the handiness of powerful computational instruments and recent improvements in multidisciplinary methods are providing researchers an ever - greater opportunity to investigate societies in their complex nature .several research outcomes have been showing that men and women differ in characteristics that could be related to their collaboration patterns .research collaboration is increasing in frequency and scope .it is driven , among other causes , by growing relationship across scientific disciplines , improvement of the efficiency in research resources in projects and development of information and communication technologies .the motivations , strategies , patterns and impacts on scientific productivity in quantity and quality in research collaboration have received great scholarly attention ( ;;ductor15 ) .the patterns vary across space ( ; ) , academic ranks , professional origins and scientific disciplines .economic science makes connections with many other scientific disciplines , like statistics or social sciences , like sociology , history or management ( ; ) .economics shows a growing increase of co - authorship ( ;; ) . on average ,a researcher in economics had less than one co - author in the 1970s , 1.24 co - authors in the 1980s and 1.67 in 1990s ( ; ) .gender differences in collaborative research concerning motivations , strategies , patterns and impacts on science performance have received little attention , contrasting with the growing importance that women hold in academia and research .the literature shows mixed results about the gender differences concerning research collaboration strategies , impacts ( ;;- ) and patterns ( - ) .bibliometric studies and survey analysis are the main methodologies to the study of research collaboration .large bibliometric databases like web of science ( ;; ) are the main sources used to bibliometric analysis . however , that bibliometric databases have a strong weakness concerning the study of the differences by gender ; they do not include information separated by male - female and the way to overcame that weakness is to obtain the information from the first name nal04 or the family name of the author .the present paper seeks to build upon the previous analysis about gender aspects in research collaboration which literature was recently surveyed in . here, we intend to contribute to at least two points of the literature : the differences of research collaboration and interdisciplinary participation by gender .focusing in economics , a scientific subject strongly connected to other scientific domains and constructing five categories of articles in a gender authorship perspective , this study addresses both issues : research collaboration and interdisciplinarity .  applying a network approach and using as unit of analysis articles indexed in the web of science ( wos ) this analysis maps the research collaboration by gender within dozen of scientific subjects , all associated with economics .the choice of network approaches to study research collaboration in economics has been extensively embraced .it often relies on the discovery of patterns of collaborations within researcher communities , aiming to find the influence of individual researchers in the networks using citation analysis .reference beaver78 , in the first complete theory of scientific collaboration , list and discuss the causes for that collaboration .they stress that it is necessary , when scientists deal with research questions , that cross disciplinary bounds .they also identify a large variation in collaboration by discipline , which is being further investigated in more recently published studies ( ; ) .its well known that the adoption of a network approach allows the modeling of social structures from a bottom - up perspective , as resulting from the interaction ( or likeness ) of individual characteristics .moreover , as the individual characterization might be driven by multiple aggregate concerns , the network approaches allow for simultaneously considering that multiplicity of individual aspects and the consequences of the aggregate structures themselves on the emergence of collective patterns .meanwhile , in the adoption of a network approach , one shall be aware that the choice of a given network representation is only one out of several other ways to look at a given set of elements .as connecting the elementary units of a system may be conceived in many different ways , that choice may depend strongly on the available empirical data and on the questions that a network analysis aims to address .the main question addressed in this paper is whether some relevant characteristics of research collaboration would emerge in networks where subjects are linked whenever they co - occur in a common paper .we hypothesized that gender imbalance in authorship of papers might influence the shape of those networks , allowing to uncover patterns from gender differences .if it happens , the emerging patterns may help to understand important characteristics of research collaboration , of the relationship among subjects and its relation to gender .the paper is organized as follows : next section presents the empirical data we work with and some preliminary statistical results .section 3 describes the network approach and the results from its application .section 4 concludes .the web of science ( wos ) is one of the major bibliometric databases ( together with google scholar and scopus ) and includes all scientific subjects .it comprises a total of 11,990 journals ( 8,778 from science and 3,212 from social sciences ) .concerning the scientific domain of economics , it includes 334 publications .the wos classifies each journal in one or more subjects ( or categories ) .taking as examples the journals * journal of informetrics * and * research policy * , the former is classified in `` computer science , interdisciplinary applications '' and `` information science & library science '' , while the latter is classified in `` management '' and `` planning & development '' .  from the original wos database a selection of articles was carried on adopting as criteria : articles published in wos indexed journals over the period 2010 - 2015 , having economics as scientific subject and at least one author affiliated to a portuguese institution .  our motivation to focus on the field of economics and on the papers whoseauthors are affiliated to portuguese institutions is twofold :  1 .economic science makes connections with many other scientific subjects .2 .  according oecd data , portugal presents the highest percentage of women in research during the period of 2004 - 2012 ( oecd , 2016 ) .consequently , our approach is applied to a data set comprising 1,138 papers published in 2010 , 2011 , 2012 , 2013 , 2014 and 2015 and having economics as the main subject matter .  besides economics, each paper may have extra ( or secondary ) subjects .table 1 presents the set of secondary ( extra ) subjects found in our data set .each paper in the data set is coded by a string that informs about the presence of extra subjects . in the broader set of 1,138 papers having economics as the main subject matter , 29 different extra ( or secondary ) subjects were found .  [ cols="<,<",options="header " , ]   table 4 : topological coefficients computed from the mst of each authorship category .although the five networks have similar sizes , there is a remarkable difference in the values obtained for the man exclusive tree ( m.exc-mst ) .when women are excluded , the network of subjects displays an much higher diameter ( ) , showing large distances among subjects are enlarged .the also important decrease in the number of leafs ( ) indicates that this network develops a entirely different structure when compared with the other msts by authorship category .the plots in figure 10 show the number of leafs ( , the diameter ( and the ratio across the different categories of authorship . as ,depending on the specific tree motif , the values of and move in opposite directions , in computing the absolute value of the difference relative to helps to emphasize the distinguish structure of the mst that characterizes the man exclusive network ( m.exc-mst ) .  in the broader set of papers published in wos indexed journals over the period 2010 - 2015 in the scientific domain of economics and having at least one author affiliated to a portuguese institution , as the percentage of female authorship decreases , the mst obtained from the corresponding network of subjects moves from a star configuration to a path motif . in so doing ,the larger distances between subjects are enlarged and the number of poorly connected subjects increases . if , conversely , the network of subjects has a high percentage of female authorship , the corresponding mst approaches a star motif , the number of leafs is enlarged and the corresponding diameter decreases .there are many ways to link the elementary units of system in order to induce a network .choosing the most suitable way depends strongly on the available empirical data and on the research questions that a network analysis aims to address .regarding available empirical data , most of bibliometric databases have a strong weakness concerning the study of the differences by gender .in what concerns research questions , gender differences in collaborative research and interdisciplinarity in scientific outputs have received little attention when compared with the growing importance that women hold in academia and research .  from the set of papers published in wos indexed journals over the period 2010 - 2015 in the scientific domain of economics and having at least one author affiliated to a portuguese institution, our results apparently converge to the hypothesis that women prefer to work in teams .however , they also indicate that when papers are exclusively authored by women , the working teams tend to be smaller than any of those that also include men .these results converge to the mixed results reported in the literature , where different units of analysis , measures , methods and samples were adopted ( ; ; - ) .regarding interdisciplinarity , our findings seem to contradict the hypothesis that women have more propensity to interdisciplinary research collaboration .moreover , we found that academic women in economics compared with their male counterparts reveal preference for the subjects environmental sciences , management and political sciences and that , conversely , the subjects social sciences , mathematics and finance display higher frequencies in papers either inclusively or exclusively authored by men .our main contribution relies in the adoption of a network approach allowing to uncover the emergence of a specific pattern when the network of scientific subjects is induced from a set of papers exclusively authored by men .such a male exclusive authorship condition is found to be the solely responsible for the emergence of that specific shape in the structure of the network .moving away from a _ star _ motif together with the loss of centrality of the subject management have an important bearing on the structure of the male exclusive authorship network : when papers authorship includes just men , the larger distances between subjects in the network become even larger and this is mainly due to a decrease in the relative number of papers having management as a secondary subject .we find enough evidence that gender imbalance in scientific authorships brings a peculiar trait to the networks of subjects .such a peculiar trait might facilitate future network analyses of research collaboration and interdisciplinarity .acknowledgement : financial support by fct ( fundao para a cincia e a tecnologia ) , portugal is gratefully acknowledged .this article is part of the strategic project : uid / eco/00436/2013 .the authors thank marilei kroetz for her work in the gender identification process .frandsen , t. f. ; jacobsen , r. h. ; wallin , j. a. ; brixen , k. ; ousager , j. gender differences in scientific performance : a bibliometric matching analysis of danish health sciences graduates . journal of informetrics 2015 , 9 , 1007 - 1017 .naldi , f. ; luzi , d. ; valente , a. ; parenti , i. v. scientific and technological performance by gender .handbook of quantitative science and technology research : the use of publication and patent statistics in studies of s&t systems 2004 , 299 - 314 .

