Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Study of the random vibration of nonlinear systems by the Gaussian closure technique

A technique is developed to study random vibration of nonlinear systems. The method is based on the assumption that the joint probability density function of the response variables and input variables is Gaussian. It is shown that this method is more general than the statistical linearization technique in that it can handle non-Gaussian excitations and amplitude-limited responses. As an example a bilinear hysteretic system under white noise excitation is analyzed. The prediction of various response statistics by this technique is in good agreement with other available results.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

Algorithms for Colouring Random k-colourable Graphs

The k-colouring problem is to colour a given k-colourable graph with k colours. This problem is known to be NP-hard even for fixed k greater than or equal to 3. The best known polynomial time approximation algorithms require n(delta) (for a positive constant delta depending on k) colours to colour an arbitrary k-colourable n-vertex graph. The situation is entirely different if we look at the average performance of an algorithm rather than its worst-case performance. It is well known that a k-colourable graph drawn from certain classes of distributions can be ii-coloured almost surely in polynomial time. In this paper, we present further results in this direction. We consider k-colourable graphs drawn from the random model in which each allowed edge is chosen independently with probability p(n) after initially partitioning the vertex set into ii colour classes. We present polynomial time algorithms of two different types. The first type of algorithm always runs in polynomial time and succeeds almost surely. Algorithms of this type have been proposed before, but our algorithms have provably exponentially small failure probabilities. The second type of algorithm always succeeds and has polynomial running time on average. Such algorithms are more useful and more difficult to obtain than the first type of algorithms. Our algorithms work as long as p(n) greater than or equal to n(-1+is an element of) where is an element of is a constant greater than 1/4.

CSR in forest industry – Case study of reporting and implementation of social responsibility in three international companies

Corporate Social Responsibility (CSR) has become increasingly important topic in forest industries, and other global companies, in recent years. Globalisation, faster information delivery and demand for sustainable development have set new challenges for global companies in their business operations. Also the importance of stakeholder relations, and pressure to become more transparent has increased in the forest industries. Three dimensions of corporate responsibility economic, environmental and social, are often included in the concept of CSR. Global companies mostly claim that these dimensions are equally important. This study analyses CSR in forest industry and has focus on reporting and implementation of social responsibility in three international companies. These case-companies are Stora Enso, SCA and Sappi, and they have different geographical base, product portfolios and therefore present interesting differences about forest industry strategy and CSR. Global Reporting Initiative (GRI) has created the most known and used reporting framework in CSR reporting. GRI Guidelines have made CSR reporting a uniform function, which can also be measured between companies and different sectors. GRI Guidelines have also made it possible to record and control CSR data in the companies. In recent years the use of GRI Guidelines has increased substantially. Typically CSR reporting on economic and environmental responsibility have been systematic in the global companies and often driven by legistlation and other regulations. However the social responsibility has been less regulated and more difficult to compare. Therefore it has previously been often less focused in the CSR reporting of the global companies. The implementation and use of GRI Guidelines have also increased dialogue on social responsibility issues and stakeholder management in global companies. This study analyses the use of GRI´s framework in the forest industry companies´ CSR reporting. This is a qualitative study and the disclosure of data is empricially analysed using content analysis. Content analysis has been selected as a method for this study because it makes it possible to use different sources of information. The data of this study consists of existing academic literature of CSR, sustainability reports of thecase-companies during 2005-2009, and the semi-structured interviews with company representatives. Different sources provide the possibility to look at specific subject from more than one viewpoint. The results of the study show that all case-companies have relatively common themes in their CSR disclosure, and the differences rise mainly from their product-portfolios, and geographic base. Social impacts to local communities, in the CSR of the companies, were mainly dominated by issues concerning creating wealth to the society and impacting communities through creation of work. The comparability of the CSR reporting, and especially social indicators increased significally from 2007 onwards in all case-companies. Even though the companies claim that three dimensions of CSR economic, environmental and social are equally important economic issues and profit improvement still seem to drive most of the operations in the global companies. Many issues that are covered by laws and regulations are still essentially presented as social responsibility in CSR. However often the unwelcome issues in companies like closing operations are covered just briefly, and without adequate explanation. To make social responsibility equally important in the CSR it would demand more emphasis from all the case-companies. A lot of emphasis should be put especially on the detail and extensiveness of the social reponsibility content in the CSR.

