edge uv. We are interested in doing this in such a way as to preserve a defined level of connectivity in V . The splitting technique is often used as a way of adding new edges into a graph or hypergraph, so as to augment the connectivity to some prescribed level. We begin by providing a short history of work done in this area. Then several preliminary results are given in a general form so that they may be used to tackle several problems. We then analyse the hypergraphs G = (V + s, E) for which there is no split preserving the local-edge-connectivity present in V. We provide two structural theorems, one of which implies a slight extension to Mader���s classical splitting theorem. We also provide a characterisation of the hypergraphs for which there is no such ���good��� split and a splitting result concerned with a specialisation of the local-connectivity function. We then use our splitting results to provide an upper bound on the smallest number of size-two edges we must add to any given hypergraph to ensure that in the resulting hypergraph we have ��(x, y) ��� r(x, y) for all x, y in V, where r is an integer valued, symmetric requirement function on V*V. This is the so called ���local-edge-connectivity augmentation problem��� for hypergraphs. We also provide an extension to a Theorem of Szigeti, about augmenting to satisfy a requirement r, but using hyperedges. Next, in a result born of collaborative work with Zolt��n Kir��ly from Budapest, we show that the local-connectivity augmentation problem is NP-complete for hypergraphs. Lastly we concern ourselves with an augmentation problem that includes a locational constraint. The premise is that we are given a hypergraph H = (V,E) with a bipartition P = {P1, P2} of V and asked to augment it with size-two edges, so that the result is k-edge-connected, and has no new edge contained in some P(i). We consider the splitting technique and describe the obstacles that prevent us forming ���good��� splits. From this we deduce results about which hypergraphs have a complete Pk-split. This leads to a minimax result on the optimal number of edges required and a polynomial algorithm to provide an optimal augmentation.

Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.

On a New Approach to Williamson's Generalization of P��lya's Enumeration Theorem

P��lya���s fundamental enumeration theorem and some results from Williamson���s generalized setup of it are proved in terms of Schur- Macdonald���s theory (S-MT) of ���invariant matrices���. Given a permutation group W ��� Sd and a one-dimensional character �� of W , the polynomial functor F�� corresponding via S-MT to the induced monomial representation U�� = ind|Sdv/W (��) of Sd , is studied. It turns out that the characteristic ch(F�� ) is the weighted inventory of some set J(��) of W -orbits in the integer-valued hypercube [0, ���)d . The elements of J(��) can be distinguished among all W -orbits by a maximum property. The identity ch(F�� ) = ch(U�� ) of both characteristics is a consequence of S-MT, and is equivalent to a result of Williamson. P��lya���s theorem can be obtained from the above identity by the specialization �� = 1W , where 1W is the unit character of W.

Maximal Number of Successors in a Nginar(1) Process

2000 Mathematics Subject Classification: 60J80, 60J20, 60J10, 60G10, 60G70, 60F99.

Estima����o e previs��o no processo INARCH(2)

In the last decades the study of integer-valued time series has gained notoriety due to its broad applicability (modeling the number of car accidents in a given highway, or the number of people infected by a virus are two examples). One of the main interests of this area of study is to make forecasts, and for this reason it is very important to propose methods to make such forecasts, which consist of nonnegative integer values, due to the discrete nature of the data. In this work, we focus on the study and proposal of forecasts one, two and h steps ahead for integer-valued second-order autoregressive conditional heteroskedasticity processes [INARCH (2)], and in determining some theoretical properties of this model, such as the ordinary moments of its marginal distribution and the asymptotic distribution of its conditional least squares estimators. In addition, we study, via Monte Carlo simulation, the behavior of the estimators for the parameters of INARCH(2) processes obtained using three di erent methods (Yule- Walker, conditional least squares, and conditional maximum likelihood), in terms of mean squared error, mean absolute error and bias. We present some forecast proposals for INARCH(2) processes, which are compared again via Monte Carlo simulation. As an application of this proposed theory, we model a dataset related to the number of live male births of mothers living at Riachuelo city, in the state of Rio Grande do Norte, Brazil.