Abstract: gender differences in collaborative research have received little attention when compared with the growing importance that women hold in academia and research . unsurprisingly , most of bibliometric databases have a strong lack of directly available information by gender . although empirical - based network approaches are often used in the study of research collaboration , the studies about the influence of gender dissimilarities on the resulting topological outcomes are still scarce . here , networks of scientific subjects are used to characterize patterns that might be associated to five categories of authorships which were built based on gender . we find enough evidence that gender imbalance in scientific authorships brings a peculiar trait to the networks induced from papers published in web of science ( wos ) indexed journals of economics over the period 2010 - 2015 and having at least one author affiliated to a portuguese institution . our results show the emergence of a specific pattern when the network of co - occurring subjects is induced from a set of papers exclusively authored by men . such a male - exclusive authorship condition is found to be the solely responsible for the emergence that particular shape in the network structure . this peculiar trait might facilitate future network analyses of research collaboration and interdisciplinarity .   keywords : co - occurrence networks , gender , research collaboration , interdisciplinarity , bibliometrics , minimum spanning tree


graphics processing units ( gpus ) are specialized for math - intensive highly parallel computation , thus more transistors are devoted to data processing rather than data caching and flow control like in cpu .so the potential tremendous performance of general non - graphics computations on gpus has recently motivated a lot of research activities on general - purpose gpu ( gpgpu ) computing ( see .e.g. owens et al .2007 for a review ) .nvidia introduced the tesla unified graphics and computing architecture in november 2006 .the tesla architecture is built around a scalable array of multithreaded streaming multiprocessors ( sm ) .a sm consists of eight streaming processor ( sp ) cores .the tesla sm uses a new processor architecture called single - instruction , multiple - thread ( simt ) .the simt unit creates , manages and executes up to concurrent threads in hardware with zero scheduling overhead .the sm also implements barrier synchronization intrinsic with a single instruction . the fast barrier synchronization , together with lightweight thread creation and zero - overhead thread scheduling support very fine - grained parallelism allowing thousands and even millions of threads to be invoked in kernel calls to achieve highly scalable parallel programming .high performance supercomputing has been important in modern astrophysical research since it became available .simulations allow astronomers to perform experiments " on astronomical objects , collide stars , galaxies , or model the entire visible universe ; all situations are clearly impossible to recreate in a terrestrial laboratory . studying the formation of stars , black holes and galaxies in the universe is particularly challenging computationally .their formation involves the nonlinear interplay of a range of physical processes including gravity , turbulence , magnetic field , shocks , radiation , chemistry , etc .those questions motivated the astrophysical community to develop robust and efficient fluid codes with all the relevant physics .studies involving astrophysical fluid dynamics in general are benefitting tremendously from using spatial and temporal adaptive mesh refinement ( amr ) .this is especially so in the studies of structure formation .for example , the radius of a star is 8 orders of magnitude smaller than the size of a molecular cloud .a uniform grid code is hopeless . on the other hand ,the amr technique has been demonstrated to work well in resolving the large dynamical range involved in those problems ( e.g. abel et al .2002 ; wang & abel 2009 ) .the mapping of computational fluid algorithms to gpu however is still at an early stage of development .harris et al .( 2003 ) performed cloud simulations using stam s method ( stam 1999 ) .this method is also used by liu et al .( 2004 ) for 3d flow calculations .using finite difference methods , brandvik & pulla ( 2008 ) solved uniform grid 3d euler equations , elsen , legresley & darve ( 2008 ) solved 3d euler equations on a multi - block meshes and zink ( 2008 ) solved einstein s equation with uniform grid . as far as we are aware of , this work is the first on mapping an adaptive mesh finite volume solver to gpu .in 2007 , nvidia released cuda for gpu computing as a language extension to c ( nvidia 2009 ) .cuda makes gpu computing application development much easier and more efficient than earlier attempts to gpgpu using various shading languages which need to translate the computation to a graphics language .cuda s parallelization model is based on abstraction of the geforce 8-series hardware .it allows programmer to define kernels which can be executed in parallel by many threads on gpu .threads are organized into 1d , 2d or 3d thread blocks , where each block is executed on one sm .the sm maps the threads inside a block to the streaming processor ( sp ) cores and each thread executes independently with its own instruction address and register state .synchronization is possible only within a block whereas global synchronization between blocks is impossible .blocks are in turn organized into 1d or 2d grid of blocks .each thread can access its thread and block indices by two built - in variables threadidx and blockidx .the sm s simt unit creates , manages , schedules and executes threads in groups of parallel threads called warps .the threads in a warp always execute a common instruction at a time , but different warps execute independently . as a result, different warps can execute on different branches .this is an enormous improvement for branching code compared to previous - generation gpus as the -thread warps are much narrower than the simd ( single - instruction multiple - data ) width of prior gpus .however , if threads of a warp diverge via a conditional branch , different execution path have to be serialized , increaing the total number of instructions executed for this warp .so branching inside a warp should still be minimized to achieve good efficiency .cuda exposes the hardware memory hierarchy by allowing threads to access data from multiple memory spaces .all threads have access to the same global memory .each thread block has a shared memory visible to all threads of the block and with the same lifetime as the block .each thread has a private local memory and a set of registers .there are also two additional read - only memories accessible by all threads : the constant and texture memory .the shared memory is much smaller than global memory , typically kb , but it is on - chip so it has very high register - level bandwidth . a typical programming pattern utilizing this fact is to stage data from global memory into shared memory , process the data there and then write the results back to global memory .in the berger & colella block - structured amr ( berger & colella 1989 ) , a subgrid will be created in regions of its parent grid needing higher resolution .the hierarchy of grids is organized in a tree structure .each grid is evolved as a separate initial boundary value problem .the whole grid hierarchy is evolved recursively . in this framework ,a single grid is a natural unit to be sent to gpu for computing .since the grids are dynamically created , arbitrary grid dimensions can arise in real applications . thus _the key issue for a parallelization scheme to couple efficiently to amr is to let it work for arbitrary grid dimensions_. many parallelization models previously proposed for uniform grid gpu fluid solvers are thus not appropriate to be coupled with amr .  