Probability Distribution of the Eigenvalues of the Random String Equation

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

Search on a hypercubic lattice using a quantum random walk. I. d > 2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d > 2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d -> infinity limit). In particular, the scaling behavior for d = 3 is only about 25% higher than the optimal d -> infinity value.

Search on a hypercubic lattice using a quantum random walk. II. d = 2

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretized according to the staggered lattice fermion formalism. d = 2 is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behavior. As a result, the construction used in our accompanying article A. Patel and M. A. Rahaman, Phys. Rev. A 82, 032330 (2010)] provides an O(root N ln N) algorithm, which is not optimal. The scaling behavior can be improved to O(root N ln N) by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi Phys. Rev. A 78, 012310 (2008)]. We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimize the proportionality constants of the scaling behavior of the algorithm by numerically tuning the parameters.

Effect of soil preparation of boreal spruce forest on air and soil temperature conditions in forest regeneration areas.

The effect of scarification, ploughing and cross-directional plouhing on temperature conditions in the soil and adjacent air layer have been studied during 11 consecutive growth periods by using an unprepared clear-cut area as a control site. The maximum and minimum temperatures were measured daily in the summer months, and other temperature observations were made at four-hour intervals by means of a Grant measuring instrument. The development of the seedling stand was also followed in order to determine its shading effect on the soil surface. Soil preparation decreased the daily temperature amplitude of the air at the height of 10 cm. The maximum temperatures on sunny days were lower in the tilts of the ploughed and in the humps of the cross-directional ploughed sites compared with the unprepared area. Correspondingly, the night temperatures were higher and so the soil preparation considerably reduced the risk of night frost. In the soil at the depth of 5 cm, soil preparation increased daytime temperatures and reduced night temperatures compared with unprepared area. The maximum increase in monthly mean temperatures was almost 5 °C, and the daily variation in the surface parts of the tilts and humps increased so that excessively high temperatures for the optimal growth of the root system were measured from time to time. The temperature also rose at the depths of 50 and 100 cm. Soil preparation also increased the cumulative temperature sum. The highest sums accumulated during the summer months were recorded at the depth of 5 cm in the humps of cross-directional ploughed area (1127 dd.) and in the tilts of the ploughed area (1106 dd.), while the corresponding figure in the unprepared soil was 718 dd. At the height of 10 cm the highest temperature sum was 1020 dd. in the hump, the corresponding figure in the unprepared area being 925 dd. The incidence of high temperature amplitudes and percentage of high temperatures at the depth of 5 cm decreased most rapidly in the humps of cross-directional ploughed area and in the ploughing tilts towards the end of the measurement period. The decrease was attributed principally to the compressing of tilts, the ground vegetation succession and the growth of seedlings. The mean summer temperature in the unprepared area was lower than in the prepared area and the difference did not diminish during the period studied. The increase in temperature brought about by soil preparation thus lasts at least more than 10 years.

Understorey vegetation as an indicator of forest site potential in Southern Finland.

The relationship between site characteristics and understorey vegetation composition was analysed with quantitative methods, especially from the viewpoint of site quality estimation. Theoretical models were applied to an empirical data set collected from the upland forests of southern Finland comprising 104 sites dominated by Scots pine (Pinus sylvestris L.), and 165 sites dominated by Norway spruce (Picea abies (L.) Karsten). Site index H100 was used as an independent measure of site quality. A new model for the estimation of site quality at sites with a known understorey vegetation composition was introduced. It is based on the application of Bayes' theorem to the density function of site quality within the study area combined with the species-specific presence-absence response curves. The resulting posterior probability density function may be used for calculating an estimate for the site variable. Using this method, a jackknife estimate of site index H100 was calculated separately for pine- and spruce-dominated sites. The results indicated that the cross-validation root mean squared error (RMSEcv) of the estimates improved from 2.98 m down to 2.34 m relative to the "null" model (standard deviation of the sample distribution) in pine-dominated forests. In spruce-dominated forests RMSEcv decreased from 3.94 m down to 3.16 m. In order to assess these results, four other estimation methods based on understorey vegetation composition were applied to the same data set. The results showed that none of the methods was clearly superior to the others. In pine-dominated forests, RMSEcv varied between 2.34 and 2.47 m, and the corresponding range for spruce-dominated forests was from 3.13 to 3.57 m.

