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Hendrik-a

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0803.2754

i

an immersion @xmath6 is _ conformally flat _ if there exists a flat metric in the conformal class of the induced metric @xmath7 : that is there exists a smooth function @xmath8 such that @xmath9 is flat . this condition is equivalent to the weyl tensor of @xmath10 being zero when @xmath11 , and to the schouten tensor @xmath12 being a codazzi tensor when @xmath13 ( i.e. , @xmath14 is a symmetric @xmath15-tensor ) . the history of conformally flat immersions is long , the search for conformally flat submanifolds being a natural task in conformal geometry . the study of conformally flat _ hypersurfaces _ in @xmath0 dates back to cartan @xcite who , demonstrated that the only such hypersurfaces for @xmath11 are the channel hypersurfaces : envelopes of a 1-parameter family of @xmath2-spheres . in particular these have ( at most ) two distinct principal curvatures . for @xmath16 the problem is uninteresting as every surface is conformally flat . for @xmath13 , however , there are more varied conformally flat hypersurfaces : not only are there the channel examples , there also exist hypersurfaces with 3 distinct curvatures . these were first discussed by hertrich jeromin @xcite , who moreover described the link between conformally flat hypersurfaces in @xmath3 , curved flats in the space of circles in @xmath3 , triply orthogonal systems , and guichard nets . the classification of these hypersurfaces , however , remained unknown . given a conformally flat immersion @xmath17 with flat normal bundle , we embed @xmath18 naturally in the _ light - cone _ @xmath19 of isotropic vectors in a lorentzian @xmath20 , and construct a _ flat lift _ @xmath21 : this @xmath22 is immersed , has flat induced metric , and flat normal bundle . since both are flat , the tangent and normal bundle decomposition of the trivial @xmath23-bundle is a _ curved flat _ @xcite in the pseudo - riemannian symmetric space @xmath24 ( the grassmannian of space - like @xmath4-planes in @xmath20 ) . we are thus immediately in the realm of integrable systems . curved flats in @xmath25 with a _ good _ co - ordinate system give rise to terng s @xmath25-system ( @xcite ) , which is constructed as follows : suppose that @xmath26 is the involution of the lie group @xmath27 defined by @xmath28 , where @xmath29 and @xmath30 is the @xmath31 identity matrix . then @xmath32 is the fixed point set of @xmath26 in @xmath27 . let @xmath33 denote the @xmath34-eigenspace decomposition of @xmath35 . @xmath32 then acts on @xmath36 by conjugation . let @xmath37 be a maximal abelian subalgebra in @xmath36 , and @xmath38 a basis of @xmath37 . _ the @xmath25-system defined by @xmath37 _ is the following system for @xmath39 : @xmath40-[a_j,\xi_{x_i}]-[[a_i,\xi],[a_j,\xi]]=0,\quad i\neq j,\ ] ] where @xmath41 is the orthogonal complement of @xmath37 with respect to the killing form . unlike in the riemannian symmetric case , not all maximal abelian subalgebras in @xmath36 are conjugate under @xmath32 ; there are both semi - simple and non - semisimple such subalgebras . we note that two maximal abelian subalgebras in @xmath36 conjugate under @xmath32 give rise to equivalent @xmath25-systems , while two non conjugate maximal abelian subalgebras in @xmath36 give non - equivalent @xmath25 systems . the normal bundle of an immersion is termed _ non - degenerate _ if the dimension of the space of shape operators at each point is equal to the co - dimension . an immersion has _ uniform multiplicity one _ if it has flat normal bundle and distinct curvature normals ( equivalently all curvature distributions have rank one ) . it follows from the definition that an @xmath4-dimensional submanifold in @xmath23 with flat and non - degenerate normal bundle has uniform multiplicity one . we prove that a conformally flat @xmath4-immersion into @xmath18 with uniform multiplicity one gives rise to a flat @xmath4-immersion in the light - cone @xmath19 with flat non - degenerate normal bundle , and that the converse is also true . to study conformally flat @xmath4-immersions in @xmath18 with uniform multiplicity one is thus the same as to study flat @xmath4-immersions in @xmath19 with flat non - degenerate normal bundle . we show that there exist line of curvature co - ordinate systems for these flat immersions , and that their gauss - codazzi equations amount to the @xmath24-system defined by a semi - simple maximal abelian subalgebra @xmath37 . conversely , given a solution to the @xmath25-system defined by @xmath37 , and a null vector @xmath42 we obtain a a conformally flat immersion in @xmath18 with uniform multiplicity one . motivated by definitions in classical differential geometry , we call a diffeomorphism @xmath43 between @xmath4-immersions in space forms with flat normal bundle a _ combescure transform _ if @xmath44 maps principal directions of @xmath45 to those of @xmath46 and they are parallel . a combescure transform @xmath44 is _ christoffel _ if it is orientation reversing . given a solution to the @xmath25-system defined by @xmath37 and a null vector @xmath47 with @xmath48 , we construct a flat @xmath4-immersion @xmath49 in @xmath19 with flat normal and non - degenerate bundle . hence @xmath49 projects to a conformally flat immersion in @xmath18 with uniform multiplicity one . moreover , if @xmath50 and @xmath51 are null vectors with euclidean length @xmath52 , then @xmath53 is a combescure transform . because of the correspondence between solutions of the @xmath25-system and conformally flat @xmath4 immersions in @xmath18 with flat and non - degenerate normal bundle , all the machinery of soliton theory applies : loop - group dressing of solutions to obtain new conformal flats or simply dressing vacuum solutions to obtain more complex explicit conformally flat immersions ; existence results such as cartan - khler and inverse scattering , etc . in particular : 1 . we may dress solutions by special , simple elements , whose action may be calculated explicitly by residues . the action of such elements is seen to be by _ ribaucour transforms _ on conformal flats : corresponding immersions envelop ( have first - order contact with ) a congruence of @xmath4-spheres in such a way that principal curvature directions on the envelopes correspond under the congruence . local analytic conformally flat @xmath4-immersions in @xmath18 are determined by @xmath54 functions of one variable . the cauchy problem for the @xmath25-system with rapidly decaying initial data on a regular line can be solved globally . is _ regular _ if @xmath55 is a injective . ] although the resulting @xmath4 dimensional submanifolds may have cusp singularities , the frame is globally defined and smooth . the moduli space of such immersions has a loop group symmetry . if the normal bundle is degenerate and the curvature distributions @xmath56 ( common eigenspaces of the shape operators ) have constant ranks , then we show that all but one of the @xmath56s have rank one . such submanifolds are thus envelopes of @xmath57-parameter families of @xmath58-spheres . if , in addition , these immersions are assumed to have line of curvature co - ordinates , then the gauss - codazzi equations are the @xmath25-system defined by a non - semisimple maximal abelian subalgebra @xmath37 in @xmath36 . conversely , given a solution of the @xmath25-system defined by @xmath37 , we obtain an @xmath59-parameter family of flat lifts , each of which gives rise to a conformally flat immersion in @xmath18 with flat normal bundle , but not with uniform multiplicity one . when @xmath13 , these give _ channel immersions_. loop group dressing still works , and we can construct channel immersions from any germ of an @xmath60-valued holomorphic map at @xmath61 that satisfies the reality condition associated to @xmath25 . most of the results for conformally flat @xmath4-immersions in @xmath18 with uniform multiplicity one hold for conformally flat @xmath4-immersions in @xmath62 with flat normal bundle , @xmath4 curvature normals such that the orthogonal complement of the subbundle spanned by @xmath4 curvature normals is flat . there exist line of curvature co - ordinates and a correspondence between such immersions and solutions of the @xmath63-system . the paper is organised as follows . in section [ sec : flatlift ] , we generalise hertrich jeromin s work on conformally flat immersions of hypersurfaces in @xmath3 to @xmath4-submanifolds in @xmath18 : we outline the light - cone model and how conformal flat immersions in the sphere correspond to genuine flat immersions in the light - cone , then consider the curvature distributions of corresponding maps , and how their fundamental forms compare . the link between conformal flats and the @xmath25-system is detailed in section [ sec : uk ] , and we explain its generalisation to conformally flat @xmath4-immersions in @xmath62 in section [ sec : codim ] . we give a discussion of the dressing transformations of a negative loop on the space of solutions to the @xmath25-system and their associated conformally flat immersions ; certain dressing transforms are shown to give rise to geometric ribaucour transforms in section [ sec : rib ] . in the final section , we show that solutions of the @xmath25-system defined by a non - semisimple maximal abelian subalgebra give rise to the channel immersions .

. cartan proved that conformally flat hypersurfaces in for have at most two distinct principal curvatures and locally envelop a one - parameter family of-spheres . we prove that the gauss - codazzi equation for conformally flat hypersurfaces in is a soliton equation , and use a dressing action from soliton theory to construct geometric ribaucour transforms of these hypersurfaces . we describe the moduli of these hypersurfaces in and their loop group symmetries . we also generalise these results to conformally flat-immersions in-spheres with flat and non - degenerate normal bundle . research supported in part by nsf advance grant ] research supported in part by nsf grant dms-0707132 ]

. cartan proved that conformally flat hypersurfaces in for have at most two distinct principal curvatures and locally envelop a one - parameter family of-spheres . we prove that the gauss - codazzi equation for conformally flat hypersurfaces in is a soliton equation , and use a dressing action from soliton theory to construct geometric ribaucour transforms of these hypersurfaces . we describe the moduli of these hypersurfaces in and their loop group symmetries . we also generalise these results to conformally flat-immersions in-spheres with flat and non - degenerate normal bundle . research supported in part by nsf advance grant ] research supported in part by nsf grant dms-0707132 ]

0907.0529

i

the @xmath0 expansion of qcd @xcite is a valuable tool for studying the nonperturbative dynamics of the strong interactions @xcite . in the limit @xmath2 , the baryon sector of qcd has an exact _ contracted _ @xmath3 spin - flavor - symmetry @xcite . for finite @xmath4 , the contracted spin - flavor - symmetry is broken by effects suppressed by powers of @xmath0 @xcite . the spin - flavor structure of the @xmath0 breaking terms is predicted at each order in the @xmath0 expansion @xcite . the spin - flavor structure of many baryon properties have been derived in a systematic expansion in @xmath0 @xcite , and the results are in excellent agreement with experiment ( for reviews , see @xcite ) . one important application of the baryon @xmath0 expansion is to baryon masses @xcite . by choosing appropriate linear combinations of the baryon masses , one can study coefficients of the baryon mass @xmath0 operator expansion with definite spin and flavor transformation properties . in the case of perturbative @xmath1 flavor - symmetry breaking , the @xmath0 analysis gives a hierarchy of baryon mass relations in powers of @xmath0 and the dimensionless @xmath1 breaking parameter @xmath5 @xcite . the analysis in ref . @xcite showed that the experimentally measured masses of the ground state octet and decuplet baryons exhibit the predicted hierarchy of the combined expansion in @xmath0 and @xmath1 flavor - symmetry breaking . the @xmath0 expansion also has been used to obtain very accurate predictions for the charm and bottom baryon masses @xcite ( to better than 10 mev accuracy ) which have been confirmed by recent experiments . in addition , ref . @xcite derived baryon mass relations which only depend on the @xmath0 expansion and which are valid even if flavor @xmath1 is not a good approximate symmetry , i.e. for large values of the strange quark mass . the predictions of the @xmath0 expansion for baryon masses are in excellent agreement with the experimental values . however , in comparing with the experimental data , one is restricted to only one value of @xmath4 and to the physical quark mass values . testing the predictions as a function of light - quark masses and @xmath4 is now possible with very accurate simulations of baryons using lattice qcd . tremendous progress in lattice qcd has been achieved recently in the simulation of baryon masses using different values of the light - quark masses . extrapolation of baryon masses on the lattice to the physical point has reproduced the experimental values at the @xmath6 level @xcite . the lattice data , however , contain important additional information about the dependence of the baryon masses on the quark masses , which can be utilized . simulations of baryon masses have been performed as a function of @xmath1 flavor - symmetry breaking ranging from small perturbative flavor - symmetry breaking to large nonperturbative flavor - symmetry breaking . there are also lattice simulations at different values of @xmath4 ( though not for baryons ) which are able to test @xmath4 scaling rules @xcite . in this paper , we show that existing lattice simulations ( at @xmath7 ) of the ground state baryon masses already are sufficiently accurate to exhibit and test interesting features of the @xmath0 and @xmath1 flavor - symmetry breaking expansions . still more accurate simulations are needed to test the most suppressed mass combinations of the @xmath0 expansion , but continued improvements in lattice simulations of baryon masses are expected in the short and long term , so it should eventually be possible to test these relations as well . we discuss in this paper how present and future lattice data can be utilized to study the spin and flavor structure of baryon masses . although we do not focus on this point here , it should eventually be possible to test the @xmath4 scaling rules in the baryon sector by lattice simulations which vary the number of colors @xmath4 . an important observation is that the @xmath0 counting rules hold at finite lattice spacing , and so are respected by the lattice results _ including _ the finite lattice spacing corrections dependent on the lattice spacing @xmath8 . thus the discretization corrections are constrained by the @xmath0 expansion . lattice computations of hadron masses are done at varying values of the light - quark masses @xmath9 , @xmath10 and @xmath11 , usually in the isospin limit @xmath12 . the lattice results are then extrapolated to the physical values of @xmath13 . it has not been possible to compute hadron masses for physical values of @xmath13 yet due to the large computational time needed , since @xmath14 . , where @xmath15 is the spatial size of the lattice . ] however , recently , with both algorithmic developments @xcite and large parallel computing machines , there are two groups simulating at or near the physical light - quark mass point @xcite . the light - quark mass dependence of the hadron masses is determined by chiral perturbation theory . there are nonanalytic in @xmath16 contributions from loop corrections which are calculable , as well as analytic terms which depend on low - energy constants ( lecs ) of the chiral lagrangian . in the baryon sector , the leading nonanalytic terms are @xmath17 and @xmath18 . the @xmath17 term , which arises from fig . [ fig : loop ] and is proportional to @xmath19 times axial couplings , radiative corrections . [ fig : loop],width=188 ] is found to be rather large , naively of order a few hundred mev . this term is absent for the pseudo - goldstone boson masses , but is present for other mesons such as the vector mesons @xcite . a surprising feature of recent lattice results is that the baryon masses as a function of @xmath20 do not show a large @xmath21 dependence . fits to the baryon masses also give much smaller values for the baryon axial couplings , and require that the @xmath22 term is almost completely cancelled by @xmath18 and @xmath23 terms . this cancellation must be accidental at the currently accessible lattice quark masses , since the terms have different @xmath16 dependence . an alternative conclusion is that lattice quark masses are too large for @xmath1 chiral perturbation theory to be valid , and that perturbative chiral behavior sets in only for much smaller quark masses than the strange quark mass . this conclusion , however , fails to explain why @xmath1 flavor - symmetry is so evident in baryon phenomenology . the @xmath0 expansion constrains the structure of baryon chiral perturbation theory @xcite . chiral corrections have to respect the spin - flavor structure of the @xmath0 expansion , and this leads to some important restrictions on the form of the chiral loop corrections . for example , the baryon mass , which is of order @xmath4 @xcite , gets nonanalytic corrections proportional to @xmath24 , which are large . this large nonanalytic contribution might lead one to expect that there should be large deviations from the gell - mann okubo mass relations , which were derived assuming that the mass operator was linear in @xmath11 . one can show , however , that the @xmath25 terms are a spin - flavor singlet , and give the same contribution to octet and decuplet baryons , whereas the @xmath24 terms are a spin - singlet flavor - octet , and the @xmath26 terms are spin - singlet flavor-@xmath27 . only the latter terms contribute to the gell - mann okubo mass combinations , so that deviations from these relations are a factor of @xmath28 smaller than naive expectation and consistent with experiment . the small size of the gell - mann okubo relation was recently confirmed for a range of light - quark masses @xcite . for qcd , the cancellation to order @xmath28 arises as a numerical cancellation between octet and decuplet intermediate states @xcite ; to see the parametric form of the cancellation in @xmath0 requires computing the chiral corrections using the @xmath1 flavor representations of baryons containing @xmath4 quarks . the mass relations of ref . @xcite project the baryon masses onto different spin - flavor channels . by studying these mass relations as a function of @xmath16 , one can investigate whether unexpected chiral behavior arises in a particular channel . the organization of this paper is as follows : in sec . ii , the baryon mass relations of the @xmath0 expansion are summarized briefly , and in sec . iii , the lattice simulation data are described . iv presents the results of a computation of @xmath0 mass combinations on the lattice for varying values of @xmath1 flavor - symmetry breaking . v discusses the lattice analysis using heavy baryon chiral perturbation theory @xcite . our conclusions are presented in sec .

baryon mass relations are compared with lattice simulations of baryon masses using different values of the light - quark masses , and hence different values of flavor - symmetry breaking . the validity of baryon mass relations derived without assuming approximate flavor - symmetry also can be tested by lattice data at very large values of the strange quark mass . this scaling is explicitly demonstrated in the present work .

baryon mass relations are compared with lattice simulations of baryon masses using different values of the light - quark masses , and hence different values of flavor - symmetry breaking . the lattice data clearly display both the and flavor - symmetry breaking hierarchies . the validity of baryon mass relations derived without assuming approximate flavor - symmetry also can be tested by lattice data at very large values of the strange quark mass . the expansion constrains the form of discretization effects ; these are suppressed by powers of by taking suitable combinations of masses . this scaling is explicitly demonstrated in the present work .

1404.1238

i

this paper considers joint estimation of multiple directed acyclic graph ( dag ) models using integer linear programming ( ilp ) . graphical models are multivariate models in which vertices in a graph @xmath0 represent random variables with edges between the vertices describing conditional independence statements concerning the variables . in many settings the edge structure of the graph is itself uncertain and then an important challenge is to estimate this structure from data . there has been considerable research into structural inference for graphical models over the last decade , including bayesian networks ( bns ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , gaussian graphical models ( ggms ; * ? ? ? * ; * ? ? ? * ) and discrete graphical models @xcite . many graphical models are based on dags and these are the focus of this paper . in many applications , data @xmath1 are collected on multiple units @xmath2 that may differ with respect to conditional independence structure , such that corresponding dags @xmath3 may be non - identical . at the same time , when the units of study are related , the graphs @xmath3 , while potentially non - identical , are expected to have similarities . it is then natural to ask whether such similarity can be exploited by borrowing strength across the estimation problems indexed by @xmath4 and that is the aim of the present paper . specifically we seek to construct a _ joint _ estimator @xmath5 that estimates a collection of dags together . we contrast such an estimator with the _ independent _ estimator @xmath6 that estimates each dag from the associated data only . the best known class of dag models are bns , but more exotic dag models exist ( e.g. * ? ? ? bns admit an extensive theory of inferred causation that has contributed to their popularity @xcite . structure learning for individual bns is a well - studied problem , with contributions including @xcite . structure learning is np - hard , but an approach that has attracted much recent attention is to cast _ maximum a posteriori _ ( map ) dag estimation as a problem in integer linear programming ( ilp ) , as developed simultaneously by @xcite and subsequently extended in @xcite . in brief , this approach solves a sequence of linear relaxations of the map estimation problem via the introduction of cutting planes and combines this with a branch - and - bound search to produce an optimal solution . if the algorithm terminates , the result is guaranteed to be a global maximum of the posterior distribution and hence inherits theoretical guarantees associated with the map estimator ( see e.g. * ? ? ? ( in this paper , algorithms with this property are termed `` exact '' . ) coupled with powerful techniques from discrete optimisation @xcite , ilps represent an efficient and attractive methodology for structural inference , as demonstrated also by recent empirical results ( e.g. * ? ? ? recent advances in this area are discussed in @xcite . the joint estimation of graphical models has recently received attention , for example @xcite put forward a penalised likelihood formulation that couples together estimation for multiple ( undirected ) ggms . however , joint estimation of multiple dags has so far received relatively little attention . the first discussion of this problem that we are aware of is @xcite ; here a greedy search was used to locate a local maximum of a joint bayesian posterior . @xcite described a markov chain monte carlo ( mcmc ) method for sampling from a joint posterior over graphical structures . however , the generic difficulties associated with stochastic search / sampling in large discrete spaces are well known ; these are exacerbated in the joint case by the size of the joint model space and stochastic search / sampling remains challenging in this setting . the focus of this paper is instead on exact , deterministic algorithms . @xcite proposed an exact algorithm based on bayesian model averaging and belief propagation , under the strong assumption that an ordering of the variables @xmath7 applies simultaneously to all units . at the same time @xcite proposed essentially the same algorithm , applied to the specific class of feed - forward dynamic bns , where an ordering of the variables is implicitly provided by the time index . the algorithmic contributions of the present paper are two - fold . first , we show how to cast exact inference over multiple dags as an ilp problem . we consider map - bayesian estimation for multiple dags and require no restriction on the ordering of the variables . this is done by extending methodology presented in @xcite to the case of multiple dags via a hierarchical bayesian formulation . second , we exploit structural constraints that are imposed by the dags in order to improve computational efficiency . as a illustrative example , our methods currently allow estimation of 10 related dags , each with 10 nodes , in time typically less than one minute on a standard laptop . in addition , we extend previous work by allowing for dependencies between the dags themselves and consider also estimation of this dependency structure . previous work on multiple dags has focused on the special case where the units are exchangeable and all pairs of units undergo an equal amount of regularisation ( including * ? ? ? * ; * ? ? ? * ) . however , in practice , relationships between units ( and their underlying graphical models ) may be complex , e.g. hierarchical , with group and sub - group structure , and such structure may itself be subject to uncertainty . @xcite performed exact inference for non - exchangeable feed - forward dynamic bns for the case where the relationships between units are known _ a priori_. @xcite addressed non - exchangeability in the context of general dag models but did not provide an exact algorithm and , again , assumed that the relationships between units are known at the outset . our approach provides a framework that allows for simultaneous learning of both unit - specific dags and the dependency structure that relates them . however , our empirical results suggest that such simultaneous learning may be extremely challenging in practice . the remainder of the paper is organised as follows : section [ def the model ] introduces a statistical framework for multiple dags and discusses regularisation based on graphical structure . section [ sec estimate ] gives exact , ilp - based estimators for multiple dags . section [ applications ] presents a simulation study and results on fmri data from a multi - subject study . finally we close with a discussion of directions for further research . a companion paper that explores the fmri application in more detail is available as @xcite .

