A suite of FRs has also been reported as present in materials and

A suite of FRs has also been reported as present in materials and products taken recently from the Swiss retail market (Zennegg, 2011). In addition, other types of compounds are also used as FRs in a variety of applications, notably PFRs. Regarding the present use of CFRs, less has been

published to date, even though some new chemicals have now been identified as CFRs. These are mainly related to the family of “Dechloranes” (Sverko et al., 2011) as further discussed below. As the number of compounds in use as FRs, and for which environmental data are being reported increases, there is a pressing need to harmonize abbreviations by which these compounds can be described in the literature (for example, using TBBPA and PBDEs as described above, and BDE47 for

2,2′,4,4′-tetrabromodiphenyl ether), with the aim of preventing future confusion. EGFR inhibitor review Unfortunately, a rather large number of abbreviations, for the less known FRs, are currently being used without any coordination. Following a request made at the BFR Symposium 2010 in Kyoto, we have now prepared a document which aims to promote improved harmonization, based on a set of criteria, of unique and practical abbreviations to be used for all BFRs, CFRs and PFRs identified to date. In this paper, we provide information relating to halogenated FRs and PFRs, including common, trade and systematic names, CAS numbers, physicochemical properties where known, together with recommended structured abbreviations (STABs) and practical abbreviations (PRABs). Also some general comments see more and suggestions are given with the aim of simplifying the abbreviation of the full chemical names of BFRs, CFRs and PFRs. All compounds listed were retrieved by reviewing the scientific literature for BFRs, CFRs and PFRs. Documents of particular use for identifying BFRs and CFRs were: WHO/IPCS, 1994 and WHO/IPCS, 1995, WHO/IPCS (1997), Örn and Bergman (2004),

Andersson et al. (2006); Harju et al. (2009), Letcher et al. (2009), Covaci et al. (2011), de Wit et al. (2011), Sverko et al. (2011); and for PFRs: van der Veen and de Boer (2012). The Liothyronine Sodium compounds are presented in three separate groups (BFRs, CFRs and PFRs) and then listed in molecular mass order within each subgroup. The sub-grouping is given below. We have chosen to list FRs holding, for example, both a phosphorus group and a halogen substituent, in each of the groups to which they belong, i.e. a BFR with a chlorine substituent is also listed in the table containing CFRs (Table 3); a PFR containing bromine substituents is also listed as a BFR. This means that some of the chemicals are listed twice. One further goal of the systematic work presented herein is to enable us to treat functional groups in chemicals in a similar way, which could also be applied for hitherto unknown BFRs, CFRs, and PFRs that may be identified as commercial products in the future.

As shown in Fig 7, the gF construct is made up of several differ

As shown in Fig. 7, the gF construct is made up of several different sources of variance. Thus, like measures of WM, gF also seems to be a multifaceted construct. These results point to the need to examine multiple joint influences on variation in a number of cognitive constructs and suggest that individual differences are due to multiple factors even within a particular construct. Thus far we have argued that capacity,

attention control, and secondary memory are three important processes of WM. However, it would be remiss not to point out that other processes are also likely important for WM and likely covary with capacity, attention control, and secondary memory retrieval. For example, these other processes would include integration and coordination processes that are specifically selleck chemicals needed in WM where processing and storage operations are combined (Bayliss et al., 2003 and Oberauer et al., 2003), updating and attention switching operations that are more likely needed in complex span

tasks (Oberauer, 2002, Unsworth and Engle, 2008 and Verhaeghen and Basak, 2005), as well as binding operations that are needed to momentarily bind items (Halford et al., 2007 and Oberauer, 2005). Each of these proceses has been linked to WM in the past and each has been suggested as possible reasons for the strong relationship between WM and gF. Clearly more work is needed to determine the extent to which these processes (as well as potentially other processes) are related with capacity, attention control,

and secondary memory, as well as whether these other processes are needed to fully account for individual differences in WM and the relation buy MK-8776 between WM and gF. Collectively, the current results are very much in line with the multifaceted view of WM, suggesting that WM is a system composed of distinct and interacting old processes. In particular, individual differences in capacity, attention control, and secondary memory jointly account for individual differences in WM and its relation with gF. Thus, the current results help resolve debates about “the” reason for the relation between WM and gF. The current results strongly suggest that multiple mechanisms drive the relation between WM and gF. In order to understand the nature of WM and why WM strongly predicts individual differences in gF we must attempt to understand the multifaceted nature of WM and understand how these various mechanisms independently and jointly lead to variation in host of higher-order cognitive activities. Thanks to Tom Redick and three anonymous reviewers for helpful comments on an earlier version of the article. “
“The publisher regrets to have the contents of the Tables 12 and 14 published similar. The right content of the Table 12 is given below: Spruce proportion [%] u β S100 ln(b) α Spruce 100 4.98 146.15 0.80 −1.37 3.93 81–99 (average 93) 5.12 167.88 0.88 −1.37 3.93 ⩽80 (average 49) 5.32 203.48 0.94 −1.37 3.

