Power law distributions in entrepreneurship : implications for theory and research

A long-held assumption in entrepreneurship research is that normal (i.e., Gaussian) distributions characterize variables of interest for both theory and practice. We challenge this assumption by examining more than 12,000 nascent, young, and hyper-growth firms. Results reveal that variables which play central roles in resource-, cognition-, action-, and environment-based entrepreneurship theories exhibit highly skewed power law distributions, where a few outliers account for a disproportionate amount of the distribution's total output. Our results call for the development of new theory to explain and predict the mechanisms that generate these distributions and the outliers therein. We offer a research agenda, including a description of non-traditional methodological approaches, to answer this call.

The effects of gas and air flow distributions on the performance of the Farleigh No. 3 boiler

As more raw sugar factories become involved in the manufacture of by-products and cogeneration, bagasse is becoming an increasingly valuable commodity. However, in most factories, most of the bagasse produced is used to generate steam in relatively old and inefficient boilers. Efficient bagasse fired boilers are a high capital cost item and the cost of supplying the steam required to run a sugar factory by other means is prohibitive. For many factories a more realistic way to reduce bagasse consumption is to increase the efficiency of existing boilers. The Farleigh No. 3 boiler is a relatively old low efficiency boiler. Like many in the industry, the performance of this boiler has been adversely affected by uneven gas and air flow distributions and air heater leaks. The combustion performance and efficiency of this boiler have been significantly improved by making the gas and air flow distributions through the boiler more uniform and repairing the air heater. The estimated bagasse savings easily justify the cost of the boiler improvements.

On optimum stratification with proportional allocation for a class of pareto distributions

Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

Analysis of recreational fish catches – dealing with highly skewed distributions with many zeros

Data from surveys of recreational anglers fishing on three estuaries in eastern Australia reveal highly skewed distributions of catches with many zeros. Such data may be analysed using a two component approach involving a binary (zero/non-zero catch) response and the non-zero catches. A truncated regression model was effective in analysing the non-zero catches. Covariates were incorporated in the modelling, and their critical assessment has led to improved measures of fishing effort for this recreational fishery.

Distributions of lesser mealworm (Coleoptera: Tenebrionidae) in litter of a compacted earth floor broiler house in subtropical Queensland, Australia

Distributions of lesser mealworm, Alphitobius diaperinus (Panzer) (Coleoptera: Tenebrionidae), in litter of a compacted earth floor broiler house in southeastern Queensland, Australia, were studied over two flocks. Larvae were the predominant stage recorded. Significantly low densities occurred in open locations and under drinker cups where chickens had complete access, whereas high densities were found under feed pans and along house edges where chicken access was restricted. For each flock, lesser mealworm numbers increased at all locations over the first 14 d, especially under feed pans and along house edges, peaking at 26 d and then declining over the final 28 d. A life stage profile per flock was devised that consisted of the following: beetles emerge from the earth floor at the beginning of each flock, and females lay eggs, producing larvae that peak in numbers at 3 wk; after a further 3 to 4 wk, larvae leave litter to pupate in the earth floor, and beetles then emerge by the end of the flock time. Removing old litter from the brooder section at the end of a flock did not greatly reduce mealworm numbers over the subsequent flock, but it seemed to prevent numbers increasing, while an increase in numbers in the grow-out section was recorded after reusing litter. Areas under feed pans and along house edges accounted for 5% of the total house area, but approximately half the estimated total number of lesser mealworms in the broiler house occurred in these locations. The results of this study will be used to determine optimal deployment of site-specific treatments for lesser mealworm control.

