Divergence Research Articles

Computational Fluid Dynamics Simulation of Thermal Runaway Reaction of Styrene Polymerization

Thermal polymerization of styrene in a lab-scale batch reactor was simulated using computational fluid dynamics (CFD). The corresponding hydrodynamic model of thermal polymerization of styrene was combined with the fluid–solid coupling model of a simulated heat exchanger by using the CFD method to construct the corresponding reactor model. The effects of stirring rate, cooling temperature, and cooling flow rate were investigated under the runaway conditions of thermal polymerization of styrene. The results showed that the increase in temperature during the reaction was sensitive to different runaway conditions. The stirring rate and cooling flow rate greatly influenced the increase in temperature during the reaction. Based on the temperature distribution inside the reactor, the optimal location of the temperature monitor was determined by employing the divergence (DIV) criterion.

Effects of Differential Geometry Parameters on Grid Generation and Segmentation of MRI Brain Image

Accurate segmentation of brain tissue in magnetic resonance images (MRI) is a difficult task due to different types of brain abnormalities. In this paper, we review the deformation method focus on the construction of diffeomorphisms to generate the 2D MRI image grids and extend it to the 3D MRI images, address clearly a new formation of the deformation problem for moving domains and construction of diffeomorphisms through a completely different approach. The idea is to control directly the first order differential operators including the Jacobian determinant (JD), divergence (DIV), and curl vector (CV) generated by the 2D and 3D MRI image grids and use them as CNN channels with other modalities (T1-weighted, T1-IR, and T2-FLAIR) or single T1-weighted modality to improve the performance of brain segmentation. More importantly, we discuss the influence of three optimization parameters to the generation of the 2D and 3D MRI image grids by both theoretical analysis and the numerical experiments. We test this method on the IBSR dataset and MRBrainS18 dataset based on VoxResNet and verify the influence of three parameters on the accuracy of MRI brain segmentation. Finally, we also compare the segmentation performance of our method in three networks, including 2D U-Net, 3D U-Net, and VoxResNet. We believe the proposed method can advance the performance in brain segmentation and clinical diagnosis.

CFD simulation to study batch reactor thermal runaway behavior based on esterification reaction

Abstract Thermal runaway is a hazardous problem frequently occurring in the chemical productions. An effective way to avoid accidents caused by thermal runaway is preliminary hazard analysis which can help determine the comparatively safe operating condition in the design phase. In this paper, a series of batch reactor thermal runaway scenarios based on esterification of isopropyl propionate has been studied and according to mixing law the optimal inhibitor injection location has been confirmed. The reactor model is established by computational fluid dynamics (CFD) technology and verified by RC1e test. The effect of cooling temperature, cooling velocity and stirring speed are investigated in detail. Based on the failure status analyses, the appropriate location of temperature probe was then determined by the divergence (DIV) criterion. Finally, the inhibitory mixing performances were evaluated by a global mixing criterion. The results indicated the mixing time and inhibitory region were greatly influenced by the injection location.

Exploring the Links in Monthly to Decadal Variability of the Atmospheric Water Balance Over the Wettest Regions in ERA‐20C

AbstractMonthly‐to‐decadal variability of the regional precipitation over Intertropical Convergence Zone and north‐Atlantic and north‐Pacific storm tracks was investigated using ERA‐20C reanalysis. Satellite‐based precipitation (P) and evaporation (E) climatological patterns were well reproduced by ERA‐20C. Regional P and E monthly time series displayed ~20% differences, but these decreased rapidly with time scale (~10% at yearly time scales). Spectral analysis showed good scale‐by‐scale statistical agreement between ERA‐20C and observations. Using ERA‐Interim showed no improvement despite the much wider range of information assimilated (including satellites). Remarkably high Detrended Cross‐Correlation Analysis coefficients (ρDCCA > 0.7 and often ρDCCA > 0.9) revealed tight links between the nonperiodic variability of P, moisture divergence (DIV), and pressure velocity (ω) at monthly‐to‐decadal time scales over all the wet regions. In contrast, ρDCCA was essentially nonsignificant between nonperiodic P and E or sea surface temperature (SST). Thus, the nonperiodic monthly‐to‐decadal variability of precipitation in these regions is almost fully controlled by dynamics and not by local E or SST (suggested by Clausius‐Clapeyron relation). Analysis of regional nonperiodic standard deviations and power spectra (and respective spectral exponents, β) provided further robustness to this conclusion. Finally, clear transitions in β for P, DIV, and ω between tropical and storm track regions were found. The latter is dominated by transient storms, with energy accumulation at synoptic scales and β < 0.1 at monthly‐to‐decadal time scales, implying that variability and information creation decrease rapidly with time scale. Larger β values (0.2 to 0.4) were found in the tropics, implying longer‐range autocorrelations and slower decreasing variability and information creation with time scale, consistent with the important forcing from internal modes of variability (e.g., El Niño–Southern Oscillation).