This project seeks to determine how forest harvest and regenerati

This project seeks to determine how forest harvest and regenerative

practices can best maintain biotic communities, spatial patterns of structure and ecosystem integrity, compared with mixed-wood landscapes originating through natural disturbances (EMEND, 2014). In another landmark project, the Eco-Gene model (Degen et al., 1996) was used to elucidate the long-term consequences of logging and forest fragmentation in seven Amazonian timber species in the Dendrogene initiative, which incorporated data on genetic structure and gene flow collected before and after logging had taken place (e.g., Sebbenn et al., 2008 and Vinson et al., 2014). As Wickneswari et al. (2014) indicate, MI-773 plantations for wood production may provide corridors and habitat for flora and fauna that support the maintenance of genetic diversity, but they may also have negative effects, such as increasing Z-VAD-FMK in vitro the pest and disease load. In addition, gene flow from alien (exotic or ‘locally exotic’, cf. Barbour et al., 2008) provenances may through hybridisation and introgression eventually swamp locally adapted genotypes in natural forests, if plantation areas are large (Fady et al., 2010; see also Thomas et al., 2014, this special issue). Such introgression may, however, not be universally bad, as indicated by Alfaro et al. (2014,

this special issue); it is sometimes advocated as a means to generate new evolutionary potential to respond to climate change and other adaptive challenges. Why do so many restoration efforts fail? Undoubtedly there are many reasons, but one that has been under-appreciated is a

persistent lack of attention to matching species and seed source to the planting site (Bozzano et al., 2014). In the fifth review of this special issue, Thomas et al. (2014) address this topic by focusing on important genetic considerations in ecosystem restoration programmes based on native tree species. The scale of importance of such work is indicated by the revised Strategic Plan of the Convention on Biological tuclazepam Diversity for 2011–2020, one aim of which is to restore 15% of degraded ecosystems globally by the end of the current decade (ABT, 2014). Since it is estimated that two billion hectares of land could benefit from restoration, this would imply successful restoration efforts on an area of 300 million hectares in the next six years. While currently applied measures of success are often not informative for determining the long-term sustainability of restored ecosystems, as noted by Thomas et al. (2014), many current restoration projects fail to reach their objectives by any measure (Cao et al., 2011 and Wuethrich, 2007). Although the reasons for failure are sometimes complex (as illustrated by examples in China; Zhai et al., 2014), inadequate attention to the genetic composition of the planting material used is a contributing factor (Bozzano et al.

Pr(Gj)(Gj) is computed under a standard population genetics model

Pr(Gj)(Gj) is computed under a standard population genetics model [1]. The unknown parameters ϕ can be replaced with estimates, or eliminated by maximisation or integration with respect to a prior distribution. Currently, there are only limited possibilities to check the validity of an algorithm for evaluating an LTDNA

LR (henceforth ltLR). One approach is to evaluate the ltLR when Q is repeatedly replaced by a random profile [3]. In that case H  p is false and we expect the majority of computed ltLRs to be selleck chemicals llc small. Here, we propose to investigate a performance indicator for ltLR algorithms when H  p is true. Under H  d, it may occur that GX=GQGX=GQ, where GXGX and GQGQ denote the genotypes of X and Q. This occurs with probability π  Q, the match probability for Q. Since Pr(E|Hd,GX=GQ)=Pr(E|Hp)(E|Hd,GX=GQ)=Pr(E|Hp), it follows that [4] equation(3) ltLR=Pr(E|Hp)Pr(E|Hd,GX=GQ)πQ+Pr(E|Hd,GX≠GQ)(1−πQ)≤1πQ.We will refer to 1/πQ as the inverse match probability (IMP). Consider first that Q is the major contributor to an LTDNA profile. Intuitively, if E   implies that GX=GQGX=GQ then equality should