Estima����o e previs��o no processo INARCH(2)

In the last decades the study of integer-valued time series has gained notoriety due to its broad applicability (modeling the number of car accidents in a given highway, or the number of people infected by a virus are two examples). One of the main interests of this area of study is to make forecasts, and for this reason it is very important to propose methods to make such forecasts, which consist of nonnegative integer values, due to the discrete nature of the data. In this work, we focus on the study and proposal of forecasts one, two and h steps ahead for integer-valued second-order autoregressive conditional heteroskedasticity processes [INARCH (2)], and in determining some theoretical properties of this model, such as the ordinary moments of its marginal distribution and the asymptotic distribution of its conditional least squares estimators. In addition, we study, via Monte Carlo simulation, the behavior of the estimators for the parameters of INARCH(2) processes obtained using three di erent methods (Yule- Walker, conditional least squares, and conditional maximum likelihood), in terms of mean squared error, mean absolute error and bias. We present some forecast proposals for INARCH(2) processes, which are compared again via Monte Carlo simulation. As an application of this proposed theory, we model a dataset related to the number of live male births of mothers living at Riachuelo city, in the state of Rio Grande do Norte, Brazil.

Self-exciting threshold binomial autoregressive processes

We introduce a new class of integer-valued self-exciting threshold models, which is based on the binomial autoregressive model of order one as introduced by McKenzie (Water Resour Bull 21:645���650, 1985. doi:10.1111/j.1752-1688.1985. tb05379.x). Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation and forecasting are addressed. Finally, the performance of these models is illustrated through a simulation study and an empirical application to a set of measle cases in Germany.

Allocating reforestation areas for sediment flow minimization: an integer programming formulation and a heuristic solution method

Policy and decision makers dealing with environmental conservation and land use planning often require identifying potential sites for contributing to minimize sediment flow reaching riverbeds. This is the case of reforestation initiatives, which can have sediment flow minimization among their objectives. This paper proposes an Integer Programming (IP) formulation and a Heuristic solution method for selecting a predefined number of locations to be reforested in order to minimize sediment load at a given outlet in a watershed. Although the core structure of both methods can be applied for different sorts of flow, the formulations are targeted to minimization of sediment delivery. The proposed approaches make use of a Single Flow Direction (SFD) raster map covering the watershed in order to construct a tree structure so that the outlet cell corresponds to the root node in the tree. The results obtained with both approaches are in agreement with expert assessments of erosion levels, slopes and distances to the riverbeds, which in turn allows concluding that this approach is suitable for minimizing sediment flow. Since the results obtained with the IP formulation are the same as the ones obtained with the Heuristic approach, an optimality proof is included in the present work. Taking into consideration that the heuristic requires much less computation time, this solution method is more suitable to be applied in large sized problems.

Surface mapping, organic matter and water stocks in peatlands of the Serra do Espinha��o meridional - Brazil

Peatlands are soil environments that store carbon and large amounts of water, due to their composition (90 % water), low hydraulic conductivity and a sponge-like behavior. It is estimated that peat bogs cover approximately 4.2 % of the Earth's surface and stock 28.4 % of the soil carbon of the planet. Approximately 612 000 ha of peatlands have been mapped in Brazil, but the peat bogs in the Serra do Espinha��o Meridional (SdEM) were not included. The objective of this study was to map the peat bogs of the northern part of the SdEM and estimate the organic matter pools and water volume they stock. The peat bogs were pre-identified and mapped by GIS and remote sensing techniques, using ArcGIS 9.3, ENVI 4.5 and GPS Track Maker Pro software and the maps validated in the field. Six peat bogs were mapped in detail (1:20,000 and 1:5,000) by transects spaced 100 m and each transect were determined every 20 m, the UTM (Universal Transverse Mercator) coordinates, depth and samples collected for characterization and determination of organic matter, according to the Brazilian System of Soil Classification. In the northern part of SdEM, 14,287.55 ha of peatlands were mapped, distributed over 1,180,109 ha, representing 1.2 % of the total area. These peatlands have an average volume of 170,021,845.00 m�� and stock 6,120,167 t (428.36 t ha-1) of organic matter and 142,138,262 m�� (9,948 m�� ha-1) of water. In the peat bogs of the Serra do Espinha��o Meridional, advanced stages of decomposing (sapric) organic matter predominate, followed by the intermediate stage (hemic). The vertical growth rate of the peatlands ranged between 0.04 and 0.43 mm year-1, while the carbon accumulation rate varied between 6.59 and 37.66 g m-2 year-1. The peat bogs of the SdEM contain the headwaters of important water bodies in the basins of the Jequitinhonha and San Francisco Rivers and store large amounts of organic carbon and water, which is the reason why the protection and preservation of these soil environments is such an urgent and increasing need.