Searching for “order” in atrial fibrillation using electrogram morphology recurrence plots

BackgroundBipolar electrograms recorded during atrial fibrillation (AF) can have an appearance of chaotic/random behavior. The aim of this study was to use a novel electrogram morphology recurrence (EMR) analysis to quantify the level of order in the morphology patterns in AF. MethodsRapid atrial pacing was performed in seven dogs at 600bpm for 3 weeks leading to sustained AF. Open chest high density electrical recordings were made in multiple atrial sites. EMR plots of bipolar electrograms at each site were created by cross-correlating morphologies of each detected activations with morphologies of every other activation. The following features of the EMR plots were quantified: recurrence rate (RR), determinism (DET), laminarity (LAM), average diagonal line length (L), trapping time (TT), divergence (DIV), and Shannon׳s entropy (ENTR). For each recording site, these measures were calculated for the normal sequence of morphologies and also after random shuffling of the electrogram orders. ResultsElectrograms recordings from a total of 3961 sites had average cycle lengths of 104±22ms resulting in an average of 100±19 activations detected per 10-s recording and an average RR of 0.38±0.28 (range 0.02–1.00). Shuffling the order of the activation morphologies resulted in significant decreases in DET, LAM, L, TT, and ENTR and significant increases in DIV. ConclusionsEMR plots of AF electrograms show varying rates of recurrence with patterns that suggest an underlying deterministic structure to the activation sequences. A better understanding of AF dynamics could lead to improved methods in mapping and treating AF.

DNA divergence as a criterion of a sweet pepper (Capsicum annuum L.) selection for heterosis

The identification of perspective parental lines for the creation of highyield hybrids is the most laborconsuming stage of selection, because it needs exte nsive trials of combining ability. Based on evaluation of the genetic divergence of the parental lines, the prediction accuracy of F1 hybrids performance was inves� tigated. The value of the divergence was calculated using biometric and molecular methods, such as inter sim� ple sequence repeats (ISSR) and random amplified polymorphic DNA (RAPD). Based on estimates of diver� gence, 10 lines were chosen for cyclic cross (scheme I) and testcross (scheme II). In most crosses, the F1 hybrids were significantly superior to the parents in the main economically valuable traits. The level of het� erosis was higher among hybrids of scheme I. Analysis of the relationship between parental divergence and F1 performance showed that the hybrid productivity of scheme I was predetermined by ISSR divergence in 86%, and productivity was caused by RAPD divergence in 69%, whereas the F1 yield of scheme II was not related to the value of genetic distances. Since the values of DNA divergence were closely associated both with mid� parent level and F1 performance, we assumed that part of the polymorphic DNA fragments of the parental lines of scheme I is related to heterotic loci (HTL), which may be considered potential key markers for the heterotic selection of the sweet pepper.

SU-E-J-135: Measurements of Non-Linearity Features of Breathing Patterns Using Recurrence Quantification Analysis (RQA) and Dynamic Complexity (DC)

Purpose: To investigate if there exists a difference in breathing patterns between patients treated with SBRT and IMRT using RQA and DC (using K2: correlation entropy and D2: correlation dimension) measures. Methods: 9 patients treated with SBRT and 8 treated with IMRT were scanned with 4D CT and the breathing patterns were acquired. One of the SBRT patients was scanned with and without meditation. Each breathing signal consisted of a scalar time series and recurrence quantification analysis (RQA) was utilized to determine the following measures: Periodicity of the system as percentage of recurrence points (%RR), determinism (DET), maximum diagonal line length (L_max) whose inverse the divergence (DIV) is measure for how fast trajectories diverge from each other, the average diagonal line length (L) that can be interpreted as the mean prediction time of the signal, and the entropy (ENTR) a measure of information complexity. In addition the invariant measures of K2 and D2 were also estimated. A locally nonlinear forecast was applied to predict future breathing signals of N time step ahead for the patient with and without meditation. Results: Our results showed %RR has significant correlation with L_max and has inverse correlation with DIV. DET has significant correlation with Lmax, L, ENTR and DIV. Independent t test suggests there is no difference between the SBRT and IMRT groups in terms of the RQA measures and K2. Patient that had undergone meditation showed improvement in %RR, L_max, DIV, K2 and had an estimated correlation dimension of 1.7. Prediction showed similar results for one and three time step ahead but meditation one had better prediction horizon when time step was higher. Conclusion: RQA is a powerful tool that allows one to analyze the dynamic nature of breathing pattern. No significant difference was found in the dynamical complexity of SBRT and IMRT patients.

