the `` carte du ciel '' ( cdc in what follows ) was one of the first large international joint astronomical projects of the history .it was officially initiated in 1887 with a double target : the construction of a sky catalogue complete down to the magnitude ( which eventually became the astrographic catalogue ) and the construction of a sky chart down to the magnitude .these projects represent the very first photographic registers of the whole sky . in consequence, they constitute a very important source of data for proper motion studies ( see , for example , geffert et al . 1996 ) because of the large time interval when comparing with today observations ( about one hundred years in most of the cases ) as well as for studies on galactic structure and kinematics .part of the data was completely measured and the results were published as `` astrographic catalogue '' . a re - reduction with these published data has been recently performed by urban & corbin ( 1996 ) .other groups are taking a complete cdc second epoch plates ( potter et al . 1996 ) . on the other hand ,carte plates have never been systematically measured because they were not intended to give positions but only to be a sky chart .but due to the deeper images taken ( we have identified stars fainter than ( hiesgen et al . in preparation ) ) these plates are of great importance because of the large amount of data they contain and the time elapsed since they were produced .the plates were exposed three times , with the exposures being placed at the vertices of an approximately equilateral triangle ( see fig .[ fig7 ] ) .they were also provided with a grid of perpendicular lines in order to ease the star position measurements .these two characteristics make the accurate measurement of positions very difficult in some specific cases because of : 1 ) merging of the three images when the star is brighter than and then the presence of an adjacency photographic effect called `` kostinsky effect '' ( kostinsky 1907 ; ross 1921 ) which increases the measured distance between the exposures , and 2 ) stars lying on a grid line or close enough to let the kostinsky effect show up . optical aberrations ( mainly spherical aberration and field curvature )are also present .these problems have prevented astrometrists till now from using these triple image plates as a valuable source of data , although there are some punctual exceptions ( see geffert et al .1996 , for a recent example ) . in this paperour aim is to show that good astrometric and photometric results are achievable , following the general procedure outlined in this work .a different procedure was proposed by bonnefond ( 1991 ) and used by geffert et al .our method is able to deal with stars brighter than the upper limit of in geffert et al .( 1996 ) because it can work with blended images .a european community human and capital mobility network was initiated in 1994 under the name of `` salvaging an astrometric treasure '' ( ortiz - gil et al .1995 , hiesgen et al .1996 ) with the scope of measuring these plates and using the data for a variety of applications , such as extension of the hipparcos reference system to fainter magnitudes , determination of proper motions with an accuracy of arsec / yr , proper motions of globular and open clusters , photographic magnitudes with an accuracy of about , or studies related to galactic structure and kinematics .different typical cdc plates have been analysed in order to study how to deal with the specific problems which arise and may vary much from plate to plate .therefore , a complete study of the characteristics of each individual plate is necessary . herewe present the complete analysis performed with a plate which was gently provided by bordeaux observatory ( france ) .it was taken in february 1922 and covers a 2 field with centre at and ( 1900 equinox ) .this field is interesting because it includes the open cluster m67 .it shows three exposures ( fig .[ fig7 ] ) , placed at the vertices of a triangle .the plate was scanned with the pds 2020 gm microdensitometer of the astronomical institute mnster ( germany ) . in the process of scanning the plate on - line search and segmentation techniqueswere employed , which produced an output file containing detected objects in the form of `` picture frames '' of individual images ( horstmann 1988 ) .these frames have a size of  pixels (  mm ) , or  pixels (  mm ) in the case of bright stars , to assure that all three exposures belonging to the same triangle are included in the frame.  visual inspection of these frames allows us to remove from the set those frames in which any of the three exposures is missing , there is confusion between exposures due to the presence of double stars or the system has identified a spurious image .this implies that we can end up with at most three different frames corresponding to the same triplet .they are identified by their equal positions on the plate and the one which will be finally used in the study of the plate characteristics and reduction will be the one giving a better fit to the triple gaussian model described later .  in the rest of this workwe have assigned the following numbers to the three exposures : exposure 1 ( top left exposure in fig .[ fig7 ] ) , exposure 2 ( top right exposure in fig . [ fig7 ] ) and exposure 3 ( bottom exposure in fig .[ fig7 ] ) .  # 1#2.35to calculate the positions of each of the components of these triple images the fitting with a model consisting on the sum of three bivariate gaussian distributions was applied ( dick et al . 1993 ) .the density , measured in pixel , is then :  ^{s_k } \right\ }  \end{array}\end{aligned}\ ] ]  in this expression is the background of the frame .as the triple images are confined to areas of  mm at most , can be considered constant in each of these frames ( see sect .[ pca ] ) . is the peak density of the -th image , while are the pixel coordinates and are the centre coordinates of the -th image . and are the parameters of an ellipse with arbitrary orientation and axis size .these three parameters are related to the ellipse semimajor and semiminor axis , and , by the expressions :   \right\ } ^ { \frac{1}{2 } }  \label{eq2}\ ] ] \right\}^{\frac{1}{2 } }  \label{eq3}\ ] ]  and the angle between x and axes is    where   \label{eq5}\ ] ]  the parameter is a flattening parameter which takes into account the saturation of the photographic emulsion .the fitting process was performed by means of the levenberg - marquardt method ( marquardt 1963 ) for non - linear least squares fitting to work out the values of the 22 free parameters in the model .the fitting was applied to small frames of mm ( pixels ) , or mm ( pixels ) for bright stars , around each set of triple images .one of our main objectives is to reduce the number of these free parameters in order to achieve better results ( see sect .[ pca ] ) . at the momentthis software has not been fully prepared for its use by other groups , but we intend to make it available to the community as soon as possible .four optical aberrations would mainly be expected to show up in an optical system of the kind used in the cdc astrographs .these are coma , spherical aberration , field curvature and chromatic aberration .in particular , coma makes the images to become asymmetric as it gives them a comet - like appearance .spherical aberration and field curvature generate extended and elongated images , respectively , from pointlike ones .how much elongated and asymmetric the images are is of importance in order to see how the optical aberrations are influencing the final results in the plate reduction .images at a radial distance from the plate centre greater than  cm show a significant ellipticity , which is defined as : +   where are the image semimajor and semiminor axes of exposure , respectively , given by eqs .( [ eq2 ] ) and ( [ eq3 ] ) .  in fig .[ fig2 ] the ellipticity as a function of the plate position is shown .segment lengths are proportional to the mean ellipticity of the three exposures , while their orientation with respect to the x axis is the mean of the three angles .we expect to encounter this effect in all cdc plates because they all were taken with a similar kind of optics .two examples of these images are shown in fig .[ fig5 ] .# 1#2.65  # 1#2.65  no significant dependence of the position error on the ellipticity can be found after performing the plate reduction with the external catalogue ( fig .[ fig13 ] ) .this suggests that the model is therefore able to deal correctly with elongated images .  #1#2.75   a study on the asymmetry of the images in the plate has been carried out by means of analysing the skewness of the marginal distribution along the `` possible '' asymmetry axis :    where is the marginal distribution along the image semimajor axis and stands for the marginal distribution standard deviation .  # 1#2.75  most of the skewness values ( ) lie on the interval [ -0.2,0.2 ] ( fig . [ fig15 ] ) , which seems to indicate that the images can be considered symmetric and , in consequence , that coma is not the dominant cause for the distortion but rather the field curvature and spherical aberration .the last one makes the pointlike images to appear as disks while the first one is responsible for the elongation of these disks .  #1#2.65  there are two other facts which reinforce the conclusion that asymmetry has no influence on the data :  \1 ) the largest skewness values correspond to the fainter images , which are much sensitive to plate defects and noise which might alter their density profile .figure [ fig16 ] shows the histograms for the skewnesses of stars with magnitude and .the standard deviation of both histograms has been calculated and the results show that the distribution for the brightest stars around 0 is narrower than the corresponding one for the faintest ones , as one can see from table [ table33 ] . at the bright end the non - linear response of the plate also contributes to this effect as the stars are increasingly broader thus masking features visible in fainter star images .lllll magnitude & data &  &  &  + & 337 & & & + & 910 & & & +  [ table33 ]  this suggests that the images are symmetric and asymmetries only arise because of noise in faint stars .this is a normal effect in photographic plates and it is not a specific problem of the cdc plates .\2 ) the residuals for positions on the plate after the plate reduction with the catalogue ( ppm ) are not a function of the skewness values ( fig .[ fig17 ] ) .1#2.65  as a conclusion one can say that at least the asymmetry in the images is not important enough to have a detectable influence on the data .anyway , it has been found that optical aberrations in cdc plates can be very complicated when the centres of the telescope lenses were misaligned , being dependent on magnitude and colour ( zacharias , private communication ) . and , as usual when working with photographic plates , plate borders are of lower quality than the plate central region as they introduce some trends in the final position residuals when performing the plate reduction .further plate characteristics influencing the final astrometric accuracy have been found .the presence of a grid in the plates prevented us from considering stars lying on or very close to the lines ( fig .[ fig6 ] ) . because of this we loose approximately of the total number of stars in the plate .these lines introduce changes in the density of the images and in the positions of the nearby ones due to the kostinsky effect ( kostinsky 1907 , ross 1921 ) .this effect shows up also when images of stars lie very close to each other .the developer is exhausted in the zones where two images are in contact or very close and the amount of the products from the development process is larger there than in other zones .these products inhibit the chemical reaction which takes place during the development and the final result is an apparent repulsion of the images . due to the small separation between the three exposures ( m ) , they begin to merge in the case of stars of magnitude , and consequently , the kostinsky effect introduces changes in the `` true '' positions of the images .these can be quite large : changes of m have been detected ( see fig . [ fig3 ] ) .this effect is very difficult to model : it changes from plate to plate as it depends on the development process of each plate individually .the determination of its variation as a function of the stellar magnitude is one of the most important targets in order to be able to correct for it .# 1#2.35  # 1#2.65   to obtain the internal accuracy of the plate , we have transformed the positions of two of the three exposures to the reference system of the third one by means of a linear transformation , and the deviations from the new computed positions were obtained . it is equivalent to consider three different single exposure plates .the linear transformation was computed by least squares fitting of the positions of 552 stars in the field whose magnitudes ranged from to to avoid large errors introduced by very bright or very faint stars .assuming that all exposures equally contribute to the deviations , the rms of these deviations can be calculated for each individual exposure using 1108 stars with ( thereby excluding the ten ones with larger errors ) . since these plates were taken originally to be complete up to the magnitude , images fainter than have poor quality .almost all the stars with larger errors were fainter than . the results are presented in the first row in table [ table1 ] .lllll field & model &  &  & no .of stars + whole plate & 22 & & & 1108 + & 22 & & & 394 + plate centre & 22 & & & 648 + whole plate & 12 & & & 1108 + plate centre & 12 & & & 648 +  [ table1 ]  this analysis was also performed over the smaller region of in the plate covering the zone in which the cluster m67 is located , since a good external catalogue is available for this area ( girard et al .the linear model was in this case computed using a total of 215 stars with magnitudes ranging from to .the final rms were obtained from a set of 394 stars brighter than 15.5 ( second row in table [ table1 ] ) .one can see that are larger than those for .this may indicate that there are some kinds of local distortions which show up when studying only a small plate region , while they are absorbed by the model when considering the whole plate .they can be due to slight emulsion displacements during the plate drying process or because storage of the plate in vertical position for almost one hundred years , to small errors in the telescope tracking , or to optical distortions as the small field considered around m67 is at the plate edge , where these distortions are expected to be stronger .also the background , and consequently the noise , was found to be larger at the plate borders ( see fig . [ fig24 ] ) .  to determineif these `` plate border effects '' could account for the fact that an internal reduction using stars closer than 5 cm to the plate centre was carried out .accuracies of were found .this result clearly reflects the poorer quality of plate borders .therefore , it seems that the triple gaussian model can deal with this trend of when considering the whole plate , although the final accuracies are poorer than when only considering the plate central region .   for the region mentioned before containing the cluster a separate reduction was performed .the external comparison was carried out with an astrometric catalogue specifically built for this field ( girard et al .it has an external error of in the star positions for 1950.8 , the catalogue weighted mean epoch .the cluster is located north of the field centre .the plate model used consisted of polynomials in and up to the second order and the reduction was performed using the mean position over the three positions corresponding to the three exposures we have per star . in this way it is possible to avoid to some degree the consequences of the kostinsky effect over the brightest stars .the rms of the deviations are shown in the second row in table [ table11 ] . in these calculationsthree stars with exceptionally large deviations were not taken into account and the star showing the largest deviation after the reduction was also rejected .lllll catalog & model &  &  & no . of stars + ppm & 22 & & & 10 + girard & 22 & & & 196 + ppm & 12 & & & 10 +  [ table11 ]  the reduction of the full plate was performed using the ppm as an external catalogue . only 10 stars ( with magnitudes )could be used in the reduction as in the ppm stars are normally brighter than .the triple images of these stars are quite blended in our plates and the errors for the parameters obtained in their gaussian fitting are a bit worse than the ones corresponding to fainter stars .the plate model used consisted of polynomials in and up to the second order and the rms of the deviations are shown in the first row in table [ table11 ] .the larger values for than for can be due to the fact that the reference stars happen to be in regions of the plate where the optical distortions are stronger along -axis than -axis and the fitting algorithm is slightly poorer in the case of the brightest stars because when the exposures merge the determination of the exposure centres is less accurate .errors during the telescope tracking can also be an explanation .  