* abstract . * this paper considers the problem of estimating the structure of multiple related directed acyclic graph ( dag ) models . . results are presented on both simulated data and fmri data obtained from multiple subjects . * keywords . * hierarchical models , directed acyclic graphs , non - exchangeability , integer linear programming , joint estimation * author footnote . * chris .

* abstract . * this paper considers the problem of estimating the structure of multiple related directed acyclic graph ( dag ) models . building on recent developments in exact estimation of dags using integer linear programming ( ilp ) , we present an ilp approach for joint estimation over multiple dags , that does not require that the vertices in each dag share a common ordering . furthermore , we allow also for ( potentially unknown ) dependency structure between the dags . results are presented on both simulated data and fmri data obtained from multiple subjects . * keywords . * hierarchical models , directed acyclic graphs , non - exchangeability , integer linear programming , joint estimation * author footnote . * chris . j. oates ( e - mail : _ c.oates@warwick.ac.uk_ ) and jim q. smith ( e - mail : _ j.q.smith@warwick.ac.uk_ ) , department of statistics , university of warwick , coventry , cv4 7al , uk . sach mukherjee ( e - mail : _ sach@mrc-bsu.cam.ac.uk_ ) , mrc biostatistics unit and school of clinical medicine , university of cambridge , cambridge , cb2 0sr , uk . james cussens ( e - mail : _ james.cussens@cs.york.ac.uk_ ) , department of computer science and york centre for complex systems analysis , university of york , york , yo10 5ge , uk .

1404.1238

c

this paper introduced a general statistical framework for joint estimation of multiple dags . we considered regularisation based on graphical structure and showed how map estimators in this setting could be characterised as the solutions to ilps that admit efficient exact algorithms based on branching - and - cutting as well as constraint propagation . we believe these are the first exact algorithms for the general case of multiple general dag models ( i.e. with no restriction on ordering of the variables ) . in our general framework for joint learning , we allowed also for dependence between the units themselves , that generalises previous exchangeable formulations . results obtained both from simulations and from an application in neuroscience demonstrate that joint estimation of dags can offer increased statistical efficiency relative to independent estimation . however we observed that the relationships between the units themselves were difficult to estimate from data . in the neuroscience application we illustrated how sophisticated likelihood models such as mdms can be used within our framework . importantly , our methodology requires only that local scores are pre - computed and cached ; it is therefore possible to apply exact algorithms retrospectively , following independent analyses of individual datasets , without the need to recompute local scores . in practice we anticipate that the rationale and appropriateness of joint modelling will need be assessed by domain experts on a case - by - case basis . our computations were performed using the gobnilp package @xcite , that includes sophisticated routines for estimation of individual dags ( see supplementary materials ) . nevertheless our simulation results for large numbers @xmath14 of variables and @xmath39 of units required considerable computational time ( in a worst - case scenario ) . it is becoming commonplace in many applications for the number of units to become very large . it remains to be seen whether our approach can scale up to larger problems . recent work where gobnilp was able to find map dags with 1614 nodes in between 3 and 42 minutes are encouraging @xcite . in practice , as discussed in @xcite , it is very hard to estimate the time required to solve an ilp in advance ; rather this depends in a highly non - trivial way on the details of the problem and is related to the `` phase - transition '' in sat solving . we note that the results of this paper are based on the ilp framework of @xcite for individual dags . an alternative ilp formulation , known as `` characteristic imsets '' , was proposed by @xcite specifically for bns . characteristic imsets are closely related to the essential graph of a bn @xcite and have the property that markov - equivalent bns are score equivalent . in contrast , the approaches we pursued involved a non - unique representation of the essential graph . this flexibility is important when dealing with general dag models including mdms , that are uniquely identifiable from data , but are less natural in the context of bns . at present , the computational performance of characteristic imsets on individual bns is inferior to the approach of @xcite pursued here @xcite . in addition it is currently unclear how prior structural information might be incorporated into that framework . on a related note , it would be interesting to design a joint version of the well - known pc algorithm @xcite that complements score - based estimation . interesting extensions include : 1 . * information sharing for parameters . * in many applications it is reasonable to assume similarity of parameter values @xmath27 between units . at present this appears to be challenging to include within our framework and represents an area for further research . * computation . * the applications discussed in this paper were performed on a single cpu and limited in computational intensity to approximately @xmath133 . since many emerging datasets , not least in biomedical applications , contain many more variables @xmath14 and many more units @xmath39 than we considered here , it would be interesting to investigate strategies for parallel and/or approximate computation that scale better to such regimes . in the other direction , our methodology applies to complex local scores that may be estimated numerically ; it would be interesting to gain a theoretical understanding of how any uncertainty in the estimates for the local scores would impact on the map estimators described here . * new statistical models . * by fixing the network @xmath42 in our general framework we can obtain a number of interesting statistical models : ( i ) taking @xmath42 to be a chain allows us to associate units with a temporal ordering and thereby model time - evolving dag structures . ( ii ) introducing auxiliary dags @xmath150 and enforcing @xmath42 to be bipartite on the partition of auxiliary / non - auxiliary dags produces a mixture model for dags , such that each latent dag is a graphical summary of the various dag structures within its cluster . ( iii ) extending this idea , with @xmath151 we recover a mixture model for dags similar to @xcite . these possibilities are currently being explored , with preliminary results for mixture models presented in @xcite . preliminary indications suggest that imposing additional restrictions on @xmath42 in this way may serve to improve the identification of higher - order structure . more generally , it is straightforward to extend our methods to the case of decomposable undirected models by imposing additional constraints that rule out immoralities . * supplementary materials : * the supplementary materials include additional a discussion of the simulated data and the actual code used to produce the results herein . * acknowledgements : * cjo was supported by the centre for research in statistical methodology ( crism ) epsrc ep / d002060/1 . jc was supported by the medical research council ( project grant g1002312 ) . sm was supported by the uk medical research council and is a recipient of a royal society wolfson research merit award . the authors are grateful to lilia carneiro da costa and tom nichols who collaborated in the analysis of fmri data and to mark bartlett who provided technical support with gobnilp . the authors also thank diane oyen and several other colleagues who provided feedback on an earlier draft . 99 acid , s. , de campos , l.m . : searching for bayesian network structures in the space of restricted acyclic partially directed graphs . _ j. artif . res . _ * 18 * , 445 - 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291 ( 2009 ) . cussens , j. : maximum likelihood pedigree reconstruction using integer programming . _ proceedings of the workshop on constraint based methods for bioinformatics ( wcb-10 ) , edinburgh _ ( 2010 ) . cussens , j. : bayesian network learning with cutting planes . _ proceedings of the 27th conference on uncertainty in artificial intelligence _ , 153 - 160 ( 2011 ) . danaher , p. , wang , p. , witten , d.m . : the joint graphical lasso for inverse covariance estimation across multiple classes . _ j. r. statist . b _ * 76*(2 ) , 373 - 397 ( 2014 ) . dawid , a.p . , lauritzen , s.l . : hyper markov laws in the statistical analysis of decomposable graphical models . stat . _ * 21*(3 ) , 1272 - 1317 ( 1993 ) . dawid , a.p . : beware of the dag ! _ j. mach . w & cp _ * 6 * , 59 - 86 ( 2010 ) . ellis , b. , wong , w.h . : learning causal bayesian network structures from experimental data . assoc . _ * 103*(482 ) , 778 - 789 ( 2008 ) . friedman , n. , koller , d. : being bayesian about network structure : a bayesian approach to structure discovery in bayesian networks . _ * 50*(1 - 2 ) , 95 - 126 ( 2003 ) . friedman , j. , hastie , t. , tibshirani , r. sparse inverse covariance estimation with the graphical lasso . _ biostatistics _ * 9*(3 ) , 432 - 441 ( 2008 ) . friston , k.j . : functional and effective connectivity : a review . _ brain connectivity _ * 1*(1 ) , 13 - 36 ( 2011 ) . he , y. , jia , j. , yu , b. : reversible mcmc on markov equivalence classes of sparse directed acyclic graphs . _ ann . _ * 41*(4 ) , 1742 - 1779 ( 2013 ) . heckerman , d. , geiger , d. , chickering , d.m . : learning bayesian networks : the combination of knowledge and statistical data . _ _ * 20*(3 ) , 197 - 243 ( 1995 ) . hill , s. , lu , y. , molina , j. , heiser , l.m . , spellman , p.t . , speed , t.p . , gray , j.w . , mills , g.b . , mukherjee , s. : bayesian inference of signaling network topology in a cancer cell line . _ bioinformatics _ * 28*(21 ) , 2804 - 2810 ( 2012 ) . jaakkola , t. , sontag , d. , globerson , a. , meila , m. : learning bayesian network structure using lp relaxations . _ proceedings of the 13th international conference on artificial intelligence and statistics _ , 358 - 365 ( 2010 ) . li , j. , wang , z.j . , palmer , s.j . , mckeown , m.j . : dynamic bayesian network modeling of fmri : a comparison of group - analysis methods . _ neuroimage _ * 41*(2 ) , 398 - 407 ( 2008 ) . l . , wainwright , m.j . : structure estimation for discrete graphical models : generalized covariance matrices and their inverses stat . _ * 41*(6 ) , 3022 - 3049 ( 2013 ) . mahajan , a. : presolving mixed - integer linear programs . _ wiley encyclopedia of operations research and management science _ ( 2010 ) . mechellia , a. , penny , w.d . , pricea , c.j . , gitelman , d.r . , friston , k.j . : effective connectivity and intersubject variability : using a multisubject network to test differences and commonalities . _ neuroimage _ * 17*(3 ) , 1459 - 1469 ( 2002 ) . meinshausen , n. , bhlmann , p. : high - dimensional graphs and variable selection with the lasso . stat . _ * 34*(3 ) , 1436 - 1462 ( 2006 ) . nemhauser , g.l . , wolsey , l.a . : _ integer and combinatorial optimization . _ wiley , new york ( 1988 ) . niculescu - mizil , a. , caruana , r. : inductive transfer for bayesian network structure learning . _ j. mach . workshop and conference proceedings _ * 27 * , 339 - 346 ( 2007 ) . oates , c.j . , mukherjee , s. : joint structure learning of multiple non - exchangeable networks . _ proceedings of the 17th international conference on artificial intelligence and statistics _ * 33 * , 687 - 695 ( 2014 ) . oates , c.j . , korkola , j. , gray , j.w . , mukherjee , s. : joint estimation of multiple networks from time course data . _ * 8*(3 ) , 1892 - 1919 ( 2014a ) . oates , c.j . , carneiro da costa , l. , nichols , t. : towards a multi - subject analysis of neural connectivity . _ neural compt . _ * 27 * , 1 - 20 ( 2014b ) . oates , c.j . , papamarkou , t. , girolami , m. : the controlled thermodynamic integral for bayesian model comparison . _ crism working paper series , university of warwick _ , * 14 * , 9 ( 2014c ) . oates , c.j . , girolami , m. , chopin , n. : control funtionals for monte carlo integration . _ crism working paper series , university of warwick _ , * 14 * , 22 ( 2014d ) . oates , c.j . , amos , r. , spencer , s.e.f . : quantifying the multi - scale performance of network inference algorithms . mo . b. _ * 13*(5 ) , 611 - 631 ( 2014e ) . oyen , d. , lane , t. : leveraging domain knowledge in multitask bayesian network structure learning . _ proceedings of the 26th aaai conference on artificial intelligence _ ( 2012 ) . oyen , d. , lane , t. : bayesian discovery of multiple bayesian networks via transfer learning . _ ieee 13th international conference on data mining ( icdm ) _ , 577 - 586 ( 2013 ) . pearl , j. : _ causality : models , reasoning and inference ( 2nd ed.)_. cambridge university press ( 2009 ) . penfold , c.a . , buchanan - wollaston , v. , denby , k.j . , wild , d.l . : nonparametric bayesian inference for perturbed and orthologous gene regulatory networks . _ bioinformatics _ * 28*(12 ) , i233-i241 ( 2012 ) . perrier , e. , imoto , s. , miyano , s. : finding optimal bayesian network given a super - structure . _ j. mach . * 9*(10 ) , 2251 - 2286 ( 2008 ) . peters , j. bhlmann , p. : structural intervention distance ( sid ) for evaluating causal graphs . _ neural compt . _ , to appear . poldrack , r.a . , mumford , j.a . , nichols , t.e . : _ handbook of fmri data analysis _ , cambridge university press ( 2011 ) . queen , c.m . , albers , c.j . : intervention and causality : forecasting traffic flows using a dynamic bayesian network . _ j. am . _ * 104*(486 ) , 669 - 681 ( 2009 ) . queen , c.m . , smith , j.q . : multiregression dynamic models . _ j. r. statist . b _ * 55*(4 ) , 849 - 870 ( 1993 ) . scott , j.g . , berger , j.o . : bayes and empirical - bayes multiplicity adjustment in the variable - selection problem . stat . _ * 38*(5 ) , 2587 - 2619 ( 2010 ) . sheehan , n.a . , bartlett , m. , cussens , j. : maximum likelihood reconstruction of very large pedigrees . _ theoretical population biology _ , in press . silander , t. , myllymkki , p. : a simple approach to finding the globally optimal bayesian network structure . _ proceedings of the 22nd conference on artificial intelligence _ , 445 - 452 ( 2006 ) . spirtes , p. , glymour , c. , scheines , r. : causation , prediction , and search . the mit press , 2nd edition ( 2000 ) . studen , m. , vomlel , j. , hemmecke , r. : a geometric view on learning bayesian network structures . j. approx . reason . _ * 51*(5 ) , 578 - 586 ( 2010 ) . studen , m. , haws , d. : on polyhedral approximations of polytopes for learning bayesian networks . _ j. algebraic stats . _ * 4*(1 ) , 59 - 92 ( 2013 ) . sugihara , g. , kaminaga , t. , sugishita , m. : interindividual uniformity and variety of the writing center " : a functional mri study . _ neuroimage _ * 32*(4 ) , 1837 - 1849 ( 2006 ) . thiesson , b. , meek , c. , chickering , d. m. , heckerman , d. : learning mixtures of bayesian networks . _ proceedings of the 14th conference on uncertainty in artificial intelligence _ , 504 - 513 ( 1998 ) . tsamardinos , i. , brown , l.e . , aliferis , c.f . : the max - min hill - climbing bayesian network structure learning algorithm . _ * 65*(1 ) , 31 - 78 ( 2006 ) . van essen , d.c . , smith , s.m . , barch , d.m . , behrens , t.e . , yacoub , e. , ugurbil , k. : the wu - minn human connectome project : an overview . _ neuroimage _ * 80 * , 62 - 79 ( 2013 ) . werhli , a.v . , husmeier , d. : gene regulatory network reconstruction by bayesian integration of prior knowledge and/or different experimental conditions . _ journal of bioinformatics and computational biology _ * 6*(3 ) , 543 - 572 ( 2008 ) . wolsey , l.a . : _ integer programming_. wiley , new york ( 1998 ) . yuan , c. , malone , b. : learning optimal bayesian networks : a shortest path perspective . _ j. artif . res . _ * 48 * , 23 - 65 ( 2013 ) . * supplement to `` exact estimation of multiple directed acyclic graphs '' * chris . j. oates ( e - mail : _ c.oates@warwick.ac.uk_ ) and jim q. smith ( e - mail : _ j.q.smith@warwick.ac.uk_ ) , department of statistics , university of warwick , coventry , cv4 7al , uk . sach mukherjee ( e - mail : _ sach@mrc-bsu.cam.ac.uk_ ) , mrc biostatistics unit and school of clinical medicine , university of cambridge , cb2 0sr , uk . james cussens ( e - mail : _ james.cussens@cs.york.ac.uk_ ) , department of computer science and york centre for complex systems analysis , university of york , yo10 5ge , uk .

building on recent developments in exact estimation of dags using integer linear programming ( ilp ) , we present an ilp approach for joint estimation over multiple dags , that does not require that the vertices in each dag share a common ordering . furthermore , we allow also for ( potentially unknown ) dependency structure between the dags j. oates ( e - mail : _ c.oates@warwick.ac.uk_ ) and jim q. smith ( e - mail : _ j.q.smith@warwick.ac.uk_ ) , department of statistics , university of warwick , coventry , cv4 7al , uk . sach mukherjee ( e - mail : _ sach@mrc-bsu.cam.ac.uk_ ) , mrc biostatistics unit and school of clinical medicine , university of cambridge , cambridge , cb2 0sr , uk . james cussens ( e - mail : _ james.cussens@cs.york.ac.uk_ ) , department of computer science and york centre for complex systems analysis , university of york , york , yo10 5ge , uk .

* abstract . * this paper considers the problem of estimating the structure of multiple related directed acyclic graph ( dag ) models . building on recent developments in exact estimation of dags using integer linear programming ( ilp ) , we present an ilp approach for joint estimation over multiple dags , that does not require that the vertices in each dag share a common ordering . furthermore , we allow also for ( potentially unknown ) dependency structure between the dags . results are presented on both simulated data and fmri data obtained from multiple subjects . * keywords . * hierarchical models , directed acyclic graphs , non - exchangeability , integer linear programming , joint estimation * author footnote . * chris . j. oates ( e - mail : _ c.oates@warwick.ac.uk_ ) and jim q. smith ( e - mail : _ j.q.smith@warwick.ac.uk_ ) , department of statistics , university of warwick , coventry , cv4 7al , uk . sach mukherjee ( e - mail : _ sach@mrc-bsu.cam.ac.uk_ ) , mrc biostatistics unit and school of clinical medicine , university of cambridge , cambridge , cb2 0sr , uk . james cussens ( e - mail : _ james.cussens@cs.york.ac.uk_ ) , department of computer science and york centre for complex systems analysis , university of york , york , yo10 5ge , uk .