Effects of anaerobic fatigue on postural control in taekwondo practitioners

Biomechanical research in combat sports usually focuses on the improvement of technique effectiveness [1,2,3]. Train ing loads are to produce specific fatigue-induced changes. Fatigue results from performance and is desired in sports training, provided it reaches a specific level. An external mea su rable symptom of fatigue is a reduction of speed, strength and precision of movements. Such a state may also lead to sports injuries. Postural control is of crucial significance in physical activity as it constitutes a basis for development of other motor abilities in upright body stance. The quality of body balance control is determined by the proper function of the vestibular system and involves a vast array of issues related to motor control, spatial orientation and effects of different forces on the human body. Many resear chers agree that physical exercise and sight do affect postural control in upright stance [4,5,6,7]. There has been a number of studies concerned with the impact of anaerobic and aerobic exercise as well as peripheral and central fatigue on body balance control [8,9,10,11,12, 13,14,15,16]. Some researchers claim that exercise has a negative influence on the quality of postural control in upper stance [5,12,17], while others stipulate that the impact of exercise depends on applied training loads [15,18]. This diver gence of researchers’ opinions may certainly be related to the application of different methods in research experiments. It was noted by Paillard T. [14] , who advocates some stan dardization of test protocols examining the impact of exer cises in sport and rehabilitation. He also concludes that the fatigue of leg muscles, proximal muscles and extensors decreases the quality of postural control to a greater degree than the fatigue of arm muscles, distal muscles, and flexors. Different authors also claim that specific forms of movement may improve parameters of postural control, e.g. Tai-chi train ing [19]. It can be assumed that a similar positive impact can

Information content of MPEF DIVergence product in diagnosing the environment of deep convection

The use of divergence fields retrieved by tracking cloud and humidity features in satellite water vapour imagery to characterise preconvective environments in cases of strong upper-level dynamics is explored. An hourly upper-troposphere DIVergence (DIV) product is inferred from Atmospheric Motion Vectors (AMVs) tracked in the 6.2μm channel of the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) onboard Meteosat Second Generation (MSG). This is an advanced satellite product operationally available since 2008.A specific colour palette is introduced to highlight the information content of the DIV product in mid latitudes. To make this product suitable for using in support to deep convection forecasting, an interpretation scheme of DIV product overlaid by the cloud top brightness temperature lower than −40°C as derived from the corresponding 10.8μm infrared (IR) image is proposed.The potential for operational applications is considered, taking into account that the divergent/convergent upper-level flow at the onset of deep moist convection is a sign of the presence of positive/negative factors, respectively, for the further development of the storm. In this study, the deep convective cells considered are limited to those, reaching the middle troposphere or above. For that purpose, 1166 convective cells with cloud top temperature lower than −50°C that developed over Europe and the Mediterranean coast of Africa from 16 June to 22 July 2010 were investigated. The results show that 76% of all studied deep convective cells developed in areas of divergence (as seen by MPEF DIV product). In 92% of the cases of deep convection appearance (at either divergent or convergent upper-level flow) the convective cells further developed in areas of divergence (as derived by the MPEF DIV product).This relation can be useful for the purposes of convection nowcasting by considering three types of observational information derived by MSG satellite data: composite images of the divergence fields, IR channel 10.8μm images and instability indices, as well as NWP parameters of tropospheric instability and upper-level dynamics.

Is local adaptation in Mimulus guttatus caused by trade-offs at individual loci?