Delineating environmental envelopes to improve mapping of species distributions, via a hurdle model with CART &/or MaxEnT

Species distribution modelling (SDM) typically analyses species’ presence together with some form of absence information. Ideally absences comprise observations or are inferred from comprehensive sampling. When such information is not available, then pseudo-absences are often generated from the background locations within the study region of interest containing the presences, or else absence is implied through the comparison of presences to the whole study region, e.g. as is the case in Maximum Entropy (MaxEnt) or Poisson point process modelling. However, the choice of which absence information to include can be both challenging and highly influential on SDM predictions (e.g. Oksanen and Minchin, 2002). In practice, the use of pseudo- or implied absences often leads to an imbalance where absences far outnumber presences. This leaves analysis highly susceptible to ‘naughty-noughts’: absences that occur beyond the envelope of the species, which can exert strong influence on the model and its predictions (Austin and Meyers, 1996). Also known as ‘excess zeros’, naughty noughts can be estimated via an overall proportion in simple hurdle or mixture models (Martin et al., 2005). However, absences, especially those that occur beyond the species envelope, can often be more diverse than presences. Here we consider an extension to excess zero models. The two-staged approach first exploits the compartmentalisation provided by classification trees (CTs) (as in O’Leary, 2008) to identify multiple sources of naughty noughts and simultaneously delineate several species envelopes. Then SDMs can be fit separately within each envelope, and for this stage, we examine both CTs (as in Falk et al., 2014) and the popular MaxEnt (Elith et al., 2006). We introduce a wider range of model performance measures to improve treatment of naughty noughts in SDM. We retain an overall measure of model performance, the area under the curve (AUC) of the Receiver-Operating Curve (ROC), but focus on its constituent measures of false negative rate (FNR) and false positive rate (FPR), and how these relate to the threshold in the predicted probability of presence that delimits predicted presence from absence. We also propose error rates more relevant to users of predictions: false omission rate (FOR), the chance that a predicted absence corresponds to (and hence wastes) an observed presence, and the false discovery rate (FDR), reflecting those predicted (or potential) presences that correspond to absence. A high FDR may be desirable since it could help target future search efforts, whereas zero or low FOR is desirable since it indicates none of the (often valuable) presences have been ignored in the SDM. For illustration, we chose Bradypus variegatus, a species that has previously been published as an exemplar species for MaxEnt, proposed by Phillips et al. (2006). We used CTs to increasingly refine the species envelope, starting with the whole study region (E0), eliminating more and more potential naughty noughts (E1–E3). When combined with an SDM fit within the species envelope, the best CT SDM had similar AUC and FPR to the best MaxEnt SDM, but otherwise performed better. The FNR and FOR were greatly reduced, suggesting that CTs handle absences better. Interestingly, MaxEnt predictions showed low discriminatory performance, with the most common predicted probability of presence being in the same range (0.00-0.20) for both true absences and presences. In summary, this example shows that SDMs can be improved by introducing an initial hurdle to identify naughty noughts and partition the envelope before applying SDMs. This improvement was barely detectable via AUC and FPR yet visible in FOR, FNR, and the comparison of predicted probability of presence distribution for pres/absence.

Row spacing and planting density effects on the growth and yield of sugarcane. 1. Responses in fumigated and non-fumigated soil.

It has been reported that high-density planting of sugarcane can improve cane and sugar yield through promoting rapid canopy closure and increasing radiation interception earlier in crop growth. It is widely known that the control of adverse soil biota through fumigation (removes soil biological constraints and improves soil health) can improve cane and sugar yield. Whether the responses to high-density planting and improved soil health are additive or interactive has important implications for the sugarcane production system. Field experiments established at Bundaberg and Mackay, Queensland, Australia, involved all combinations of 2-row spacings (0.5 and 1.5 m), two planting densities (27 000 and 81 000 two-eyed setts/ha), and two soil fumigation treatments (fumigated and non-fumigated). The Bundaberg experiment had two cultivars (Q124, Q155), was fully irrigated, and harvested 15 months after planting. The Mackay experiment had one cultivar (Q117), was grown under rainfed conditions, and harvested 10 months after planting. High-density planting (81 000 setts/ha in 0.5-m rows) did not produce any more cane or sugar yield at harvest than low-density planting (27 000 setts/ha in 1.5-m rows) regardless of location, crop duration (15 v. 10 months), water supply (irrigated v. rainfed), or soil health (fumigated v. non-fumigated). Conversely, soil fumigation generally increased cane and sugar yields regardless of site, row spacing, and planting density. In the Bundaberg experiment there was a large fumigation x cultivar x density interaction (P<0.01). Cultivar Q155 responded positively to higher planting density in non-fumigated soil but not in fumigated soil, while Q124 showed a negative response to higher planting density in non-fumigated soil but no response in fumigated soil. In the Mackay experiment, Q117 showed a non-significant trend of increasing yield in response to increasing planting density in non-fumigated soil, similar to the Q155 response in non-fumigated soil at Bundaberg. The similarity in yield across the range of row spacings and planting densities within experiments was largely due to compensation between stalk number and stalk weight, particularly when fumigation was used to address soil health. Further, the different cultivars (Q124 and Q155 at Bundaberg and Q117 at Mackay) exhibited differing physiological responses to the fumigation, row spacing, and planting density treatments. These included the rate of tiller initiation and subsequent loss, changes in stalk weight, and propensity to lodging. These responses suggest that there may be potential for selecting cultivars suited to different planting configurations.

