The effect of a large freshwater perturbation on the glacial north Atlantic Ocean using a coupled general circulation model

The commonly held view of the conditions in the North Atlantic at the last glacial maximum, based on the interpretation of proxy records, is of large-scale cooling compared to today, limited deep convection, and extensive sea ice, all associated with a southward displaced and weakened overturning thermohaline circulation (THC) in the North Atlantic. Not all studies support that view; in particular, the "strength of the overturning circulation" is contentious and is a quantity that is difficult to determine even for the present day. Quasi-equilibrium simulations with coupled climate models forced by glacial boundary conditions have produced differing results, as have inferences made from proxy records. Most studies suggest the weaker circulation, some suggest little or no change, and a few suggest a stronger circulation. Here results are presented from a three-dimensional climate model, the Hadley Centre Coupled Model version 3 (HadCM3), of the coupled atmosphere - ocean - sea ice system suggesting, in a qualitative sense, that these diverging views could all have occurred at different times during the last glacial period, with different modes existing at different times. One mode might have been characterized by an active THC associated with moderate temperatures in the North Atlantic and a modest expanse of sea ice. The other mode, perhaps forced by large inputs of meltwater from the continental ice sheets into the northern North Atlantic, might have been characterized by a sluggish THC associated with very cold conditions around the North Atlantic and a large areal cover of sea ice. The authors' model simulation of such a mode, forced by a large input of freshwater, bears several of the characteristics of the Climate: Long-range Investigation, Mapping, and Prediction (CLIMAP) Project's reconstruction of glacial sea surface temperature and sea ice extent.

Diagnosis of variability and trends in a global precipitation dataset using a physically motivated statistical model

A physically motivated statistical model is used to diagnose variability and trends in wintertime ( October - March) Global Precipitation Climatology Project (GPCP) pentad (5-day mean) precipitation. Quasi-geostrophic theory suggests that extratropical precipitation amounts should depend multiplicatively on the pressure gradient, saturation specific humidity, and the meridional temperature gradient. This physical insight has been used to guide the development of a suitable statistical model for precipitation using a mixture of generalized linear models: a logistic model for the binary occurrence of precipitation and a Gamma distribution model for the wet day precipitation amount. The statistical model allows for the investigation of the role of each factor in determining variations and long-term trends. Saturation specific humidity q(s) has a generally negative effect on global precipitation occurrence and with the tropical wet pentad precipitation amount, but has a positive relationship with the pentad precipitation amount at mid- and high latitudes. The North Atlantic Oscillation, a proxy for the meridional temperature gradient, is also found to have a statistically significant positive effect on precipitation over much of the Atlantic region. Residual time trends in wet pentad precipitation are extremely sensitive to the choice of the wet pentad threshold because of increasing trends in low-amplitude precipitation pentads; too low a choice of threshold can lead to a spurious decreasing trend in wet pentad precipitation amounts. However, for not too small thresholds, it is found that the meridional temperature gradient is an important factor for explaining part of the long-term trend in Atlantic precipitation.

Urban smoke concentrations at Kew, London, 1898-2004

Historical smoke concentrations at monthly resolution for the early twentieth century are found for Kew Observatory, London, using the atmospheric electricity proxy technique. Smoke particles modify the electrical properties of urban air: an increase in smoke concentration reduces air's electrical conductivity and increases the Potential Gradient (PG). Calibrated PG data are available from Kew since 1898, and air conductivity was measured routinely between 1909 and 1979 using the technique developed by C.T.R. Wilson. Automated smoke observations at the same site overlap with the atmospheric electrical measurements from 1921, providing an absolute calibration to smoke concentration. This shows that the late nineteenth century winter smoke concentrations at Kew were approximately 100 times greater than contemporary winter smoke concentrations. Following smoke emission regulations reducing the smoke concentration, the electrical parameters of the urban air did not change dramatically. This is suggested to be due to a composition change, with an increase in the abundance of small aerosol compensating for the decrease in smoke. (c) 2006 Elsevier Ltd. All rights reserved.