Local adaptation is considered to be the result of fitness trade-offs for particular phenotypes across different habitats. However, it is unclear whether such phenotypic trade-offs exist at the level of individual genetic loci. Local adaptation could arise from trade-offs of alternative alleles at individual loci or by complementary sets of loci with different fitness effects of alleles in one habitat but selective neutrality in the alternative habitat. To evaluate the genome-wide basis of local adaptation, we performed a field-based quantitative trait locus (QTL) mapping experiment on recombinant inbred lines (RILs) created from coastal perennial and inland annual races of the yellow monkeyflower (Mimulus guttatus) grown reciprocally in native parental habitats. Overall, we detected 19 QTLs affecting one or more of 16 traits measured in two environments, most of small effect. We identified 15 additional QTL effects at two previously identified candidate QTLs [DIVERGENCE (DIV)]. Significant QTL by environment interactions were detected at the DIV loci, which was largely attributable to genotypic differences at a single field site. We found no detectable evidence for trade-offs for any one component of fitness, although DIV2 showed a trade-off involving different fitness traits between sites, suggesting that local adaptation is largely controlled by non-overlapping loci. This is surprising for an outcrosser, implying that reduced gene flow prevents the evolution of individuals adapted to multiple environments. We also determined that native genotypes were not uniformly adaptive, possibly reflecting fixed mutational load in one of the populations.

Vorticity, deformation and divergence signals associated with stratosphere-troposphere exchange

The dynamical tropopause of the extratropics, defined as an isosurface of potential vorticity, acts as a barrier to stratosphere–troposphere exchange (STE). Therefore, any transport across this barrier is necessarily associated with diabatic or frictional processes such as turbulence, radiative forcing or condensational heating. Most of these processes are linked to distinct flow phenomena and hence with distinct signatures of the velocity field. The focus of this study is on the characteristics of the velocity field at the time and location of the tropopause crossing, as given by the flow-components divergence (DIV), deformation (DEF) and vorticity (VORT). Firstly, the prevalence of distinct signals is shown for three case studies. Then a Lagrangian climatology of STE is used to assess the climatological aspects of this link for the year 1990. Methodologically, the flow-field components are traced along the STE trajectories, both derived from ERA-40. Some key results of this study are as follows. (1) DEF, positive values of VORT and negative values of DIV are markedly correlated with stratosphere-to-troposphere transport (STT). Therefore, the typical flow field associated with STT is deformative, cyclonic and convergent. (2) For troposphere-to-stratosphere transport (TST), the link with the flow-field components is less pronounced. DEF, VORT and DIV all show small, but distinct local maxima just before the exchange. The flow field during TST is therefore rather divergent and less cyclonic. (3) Sensitivity studies reveal that these findings are robust with respect to temporal and spatial variability. Copyright © 2009 Royal Meteorological Society

Evaluation of Precipitation and High-Level Cloud Areas Associated with Large-Scale Circulation over the Tropical Pacific in the CMIP3 Models

Precipitation and high-level cloud (HLC) areas in association with the large-scale circulation over the tropical Pacific are analyzed for simulations of nineteen Coupled Model Intercomparison Project Phase 3 (CMIP3) models with observations for 16 years of 1984–1999. The distribution of rainfall and HLC areas are composited around the geographical center of tropospheric upper-level (200 hPa) divergence (DIV) along Intertropical Convergence Zone (ITCZ) using monthly anomaly data. Datasets with a finer temporal sampling than monthly means were not available for the present purposes. The most notable feature is that the horizontal spread of enhanced circulation and the related rainfall and HLC areas are all underestimated around the DIV center in the models compared to the observation. Particularly, the underestimation is pronounced in HLC, presumably owing to di‰culties in the physical processes relevant to the spatial distribution of HLC area. In general, a model with a higher correlation between the large-scale circulation field and rainfall tends to have a wider spread of HLC area around the DIV center.

RELATIONSHIPS BETWEEN SEA SURFACE TEMPERATURE, LARGE-SCALE ATMOSPHERIC CIRCULATION, AND CONVECTION OVER THE TROPICAL INDIAN AND PACIFIC OCEANS