Row spacing and planting density effects on the growth and yield of sugarcane. 3. Responses with different cultivars.

The promotion of controlled traffic (matching wheel and row spacing) in the Australian sugar industry is necessitating a widening of row spacing beyond the standard 1.5 m. As all cultivars grown in the Australian industry have been selected under the standard row spacing there are concerns that at least some cultivars may not be suitable for wider rows. To address this issue, experiments were established in northern and southern Queensland in which cultivars, with different growth characteristics, recommended for each region, were grown under a range of different row configurations. In the northern Queensland experiment at Gordonvale, cultivars Q187((sic)), Q200((sic)), Q201((sic)), and Q218((sic)) were grown in 1.5-m single rows, 1.8-m single rows, 1.8-m dual rows (50 cm between duals), and 2.3-m dual rows (80 cm between duals). In the southern Queensland experiment at Farnsfield, cvv. Q138, Q205((sic)), Q222((sic)) and Q188((sic)) were also grown in 1.5-m single rows, 1.8-m single rows, 1.8-m dual rows (50 cm between duals), while 1.8-m-wide throat planted single row and 2.0-m dual row (80 cm between duals) configurations were also included. There was no difference in yield between the different row configurations at Farnsfield but there was a significant row configuration x cultivar interaction at Gordonvale due to good yields in 1.8-m single and dual rows with Q201((sic)) and poor yields with Q200((sic)) at the same row spacings. There was no significant difference between the two cultivars in 1.5-m single and 2.3-m dual rows. The experiments once again demonstrated the compensatory capacity that exists in sugarcane to manipulate stalk number and individual stalk weight as a means of producing similar yields across a range of row configurations and planting densities. There was evidence of different growth patterns between cultivars in response to different row configurations (viz. propensity to tiller, susceptibility to lodging, ability to compensate between stalk number and stalk weight), suggesting that there may be genetic differences in response to row configuration. It is argued that there is a need to evaluate potential cultivars under a wider range of row configurations than the standard 1.5-m single rows. Cultivars that perform well in row configurations ranging from 1.8 to 2.0 m are essential if the adverse effects of soil compaction are to be managed through the adoption of controlled traffic.

Row spacing and planting density effects on the growth and yield of sugarcane. 2. Strategies for the adoption of controlled traffic.