in this work, we use the implementation of berger & colella amr in the publicly available hydrodynamics code enzo ( enzo 2009 ) .previously we have implemented our own hydrodynamics and magnetodynamics code using the enzo amr framework ( wang et al .2008 ; wang & abel 2009 ) . often , the hydrodynamics / magnetohydrodynamics solver is the computationally dominant part ( typically more than 10 times expensive than the amr part in single core run ) .so in this work we consider the mapping of hydrodynamics solver onto gpu while leaving the creation and refinement of the grid hierarchy on cpu .the flows involved in star and galaxy formation are highly supersonic and the reynolds number in those flows are very large ( spitzer 1978 ) .thus we are interested in solving the equations of compressible inviscid hydrodynamics .however , the parallelization scheme we implemented can be applied to any hyperbolic conservation laws .we will demonstrate this explicitly in section [ sec : mhd ] by implementing a amr magnetohydrodynamics ( mhd ) solver on gpu .the equations of compressible inviscid hydrodynamics can be written in the form of conservation laws , the conserved variable is given by where is density , are the three components of velocity for , is the total energy and is the internal energy .the fluxes are given by where is the enthalpy . in this workwe assume the ideal gas equation of state : where is the adiabatic index .many numerical schemes have been developed to solve hyperbolic conservation laws of the form ( [ hydro ] ) .we are interested in a class of finite volume methods called high - resolution shock - capturing ( hrsc ) schemes developed since the mid-1980s .those schemes are designed to capture the correct shock speed even with very low resolutions ( see e.g. leveque 2002 for a comprehensive review ) .this property makes it ideal for adaptive mesh fluid simulations where shocks outside the refined regions may not be well resolved .hrsc schemes represent the most popular scheme in modern astrophysical codes ( e.g. stone et al .2008 ; mignone et al . 2007 ;wang et al . 2008 ) .thus we will focus on mapping the hrsc schemes onto gpu .we use the method of lines ( mol ) to discretize the system ( [ hydro ] ) spatially , where refers to the discrete cell index in directions , respectively . , and are the fluxes at the cell interface .as discussed by shu & osher ( 1988 ) , if one uses a high order scheme to reconstruct flux spatially , one must also use the appropriate multi - level total variation diminishing ( tvd ) runge - kutta schemes to integrate the ode system ( [ ode ] ) .so instead of the forward euler time integration in the original berger - collela amr ( berger & colella 1989 ) , we have implemented the second order tvd runge - kutta scheme : see wang et al .( 2008 ) for further details of the implementation of runge - kutta scheme in an amr framework .generally speaking , there are two classes of spatial reconstruction schemes ( leveque 2002 ) .one is reconstructing the unknown variables at the cell interfaces and then use exact or approximate riemann solver to compute the fluxes .another is direct flux reconstruction , in which we reconstruct the flux directly using the fluxes at cell center .we will adopt the first class in this work .but our framework can also be applied directly to the second class .   by equations ( [ ul ] ) to ( [ flux]).,width=211,height=57 ]  for example , to calculate the flux at cell interface ( see fig.[grid1d ] ) , we need to reconstruct the left and right states and . in this work , we use the piecewise linear method ( plm ) ( van leer 1979 ) for reconstruction , in which the values of primitive variable at are needed .the formula for plm reconstruction is where and the minmod function is given as   with those two states , we use the harten - lax - van leer ( hll ) approximate riemann solver ( harten et al .1983 ) to calculate the flux by , where and for .the important property of this mol approach is that the cells required for flux calculation in any direction are all along that direction .as we will see below , this property is crucial for a efficient parallelization scheme in 2d and 3d .in this section , we discuss a parallelization scheme for the 1d case . in the next section we will extend this scheme to 2d and 3d .first , we note that one drawback of putting all the steps of the 2nd order runge - kutta scheme ( [ rk2 ] ) to gpu is that it needs to send both the old value and intermediate value to gpu in the second step . from our experience ,data transfer between cpu and gpu is quite expensive so it needs to be minimized .this would also double the gpu memory usage .however , the 2nd order runge - kutta scheme can also be written as thus , if we only put the first and second step to gpu , which is the computationally intensive part , and leave the third part on cpu , which is just the addition of two vectors , we may still get large speed - up. this will be the strategy we take .since the first and second steps have exactly the same form , we only need to write one routine computing and call it twice .the pseudocode for this routine reads :   + allocate memory for primitives and fluxes on gpu + copy primitives to gpu + call kernel for flux computation + call kernel for computation + call kernel for time update + copy back to cpu + free memory on gpu +  since the computation of flux vector and time update use only local information and involve only one read and one computation , their implementations are simple : just launch one thread for every active cell .the most computational intensive and tricky part is the flux computation , which happens at cell interfaces and needs a different treatment compared to the other two kernels .our basic scheme is that every flux is calculated by a single thread ( see fig .[ gridthread ] ) .so for a problem with grid cells ( including the ghost cells ) , the number of threads should be .we take the number of threads per block to be a fixed number .thus the number of blocks to be launched is .the final block will have some threads that do not correspond to flux computation , we add a conditional statement in the kernel to just let those threads do nothing .since this affect only the last one or two warps , this remains efficient .for example , in the block , we want to calculate fluxes at cell interfaces with . according to eqs .( [ ul ] ) to ( [ flux ] ) , every thread needs 4 cells around it to calculate the flux .so in total , cells are needed for the calculation .  .every thread , except the first and last , loads the data in the cell to the right of it .the first thread loads in two more cells to the left of it while the last thread loads in one more cell to the right of it.,width=384,height=96 ]  as discussed in section [ sec : cuda ] , the memory bandwidth is much higher on the shared memory .so in the computation of a block , we will first load the cells from global memory to a shared memory array primline[n+3 ] .after the computation is finished , we will then write the flux back to global memory . as shown in fig.[gridthread ] , our memory loading scheme goes as follows : thread will read in primitive variables in cell .to read in all the necessary data , the zeroth thread will then need to read in two more cells and and the ( n-1)th thread will read in one more cell .the kernel code for this flux computation are : +  # define cuda_block_size 64 + # define neq_hydro 5 + ... +  + //get thread and block index + const long tx = threadidx.x ; + const long bx = blockidx.x ; +  + int igrid = tx + bx*cuda_block_size ; //array index in the data field + int idx_prim , idx_prim1 ; +  + _ _ shared _ _ float primline[neq_hydro*(cuda_block_size+3 ) ] ; // input primitive variable + _ _ shared _ _ float fluxline[neq_hydro*cuda_block_size ] ; // output flux +  + if = ( igrid 2 & & igrid size - 2 ) \ { // only do flux computation for active cells +  + // load data from device to shared . + idx_prim1 = ( tx+2)*neq_hydro ; + primline[idx_prim1++ ] = rho[igrid ] ; + primline[idx_prim1++ ] = eint[igrid ] ; + primline[idx_prim1++ ] = vx[igrid ] ; + primline[idx_prim1++ ] = vy[igrid ] ; + primline[idx_prim1 ] = vz[igrid ] ; + // if the first , load in two more cells for boundary condition + if ( tx = = 0 igrid = = 2 ) \ { + for ( int i = -2 ; i - 1 ; i++ ) \ { +idx_prim = igrid + i ; + idx_prim1 = ( i+tx+2)*neq_hydro ; + primline[idx_prim1++ ] = rho[idx_prim ] ; + primline[idx_prim1++ ] = eint[idx_prim ] ; + primline[idx_prim1++ ] = vx[idx_prim ] ; + primline[idx_prim1++ ] = vy[idx_prim ] ; + primline[idx_prim1 ] = vz[idx_prim ] ; + } + } +  + //if the last , load in one more cell for boundary condition + if ( tx = = cuda_block_size - 1 igrid = = size - 2 ) \ { + idx_prim = igrid + 1 ; + idx_prim1 = ( tx+3)*neq_hydro ; + primline[idx_prim1++ ] = rho[idx_prim ] ; + primline[idx_prim1++ ] = eint[idx_prim ] ; + primline[idx_prim1++ ] = vx[idx_prim ] ; + primline[idx_prim1++ ] = vy[idx_prim ] ; + primline[idx_prim1 ] = vz[idx_prim ] ; + } + } +  + // synchronize to ensure all the data are loaded + _ _ syncthreads ( ) ; +  + if ( igrid 2 & & igrid size - 2 ) \ { + // the main computation : calculating the flux at tx + llf_plm(primline , fluxline , tx ) ; +  + //copy 1d flux back to flux + idx_prim1 = tx*neq_hydro ; + fluxd[igrid ] = fluxline[idx_prim1++ ] ; + fluxs1[igrid ] = fluxline[idx_prim1++ ] ; + fluxs2[igrid ] = fluxline[idx_prim1++ ] ; + fluxs3[igrid ] = fluxline[idx_prim1++ ] ; + fluxtau[igrid ] = fluxline[idx_prim1 ] ; + }   in higher dimension , the main trick is that in the mol , 2d and 3d flux computation can be reduced to 1d problems and thus the parallelization scheme discussed above for 1d problem can be applied directly to 2d and 3d problems .   