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 λ(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 Zoltán Király 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.

Transport impacts on atmosphere and climate: metrics

The transport sector emits a wide variety of gases and aerosols, with distinctly different characteristics which influence climate directly and indirectly via chemical and physical processes. Tools that allow these emissions to be placed on some kind of common scale in terms of their impact on climate have a number of possible uses such as: in agreements and emission trading schemes; when considering potential trade-offs between changes in emissions resulting from technological or operational developments; and/or for comparing the impact of different environmental impacts of transport activities. Many of the non-CO2 emissions from the transport sector are short-lived substances, not currently covered by the Kyoto Protocol. There are formidable difficulties in developing metrics and these are particularly acute for such short-lived species. One difficulty concerns the choice of an appropriate structure for the metric (which may depend on, for example, the design of any climate policy it is intended to serve) and the associated value judgements on the appropriate time periods to consider; these choices affect the perception of the relative importance of short- and long-lived species. A second difficulty is the quantification of input parameters (due to underlying uncertainty in atmospheric processes). In addition, for some transport-related emissions, the values of metrics (unlike the gases included in the Kyoto Protocol) depend on where and when the emissions are introduced into the atmosphere – both the regional distribution and, for aircraft, the distribution as a function of altitude, are important. In this assessment of such metrics, we present Global Warming Potentials (GWPs) as these have traditionally been used in the implementation of climate policy. We also present Global Temperature Change Potentials (GTPs) as an alternative metric, as this, or a similar metric may be more appropriate for use in some circumstances. We use radiative forcings and lifetimes from the literature to derive GWPs and GTPs for the main transport-related emissions, and discuss the uncertainties in these estimates. We find large variations in metric (GWP and GTP) values for NOx, mainly due to the dependence on location of emissions but also because of inter-model differences and differences in experimental design. For aerosols we give only global-mean values due to an inconsistent picture amongst available studies regarding regional dependence. The uncertainty in the presented metric values reflects the current state of understanding; the ranking of the various components with respect to our confidence in the given metric values is also given. While the focus is mostly on metrics for comparing the climate impact of emissions, many of the issues are equally relevant for stratospheric ozone depletion metrics, which are also discussed.

The transition of the Polish real estate market within a Central and Eastern European context

The real estate market in Poland is a relatively immature market, but one that has been experiencing substantial transformation. The development of the market has been encouraged by a number of factors, including changes arising as a result of new legislation and the migration of capital between capital markets. The progress of the real estate sector towards a western style competitive market has taken place within the gradual transformation of the Polish economy into a free market economy. As investment grade property is in relatively short supply in Poland, investors consider opportunities within the wider CEE block. An analysis of the risk-return characteristics of the three largest CEE real estate markets namely, Poland, Hungary and Czech Republic, shows that the returns in these markets have been negatively correlated with the UK. As these economies and markets evolve, and being part of the wider EU trading block, their economic performance will slowly converge and become more synchronized with their western counterparts. However, the catch-up of the CEE markets to western European performance cycles will be protracted and consequently there are likely to be significant ongoing portfolio risk reduction opportunities

Timing and the holding periods of institutional real estate

The literature on investors’ holding periods for equities and bonds suggest that high transaction costs are associated with longer holding periods. Return volatility, by contrast, is associated with short-term trading and hence shorter holding periods. High transaction costs and the perceived illiquidity of the real estate market leads to an expectation of longer holding periods. Further, work on depreciation and obsolescence might suggest that there is an optimal holding period. However, there is little empirical work in the area. In this paper, data from the Investment Property Databank are used to investigate sales rate and holding period for UK institutional real estate between 1981 and 1994. Sales rates are investigated using the Cox proportional hazards framework. The results show longer holding periods than those claimed by investors. There are marked differences by type of property and sales rates vary over time. Contemporaneous returns are positively associated with an increase in the rate of sale. The results shed light on investor behaviour.

Commercial real estate return distributions: a review of literature and empirical evidence

This paper review the literature on the distribution of commercial real estate returns. There is growing evidence that the assumption of normality in returns is not safe. Distributions are found to be peaked, fat-tailed and, tentatively, skewed. There is some evidence of compound distributions and non-linearity. Public traded real estate assets (such as property company or REIT shares) behave in a fashion more similar to other common stocks. However, as in equity markets, it would be unwise to assume normality uncritically. Empirical evidence for UK real estate markets is obtained by applying distribution fitting routines to IPD Monthly Index data for the aggregate index and selected sub-sectors. It is clear that normality is rejected in most cases. It is often argued that observed differences in real estate returns are a measurement issue resulting from appraiser behaviour. However, unsmoothing the series does not assist in modelling returns. A large proportion of returns are close to zero. This would be characteristic of a thinly-traded market where new information arrives infrequently. Analysis of quarterly data suggests that, over longer trading periods, return distributions may conform more closely to those found in other asset markets. These results have implications for the formulation and implementation of a multi-asset portfolio allocation strategy.