Cusp observations during a sequence of fast IMF B-Z reversals

In recent years, a large number of papers have reported the response of the cusp to solar wind variations under conditions of northward or southward Interplanetary Magnetic Field (IMF) Z-component (BZ). These studies have shown the importance of both temporal and spatial factors in determining the extent and morphology of the cusp and the changes in its location, connected to variations in the reconnection geometry. Here we present a comparative study of the cusp, focusing on an interval characterised by a series of rapid reversals in the BZ-dominated IMF, based on observations from space-borne and ground-based instrumentation. During this interval, from 08:00 to 12:00 UT on 12 February 2003, the IMF BZ component underwent four reversals, remaining for around 30 min in each orientation. The Cluster spacecraft were, at the time, on an outbound trajectory through the Northern Hemisphere magnetosphere, whilst the mainland VHF and Svalbard (ESR) radars of the EISCAT facility were operating in support of the Cluster mission. Both Cluster and the EISCAT were, on occasion during the interval, observing the cusp region. The series of IMF reversal resulted in a sequence of poleward and equatorward motions of the cusp; consequently Cluster crossed the high altitude cusp twice before finally exiting the dayside magnetopause, both times under conditions of northward IMF BZ. The first magnetospheric cusp encounter, by all four Cluster spacecraft, showed reverse ion dispersion typical of lobe reconnection; subsequently, Cluster spacecraft 1 and 3 (only) crossed the cusp for a second time. We suggest that, during this second cusp crossing, these two spacecraft were likely to have been on newly closed field lines, which were first reconnected (opened) at low latitudes and later reconnected again (re-closed) poleward of the northern cusp.

Time series analysis of lava flux

We have applied time series analytical techniques to the flux of lava from an extrusive eruption. Tilt data acting as a proxy for flux are used in a case study of the May–August 1997 period of the eruption at Soufrière Hills Volcano, Montserrat. We justify the use of such a proxy by simple calibratory arguments. Three techniques of time series analysis are employed: spectral, spectrogram and wavelet methods. In addition to the well-known ~9-hour periodicity shown by these data, a previously unknown periodic flux variability is revealed by the wavelet analysis as a 3-day cycle of frequency modulation during June–July 1997, though the physical mechanism responsible is not clear. Such time series analysis has potential for other lava flux proxies at other types of volcanoes.

Modelling the lava dome extruded at Soufrière Hills Volcano, Montserrat, August 2005–May 2006. Part II: Rockfall activity and talus deformation

During many lava dome-forming eruptions, persistent rockfalls and the concurrent development of a substantial talus apron around the foot of the dome are important aspects of the observed activity. An improved understanding of internal dome structure, including the shape and internal boundaries of the talus apron, is critical for determining when a lava dome is poised for a major collapse and how this collapse might ensue. We consider a period of lava dome growth at the Soufrière Hills Volcano, Montserrat, from August 2005 to May 2006, during which a 100 × 106 m3 lava dome developed that culminated in a major dome-collapse event on 20 May 2006. We use an axi-symmetrical Finite Element Method model to simulate the growth and evolution of the lava dome, including the development of the talus apron. We first test the generic behaviour of this continuum model, which has core lava and carapace/talus components. Our model describes the generation rate of talus, including its spatial and temporal variation, as well as its post-generation deformation, which is important for an improved understanding of the internal configuration and structure of the dome. We then use our model to simulate the 2005 to 2006 Soufrière Hills dome growth using measured dome volumes and extrusion rates to drive the model and generate the evolving configuration of the dome core and carapace/talus domains. The evolution of the model is compared with the observed rockfall seismicity using event counts and seismic energy parameters, which are used here as a measure of rockfall intensity and hence a first-order proxy for volumes. The range of model-derived volume increments of talus aggraded to the talus slope per recorded rockfall event, approximately 3 × 103–13 × 103 m3 per rockfall, is high with respect to estimates based on observed events. From this, it is inferred that some of the volumetric growth of the talus apron (perhaps up to 60–70%) might have occurred in the form of aseismic deformation of the talus, forced by an internal, laterally spreading core. Talus apron growth by this mechanism has not previously been identified, and this suggests that the core, hosting hot gas-rich lava, could have a greater lateral extent than previously considered.