Non-industrial private forest landowners’ choices of timber management strategies and potential allowable cut.

In the study, the potential allowable cut in the district of Pohjois-Savo - based on the non-industrial private forest landowners' (NIPF) choices of timber management strategies - was clarified. Alternative timber management strategies were generated, and the choices and factors affecting the choices of timber management strategies by NIPF landowners were studied. The choices of timber management strategies were solved by maximizing the utility functions of the NIPF landowners. The parameters of the utility functions were estimated using the Analytic Hierarchy Process (AHP). The level of the potential allowable cut was compared to the cutting budgets based on the 7th and 8th National Forest Inventories (NFI7 and NFI8), to the combining of private forestry plans, and to the realized drain from non-industrial private forests. The potential allowable cut was calculated using the same MELA system as has been used in the calculation of the national cutting budget. The data consisted of the NIPF holdings (from the TASO planning system) that had been inventoried compartmentwise and had forestry plans made during the years 1984-1992. The NIPF landowners' choices of timber management strategies were clarified by a two-phase mail inquiry. The most preferred strategy obtained was "sustainability" (chosen by 62 % of landowners). The second in order of preference was "finance" (17 %) and the third was "saving" (11 %). "No cuttings", and "maximum cuttings" were the least preferred (9 % and 1 %, resp.). The factors promoting the choices of strategies with intensive cuttings were a) "farmer as forest owner" and "owning fields", b) "increase in the size of the forest holding", c) agriculture and forestry orientation in production, d) "decreasing short term stumpage earning expectations", e) "increasing intensity of future cuttings", and f) "choice of forest taxation system based on site productivity". The potential allowable cut defined in the study was 20 % higher than the average of the realized drain during the years 1988-1993, which in turn, was at the same level as the cutting budget based on the combining of forestry plans in eastern Finland. Respectively, the potential allowable cut defined in the study was 12 % lower than the NFI8-based greatest sustained allowable cut for the 1990s. Using the method presented in this study, timber management strategies can be clarified for non-industrial private forest landowners in different parts of Finland. Based on the choices of timber managemet strategies, regular cutting budgets can be calculated more realistically than before.

Wood and fiber properties of Norway spruce and its suitability for thermomechanical pulping.

In the first part of the study, the selected wood and fiber properties were investigated in terms of their occurrence and variation in wood, as well as their relevance from the perspective of thermomechanical pulping process and related end-products. It was concluded that the most important factors were the fiber dimensions, juvenile wood content, and in some cases, the content of heartwood being associated with extremely dry wood with low permeability in spruce. With respect to the above properties, the following three pulpwood assortments of which pulping potential was assumed to vary were formed: wood from regeneration cuttings, first-thinnings wood, and sawmill chips. In the experimental part of the study the average wood and fiber characteristics and their variation were determined for each raw material group prior to pulping. Subsequently, each assortment - equaling about 1500 m3 roundwood - was pulped separately for a 24 h period, at constant process conditions. The properties of obtained newsgrade thermomechanical pulps were then determined. Thermomechanical pulping (TMP) from sawmill chips had the highest proportion of long fibers, smallest proportion of fines, and had generally the coarsest and longest fibers. TMP from first-thinnings wood was just the opposite, whereas that from regeneration cuttings fell in between the above two extremes. High proportion of dry heartwood in wood originating from regeneration cuttings produced a slightly elevated shives content. However, no differences were found in pulp specific energy consumption. The obtained pulp tear index was clearly best in TMP made from sawmill chips and poorest in pulp from first-thinnings wood, which had generally inferior strength properties. No dramatical differences in any of the strength properties were found between pulp from sawmill residual wood and regeneration cuttings. Pulp optical properties were superior in TMP from first-thinnings. Unexpectedly, no noticeable differences, which could be explained with fiber morphology, were found in sheet density, bulk, air permeance or roughness between the three pulps. The most important wood quality factors in this study were the fiber length, fiber cross-sectional dimensions and percentage juvenile wood. Differences found in the quality of TMP manufactured from the above spruce assortments suggest that they could be segregated and pulped separately to obtain specific product characteristics, i.e., for instance tailor-made end-products, and to minimize unnecessary variation in the raw material quality, and hence, pulp quality.