in fig .[ fig11 ] the residuals in the mean position are plotted as a function of the plate position .they are uncorrelated so it seems that there are no global systematic errors present in the plate although ten reference stars are clearly too few to categorically affirm that there are no systematic errors left .an internal instrumental magnitude was computed from the measured density of each exposure . for this purpose ,the volume under each gaussian was considered and an internal instrumental magnitude was defined as    where , being the peak density of the -th exposure in the triple image , and the semiaxes of the elliptical contour . but this is true only in the case of non - saturated images for which a gaussian model is correct .  for saturated imagesit happens that the volume of the fitted gaussian is smaller than the one which would correspond to a linear detector without saturation because the image is , in some way , cut by the saturation limit of the plate .let us suppose that we have a gaussian and that we cut it in two parts at a certain height .the ratio between the volume of the `` lower '' part , , and the total one , , is found to be :    where is the truncation height and the total height is assumed to be 1 .this allows to obtain the `` true '' gaussian volume in the case of saturated ( truncated ) images as a function of the plate saturation peak ( truncation ) , the image area , and the measured volume :    this is an estimation of the volume which can be used in the evaluation of the internal magnitude when dealing with saturated images .the measured volume is a gaussian one , corresponding to the volume under a bivariate gaussian : it is the semimajor times the semiminor image axis times maximum amplitude of image peak density .we are interested also in comparing the magnitudes estimated from ( uncorrected ) and the ones from ( corrected ) .  # 1#2.75the photometric reduction was performed with 102 stars from the simbad data base which have been identified in the plate .more than of these data comes from a work by eggen & sandage ( 1964 ) , which ensures that we are dealing with a mostly homogeneous sample .a second order polynomial was used to fit the data and accuracies of ( case of uncorrected magnitudes ) and ( when corrected magnitudes are introduced ) were obtained .a total of two outliers and seven poor quality stars were removed from the sample prior to the fitting .an analysis of these poor quality stars revealed that six of them are the brightest stars in the sample located at a distance from the plate center larger than cm , where optical aberrations produce important distortions on the images .the seventh one removed is the brightest star in the whole sample .as the method of corrected volumes relies on the proper estimation of the image area , it is very sensitive to distorted cases such as the ones just described .thus , a wrong estimation of the image area produces a wrong estimation of the correction to the image volume and this method can not deal with these pathological cases .the method of corrected magnitudes constitutes an experimental model which forces the calibration curve to be closer to linear at the bright end and may be used if such a property were essential . in figure [ fig20 ]we show how the fitting looks like when using uncorrected magnitudes , after dropping off the seven problematic cases .the error bars in this figure are the propagated errors of the profile parameter errors.  one can compare the accuracy obtained here , with the accuracy in eggen & sandage paper , which is .it is clear that is negligible in comparison with , therefore one can state that the main sources of the found rms error must be related to the quality of our cdc plate and to the specific reduction method described here .a problem present in the three - gaussian model fitted to the data is the large number of free parameters , 22 in total per triple image .it is clear that some of these parameters must be correlated as the three exposures were intended to be as similar as possible .therefore a model with smaller number of degrees of freedom would be interesting to consider because :  \a ) the fitting process would be more robust with a smaller number of free parameters  \b ) the fitting algorithm would be faster  principal components analysis ( pca ) ( brosche 1973 ; whitney 1983 , for example ) is a method which first obtains a new set of uncorrelated variables by determining the set of eigenvectors of the original data correlation matrix .the corresponding eigenvalues give the portion of total variation in the original data for which each eigenvector accounts for .then the eigenvalues are sorted and split into two groups : the ones with larger values putatively represent the signal , and the remaining ones represent the noise . the programme used ( lentes 1985 ) contains a modification of the correlation matrix in order to take care for error covariance .we found that it is possible to reduce the number of free parameters to not less than 7 .this minimum is defined by the number of eigenvalues with larger values representing the actual data .a question can be posed now : is there any set of less than 22 parameters which seems suitable _ a priori _ to represent the data ? some characteristics in our problem can help us to find a possible candidate .for example , the three exposures should in principle be identical , as they were supposed to be given the same exposure time in each individual plate and were taken under approximately the same atmospheric conditions , as there was only about half an hour between consecutive exposures .more explicitly , we have found that , in average , in the current data the values of the parameters in an individual exposure are compatible with the case of being equal to the analogue ones in the other two exposures for each single star .this means that it is basically correct to use only one peak density value for the three exposures , and the same holds for , , and .the only parameter left , the background , was found to be varying in a not at all regular way over the plate ( fig .[ fig24 ] ) .however , the scale of this variation is much larger than just the mm windows containing the triple images and no errors are introduced when taking it to be constant .thus , it was considered to be the same inside the whole frame containing the triple image  the reasonings above , thus , lead in total to a set of 12 free parameters , that is , the 6 mentioned just before and 6 position coordinates for the centres of the three exposures .these have been the degrees of freedom of the new model applied in sect .[ sec1 ] .the question remains whether it is possible to only have 7 degrees of freedom without loosing an important fraction of the original information .first , one would expect a strong correlation between and ( and it is so indeed ) hence one of them can be computed as a function of the other one .one has to pay attention to the fact that because of the presence of field curvature this function will depend on the distance to the plate centre .moreover , could it be possible to know the position of each exposure only knowing the triangle central coordinates ?for this to be correct the triangle geometry should be constant through the plate .the angles which the position vectors of each exposure in a triplet form with an -axis parallel to the plate scan axis and as origin the triangles geometric centre have been calculated , together with their rms .its dependence on the position in the plate and on the distance to the plate centre was studied and it was found that exposure 1 suffers a displacement when approaching one of the plate corners. it also happens to exposure 3 , but to a smaller degree .the total dispersion of the angle values is equivalent to an image displacement along an arc of length of , and for exposures 1 , 2 and 3 , respectively .one can compare this with the residuals when performing the comparison with an external catalogue ( table [ table11 ] ) .if the total error in the image position is taken to be , we obtain , which is larger than .thus , angle dispersion is not the main source of error in the position in this case .we have also checked that the ratios among the triangle sides are not dependent on the magnitude .a model for the three exposure positions as a function only of the geometrical triangle centre position in the plate is then possible and this would lead to a set of 7 free parameters , as predicted by the pca : , ( or ) , , , , and the background ( ) .  #a new reduction was then performed , modeling the data now with a 12 parameter model instead of the 22 parameter one used before .this new model was simply the addition of three gaussian curves with identical , , , , and , together with the corresponding 6 coordinates for the three image centres :  ^{s } \right\ } \end{array}\end{aligned}\ ] ]   an internal comparison of the plate was again performed following the same method already described .there is an improvement in comparison with the results obtained when using the 22 free parameter model , as can be seen in the fourth row in table [ table1 ] .we noted that , again due to border effects as we obtained when working with a circular area of radius 5 cm around the plate centre ( note that it is the same obtained for the same region with the 22 parameter model ) .it seems from table [ table1 ] that the 22 free parameter model was able to deal with this trend when considering the whole plate while the 12 parameter model was not .this means that distortions in the plate borders introduce significant deviations from the hypothetical identity of the three exposures , which is assumed in the 12 parameter model .a remarkable improvement is obtained when working with the 12 parameter model when performing the reduction with the ppm as before ( see last row in table [ table11 ] ) .again , due to the poor quality of the reference stars and possible telescope tracking errors , as explained in sect .[ sec2 ] .a second order polynomial has been fitted to the data as before , after removing from the sample the seven ones which were found to be to severely affected by saturation and optical aberrations ( see sect . [ photometry ] ) .the magnitudes are obtained with an accuracy of , to be compared with the one obtained with the 22 parameter model , .it is clear that both methods lead to the same accuracy in the photometry .we showed that it is possible to make use of the information stored in the cdc plates in spite of the large variety of problems that they exhibit ( triple exposures , optical aberrations , grid lines , emulsion saturation ) .a general procedure in their analysis has been developed , based in the fitting to these triple exposures of a model consisting on the sum of three bi - variate gaussian distributions in arbitrary position .a detailed analysis of some problems in the plates was carried out .it was found that optical aberrations which result in symmetrically elongated images ( spherical aberration and field curvature ) dominate others which could be also present and would introduce asymmetries in the images ( coma ) .we have seen that these particular aberrations have no influence in the final astrometric accuracy as the bivariate gaussians are able to correctly model these elliptical images present mainly in the plate corners .the internal plate accuracies obtained per exposure are and .improvement is obtained when considering only a circular area around the plate centre as in this case accuracies were for both the 22 and 12 parameter models .this demonstrates the poorer quality of images at the plate borders due to optical distortions mainly .the reduction with an external catalogue ( ppm ) gives values of and .this reduction was done with problematic data as all the stars considered were among the brightest ones on the plate and they exhibited larger errors in the fitting due to the blending of the three exposures .only 10 stars could be used as reference stars .the differences among these and are most probably due to the poorer quality of the bright images and/or problems in the telescope tracking .the 12 free parameter model is found to be equivalent to the 22 parameter model for the internal reduction but for the external reduction results are better with the first one .this is because although the 22 parameter model is capable of reproducing the data in a more detailed way it is also more sensitive to individual image errors .a photometric reduction was also performed using a homogeneous sample of data from eggen & sandage ( 1964 ) mainly , with a resulting accuracy of .photometry with the 12 parameter model gives the same result , so the photometry is not affected by the change in the model in these two particular cases .improvements to the algorithm have been also outlined on the basis of the results obtained with a principal component analysis of the data which indicates that a model with at least 7 free parameters instead of 22 is possible .these parameters are : one peak density ( ) , one profile width , one saturation parameter ( ) , one orientation parameter ( ) , one background ( ) and the triangle centre coordinates ( ) .the authors wish to thank drs .tucholke and m. geffert for providing us with part of the software used in this work , together with dr .m. odenkirchen , dr . a. fernndez - soto and prof .k. s. de boer for very useful discussions and comments .lentes provided us with his software to perform the principal components analysis .we are very grateful to bordeaux observatory for providing us several cdc plates from their archives .we also thank simbad data base at the cds ( strasbourg , france ) for providing us part of the data used .this work has been carried out in the frame of a european community ( ec ) network entitled `` salvaging an astrometric treasure '' ( project no .chrx - ct94 - 0533 ) within the `` human and capital mobility '' program .the authors duly acknowledge the support of the ec , specially a. ortiz - gil and m. hiesgen with regards to their fellowships .horstmann , h. , 1988 , in .seitter , w.c ., duerbeck , h.w . , tacke , m. large - scale structures in the universe , observational and analytical methods , lecture notes in physics , 310 , springer , berlin , heidelberg , p. 111potter , h . ,polyakov , e. , kopylov , i. , kanayev , i. , evdokimov , a. , lpez , a. , flores , a. , zalles , r. , 1996 , new observational projects , in .lpez , a. , yagudina , e. i. , martnez us , m. j. , cordero barbero , a. third international workshop on positional astronomy and celestial mechanics .observatorio astronmico universidad de valencia , valencia ( spain ) , p. 19

Abstract: a new procedure for the reduction of `` carte du ciel '' plates is presented . a typical `` carte du ciel '' plate corresponding to the bordeaux zone has been taken as an example . it shows triple exposures for each object and the modeling of the data has been performed by means of a non - linear least squares fitting of the sum of three bivariate gaussian distributions . a number of solutions for the problems present in this kind of plates ( optical aberrations , adjacency photographic effects , presence of grid lines , emulsion saturation ) have been investigated . an internal accuracy of in and was obtained for the position of each of the individual exposures . the external reduction to a catalogue led to results with an accuracy of in and in for the mean position of the three exposures . a photometric calibration has also been performed and magnitudes were determined with an accuracy of .