and sweeps.,width=451,height=240 ]  for example , in 2d application of mol , one sweeps through a 1d grid of lines extending in the other direction , calculating the fluxes on every line in every sweep . to compute flux in all two directions , one does two sweeps .the trick is that in every sweep , we conceptually regard the 2d grid to be a large 1d grid , including the ghost cells , which is continuous in the direction we are sweeping . thus ,when we apply thread decomposition to the grid , we send the large 1d array to it and use exactly the same scheme discussed in previous section for 1d problems .this is illustrated in fig .[ sweep ] for a 2d problem , where we show the original 2d grid and the 1d grid sent to the kernel for and sweeps .the 3d case is exactly the same .the additional cost of this method is that we will also calculate fluxes for all the ghost cells since now we regard them as normal cells so some calculation is wasted .however , this is only a small cost .but the gain is that the parallelization scheme now works for any grid dimensions .one only need to use two if " statements to handle the first and last points in the grid , which will lead to execution branching only in the first and last two warps . note that in sweeping , when reading from global to shared memory , the reading is from non - continuous locations .thus reading is non - coalesced in those cases .we have also experimented reshuffling the large 3d array in cpu so that the reading can be coalesced but we found this leads to lower performance because of the reshuffling cost on cpu and additional data transfer .[ quadro ]  .technical specifications of nvidia s quadro fx 5600 graphics card . [ cols="^,^ " , ]all the problems in this work are run on a quadro fx 5600 card . for readers convenience , the technical specifications of quadro fx 5600 card are listed in table 1 .the corresponding cpu comparison cases are run on a single ghz core .    for the sod test problem with .solid line is the cpu solution and squares are the gpu solution.,height=240 ]  to evaluate the accuracy of the gpu solution , we first run a 1d sod shock tube problem ( sod 1978 ) with both the cpu code and gpu code .the initial condition for this problem is two uniform states separated at .the left and right density and pressure are and .the initial velocity is zero everywhere and the adiabatic index is .we use grid points for this test .the result is shown in fig.[sod ] .it can be seen that the gpu solution agrees with the cpu solution very well .this validates our gpu implementation of fluid solver .   .the diamonds show the ratio of the cpu and gpu running time.,height=288 ]  next , we study the performance of gpu code in 3d using the sedov - taylor blast wave problem ( sedov 1959 ) .this section will use a uniform grid .an amr example is given in the next section .to set up the problem , we deposit a total energy into a spherical region of radius ( the explosion region " ) at the center of the simulation box which has length .the pressure inside the explosion region can then be calculated as , where for this problem .the initial density is uniform throughout the box with and the pressure is set to a small value outside the explosion region .[ sedovtime ] shows the performance comparison of the cpu and gpu code for uniform grid sizes  .it can be seen that we get fairly uniform times speed - up for two orders of magnitude difference in grid sizes .this is very encouraging as a wide variety of grid sizes can arise in real amr applications and a uniform speed - up for a large range of grid sizes is a necessary condition for good performance in amr applications .   in this sectionwe show a case of cloud disruption by blast wave , demonstrating that our implementation also lead to good speed - up on amr applications .we put a uniform density cloud with radius at distance away from the center of the blast wave .the cloud is times denser than the medium and is in pressure equilibrium with the medium .the topgrid has resolution and we use six levels of refinement to resolve the cloud disruption , which correspond to an effective uniform resolution .  for this problem , the running time of a single timestep in gpu case is times faster than the cpu case .this is consistent with the behavior we saw in last section for uniform grid tests with various grid sizes .  .six levels of refinement is used to resolve the cloud disruption .the dotted lines show the boundary of subgrids.,width=480,height=240 ]magnetic field has been known to play a very important role in the formation of stars ( shu et al .1987 ) and its role in galaxy formation has also been investigated recently ( wang & abel 2009 ) .thus for astrophysical applications , a mhd solver is of great interest .our parallelization scheme discussed above can be easily extended to the case of mhd . in this section , after discussing the mhd equations , we will show some results of this gpu mhd solver .mhd equations can also be written in the form of conservation laws .thus any schemes for hydrodynamics in principle can also be applied to mhd .the main numerical problem of solving mhd equations is cleaning up the numerically generated magnetic monopoles as magnetic field is divergence - free physically .various schemes have been proposed for this purpose and there is still no universal agreement which scheme is the best ( see toth 2000 for a comparison of various schemes ) . in this work, we will adopt the so - called hyperbolic clean approach ( dedner et al .2002 ) , which nicely fit in our developed framework .this may not be the best scheme for all applications .but other schemes , like the projection scheme , requires the solution of a poisson equation . thus mapping them to gpu requires additional work on sparse matrix solvers .following dedner et al .( 2002 ) , we consider the generalized lagrange multiplier ( glm ) formulation of the mhd equations , which can be written in the conservative form ( [ hydro ] ) with the conserved variables given by where with are the three components of magnetic fields and is the additional scalar field introduced in the glm formulation for the divergence cleaning .  and the fluxes are given by where is a constant controlling the propagation speed and damping rate of ( dedner et al . 2002 ) .solving the glm - mhd system in our framework is straightforward .all we need to do is to add the additional primitive variables to our hydrodynamics solver .    for the brio - wu test problem with .solid line is the cpu solution and squares are the gpu solution.,height=240 ]  first , to evaluate the accuracy of the gpu solution , we run a 1d brio - wu shock tube problem ( brio & wu 1988 ) with both the cpu code and gpu code .the setup of brio - wu problem is similar to the sod problem discussed in section [ sec : sod ] , with two uniform states separated at .but here there is non - zero magnetic field in the initial condition .the left and right states are and .the adiabatic index is taken to be .we use grid points for this test .the result is shown in fig.[briowu ] .it can be seen that the gpu solution agrees with the cpu solution very well .this validates our gpu implementation of mhd solver .   .the diamonds are the ratio of the two running times.,height=288 ]  to compare the performance of the mhd solver to the hydrodynamics solver , we apply the mhd solver to the sedov - taylor blast wave problem discussed in section [ sec : sedov ] .[ mhdsedovtime ] shows the performance comparison of the cpu and gpu mhd solvers for uniform grid sizes .note that for the mhd case , the memory requirement for a run is gb ( three primitives , flux and of the nine mhd fields in a grid size ) .thus it can not fit in the gb memory of a quadro fx 5600 card .  from fig.[mhdsedovtime ] we can see that in the mhd case we also get speedup for a large range of grid sizes .this demonstrates the efficiency of our scheme as applied to more complicated physical problems .       finally , we present the results of an application of our gpu mhd solver to a problem that is of great astrophysical interest related to star formation : the decay of mhd turbulence ( stone et al .1998 ; mac low et al . 1998 ) . following stoneet al . ( 1998 ) , we set initial density to be uniform . an isotropic turbulent velocity with burger - like power spectrum is imposed .the initial mach number is .we use an isothermal equation of state by setting .the resolution is taken to be uniform .[ turbulence ] shows the results of density field after one dynamical time .the code takes about minutes to evolve to this point .[ mach ] shows the time evolution of the average mach number and total magnetic energy .consistent with the findings in stone et al .