Carbon Stocks in Compartments of Soil Organic Matter 31 Years after Substitution of Native Cerrado Vegetation by Agroecosystems

ABSTRACT Changes in carbon stocks in different compartments of soil organic matter of a clayey Latossolo Vermelho Distr��fico (Typic Haplustox), caused by the substitution of native savanna vegetation (cerrado sensu stricto) by agroecosystems, were assessed after 31 years of cultivation. Under native vegetation, a stock of 164.5 Mg ha-1 C was estimated in the 0.00-1.00 m layer. After 31 years of cultivation, these changes in soil C stocks were detected to a depth of 0.60 m. In the case of substitution of cerrado sensu stricto by no-tillage soybean-corn rotation, a reduction of at least 11 % of the soil C pools was observed. However, the adoption of no-tillage as an alternative to tillage with a moldboard plow (conventional system) reduced CO2 emissions by up to 12 %.

Developing an Improved System for Allocating Support Unit Costs to Business Units

The objective of this study is to develop an improved support unit cost allocation system for a medium-sized technology company, and to examine which options for overhead cost accounting exist. The study begins with presenting the terminology and methods associated with overhead cost accounting and responsibility accounting. Also the most common challenges and resulting benefits of overhead cost allocation system development are brought up. As one research method two case studies were conducted for benchmarking purposes. These external cases are compared with the principal company���s cost allocation system and reflected against the theoretical background. In the empirical section interviews were used as the primary source of information alongside self studying principal company���s old cost allocation method. Interviews revealed the main weaknesses of the old system and proposals for a new one, which were utilized in setting targets for developing the new system. As a result of the development process an improved support unit cost allocation system was realized for year 2009. The new system is able to handle support unit costs in more detail enhancing the transparency and fairness of resulting cost allocations. Parts of support unit costs are now seen as business units��� own costs rather than group-level overhead. Also recommendations for further development are made after analyzing how well the targets were reached.

Soil organic matter pools in a tropical savanna under agroforestry system in Northeastern Brazil

This study aimed at quantifying total organic carbon stocks and its pools in Acrisol under agroforestry systems with six (AFS6) and thirteen years old (AFS13), slash-and-burn agriculture (SBA) and savanna native forest (SNF) in northeastern Brazil. Soil samples were collected at 0-0.05 m, 0.05-0.10 m, 0.10-0.20 m and 0.20-0.40 m depths in the dry and rainy seasons to evaluate total organic carbon (TOC) stocks and labile carbon (LC), fulvic acid fraction (C-FAF), humic acid fraction (C-HAF), humin (C-HF) and microbial biomass carbon (Cmic) contents. Additionally, carbon management index (CMI) was determined. Higher TOC stocks (97.7 and 81.8 Mg ha-1 for the 0-0.40 m depth in the dry and rainy seasons, respectively) and LC, humic substances and Cmic contents were observed in the AFS13 in all the depths. CMI also was higher in the AFS13 (0-0. 05 m: 158 and 86; 0.05-0.10 m: 171 and 67, respectively for the dry and rainy seasons) especially when compared to the SBA (0-0.05 m: 5.6 and 5.4; 0.05-0.10 m: 5.3 and 5.8, respectively for dry and rainy seasons). The agroforestry systems increased soil quality through the conservation of organic matter and can be considered an excellent strategy to assurance sustainability in tropical soil of Northeastern Brazil