Decadal-scale rainfall variability in Ethiopia recorded in an annually laminated, Holocene-age, stalagmite

An annually laminated, uranium-series dated, Holocene stalagmite from southeast Ethiopia has been analysed for growth rate and δ13C and δ18O variations at annual to biennial resolution, in order to provide the first long duration proxy record of decadal-scale rainfall variability in this climatically sensitive region. Our study site (10°N) is climatically influenced by both summer (June—August) and spring (March—May) rainfall caused by the annual movement of the Inter-Tropical Convergence Zone (ITCZ) and modulated by large-scale anomalies in the atmospheric circulation and in ocean temperatures. Here we show that stalagmite growth, episodic throughout the last 7800 years, demonstrates decadal-scale (8—25 yr) variability in both growth rate and δ 18O. A hydrological model was employed and indicates that this decadal variability is due to variations in the relative amounts of rainfall in the two rain seasons. Our record, unique in its combination of length (a total of ~1000 years), annual chronology and high resolution δ18O, shows for the first time that such decadal-scale variability in rainfall in this region has occurred through the Holocene, which implies persistent decadal-scale variability for the large-scale atmospheric and oceanic driving factors.

Iron Uptake and Homeostasis in Microorganisms

Preface. Iron is considered to be a minor element employed, in a variety of forms, by nearly all living organisms. In some cases, it is utilised in large quantities, for instance for the formation of magnetosomes within magnetotactic bacteria or during use of iron as a respiratory donor or acceptor by iron oxidising or reducing bacteria. However, in most cases the role of iron is restricted to its use as a cofactor or prosthetic group assisting the biological activity of many different types of protein. The key metabolic processes that are dependent on iron as a cofactor are numerous; they include respiration, light harvesting, nitrogen fixation, the Krebs cycle, redox stress resistance, amino acid synthesis and oxygen transport. Indeed, it is clear that Life in its current form would be impossible in the absence of iron. One of the main reasons for the reliance of Life upon this metal is the ability of iron to exist in multiple redox states, in particular the relatively stable ferrous (Fe2+) and ferric (Fe3+) forms. The availability of these stable oxidation states allows iron to engage in redox reactions over a wide range of midpoint potentials, depending on the coordination environment, making it an extremely adaptable mediator of electron exchange processes. Iron is also one of the most common elements within the Earth’s crust (5% abundance) and thus is considered to have been readily available when Life evolved on our early, anaerobic planet. However, as oxygen accumulated (the ‘Great oxidation event’) within the atmosphere some 2.4 billion years ago, and as the oceans became less acidic, the iron within primordial oceans was converted from its soluble reduced form to its weakly-soluble oxidised ferric form, which precipitated (~1.8 billion years ago) to form the ‘banded iron formations’ (BIFs) observed today in Precambrian sedimentary rocks around the world. These BIFs provide a geological record marking a transition point away from the ancient anaerobic world towards modern aerobic Earth. They also indicate a period over which the bio-availability of iron shifted from abundance to limitation, a condition that extends to the modern day. Thus, it is considered likely that the vast majority of extant organisms face the common problem of securing sufficient iron from their environment – a problem that Life on Earth has had to cope with for some 2 billion years. This struggle for iron is exemplified by the competition for this metal amongst co-habiting microorganisms who resort to stealing (pirating) each others iron supplies! The reliance of micro-organisms upon iron can be disadvantageous to them, and to our innate immune system it represents a chink in the microbial armour, offering an opportunity that can be exploited to ward off pathogenic invaders. In order to infect body tissues and cause disease, pathogens must secure all their iron from the host. To fight such infections, the host specifically withdraws available iron through the action of various iron depleting processes (e.g. the release of lactoferrin and lipocalin-2) – this represents an important strategy in our defence against disease. However, pathogens are frequently able to deploy iron acquisition systems that target host iron sources such as transferrin, lactoferrin and hemoproteins, and thus counteract the iron-withdrawal approaches of the host. Inactivation of such host-targeting iron-uptake systems often attenuates the pathogenicity of the invading microbe, illustrating the importance of ‘the battle for iron’ in the infection process. The role of iron sequestration systems in facilitating microbial infections has been a major driving force in research aimed at unravelling the complexities of microbial iron transport processes. But also, the intricacy of such systems offers a challenge that stimulates the curiosity. One such challenge is to understand how balanced levels of free iron within the cytosol are achieved in a way that avoids toxicity whilst providing sufficient levels for metabolic purposes – this is a requirement that all organisms have to meet. Although the systems involved in achieving this balance can be highly variable amongst different microorganisms, the overall strategy is common. On a coarse level, the homeostatic control of cellular iron is maintained through strict control of the uptake, storage and utilisation of available iron, and is co-ordinated by integrated iron-regulatory networks. However, much yet remains to be discovered concerning the fine details of these different iron regulatory processes. As already indicated, perhaps the most difficult task in maintaining iron homeostasis is simply the procurement of sufficient iron from external sources. The importance of this problem is demonstrated by the plethora of distinct iron transporters often found within a single bacterium, each targeting different forms (complex or redox state) of iron or a different environmental condition. Thus, microbes devote considerable cellular resource to securing iron from their surroundings, reflecting how successful acquisition of iron can be crucial in the competition for survival. The aim of this book is provide the reader with an overview of iron transport processes within a range of microorganisms and to provide an indication of how microbial iron levels are controlled. This aim is promoted through the inclusion of expert reviews on several well studied examples that illustrate the current state of play concerning our comprehension of how iron is translocated into the bacterial (or fungal) cell and how iron homeostasis is controlled within microbes. The first two chapters (1-2) consider the general properties of microbial iron-chelating compounds (known as ‘siderophores’), and the mechanisms used by bacteria to acquire haem and utilise it as an iron source. The following twelve chapters (3-14) focus on specific types of microorganism that are of key interest, covering both an array of pathogens for humans, animals and plants (e.g. species of Bordetella, Shigella, , Erwinia, Vibrio, Aeromonas, Francisella, Campylobacter and Staphylococci, and EHEC) as well as a number of prominent non-pathogens (e.g. the rhizobia, E. coli K-12, Bacteroides spp., cyanobacteria, Bacillus spp. and yeasts). The chapters relay the common themes in microbial iron uptake approaches (e.g. the use of siderophores, TonB-dependent transporters, and ABC transport systems), but also highlight many distinctions (such as use of different types iron regulator and the impact of the presence/absence of a cell wall) in the strategies employed. We hope that those both within and outside the field will find this book useful, stimulating and interesting. We intend that it will provide a source for reference that will assist relevant researchers and provide an entry point for those initiating their studies within this subject. Finally, it is important that we acknowledge and thank wholeheartedly the many contributors who have provided the 14 excellent chapters from which this book is composed. Without their considerable efforts, this book, and the understanding that it relays, would not have been possible. Simon C Andrews and Pierre Cornelis