be achieved in Eq. (3). The key idea of this paper is that if H  p is true then increasing numbers of LTDNA replicates should provide increasing evidence that GX=GQGX=GQ, and so the ltLR should converge to the IMP. selleck screening library This holds even for mixtures second if Q is the major contributor, since differential dropout rates should allow the alleles of Q to be identified from multiple replicates. However, any inadequacies in the underlying mathematical model or numerical approximations may become more pronounced with increasing numbers of replicates, preventing the ltLR from approaching the IMP. Therefore we propose to consider convergence of the ltLR towards the IMP as the number

of replicates increases as an indicator of the validity of an algorithm to compute the ltLR when Q is the major contributor. If Q is not the major contributor, even for many replicates there may remain ambiguity about the alleles of Q so that there remains a gap between the ltLR and IMP. However, the bound (3) still holds, and there is a useful guide to the appropriate value of the ltLR provided by the mixture LR for good-quality CSPs computed using only presence/absence of alleles [5]. If under Hp the contributors are Q and U, where U denotes an unknown, unprofiled individual, and Hd corresponds to two unknown contributors X and U, an example of a mixture LR is equation(4) mixLR=Pr(CSP=ABC,GQ=AB|Q,U)Pr(CSP=ABC,GQ=AB|X,U)=Pr(GUisoneofAC,BC,CC)Pr((GX,GU)isoneof(AA,BC),(AC,BB),(AB,CC),(AB,AC),(AB,BC),(AC,BC)),where within-pair ordering is ignored in the denominator.

(2010) One or five days following saline or P berghei administr

(2010). One or five days following saline or P. berghei administration, mice were sedated (diazepam, 1 mg PF 2341066 i.p.), anaesthetised (sodium thiopental, 20 mg/kg i.p.), tracheotomised, paralysed (vecuronium bromide, 0.005 mg kg−1 i.v.), and mechanically ventilated with a constant flow ventilator (Samay VR15; Universidad de la Republica, Montevideo, Uruguay) using the following settings: respiratory rate = 100 breaths/min, tidal volume (VT) = 0.2 ml, and fraction of inspired oxygen (FiO2) = 0.21. The anterior chest wall was

surgically removed, and a positive end-expiratory pressure (PEEP) of 2 cmH2O was applied. After a 10-min ventilation period, lung mechanics were computed. Airflow and tracheal pressure (Ptr) were measured ( Burburan et al., 2007). In an open chest preparation, Ptr reflects transpulmonary pressure (PL). Lung resistive (ΔP1) and viscoelastic/inhomogeneous (ΔP2) pressures, as well as static elastance (Est), were computed by the end-inflation occlusion method ( Bates et al., 1988). Lung www.selleckchem.com/products/abt-199.html mechanics measurements were performed 10 times in each animal. All data were analysed using

the ANADAT data analysis software (RHT-InfoData, Inc., Montreal, Quebec, Canada). Laparotomy was performed immediately after determination of lung mechanics, and heparin (1000 IU) was injected into the vena cava. The trachea was clamped at end-expiration (PEEP = 2 cmH2O), and the abdominal aorta and vena cava were sectioned, producing massive haemorrhage and rapid death. The right lung was then removed, fixed in 4% buffered formaldehyde and embedded in paraffin. Slices (thickness = 4 μm) were cut and stained with haematoxylin and eosin. Lung morphometric analysis was performed using an integrating eyepiece with a coherent system consisting of a grid with 100 points and 50 lines (known length) coupled to a conventional light microscope (Olympus BX51, Olympus Latin America, Inc., Brazil). The volume fractions of the lung occupied by collapsed

alveoli and normal pulmonary areas were determined by the point-counting technique (Weibel, 1990) at a magnification of 200× across 10 random, non-coincident microscopic fields. Neutrophils Dimethyl sulfoxide and mononuclear (MN) cells and lung tissue were evaluated at 1000× magnification. Points falling on neutrophils and MN cells were counted and divided by the total number of points falling on lung tissue in each field of view. For quantification of interstitial oedema, 10 arteries were transversely sectioned. The number of points falling on areas of perivascular oedema and the number of intercepts between the lines of the integrating eyepiece and the basement membrane of the vessels were counted at a magnification of 400×. The interstitial perivascular oedema index was calculated as follows: number of points/number of intercepts (Hizume et al., 2007). At days 1 and 5, the W/D ratio was determined in a separate group of mice (n = 6/group), which was subjected to an identical protocol to the one described above.