let us consider the constrained optimization subject to the unilateral constraint the bilateral constraint can be transformed into the unilateral constraint , and we only consider without loss of generality .we assume is a smooth functional on and is onto .inequality constrained optimization problems appear in a vast range of applications such as contact problems , obstacle problems , topology optimization , robotics and gait analysis , contact mechanics , and there are several numerical methods which can be used as practical tools for solving the problems ; . for references to the literature on the numerical methods for optimization problems, one may also refer to the monographs .interior or exterior penalty methods require solving a sequence of unconstrained problems in which the penalty parameter ( the controlling parameter ) approaches 0 or infinity .this yields the ill - conditioning of the unconstrained problem , which is the main drawback of the penalty method .in contrast , exact penalty methods transform the constrained problem - into a single unconstrained problem .surprisingly , the penalized unconstrained problems are exact under certain sufficient conditions for a local optimality in the problem - , i.e. , all solutions of the penalized unconstrained problem are also solutions of the original problem for all values of the penalty parameter grater than some positive value .for this reason , considerable attention has been devoted to the use of exact penalty approaches in solving constrained optimization problems .a survey of the chronological development of the penalty methods ( including multiplier methods ) since 1968 to 1993 can be found in .the exact penalty methods require , however , minimization of a nondifferentiable cost functional .one may not employ a standard optimization solver that are customized for optimization problems with smooth functions .therefore numerical techniques should be developed by utilizing the particular structures of the penalty functions that compensate for the absence of differentiability .numerical methods to approximate the solution of exact penalty methods have been considered by several authors .we only mention the articles of . in this articlewe consider the exact penalty formulation where max is used for the penalty ; \displaystyle \mbox{with } \ ; \psi(y ) = \sum_i\max(0 , y_i),\quad y\in { \mathbb{r}}^m , \end{array}\ ] ] for , and we develop fast iterative methods for finding the minimizer based on the nonsmooth optimization theory .the optimality condition of is given by where is the convex sub - differential of , i.e. , , &  s=0 , \\    1 , &  s>0 .\end{array}\right . \end{array}\ ] ] on the other hand , the necessary optimality of - is given by where is the lagrange multiplier of the unilateral constraint .let the pair be a solution to .then is also a solution to provided that , ( e.g., ) .  due to the singularity and the non - uniquness of the subgradient of , the direct treatment of the conditionmany not be feasible for numerical computation .the common strategy to alleviate the technical difficulty resulting from the non - differentiability of the penalty functional is to introduce a regularized penalty functional : let us consider the regularized problem to ; \displaystyle \mbox{with } \ ;\psi_\epsilon(y ) = \sum_i\phi_\epsilon(y_i),\quad y\in { \mathbb{r}}^m , \end{array}\ ] ] where for is a regularization of the function defined by \\ \\ s &  s \ge \epsilon . \end{array } \right.\ ] ] an arbitrary in is used to avoid the singularity and to determine a single value in the subdifferential . since , the necessary optimality condition of is given by the equation although the non - uniqueness for concerning subdifferential in the optimality condition is now bypassed through regularization , the optimality condition is still nonlinear .one of the strategies for solving is to use the asymptotic solution at infinity of the nonlinear ode with some positive definite matrix which serves as a precondition of .( see ) .the method is simple and easy to implement , however , the convergence speed is quite slow and the numerical solution obtained by the algorithm is not accurate .this is due to the fact that the nonlinearity in is not fully taken into account and not incorporated in algorithms .one of the objective of this paper is to design the fast , accurate numerical algorithm for by taking the nonlinearity into consideration .the outline of the paper is as follows . in section 2an implicit iterative algorithm for is proposed .the property and convergence of the proposed algorithm are analyzed . in section 3 the primal - dual active methodis introduced and the relation to the proposed method is discussed . in section 4 several numerical tests are reported to assess the performance of the method .in this section we introduce the algorithm for and analyze its convergence .first , we have the consistency result as .[ thm : converge ] let be a solution of the regularized problem. for an arbitrary , any cluster point of is also a solution of .let be a solution to .then we have let be a cluster point of . from, we have thus , from continuity of , and the fact that for all , we obtain   as a consequence of theorem [ thm : converge ] , we have that  suppose that each of the problem and admits the unique solution .if is sufficiently large , converges to the solution of .we propose the fast algorithm that provides an accurate numerical solution of .for this objective , we first observe that the necessary optimality condition is written as where denotes a diagonal matrix with the entries {j , j}=\left\{\begin{array}{ll } { \displaystyle}\frac{1}{\max(\epsilon,(gx - g)_j)}~ , & ( gx - g)_j\ge0\\ 0~ , &  ( gx - g)_j  < 0 \end{array}\right . \end{array}\ ] ] and is a column vector depending on defined by =\left\{\begin{array}{ll } { \displaystyle}\frac { g_j}{\max(\epsilon,(gx -g)_j)}~ , & ( gx - g)_j\ge0 \\ 0~ , &  ( gx - g)_j < 0 \end{array}\right . \end{array}\ ] ] the optimality condition in the form suggests the following fixed point iteration ; where is positive , symmetric and serves a pre - conditioner for .the parameter serves a stabilizing and acceleration stepsize ( see , theorem 3 ) .let . equation for is equivalent to the equation for  which gives us   * lemma 1 * the direction is a descent direction for at .  from where we used the fact that is strictly positive definite .so the iteration can be seen as a descent method and is written as ;  * algorithm 1 : fixed point iteration . *set parameters : .compute the direction by .+ [ 10pt ] step 2 .update + if , then stop. otherwise repeat step 1 - step 2 .+ let us make some remarks on the algorithm :  in many applications , the structure of , and are sparse block diagonals , and the resulting system for the direction then becomes a linear system with a sparse symmetric positive - definite matrix , and can be efficiently solved by , for example the cholesky decomposition method .  if , then we have . for this case we may use the alternative update assuming that it does nt cost much to perform   algorithm 1 is globally and rapidly convergent and the following results justify the factlet us introduce some notations ; and .[ lem : r ] let and .the following identity holds for all ; {j , j},|(gx^{k+1}-g)_{j}|^2-   multiplying by  where from the identity with and , we obtain {j , j},|(gx^{k+1}-g)_{j}|^2-   assume there exists such that if there exists such that for all , then and is globally convergent .  since on is concave( see for the definition of ) , we have thus {j , j},|(gx^{k+1}-g)_{j}|^2-|(gx^{k}-g)_{j}|^2 ) \ge \phi_\epsilon((gx^{k+1}-g)_{j})-\phi_\epsilon((gx^k - g)_{j}),\quad \forall j\in { \cal a}^k.\ ] ] hence {j , j},|(gx^{k+1}-g)_{j}|^2-|(gx^{k}-g)_{j}|^2 ) \ge \sum_{j\in  { \cal a}^k}\left [  \phi_{\epsilon}((gx^{k+1}-g)_{j})-\phi_{\epsilon}((gx^{k}-g)_{j})\right]\\  & = \psi_\epsilon(gx^{k+1}-g)-\psi_\epsilon(gx^k - g ) -\sum_{i\in{\cal i}^k  } \left[\phi_{\epsilon}((gx^{k+1}-g)_{i})-\phi_{\epsilon}((gx^{k}-g)_{i } ) \right]\\ & \ge \psi_\epsilon(gx^{k+1}-g)-\psi_\epsilon(gx^k - g).\end{aligned}\ ] ] thus , we obtain if we assume for some , then is monotonically decreasing and   suppose but .assume with , then the algorithm is globally convergent .algorithm 1 closely resembles to the semismooth newton s method applied to the equation : the gradient at has a newton derivative where the diagonal matrix is defined by {i , i } = \left\{\begin{array}{cc } { \displaystyle}\frac{1}{\epsilon } , &  ( gx^k - g)_i  \in ( 0,\epsilon ) \\[10pt ]  0 ,  & \mbox{otherwise}. \end{array } \right.\ ] ] replacing step 1 with the system for the semi - smooth newton step one arrives at a semismooth newton s method . in general , the sequence generated by the newton s method is guaranteed to converge when the initial guess is sufficiently close to the true solution .when is not close enough to the minimum , taking the full newton step need not decrease the objective function , moreover it may generate a non - convergence sequence . on the other hand , through several numerical experimentthe sequence generated by algorithm 1 converges to the true solution within a few iterations even when an initial guess is far from the true solution .if the iterate is close to the solution and satisfies , then and algorithm 1 enjoys the superlinear convergence of semi - smooth newton s method.  we shall investigate algorithm 1 and the semi - smooth newton through a simple problem : we consider the optimization problem in this case and are explicitly given as and it is easy to prove that the sequence generated by the iteration and converges to for any initial provided that and .on the other hand , if we assume that , then for any initial we have for all .  