( 1998 ) , a significant fraction of the kinetic energy decays in one dynamical time , and the presence of magnetic field can not delay it .those results are not new. however , the much shorter running time of the gpu code makes it possible to do many runs in a reasonable time to build up statistics , which is crucial for some aspects of star formation such as the core mass function .currently , this has only been possible in 2d ( e.g. basu & ciolek 2009 ) .resolution sedov - taylor blast wave simulations.,height=240 ]  to be competitive with current state of the art simulations which are usually run on large cpu clusters , a gpu implementation should also be mpi parallel .a simple setup would be building a small cpu cluster with each cpu node containing one or a few gpu cards . as a simple experiment, we built a 4 nodes cpu cluster with 4 mac pro workstations and a nvidia geforce 8800 gt graphics card on each node .the cpu nodes communicate with each other using the standard mpi library over gigabit ethernet .as discussed above , in our scheme , a grid is the basic unit of gpu computing .this makes it trivial to combine our scheme with the standard mpi parallel scheme of berger - collela amr , which also use grids as the basic unit for distribution among processors .the code first calls mpi library to distribute grids to different processors .then each processor sends its grids , one by one , to its gpu for computing .we have tested the resulting mpi - cuda hybrid code on up to 4 gpus .the results of the sedov - taylor blast wave simulations with a uniform resolution using 1 , 2 and 4 gpus are shown in fig .[ speed ] .it shows that our code archived very good , close to ideal speedup for up to four gpus .thus it seems realistic that large gpu clusters may offer significant cost saving as compared to a cpu clusters giving the same performance the magneto hydrodynamical problems our implementation can study .in this work we described how to map hrsc schemes for hyperbolic conservation laws to gpu using nvidia s cuda .we demonstrated that our framework as applied to the equations of inviscid compressible hydrodynamics and mhd can lead to a significant speedup .specifically , on a quadro fx 5600 card , saw approximately a factor of ten speedup compared to a single 3 ghz cpu core .an important purpose of our gpu parallel scheme design is achieving good scalability . in typical fluid simulations with as many as millions of cells per grid ,our parallelization scheme will launch millions of threads at the same time on gpu to perform the computation .this exceeds the quadro fx 5600 s ability of running threads concurrently by more than two orders of magnitude .thus we expect that the speedup factor of our parallelization scheme will increase linearly with the number of sms on the gpu .this makes our scheme highly scalable to future generation of graphics hardwares .one important topic we would like to concentrate on in the near future is sparse matrix solvers for poisson equation .if one can also speed up poisson solvers by a similar factor on gpu , then coupled with the fluid solvers we implemented in this work , a whole range of astrophysical simulations will be open to processing on the gpu as we can then model astrophysical fluids with self - gravity , viscosity and other non - ideal effects .an implementation of poisson solver will also make it possible to use projection method for divergence cleaning and implicit fluid solvers .we would like to thank sean treichler for helpful discussions .we are also grateful to the slac computing group , especially adeyemi adesanya , stuart marshall , ken zhou , for technical support on gpu hardware .zink , b. , 2008 : a general relativistic evolution code on cuda architectures , in the 9th lci international conference on high - performance clustered computing at the national center for supercomputing applications in urbana , il , usa

Abstract: we describe an implementation of compressible inviscid fluid solvers with block - structured adaptive mesh refinement on graphics processing units using nvidia s cuda . we show that a class of high resolution shock capturing schemes can be mapped naturally on this architecture . using the method of lines approach with the second order total variation diminishing runge - kutta time integration scheme , piecewise linear reconstruction , and a harten - lax - van leer riemann solver , we achieve an overall speedup of approximately 10 times faster execution on one graphics card as compared to a single core on the host computer . we attain this speedup in uniform grid runs as well as in problems with deep amr hierarchies . our framework can readily be applied to more general systems of conservation laws and extended to higher order shock capturing schemes . this is shown directly by an implementation of a magneto - hydrodynamic solver and comparing its performance to the pure hydrodynamic case . finally , we also combined our cuda parallel scheme with mpi to make the code run on gpu clusters . close to ideal speedup is observed on up to four gpus .   multi - scale methods , finite volume methods , hydrodynamics , magnetohydrodynamics and plasma 47.11.st , 47.11.df , 95.30.lz , 95.30.qd


multivariate statistical methods have been used for many decades to deal with situations in which two or more variables are measured or recorded for each unit .a classical example of this situation is guerry s data set , in which several variables meant to capture `` moral qualities '' ( e.g. , literacy , crime rate , suicide rate ) were tabulated for each of the departments in which france was divided at the time ( 1833 ) .this data set suggests that one can be interested in how the variables change as one moves around in france , or one can be interested in how the departments compare to each other based on the measured characteristics .it is of special interest how these two approaches can be combined ; this is considered in detail in .  besides having a combination of two essentially multidimensional sources of information , like geographic location plus recorded data , another layer of complexityis added when one more variable like time is added , leading to what essentially are two or more data cubes .a typical example of this is ecological data , where species abundances are measured at different , specified locations , over the course of time .the different approaches used in this setting are reviewed in , using the duality diagram setting as a unifying framework .such an approach is not limited to animal or plant species spread over a geographic area ; the advent of _ metagenomics _ has made it possible to study the abundances of bacterial species in locations like ocean or pond water , or even the human gut . in this caseit becomes important to incorporate information not only about location in space , but also in the phylogenetic landscape , by using established or inferred phylogenetic trees for the bacterial species detected .this problem is addressed , using the duality diagram formalism , in .  as an outgrowth of methods favored by french statisticians, proposed a unifying framework capable of including many methods reinvented and used by different groups in different countries as special cases .this framework is based on the analysis of certain linear operators between inner - product spaces which can be naturally associated to a data matrix , in the same way kernel matrices are used today in machine learning .this is explained in detail in works like and . in this articlewe present some motivations behind the choices made for this approach in the accompanying papers .the notion of duality is everywhere in mathematics , appearing under different guises in the most diverse fields ; and it is often remarkably useful .the idea of duality was introduced in the analysis of multivariate data by the french school of data analysts as a way to unify a suite of methods that turned out to be exactly or almost exactly equivalent to methods known by a different name , and the duality - diagram formalism provides a simple way to put all these methods in the same context .since this approach is the basis of the special articles presented together here [ , , ] , this short introduction aims to establish the basic facts and notation .the abstract approach in the duality diagram setup is often intimidating and it possibly turns away some interested readers ; we hope we can show here that these notions are actually natural , and that the overhead due in understanding the notation pays off handsomely in the breadth and complexity of applications .today the distinction between the space of rows of the matrix as a sample from a population and the space of columns as the fixed variables on which the observations were measured has been softened and we often hear the term ` transposable ' data .the definitions presented here explain this row - column duality .  