Before human development, the Missouri River transported more tha

Before human development, the Missouri River transported more than 298 million metric tons of sediment per year (Jacobson et al., 2009 and Heimann et al., 2011). Anthropogenic

impacts have reduced this transport to 55 million metric tons in the present day. It is estimated that reservoirs along the Missouri trap roughly 33 million metric tons of sediment each year (USACE, 2000). Human alterations and their impacts on the system’s ecology have been considerable. http://www.selleckchem.com/products/MK-2206.html The development of the Missouri River basin has ultimately resulted in many endangered or threatened species of flora and fauna (Whitmore and Keenlyne, 1990 and National Research Council, 2002). The conservation organization, American Rivers, listed the Missouri River as North America’s fourth most endangered river in 2012 because of flow regulation and management practices (http://www.americanrivers.org/assets/pdfs/mer2012/2012-compiled.pdf, accessed 2/5/2013). The study segment in Upper Missouri River extends 512 river km from the Garrison Dam in ND and the Oahe Dam in SD (Fig. 1). The free-flowing (but regulated) segment is approximately 129 river km (80 miles) long with over 81 additional river

kms of variability (50 miles) dependent on reservoir levels at Lake Oahe. At low reservoir levels the free-flowing segment of river ends near the SD border while at high levels the free-flowing segment of the river may end near Bismarck, ND. Two primary tributaries contribute to the free-flowing segment: the

Knife River enters the Missouri River near Stanton, ND and the Heart River joins the Missouri ABT-263 solubility dmso immediately downstream of Mandan, ND. The river segment is used for recreation, irrigation, flood control, water however supply, fisheries, and habitat for threatened and endangered species including the Least Tern (Sternula antillarum), Piping Plover (Charadrius melodus), and Pallid Sturgeon (Scaphirhynchus albus). The Least Tern and Piping Plover utilize sand bars for breeding season habitat, which has resulted in extensive efforts to characterize the patterns and trends of these features in addition to habitat management by plant removal and sand replenishment efforts. Construction of the Garrison Dam began in 1946, and was completed in 1953. Releases for the production of hydroelectricity began in 1956. The Oahe Dam was completed in 1959. The impact on hydrology of the Garrison Dam is typical of large dams: reduction in peak discharges and increases in baseflow (Fig. 2). The river discharge varies several m3/s daily due to demand for power generation and seasonally to accommodate technical, environmental, and navigational needs. Mean annual peakflow prior to dam construction was 3398 m3/s. The peak of record occurred immediately before dam completion in 1953 with a peak discharge of 10,279 m3/s (Fig. 2). Mean baseflow prior to dam construction (1928–1953) was 121 m3/s.

With advances in human genetics over the past 30 years, this scen

With advances in human genetics over the past 30 years, this scenario now seems highly unlikely. The African diaspora of AMH that resulted in the colonization of the entire Earth in ∼70,000 years or less now suggests an alternative scenario in which a unique human biology, a propensity for technological innovation, and shared adaptive resilience may underlie the development of agriculture and complex societies in far-flung parts of the world within just selleck chemical a few millennia, a virtual eyeblink in geological time. The specific nature of this biological change is not currently known—and the behavioral differences between AMH

and contemporary archaic hominins are still hotly debated—but certain facts should not be ignored. H.

erectus, H. heidelbergensis, and H. neandertalensis never moved beyond Africa and Eurasia, for instance, never colonized Australia, the Americas, or the many remote islands of the Pacific, Indian, and Atlantic oceans, they rarely (if ever) drove animal or plant species Raf inhibitor to extinction, never domesticated plants and animals or developed pottery, weaving, metallurgy, and many other technologies, and they never dominated the Earth. With the appearance of AMH, in contrast, humanity began a rapid demographic and geographic expansion, accomplished over the past 70,000 years or less, and facilitated by a progressive acceleration of technological change that continues Reverse transcriptase today. Within this remarkable biological and cultural history, multiple tipping points can be identified along a developmental trajectory that resulted in human

domination of the Earth. These include: (1) the appearance of AMH in Africa, with the seeds of ingenuity, innovation, adaptive resilience, and rapid technological change that progressed from the Middle Stone Age through the Upper Paleolithic, Mesolithic, Neolithic, Iron Age, and Industrial Revolution; All these historical events contributed to the peopling of the Earth and the profound and cumulative effects humans have had on the ecology of our planet. They are all part of the process that led to human domination of the Earth and, as such, a logical case might be made for any one of these ‘tipping points’ being a marker for the onset of the Anthropocene epoch. It seems unlikely that a global case can be made for the Anthropocene prior to about 10,000 years ago, however, when humans had reached every continent other than Antarctica, had begun to domesticate plants and animals, were contributing to extinctions on a broad scale, and were reaching population levels capable of more pervasive ecological footprints. At the end of this volume, we will return to these issues, informed by the papers that follow.