In this paper, the quantitative estimates of the effect of large-scale circulations on the sea surface temperature (SST)-tropical convection relationship and the effect of SST on the large-scale circulation-convection relationship over the tropical Indian and Pacific Oceans are presented. Although convection tends to maximize at warm SSTs, increased deep convection is also determined by the divergence (DIV) associated with large-scale circulation. An analysis of the relationship between SST and deep convection shows that under subsidence and clear conditions, there is a decrease in convection or increase in Outgoing Longwave Radiation (OLR) at a maximum rate of 3.4 Wm -2 °C -1 . In the SST range of 25°C to 29.5°C, a large increase in deep convection (decrease in OLR) occurs in the tropical Indian and Pacific Oceans. The OLR reduction is found to be a strong function of the large-scale circulation in the Indian and western Pacific Oceans. Under a weak large-scale circulation, the rate of OLR reduction is about -3.5 Wm -2 °C -1 to -8.1 Wm -2 °C -1 . Under the influence of strong rising motions, the rate can increase to about -12.5 Wm -2 °C -1 for the same SST range. The overall relationship between large-scale circulation and deep convection is nearly linear. A maximum rate of OLR reduction with respect to DIV is -6.1 Wm -2 (10 -6 s -1 ) in the western Pacific Ocean. It is also found that the DIV-OLR relationship is less dependent on SST. For example, the rate of OLR reduction over the western Pacific Ocean for 26°C < SST £ 27°C is -4.2 Wm -2 (10 -6 s -1 ), while that for 28°C < SST £ 29°C is -5.1 Wm -2 (10 -6 s -1 ). These results are expected to have a great importance for climate feedback mechanisms associated with clouds and SST and for climate predictability.

The Border Within: Citizenship Facilitated and Impeded

Immigration is roiling American politics, with controversy continuing and no clear solution in sight. As all parties concur, the system is broken, frustrating the new, would-be, and established Americans, while yielding sub stantial social costs and tensions from the Mexican to the Canadian border, and just about everywhere in between. Beyond this point of agreement, however, dissonance is all that can be heard. Many voices are shout ing; no one knows where to go. Uncertainty reigns as to how best to con trol the borders. Meanwhile, there is another option which governments in the United States have decided to avidly pursue: name ly, create differences between the people of the state and all other people in the state. Hence, expanding immigrant numbers have gone hand in hand, both with a restriction on immigrants' rights and with a growing diver gence between demography and democracy. While unable to prevent unauthorized immi grants from crossing the border, governments have found it much easier to prevent the il legal immigrants residing on U.S. soil from obtaining public services. As a driver's li cense is too fine a privilege to be granted to the country's 12 million undocumented im migrants-let them take the bus!-an every day illegality involved in living in the United States without authorization has become a tool for deporting the unwanted. Likewise, the divide between citizens and permanent residents, which had narrowed in the after math of the civil rights era, has once again begun to widen, with legally resident non citizens no longer eligible for benefits that are now available to citizens alone, and at risk of deportation should they be convicted of a felony. Though not voiceless, non-citi zens are voteless, at little cost to those Amer icans enjoying the vote. The damage, rather, is to the American democracy, decreasingly a government of and for the people, when barely a third of all foreign-born persons liv ing on U.S. soil are eligible to vote. America's resistance to integration with the world and those of its people that have Becoming a Citizen: Incorporating Immigrants and Refugees in the United States and Canada, by Irene Bloemraad. Berkeley, CA: University of California Press, 2006. 382pp. $55.00 cloth. ISBN: 9780520248984.

A description of a new species of Diasemopsis (Diptera, Diopsidae) from the Comoro Islands with morphological, molecular and allometric data

A new specie s of Diasemopsis (Diptera, Diopsidae ) from Comoro Islands is described and illustrated for the first time wi th a llometric datasets . Diasemopsis comoroensis Carr & Földvár i is shown t o be genetically close, but morphologically distinct from th e widesprea d Afro-tropical species D. meigenii (Westwood); notably a significant dive rgence in the degree of sexual dimorphism within eye spa n has occurre d between the two species. A revised molecula r phylogeny of th e genus Diasemopsis is presente d based on the partial sequenc es of four genes.

Estimates of genetic parameters and prediction of additive genetic values in Pinus kesya progenies

The objeetive ofthis study was to seleet Pinus kesya prog enies by lhe estimation of g enetic p arameters using lhe method of restricted maximum likelihood (Remi) and prediction of additive genetic values by the best linear unbiased prediction (Blup ). The Pinus kesya progeny tesl was installed in randomized b/oeks. which consist ed of 30 progenies and three replications. Tlze twenty-year-old trees were evaluated for lhe traits diameter at breast heiglit (DBH), height (HT) and st em form (FOR). The DBH, HT and FOR means \Vere, respectively, 21.89 em, 21.89111 and 1.56 and their respective mean herit ability estimares of progenies were 0.58, 0.39 and 0.66. DBH presented the highest coefficient of additive genetic variation (17.89%). Tlze selection ofthe 80 best t rees whicli belon ged 1021 progenies provided a gain 0/,9.62%for FOR witli a mean of 3.81 trees selected per prog eny, an effective population si:e 0/,30.86 and g enetic diverg ence ofO.37.