Investigating age related changes in taste and affects on sensory perceptions of oral nutritional supplements

Background: sip feeds are oral nutritional supplements (ONSs) that are commonly prescribed to malnourished patients to improve their nutritional and clinical status. However, ONSs are poorly consumed and frequently wasted, with sweetness being identified as one of the factors leading to patients’ dislike of ONSs. Objectives: to investigate if age affects sweetness thresholds and if this impacts upon perceived sweetness intensity, hedonic (sweetness and overall) and ranked preference of ONS products. Design: prospective, observational. Subjects: thirty-six young adults (18–33 years) and 48 healthy older adults (63–85 years). Setting: Department of Food and Nutritional Sciences and the Clinical Health Sciences at the University of Reading. Methods: detection and recognition threshold levels, basic taste identification and ‘just about right’ level of sweetness were examined. Three ONSs (chocolate, vanilla, strawberry) and sucrose solutions were evaluated for hedonic sweetness, overall hedonic liking, sweetness intensity and rank preference. Results: significant differences were found in both sweetness detection and recognition thresholds (P = 0.0001) between young and older adults, with older adults more likely to incorrectly identify the taste (P = 0.0001). Despite the deterioration in sweetness sensitivity among the older adults, there were no significant differences found in sweetness intensity perceived for the ONS products presented (P > 0.05) when compared with the young adults. However, across both groups sweetness intensity was found to be correlated with overall product dislike across all flavour variants tested (R = 0.398, P = 0.0001). Conclusions: sweetness appears to be one of many factors contributing to the dislike of ONSs. Manufacturers are encouraged to reconsider the formulations of these products so that beneficial effects of ONSs can be delivered in a more palatable and acceptable form and wastage reduced.

