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Modern property investment allocation techniques are typically based on recognised measures of return and risk. Whilst these models work well in theory under stable conditions, they can fail when stable assumptions cease to hold and extreme volatility occurs. This is evident in commercial property markets which can experience extended stable periods followed by large concentrated negative price fluctuations as a result of major unpredictable events. This extreme volatility may not be fully reflected in traditional risk calculations and can lead to ruin. The paper aims to discuss these issues.

This research studies 28 years of quarterly Australian direct commercial property market performance data for normal distribution features and signs of extreme downside risk. For the extreme values, Power Law distribution models were examined as to provide a better probability measure of large negative price fluctuations.

The results show that the normal bell curve distribution underestimated actual extreme values both by frequency and extent, being by at least 30 per cent for the outermost data point. For the statistical outliers beyond 2 SD, a Power Law distribution can overcome many of the shortcomings of the standard deviation approach and therefore better measure the probability of ruin, being extreme downside risk.

In highlighting the challenges to measuring property market performance, analysis of extreme downside risk should be separated from traditional standard deviation risk calculations. In recognising these two different types of risk, extreme downside risk has a magnified domino effect with the tendency of bad news to come in crowds. Big price changes can lead to market crashes and financial ruin which is well beyond the standard deviation risk measure. This needs to be recognised and developed as there is evidence that extreme downside risk determinants are increasing by magnitude, frequency and impact.

Analysis of extreme downside risk should form a key part of the property decision process and be included in the property investment manager’s toolkit. Modelling techniques for estimating measures of tail risk provide challenges and have shown to be beyond traditional risk management practices, being too narrow and constraining a definition. Measuring extreme risk and the likelihood of ruin is the first step in analysing and dealing with risk in both an asset class and portfolio context.

The purpose of this paper is to propose a complex network model which can study the specified objects in a complex system within which the number of agents is fixed while the interactions and the outside environments are evolving with time.

The complex network model is analyzed by the master equation method and the rigorous four‐step statistical test is applied to test whether the degree distribution in the real world fits power law or not.

By theoretical analysis, the vertex degrees of the model follow power law distribution p(k)∼k⁻² which is different from that of the Barabási‐Albert model. By empirical research, the result shows that the citations of papers published in 2001 on the small‐world networks follow a power law distribution which is tested by the statistical test.

The small sample and short evolving time may cause some deviation from the theoretical expectation.

This evolving complex network model with fixed number of vertices and the statistical test process for power‐law will have a great significance for the theoretical and empirical study on complex networks.

This paper presents a new model of evolving complex networks which can be used to analyze the specified objects in a dynamic system and a quantitative method for power law test.

One challenge for tourism recommendation systems (TRSs) is the long-tail phenomenon of ratings or popularity among tourist products. This paper aims to improve the diversity and efficiency of TRSs utilizing the power-law distribution of long-tail data.

Using Sina Weibo check-in data for example, this paper demonstrates that the long-tail phenomenon exists in user travel behaviors and fits the long-tail travel data with power-law distribution. To solve data sparsity in the long-tail part and increase recommendation diversity of TRSs, the paper proposes a collaborative filtering (CF) recommendation algorithm combining with power-law distribution. Furthermore, by combining power-law distribution with locality sensitive hashing (LSH), the paper optimizes user similarity calculation to improve the calculation efficiency of TRSs.

The comparison experiments show that the proposed algorithm greatly improves the recommendation diversity and calculation efficiency while maintaining high precision and recall of recommendation, providing basis for further dynamic recommendation.

TRSs provide a better solution to the problem of information overload in the tourism field. However, based on the historical travel data over the whole population, most current TRSs tend to recommend hot and similar spots to users, lacking in diversity and failing to provide personalized recommendations. Meanwhile, the large high-dimensional sparse data in online social networks (OSNs) brings huge computational cost when calculating user similarity with traditional CF algorithms. In this paper, by integrating the power-law distribution of travel data and tourism recommendation technology, the authors’ work solves the problem existing in traditional TRSs that recommendation results are overly narrow and lack in serendipity, and provides users with a wider range of choices and hence improves user experience in TRSs. Meanwhile, utilizing locality sensitive hash functions, the authors’ work hashes users from high-dimensional vectors to one-dimensional integers and maps similar users into the same buckets, which realizes fast nearest neighbors search in high-dimensional space and solves the extreme sparsity problem of high dimensional travel data. Furthermore, applying the hashing results to user similarity calculation, the paper greatly reduces computational complexity and improves calculation efficiency of TRSs, which reduces the system load and enables TRSs to provide effective and timely recommendations for users.