Non-industrial private forest landowners’ choices of timber management strategies.

The factors affecting the non-industrial, private forest landowners' (hereafter referred to using the acronym NIPF) strategic decisions in management planning are studied. A genetic algorithm is used to induce a set of rules predicting potential cut of the landowners' choices of preferred timber management strategies. The rules are based on variables describing the characteristics of the landowners and their forest holdings. The predictive ability of a genetic algorithm is compared to linear regression analysis using identical data sets. The data are cross-validated seven times applying both genetic algorithm and regression analyses in order to examine the data-sensitivity and robustness of the generated models. The optimal rule set derived from genetic algorithm analyses included the following variables: mean initial volume, landowner's positive price expectations for the next eight years, landowner being classified as farmer, and preference for the recreational use of forest property. When tested with previously unseen test data, the optimal rule set resulted in a relative root mean square error of 0.40. In the regression analyses, the optimal regression equation consisted of the following variables: mean initial volume, proportion of forestry income, intention to cut extensively in future, and positive price expectations for the next two years. The R2 of the optimal regression equation was 0.34 and the relative root mean square error obtained from the test data was 0.38. In both models, mean initial volume and positive stumpage price expectations were entered as significant predictors of potential cut of preferred timber management strategy. When tested with the complete data set of 201 observations, both the optimal rule set and the optimal regression model achieved the same level of accuracy.

A participatory approach to tactical forest planning.

The paper examines the needs, premises and criteria for effective public participation in tactical forest planning. A method for participatory forest planning utilizing the techniques of preference analysis, professional expertise and heuristic optimization is introduced. The techniques do not cover the whole process of participatory planning, but are applied as a tool constituting the numerical core for decision support. The complexity of multi-resource management is addressed by hierarchical decision analysis which assesses the public values, preferences and decision criteria toward the planning situation. An optimal management plan is sought using heuristic optimization. The plan can further be improved through mutual negotiations, if necessary. The use of the approach is demonstrated with an illustrative example, it's merits and challenges for participatory forest planning and decision making are discussed and a model for applying it in general forest planning context is depicted. By using the approach, valuable information can be obtained about public preferences and the effects of taking them into consideration on the choice of the combination of standwise treatment proposals for a forest area. Participatory forest planning calculations, carried out by the approach presented in the paper, can be utilized in conflict management and in developing compromises between competing interests.

Factors affecting partitioning of private forest holdings in Finland.

Questions of the small size of non-industrial private forest (NIPF) holdings in Finland are considered and factors affecting their partitioning are analyzed. This work arises out of Finnish forest policy statements in which the small average size of holdings has been seen to have a negative influence on the economics of forestry. A survey of the literature indicates that the size of holdings is an important factor determining the costs of logging and silvicultural operations, while its influence on the timber supply is slight. The empirical data are based on a sample of 314 holdings collected by interviewing forest owners in the years 1980-86. In 1990-91 the same holdings were resurveyed by means of a postal inquiry and partly by interviewing forest owners. The principal objective in compiling the data is to assist in quantifying ownership factors that influence partitioning among different kinds of NIPF holdings. Thus the mechanism of partitioning were described and a maximum likelihood logistic regression model was constructed using seven independent holding and ownership variables. One out of four holdings had undergone partitioning in conjunction with a change in ownership, one fifth among family owned holdings and nearly a half among jointly owned holdings. The results of the logistic regression model indicate, for instance, that the odds on partitioning is about three times greater for jointly owned holdings than for family owned ones. Also, the probabilities of partitioning were estimated and the impact of independent dichotomous variables on the probability of partitioning ranged between 0.02 and 0.10. The low value of the Hosmer-Lemeshow test statistic indicates a good fit of the model and the rate of correct classification was estimated to be 88 per cent with a cutoff point of 0.5. The average size of holdings undergoing ownership changes decreased from 29.9 ha to 28.7 ha over the approximate interval 1983-90. In addition, the transition probability matrix showed that the trends towards smaller size categories mostly involved in the small size categories, less than 20 ha. The results of the study can be used in considering the effects of the small size of holdings for forestry and if the purpose is to influence partitioning through forest or rural policy.