These data indicate that epigenetic inheritance of modified

These data indicate that epigenetic inheritance of modified Cyclopamine order histones may proceed via more than one pathway. Another example of templating comes from Drosophila, in which the centromeric histone variant CID

derived from the sperm is used to template CID deposition at the centromere during embryogenesis [ 34•]. While fertilization can occur with sperm that lack CID, the embryos do not develop normally, and paternal chromosomes lose the ability to recruit maternal CID and re-establish functional centromeres. Thus CID deposition during embryogenesis also appears to depend on a templating mechanism, although it is unclear whether it proceeds via direct or indirect recruitment. Interestingly, several epigenetic marks on the H3 histones appear to be important for proper recycling of old histones to the newly replicated DNA, and these marks have been shown to change under conditions of replication stress [ 35]. However, the mechanism by which nucleosome inheritance is regulated still remains unexplored. Investigations Crizotinib concentration into the influence of transcription rate, histone availability, and timing of replication may all provide important insights into how histones provide the genome with a molecular memory. The ability of chromatin to protect DNA from ionizing radiation was established in a seminal study over 20 years ago. When DNA was completely

stripped of its nucleosomes Loperamide and exposed to 20 Gy of gamma-radiation, the occurrence of double strand breaks (DSBs) was 10 times greater than that of intact cells [36]. However the discovery that histone variants are intimately tied to proper DNA damage response (DDR) progression is relatively recent. In particular, work has focused on the role played by variants of the H2A family: (γ)H2A.X, H2A.Z and macroH2A. While the localized phosphorylation of H2A.X has been

implicated in the response to DSBs for some time, it is only recently that the behavior of H2A.X in response to clustered DNA lesions has been elucidated. Interestingly, when clustered DSBs were induced by ionizing radiation in skin fibroblasts, H2A.X phosphorylation, monitored by immunostaining, was not limited to the region directly surrounding the break, but occurred throughout the genome in a dose dependent manner [37]. This response, catalyzed by two kinases, ATM and DNA-PK, was transient and not linked to apoptosis. Recently, using ChIP at a defined DSB, a second H2A variant usually involved in transcriptional regulation, H2A.Z, was found at the break site [38]. H2A.Z is deposited at the DSB by the ATP-dependent chromatin remodeler p400, and is thought to re-organize the chromatin surrounding the DSB into a more fluid conformation by promoting H4 acetylation (Figure 3).

31 Studies in patients who received liver transplant demonstrated

31 Studies in patients who received liver transplant demonstrated that ALD has been well tolerated without deleterious effects on liver

function tests.32 Patients taking ALD and diagnosed with primary biliary cirrhosis did not present significant hepatic effects regarding biochemical parameters of liver disease.33 Our study also revealed significant inhibition of TALP serum levels after 11 days of periodontitis in animals receiving either saline or ALD. This inhibition may be due to the reduction of the bone isoform, since BALP represents about 90% of the TALP.16 We also observed that ALD prevented neutrophilia LY294002 nmr and lymphomonocytosis. These findings are in accordance with a previous report in which ALD treatment induced a significant decrease in total white Enzalutamide cell line blood cell, neutrophil and lymphocyte counts, in patients with Paget’s disease.34 The reduction in neutrophil count may effect neutrophil migration and activity, once it was seen that ALD decreased on neutrophil influx using a carrageenan-induced peritonitis model and reduced myeloperoxidase activity as well.20 In addition, the reduction

in peripheral mononuclear cells, which includes monocytes and lymphocytes, was also an important finding considering that circulating monocytes can migrate and differentiate locally on osteoclasts, thereby exerting bone resorption activity.22 Thus, the reduction of mononuclear cells Tolmetin may contribute to the bone-sparing effect of ALD in this model. In summary, our results demonstrated that ALD prevented BALP reduction and ABL, and reduced inflammatory infiltrate, without causing systemic alterations. This work was supported by Brazilian grants from the Conselho Nacional de Desenvolvimento Cientifico e Tecnológico (CNPq, Grants 471407/2009-7), Coordenação de Aperfeiçoamento