we depict , in fig .[ fig : ours ] and [ fig : newton ] respectively .the outcomes after three iterations starting from are also plotted to visualize the iteration process .the parameters , and were used to draw these graphs .( we select a large just for the purpose of the visualization . in practice, we will take much smaller number , say , . )we observe from the figure that the performance of algorithm 1 is much better than the one of the semismooth newton s method .  .]  . ]since determined by is a descent direction of , one can use the line search method ;  * algorithm 2 : successive iteration with line search * + step 0 . set parameters : .compute the direction by step 2 .determine the steplength by minimizing , i.e. , + step 3 .update + if , then stop. otherwise repeat step 1 - step 3 .+ step 2 can be replaced by the line search algorithms such as armijo s rule .the proof of the convergence of algorithm 2 is quite standard and we omit the proof .an alternative to our gradient - based algorithm is the newton update .the semi - smooth newton method in is based on complementarity condition for ; the semi - smooth newton method reduces to the primal - dual active set method ;  * primal - dual active set method *  * choose and set . * set and . *solve for  * convergent or set and return to step 2 .\(1 ) if is quadratic , i.e. , , then step 3 is written as if , then step 3 is solvable .otherwise , we assume that is positive on .\(2 ) if is , the newton step for step 3 is given by   \(3 ) in general one may use the regularized update to avoid the possible singularity of linear system .it reduces to which is very similar to with .consequently , algorithm 1 is much stabler than prima - dual active method .\(4 ) but , it is shown in if the primal - dual active method converges , it converges q - super linearly and in a finite step .\(5 ) one can hybrid algorithm 1 and prima - dual active method so that one may accelerate the convergence .in this section we show some numerical experiments using algorithm 1 proposed in section 2 for unilateral constrained quadratic optimization problems with several and .all tests confirm the fact convergence and effectiveness of the proposed algorithm .let \times[0,1] ] , and the space of shape functions is given by \otimes [ 1,\frac{y - y_{i , j}}{\delta x}][u_{i , j},u_{i+1,j},u_{i+1,j+1},u_{i , j+1}]^\top.\ ] ] and is nodal variables at the grid points .the subscript indicates the mesh size .the finite element discretization yields the discrete energy functional for , where and and denote the stiffness matrix and the load vector associated with the discretization .the inequality constrained is approximated by , which is equivalent to , where .let denote the generated sequence by algorithm 1 .we report and the sup norm of the gradient of :   we run algorithm 1 with the following parameters and preconditioner :  1 .mesh size , , , , .mesh size , , , , [ fig : j_r_implicit2 ] shows the monotone convergence of the objective function : the convergence achieves after 11 iteration for , and 20 iteration for .   and of the finite element solutions generated by algorithm 1 with , , and .,title="fig:",height=170 ]  and of the finite element solutions generated by algorithm 1 with , , and .,title="fig:",height=170 ]   let ^ 2 ] , and is the noise level . the unknown source ( exact solution ) and the noise free data are depicted in the first row of fig .[ fig : is ] .the domain ^ 2 ] , , represent finite differences in and direction and denotes a discrete laplacian . the problem is obtained by discretizing the multi - parameter nonsmooth tikhonov regularization for a denoising problem here are regularization parameters which must be appropriately selected in order to obtain a desired reconstructed image .we define , the regularization of , by \\ \\{ \displaystyle}\frac{s^2}{2\epsilon}+\frac{\epsilon}{2 } & s \in [ -\epsilon,0 ] \\ \\ -s & s \le-\epsilon . \end{array } \right.\ ] ] the derivative is written as , and one follows the similar argument in section 2 to arrive at the successive iteration algorithm : here the diagonal matrix for is defined by {j , j}= \frac{1}{\max(\epsilon,\vert v_j\vert ) } ~,\ ] ] and is a regularization of ; {i } ) + \phi_\epsilon([d_y u]_{i } ) \right ) + \eta_2 \sum_{i=1}^{n^2 } \phi_\epsilon ( [ h u]_{i}).\ ] ] another example that the proposed method can handle includes the denosing problem by total variation : let be a function defined for by   s &  \epsilon \le s  \end{array}\right.\quad  \phi^\prime_\epsilon(s ) = \left\{\begin{array}{cc }  { \displaystyle}\frac{s } { \epsilon } &  0\le s\le \epsilon \\[10pt ]  1 &  \epsilon \le s  \end{array}\right.\ ] ] the regularized objective functional takes the form let be a discretization of the second term ^ 2_i + [ d_yu]_i^2 } ) \delta x\delta y=  \sum_i  \phi_\epsilon ( r_i ) \delta x \delta y\ ] ] where ^ 2_i + [ d_yu]_i^2}$ ] .the derivative of  d_x(i , k ) + [ d_yu]_i d_y(i , k)}{r_i } \\ & = \sum_i \frac{r_i}{\max(\epsilon , r_i)}\frac{1}{r_i}\left([d_xu]_i d_x(i , k ) + [ d_yu]_i d_y(i , k )  \right)\end{aligned}\ ] ] thus we have here the diagonal matrix is defined by {i , i}= \frac{1}{\max(\epsilon , r_i)}.\ ] ] from the observation we arrive at the successive iteration algorithm for solving the nonlinear equation : the details of the method and the numerical tests will be reported elsewhere .                         , _ contact problems in elasticity : a study of variational inequalities and finite element methods _ , vol .8 of siam studies in applied mathematics , society for industrial and applied mathematics ( siam ) , philadelphia , 1988 .

Abstract: we propose an implicit iterative algorithm for an exact penalty method arising from inequality constrained optimization problems . a rapidly convergent fixed point method is developed for a regularized penalty functional . the applicability and feasibility of the proposed method is demonstrated using large scale inequality constrained problems .  * . * + * . *


and have drawn attention to the fact that decay - rate measurements made at the brookhaven national laboratory ( bnl ; ) and at the physikalisch - technische bundesanstalt ( ptb ; ) show clear evidence of periodic annual modulations . according to their analyses ,the decay rates appear to peak in winter , suggesting that some kind of radiation from the sun is influencing the decay rates . however , the dates of maximum rate differ significantly from january 3 , which is the date of minimum sun - earth distance , which argues against a simple model in which decay rates are solely influenced by an unidentified but isotropic radiation from the sun .the purpose of this article is to propose an interpretation of the phases of the annual oscillations .the suggestion that nuclear decay rates may be variable has of course been questioned by a number of other groups :  1 . and others suggested that these fluctuations have their origin in environmental influences on the detector systems , or other systematic effects .however , have shown that the results of their bnl and ptb analyses can not be explained by variations of temperature , pressure , humidity , etc . , re - examined data from several nuclear - decay experiments , but found no evidence for a correlation with sun - earth distance . however , we have re - analyzed data for and decay rates , which norman and his collaborators generously provided to our collaboration .norman and his colleagues compared these data with a sinusoidal modulation of fixed amplitude 0.15% , and fixed phase of year ( 0.01 ) , to conform with the results found by in their analyses of bnl and ptb data .however , we have carried out a power spectrum analysis of the norman data , which searches for evidence of periodicity and yields estimates of the amplitude and phase of any oscillation .our analysis yields evidence of an annual modulation , with significance estimated at 1% .we estimate the amplitude to be 0.034% [ smaller than that considered by norman et al . by a factor of 5 ] , and the phase to be 0.06 0.05 , which is compatible with the value [ 0.01 ] assumed by norman et al . the fact that the amplitude inferred from the data of norman , et al . is smaller than what is observed in the bnl or ptb datais compatible with the standard weak interaction theory , as noted by .3 .  