Controlled traffic (matching wheel and row spacing) is being promoted as a means to manage soil compaction in the Australian sugar industry. However, machinery limitations dictate that wider row spacings than the standard 1.5-m single row will need to be adopted to incorporate controlled traffic and many growers are reluctant to widen row spacing for fear of yield penalties. To address these concerns, contrasting row configuration and planting density combinations were investigated for their effect on cane and sugar yield in large-scale experiments in the Gordonvale, Tully, Ingham, Mackay, and Bingera (near Bundaberg) sugarcane-growing regions of Queensland, Australia. The results showed that sugarcane possesses a capacity to compensate for different row configurations and planting densities through variation in stalk number and individual stalk weight. Row configurations ranging from 1.5-m single rows (the current industry standard) to 1.8-m dual rows (50 cm between duals), 2.1-m dual (80 cm between duals) and triple ( 65 cm between triples) rows, and 2.3-m triple rows (65 cm between triples) produced similar yields. Four rows (50 cm apart) on a 2.1-m configuration (quad rows) produced lower yields largely due to crop lodging, while a 1.8-m single row configuration produced lower yields in the plant crop, probably due to inadequate resource availability (water stress/limited radiation interception). The results suggest that controlled traffic can be adopted in the Australian sugar industry by changing from a 1.5-m single row to 1.8-m dual row configuration without yield penalty. Further, the similar yields obtained with wider row configurations (2 m or greater with multiple rows) in these experiments emphasise the physiological and environmental plasticity that exists in sugarcane. Controlled traffic can be implemented with these wider row configurations (>2 m), although it will be necessary to carry out expensive modifications to the current harvester and haul-out equipment. There were indications from this research that not all cultivars were suited to configurations involving multiple rows. The results suggest that consideration be given to assessing clones with different growth habits under a range of row configurations to find the most suitable plant types for controlled traffic cropping systems.

The effect of initial spacing and thinning on wood quality and graded sawn recovery of mature Caribbean pine grown in Queensland.

A mature Caribbean pine (Pinus caribaea var. hondurensis) silviculture experiment provided initial square spacing treatments of 1.8 m2, 2.4 m2, 3.0 m2 and 3.6 m2 (equal to 3088, 1737, 1111 and 772 stems/ha) that were thinned at age 10 years to 600, 400 and 200 stems/ha, retaining an unthinned control for each initial spacing. The trial was destructively sampled at age of 28 years and discs taken along 8 various stem heights were analysed for variation in basic density and SilviScan wood properties. In addition, the logs from ten stocking × thinning treatments were processed in a sawing study. Results indicate thinning effects were generally more pronounced than initial spacing effects. Fast growing trees produced wood with significantly higher average wood densities and higher average stiffness values. Detailed SilviScan densitometry results obtained radially and at various stem heights enabled construction of tree maps for wood properties, providing insights into the variation in juvenile to mature wood proportion across the initial and post-thinning stocking treatments studied. Dried dressed recovery was strongly related to tree size, and log value decreased consistently from butt to top logs across all treatments. The estimated value per hectare was highest in unthinned plots due to values being multiplied by high stem numbers per hectare. However, a complete economic analysis considering all cost structures is required to investigate the optimal silviculture to maximise economic returns to growers and processors. Improved understanding of the relationship between initial spacing, post-thinning stocking and wood and end-product quality should help to customize future forest management strategies required to produce better quality wood and wood products.

The Influence of Bilayer Composition on the Gel to Liquid Crystalline Transition

We report molecular dynamics simulations of bilayers using a united atom model with explicit solvent molecules. The bilayer consists of the single tail cationic surfactant behenyl trimethyl ammonium chloride (BTMAC) with stearyl alcohol (SA) as the cosurfactant. We study the gel to liquid crystalline transitions in the bilayer by varying the amount of water at fixed BTMAC to SA ratio as well as by varying the BTMAC to SA ratio at fixed water content. The bilayer is found to exist in the tilted, Lβ′ phase at low temperatures, and for the compositions investigated in this study, the Lβ′ to Lα melting transition occurred in the temperature range 330−338 K. For the highest BTMAC to SA composition (2:3 molar ratio), a diffuse headgroup−water interface is observed at lower temperatures, and an increase in the d-spacing occurs prior to the melting transition. This pretransition swelling is accompanied by a sharpening in the water density variation across the headgroup region of the bilayer. Signatures of this swelling effect which can be observed in the alkane density distributions, area per headgroup, and membrane thickness are attributed to the hydrophobic effect. At a fixed bilayer composition, the transition temperature (>338 K) from the Lβ′ to Lα transition obtained for the high water content bilayer (80 wt %) is similar to that obtained with low water content (54.3 wt %), confirming that the melting transition at these water contents is dominated by chain melting.