Poverty and Social Disqualification: a Comparative Analysis of Cumulative Social Disadvantage in Europe

This article attempts to extend the classical monetary approach to poverty by the use of non-monetary indicators. Poverty will be looked at as a cumulative process of social dis advantage and a comparison made of the dif ferent forms this takes across Europe. This study is based on the results of a research pro ject commissioned by Eurostat to define and correlate several indicators in seven west European countries (Germany, Denmark, Spain, France, Great Britain, Italy and the Netherlands). There is a convergence in some respects, but also notable examples of diver gence from one country to another. With regard to convergent factors, some are unsur prising. Precariousness on the labour market, defined as lack of job security or short and long term unemployment, is correlated with low incomes and poor housing conditions. The likelihood of living as a single person, or of experiencing marital breakdown or divorce, is also much greater for people whose status on the labour market is insecure. Precari ousness and unemployment also lead to an in creased dependence on state welfare benefits, and an increased risk of health problems. The most obvious divergences are in those areas which reflect the strength of an individ ual's social connections. Precariousness is not correlated with weak family connections or the non-availability of a private support net work in all of the countries studied. In Spain and the Netherlands, those who are without employment do not have a poorer quality of relationships with their family than those who are working. In Italy, this quality is, indeed, stronger. In these countries, along with Denmark, the general situation is one of a high level of support for individuals from family and friends, and this is equally true of those people facing social problems. By contrast, in France, Germany and Great Britain, it appears that job insecurity and unemployment are as sociated with impoverished social relation ships.

A generalization of lin divergence and the derivation of a new information divergence

AbstractThe f‐divergence is a general class of divergences which includes various divergences used in representing the difference between two probability densities. It was introduced by Csiszár. Lin, on the other hand, in 1991 introduced a divergence based on a new idea. the inequalities relating the divergence to the existing two divergences are shown, and the results are applied to the problems in information theory.This paper discusses the relation between the inequality concerning Lin's divergence and the inequality concerning the f‐divergence. Based on Lin's method of constructing the divergence, a new divergence called Hermite‐Hadamard divergence is introduced. the property of the proposed divergence, as well as its relation to Lin's inequality, are discussed. Using the proposed divergence, an inequality which is improved further compared to the inequality relating the Kullback diver gence and Hellinger distance is derived. Those results are derived in this paper.

Organizational Analysis in North America and Europe: A Comparison of Co-citation Networks

Over the last decade, the field of organization studies has been characterized by a proliferation of divergent perspectives. Using bibliometric techniques, this paper examines the extent to which this state of differentiation may be associ ated with regional differences in scholarly orientation, specifically, between North America and Europe. The study is based on citation and co-citation analyses of articles published by North American authors in Administrative Science Quarterly and by European authors in Organization Studies in the three-year period from 1990 to 1992. Results do show that there is divergence in the perspectives that are currently dominant in Europe and North America, and, to some degree between Britain and elsewhere in Europe. The discussion section elaborates on the nature of the differences in orientation and speculates on factors that may have fostered and helped to maintain this diver gence.

Gene duplications and the origins of vertebrate development

All vertebrates possess anatomical features not seen in their closest living relatives, the protochordates (tunicates and amphioxus). Some of these features depend on developmental processes or cellular behaviours that are again unique to vertebrates. We are interested in the genetic changes that may have permitted the origin of these innovations. Gene duplication, followed by functional divergence of new genes, may be one class of mutation that permits major evolutionary change. Here we examine the hypothesis that gene duplication events occurred close to the origin and early radiation of the vertebrates. Genome size comparisons are compatible with the occurrence of duplications close to vertebrate origins; more precise insight comes from cloning and phylogenetic analysis of gene families from amphioxus, tunicates and vertebrates. Comparisons of Hox gene clusters, other homeobox gene families, Wnt genes and insulin-related genes all indicate that there was a major phase of gene duplication close to vertebrate origins, after divergence from the amphioxus lineage; we suggest there was probably a second phase of duplication close to jawed vertebrate origins. From amphioxus and vertebrate homeobox gene expression patterns, we suggest that there are multiple routes by which new genes arising from gene duplication acquire new functions and permit the evolution of developmental innovations.