by dispensing of the traditional probabilistic sample - population interpretation, european data analysts in the 1970s [ , , ] can be seen in hindsight as precursors of the current machine learning schools .it is interesting to remember that all these schools had precursors who spent time at the at&t laboratories in new jersey at a time when john tukey was active there .consider an matrix containing data for variables collected from individuals or units .this matrix defines an operator by the rule .what interpretation can we give to such a map ?the vector can be considered to contain the coefficients for linearly combining the variables into a new , synthetic , variable . in that sense, it becomes apparent that actually we should consider this a map from , the dual space of , into .the map provides a way to fill in the values for the new synthetic variable , which could have been defined even before collecting the data . from now on we will abuse notation and identify the operator and the matrix ( and will do the same with other similarly defined operators and matrices ) .we have then the following portion of the diagram : ^{\mathbf{x } } & \mathbb{r}^n . } \ ] ]   recall that the adjoint of a linear transformation between inner product spaces is defined as the mapping that satisfies ( for simplicity , we will only consider spaces with scalars in in this article ; this is enough for most data analyses ) .this can be seen as just a clever way of extending the notion of matrix transpose to a more general setting , but it is actually a powerful formalism , especially when dealing with multiple inner products on the same spaces ( notice that depends not only on but also on and ) .it is convenient sometimes to think of as a map from to ; this matches the corresponding situation when it is generalized to banach spaces . in our setting this distinction might be considered moot , since all spaces considered are naturally isomorphic to their duals , but we will continue using the star notation ; the diagrams , and all the matrix operations obtained from them , work equally well if the stars are dropped from the spaces .then we have the following : ^{\mathbf{x } } & \mathbb{r}^n \ar@{=}[d]_{\wr}\\ % { x}^*(=\mathbf{x}^t ) } % } \ ] ] since we are considering the standard inner products on and ( and their dual spaces ) , corresponds just to the transpose of .thus , , , these two symmetric matrices have the same eigenvalues ( except possibly for zeros to account for the difference between  and ) , and the two sets of eigenvectors can be used to form the singular value decomposition ( svd ) of [ ] .consider now the situation where the inner products ( i.e. , the geometries ) on and are not standard .that is , assume that there are symmetric , positive definite matrices  and  such that the inner products and somehow make more sense for a particular data analysis than the standard inner products .a typical example is when is a diagonal matrix of ( positive ) weights , one for each individual , down - weighting individuals that are known to have been measured with a larger error ; another example is when is the diagonal matrix containing the reciprocals of the sample variances for the columns of , which corresponds to standardizing the variables ( assuming they are already centered ) ; a related example is when is the inverse of the sample variance covariance matrix obtained from , in which case the new geometry corresponds to the _ mahalanobis distance_. often , we want to consider the case in which and we are interested in a set of transformed variables obtained from by multiplication by , leading to a transformed data matrix .different multivariate procedures can be obtained by appropriately choosing and ; see section [ section : particular - cases ] for some examples .  instead of and its adjoint, consider now the transformation .that is , a vector of coefficients is first transformed into , which is in the scale of the transformed data matrix , and then used to create a linear combination of the variables .then , for all , , so . then , and are self - adjoint operators on and , respectively , but they are not necessarily symmetric matrices .nevertheless , they have real eigenvalues ( which match , except for zeros to account for the difference between and ) , because they are similar to symmetric matrices by way of positive definite matrices ; for example , where is obtained by replacing each eigenvalue of with .the eigenvectors of and are also real ; however , they need not be orthogonal .nevertheless , the eigenvectors of can be taken to be orthogonal with respect to , and those of to be orthogonal with respect to .( this can be interpreted as leading to a generalized version of the svd . )  in diagram form , we have the following : ^{\mathbf{x } } & \mathbb{r}^n \ar[d]^{\mathbf{d } } % & { \mathbb{r}^n}^ * \ar[l]^{\mathbf{x}^t } % } \ ] ] this way , the triplet of matrices defines a multivariate data analysis setup , in which the main strategy is the computation of the eigendecompositions of the matrices and .it is also customary to denote and , so that the two operators of interest become and .the eigendecomposition can be computed for the smaller of the two matrices ( which is usually much smaller than the other ) , and , if needed , the eigenvectors for the other one can be easily obtained : for example , if , then satisfies furthermore , orthogonality is also preserved among eigenvectors : if are -orthogonal eigenvectors for , then thus , whole eigendecompositions are easily transferred .the operator can be seen as a precursor of the more general kernel matrices used in today s kernel pca type methods [ ] .  in the kernel approach to data analysisone assumes that the data is provided as a matrix containing proximity scores for each pair of individuals ; these scores might have been computed from measured variables ( as in the case of the matrix , the _ linear kernel _ ; nonlinear functions of the variables offer a great variety of other possibilities ) , or by directly comparing the individuals ; see for a review of the theory and examples of applications in computational biology .kernel matrices are similarity matrices , that is , the proximity score for two individuals is high when they are similar and low ( even negative ) when they are dissimilar .( distance matrices , on the other hand , have higher values for dissimilar pairs of individuals . )what is the meaning of as an operator on ?a useful interpretation is to consider it as a smoothing operator acting on real - valued functions defined on the set of individuals : the value of at the individual is a weighted sum of all the values of , with higher weights for those individuals more similar to the ; in other words , is averaged locally ( up to a multiplicative constant ) .this offers one explanation of why the eigendecomposition of is useful , since repeated application of to ( which should produce a very smooth function ) converges toward an eigenvector of the leading eigenvalue , and `` very smooth '' functions of the data points can be used as coordinates . explores the similarities between the duality diagram and kernel approaches in appendix b , for the case of kernel canonical correspondence analysis .here we briefly describe how some well - known multivariate methods can be expressed as particular cases of the duality diagram , by appropriately choosing and .we will assume that is centered by columns ( i.e. , the mean has been subtracted for each variable ) .pca seeks to find linear combinations of the variables that explain most of the variability in the data ; see , for example , for more details .take , and .this corresponds to pca in the original scales ; it is equivalent to a straightforward svd on ( except for the factor  ) .if one standardizes the variables , as it is often appropriate to eliminate unit scale effects , then is taken to be the diagonal matrix containing the reciprocals of the sample variances of the columns of ( so contains the reciprocals of the standard deviations ) . while the eigenvector of the ( -weighted ) sample covariance matrix provides the loadings of the variables for the principal component ( so that the actual components have to be obtained by ) , can be obtained directly as an eigenvector for : indeed , computing the principal components does not require the explicit decomposition of as .a total of observations are classified according to two categorical variables , one with categories or levels , and the other with , producing a matrix of counts for each combination of levels ( a _ contingency table _ ) .one wants to study how the counts differ from the expected counts under the assumption of independence between the two variables . to cast ca as a duality diagram, we first define the frequency matrix and the marginal frequency vectors and ; then , the expected counts ( conditionally on the marginals ) are given by .using the matrices and , we can standardize by the matrix seems like a reasonable choice to study by eigendecomposition .however , all rows and columns have been reduced to the same importance , while , heuristically , categories with larger marginal counts should provide more accurate information on the distribution of the other variable , and thus should be given greater weight .this can be achieved by defining the triplet .notice that actually is centered by rows and by columns with respect to the inner products