Pliocene seasonality across the North Atlantic inferred from cheilostome bryozoans

Previous studies have shown an inverse correlation between zooid size in cheilostome bryozoans and ambient water temperature. This relationship underlies the MART technique which uses intracolonial variation in zooid size to predict mean annual range in temperature experienced by bryozoan colonies during their life. Here we apply the MART technique to study Early and Mid Pliocene bryozoans from Central America (Panama, Costa Rica), the USA (Florida, South Carolina, North Carolina, Virginia) and the UK (Suffolk) to reconstruct palaeoseasonality across a range of latitudes for the North Atlantic during the Pliocene Epoch. Compared to the present-day, our analyses suggest greater seasonality (ca 4.5 degrees C) in the southern Caribbean at the time of Cayo Agua Formation deposition (ca 4.25 Ma), in keeping with inferred upwelling prior to the closure of the isthmian barrier at 2.7 Ma. Bryozoans also indicate seasonal upwelling on the Gulf Coast of Florida in a similar manner to the present-day. Because upwelling can be highly localised and prone to spatial and temporal variation in the Gulf of Mexico today, it contributes little to a broad understanding of Pliocene North Atlantic waters. However, MART estimates for the coastal plain region indicate a general reduction in the annual range in temperature relative to the present, suggesting that the colder surface waters that today reach south to Cape Hatteras had less influence in Early to Mid Pliocene times. These results, along with evidence from other proxies, strongly support reduced seasonality and warmer conditions along the eastern seaboard of the USA in the Early to Mid Pliocene. Finally, the MART estimates amongst Coralline Crag localities provide evidence for an increased annual range in temperature in the southern North Sea than at present. Our study shows that bryozoan MART estimates provide a powerful, independent proxy for palaeoseasonality and is the first to demonstrate that the MART technique can be applied to infer palaeoclimates across a wide range of latitudes focusing on a variety of geological formations and geographical regions. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Diagnosis of variability and trends in a global precipitation dataset using a physically motivated statistical model

A physically motivated statistical model is used to diagnose variability and trends in wintertime ( October - March) Global Precipitation Climatology Project (GPCP) pentad (5-day mean) precipitation. Quasi-geostrophic theory suggests that extratropical precipitation amounts should depend multiplicatively on the pressure gradient, saturation specific humidity, and the meridional temperature gradient. This physical insight has been used to guide the development of a suitable statistical model for precipitation using a mixture of generalized linear models: a logistic model for the binary occurrence of precipitation and a Gamma distribution model for the wet day precipitation amount. The statistical model allows for the investigation of the role of each factor in determining variations and long-term trends. Saturation specific humidity q(s) has a generally negative effect on global precipitation occurrence and with the tropical wet pentad precipitation amount, but has a positive relationship with the pentad precipitation amount at mid- and high latitudes. The North Atlantic Oscillation, a proxy for the meridional temperature gradient, is also found to have a statistically significant positive effect on precipitation over much of the Atlantic region. Residual time trends in wet pentad precipitation are extremely sensitive to the choice of the wet pentad threshold because of increasing trends in low-amplitude precipitation pentads; too low a choice of threshold can lead to a spurious decreasing trend in wet pentad precipitation amounts. However, for not too small thresholds, it is found that the meridional temperature gradient is an important factor for explaining part of the long-term trend in Atlantic precipitation.

Amphioxus molecular biology: insights into vertebrate evolution and developmental mechanisms

The cephalochordate amphioxus is the best available proxy for the last common invertebrate ancestor of the vertebrates. During the last decade, the developmental genetics of amphioxus have been extensively examined for insights into the evolutionary origin and early evolution of the vertebrates. Comparisons between expression domains of homologous genes in amphioxus and vertebrates have strengthened proposed homologies between specific body parts. Molecular genetic studies have also highlighted parallels in the developmental mechanisms of amphioxus and vertebrates. In both groups, a similar nested pattern of Hox gene expression is involved in rostrocaudal patterning of the neural tube, and homologous genes also appear to be involved in dorsoventral neural patterning. Studies of amphioxus molecular biology have also hinted that the protochordate ancestor of the vertebrates included cell populations that modified their developmental genetic pathways during early vertebrate evolution to yield definitive neural crest and neurogenic placodes. We also discuss how the application of expressed sequence tag and gene-mapping approaches to amphioxus have combined with developmental studies to advance our understanding of chordate genome evolution. We conclude by considering the potential offered by the sequencing of the amphioxus genome, which was completed in late 2004.