1212.2061

i

in this article we study differential inclusions of the form @xmath0 where @xmath1 denotes the derivative with respect to time and @xmath2 is assumed to be a maximal monotone relation in time and space . the bounded linear operator @xmath3 , also acting in time and space , is a so - called linear material law , as it was introduced in @xcite . since we are dealing with the autonomous case , the operator @xmath3 and the relation @xmath2 are assumed to commute with the temporal translation operator . we will show that under suitable conditions on @xmath3 and @xmath2 the problem is well - posed , i.e. hadamard s requirements on existence and uniqueness of a solution @xmath4 and its continuous dependence on the given data @xmath5 are satisfied . moreover the issue of causality is addressed , meaning that the behaviour of the solution up to a certain time @xmath6 just depends on the behaviour of the given right hand side up to the same time @xmath6 . + originally this class of problems was discussed in @xcite , where the relation @xmath2 was given by a skew - selfadjoint spatial operator . there , well - posedness and causality were shown under a positive - definiteness constraint on the operator @xmath3 . moreover , the abstract solution theory was applied to several examples of linear equations in mathematical physics . this solution theory was generalized by the author to the case of @xmath2 being a maximal monotone relation in space in @xcite , where @xmath3 was of the particular form @xmath7 we will adopt the proof for the solution theory presented in @xcite to show the well - posedness of problems of the form . the proof mainly relies on the realization of the derivative @xmath1 as a maximal monotone operator on an exponentially weighted @xmath8-space ( see e.g. @xcite or subsection 2.1 of this article ) and the application of a well - known perturbation result for maximal monotone relations ( see ) . for the theory of maximal monotone relations we refer to the monographs @xcite . inclusions of the form cover a large class of possible evolutionary problems , such as integro - differential equations @xcite , delay and neutral differential equations @xcite , certain types of control problems @xcite and equations of mathematical physics involving hysteresis @xcite . + the article is structured as follows . in section 2 we recall the definition of the time - derivative , of linear material laws and some basic facts on maximal monotone relations on hilbert spaces . moreover , we recall the notion of so - called abstract boundary data spaces ( see @xcite ) , which will enable us to formulate evolutionary equations with nonlinear boundary condition as an inclusion of the form . in section 3 the solution theory for is presented . in the remaining part of the article we consider a certain type of partial differential equations with nonlinear boundary conditions . those problems occur for instance in frictional contact problems ( see e.g. @xcite ) in the field of elasticity , where the boundary condition is given by a differential inclusion . in subsection 4.1 we study an abstract nonlinear differential operator @xmath2 , which is given by the restriction of a linear operator to elements , which satisfy the nonlinear boundary condition . we show that under certain constraints on the relation , which occurs in the boundary condition , the operator @xmath2 gets maximal monotone and thus , the solution theory developed in section 3 applies . we illustrate our results in subsection 4.2 . there , in a first example we consider the wave equation with an impedance - type boundary condition . this problem was originally considered in @xcite and we show that it fits in our framework . the second example deals with the equations of visco - elasticity with a frictional boundary condition , which is modelled by a differential inclusion on the boundary . a similar kind of this problem was considered in @xcite for a cylindrical domain and antiplane shear deformations . again we show that the equations are covered by our abstract inclusion . + throughout every hilbert space is assumed to be complex . its inner product and its norm are denoted by @xmath9 and @xmath10 respectively , where the inner product is assumed to be linear with respect to the second and conjugate linear with respect to the first argument . moreover , for a hilbert space @xmath11 and a closed subspace @xmath12 we denote by @xmath13 the orthogonal projection onto @xmath14 is just the canonical embedding . ] then @xmath15 is the orthogonal projector on @xmath16 .

* abstract . * we study an abstract class of autonomous differential inclusions in hilbert spaces and show the well - posedness and causality , by establishing the operators involved as maximal monotone operators in time and space . then the proof of the well - posedness relies on a well - known perturbation result for maximal monotone operators . moreover , we show that certain types of nonlinear boundary value problems are covered by this class of inclusions and we derive necessary conditions on the operators on the boundary in order to apply the solution theory .

* abstract . * we study an abstract class of autonomous differential inclusions in hilbert spaces and show the well - posedness and causality , by establishing the operators involved as maximal monotone operators in time and space . then the proof of the well - posedness relies on a well - known perturbation result for maximal monotone operators . moreover , we show that certain types of nonlinear boundary value problems are covered by this class of inclusions and we derive necessary conditions on the operators on the boundary in order to apply the solution theory . we exemplify our findings by two examples . evolutionary inclusions , well - posedness , causality , maximal monotonicity , impedance type boundary conditions , frictional boundary conditions . 34g25 , 35f30 , 35r20 , 46n20 , 47j35

1303.3847

i

density functional theory ( dft ) and coupled - cluster ( cc ) theory are the two dominant paradigms for the computation of many - electron ground states with complementary capabilities . both theories are built upon the independent - orbital and self - consistent field ( scf ) structure of hartree - fock ( hf ) theory @xcite . dft proves the existence of an exact density functional @xcite for which there are approximations @xcite enabling routine simulation of thousands of electrons @xcite that scale as @xmath1 operations and @xmath3 memory for @xmath2 electrons . cc theory is a systematically improvable hierarchy of methods @xcite indexed by @xmath6 that scale as @xmath7 operations and @xmath8 memory . in practice , dft is limited by accuracy and cc theory is limited by cost . the random phase approximation ( rpa ) is a natural point of convergence in the ongoing development of cc theory and dft . rpa emerges from truncated versions of cc methods as reduced - complexity methods that retain a significant fraction of the cc correlation energy @xcite . rpa also occurs when dft is used to approximate the polarization function in the adiabatic - connection fluctuation - dissipation formula for the correlation energy @xcite . this formula might become a part of more accurate density functionals , but it has a higher cost and complexity @xcite than conventional density functionals . in both cases , a balance of cost and accuracy is being sought with rpa . the electron correlation energy model that we consider in this paper is the rpa correlation energy plus the second - order screened exchange ( sosex ) energy @xcite . rpa+sosex is exact for one electron and to second order in perturbation theory . it agrees with quantum monte carlo benchmarks of the uniform electron gas @xcite to within 0.002 ha / electron @xcite . benchmarks on inhomogeneous systems show mean absolute errors of 0.002 ha / atom for cohesive energies of solids in a 5-solid test set @xcite , 0.008 ha / molecule for atomization energies of molecules in the g2 - 1 test set @xcite , and 0.010 ha / atom for correlation energies of first and second row atoms @xcite . these atomic and molecular rpa+sosex results approach but fail to surpass the accuracy of second - order mller - plesset ( mp2 ) perturbation theory @xcite and the b3lyp density functional @xcite . also , any rpa+sosex energy depends on a mean field choice and is not unique @xcite . the goal of this paper is to further develop rpa+sosex as a compromise between the cost of dft and the accuracy of cc theory . known algorithms for rpa+sosex @xcite and similar models @xcite require @xmath0 operations and either @xmath1 or @xmath9 memory . by utilizing an auxiliary basis set @xcite , fast interaction kernel summation @xcite , and a low - rank approximation of energy denominators @xcite , we design a new algorithm to reduce the cost to @xmath1 operations and @xmath3 memory . we define a precise rpa+sosex total energy with a unique choice of mean field based on brueckner orbitals @xcite that is designed to approximate brueckner coupled - cluster doubles ( bccd ) theory @xcite . this is referred to as brueckner rpa ( brpa ) theory . it is important to be pragmatic about the short - term value of brpa theory and a fast rpa+sosex algorithm . despite its construction , brpa is not a good approximation of bccd . the approximations used to retain the rpa+sosex form are too crude . for a given basis , a fast rpa+sosex calculation will have a large cost relative to conventional dft . with the continued reduction of average errors in density functionals @xcite and a correlation of dft and rpa error outliers @xcite , it is unclear whether the cost is warranted without additional research . the paper proceeds as follows . brpa theory is derived in sec . [ brpatheory ] as a truncation of bccd theory . the scf structure of brpa theory is emphasized . the three main components of a fast rpa+sosex algorithm are introduced in sec . [ fast_components ] . this includes a nonstandard choice of primary and auxiliary basis , which simplifies the cost accounting and algorithm design . in sec . [ rpastructure ] , the tensor structure in existing rpa algorithms @xcite is reviewed and extended to rpa+sosex . the novel structure of rpa+sosex theory enables a significant reduction in the number of its variables . fast and conventional rpa+sosex algorithms are designed in sec . [ fast_design ] as pseudocode . a detailed leading - order cost analysis is given instead of a crude scaling analysis . we study applications to a semiempirical h@xmath5 model in sec . [ applications ] . the accuracy of brpa theory is tested on h@xmath4 , and the scaling of rpa+sosex algorithms is confirmed with h@xmath5 calculations for large @xmath2 . the implications for future work are discussed in sec . [ discussion ] . this includes implementation in established electronic structure codes , basis set convergence problems , and further development of correlation models . we conclude in sec . [ conclusions ] with a brief consideration of rpa as a distinct electronic structure paradigm .

+ the random - phase approximation with second - order screened exchange ( rpa+sosex ) is a model of electron correlation energy with two caveats : its accuracy depends on an arbitrary choice of mean field , and it scales as operations and memory for electrons . we derive a new algorithm that reduces its scaling to operations and memory using controlled approximations and a new self - consistent field that approximates brueckner coupled - cluster doubles ( bccd ) theory with rpa+sosex , referred to as brueckner rpa ( brpa ) theory . the algorithm comparably reduces the scaling of second - order mller - plesset ( mp2 ) perturbation theory with smaller cost prefactors than rpa+sosex . within a semiempirical model , we study h dissociation to test accuracy and h rings to verify scaling .

+ the random - phase approximation with second - order screened exchange ( rpa+sosex ) is a model of electron correlation energy with two caveats : its accuracy depends on an arbitrary choice of mean field , and it scales as operations and memory for electrons . we derive a new algorithm that reduces its scaling to operations and memory using controlled approximations and a new self - consistent field that approximates brueckner coupled - cluster doubles ( bccd ) theory with rpa+sosex , referred to as brueckner rpa ( brpa ) theory . the algorithm comparably reduces the scaling of second - order mller - plesset ( mp2 ) perturbation theory with smaller cost prefactors than rpa+sosex . within a semiempirical model , we study h dissociation to test accuracy and h rings to verify scaling .

astro-ph0002070

c

all the previous section should have made clear that globular clusters can be used for a very wide variety of studies . they can constrain the star formation history of galaxies , in particular on the two or more distinct epochs of star formation in early - type galaxies . they can help explaining the building up of spiral galaxies , and the star formation in violent interactions . they can be useful to study galaxy dynamics at large galactocentric radii . and finally , they provide an accurate distance indicator , independent of cepheids and the distance to the lmc . this makes the study of globular cluster systems one of the most versatile fields in astronomy . extragalactic globular cluster research experienced a boom in the early 90s with the first generation of reliable ccds , and the first imaging from space . we can expect a continuation of the improvement of optical imaging , but more important , the field will benefit from the advancement in near - infrared imaging , and most of all , of the upcoming multi - object spectrographs on 10 m telescopes . the next little revolution in this subject will come with the determination of hundreds of globular cluster abundances around a large number of galaxies . the next 5 years will be an exiting time . first of all , i would like to thank the astronomische gesellschaft for awarding me the ludwig - bierman price . i feel extremely honored and proud . for his constant support , i would like to thank tom richtler , who introduced me to the fascinating subject of globular clusters . for the most recent years , i would like to thank jean brodie for her collaboration and for giving me the first opportunity to use a 10 m telescope to satisfy my curiosity . i am grateful to my current collaborators thomas puzia , claudia maraston , daniel thomas , denis burgarella , veronique buat , sandra chapelon , michael hilker , dante minniti , paul goudfrooij , linda schroder and many others , for helping me to keep up the flame . as usual , i would be lost without karl gebhardt s codes and sharp ideas . i am grateful to klaas de boer and simona zaggia for comments on various points . and last but not least , i am very thankful to steve zepf for a critical reading of the manuscript .

in particular , we address the star - formation histories of early - type galaxies ; globular cluster population in late - type galaxies and their link to early - type galaxies ; star and cluster formation during mergers and violent interactions ; and the kinematics at large radii in early - type galaxies .

_ we present an overview of observational progress in the study of extragalactic globular cluster systems . globular clusters turn out to be excellent tracers not only for the star - formation histories in galaxies , but also for kinematics at large galactocentric radii . their properties can be used to efficiently constrain galaxy formation and evolution . after a brief introduction of the current methods and futures perspectives , we summarize the knowledge gained in various areas of galaxy research through the study of globular clusters . in particular , we address the star - formation histories of early - type galaxies ; globular cluster population in late - type galaxies and their link to early - type galaxies ; star and cluster formation during mergers and violent interactions ; and the kinematics at large radii in early - type galaxies . the different points are reviewed within the context of galaxy formation and evolution . _ finally , we revisit the globular cluster luminosity function as a distance indicator . despite its low popularity in the literature , we demonstrate that it ranks among one of the most precise distance indicators to early - type galaxies , provided that it is applied properly . * extragalactic globular cluster systems * + * a new perspective on galaxy formation and evolution * + markus kissler - patig + european southern observatory + karl - schwarzschild - str . 2 , 85748 garching , germany + mkissler@eso.org , http://www.eso.org/mkissler

1203.0760

i

this paper concerns the theory of constant mean curvature ( _ cmc _ for short ) surfaces @xmath3 in @xmath1 . the value @xmath3 is critical in the sense that there is no compact cmc surface for @xmath4 while for @xmath5 there are rotational compact examples . a half - space theorem in @xmath1 ( see @xcite ) proves that for cmc @xmath3 , complete multigraphs are entire graphs over @xmath2 . entire graphs are classified by i. fernndez and p. mira @xcite and their moduli space is modeled on the set of quadratic holomorphic differential @xmath6 defined on the complex plane @xmath7 or the unit disk @xmath8 . the link between @xmath6 and the geometry of the graph is not very well understood . we first deal with complete conformal immersions of the disk @xmath8 , properly immersed into the half - space @xmath9 ( @xmath10 ) , which are entire vertical graphs over @xmath2 . we assume that the third coordinate @xmath11 on any diverging sequence of points in @xmath8 , which means the height function is proper . up to this date , the only simply connected example is a rotational example called the _ hyperboloid _ @xmath12 . in the poincar disk model of @xmath1 see below with polar coordinates @xmath13 , a parametrization of @xmath12 as a graph over @xmath2 is : @xmath14 we describe a family of examples endowed with a structure of infinite dimensional smooth manifold . the manifold structure arises from a suitable _ compactification _ of the mean curvature operator at infinity ( theorem [ thm : compcourb ] ) and is diffeomorphic to a codimension one submanifold of @xmath15 ( theorem [ thm : structg ] ) . this construction comes with a control of the asymptotic behavior in terms of the horizontal ( hyperbolic ) distance from the hyperboloid @xmath12 , namely : for any small @xmath16 such that @xmath17 has unit @xmath18-norm , there exists a cmc-@xmath0 complete entire graph at asymptotic horizontal signed distance @xmath19 from @xmath12 . these graphs are interesting , since any connected complete embedded cmc-@xmath0 surface in @xmath1 which is contained in the half - space @xmath9 and has a proper height function is a vertical entire graph . indeed , apply alexandrov reflection principle to such an immersion with respect to the horizontal slices . namely , reflect through the slice the part of the surface situated below it to obtain a surface which is a bigraph i.e. a graph over each side of the slice . there will be no first point of tangent contact between the initial surface and the part of the bigraph which is not a part of the surface , since there is no compact cmc-@xmath0 surface in @xmath1 . we also prove a half - space property for these entire graphs : let @xmath20 be a cmc-@xmath0 surface which is properly immersed in @xmath1 , lies on one side of a cmc-@xmath0 entire graph @xmath21 in the aforementioned family and is well oriented with respect to @xmath21 . then @xmath20 coincides with @xmath21 up to a vertical translation . the `` well oriented '' assumption is in the sense of l. mazet @xcite and means that if @xmath20 is below @xmath21 , its mean curvature vector points to @xmath21 . we use this result to show an asymptotic rigidity in our family of cmc-@xmath0 entire graphs ( theorem [ thm : rigidinf ] ) . namely , if two graphs in the family are at the same asymptotic horizontal signed distance from the hyperboloid @xmath12 , they coincide up to a vertical translation . in @xmath1 , r. s earp and e. toubiana @xcite construct a one - parameter family of cmc @xmath3 annuli which are rotationally invariant around a vertical geodesic . recently , l. mazet has shown @xcite that for @xmath5 , cmc annuli which are cylindrically bounded around a vertical geodesic are rotational examples . though annuli are not cylindrically bounded for @xmath3 , we prove that in a bounded tubular neighborhood of a rotational example , there are annuli , eventually embedded , which are asymptotic to different rotational examples with different axis : there exist cmc-@xmath0 annuli in @xmath1 with vertical ends , that are asymptotic regarding the horizontal hyperbolic distance to rotational examples with different vertical axis . it means that contrary to the case of embedded minimal surfaces in @xmath22 with finite total curvature and horizontal ends @xcite , the notion of _ axis _ is not relevant in general for cmc-@xmath0 annuli with vertical ends in @xmath1 . let @xmath23 |z| < 1 \rac$ ] be the open unit disk , @xmath24 |z| \leq 1 \rac$ ] its closure and @xmath13 the polar coordinates on @xmath25 . we use two standard models of @xmath1 , which are the minkowski model : @xmath26 where @xmath1 is seen as a subspace of the @xmath27-dimensional minkowski space @xmath28 , and the poincar disk model : @xmath29 the vector field associated to the third coordinate is denoted @xmath30 . in the poincar disk model , the hyperbolic radius @xmath31 of a point @xmath32 is : @xmath33 and we will need the following formula in the proof of proposition [ prop : graphdeform ] : @xmath34 we call vertical graphs in @xmath1 , immersions which are complete graphs over an open subset of the slice @xmath35 , and we call vertical annuli in @xmath1 , immersions which are complete vertical bigraphs . given surfaces @xmath36 in @xmath1 admitting parametrizations in the poincar disk model respectively : @xmath37 the hyperbolic horizontal signed distance @xmath38 between @xmath21 and @xmath39 at height @xmath40 and in the direction @xmath41 is the difference of their hyperbolic radii in the slice @xmath42 and direction @xmath41 : @xmath43 when it exists , the _ asymptotic hyperbolic horizontal signed distance _ between @xmath21 and @xmath39 in the direction @xmath41 is the limit @xmath44 . for any @xmath45 , let @xmath46 be the domain @xmath47 . we consider the set of _ admissible domains _ @xmath48 . the boundary at infinity @xmath49 of @xmath2 is identified with @xmath50 . given @xmath51 , the spaces @xmath52 and @xmath53 , with @xmath54 and @xmath55 , are respectively the usual hlder space and the subspace of functions that are zero on the boundary of @xmath56 . finally , we consider the spaces @xmath57 endowed with the natural scalar product denoted @xmath58 and hilbert norm @xmath59 .

we show that a particular family of complete entire graphs over admits a structure of infinite dimensional manifold with local control on the behaviors at infinity . deforming non degenerate constant mean curvature annuli , we provide a large class of ( non rotational ) examples and construct ( possibly embedded ) annuli without axis , i.e. with two vertical , asymptotically rotational , non aligned ends .

_ we study constant mean curvature surfaces in that admit a compactification of the mean curvature operator . we show that a particular family of complete entire graphs over admits a structure of infinite dimensional manifold with local control on the behaviors at infinity . these graphs also appear to have a half - space property and we deduce a uniqueness result at infinity . deforming non degenerate constant mean curvature annuli , we provide a large class of ( non rotational ) examples and construct ( possibly embedded ) annuli without axis , i.e. with two vertical , asymptotically rotational , non aligned ends . _ _ mathematics subject classification : _ _ 53a10 , 53c42_.