given by and .this approach matches the traditional definition of ca . shows how the information about relationships between the rows of the contingency table can be incorporated into the duality diagram in the special case where there are binary trees that connects the rows of the abundance matrix .the study of variability of one continuous variable is done through the use of the variance ; this notion is generalized in several different directions to accommodate the complexities of dealing with multiple tables , graphs , etc ., through the concept of inertia . as in physics, we define inertia as a weighted sum of squared distances of the weighted points . for each of the diagrams studied above, the inertia designates the trace of the operator , and we have . as pointed out in , in the case of ca , the inertia is proportional to the statistic , whereas in ordinary pca it is just the total variance of all the variables . in discriminant analysis ,the inertia is decomposed into between - groups and within - group components ; these are also used in the bca analysis [ , ] .the weighted distances between columns have another interpretation in ecology and shows how they can be associated to different measures of diversity .the decomposition of total inertia can be seen as a generalization to manova which is the special case of a variance decomposition . uses this effectively to show how to decompose the total diversity across all locations into the average diversity of individual locations and plus the average of pairwise dissimilarities of locations . use similar decompositions to show what part of the inertia can be assigned to spatially local variation in their bca approach to multivariate spatial data .they also show how the graphical relationships between rows can be encoded in a special metric built from the weighted connectivity matrix .( in their paper , they call these weights . )interesting results can be obtained by combining two or more triplets .the usual assumption is that two ( or more ) sets of variables are measured on the same set of  individuals ; thus , the matrix is assumed to be common , but each set of variables has its own version of , of the appropriate size .  for example , one of the triplets might contain data from variables measured on each of the individuals , while the other might encode known relationships between the individuals .a key element in the comparison of the operators arising from two duality diagrams is the rv coefficient .it can be considered as a generalization of the squared correlation coefficient by using the froebenius matrix product .  given two symmetric matrices of the same size ,we define , and whenever . many nice properties of these definitions arise from the fact that defines an inner product on the vector space of symmetric matrices of a given size .this can be adapted to the general setting of multiple duality diagrams : having fixed , call the vector space of -symmetric matrices , that is , matrices satisfying ( equivalently ,  is self - adjoint with respect to ) .then defines an inner product on .when comparing two duality diagrams , then numbers of variables might be different , yielding matrices of different size ; however , we will be comparing the matrices ( operators )  and , which are of the same size and -symmetric .we define the rv coefficient of the two diagrams as .some immediate properties of the rv coefficient are as follows : its values are always in $ ] ; it equals 1 only when , for some nonzero scalar  ; and it equals 0 only when ( provided are nonsingular ) .the proofs are not too hard ; more details can be found in .  the rv coefficient between diagrams ( or triplets )can be used for justifying the use of eigenvalues and eigenvectors in this setting .for example , performing pca based on and selecting the top components is equivalent to finding a matrix such that the rv coefficient between and is maximized .when one data set  has the special status of a response that we would like to predict or explain from the other data set of explanatory variables , we can generalize ordinary regression to a multivariate response through the same diagram framework .this is called _ pca with respect to instrumental variables _ , abbreviated pca - iv ( also known as redundancy analysis , rda ) , first described by . in terms of the comparison of duality diagrams and rv coefficients , this problem can be rephrased as that of finding the metric to associate to so that is _ as close as possible _ to in the rv sense .that is , we want to maximize .we abbreviate the cross - products by writing and then for any  the first term on the right - hand side does not depend on , and the second term will be zero for the choice .  if we add the extra constraint that we only allow ourselves a rank approximation , with , the optimal choice of a positive definite matrix is to take where the columns of  are the eigenvectors of with the pca with regards to instrumental variables of rank is equivalent to the pca of rank of the triple where    consider diagrams .this could correspond , for example , to different studies on the same subjects , using different variables , or the same variables measured on the same units at different points in time ( time course study ) ; a review of this problem in the setting of community ecology is found in .it is often important to summarize the relationships between the diagrams in a compact and intelligible way .the rv coefficients in fact allow us to consider this as performing a pca of the pcas .we compute the multivariate correlation coefficients between tables and use those as the matrix to be diagonalized , similarly to what happens in ordinary pca .the values of the pairwise computations of the covv and rv coefficients are arranged into symmetric matrices and , respectively , and the eigendecomposition of these matrices can lead to useful low - dimensional representations , just as in the case of pca using the covariance or correlation matrices , respectively . in this case , a 2- or 3-dimensional plot can be created in which each point represents one of the studies ( diagrams ) .  furthermore , since and have nonnegative entries , the eigenvector corresponding to the largest eigenvalue can be taken to have only nonnegative entries , adding up to 1 . then , defining , the operator can be taken as a compromise or summary of all the diagrams , and one can study how far , in the rv sense , different studies are from the compromise .these steps are part of the so - called statis procedure [ ] .one can think of these data sets as a data cube , with three indices ; then a similar procedure can be used to compare two or more such cubes .the duality diagram is a useful formalism that allows one to easily compare many classical multivariate methods , revealing what they have in common and where they differ .but , furthermore , it has become a valuable tool for dealing with two problems that have become very common : ( 1 ) combining and amalgamating data which , although collected from different sources and using different methods , shed light on different aspects of the same phenomenon ; and ( 2 ) taking advantage of complex , nontraditional data types , like tree and network information .these two problems are closely related , as the data to be amalgamated are often of complex type .the overhead in effort to understand the abstract definitions in the duality diagram approach to data analysis is amply offset by the clearer picture that is gained and by the wealth of applications that become available . in this articlewe have tried to reduce that overhead by laying out arguments that show that those definitions are actually quite natural .the three articles [ , , ] in this group are excellent examples of the power of this approach , but are only a small sample from a large and growing body of work .most of the methods presented in these papers have been coded into functions for the statistical computation environment r [ ] , many available in the library ` ade4 ` , for which exemplary presentations have been published [ see , , ] . in the case of , you can even run in an interactive way through all the commands generating each and every plot through the reproducible website at http://pbil.univ - lyon1.fr / saoasopet/.   baty , f. , facompr , m. , wiegand , j. , schwager , j. and brutsche , m. ( 2006 ) .analysis with respect to instrumental variables for the exploration of microarray data structures ._ bmc bioinformatics _ * 7 * 422 .baty , f. , jaeger , d. , preiswerk , f. , schumacher , m. and brutsche , m. ( 2008 ) .stability of gene contributions and identification of outliers in multivariate analysis of microarray data ._ bmc bioinformatics _ * 9 * 289 .shinkareva , s. , mason , r. , malave , v. , wang , w. , mitchell , t. and just , m. ( 2008 ) . using fmri brain activation to identify cognitive states associated with perception of tools and dwellings ._ plos one _ * 3 * e1394 .