Oxidation of biogenic and water-soluble compounds in aqueous and organic aerosol droplets by ozone: a kinetic and product analysis approach using laser Raman tweezers

The results of an experimental study into the oxidative degradation of proxies for atmospheric aerosol are presented. We demonstrate that the laser Raman tweezers method can be used successfully to obtain uptake coeffcients for gaseous oxidants on individual aqueous and organic droplets, whilst the size and composition of the droplets is simultaneously followed. A laser tweezers system was used to trap individual droplets containing an unsaturated organic compound in either an aqueous or organic ( alkane) solvent. The droplet was exposed to gas- phase ozone and the reaction kinetics and products followed using Raman spectroscopy. The reactions of three different organic compounds with ozone were studied: fumarate anions, benzoate anions and alpha pinene. The fumarate and benzoate anions in aqueous solution were used to represent components of humic- like substances, HULIS; a alpha- pinene in an alkane solvent was studied as a proxy for biogenic aerosol. The kinetic analysis shows that for these systems the diffusive transport and mass accommodation of ozone is relatively fast, and that liquid- phase di. ffusion and reaction are the rate determining steps. Uptake coe. ffcients, g, were found to be ( 1.1 +/- 0.7) x 10(-5), ( 1.5 +/- 0.7) x 10 (-5) and ( 3.0 - 7.5) x 10 (-3) for the reactions of ozone with the fumarate, benzoate and a- pinene containing droplets, respectively. Liquid- phase bimolecular rate coe. cients for reactions of dissolved ozone molecules with fumarate, benzoate and a- pinene were also obtained: k(fumarate) = ( 2.7 +/- 2) x 10 (5), k(benzoate) = ( 3.5 +/- 3) x 10 (5) and k(alpha-pinene) = ( 1-3) x 10(7) dm(3) mol (-1) s (- 1). The droplet size was found to remain stable over the course of the oxidation process for the HULIS- proxies and for the oxidation of a- pinene in pentadecane. The study of the alpha- pinene/ ozone system is the first using organic seed particles to show that the hygroscopicity of the particle does not increase dramatically over the course of the oxidation. No products were detected by Raman spectroscopy for the reaction of benzoate ions with ozone. One product peak, consistent with aqueous carbonate anions, was observed when following the oxidation of fumarate ions by ozone. Product peaks observed in the reaction of ozone with alpha- pinene suggest the formation of new species containing carbonyl groups.

Are we wasting our money on food supplements in elder care wards?

Background. It is reported that undernutrition in older hospitalized patients is commonly found, but estimates of its prevalence vary. It is also not clear which treatment approaches are best because poor methodology prevents comparison of outcomes between different studies. Rationale. The rationale of this observational study was to look at typical elder care wards in order to determine what food supplements were being prescribed. We wished to determine whether serum albumin and/or body mass index (BMI) were appropriately related to the prescription of sip feeds and also to determine the palatability of supplements provided. Method. We monitored the wastage of sip feeds over a 24-hour period and extrapolated an estimated cost. Ninety-six patients were studied, including 23 patients with a BMI of less than 20, of whom 30% were on supplementary feeds. Results. Seventy percentage of prescribed sip feeds were being given to people with a BMI of 20 or more. The mean wastage in this 24-hour period was 63% (pound79.56) in four wards containing 96 older patients. Conclusion. We concluded that there was no relationship between the numbers of patients with a low albumin and BMI and the prescription of sip feeds. We found compliance to be low (37%) because of poor palatability, with a large number of patients who appeared to require sip feeds not being prescribed them and those who received them wasting more than they drank.

Opportunistic cooperative diversity protocols for wireless networks

In this paper we consider a cooperative communication system where some a priori information of wireless channels is available at the transmitter. Several opportunistic relaying strategies are developed to fully utilize the available channel information. Then an explicit expression of the outage probability is developed for each proposed cooperative scheme as well as the diversity-multiplexing tradeoff by using order statistics. Our analytical results show that the more channel information available at the transmitter, the better performance a cooperative system can achieve. When the exact values of the source-relay channels are available, the performance loss at low SNR can be effectively suppressed. When the source node has the access to the source-relay and relay-destination channels, the full diversity can be achieved by costing only one extra channel used for relaying transmission, and an optimal diversity-multiplexing tradeoff can be achieved d(r) = (N + 1)(1 - 2r), where N is the number of all possible relaying nodes.