1009.2741

i

transport coefficients are essential inputs to describe the space - time evolution of systems not far from equilibrium . during the last years there has been a very active effort to analyze them from both the theoretical and phenomenological points of view in the context of heavy - ion collisions , condensed matter physics , astrophysics and cosmology . the calculation of transport coefficients in quantum field theory at intermediate and strong coupling is still a challenge from both the analytical and the numerical points of view . due to their intrinsic non - perturbative nature , even in weakly interacting theories a resummation of an infinite number of diagrams is needed in order to obtain the leading - order result . in the strongly coupled regime , the most prominent method available is the ads / cft correspondence , although it is only applicable to a limited class of field theories . on the other hand , lattice simulations are still not accurate enough regarding the calculation of spectral densities , and the introduction of a finite quark chemical potential makes things even more difficult because of the sign problem . it was recently conjectured , based on a sum rule for the spectral density of the trace of the energy - momentum tensor in yang - mills theory @xcite , that a maximum of the trace anomaly near the critical temperature might drive a maximum for the bulk viscosity near that temperature . the corresponding sum rule was later corrected in @xcite , and the ansatz for the spectral density used to extract the bulk viscosity questioned @xcite . since the trace anomaly measures the breaking of scale invariance in a system , and the bulk viscosity @xmath1 essentially represents the difficulty for a system to relax back to equilibrium after a scale transformation , it seems in principle reasonable to think that @xmath1 would be maximum when the breaking of scale invariance is maximum . in heavy - ion phenomenology , bulk viscosity has usually been neglected because it is expected to be much smaller than the shear viscosity even at temperatures not very high @xcite . however , as suggested by the analysis of @xcite , non - perturbative phenomena responsible for the main contribution to the trace anomaly near @xmath2 could also produce a significant increase in the bulk viscosity . in this paper i will present an explicit calculation in the massive gross - neveu model in @xmath3 dimensions , where the correlation between trace anomaly and bulk viscosity can be accurately tested . i will not try to give an estimation for the absolute value of @xmath1 in qcd near the phase transition though ; as we will see this model is not suitable for that purpose . there are several works analyzing this issue employing different approaches ( see for instance @xcite and references therein ) , but still the order of magnitude of the bulk viscosity near the crossover temperature is uncertain . in 1 + 1 dimensions , transverse flow of momentum is not possible , and the bulk viscosity is the only viscous coefficient present to linear order in gradients . in this paper i will analyze only finite temperature effects , considering a vanishing fermion chemical potential , thus the thermal conductivity will be zero in this case . therefore , the only constitutive equation relevant for us is . ] @xmath4 with @xmath5 the non - equilibrium expectation value for the spatial component of the energy - momentum tensor , @xmath6 is the pressure in equilibrium , and @xmath7 is the fluid velocity . the bulk viscosity can be in principle calculated perturbatively in field theory @xcite : @xmath8 where @xmath9 is the spectral density corresponding to the thermal propagator @xmath10 . here though , i will use a kinetic theory approach , which should be equivalent to the diagrammatic one in the perturbative ( and dilute ) regime @xcite . this paper is organized as follows . in sections [ sec : mgnvac ] and [ sec : mgntemp ] , i review well known properties of the massive gross - neveu model at zero and finite temperature , and i prove the breaking of integrability in the large-@xmath0 limit when a mass term for the fermion field is explicitly introduced . then in section [ sec : kinetictheory ] , the calculation of the bulk viscosity within kinetic theory is presented . in section [ sec : discussion ] , i comment on sum rules and implications of the previous analysis for other systems . finally in [ sec : conclusions ] i summarize the main conclusions . there is also the appendix [ app : fermions ] , where the result of factorization for fermion loops in @xmath3 dimensions is derived , and appendix [ app : amplitudes ] where the reader can find some details on the calculation of the inelastic scattering amplitude .

a calculation of the bulk viscosity for the massive gross - neveu model at zero fermion chemical potential is presented in the large- limit . the main motivation is , by decreasing the bare mass , to analyze whether there is a correlation between the maximum in the trace anomaly and a possible maximum in the bulk viscosity , as recently conjectured . i also comment on the sum rule for the spectral density in the bulk channel , as well as on implications of this analysis for other systems .

a calculation of the bulk viscosity for the massive gross - neveu model at zero fermion chemical potential is presented in the large- limit . this model resembles qcd in many important aspects : it is asymptotically free , has a dynamically generated mass gap , and for zero bare fermion mass it is scale invariant at the classical level ( broken through the trace anomaly at the quantum level ) . for our purposes , the introduction of a bare fermion mass is necessary to break the integrability of the model , and thus to be able to study momentum transport . the main motivation is , by decreasing the bare mass , to analyze whether there is a correlation between the maximum in the trace anomaly and a possible maximum in the bulk viscosity , as recently conjectured . after numerical analysis , i find that there is no direct correlation between these two quantities : the bulk viscosity of the model is a monotonously decreasing function of the temperature . i also comment on the sum rule for the spectral density in the bulk channel , as well as on implications of this analysis for other systems .

1207.0644

i

a relativistic charge in a rectilinear and uniform motion can originate an electromagnetic radiative mechanism crossing the dielectric interface between two different media . the fast dipolar oscillation of the polarization charge , induced on the dielectric interface by the relativistic charge , generates indeed an instantaneous , broad spectral band , radially polarized and highly directional radiation emission , the so called transition radiation @xcite . a photon pulse propagates backward and forward from the dielectric interface according to a double conical spatial distribution whose angular aperture scales down with the lorentz @xmath1 factor of the charge . the higher and steeper the discontinuity of the dielectric constant across the interface , the more intense the radiation emission . thanks to the relativistic origin , transition radiation can be fruitfully exploited for energy detection or mass identification of high energy particles @xcite . transition radiation based diagnostics is commonly used in a particle accelerator to monitor the transverse @xcite or the longitudinal profile of a charged beam @xcite . transition radiators , typically made of a thin metallic foil or a thin polished aluminium coating on dielectric substrates , respond as an ideal conductor over a wide spectral range , from the long wavelength to far beyond the visible optical region @xcite . this experimental situation is supposed in the present work . in particular , the case of a @xmath0 electron bunch colliding at a normal angle of incidence onto a flat ideal conductor surface will be considered in the following . an ideal conductor surface being assimilable to a double layer of charge , transition radiation emission can be thus schematized as the result of the interaction of an incident charge with the conduction electrons of the ideal conductor surface . as the relativistic charge approaches the metallic surface , the charge induced conduction electrons freely move in the transverse plane to maintain the metallic surface equipotential . the sudden and fast dipolar oscillation of the double layer of charge is thus responsible for the emission of the radiation pulse as confirmed by the emission of backward radiation . in the relativistic limit , the electromagnetic field travelling with a relativistic electron can be assimilated to a transverse electromagnetic wave , the so called _ virtual quanta _ field @xcite . in the case of a single relativistic electron , the harmonic component of the electric field at a given wavelength @xmath2 extends indeed in the transverse plane over an efficacious range in the order of @xmath3 , the ratio of the longitudinal to the transverse component being @xmath4 . the _ virtual quanta _ field showing the nature of a quasi - plane wave front , the radiation emission can be formally described as the result of the wave propagation of the _ virtual quanta _ scattered by the metallic surface according to the huygens - fresnel principle @xcite . under the far field approximation @xcite , the harmonic components of the transition radiation field at the observation point can be calculated as the fourier transform of the _ virtual quanta _ field with respect to the spatial coordinates of the radiator surface . the transition radiation energy spectrum can be finally obtained as the flux of the poynting vector . a single and individually radiating electron and a high density electron beam are in general different from the point of view of the features of the spectral and the angular distribution of the emitted radiation . compared to the case of a single and individually radiating electron , bunch - density effects may strongly affect the electromagnetic radiative mechanism by an electron beam . for a fixed energy of the beam , the number and the angular distribution of the photons radiated at a given wavelength may indeed change as a function of the density of the electron beam . in the formula of the radiation energy spectrum , the charge form factor accounts for bunch collective effects . this is , in principle , defined as the square module of the fourier transform of the distribution function of the particle density of the charged beam . aim of the present paper is to verify how well such a theoretical definition of the charge form factor fits into a covariant formulation of the radiation energy spectrum or if , instead , under the covariance and the temporal causality constraints , the radiation energy spectrum shows a dependence on the charge density that goes beyond the above mentioned formal definition of the charge form factor . in fact , the transverse density of the electron beam is a relativistic invariant under a lorentz transformation with respect to the direction of motion of the beam . the invariance of the projection of the electron beam density onto the transverse plane with respect to the direction of motion is expected to leave , on the _ virtual quanta _ field and , consequently , on the radiation field , a covariant mark whose observability , for a given harmonic component of the radiation field , only depends on the transverse dimension of the electron beam compared to the transverse component of the wave - vector which is itself a lorentz invariant with respect to the direction of motion of the beam . in the following , the charge - density - like covariance of the transition radiation energy spectrum by an electron beam will be investigated . first , the formal steps leading from the electromagnetic field of a @xmath0 electron bunch to the transition radiation energy spectrum will be analyzed with regard to the temporal causality constraint . finally , the covariance of the given formula of the electromagnetic field of the @xmath0 electron bunch will be checked by verifying that , under a lorentz transformation from the laboratory to the rest reference frame , the expected formula of the electric field of a charge distribution at rest is obtained .

the case of a electron bunch hitting at a normal angle of incidence a flat metallic surface with arbitrary size and shape will be considered . the covariance feature of the transition radiation energy spectrum deals instead with the lorentz invariance of the projection of the electron spatial density in the transverse plane with respect to the direction of motion of the electron beam .

a charge - density - like covariance is expected to characterize the transition radiation energy spectrum of a electron bunch as far as the charge form factor is intended to account for bunch - density effects in the radiation emission . the beam charge passing from a single electron to a high density electron bunch , the covariance of the transition radiation energy is expected to evolve from a charge - point - like to a charge - density - like one . besides covariance , the radiation energy spectrum is expected to conform to the temporal causality principle : the single electron amplitudes composing the radiation field are expected to propagate from the metallic screen with relative emission phases causally correlated with the temporal sequence of the particle collisions onto the metallic screen . in the present paper , the case of a electron bunch hitting at a normal angle of incidence a flat metallic surface with arbitrary size and shape will be considered . for such an experimental situation , the distribution function of the electron longitudinal coordinates rules the temporal causality constraint into the transition radiation energy spectrum . the covariance feature of the transition radiation energy spectrum deals instead with the lorentz invariance of the projection of the electron spatial density in the transverse plane with respect to the direction of motion of the electron beam . because of the invariance of the electron transverse density under a lorentz transformation with respect to the direction of motion of the electron beam , the single electron radiation amplitudes composing the radiation field show a covariant dependence on the distribution function of the electron transverse coordinates , the relative emission phases of the single electron radiation amplitudes being indeed only a function of the electron longitudinal coordinates because of the temporal causality constraint . as a consequence of the temporal causality and the covariance , both the temporal coherent and incoherent components of the radiation energy spectrum bear the covariant imprinting of the distribution function of the electron transverse coordinates as in the following argued . virtual quanta , coherence , fourier transform , collective effects 41.60.-m , 41.75.-i , 42.25.kb , 42.30.kq

1207.0644

c

in the present paper , the issue of the covariant formulation of the radiation energy spectrum and , consequently , of the charge form factor of a @xmath0 electron bunch is argued . the @xmath0 electron bunch is supposed to collide , at a normal angle of incidence , onto a metallic screen @xmath7 which has an arbitrary shape and size ( either finite @xmath31 or infinite @xmath30 ) and is supposed to behave as an ideal conductor in the wavelength region of interest . as the covariance of a charged distribution is expected to evolve from a charge - point - like into a charge - density - like one when passing from a single electron to a @xmath0 electron bunch , the covariance of the radiation energy spectrum as well is expected to behave in the same way when a @xmath0 electron bunch is considered instead of a single electron . in order to verify the covariant formulation of the radiation energy spectrum , the formal steps leading from the virtual quanta field to the transition radiation energy spectrum of a @xmath0 electron bunch have been explicitly derived and checked to meet , first , the temporal causality constraint and , then , to be covariance consistent . finally , the expression of the _ virtual quanta _ field , which , in the present paper and in other papers @xcite , is the starting point to achieve the formula of the radiation energy spectrum , has been checked to transform in a covariant way under a lorentz transformation from the laboratory reference frame ( @xmath45 ) to the reference frame of rest of the @xmath0 electron bunch ( @xmath48 ) . in order to perform such a covariance check , the fourier representations of fields and charged distributions have been suitably extended from the ordinary @xmath41-dimensional space of the spatial coordinates and the conjugate fourier wave - vectors into the lorentz @xmath42-spaces of the space - time and of the conjugate fourier wavevector - frequency in both @xmath45 and @xmath48 . in a temporal causal and covariant formulation of the transition radiation energy spectrum of a @xmath0 electron bunch , the invariance of the projection of the electron density in the transverse plane with respect to the direction of motion manifests itself as a covariant feature of the @xmath0 single electron amplitude composing the radiation field and , consequently , of both the temporal coherent and incoherent components of the transition radiation energy spectrum .

a charge - density - like covariance is expected to characterize the transition radiation energy spectrum of a electron bunch as far as the charge form factor is intended to account for bunch - density effects in the radiation emission . the beam charge passing from a single electron to a high density electron bunch , the covariance of the transition radiation energy is expected to evolve from a charge - point - like to a charge - density - like one . besides covariance

a charge - density - like covariance is expected to characterize the transition radiation energy spectrum of a electron bunch as far as the charge form factor is intended to account for bunch - density effects in the radiation emission . the beam charge passing from a single electron to a high density electron bunch , the covariance of the transition radiation energy is expected to evolve from a charge - point - like to a charge - density - like one . besides covariance , the radiation energy spectrum is expected to conform to the temporal causality principle : the single electron amplitudes composing the radiation field are expected to propagate from the metallic screen with relative emission phases causally correlated with the temporal sequence of the particle collisions onto the metallic screen . in the present paper , the case of a electron bunch hitting at a normal angle of incidence a flat metallic surface with arbitrary size and shape will be considered . for such an experimental situation , the distribution function of the electron longitudinal coordinates rules the temporal causality constraint into the transition radiation energy spectrum . the covariance feature of the transition radiation energy spectrum deals instead with the lorentz invariance of the projection of the electron spatial density in the transverse plane with respect to the direction of motion of the electron beam . because of the invariance of the electron transverse density under a lorentz transformation with respect to the direction of motion of the electron beam , the single electron radiation amplitudes composing the radiation field show a covariant dependence on the distribution function of the electron transverse coordinates , the relative emission phases of the single electron radiation amplitudes being indeed only a function of the electron longitudinal coordinates because of the temporal causality constraint . as a consequence of the temporal causality and the covariance , both the temporal coherent and incoherent components of the radiation energy spectrum bear the covariant imprinting of the distribution function of the electron transverse coordinates as in the following argued . virtual quanta , coherence , fourier transform , collective effects 41.60.-m , 41.75.-i , 42.25.kb , 42.30.kq

1003.2184

i

[ s-01 ] the surfaces possessing nontrivial deformations which preserve principal curvatures and directions ( or , equivalently , the shape operator ) were investigated by several authors , see @xcite , @xcite and review with bibliography in @xcite . it is known that surfaces with one family of principal curves being geodesic ( as for parallel curved ( pc ) surfaces recently studied in @xcite@xcite ) represent degenerate case in studying immersions of simply connected surfaces with a prescribed shape operator . recent studying of reconstruction of surfaces by their partially given principal curvatures and directions may be useful for applications of differential geometry to computer graphics , the wavefront analysis in applied optics , etc . in what follows , @xmath1 denotes a @xmath2-regular riemannian 3-space with coordinates @xmath3 , @xmath4 ( @xmath5 ) for some @xmath6 , @xmath7 a @xmath2-regular surface , @xmath8 the coordinate curve , and @xmath9 the _ curvilinear projection_. in the paper we consider surfaces - graphs @xmath10 with _ prescribed curvilinear projection ( onto @xmath0 ) of one field of principal directions_. we show ( see theorem [ t - main0 ] ) that such surfaces depend on two arbitrary functions of one variable , namely , the principal curvatures over @xmath11 which are assumed close enough to corresponding values for @xmath0 . more precisely , we study the following . [ prob-1]given @xmath1 , a vector field @xmath12 transversal to @xmath11 on @xmath0 , functions @xmath13 and @xmath14 of class @xmath15 , * find * a function @xmath16 of class @xmath17 , whose graph @xmath18 in @xmath19 satisfies the conditions : \(i ) _ the projection ( @xmath20 ) onto @xmath0 of the field @xmath21 of principal directions _ _ corresponding to the principal curvature @xmath22 ( of @xmath23 ) coincides with @xmath12 _ , \(ii ) _ the principal curvatures @xmath24 ( of @xmath23 ) over @xmath11 coincide with @xmath25 : @xmath26 _ , \(iii ) _ the values of @xmath16 and @xmath27 at the point @xmath28 of @xmath11 are given_. our approach is based on reducing the * problem [ prob-1 ] * to the cauchy problem for a quasilinear system of pde s which , under certain conditions for data , is hyperbolic and admits a unique local smooth solution . the pc surfaces in @xmath29 represent a special class of solutions when a family of curvature lines projects onto @xmath0 as parallel lines or concentric circles . such surfaces are recovered by an iteration function sequence and using the reconstruction of planar curves by their curvature ( see theorem [ t - rpc2 ] and proposition [ t - rpc1 ] ) . notice that the space of pc surfaces free of umbilics and having the same shape operator depends on arbitrary function of one variable , see @xcite . the structure of the work is the following . * section [ sec : main - res ] * represents main results ( theorems [ t - main0][t - rpc2 ] and corollary [ t - main3 ] for @xmath30 ) . * section [ sec : proofs ] * contains proofs . * section [ sec : appendix ] * contains necessary facts on pc surfaces and examples .

a class of surfaces - graphs in a riemannian 3-space with a prescribed projection of one field of principal directions onto a surface is considered . a problem of determination of such surfaces when both principal curvatures are given over a line in is formulated and studied . the geometric problem is reduced to the cauchy problem for quasilinear pde s which , under certain conditions for data , are hyperbolic and admit a unique solution . such solutions may be found by an iteration function sequence .

a class of surfaces - graphs in a riemannian 3-space with a prescribed projection of one field of principal directions onto a surface is considered . a problem of determination of such surfaces when both principal curvatures are given over a line in is formulated and studied . the geometric problem is reduced to the cauchy problem for quasilinear pde s which , under certain conditions for data , are hyperbolic and admit a unique solution . it is shown that the parallel curved ( pc ) surfaces in space forms provide a special class of global solutions to the geometrical problem with weaker regularity assumptions . such solutions may be found by an iteration function sequence . riemannian space , surface , principal curvature / direction , hyperbolic pde s * ams subject classification : * 53b20 , 53b25 , 53c99 , 53a05