Abstract: today s data - heavy research environment requires the integration of different sources of information into structured data sets that can not be analyzed as simple matrices . we introduce an old technique , known in the european data analyses circles as the duality diagram approach , put to new uses through the use of a variety of metrics and ways of combining different diagrams together . this issue of the annals of applied statistics contains contemporary examples of how this approach provides solutions to hard problems in data integration . we present here the genesis of the technique and how it can be seen as a precursor of the modern kernel based approaches .  and  .


deep learning models have achieved remarkable results in computer vision and speech recognition in recent years . within natural language processing ,much of the work with deep learning methods has involved learning word vector representations through neural language models ( bengio et al . , 2003 ; yih et al . , 2011 ; mikolov et al . , 2013 ) and performing composition over the learned word vectors for classification .word vectors , wherein words are projected from a sparse , 1-of- encoding ( here is the vocabulary size ) onto a lower dimensional vector space via a hidden layer , are essentially feature extractors that encode semantic features of words in their dimensions . in such dense representations ,semantically close words are likewise close in euclidean or cosine distance in the lower dimensional vector space .convolutional neural networks ( cnn ) utilize layers with convolving filters that are applied to local features . originally invented for computer vision , cnn models have subsequently been shown to be effective for nlp and have achieved excellent results in semantic parsing , search query retrieval , sentence modeling , and other traditional nlp tasks .  in the present work ,we train a simple cnn with one layer of convolution on top of word vectors obtained from an unsupervised neural language model .these vectors were trained by mikolov et al . on 100 billion words of google news , and are publicly available .we initially keep the word vectors static and learn only the other parameters of the model . despite little tuning of hyperparameters, this simple model achieves excellent results on multiple benchmarks , suggesting that the pre - trained vectors are ` universal ' feature extractors that can be utilized for various classification tasks . learning task - specific vectors through fine - tuning results in further improvements .we finally describe a simple modification to the architecture to allow for the use of both pre - trained and task - specific vectors by having multiple channels .our work is philosophically similar to razavian et al . which showed that for image classification , feature extractors obtained from a pre - trained deep learning model perform well on a variety of tasks including tasks that are very different from the original task for which the feature extractors were trained .the model architecture , shown in figure 1 , is a slight variant of the cnn architecture of collobert et al . .let be the -dimensional word vector corresponding to the -th word in the sentence .a sentence of length ( padded where necessary ) is represented as      where is the concatenation operator . in general , let refer to the concatenation of words .a convolution operation involves a _ filter _ , which is applied to a window of words to produce a new feature .for example , a feature is generated from a window of words by here is a bias term and is a non - linear function such as the hyperbolic tangent .this filter is applied to each possible window of words in the sentence to produce a _ feature map _ ,\ ] ] with .we then apply a max - over - time pooling operation over the feature map and take the maximum value as the feature corresponding to this particular filter .the idea is to capture the most important feature one with the highest value for each feature map .this pooling scheme naturally deals with variable sentence lengths .we have described the process by which feature is extracted from filter .the model uses multiple filters ( with varying window sizes ) to obtain multiple features .these features form the penultimate layer and are passed to a fully connected softmax layer whose output is the probability distribution over labels .  in one of the model variants , we experiment with having two ` channels ' of word vectors one that is kept static throughout training and onethat is fine - tuned via backpropagation ( section 3.2 ) . in the multichannel architecture ,illustrated in figure 1 , each filter is applied to both channels and the results are added to calculate in equation ( 2 ) .the model is otherwise equivalent to the single channel architecture .for regularization we employ dropout on the penultimate layer with a constraint on -norms of the weight vectors .dropout prevents co - adaptation of hidden units by randomly dropping out i.e . , setting to zero a proportion of the hidden units during foward - backpropagation .that is , given the penultimate layer  ] where was chosen such that the randomly initialized vectors have the same variance as the pre - trained ones. it would be interesting to see if employing more sophisticated methods to mirror the distribution of pre - trained vectors in the initialization process gives further improvements .* we briefly experimented with another set of publicly available word vectors trained by collobert et al .on wikipedia , and found that ` word2vec ` gave far superior performance . it is not clear whether this is due to mikolov et al . sarchitecture or the 100 billion word google news dataset .* adadelta gave similar results to adagrad but required fewer epochs .in the present work we have described a series of experiments with convolutional neural networks built on top of ` word2vec ` . despite little tuning of hyperparameters ,a simple cnn with one layer of convolution performs remarkably well .our results add to the well - established evidence that unsupervised pre - training of word vectors is an important ingredient in deep learning for nlp .

Abstract: we report on a series of experiments with convolutional neural networks ( cnn ) trained on top of pre - trained word vectors for sentence - level classification tasks . we show that a simple cnn with little hyperparameter tuning and static vectors achieves excellent results on multiple benchmarks . learning task - specific vectors through fine - tuning offers further gains in performance . we additionally propose a simple modification to the architecture to allow for the use of both task - specific and static vectors . the cnn models discussed herein improve upon the state of the art on 4 out of 7 tasks , which include sentiment analysis and question classification .