de Pessoal de Nível Superior (CAPES) and Fundação Cearense de Apoio ao Desenvolvimento Científico e Tecnológico (FUNCAP, Grants 247.01.00/09). None declared. The experimental protocols were executed following ethical principles for laboratory animal use in accordance with the European Convention for the Protection of Vertebrate Animals used for Experimental and Other Scientific Purposes, and they were approved by Institutional Ethical Committee of Animal Research (Process No. 101/2009). “
“Theoretical models of degenerative temporomandibular joint (TMJ) disease predict that mechanical overloading is the major direct cause of condylar cartilage breakdown.1 Biomechanical factors such as loss of posterior teeth and unilateral chewing have been implicated in the aetiology of degenerative TMJ disease through absolute or relative overloading of joint structures.2 However, this assumption is usually based on autopsy and skull studies where ageing was a confounding factor, since tooth loss and signs of osteoarthritis increase with age.

In particular, the experiments discussed above showed that the av

In particular, the experiments discussed above showed that the average ratio between the cross-wind and up-wind mean square slope components varies from 0.75 to 1.03 on slick-covered ocean surfaces. Such a large value of the cross-wind slope component cannot be explained satisfactorily with the unimodal directional distribution, and better agreement is obtained when,

for wave components shorter than the dominant wavelength, the bimodality of directional LY2109761 spreading is taken into account ( Hwang & Wang 2001). In particular, the ATM data (airborne topographic mapper) of the 3D surface topography and bimodal directional function showed that the average ratio between cross-wind and up-wind slope components can reach a value of 0.88 ± 1.0. In this section we will follow mainly the ideas developed by Massel (2007). Thus, let us define ε as a module of the local surface slope in the direction θ1 against the x axis. For two slope components along the x and y axes we have equation(30) εx=∂ζ∂x=εcosθ1,εy=∂ζ∂y=εsinθ1,in which angle θ1 increases

anticlockwise from the x axis. We assume that the x axis is the wind direction. Therefore, the up- and cross-wind of waves surface slopes are εu = εx and εc = εy respectively. To determine the statistical characteristics of wave slopes, we express the two-dimensional probability density function Anti-cancer Compound Library f(ε, θ1) for the module slope ε and direction θ1 in the form suggested by Longuet-Higgins (1957): equation(31) f(ε,θ1)=ε2πΔ××exp−ε2(σy2cos2θ1−2σxy2sinθ1cosθ1+σx2sin2θ1)2Δ,in Racecadotril which the corresponding mean square slopes are equation(32) σx2=(∂ζ∂x)2¯,σy2=(∂ζ∂y)2,¯σxy2=∂ζ∂x∂ζ∂y¯and equation(33) Δ=|σx2σxy2σxy2σy2|.The bar symbolizes the statistical averaging for a given time series of slopes. For the x   axis, parallel to the main wave direction,

the mean square slope σζxy2 is equal to zero, and eq. (31) becomes equation(34) f(ε,θ1)=ε2πΔexp−−ε2(σc2cos2θ1+σu2sin2θ1)2Δ,with Δ=σu2σc2. The subscripts c and u refer to the cross-wind and up-wind components respectively. In order to compare the theoretical distribution of slopes with the Cox & Munk (1954) experiment, we rewrite eq. (24) as a function of two slope components εu and εc, i.e. equation(35) f(εu,εc)=f(ε,θ1)⋅J=f(ε,θ1)|∂ε∂εu,∂ε∂εc∂θ1∂εu,∂θ1∂εc|.Using the fact that equation(36) ε=εu2+εc2andθ1=arctan(εcεu),we obtain equation(37) J=1εu2+εc2.Substituting the above expression in eq. (35) yields equation(38) f(ξ,η)=12πσuσcexp[−12(ξ2+η2)],where equation(39) ξ=εuσu,η=εcσc. Equation (38) takes the form of a two-dimensional Gaussian distribution. It should be noted that Cox & Munk (1954) used the two-dimensional, slightly modified Gaussian distribution (the so-called Gram-Charlier distribution) to fit their experimental data. The Gram-Charlier distribution takes the general form (Massel 1996) equation(40) f=[Gaussain distribution]×[1+∑i,jcijHiHj],in which Hi(x) are Hermite polynomials.