1107.4784

i

conformal blocks , which are defined on the ( punctured ) riemann surfaces , holomorphic in each @xmath1 coordinate except when they meet each other , play an essential role in building correlation functions in two dimensional ( euclidean ) conformal field theories@xcite . they can be best understood as sewing together chiral vertex operators@xcite , which by definition , are not local objects , but the correlation functions are . the later combine both holomorphic and anti - holomorphic conformal blocks in a consistent way to make modular covariant objects . on the sphere , the @xmath2-point conformal block is represented graphically as in fig.[confblock ] , where @xmath3 is the conformal dimension of the primary field inserted at coordinate @xmath1 , and @xmath4 labels the contribution arising from the conformal family descending from a primary field with the conformal dimension @xmath4 . the global conformal invariance is @xmath5 , which may be used to fix three coordinates @xmath6 , @xmath7 and @xmath8 . so the independent variables are @xmath1 , @xmath9 , with the degrees of freedom @xmath10 for the @xmath2-point conformal blocks on the sphere . the calculation of conformal blocks is based on the conformal ward - identities , @xmath11=(z^{n+1}\partial_z + ( n+1)h z^n ) v_h(z).\ ] ] and carried out perturbatively level by level @xcite . in some special cases , the decoupling of the virasoro null vectors can be implemented as differential equations for the conformal blocks . for the general case , recursion relations have been proposed by zamolodchikov@xcite on the meromorphic structures of the conformal blocks either in complex @xmath12-plane or @xmath13-plane . however , in general , the global perspective of the sewing procedure for the conformal blocks was still not fully understood until recently when the agt duality @xcite had been proposed . agt conjecture relates 2d liouville conformal field theories to 4d @xmath14 supersymmetric gauge theories of the @xmath15 type . the main idea is coupling to the liouville field a @xmath16 field field is a gauge symmetry and can be fixed to any desired value . ] , then this system is dual to a @xmath17 superconformal 4d theory . in this case , the partition function by nekrasov instanton counting(nic)@xcite of the 4d @xmath18 theory is to be identified with the conformal blocks of the @xmath16 coupled liouville type . the liouville cft is characterized by a 2d one boson theory with center charge @xmath19 . finally , one can decouple the @xmath20 factor and obtain the instanton partition function of the @xmath21 theory which duals to liouville conformal blocks . liouville interaction breaks down the charge conservation explicitly and leads to the introduction of the screening charges . because of the existence of the screening charges , the conformal blocks of the liouville type is much more complicated than its counterpart of the @xmath16 free boson theory . however , the agt conjecture , if proven true , means that there exists an orthogonal basis upon which the @xmath22 conformal blocks are built . from the above reasoning , there exists a tree - like structure which describes the duality in coupling space of the @xmath14 4d superconformal linear quiver gauge theory . the primary objects for this tree - like structure is the `` bifundmental '' matter coupling , which , if translated correctly , should be represented by the inner products of the bra and ket descendant fields in 2d conformal families sandwiched by a `` primary '' vertex operator at position , say , @xmath23 . such kind of pants - like diagram can be sewed together to form a linear quiver diagram , which , on the 2d cft side , is just the @xmath2-point functions on the sphere for our consideration . of course , in the present context , we mean the @xmath0 2d cft . at first sight , it seems that such duality does not bring in any conveniences . however , the nekrasov instanton counting on the 4d field theory shows a rather compact form for the summands which are completely factorized in `` momentum '' @xmath24 . and the summation is well organized into the combinatorial enumeration of the young tableuax . this simple structure implies liouville theory , in particular , the evaluation of the liouville conformal blocks , could be resolved by embedding it into a bigger system . so one may expect a new construction for the liouville conformal blocks from the corresponding nic . -point conformal block on @xmath25,height=144 ] as pointed out by nakajima@xcite , the instanton counting for @xmath14 gauge theory is equivalent to the hilbert scheme of points on the corresponding seiberg - witten curve ( blow - up riemann surface)@xcite . this can be translated into a topological string description from physicists point of view . by invoking the d4-d0 brane setup@xcite for adhm construction@xcite of the instanton moduli space and the resolving process for ale singularities@xcite , these indicate that the instanton counting is a counting for d0 branes in a toric calabi - yau 3-fold . actually , there are two kinds of d0 branes in the calabi - yau 3-fold , one is the regular d0 brane , which is in regular representation of @xmath26 , the center of the corresponding ade group . it carries no flux and can move freely on the riemann surface . the other is the fractional d0 brane , which is a d2 brane wrapping on a zero - sized two sphere . it is always attached to the ale singularity since it has a nontrivial monodromy while moving around the singularity . it is these fractional d0 branes that resolve the ale singularity , and leave fluxes on the blow - up riemann surface . this property ensures that one can identify these fractional instantons as `` anyons '' on the riemann surface . on the other hand , the regular ones are `` electric charged '' particles on the riemann surface . so the total counting is equvalent to solving the problem of `` electron gas '' system with insertions of anyons at the blow - up singularity on the riemann surface . this point of view is partialy included in dijkgraaf and vafa s article@xcite . for each pants of the pants decomposition for the ( punctured ) riemann surface , one can guess that the instanton partition function can be rewritten as summation over all the intermediate states passing through the sewn holes@xcite . for the interests of the present paper , we concern ourselves only with the special pants diagram that one of the tubes is replaced by the blow - up singularity . then the summand in the instanton partition function represents itself as an inner product of the bra and ket states , sandwiched by the anyonic vertex operator . these bra and ket states should come from the interacting `` electronic '' particles . a candidate description of the `` electronic gas '' system is the integrable system of multiple calogero - sutherland model , each living on a cycle . the whole ( punctured ) riemann surface , can be obtained by sewing together these pants on nonintersecting cycles . there are many efforts on relating the conformal blocks to the nic@xcite from various points of views , and these works confirm the validity of the agt duality . however , the explicit construction for the liouville conformal blocks has remained largely unclear until the recent work @xcite by alba , fateev , litvinov and tarnopolsky . in @xcite , they have put forward the agt duality in a more explicit form [ aflt ] & = & z_bif(|p, ; p , ) , here specifically for a free field realization , @xmath27 with @xmath28 , and @xmath29 is the screening charge in the virasoro sector . the l.h.s . of eq([aflt ] ) is the pants - like ( with one of the tubes labeled by @xmath30 shrinks to a line ) conformal block . the r.h.s . of ( [ aflt ] ) reproduces @xmath31 for the instanton counting , which is given by [ zbif]z_bif(|p, ; p , ) = _ i , j=1 ^ 2 _ sy_i(q - e_y_i , y_j(p_i - p_j|s ) - ) _ ty_j ( e_y_j , y_i(p_j - p_i|t)-),where @xmath32 , @xmath33 and e_y , y(p|s ) p+b^-1(a_y(s)+1)-bl_y(s ) . here @xmath34 and @xmath35 resp . are the arm length and the leg length resp . of the box @xmath36 in the young tableau @xmath37 , defined as @xmath38 @xmath39 and @xmath40 resp . are the @xmath41-th part of the partition @xmath42 and the @xmath43-th part of the transpose partition @xmath44 respectively . ( [ aflt ] ) means that the matrix elements of a special `` chiral vertex operator '' @xmath45 in a suitably chosen basis , can be translated into a 4d theory as an instanton contribution for a special bifundamental contribution of the nic . by sewing together pants - like diagrams one gets any desired duality diagrams in the coupling space of the linear quiver gauge theory . so , the checking of the agt duality reduces to the construction of the states @xmath46 , which we shall call the aflt states@xcite , with @xmath47 the young tableaux . here the @xmath37 s , the partitions of natural numbers , or equivalently represented by young tableaux , are labels for the orthogonal basis for the descendant fields ( verma modules ) in a @xmath0 conformal family from the 2d cft point of view . by definition , the aflt states form a complete set of states for the family members in a given @xmath0 conformal family and the inner products between them , sandwiched by a vertex operator of the particular form , @xmath48 , at position , say , @xmath49 , is factorized exactly as the nic @xmath31 presented on the r.h.s . of ( [ aflt ] ) . the explicit formula , ( [ aflt ] ) , puts strong constraints on the possible forms of the aflt states and make a systematic construction of them unaccessible at first glance . in @xcite , only the explicit form of the state @xmath50 has been found , @xmath51 with @xmath52 the creator @xmath53 s valued jack symmetric function , and @xmath54 the normalization constant . in our opinion , the agt conjecture , written in the form of ( [ aflt ] ) , strongly suggests that the @xmath0 conformal family is a hamiltonian system with @xmath46 the hamiltonian eigenstates . so the construction of the aflt states becomes a quantum mechanical problem of solving the schrodinger equation . put things in this way , we propose a possible form of the hamiltonian @xmath55 and construct its eigenstates explicitly . we shall identify those eigenstates as the aflt states desired . for in all the cases we have checked , ( [ aflt ] ) is verified to be true , using the aflt states we have constructed . we shall present now as the main results of our present paper the explicit form of the hamiltonian @xmath55 along with the complete construction of the aflt states , @xmath46 . more elaborated exposition will come in the subsequent sections . [ main1 ] h&=&h_0+h_i + _ & = & j_-|p_(p).here , @xmath56 are the jack states constructed in terms of the oscillators @xmath57 s or @xmath58 s ( @xmath59 ) solely , @xmath60 the corresponding hamiltonian for the jack symmetric functions , @xmath61 . thus the eigenstate of @xmath62 is just @xmath63 with the eigenvalue @xmath64 . @xmath60 in our formalism is defined to include zero modes @xmath65 also , @xmath66 . it is important that @xmath67 is strictly triangular with respect to the basis vectors of the @xmath62 eigenstates . by `` strictly triangular '' we mean the ( upper or lower ) triangular matrix with zero diagonal entries . it is easy to see that if the interaction term @xmath67 is strictly triangular , then the eigenvalue spectrum of @xmath62 remains unperturbed and @xmath46 in ( [ main1 ] ) well defined for non - degenerate @xmath62 spectrum descending from a mother state @xmath68 for generic values of @xmath24 s . putting things all together , we have [ main2 ] & & h = h_0+h_i , h_0= h^+ + h^- , h_i=_n=1 ^ 2qn a_-n^+a_n^- , + & & h^=(z_z^)^3 + _ n=1^q n a_-n^a_n^ , + & & e_(p)=e_y_1+e_y_2 + 2p(|y_1|-|y_2| ) , e_y=_i ( y^2_ib^-1+(2i-1)y_i b ) , + & & _ ( p)= ( -)^|y_1|b^|y_1|+|y_2|_y_1(2p+(a_y_1 + 1)b^-1-l_y_2b ) _ y_2(2p - a_y_2b^-1 + ( l_y_1 + 1)b ) , + & & _ = j_-|p_(p ) , + & & h_0j_-=e_(p)j_- , h_=e_(p ) _ , -i a^_0=p notice that + 1 ) @xmath50 constructed in @xcite are included in our construction as subcases . + 2 ) the hamiltonian @xmath55 constructed by us , albeit in a disguised form , turns out to coincide up to some trivial factor with @xmath69 , one of the integrals of motion found in a different context in appendix c of @xcite . @xmath69 in @xcite , written in the form of @xmath0 , makes the virasoro symmetry manifest , but is not suitable for solving a perturbation theory with perturbation parameter @xmath70 . the hamiltonian @xmath55 written in terms of the interacting bi - jack polynomial system as in ( [ main2 ] ) , shows virasoro symmetry only implicitly , but makes the perturbation theory exactly solvable as we shall see soon after . the procedure is outlined as follows . on the 2d cft side , the @xmath71 theory can be represented as a theory of two independent scalars @xmath72 and @xmath73 . @xmath72 part is essentially a free theory of timelike oscillators , while the scalar field @xmath74 is spacelike but engaged in a liouville type interaction . the two scalars can be linearly combined to form the `` light - cone '' scalars . @xmath75 and @xmath76 . the labeling @xmath77 of the basis vectors strongly suggests that there exist a bi - jack polynomial structure , plus possibly some interactions between these two sectors . that is , the `` free '' @xmath60 spectrums should be described by @xmath78 and @xmath79 respectively , here @xmath80 denotes jack states related to young tableau @xmath37 . first we construct the `` unperturbed '' energy operator @xmath62 which just sums up the `` energies '' in @xmath81 sectors , @xmath82 . the next thing is to specify the interaction between these two sectors . strictly speaking , @xmath62 does not describe a free theory , since it also contains the interaction terms proportional to @xmath83 . but the new interaction term @xmath67 further mixes the @xmath84 s and the coupling is also a first order in @xmath83 . it is good to see that @xmath67 is strictly triangular with respect to the basis vectors of @xmath62 eigenstates . our method can be easily generalized to wider classes of integrable models , in which the interacting hamiltonian splits into two parts , @xmath85 and @xmath86 , representing respectively the shift of energies and the rotations ( mixings ) of states . the later keeps the eigenvalue spectrum untouched@xcite . besides being triangular , the form of the interaction term is however much restricted , also by the virasoro symmetry . since the total hamiltonian is of the form @xmath0 , an `` interaction energy operator '' @xmath67 is needed to make the `` full energy operator '' @xmath87 the combination of @xmath88 s and @xmath89 s only . once the hamiltonian structure is determined , then the construction of the hamiltonian eigenstate @xmath46 is just a quantum mechanical problem . @xmath62 and @xmath55 share the same eigenvalue spectrum , but only the eigenstates of @xmath55 , represented by @xmath46 s , form a complete set of basis vectors for the @xmath0 conformal family . we have checked by examples the corresponding agt duality formula , ( [ aflt ] ) up to level 4 , and have found that indeed nekrasov instanton counting can be reproduced with this construction , ( [ main2 ] ) . in fact , we have also checked more general cases and all get positive answers . but those more general results will appear elsewhere due to lacking of space to include them in this paper . the insertions of the screening charges play an important role in checking the agt duality . however , in the present work we concern ourselves only with the cases in which the screening charges can be detached away from the vertex operator @xmath45 and moved on to act on the aflt states ( similar to the felder s brst operators)@xcite . the more general cases in which screening charges can not be moved away from @xmath45 will be under our future studies . it is well known that it is possible to map the liouville theory to the analytic continuation of the calogero - sutherland(cs ) model , which was originally and in most cases considered to be a theory with the parameter @xmath90 , while in the liouville case @xmath91 is required . some explanation is given in @xcite . the physical space of the cs model are created by jack polynomials , which are symmetric functions studied in great detail in mathematics and physics literatures@xcite . the integrability of the cs model may be derived in different ways , e.g. , from the knowledge of the hidden @xmath92 symmetry of the model . a recursion relation related to the virasoro singular vectors and an integral representation based on it has appeared recently in @xcite , in which more references can be found on the subjects of the cs model and the jack symmetric functions . it should be stressed again that for @xmath90 , there is no null vectors in the cs model . so the `` null '' vectors are not the true null vectors of the cs model , since the virasoro algebra based on which the null vectors are constructed is not the true conformal algebra of the cs model in that case . but for @xmath91 , yes , there are null vectors in the cs model . it is possible to describe the @xmath93 theory in terms of the jack polynomials considered as analytic continuation from @xmath94 to @xmath95 . there is another hint that the @xmath93 theory has something to do with @xmath91 cs model . it can be found from the nekrasov partition function , in which each term in the summation can be written in the form of the carlsson - okounkov formula@xcite , for the special cases when no screening charges are inserted . carlsson - okounkov formula is a formula for the inner products between the bra jack states and the ket jack states sandwiched with a modified vertex operator . this extraordinary formula is of great help in checking the agt duality with our construction for the orthogonal basis vectors @xmath46 s defined in ( [ aflt ] ) . we notice that the construction we found shares many similarities with the construction of the jack functions themselves . namely , we take the state @xmath96 as the mother state and its descendants are constructed in such a manner that two partitions are `` squeezed '' into other pairs . the squeezing does not change the total level of the two partitions , but does make the inner products of the descendants a triangular form . although the 4d to 2d duality has just begun to be understood , it has been known for sometime that 2d conformal blocks can be equivalently described as insertions of wilson lines in 3d pure chern - simons topological gauge theory . in fact , we can interpret the @xmath2-point conformal block represented by fig.1 as a wilson line insertion inside a three - ball . the path integral in chern - simons - witten gauge theory thus creates a state living on the boundary of the three ball , which is punctured @xmath25 . so it should not be a too big surprise that 2d conformal field theory has something to do with higher dimensional quantum field theories . taking into account that jack symmetric polynomials can be taken as some special limit of the two parameter macdonald symmetric polynomials , one natural guess is that our construction can be generalized to the case of macdonald symmetric polynomials . in that case there should be a 5d to 3d duality . this paper is organized in the following way . our general formalism on the construction of the aflt states is presented in the introduction . in section 2 , we explore the general structure of the @xmath0 conformal family . we found in some cases it is more convenient to work with the bi - jack function basis . section 3 contains the major derivation of our construction . section 4 is the conclusion . and in appendix a the explicit construction of the aflt states up to level 3 is presented .

a complete construction of the aflt states is proposed . with this construction and for all the cases we have checked , the agt conjecture on the equivalence of nekrasov instanton counting ( nic ) to the conformal block has been verified to be true . bao shou , jian - feng wu , and ming yu .5 cm _ institute of theoretical physics , + chinese academy of sciences , beijing , 100190 , china _

a complete construction of the aflt states is proposed . with this construction and for all the cases we have checked , the agt conjecture on the equivalence of nekrasov instanton counting ( nic ) to the conformal block has been verified to be true . bao shou , jian - feng wu , and ming yu .5 cm _ institute of theoretical physics , + chinese academy of sciences , beijing , 100190 , china _

1407.6547

i

in 2012 , a higgs boson was discovered at the cern large hadron collider ( lhc ) @xcite . its observed properties are consistent with the prediction in the standard model ( sm ) within the current experimental uncertainties @xcite . in addition , so far , no report has been delivered to us for discovery of the other new particles . therefore , it has been found that the sm is a good description for particle physics at the scale of hundred gev , not only in the gauge interactions but also in the sector of electroweak symmetry breaking . although the higgs boson has been discovered and its property has turned out to be sm - like , we know nothing about the structure of the higgs sector . in fact , the minimal higgs sector with one isospin doublet scalar field is just an assumption without any theoretical principle . thus , it is natural to consider a possibility that the higgs sector takes a non - minimal form with additional isospin multiplet scalar fields , such as extra singlet , doublet , triplet and so on . most of these non - minimal higgs sectors can explain current experimental data as well . furthermore , these extended higgs sectors are often introduced in the context of new physics models which try to explain the phenomena beyond the sm ; i.e. , neutrino masses , dark matter , and baryogenesis . therefore , it is very important to experimentally explore the possibility of extended higgs sectors . we then may be able to discriminate new physics models from the property of the higgs sector . for example , extended higgs sectors with multi - doublet scalar fields are introduced in supersymmetric extensions of the sm . they are also motivated to introduce an additional source of cp violation @xcite , and to realize the strong 1st - order phase transition @xcite , both of which are required to have successful electroweak baryogenesis @xcite . singlet scalar fields are often introduced in models with the spontaneously broken @xmath4 gauge symmetry @xcite . the higgs sector with a complex triplet scalar field appears in models that can explain neutrino masses via the seesaw mechanism @xcite . tiny neutrino masses can also be explained via the loop - induced effects of extended scalar sectors @xcite . extended scalar sectors with a discrete symmetry such as @xmath5 can provide a candidate of dark matter @xcite . we here focus on the higgs triplet model ( htm ) @xcite . its higgs sector is composed of an isospin doublet higgs field with a hypercharge as @xmath6 , where @xmath7 is the electric charge and @xmath8 is the third component of the isospin . ] @xmath9 and an isospin triplet higgs field with @xmath10 . in this model , majorana masses of neutrinos are generated via new yukawa interactions among the left - handed lepton doublets and the higgs triplet field ; @xmath11 , where @xmath12 is the vacuum expectation value ( vev ) of the triplet field , and @xmath13 is a matrix in the lagrangian for the yukawa interactions . one of the most characteristic features of the htm is the existence of doubly - charged higgs bosons @xmath0 , in addition to the other additional higgs bosons ; i.e. , singly - charged @xmath14 , cp - even @xmath15 and cp - odd @xmath16 higgs bosons . the discovery of @xmath0 at collider experiments is the direct evidence of the htm . production of these bosons at collider experiments has been studied in refs . . for the decay of @xmath0 , there are three sources ; i.e. , the yukawa interactions with left - handed lepton doublets , electroweak gauge interactions in the gauge - gauge - scalar type , and those in the gauge - scalar - scalar type . they cause the same - sign dilepton decay @xmath17 , the same - sign diboson decay @xmath18 and the cascade decay @xmath19 , respectively decay occurs via the scalar triple couplings , if there is a large mass difference between @xmath0 and @xmath20 . however , such a situation is severely constrained by electroweak precision measurements @xcite . ] . although the dominant decay mode of @xmath0 is determined by parameters in the model , the dilepton decay scenario has been considered as the most promising one for discovery @xcite , because of its cleanness for the detection at colliders . it is also quite appealing that the structure of neutrino mass matrix can be directly tested by measuring the dileptonic branching ratios of @xmath0 @xcite and @xmath20 @xcite , because the branching ratios are predominantly determined by the neutrino yukawa couplings . in this scenario , a sharp peak in the invariant mass distribution of the same - sign dilepton is the characteristic signal of @xmath0 . the experimental searches for @xmath0 in the same - sign dilepton events have been performed at lep @xcite , hera @xcite , tevatron @xcite and the lhc @xcite . assuming that the branching ratio of @xmath0 decay into @xmath21 is 100% , the strongest lower bound on the mass of doubly - charged higgs bosons has been obtained as 459 gev at the lhc @xcite . current bounds have also been set at around 400 gev in several benchmark points for the structure of the neutrino mass matrix @xcite . in this paper , we discuss the direct searches for @xmath0 in the diboson decay scenario , where @xmath0 predominantly decay into same - sign w bosons , at the past , current and future collider experiments , such as lep , the lhc with 7 - 8 tev run and 13 - 14 tev run . the same - sign diboson decay scenario is equally important to the same - sign dilepton decay scenario in the htm . collider phenomenology for this decay mode has been studied in refs . @xcite . in ref . @xcite , the lower limit on the mass of @xmath0 has been derived by using the same - sign dilepton events collected by atlas collaboration at the lhc with 7 tev and 4.7 fb@xmath3 data @xcite . up to our knowledge , this is the first analysis for the constraints on @xmath0 in the diboson scenario . the aim of the present paper is to explain details of the analysis done in ref . @xcite , and to make update on the results by including the qcd correction to the production cross sections . this paper is organized as follows . in section ii , we briefly review the htm . after we define the mass eigenstates for the higgs bosons , we derive the yukawa interaction and the gauge interaction for the triplet - like higgs bosons at the tree level . in section iii , we give expressions for the decay rates of @xmath0 in the all three decay modes . partial decay widths of @xmath0 are evaluated with particular attention to the case of relatively small masses where one or both of the w bosons are forced off - shell . we then show the phase diagram indicating the main decay mode of @xmath0 . next , we evaluate the cross section of @xmath0 productions at the lhc in the leading order ( lo ) and the next - to - leading order ( nlo ) of qcd . in section iv , we exhibit constraints on the mass of @xmath0 in the diboson decay scenario at the lep experiments and also at the lhc . at the lep i experiment , the lower limit on the mass of @xmath0 can be obtained from the total width of the z boson . we also evaluate the expected number of events for the various final states in the process of @xmath22 at the lep ii experiment . we then discuss the mass bound on @xmath0 by using the current lhc limit on the cross section for anomalous production of same - sign dileptons . section v is devoted to our conclusion . in appendix , the cross sections for @xmath0 production at the lhc with various collision energies are collected for reader s convenience .

, the lower limit on the mass of has been set at about 400 gev by atlas and cms collaborations . on the other hand , for the case where the latter decay mode is dominant , no dedicated search has been performed in the past . by taking into account characteristic signals of in the diboson decay scenario at lep and the lhc experiments , we find that the lower mass bound of 60 - 68 gev can be obtained using the same - sign dilepton search performed by atlas collaboration with 4.7 fb data at the collision energy of 7 tev . we give detailed explanations on the decay properties of for relatively small mass cases and also on production cross sections of at the next - to - leading order of qcd at the lhc .

a direct search for doubly - charged higgs bosons is one of the most important probe in the higgs triplet model , which is motivated by generation mechanisms of tiny neutrino masses . there are two major decay modes of ; i.e. , the same - sign dilepton decay and the same - sign diboson decay . for the case where the former decay mode is dominant , the lower limit on the mass of has been set at about 400 gev by atlas and cms collaborations . on the other hand , for the case where the latter decay mode is dominant , no dedicated search has been performed in the past . by taking into account characteristic signals of in the diboson decay scenario at lep and the lhc experiments , we find that the lower mass bound of 60 - 68 gev can be obtained using the same - sign dilepton search performed by atlas collaboration with 4.7 fb data at the collision energy of 7 tev . we also show that the limit can be extended up to about 85 - 90 gev , assuming the integrated luminosity of 20 fb and 7 tev for the collision energy . we give detailed explanations on the decay properties of for relatively small mass cases and also on production cross sections of at the next - to - leading order of qcd at the lhc .