analyzed data from the power output of the radioisotope thermoelectric generators ( rtgs ) aboard the cassini spacecraft , but found no significant deviations from exponential decay .however , have shown that there is in fact no conflict between cooper s results and their results .this is due in part to the fact that the cassini rtgs derive their power from the alpha decay of , whereas the periodic effects observed in various data sets always involve beta decays .we have recently presented evidence that both bnl and ptb measurements also exhibit a periodicity suggestive of the influence of solar rotation possibly of the solar core .such a periodicity would indicate that the radiation is anisotropic , indicating specifically a longitudinal ( east - west ) asymmetry .if the radiation has a longitudinal asymmetry , it is reasonable to suspect that it may also have a latitudinal ( north - south ) asymmetry .the goal and scope of this article are limited to investigating the consequences of the following two hypotheses :  1 ._ some nuclear decay rates are influenced by an unknown solar radiation ; _ and 2 ._ the flux of this radiation , as it might be measured at earth , is influenced by two factors : the variation in the sun - earth distance due to the eccentricity of the earth s orbit , and a north - south asymmetry in the solar radiation ._  in section [ sec : model ] , we analyze the properties of a model based on these two hypotheses .we find that , according to this model , the maximum decay rate should occur in the range approximately september 6 to march 8 . in section [ sec : data ] , we compare this model with data from the bnl and ptb experiments , and find that the phases of maximum variability appear to be compatible with this model .we discuss these results in section [ sec : disc ] .it is convenient to measure phase of the year so as to run from 0 to 1 .we denote by the phase of the minimum sun - earth distance , and by a phase related to the solar axis of rotation . since the sun - earth distance is a minimum on january 3 , .the earth has maximum exposure to the southern solar hemisphere on march 6 and maximum exposure to the northern hemisphere on september 8 , corresponding to phases 0.178 and 0.687 , respectively .the fact that the difference is not exactly 0.5 is due to the eccentricity of the earth s orbit . approximating the elliptical orbit by a circular orbit for the purpose of representing the north - south asymmetry ,we adopt , which gives maximum exposure to the southern hemisphere at phase 0.183 ( march 8) and maximum exposure to the northern hemisphere at phase 0.683 ( september 6 ) .we also point out that we are implicitly invoking a third hypothesis :  1 ._ whatever region of the sun is responsible for a solar influence on decay rates has an axis of rotation that is indistinguishable from that determined by observation of the solar photosphere . _  the eccentricity of the earth s orbit leads to a variation in the flux of the hypothetical radiation influencing decay rates , normalized to mean value unity , given by   , \label{eq1}\ ] ]  where .the variation of the flux due to a north - south asymmetry is given by   , \label{eq2}\ ] ]  where the `` asymmetry coefficient '' is chosen so that :  1 .  if , the amplitude of the variation due to north - south asymmetry is equal to the amplitude of the variation due to the eccentricity of the earth s orbit , and 2 .if , radiation from the northern hemisphere exceeds that from the southern hemisphere ( and vice versa ) . since is small ( and if is not large ) , the total variation in the flux ( retaining the normalization to mean value unit ) is given by  -a\cos\left[2\pi\left(\phi-\phi_a\right)\right]\right\rbrace , \label{eq3}\end{aligned}\ ] ]  if the average flux is responsible for an increase in the decay rate by the small `` coupling coefficient '' , then the annual modulation of the decay rate , normalized to mean value unity , is given by -a\cos\left[2\pi\left(\phi-\phi_a\right)\right]\right\rbrace , \label{eq4}\end{aligned}\ ] ]  [ we should note , however , that it is conceivable that the unknown radiation may act on some isotopes to reduce the decay rate . in this case the coupling coefficient would be negative . ]we find from inspection of this formula that , since , the maximum value of is to be found only in the range or , equivalently , in the two ranges and , i.e. 0 to 0.183 and 0.683 to 1 .the range , i.e. 0.183 to 0.683 , is `` forbidden . '' [ for the case that the solar radiation acts to suppress the decay rate , these ranges would be reversed .] one may understand this result by noting that if we sum two sine waves , with phases , the peak will be found in the range if , and outside that range if .expressed in the form in which it would be measured experimentally , this formula becomes   , \label{eq5}\ ] ]  in which is the amplitude of the variation , and is the phase of the peak . by comparing eqs .[ eq4 ] and [ eq5 ] and separating out coefficients of and , we find that  \\ k\cos\left(2\pi{}\kappa{}\right)&=&\gamma{}c\left[\sin\left(2\pi{}\phi_o{}\right)-a\sin\left(2\pi{}\phi_a{}\right)\right ] \label{eq6}\end{aligned}\ ] ]  from which we find that the asymmetry coefficient is related to by  }{\sin\left[2\pi{}\left(\kappa{}-\phi_a\right)\right ] } \label{eq7}\ ] ]  this coefficient is shown as a function of phase in figure [ fig1 ] .the coefficient is negative for to and positive for to 1 . if , the coefficient is zero , as we would expect . if , the coefficient is infinite , again as we would expect .we also find from eq .[ eq6 ] that the coupling coefficient is given by    where the `` coupling factor '' is given by  }{\sin\left[2\pi{}\left(\phi_a-\phi_o\right)\right]}. \label{eq9}\ ] ]  this factor is shown as a function of phase in figure [ fig2 ] . if , the factor is unity . if or , the factor is zero .figures [ fig1 ] and [ fig2 ] confirm that there are no valid solutions to the relevant equations for in the range .we now compare this model with bnl and ptb data . in our earlier power spectrum analysis , we followed and considered only the ratio of the and decay rates .however , since we are now interested primarily in the phases of the decay - rate oscillations ( rather than their amplitudes ) , it is necessary to consider the two datasets separately .we determine the phase of the maximum in the annual variation of each dataset by using a likelihood method previously introduced for the analysis of solar neutrino data .however , rather than scan the power as a function of frequency , we now set the frequency at 1 yr and scan the power as a function of phase .we show the results in figures [ fig3 ] , [ fig4 ] , and [ fig5 ] for bnl , bnl , and ptb , respectively .the results are summarized in table [ tbl:1 ] where we list , for each element of each experiment , the phase of the maximum power , the maximum power , the amplitude of the modulation , and the phases , for which the power is less than the maximum by 0.5 . the phases and denote the `` 1-sigma '' offsets .crrrrrr experiment & element & & & amplitude & & + bnl & & 0.695 & 14.46 & 5.29 & 0.688 & 0.722 + bnl & & 0.899 & 3.52 & 2.72 & 0.836 & 0.962 + ptb & & 0.085 & 495.05 & 8.40 & 0.080 & 0.090 +  for and , we can state with some confidence that the phases fall in the allowed range .however , we see from figure [ fig3 ] that , for , we can state only that there appears to be 50% probability that the phase is in the allowed range .an interesting fact to note is that the and were measured concurrently , in an alternating fashion , on the same instrument .the fact that these two nuclides do not show the same phase properties further supports the consideration that the observed effects are not systematic in nature , as well as reinforcing the notion that different isotopes will have different inherent sensitivities .it is important to note that our model refers implicitly to the timing of the unknown solar radiation responsible for the decay - rate variations .since there may be a time lag between the arrival of the radiation and the emission of a beta particle , there may be a discrepancy between the timings of the two events .this point is relevant to the bnl measurements of the and count rates summarized in table [ tbl:1 ] .what is experimentally observed in decay is the 1709 kev beta particle emitted by in the sequence , since the 225 kev beta particle emitted from the transition has too low an energy to have been detected by the bnl experiment .since the half - life of is 14.28 days , comes into equilibrium with the parent on a time scale of order .hence the response of the beta - detector lags the initial decay by about 21 days .by contrast , decays directly to with the emission of a 709 kev beta particle .hence the calculated phase difference between the and measurements of about 75 days , shown in table [ tbl:1 ] , is probably due in part to the mechanisms responsible for the decay - rate variations .more generally , we draw attention to the following points : the phase distribution that follows from our model rests on the assumptions that decay - rate variations are due entirely to an unknown solar radiation , and that the axis of rotation of the core is parallel to that of the photosphere .if we find that , for some isotopes , the timing of decays does not conform to the expectations of this model , we must question these assumptions .one would then need to consider the possibilities that decays may be due in part to a cosmological particle or radiation flux , as has been suggested by , or that the axis of rotation of the solar core is not parallel to that of the photosphere .  