Dynamics of dense sheared granular flows. Part II. The relative velocity distributions

The distribution of relative velocities between colliding particles in shear flows of inelastic spheres is analysed in the Volume fraction range 0.4-0.64. Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to line joining the centres). The distribution or pre-collisional normal relative velocities (along the line Joining the centres of the particles) is Found to be an exponential distribution for particles with low normal coefficient of restitution in the range 0.6-0.7. This is in contrast to the Gaussian distribution for the normal relative velocity in all elastic fluid in the absence of shear. A composite distribution function, which consists of an exponential and a Gaussian component, is proposed to span the range of inelasticities considered here. In the case of roughd particles, the relative velocity tangential to the surfaces at contact is also evaluated, and it is found to be close to a Gaussian distribution even for highly inelastic particles.Empirical relations are formulated for the relative velocity distribution. These are used to calculate the collisional contributions to the pressure, shear stress and the energy dissipation rate in a shear flow. The results of the calculation were round to be in quantitative agreement with simulation results, even for low coefficients of restitution for which the predictions obtained using the Enskog approximation are in error by an order of magnitude. The results are also applied to the flow down an inclined plane, to predict the angle of repose and the variation of the volume fraction with angle of inclination. These results are also found to be in quantitative agreement with previous simulations.

A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: Application to robust clustering

We propose a family of multivariate heavy-tailed distributions that allow variable marginal amounts of tailweight. The originality comes from introducing multidimensional instead of univariate scale variables for the mixture of scaled Gaussian family of distributions. In contrast to most existing approaches, the derived distributions can account for a variety of shapes and have a simple tractable form with a closed-form probability density function whatever the dimension. We examine a number of properties of these distributions and illustrate them in the particular case of Pearson type VII and t tails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering examples.

Bayesian mixture model estimation of aerosol particle size distributions

In this paper, we examine approaches to estimate a Bayesian mixture model at both single and multiple time points for a sample of actual and simulated aerosol particle size distribution (PSD) data. For estimation of a mixture model at a single time point, we use Reversible Jump Markov Chain Monte Carlo (RJMCMC) to estimate mixture model parameters including the number of components which is assumed to be unknown. We compare the results of this approach to a commonly used estimation method in the aerosol physics literature. As PSD data is often measured over time, often at small time intervals, we also examine the use of an informative prior for estimation of the mixture parameters which takes into account the correlated nature of the parameters. The Bayesian mixture model offers a promising approach, providing advantages both in estimation and inference.

Weed growth and crop yield loss in wheat as influenced by row spacing and weed emergence times

Reducing crop row spacing and delaying time of weed emergence may provide crops a competitive edge over weeds. Field experiments were conducted to evaluate the effects of crop row spacing (11, 15, and 23-cm) and weed emergence time (0, 20, 35, 45, 55, and 60 days after wheat emergence; DAWE) on Galium aparine and Lepidium sativum growth and wheat yield losses. Season-long weed-free and crop-free treatments were also established to compare wheat yield and weed growth, respectively. Row spacing and weed emergence time significantly affected the growth of both weed species and wheat grain yields. For both weed species, the maximum plant height, shoot biomass, and seed production were observed in the crop-free plots, and delayed emergence decreased these variables. In weed-crop competition plots, maximum weed growth was observed when weeds emerged simultaneously with the crop in rows spaced 23-cm apart. Less growth of both weed species was observed in narrow row spacing (11-cm) of wheat as compared with wider rows (15 and 23-cm). These weed species produced less than 5 seeds plant-1 in 11-cm wheat rows when they emerged at 60 DAWE. Presence of weeds in the crop especially at early stages was devastating for wheat yields. Therefore, maximum grain yield (4.91tha-1) was recorded in the weed-free treatment at 11-cm row spacing. Delay in time of weed emergence and narrow row spacing reduced weed growth and seed production and enhanced wheat grain yield, suggesting that these strategies could contribute to weed management in wheat.