1601.06502

i

a _ multiset _ is a generalization of a set in which each element has an associated integer _ multiplicity_. given a possibly infinite set @xmath4 , a set ( resp . multiset ) homomorphic hash function on @xmath4 maps finite subsets of @xmath4 ( resp . finitely - supported multisets on @xmath4 ) to fixed - length hash values , allowing incremental updates : when new elements are added to the ( multi)set , the hash value of the modified ( multi)set can be computed in time proportional to the degree of modification . the incremental update property makes homomorphic hashing a very useful and versatile primitive . it has found applications in many areas of computer security and algorithmics , including network coding @xcite and verifiable peer - to - peer content distribution @xcite , secure internet routing @xcite , byzantine fault tolerance @xcite , _ streaming _ set and multiset equality comparison @xcite , and various aspects of database security , such as access pattern privacy @xcite and integrity protection @xcite . this latter use case provides a simple example of how the primitive is used in practice : one can use homomorphic hashing to verify the integrity of a database with a transaction log , by computing a hash value for each transaction in such a way that the hash of the complete database state is equal to the ( appropriately - defined ) sum of the hashes of all transactions . another observation @xcite is that homomorphic hashing can be used for incremental and parallel hashing of lists , arrays , strings and other similar data structures : for example , the list @xmath5 can be represented as the set @xmath6 , and it suffices to apply the homomorphic hash function to that set . a framework for constructing provably secure homomorphic hash functions ( in some suitably idealized model , such as the random oracle model ) was introduced by bellare and micciancio @xcite , and later extended to the multiset hash setting by clarke et al . @xcite , and revisited by cathalo et al . @xcite . roughly speaking , the framework of bellare and micciancio can be described as follows . to construct a ( multi)set homomorphic hash function on @xmath4 , one can start with a usual hash function @xmath7 from @xmath4 to some additive group @xmath8 , and extend it to finite subsets of @xmath4 ( resp . multisets on @xmath4 ) by setting @xmath9 ( resp . @xmath10 , where @xmath11 is the multiplicity of @xmath12 ) . and in fact , it is clear that all possible homomorphic hash functions arise in that way . note that as in clarke et al . @xcite , and unlike the original framework of bellare and miciancio @xcite , there is no block index @xmath13 included in the hash @xmath14 of each element @xmath12 , because we are hashing unordered sets / multisets , rather than ordered sequences of blocks . assume that the underlying hash function @xmath7 is ideal ( i.e. it behaves like a random oracle ) . then we can ask when the corresponding homomorphic hash function @xmath15 is secure ( collision resistant , say ) . this translates to a knapsack - like number - theoretic assumption on the group @xmath8 , which bellare and micciancio show holds , for example , when the discrete logarithm problem is hard in @xmath8 . concretely , bellare and micciancio and the authors of subsequent works propose a number of possible instantiations for @xmath15 which essentially amount to choosing @xmath16 or @xmath17 for suitable parameters @xmath18 . these concrete instantiations yield simple implementations , but they all suffer from suboptimal output size ( they require outputs of several thousand bits to achieve collision resistance at the @xmath19 security level ) , and their efficiency is generally unsatisfactory . essentially all practical applications of homomorphic hashing in the security literature seem to focus on the case @xmath20 , called ` muhash ` . within bellare and micciancio s framework , constructing a homomorphic hash function amounts to choosing a group @xmath8 where the appropriate number - theoretic assumption holds , together with a hash function to @xmath8 whose behavior is close enough to ideal for the security proof to go through . in this paper , we propose a novel concrete construction of a multiset hash function by choosing @xmath8 as the group of points of a binary elliptic curves , and picking the hash function following the approach of brier et al . @xcite ( which we improve upon slightly ) applied to the binary curve variant of shallue and van de woestijne s encoding function @xcite . we also describe a software implementation of our proposal ( building upon the work of aranha et al . @xcite for binary curve hashing , and using blake2 @xcite as the actual underlying hash function ) and provide extensive performance results showing that our function outperforms existing methods by a large margin on modern cpu architectures ( especially those supporting carry - less multiplication ) . furthermore , choosing an elliptic curve ( with small cofactor ) for the group of hash values solves the `` output size '' problem of homomorphic hashing outright : @xmath21 collision security is achieved with roughly @xmath22-bit long digests . yet , they do not seem to have been used in concrete implementations of homomorphic hashing so far for a more detailed discussion . ] . one can wonder why ; the most likely explanation is that usual methods for hashing to elliptic curves are far too inefficient to make curves attractive from a performance standpoint : almost all such methods require at least one full size exponentiation in the base field of the curve , which will be much more costly by itself than the single multiplication ( in a much larger field ) required by ` muhash`even on curves over fast prime fields at the 128-bit security level @xcite , such an encoding function is over @xmath23 times slower than ` muhash ` at equivalent security on haswell , and over @xmath24 times slower than our construction . only by using binary curves and relatively sophisticated implementation techniques do we avoid that stumbling block and prove that elliptic curves can be competitive . as a result , we achieve a processing speed of over 3 million set elements per second on a intel haswell cpu at the @xmath19-bit security level . speedups are expected with the release of intel broadwell processors and its improved implementation of carry - less multiplication . recently , new developments have been announced regarding the asymptotic complexity of the discrete logarithm problem on binary elliptic curves , particularly by semaev @xcite . these results are somewhat controversial , since they are based on heuristic assumptions that prevailing evidence suggests are unlikely to hold @xcite , and their storage requirements appear to make them purely theoretical anyway @xcite . however , if semaev s claims of an @xmath25 $ ] attack turn out to be correct , the asymptotic security of binary elliptic curve - based ecmh would be reduced . concrete _ security of our construction , on the other hand , would be completely unaffected on curves of up to 300 + bits ( and in particular at the 128-bit security level on gls254 ) , since the claimed attack is worse than generic attacks on such curves . moreover , even if _ actually practical _ @xmath25 $ ] attacks were to be found , ecmh on binary curves is likely to remain attractive , since it mainly competes against ` muhash ` , which is vulnerable to an @xmath26 $ ] subexponential attack . for all these reasons , we believe that ecmh on binary elliptic curves is a safe choice for security - minded practitioners , and that the switch from ` muhash ` to ecmh is entirely justified in view of the considerable performance gain ( which lets designers choose a higher security margin and still come out far ahead ) .

a homomorphic , or incremental , multiset hash function , associates a hash value to arbitrary collections of objects ( with possible repetitions ) in such a way that the hash of the union of two collections is easy to compute from the hashes of the two collections themselves : it is simply their sum under a suitable group operation . in particular , hash values of large collections can be computed incrementally and/or in parallel . homomorphic hashing is thus a very useful primitive with applications ranging from database integrity verification to streaming set / multiset comparison and network coding . unfortunately , constructions of homomorphic hash functions in the literature are hampered by two main drawbacks : they tend to be much longer than usual hash functions at the same security level ( e.g. to achieve a collision resistance of , they are several thousand bits long , as opposed to bits for usual hash functions ) , and they are also quite slow . in this paper , we demonstrate a highly - efficient software implementation of ecmh , which our thorough empirical evaluation shows to be capable of processing over 3 million set elements per second on a intel haswell machine at the 128-bit security level many times faster than previous practical methods . while incremental hashing based on elliptic curves has been considered previously , the proposed method was less efficient , susceptible to timing attacks , and potentially patent - encumbered , and no practical implementation was demonstrated .

a homomorphic , or incremental , multiset hash function , associates a hash value to arbitrary collections of objects ( with possible repetitions ) in such a way that the hash of the union of two collections is easy to compute from the hashes of the two collections themselves : it is simply their sum under a suitable group operation . in particular , hash values of large collections can be computed incrementally and/or in parallel . homomorphic hashing is thus a very useful primitive with applications ranging from database integrity verification to streaming set / multiset comparison and network coding . unfortunately , constructions of homomorphic hash functions in the literature are hampered by two main drawbacks : they tend to be much longer than usual hash functions at the same security level ( e.g. to achieve a collision resistance of , they are several thousand bits long , as opposed to bits for usual hash functions ) , and they are also quite slow . in this paper , we introduce the elliptic curve multiset hash ( ecmh ) , which combines a usual bit string - valued hash function like blake2 with an efficient encoding into binary elliptic curves to overcome both difficulties . on the one hand , the size of ecmh digests is essentially optimal :-bit hash values provide collision resistance . on the other hand , we demonstrate a highly - efficient software implementation of ecmh , which our thorough empirical evaluation shows to be capable of processing over 3 million set elements per second on a intel haswell machine at the 128-bit security level many times faster than previous practical methods . while incremental hashing based on elliptic curves has been considered previously , the proposed method was less efficient , susceptible to timing attacks , and potentially patent - encumbered , and no practical implementation was demonstrated . * keywords : * homomorphic hashing , elliptic curves , efficient implementation , gls254 , pclmulqdq .

1703.10128

i

rapid experimental advances in the creation of finite systems of ultracold atoms using few optical traps ( bottom - up ) @xcite or through the use of extended optical lattices ( top - down ) @xcite are promising approaches toward realization of feynman s vision of a quantum simulator @xcite , capable of finding solutions to systems that are otherwise numerically and/or analytically intractable . however , apart from a few double - well investigations @xcite , to date model - independent microscopic studies of multiwell systems providing theoretical insights and guidance to experimental efforts are largely lacking . here we introduce a configuration - interaction ( ci ) schrdinger - equation methodology @xcite for exploring finite plaquette systems assembled from individual optical traps ; for a brief description of the ci method , see appendix [ cime ] . these systems are fundamental stepping stones toward bottom - up realization of large scale checkerboard or square ulracold atom lattices which are promising candidates for emulating the physics underlying @xmath3-wave high - t@xmath4 superconductivity @xcite in optical lattices @xcite . the work described here , demonstrating the feasibility of such exact ci calculations for interatomic contact interactions , can be extended to electronic plaquettes , i.e. , to quantum - dot - arrays , governed by long - range coulomb interactions . the plan of the paper is as follows : in section [ sp ] we explore first the properties of ultracold fermionic atoms ( @xmath0li ) confined in a single square plaquette ( 4-sites ) in the regime of hole pairing , and subsequently analyze the entanglement physics of two coupled plaquettes in the hole - pairing regime . in section [ dp ] , for the `` hole - doped '' coupled plaquettes ( 8-sites , six atoms ) , we analyze the wave function anatomy of the entangled @xcite ( schrdinger - cat ) two almost - degenerate manifolds , comprising : ( @xmath5 ) the ground state ( gs ) and 1st excited ( 1ex ) state , and ( @xmath6 ) the two higher excited states ( 2ex and 3ex ) . the almost - degenerate states have good , but opposite , parities . when symmetry - broken ( sb ) either by superposing @xmath7 the degenerate pair in each manifold , or via offsetting the energies ( tilting ) of the two plaquettes the sb states coming from @xmath5 are characterized by a particle ( `` charge'')-density modulation ( `` wave '' ) , i.e , a cdw portraying the hole - paired , ( 4,2 ) or ( 2,4 ) , components , whereas the sb states originating from @xmath6 remain in a ( 3,3 ) particle distribution ( each of the plaquettes having an unpaired hole ) , but exhibit a spin - polarizarion density modulation ( `` wave '' ) , i.e. , a sdw . for the the double - plaquette case , we further explore effects brought about by breaking the symmetry between two weakly - coupled plaquettes , either by distorting one of the plaquettes , or by tilting and detuning one of the plaquettes with respect to the other . spectral changes caused by increased tunnel coupling ( e.g. , by decreased inter - plaquette distance ) between the two plaquettes are also considered . noteworthy is our finding that the gs @xmath3-wave resonating valence bond ( rvb ) state contributes only partially to the exact many - body wave function i.e. , double occupancies ( referred also as doublons ) need be included . indeed , our microscopic results map properly onto a hubbard hamiltonian ( including extended hubbard models @xcite depending upon the range of the experimental parameters ) , but not onto the double - occupancy - excluding @xmath1-@xmath2 model @xcite . our conclusions agree with recent @xcite observations of doublons in two - dimensional ( 2d ) optical lattices . the rest of the paper comprises the summary ( sec . [ summ ] ) and three appendices , concerning a brief description of the ci method ( appendix [ cime ] ) , the mathematical definitions of single - particle densities and two - body and @xmath8-body conditional probability distributions ( appendix [ defs ] ) , and the specification of the correspondence between spin and rvb functions and ci many - body wave functions ( appendix [ spin ] ) .

a microscopic configuration - interaction ( ci ) methodology is introduced to enable bottom - up schrdinger - equation emulation of unconventional superconductivity in ultracold optical traps . we illustrate the method by exploring the properties ofli atoms in a single square plaquette in the hole - pairing regime , and by analyzing the entanglement ( symmetry - preserving ) and disentanglement physics ( via symmetry - breaking , associated with the separation of charge and spin density waves ) of two coupled plaquettes in the same regime . the single - occupancy rvb states contribute only partially to the exact many - body solutions , and the ci results map onto a hubbard hamiltonian , but not onto the double - occupancy - excluding- one . for the double - plaquette case , effects brought about by breaking the symmetry between two weakly - interacting plaquettes , either by distorting , or by tilting and detuning , one of the plaquettes with respect to the other , as well as spectral changes caused by increased coupling between the two plaquettes , are explored .

a microscopic configuration - interaction ( ci ) methodology is introduced to enable bottom - up schrdinger - equation emulation of unconventional superconductivity in ultracold optical traps . we illustrate the method by exploring the properties ofli atoms in a single square plaquette in the hole - pairing regime , and by analyzing the entanglement ( symmetry - preserving ) and disentanglement physics ( via symmetry - breaking , associated with the separation of charge and spin density waves ) of two coupled plaquettes in the same regime . the single - occupancy rvb states contribute only partially to the exact many - body solutions , and the ci results map onto a hubbard hamiltonian , but not onto the double - occupancy - excluding- one . for the double - plaquette case , effects brought about by breaking the symmetry between two weakly - interacting plaquettes , either by distorting , or by tilting and detuning , one of the plaquettes with respect to the other , as well as spectral changes caused by increased coupling between the two plaquettes , are explored .