Are property prices non-linear? An investigation of the behaviour of US REITs and UK property company shares

Linear models of market performance may be misspecified if the market is subdivided into distinct regimes exhibiting different behaviour. Price movements in the US Real Estate Investment Trusts and UK Property Companies Markets are explored using a Threshold Autoregressive (TAR) model with regimes defined by the real rate of interest. In both US and UK markets, distinctive behaviour emerges, with the TAR model offering better predictive power than a more conventional linear autoregressive model. The research points to the possibility of developing trading rules to exploit the systematically different behaviour across regimes.

Valuation and arbitrage

The use of discounted cash flow (DCF) methods in investment valuation and appraisal is argued by many academics as being rational and more rigorous than the traditional capitalisation model. However those advocates of DCF should be cautious in their claims for rationality. The various DCF models all rely upon an all-encompassing equated yield (IRR) within the calculation. This paper will argue that this is a simplification of the risk perception which the investor places on the income profile from property. In determining the long term capital value of a property an 'average' DCF method will produce the 'correct' price, however, the individual short term values of each cash-flow may differ significantly. In the UK property market today, where we are facing a period in which prices are not expected to rise generally at the same rate or with such persistence as hitherto, investors and tenants are increasingly concerned with the down side implications of rental growth and investors may indeed be interested in trading property over a shorter investment horizon than they had originally planned. The purpose of this paper is therefore to bring to the analysis a rigorous framework which can be used to analyse the constituent cash flows within the freehold valuation. We show that the arbitrage analysis lends itself to segregating the capital value of the cash flows in a way which is more appropriate for financial investors

Property company performance and real interest rates: a regime-switching approach

Linear models of property market performance may be misspecified if there exist distinct states where the market drivers behave in different ways. This paper examines the applicability of non-linear regime-based models. A Self Exciting Threshold Autoregressive (SETAR) model is applied to property company share data, using the real rate of interest to define regimes. Distinct regimes appear exhibiting markedly different market behaviour. The model both casts doubt on the specification of conventional linear models and offers the possibility of developing effective trading rules for real estate equities.

The information content of REIT credit rating actions and transparency

We examine the short-run and long-run price reaction of equity REIT shares following credit rating actions, testing the transparency of the REIT structure. Generally, the economic effect on the stock price is subdued for both upgrades and downgrades compared to prior literature examining the broader U.S. equity market. An examination of trading volume revealed a significant increase in trading in reaction to downgrade credit rating changes, with a more subdued response to upgrades. The findings support the notion that REITs are more publicly forthcoming about the expectation of positive news in comparison to negative news.

The credit relationship between Henry III and merchants of Douai and Ypres, 1247-70

This article looks at an important but neglected aspect of medieval sovereign debt, namely ‘accounts payable’ owed by the Crown to merchants and employees. It focuses on the unusually well-documented relationship between Henry III, King of England between 1216 and 1272, and Flemish merchants from the towns of Douai and Ypres, who provided cloth on credit to the royal wardrobe. From the surviving royal documents, we reconstruct the credit advanced to the royal wardrobe by the merchants of Ypres and Douai for each year between 1247 and 1270, together with the king's repayment history. The interactions between the king and the merchants are then analysed. The insights from this analysis are applied to the historical data to explain the trading decisions made by the merchants during this period, as well as why the strategies of the Yprois sometimes differed from those of the Douaissiens.

Assessing continental-scale risks for generalist and specialist pollinating bee species under climate change

Increased risks of extinction to populations of animals and plants under changing climate have now been demonstrated for many taxa. This study assesses the extinction risks to species within an important genus of pollinating bees (Colletes: Apidae) by estimating the expected changes in the area and isolation of suitable habitat under predicted climatic condition for 2050. Suitable habitat was defined on the basis of the presence of known forage plants as well as climatic suitability. To investigate whether ecological specialisation was linked to extinction risk we compared three species which were generalist pollen foragers on several plant families with three species which specialised on pollen from a single plant species. Both specialist and generalist species showed an increased risk of extinction with shifting climate, and this was particularly high for the most specialised species (Colletes anchusae and C. wolfi). The forage generalist C. impunctatus, which is associated with Boreo-Alpine environments, is potentially threatened through significant reduction in available climatic niche space. Including the distribution of the principal or sole pollen forage plant, when modelling the distribution of monolectic or narrowly oligolectic species, did not improve the predictive accuracy of our models as the plant species were considerably more widespread than the specialised bees associated with them.