This paper aims to assess the effectiveness of Hall currents and power-law slip condition on the hydromagnetic convective flow of an electrically conducting power-law fluid over an exponentially stretching sheet under the effect of a strong variable magnetic field and thermal radiation. Flow formation is developed using the rheological expression of a power-law fluid.

The nonlinear partial differential equations describing the flow are transformed into the nonlinear ordinary differential equations by employing the local similarity transformations and then solved numerically by an effective numerical approach, namely, fourth-order Runge–Kutta integration scheme, along with the shooting iteration technique. The numerical solution is computed for different parameters by using the computational software MATLAB bvp4c. The bvp4c function uses the finite difference code as the default. This method is a fourth-order collocation method. The impacts of thermophysical parameters on velocity and temperature distributions, skin friction coefficients and Nusselt number in the boundary layer regime are exhibited through graphs and tables and deliberated with proper physical justification.

Our investigation conveys that Hall current has an enhancing behavior on velocity profiles and reduces skin friction coefficients. An increase in the power-law index is observed to deplete velocity and temperature evolution. The temperature for the pseudo-plastic (shear-thinning) fluid is relatively higher than the corresponding temperature of the dilatant (shear-thickening) fluid. The streamlines are more distorted and have low intensity near the surface of the sheet for the dilatant fluid than the pseudo-plastic fluid.

The study is pertinent to the expulsion of polymer sheet and photographic films, hydrometallurgical industry, electrically conducting polymer dynamics, magnetic material processing, solutions and melts of polymer processing, purification of molten metals from nonmetallic. The results obtained in this work can be relevant in fluid mechanics and heat transfer applications.

The present problem has, to the authors' knowledge, not communicated thus far in the scientific literature. A comparative study with the published works is conducted to verify the accuracy of the present study. The results obtained in this analysis are significant in providing the standards for validating the accuracies of some numerical or empirical methods.

The purpose of this paper is to investigate the flow and heat transfer of power-law fluids over a non-linearly stretching sheet with non-Newtonian power-law stretching features.

The governing non-linear partial differential equations are reduced to a series of ordinary differential equations by suitable similarity transformations and the numerical solutions are obtained by the shooting method.

As the temperature power-law index or the power-law number of the fluids increases, the dimensionless stream function, dimensionless velocity and dimensionless temperature decrease, while the velocity boundary layer and temperature boundary layer become thinner for other fixed physical parameters. The thermal diffusivity varying as a function of the temperature gradient can be used to present the characteristics of flow and heat transfer of non-Newtonian power-law fluids.

Unlike classical works, the effect of power-law viscosity on the temperature field is considered by assuming that the temperature field is similar to the velocity field with modified Fourier’s law heat conduction for power-law fluid media.

The purpose of this paper is to investigate non-linear radiation heat transfer problem for stagnation-point flow of non-Newtonian fluid obeying the power-law model. Power-law fluids of both shear-thinning and shear-thickening nature have been considered.

Boundary layer equations are non-dimensionalized and then solved for the numerical solutions by fourth-fifth order Runge-Kutta integration based shooting technique.

The results reveal an existence of point of inflection for the temperature distribution for sufficiently large wall to ambient temperature ratio. Moreover temperature increases and heat transfer from the plate decreases with an increase in the radiation parameter. Heat transfer rate at the sheet is bigger in dilatant (shear-thickening) fluids when compared with the pseudoplastic (shear-thinning) fluids.

Different from the linear radiation heat transfer problem (which can be simply reduced to rescaling of Prandtl number by a factor containing the radiation parameter), here the energy equation is strongly non-linear and it involves an additional temperature ratio parameter _w =T _w /T _∞. This parameter allows studying the thermal characteristics for small/large temperature differences in the flow.