astro-ph0508178

c

sources qr6 , qr8 , and qr9 show the major properties of stellar wind emission : ( 1 ) they have rising spectral indices in the range of + 0.5 to + 1.0 , ( 2 ) they are unresolved sources at the resolutions observed , which means their physical sizes are @xmath14 0.2 ( 0.009 pc ) at 22.5 ghz and @xmath140.5 ( 0.02 pc ) at 8.5 ghz , and ( 3 ) they are coincident positionally with young , massive stars . therefore , these three radio sources are interpreted to be stellar winds from quintuplet cluster stars . the flux densities of radio detections of stellar winds can be used to calculate mass loss rates ( @xmath23 ) . based on panagia & felli ( 1975 ) and wright & barlow ( 1975 ) , the mass loss rate can be estimated for an isotropic , homogeneous wind with constant velocity , electron density and chemical composition . however , 20 - 25% of early - type stars are known to have a nonthermal ( and variable ) component in their winds ( abbott et al . 1984 ; bieging et al . 1989 ) . the typical spectral index of such sources is in the range of @xmath18@xmath5@xmath70.6 to + 0.3 for frequencies between 5 and 43 ghz ( beiging et al . 1989 ; contreras et al . 1996 ) . contamination of the flux density by the nonthermal component can occur at the lower frequencies . therefore , higher frequency observations ( i.e. , 23 ghz compared to 5 ghz ) may be a better tracer of the thermal component and give more reliable mass - loss rates ( contreras et al . 1996 ) . the mass - loss rate can be estimated from our 22.5 ghz observations using : @xmath24 where s@xmath25 is the flux density of the source at 22.5 ghz , v@xmath26 is the terminal velocity of the wind ( assumed to be 1000 km s@xmath3 ; cotera et al . 1996 ; nagata et al . 1995 ) , and d is the distance to the source ( 8 kpc ) . we have assumed an electron temperature of 10@xmath27 k , z=1 , and a mean molecular weight , @xmath17=2 , due to the enrichment in heavy elements of the late - type wn stars ( leitherer et al . 1997 ) , a classification which figer et al . ( 1999 ) and figer et al . ( 2002 ) has assigned to most of the quintuplet and arches cluster stars . leitherer et al . ( 1997 ) suggest that there is very little variation in the mass - loss rates for wr stars , with an average value of @xmath54 @xmath0 10@xmath1 m@xmath2 yr@xmath3 . cappa et al . ( 2004 ) recently carried out a survey of galactic wr stars and came to similar conclusions concerning the measured radio mass - loss rates ; the average values from their study were 2 - 4 @xmath0 10@xmath1 m@xmath2 yr@xmath3 . values for the mass - loss rates of qr6 , qr8 and qr9 range from 3.2@xmath010@xmath1 m@xmath2 yr@xmath3 to 4.3@xmath010@xmath1 m@xmath2 yr@xmath3 ( see table 4 ) . these values agree well with those found for wr stars described above as well as for other young , massive stellar types . the nature of radio emission from sources qr4 , qr5 and qr7 is less clear than that from qr6 , qr8 and qr9 . although qr4 , qr5 and qr7 show rising spectra and are coincident with near - ir sources , their sizes are more extended ( @xmath131 at 8.5 ghz ) than expected for stellar wind sources . according to rodriguez et al . ( 1980 ) , the angular size of a stellar wind can be related directly to its flux density , independent of mass - loss rate and terminal wind velocity . for the 8.5 ghz flux densities of qr4 , qr5 and qr7 , the expected angular size of the corresponding stellar wind should be @xmath140.05 . the actual sizes of the sources ( 0.3 to 4 ) are clearly larger than the predicted value . however , as mentioned previously ( in @xmath152.2 ) , the quintuplet radio sources are located amidst a very complicated set of extended features , which includes the sickle and pistol h2 regions as well as the linear , nonthermal filaments of the radio arc . although filtering in the _ ( u , v ) _ plane can help by removing the extended structures , the quintuplet sources may still be contaminated by residual background emission , which can make determination of flux densities and sizes difficult . although the errors in size determination are substantial ( 0.3@xmath70.5 ; 20 - 50% ) , the sizes are still much more extended than the predicted values for stellar winds ( e.g. , @xmath140.05 ) . mass - loss rates are calculated for these sources as described above , and the values for qr4 , qr5 and qr7 ( average m of 1.2 @xmath0 10@xmath28 m@xmath2 yr@xmath3 ) are significantly larger than for the stellar wind sources qr6 , qr8 and qr9 ( average m of 3.7@xmath010@xmath1 m@xmath2 yr@xmath3 ) . while values for m of @xmath5 10@xmath28 m@xmath2 yr@xmath3 are not unexpected for some mass - losing stars , they typically correspond to epochs when the star may be experiencing an enhanced rate of mass - loss from its surface ( i.e. , the lbv phase ; white et al . 1994 ) . therefore , the simple interpretation of stellar wind emission may not apply for qr4 , qr5 and qr7 . however , the rising spectra and extended sizes of these sources are consistent with partially - thick free - free emission associated with an inhomogeneous , but spatially unresolved , h2 region . therefore , qr4 , qr5 and qr7 could be inhomogeneous h2 regions or even combinations of stellar wind emission and optically - thin , free - free emission from associated ionized material ( perhaps leftover from the formation of the stars ) . based on mezger & henderson ( 1967 ) , we can estimate the physical properties of these regions of ionized gas , assuming they have become optically - thin at the highest frequency at which they are detected , using the deconvolved sizes of these sources , and using an electron temperature of 10@xmath27 k. table 4 lists the electron density , n@xmath29 , mass of ionized hydrogen , m@xmath30 , emission measure , em , and the production rate of ionizing photons , n@xmath9 for these sources . the values of these h2 properties for qr4 , qr5 and qr7 ( in addition to their linear sizes of 0.03 - 0.05 pc ) are consistent with those for compact and ultra - compact h2 regions ( wood & churchwell 1990 ) . the properties of qr1 - 3 differ from the other radio sources in the quintuplet . as described in @xmath153.1.1 , qr1 - 3 are more spatially extended than qr6 , qr8 and qr9 by at least a factor of 2 . more significantly , qr1 - 3 are the only radio sources in the two clusters without closely associated near - ir counterparts . these sources also define the northern edge of the quintuplet cluster ( 5 - 10 north of qr4 - 7 and the main concentration of stellar members ) . table 4 shows that the spectral indices are close to flat with large errors ( i.e. @xmath18=@xmath70.3@xmath190.2 for @xmath21 for qr1 ) . such spectra can be attributed to optically thin , free - free emission associated with h2 regions . since there are no stellar counterparts to qr1 - 3 , a likely explanation for these sources is that they may represent embedded massive stellar sources ( churchwell 1990 ) . the linear sizes of qr1 - 3 of @xmath50.1 pc are consistent with the upper end of the size distribution of ultra - compact h2 regions in the sample of kurtz , churchwell , & wood ( 1994 ) . as only @xmath31% of ultra - compact h2 regions are detectable at near - ir wavelengths ( hanson , luhman , & rieke 2002 ) , the lack of near - ir emission associated with qr1 - 3 is also consistent with their being ultra - compact h2 regions . as described above , the h2 properties for qr1 - 3 are derived from the radio continuum and listed in table 4 . the production rate of ionizing photons , n@xmath9 , can provide an estimate of the embedded stellar type that is responsible for the associated radio emission ( assuming a single ionizing star ) . values for n@xmath9 range from @xmath32 s@xmath3 . these ionizing fluxes are consistent with embedded b - type massive stars ( @xmath5 b1v - b2v ; @xcite ) . however , a number of galactic ultra - compact h2 regions are observed to be associated with diffuse extended emission @xcite . these studies conclude that typically @xmath33% of the ionizing flux from the embedded stars in uc h2s escapes to the outer envelope . thus , the inferred stellar content from the @xmath34 values determined for sources qr1 - 3 may be an underestimate , in which case they could have spectral types earlier than b. therefore , we tentatively identify qr1 - 3 as ultracompact or compact h2 regions . the proximity of the quintuplet cluster radio sources ( and in particular , sources qr1 - 3 ) to the edge of a molecular cloud identified by serabyn & gsten ( 1991 ) may indicate that these sources are physically associated with this molecular cloud . in the cs ( j=3 - 2 ) image of serabyn & gsten , a finger of emission extends toward the projected location of qr1 - 3 , indicating the presence of moderately dense gas . the apparent physical association between qr1 - 3 and the edge of the molecular cloud suggests that these young stellar objects have recently emerged from the molecular cloud , probably as a result of erosion due to the more evolved massive stars in the quintuplet cluster . indeed , the quintuplet cluster is thought to be the source of ionization for the larger sickle h2 region ( lang , goss & wood 1997 ; figer et al . 1999a ) , which traces the inner edge of the molecular cloud . alternatively , the radio sources which are not interpreted to be stellar winds ( qr1 - 3 , qr4 , qr5 , and qr7 ) may represent clumps of molecular material leftover from the formation of the stars in the cluster that are externally ionized by the quintuplet cluster members . assuming these clumps are located at approximately the projected distances from the center of the cluster , the quintuplet could easily account for their ionization as it is responsible for the ionization of the much larger sickle h2 region ( located 1 or 2.5 pc to the ne ) and the north side of the pistol nebula ( lang et al . 1997 ; figer et al . if any of the quintuplet radio sources are confirmed to be compact or uc h2s , this detection will lead to the study of the earliest stages of stellar evolution in one of the most extreme environments in the milky way . in particular , these objects are located in a region of strong magnetic fields , high turbulent velocities , and extremely high metallicities ( morris & serabyn 1996 ) . figure 5 shows that the radio emission associated with the pistol star has a bipolar morphology centered around the position of the star and has a flat spectral index ( @xmath21 = + 0.1@xmath190.4 ) . one explanation for this source is that it represents the current mass - loss of the star . ( the outer `` pistol - shaped '' nebula is thought to contain the mass associated with an episode of previous mass - loss ( @xmath5 11 m@xmath2 , @xmath55000 years ago ; figer et al . 1998 ) ) . in this case , the integrated flux density would imply a mass - loss rate of 2.7@xmath010@xmath28 m@xmath2 yr@xmath3 . this value is much higher than the average value for wr stellar types ( see @xmath154.1.1 ) , but similarly high mass - loss rates have been detected in other lbv stars during epochs of extreme mass - loss ( e.g. , @xmath4 car ; white et al . 1994 ) and in several wr colliding - wind binary systems ( contreras et al . 1996 ) . however , as for sources qr4 , qr5 , and qr7 , the extended size of the pistol star radio emission is much larger than the expected angular size for a stellar wind source ( @xmath50.1 ) using the methods of rodrguez et al . another problem with the interpretation of the pistol as a stellar wind source is that its double - lobed radio emission is not well modelled by a spherically - symmetric stellar wind surrouding the star . it is possible to calculate a mass - loss rate for the source using the total mass and assuming an expansion velocity for the radio emission . assuming that the radio emission is optically - thin , free - free emission , with t@xmath29@xmath510@xmath27 k , and taking the deconvolved angular sizes of the lobes to be 1@xmath35 , we can estimate the total mass in the lobes to be @xmath5 0.02 @xmath36 . the separation between the pistol star and each of the lobes is @xmath37 cm . assuming that the lobes are expanding at a velocity of 1000 km s@xmath3 , we estimate a mass - loss rate of @xmath38 @xmath36 yr@xmath3 . this value is roughly consistent with the value obtained by using equation ( 1 ) . in addition , it is possible to calculate the ionizing flux required to maintain the bipolar radio source . at a distance of 8 kpc and with the integrated flux density measured , n@xmath9 has a value of @xmath39 s@xmath3 , which can be provided by an early b - type star . however , the two lobes that constitute the radio source are intersecting only a fraction of the 4@xmath40 radians around the star . furthermore , the ionized nebula may be density - bounded , with most of the ionizing flux of the pistol star escaping to the interstellar medium , so the star is likely to be of an earlier spectral type . the physical properties of the radio emission associated with the pistol star are similar to the nebula surrounding the well - known lbv binary system @xmath4 carina ( davidson & humphreys 1997 ) . the bipolar - shaped radio emission around @xmath4 carina has a flat spectral index and a linear size of 0.12 pc ( 10 at 2.5 kpc ; white et al . 1994 ) , similar to the pistol star nebula . in fact , a variety of types of nebular features are detected around other lbv stars and are thought to be the result of stellar wind emission interacting with the surrounding interstellar medium ( nota et al . 1995 ) . in the cases of galactic sources hg car , ag car , wra-751 and he3 - 519 , both extended nebular shells and compact stellar wind emission are detected in the radio continuum ( duncan & white 2002 ) . these authors also calculate substantial mass - loss rates from the central lbv stars ( @xmath135 - 10 @xmath0 10@xmath1 m@xmath2 yr@xmath3 ) . the bipolar morphology of such radio nebulae suggests that the mass - loss is not isotropic ( e.g. , @xmath4 car ) . this type of non - spherical wind emission has been explained by several different mechanisms : ( 1 ) _ internal _ processes , such as the stellar rotation of such massive stars and the resulting mass - loss geometry ( owocki & gayley 1997 ; maeder & maynet 2000 ; smith et al . 2004 ) , and ( 2 ) _ external _ processes , such as the influence of a binary companion on the mass - loss geometry ( iben & livio 1993 ) or expansion of the nebula into a region of high density - contrast interstellar medium ( nota et al . 1995 ) . a comparison of the 8.5 ghz observation of the arches cluster presented here and the observation of lang et al . ( 2001b ) shows that the majority of the sources do not exhibit any strong variability in their flux density . however , moderate variability ( at the level of 12 - 30% ) is detected in several of the arches radio sources previously detected ( ar1 , ar3 , ar4 , ar8 ) and possibly explains the new detection of ar9 . the flux densities of two of the four sources decreased , while the flux density of the other two sources increased . therefore , we can rule out a systematic calibration problem . this moderate variability may indicate ( i ) the presence of a time - variable nonthermal component ( due to shocks in the wind , or colliding winds for a binary system ) and/or ( ii ) variability in the mass - loss rate or wind velocity ( contreras et al . 1996 ; leitherer et al . 1997 ) . nine of the ten arches sources are unresolved in both the 8.5 and 22.5 ghz observations . the major axis of ar1 is resolved at both 8.5 and 22.5 ghz and its deconvolved size is @xmath50.1 . this size is consistent with the expected angular size of 0.06 for an ionized stellar wind source of 1.9 mjy flux density at 8.5 ghz ( rodrguez et al . therefore , all radio sources in the arches cluster exhibit the properties of stellar wind sources ( see @xmath154.1.1 ) . mass - loss rates are also calculated for the arches sources and are listed in table 5 . ar1 has the largest value of m = 2.2 @xmath0 10@xmath28 m@xmath2 yr@xmath3 . such a high value of m is usually attributed to a particular mass - loss epoch during the evolution of a massive star or a colliding wind binary system ( white et al . 1994 ; contreras et al . 1996 ) . the remainder of the arches sources have an average value of @xmath53 @xmath0 10@xmath1 m@xmath2 yr@xmath3 , typical for the types of stars present in the arches and quintuplet clusters ( @xmath154.1.1 ; leitherer et al . 1997 ; cappa et al . 2004 ) . as reported recently by law & yusef - zadeh ( 2004 ) and previously by yusef - zadeh et al . ( 2002 ) , a number of the radio sources in the arches and quintuplet clusters have x - ray counterparts detected with the _ chandra x - ray observatory_. the x - ray emission associated with the arches cluster itself is one of the most luminous x - ray sources in the galactic center region with an x - ray luminosity in the 2 - 10 kev range of @xmath510@xmath41 ergs s@xmath3 ( wang , gotthelf & lang 2002 ) . three x - ray point like sources are detected in the arches cluster : a1s , a1n and a2 ( law & yusef - zadeh 2004 ) . the x - ray sources a1s and a1n can be associated with the radio sources ar4 and ar1 as well as near - ir sources from figer et al . the x - ray emission in these sources is thought to arise from shocks formed in the winds of massive stars ( o- and wr - types ) as are found in the arches and quintuplet clusters ( law & yusef - zadeh 2004 ) . the characteristics of several arches radio sources that have x - ray counterparts suggest that these sources are likely to have shocks in their winds and/or be colliding wind binaries . radio emission from the colliding winds of binary massive stars is well known to have a nonthermal component that flattens the spectral index ( dougherty & williams 2000 ) as well as showing time - variable emission ( abbott et al . 1984 ) . in the case of the radio source ar1 , the spectral index ( @xmath18=+0.3@xmath190.04 ; lang et al . 2001b ) is flatter than the canonical @xmath18=+0.6 value for stellar wind emission and the flux density of the source varies by 12% between epochs . ar4 has a steeper spectral index ( although the errors are larger ) , @xmath18=+0.6@xmath190.2 , but its flux density varied by 30% in the two observed epochs . in the quintuplet cluster , law & yusef - zadeh ( 2004 ) report that two of the radio sources ( qr6 and qr7 ) have probable x - ray counterparts . it is not possible to determine whether the spectral index of qr6 is flattened ( @xmath18=+0.4@xmath190.4 ) or consistent with the value of @xmath18=+0.6 . however , this source was not detected in the results of lang et al . ( 1999 ) , either because of its time - variable nature or because the resolution was too coarse . the possible detection ( 2.6@xmath22 as reported by law & yusef - zadeh 2004 ) of x - ray emission associated with quintuplet source qr7 is interesting as not much is known about the nature of the near - ir counterpart ( @xmath153.1.2 ; figer et al . 1999 ) . the arches and quintuplet clusters are two of the most massive and luminous clusters in our galaxy ( figer et al . 1999a ) . in particular , the stellar density of the arches cluster ( @xmath42 @xmath5 3 @xmath010@xmath43 m@xmath2 pc@xmath44 ) is comparable only to that found in the centers of clusters such as hd in ngc3603 ( moffat et al . 1994 ) and r136 in the large magellanic cloud , associated with the 30 doradus nebula ( massey & hunter 1998 ) . therefore , these clusters should have a profound effect on the surrounding ism . indeed , these clusters are thought to be responsible for the ionization of the adjacent h2 regions , the sickle and the arched filaments ( lang et al . 1997 ; lang et al . 2001a ) . the presence of x - ray emission associated with individual stellar wind sources ( see above ) also indicates that the winds of these massive stars are powerful . in addition to the point - like x - ray sources , both clusters also show diffuse x - ray emission ( yusef - zadeh et al . 2002 ; law & yusef - zadeh 2004 ) . in the arches cluster , the diffuse x - ray emission is apparent for @xmath51 pc surrounding the cluster , and in the quintuplet , the diffuse x - ray emission has a slightly larger extent ( @xmath51.2 pc ) but is not detected with high signal to noise ( law & yusef - zadeh 2004 ) . several authors have suggested that the diffuse emission is related to a `` cluster wind '' triggered by the collective effect of a large number of massive star winds in the cluster core ( cant et al . 2000 ; raga et al . 2001 ; yusef - zadeh et al . such processes can lead to shock acceleration of the wind particles and heating of the gas to high temperatures ( 10@xmath8 to 10@xmath45 k ) . nonthermal radio emission has been detected within a 9 radius ( 0.3 pc ) of the cluster core and is believed to provide additional evidence that particle acceleration occurs here ( yusef - zadeh et al . 2003 ) . the physical parameters of the `` cluster wind '' and the resulting region of x - ray emitting gas depend primarily on the individual mass - loss rates of the stellar wind sources ( stevens & hartwell 2003 ; cant et al . 2000 ; raga et al . the total stellar wind mass injection rate is dependent on the sum of mass - loss rates of individual stars multiplied by the square of the terminal wind velocity . using an estimate for the velocity , predicted by the models in stevens & hartwell ( 2003 ) , or by using the average value of @xmath51000 km s@xmath3 , measured by cotera et al . ( 1996 ) , it is possible to derive the total stellar wind kinetic energy injection rate . the observations presented here provide the most reliable mass - loss rate estimates for the stellar wind sources in the arches and quintuplet clusters . based on the mass - loss rates presented here , the total stellar wind mass injection rate for the arches cluster is @xmath54 @xmath0 10@xmath28 m@xmath2 yr@xmath3 , and for the quintuplet ( including the pistol star as well as sources qr4 , qr5 , and qr7 ) is @xmath57 @xmath0 10@xmath28 m@xmath2 yr@xmath3 . these values for total m are in close agreement with those used by stevens & hartwell ( 2003 ) and raga et al . ( 2001 ) in their calculation of the total stellar wind kinetic energy injection rate . two types of numerical calculations have also been made recently to characterize the x - ray `` cluster wind '' that arises from the arches ( and presumably , the quintuplet ) clusters . cant et al . ( 2000 ) and raga et al . ( 2001 ) present a solution for an adiabatic flow and predict an envelope of x - ray emission of t@xmath55 @xmath010@xmath8 k , extending well beyond ( 10 s of pc ) the cluster core ( 0.2 pc ) . in contrast , silich et al . ( 2004 ) employ radiative cooling in their work , and predict , for the arches cluster , a quasi - adiabatic solution that suggests a much smaller boundary around the cluster of x - ray emission . depending on the values chosen for m and the terminal velocity , silich et al . ( 2004 ) estimate 3 - 7 pc for the extent of the x - ray emitting region . these authors argue that this smaller size for the x - ray emitting region is in part due to the slowing of wind emission by interactions of the wind with cooler surrounding ism material . the arches cluster , in particular , is located in the midst of a dense molecular and ionized environment ( lang et al . 2002 ) and there is a large reservoir of cooler material which may decelerate the wind . morphologically , the arched filaments h2 regions and molecular cloud extend for as much as 20 pc in projection around the cluster . x - ray observations near the arched filaments show that the diffuse emission appears to be confined to the area near the easternmost of the arched filaments ( @xmath14 10 pc ) , as predicted by silich et al . however , the short - integration nature of these observations ( @xmath14 50 ks ) with _ chandra _ and the subsequent low sensitivity to diffuse objects have so far prevented detailed spectral fitting and spatial imaging of the diffuse x - ray emission associated with these clusters ( yusef - zadeh et al . 2002 ; wang , gotthelf & lang 2002 ) . several examples of radio clusters associated with regions of recent star formation have been reported in the literature over the last ten years ( e.g. , garay et al . 1987 ; churchwell et al . 1987 ; becker & white 1988 ; stine & oneal 1998 ; rodrguez et al . 1999 ; gmez et al . 2000 ; lang et al . the compact radio sources in the stellar clusters have a variety of origins : ionized stellar winds , ultracompact h2 regions , externally ionized proplyds , and magnetically active stars with gyrosynchrotron emission are the dominant types of sources . in table 6 we summarize the parameters of the radio sources in these clusters . although more of these clusters should be studied to have a reliable statistical base , some interesting trends are evident . the diameters of the radio clusters are in the 0.2 to 1.0 pc range ( with the exception of the quintuplet cluster with the pistol star included , that reaches up to 2 pc ) . the radio luminosity of the most luminous member is correlated with the bolometric luminosity of the cluster . clearly , the arches and quintuplet cluster have their most luminous radio member with luminosities one to three orders of magnitude larger than typical young clusters in the galactic disk . these clusters of radio sources could be a valuable observational tool to study the stellar population of heavily obscured regions of star formation when combined with high resolution spectroscopic observations .

a multi - frequency , multi - configuration study has been made of the compact radio sources in the galactic center quintuplet and arches stellar clusters using the very large array . we conclude that the three most compact of these sources are produced by stellar wind emission ; thus , mass - loss rates can be derived and have an average value of 3 m yr . the remainder of the sources are likely to be a combination of stellar wind emission and free - free emission from surrounding ionized gas . in three cases , the radio sources have no stellar counterpart and the radio emission is thought to arise from compact or ultra - compact h2 regions . the radio nebula associated with the pistol star resembles the nebula surrounding the lbv star carina and may be related to the stellar wind of the pistol star . several of the sources show moderate variability ( 10 - 30% ) in their flux density , possibly related to a nonthermal component in the wind emission . a number of radio sources in both clusters have x - ray counterparts , which have been interpreted to be the shocked , colliding winds of massive binary systems .

a multi - frequency , multi - configuration study has been made of the compact radio sources in the galactic center quintuplet and arches stellar clusters using the very large array . ten radio sources have been detected in the quintuplet cluster . the majority of these radio sources have rising spectral indices and are positionally coincident with young massive stars that are known to have powerful stellar winds . we conclude that the three most compact of these sources are produced by stellar wind emission ; thus , mass - loss rates can be derived and have an average value of 3 m yr . the remainder of the sources are likely to be a combination of stellar wind emission and free - free emission from surrounding ionized gas . in three cases , the radio sources have no stellar counterpart and the radio emission is thought to arise from compact or ultra - compact h2 regions . if so , these sources would be the first detections of embedded massive stars to be discovered in the galactic center clusters . the radio nebula associated with the pistol star resembles the nebula surrounding the lbv star carina and may be related to the stellar wind of the pistol star . ten compact radio sources are detected in the arches cluster and are interpreted to be stellar wind sources , consistent with previous findings . several of the sources show moderate variability ( 10 - 30% ) in their flux density , possibly related to a nonthermal component in the wind emission . a number of radio sources in both clusters have x - ray counterparts , which have been interpreted to be the shocked , colliding winds of massive binary systems .

astro-ph0508178

c

we have made multi - frequency radio observations of both the quintuplet and arches clusters using the vla . our conclusions can be summarized as follows : \(1 ) ten radio sources have been detected in the quintuplet cluster . the majority of these sources have rising spectral indices and are positionally coincident with near - ir sources which have been classified as young , massive stars . sources qr6 , qr8 and qr9 are unresolved and thought to be very compact in size ( @xmath140.01 pc ) ; therefore , these three sources are interpreted to be stellar winds . sources qr4 , qr5 and qr7 are more extended ( 0.3@xmath71.5 ; 0.015 to 0.06 pc ) and likely represent a combination of stellar wind and free - free emission associated with h2 regions . sources qr1 - 3 do not have near - ir counterparts and these are interepreted to be the first detections of embedded massive stars in the quintuplet cluster . \(2 ) an observation of the pistol star shows that its structure is extended and distinctly bipolar , centered on the pistol star near - ir source . the radio emission from this nebula has a flat spectral index . assuming that this emission is optically thin , free - free emission , we can roughly calculate a mass - loss rate of 5 @xmath0 10@xmath28 m@xmath2 yr@xmath3 . the pistol star radio source resembles the nebula that surrounds the luminous blue variable star @xmath4 carina . \(3 ) ten compact radio sources have also been detected in the arches cluster . nine of the sources have spectral indices consistent with a rising spectrum and only one of the sources may be resolved . as found in lang et al . ( 2001b ) , these sources are interpreted to be stellar winds from the young massive stars in the cluster . the average mass - loss rate for these stellar winds is 3 @xmath0 10@xmath1 m@xmath2 yr@xmath3 . \(4 ) both point - like and diffuse x - ray emission has been identified with the arches and quintuplet clusters and thought to be related to the presence of colliding wind binaries in these clusters . the mass - loss estimates from our radio observations here provide the best estimates of one of the parameters used to model the x - ray `` cluster winds '' which are observed to be associated with a number of massive stellar clusters . c.c.l . acknowledges that this material is based on work supported by the national science foundation ( nsf ) under grant no . 0307052 . k.e.j gratefully acknowledges support for this work provided by the nsf through an astronomy & astrophysics postdoctoral fellowship , and nasa through hubble fellowship grant # hf-01173.02-a awarded by the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , for nasa , under contract nas 5 - 26555 . lcccccc quintuplet&17 46 15.00 & @xmath728 49 35.0&4.9 & bna&june 2002 & 4 + quintuplet&17 46 15.00 & @xmath728 49 35.0&8.5 & bna&june 2002 & 4 + quintuplet&17 46 15.00 & @xmath728 49 35.0&22.5 & bna&sept 2003&2 + quintuplet&17 46 15.00 & @xmath728 49 35.0&22.5 & b&jan . 2004&3 + quintuplet&17 46 15.00&@xmath728 49 35.0&22.5 & dnc , d&june 2004&3.5 + qr1 - 3 sources&17 46 14.60&@xmath728 49 20.0&43.4 & dnc&june 2004&2.5 + qr1 - 3 sources&17 46 14.60&@xmath728 49 20.0&43.4 & d & july 2004&3 + pistol & 17 46 15.24 & @xmath728 50 04.0 & 8.5 & b , bna & nov . 1999 & 4 + arches&17 45 50.41 & @xmath728 49 21.8 & 8.5 & a&jan . 2002&4 + arches&17 45 50.41 & @xmath728 49 21.8 & 22.5 & bna&sept . 2003 & 2.5 + lclccc quintuplet & 4.9 & 1.15 @xmath0 0.85 , pa=62.8&75&10&20.6 + quintuplet & 8.5 & 0.64 @xmath0 0.50 , pa=62.0&55&10&20.6 + quintuplet&22.5 & 0.39 @xmath0 0.22 , pa=52.7&65&15&13.8 + quintuplet & 22.5 & 1.45 @xmath0 0.87 , pa=06.8&75&@xmath7&@xmath7 + quintuplet ( qr1 - 3 ) & 43.4 & 2.54 @xmath0 1.35 , pa=03.3&100&@xmath7&@xmath7 + pistol & 8.5 & 1.17 @xmath0 0.59 , pa=15.2&75&25&8.2 + arches&8.5 & 0.42 @xmath0 0.20 , pa=01.6&25&20&10.3 + arches&22.5 & 0.33 @xmath0 0.20 , pa=47.8&85&10&20.6 + lcccccccc qr1 & 17 46 15.16 & @xmath728 49 22.5 & 2.2@xmath190.4 & 1.9@xmath190.2&1.4@xmath190.3&1.0@xmath190.5&2.5@xmath01.5 & 0.10@xmath00.06 + qr2 & 17 46 14.95 & @xmath728 49 20.2 & 3.6@xmath190.7 & 3.4@xmath190.3 & 2.4@xmath190.4 & 1.4@xmath190.6&4.0@xmath02.5 & 0.17@xmath00.10 + qr3 & 17 46 14.42 & @xmath728 49 19.4 & 1.7@xmath190.4 & 1.5@xmath190.2 & 1.1@xmath190.3 & 0.3@xmath190.2&2.5@xmath02.5 & 0.10@xmath00.10 + qr4 & 17 46 15.06 & @xmath728 49 29.4 & 0.60@xmath190.30 & 1.30@xmath190.30 & ... & ... & 1.4@xmath00.9&0.04@xmath00.03 + qr5 & 17 46 15.11 & @xmath728 49 37.2 & 0.35@xmath190.10 & 0.54@xmath190.10 & 1.50@xmath190.20 & ... & 0.3@xmath00.3 & 0.01@xmath00.01 + qr5ext ... & ... & ... & ... & ... & 2.60@xmath191.00 & 2.80@xmath191.6 & 1.6@xmath01.2 & 0.06@xmath00.05 + qr6 & 17 46 15.14 & @xmath728 49 32.7 & 0.25@xmath190.10 & 0.33@xmath190.10 & 0.48@xmath190.08 & ... & ps & ... + qr7 & 17 46 14.71 & @xmath728 49 40.8 & @xmath140.24 & 0.80@xmath190.20 & ... & ... & 1.3@xmath00.7&0.05@xmath00.03 + qr8 & 17 46 14.04 & @xmath728 49 16.7 & @xmath140.24 & 0.28@xmath190.10 & 0.57@xmath190.08 & ... & ps & ... + qr9 & 17 46 17.98 & @xmath728 49 03.4 & @xmath140.24 & 0.27@xmath190.06 & ... & ... & ps & ... + pistol & 17 46 15.32 & @xmath728 50 04.2 & 3.2@xmath191.0 & 3.4@xmath191.0&3.5@xmath191.0 & 3.4@xmath191.0 & 4.0@xmath02.5 & 0.17@xmath00.10 + lccccccccccc qr1 & @xmath70.3@xmath190.4&@xmath70.3@xmath190.2 & @xmath70.3@xmath190.3&@xmath70.5@xmath190.8 & @xmath7 & 1.5@xmath010@xmath46 & 0.023&2.4@xmath010@xmath43&1.2@xmath010@xmath47 & @xmath7 + qr2 & @xmath70.1@xmath190.4 & @xmath70.4@xmath190.2&@xmath70.3@xmath190.3&@xmath70.8@xmath190.7 & @xmath7 & 0.9@xmath010@xmath46 & 0.065&1.6@xmath010@xmath43 & 2.1@xmath010@xmath47 & @xmath7 + qr3 & @xmath70.2@xmath190.5 & @xmath70.3@xmath190.3&@xmath70.3@xmath190.4&@xmath72.0@xmath191.0 & @xmath7 & 0.9@xmath010@xmath46 & 0.030&1.1@xmath010@xmath43&1.0@xmath010@xmath47 & @xmath7 + qr4 & + 1.4@xmath191.0 & @xmath7 & @xmath7 & @xmath7 & 1.5@xmath010@xmath28 & 2.7@xmath010@xmath46 & 0.008&4.8@xmath010@xmath43&7.9@xmath010@xmath48 & f270s + qr5 & + 0.8@xmath190.6 & + 1.0@xmath190.2 & + 0.9@xmath190.3 & 0.1@xmath190.1 & 1.1@xmath010@xmath28 & 3.0@xmath010@xmath46 & 0.017&7.1@xmath010@xmath43&1.8@xmath010@xmath47 & f241 + qr6 & + 0.5@xmath190.8&+0.4@xmath190.4&+0.4@xmath190.4&@xmath7 & 3.7@xmath010@xmath1 & @xmath7&@xmath7&@xmath7&@xmath7 & f257 + qr7 & + 2.0@xmath190.8&@xmath7&@xmath7&@xmath7 & 9.5@xmath010@xmath1 & 2.7@xmath010@xmath46 & 0.005&4.1@xmath010@xmath43&4.8@xmath010@xmath48 & f231 + qr8 & @xmath13 + 0.3&+0.7@xmath190.4&@xmath13 + 0.6&@xmath7 & 4.3@xmath010@xmath1 & @xmath7&@xmath7&@xmath7&@xmath7 & f320 + qr9 & @xmath13 + 0.2 & @xmath7&@xmath7&@xmath7 & 3.2@xmath010@xmath1 & @xmath7&@xmath7&@xmath7&@xmath7 & f362 + pistol & + 0.1@xmath190.8&+0.0@xmath190.4&+0.1@xmath190.4&+0.0@xmath190.6 & 2.7@xmath010@xmath28 & @xmath7 & @xmath7 & @xmath7 & @xmath7 & f134 + lcccccccc ar1 & 17 45 50.42&@xmath728 49 22.3 & 1.90@xmath190.05&1.49@xmath190.27&@xmath7&2.2@xmath010@xmath28&f6 , n8 , c8 & 0.14 @xmath00.10 + ar2 & 17 45 50.39&@xmath728 49 21.3 & 0.25@xmath190.03&0.60@xmath190.09&+0.9@xmath190.2 & 4.6@xmath010@xmath1 & f8 , n7 , c6&ps + ar3 & 17 45 50.20&@xmath728 49 22.3 & 0.12@xmath190.03&@xmath140.25&@xmath130.8&1.9@xmath010@xmath1&f1 , n4 , c9&ps + ar4 & 17 45 50.47&@xmath728 49 19.5 & 0.34@xmath190.03&0.61@xmath190.09&+0.6@xmath190.2&4.8@xmath010@xmath1&f37 , n10 , c5&ps + ar5 & 17 45 50.57&@xmath728 49 17.5 & 0.16@xmath190.03&@xmath140.25&@xmath130.5&1.9@xmath010@xmath1 & f4 , n11,c2&ps + ar6 & 17 45 49.76&@xmath728 49 26.0 & 0.25@xmath190.03&@xmath140.25&@xmath130.0&3.0@xmath010@xmath1&f19&ps + ar7 & 17 45 50.83&@xmath728 49 26.4 & 0.23@xmath190.03&0.57@xmath190.09&+0.9@xmath190.2&4.3@xmath010@xmath1&f3 , n14 , c11&ps + ar8 & 17 45 50.45&@xmath728 49 31.9 & 0.16@xmath190.03&0.48@xmath190.09&+1.1@xmath190.3&3.7@xmath010@xmath1&f5 , n9&ps + ar9 & 17 45 50.47&@xmath728 49 17.9 & 0.15@xmath190.04&@xmath140.25&@xmath130.5&1.9@xmath010@xmath1&f18&ps + ar10 & 17 45 49.69&@xmath728 49 25.9 & 0.06@xmath190.03&@xmath140.25&@xmath131.5&1.9@xmath010@xmath1&f2 , n1 , c13&ps + lccccc orion & @xmath52@xmath010@xmath43 & 77 & 8.8 & 0.3 & zapata et al . ( 2004 ) + ngc 1579 & @xmath52@xmath010@xmath46 & 16 & 0.6 & 0.3 & stine & oneal ( 1998 ) + ggd 14 & @xmath510@xmath27 & 6 & 0.2 & 0.2 & gmez et al . ( 2002 ) + ngc 1333 & @xmath5120 & 44 & 0.3 & 0.7 & rodrguez et al . ( 1999 ) + ngc 2024 & @xmath55@xmath010@xmath27 & 25 & 3.0 & 0.5 & rodrguez et al . ( 2003 ) + w40 & @xmath55@xmath010@xmath27 & 14 & 2.8 & 0.2 & rodrguez & reipurth ( 2005 ) + quintuplet & @xmath5 10@xmath45 & 10 & 218 & 2.0 & this paper + arches & @xmath510@xmath45 & 10 & 122 & 0.7 & this paper + ngc3603 & @xmath55@xmath0 10@xmath8 & 2 & 147 & 0.7 & moffat et al . ( 2002 ) + ngc3603 & @xmath5 5@xmath0 10@xmath8 & 4 & 687 & 5.0 & mcke et al . ( 2002 ) + 0.22 , pa=52.7 . the rms noise level in this image is 65 @xmath17jy beam@xmath3 and the contours correspond to -3 , 3 , 5 , 7 , 9 and 12 times this level . this image has not been corrected for primary beam attenuation . [ fig3 ] ] ra=0.9 was introduced to align the radio and _ hst _ near - ir images ) . the 8.5 ghz image ( top ) is an inset from figure 2 , with a resolution of 0.64@xmath00.50 , pa=62 ; the 22.5 ghz image ( middle ) is the `` low '' resolution image and has a resolution of 1.45@xmath00.87 , pa=6.8 ; the 43.4 ghz ( bottom ) image has a resolution of 2.54@xmath01.35 , pa=3.3 . contours in each case correspond to -3 , 3 , 5 , 7 , 9 , and 12 times the rms levels of 55 @xmath17jy beam@xmath3 ( 8.5 ghz ) , 75 @xmath17jy beam@xmath3 ( 22.5 ghz ) and 100 @xmath17jy beam@xmath3 ( 43.4 ghz ) . none of these images have been corrected for primary beam attenuation .

ten radio sources have been detected in the quintuplet cluster . the majority of these radio sources have rising spectral indices and are positionally coincident with young massive stars that are known to have powerful stellar winds . if so , these sources would be the first detections of embedded massive stars to be discovered in the galactic center clusters . ten compact radio sources are detected in the arches cluster and are interpreted to be stellar wind sources , consistent with previous findings .

a multi - frequency , multi - configuration study has been made of the compact radio sources in the galactic center quintuplet and arches stellar clusters using the very large array . ten radio sources have been detected in the quintuplet cluster . the majority of these radio sources have rising spectral indices and are positionally coincident with young massive stars that are known to have powerful stellar winds . we conclude that the three most compact of these sources are produced by stellar wind emission ; thus , mass - loss rates can be derived and have an average value of 3 m yr . the remainder of the sources are likely to be a combination of stellar wind emission and free - free emission from surrounding ionized gas . in three cases , the radio sources have no stellar counterpart and the radio emission is thought to arise from compact or ultra - compact h2 regions . if so , these sources would be the first detections of embedded massive stars to be discovered in the galactic center clusters . the radio nebula associated with the pistol star resembles the nebula surrounding the lbv star carina and may be related to the stellar wind of the pistol star . ten compact radio sources are detected in the arches cluster and are interpreted to be stellar wind sources , consistent with previous findings . several of the sources show moderate variability ( 10 - 30% ) in their flux density , possibly related to a nonthermal component in the wind emission . a number of radio sources in both clusters have x - ray counterparts , which have been interpreted to be the shocked , colliding winds of massive binary systems .

0905.2026

i

the @xmath11 reaction is one of the critical links in the @xmath12 and @xmath13 branches of the @xmath14chain of solar hydrogen burning [ 13 ] . the total capture rate determined by processes of this chain is sensitive to the cross section @xmath15 ( or the astrophysical @xmath0 factor @xmath6 ) for the @xmath16 reaction and predicted neutrino rate varies as @xmath17^{0.8}$ ] @xcite . despite the impressive improvements in our understanding of the @xmath11 reaction made in the past decades ( see refs [ 411 ] and references therein ) , however , some ambiguities connected with both the extrapolation of the measured cross sections for the aforesaid reaction to the solar energy region and the theoretical predictions for @xmath15 ( or @xmath6 ) still exist and they may influence the predictions of the standard solar model @xcite . experimentally , there are two types of data for the @xmath16 reaction at extremely low energies : i ) six measurements based on detecting of @xmath18-rays capture ( see @xcite and references therein ) from which the astrophysical @xmath0 factor @xmath19 extracted by the authors of those works changes within the range 0.47@xmath200.58 @xmath21 and ii ) six measurements based on detecting of @xmath12 ( see @xcite references therein as well as [ 6 - 11 ] ) from which @xmath19 extracted by the authors of these works changes within the range 0.53@xmath220.63 @xmath23 . all of these measured data have a similar energy dependence for the astrophysical @xmath0 factors @xmath6 . nevertheless , the adaptation of the available energy dependencies predicted in @xcite for the extrapolation of each of the measured data to low experimentally inaccessible energy regions , including @xmath8=0 , leads to a value of @xmath19 that differs from others and this difference exceeds the experimental uncertainty . the theoretical calculations of @xmath19 performed within different methods also show considerable spread [ 12,1419 ] and the result depends on a specific model used . for example , the resonating - group method calculations of @xmath19 performed in ref.@xcite show considerable sensitivity to the form of the effective nn interaction used and the estimates have been obtained within the range of 0.312@xmath20 0.841 @xmath23 . the estimation of @xmath19=0.52@xmath24 0.03 @xmath25 @xcite also should be noted . the latter has been obtained from the analysis of the experimental astrophysical @xmath0 factors @xcite , which were performed within the framework of the standard two - body potential model in the assumption that the dominant contribution to the peripheral reaction comes from the surface and external regions of the nucleus @xmath12 @xcite . at this , in @xcite the contribution from the nuclear interior ( @xmath26 , @xmath27=4 fm ) to the amplitude is ignored . in this case , the astrophysical @xmath0 factor is directly expressed in terms of the nuclear vertex constants ( nvc ) for the virtual decays @xmath28 ( or respective the asymptotic normalization coefficients ( anc ) for @xmath29 ) @xcite . as a result , in ref . @xcite , the nvc - values for the virtual decays @xmath30 and @xmath31 were obtained , which were then used for calculations of the astrophysical @xmath0 factors at @xmath32180 kev , including @xmath8=0 . however , the values of the ancs ( or nvcs ) @xmath33 and the @xmath19 obtained in @xcite may not be enough accurate associated both with the aforesaid assumption in respect to the contribution from the nuclear interior ( @xmath26 ) and with a presence of the spread in the experimental data @xcite used for the analysis . as far available values of these ancs obtained in @xcite , they depend noticeably on a specific model used . therefore , determination of precise experimental values of the ancs for @xmath33(g.s . ) and @xmath29(0.429 mev ) is highly desirable since it has direct effects in the correct extrapolation of the @xmath34 astrophysical @xmath0 factor at solar energies . recently , a modified two - body potential approach ( mtbpa ) was proposed in @xcite for the peripheral direct capture @xmath35 reaction , which is based on the idea proposed in paper @xcite that low - energy direct radiative captures of particle @xmath36 by light nuclei @xmath37 proceed mainly in regions well outside the range of the internuclear @xmath38 interactions . one notes that in mtbpa the direct astrophysical @xmath0 factor is expressed in terms of anc for @xmath39 rather than through the spectroscopic factor for the nucleus @xmath40 in the ( @xmath41 ) configuration as it is made within the standard two - body potential method @xcite . in refs.@xcite , mtbpa has been successfully applied to the radiative proton and @xmath9-particle capture by some light nuclei . therefore , it is of great interest to apply the mtbpa for analysis of the @xmath42 reaction . in this work new analysis of the modern precise experimental astrophysical @xmath0 factors for the direct capture @xmath16 reaction at extremely low energies ( @xmath43 90 kev ) [ 6 - 11 ] is performed within the mtbpa @xcite to obtain @xmath3indirectly determined values both of the ancs ( the nvcs ) for @xmath4(g.s . ) and @xmath5(0.429 mev ) , and of @xmath6 at @xmath44 90 kev , including @xmath8=0 . in this work we quantitatively show that the @xmath45 reaction within the aforesaid energy region is mainly peripheral and one can extract ancs for @xmath46 directly from the @xmath47 reaction where the ambiguities inherent for the standard two -body potential model calculation of the @xmath48 reaction , which is connected with the choice of the geometric parameters ( the radius @xmath49 and the diffuseness @xmath36 ) for the woods saxon potential and the spectroscopic factors @xcite , can be reduced in the physically acceptable limit , being within the experimental errors for the @xmath6 . the contents of this paper are as follows . in section 2 the results of the analysis of the precise measured astrophysical @xmath0 factors for the direct radiative capture @xmath45 reaction is presented ( subsections 2.12.3 ) . the conclusion is given in section 3 . in appendix basic formulae of the modified two - body potential approach to the direct radiative capture @xmath16 reaction are given .

a new analysis of the modern precise measured astrophysical factors for the direct capture reaction [ b.s . new estimates are obtained for theindirectly determined values of the asymptotic normalization constants ( the nuclear vertex constants ) for(g.s . ) and(0.429 mev ) as well as the astrophysical factors at e 90 kev , including=0 .

a new analysis of the modern precise measured astrophysical factors for the direct capture reaction [ b.s . nara singh _ et al . _ , phys.rev.lett . * 93 * , 262503 ( 2004 ) ; d. bemmerer _ et al . _ , phys.rev.lett . * 97 * , 122502 ( 2006 ) ; f.confortola _ et al . _ , phys.rev.c * 75 * , 065803 ( 2007 ) , t.a.d.brown _ et al . _ , phys.rev . c * 76 * , 055801 ( 2007 ) and a di leva , _ et al._,phys.rev.lett . * 102 * , 232502 ( 2009 ) ] populating to the ground and first excited states of is carried out based on the modified two - body potential approach . new estimates are obtained for theindirectly determined values of the asymptotic normalization constants ( the nuclear vertex constants ) for(g.s . ) and(0.429 mev ) as well as the astrophysical factors at e 90 kev , including=0 . the values of asymptotic normalization constants have been used for getting information about the-particle spectroscopic factors for the mirror ()-pair . pacs : 25.55.-e;26.35.+c;26.65.+t +