as we see from table [ tbl:1 ], there is a huge variation in maximum power among the three cases , but a comparatively small range in amplitude .the very large power for the ptb case is due in part to the longer duration of the experiment ( 14.8 years for ptb as against 7.8 years for bnl ) .however , even allowing for this difference , we see that different elements have very different sensitivities to whatever is causing the annual modulation .as noted above , this is consistent with expectations from standard weak interaction theory , as noted by .for the purposes of this article , we refer to `` decays '' as if a decay event is a simple process , but this is typically not the case . for instance, the decay of is a complex process . although the decay of a nucleus begins with alpha emission , and although after about 20 years nuclei are in secular equilibrium with the majority of its 13 radioactive daughters , it takes about 200 years for the processes to effectively reach equilibrium .when equilibrium is reached , 42% of the photon emissions are due to beta - decaying daughters .the ionization chamber utilized in the ptb experiment can not discriminate between either ( alpha or beta ) type of decay : the chamber measures only the total energy deposited by the incident photons , which have their origins in both types of decay from several different isotopes .  the asymmetry coefficient and the coupling factor , given by eqs . [ eq7 ] and [ eq9 ] , respectively , are listed in table [ tbl:1 ] and shown in figures [ fig1 ] and [ fig2 ] , respectively .we see that the phases fall in the `` allowed '' range 0.683 to 0.183 ( avoiding the `` forbidden '' range 0.183 to 0.683 ) .we identify in these figures the phases of maximum power listed in table [ tbl:1 ] . on applying the results shown in these two figures to the data shown in table [ tbl:1 ] , we obtain the values of the asymmetry coefficient and of the coupling coefficient listed in table [ tbl:2 ] .cccccc & & & & asymmetry & coupling + experiment & element & amplitude & phase & coefficient & coefficient + & & & 0.688 & n / s & n / s + bnl & & 5.29 & 0.695 & 12.25 & 0.0013 + & & & 0.722 & 4.02 & 0.0043 + & & & & & + & & & 0.836 & 1.08 & 0.0076 + bnl & & 2.72 & 0.899 & 0.65 & 0.0090 + & & & 0.962 & 0.29 & 0.0090 + & & & & & + & & & 0.080 & -0.72 & 0.0171 + ptb & & 8.40 & 0.085 & -0.80 & 0.0163 + & & & 0.090 & -0.89 & 0.0156 +  in reviewing the results shown in table [ tbl:2 ] , we see that the results for the experiment are ill - determined , since the phase is close to the critical phase 0.683 . in comparing the results for the bnl experiment and the ptb experiment, we see that there is no substantial difference between the estimates of the magnitudes of the asymmetry and coupling coefficients , despite the fact that the powers differ greatly .it is interesting to note the difference in sign between these two experiments : for both elements investigated in the bnl data , the modulation shows evidence of a larger influence arising from the northern solar hemisphere , whereas for the ptb experiment , the modulation shows evidence of a larger influence arising from the southern hemisphere . since the time intervals of the two experiments are different ( 1982.13 to 1989.93 for bnl and 1983.86 to 1999.17 for ptb ) , we can not infer whether the difference is due to variability of the solar influence , or to a difference in the `` sensitivity '' of the specific decaying isotopes .it will therefore be important to study a variety of isotopes concurrently for precisely the same time interval . a framework to describe a possible class of mechanismsis presented in .we have found evidence , reported in previous publications , of modulations in decay rates that may be attributable to rotation at or near the solar core .we have also recently found evidence of a rieger - type modulation that we may attribute to an `` inner tachocline '' separating the core from the radiative zone .these results show that whatever radiation is responsible for influencing decay rates propagates essentially freely through the solar radiative and convection zones , suggesting that some flavor of neutrinos may be responsible for decay - rate variations .however , the standard theory of neutrino physics does not provide for a mechanism by which neutrinos could have such an effect , raising the possibility of new physics .  in view of these conflicting considerations , it is clearly desirable that we obtain further information relevant to the mechanism by which the sun influences decay rates .if neutrinos or some other particles ( or quanta of radiation ) influence radioactive atoms , it is conceivable that they may transfer their momentum to the decaying nuclei , and thus exert a force on a bulk sample of radioactive material .this raises the possibility of carrying out a `` fifth force '' type of experiment on a macroscopic radioactive sample , using techniques recently developed to search for deviations from newtonian gravity .we are indebted to d. alburger and g. harbottle for supplying us with the bnl raw data , and to h. schrader for supplying us with the ptb raw data .we are also indebted to an anonymous referee for suggestions that materially improved the article .the work of pas was supported in part by the nsf through grant ast-06072572 , and that of ef was supported in part by u.s .doe contract no .de - ac02 - 76er071428 .alburger , d.e . ,harbottle , g. , & norton , e.f . , 1986 ,earth planet .lett . , 78 , 168 baurov , yu .a. , sobolov , yu .g. , ryabov , yu .v. , & kushniruk , v. f. 2007 , phys .atomic nuclei , 70 , 825 .chist , v. , be , m. , & dulieu , c. 2008 , proc .int . conf . on nuclear decay for science and technology ( eds .o. bersillon , et al ., edp sciences , france ) .christmas , p. , mercer , r. a. , woods , m. j. , & judge , s. m. 1983 , j. appl . radiat .isot . , 34 , 1555 .cooper , p. s. 2009 , astropart . phys . , 31 , 267 fischbach , e. , et al .2009 , , 145 , 285 fischbach , e. and talmadge , c.l .1999 , the search for non - newtonian gravity ( springer , new york ) .jenkins , j.h .. 2009b , astropart .32 , 42 jenkins , j. h. , mundy , d. w. , & fischbach , e. 2010 , nucl .inst . & meth . a , 620 , 332 norman , e. b. et al .2009 , astropart .phys . , 31 , 135 okeefe , d. , et al .( in preparation , 2011 ) .semkow , t.m . , et al .2009 , phys .b , 675 , 415 .siegert , h. , schrader , h. , & schtzig , u. 1998 , appl .isot . , 79 , 1397 .sturrock , p.a . ,caldwell , d.o . ,scargle , j.d . , & wheatland , m.s . , 2005 ,d 72 , 113004 .sturrock , p. a. , et al . 2010a , astropart .phys . , 34 , 121 sturrock , p. a. , et al .2010b , , 267(2 ) , 251 sturrock , p.a ., fischbach , e. , & jenkins , j.h . , 2011 , solar phys .( in press ) .

Abstract: recent analyses of datasets acquired at the brookhaven national laboratory and at the physikalisch - technische bundesanstalt both show evidence of pronounced annual variations , suggestive of a solar influence . however , the phases of decay - rate maxima do not correspond precisely to the phase of minimum sun - earth distance , as might then be expected . we here examine the hypothesis that decay rates are influenced by an unknown solar radiation , but that the intensity of the radiation is influenced not only by the variation in sun - earth distance , but also by a possible north - south asymmetry in the solar emission mechanism . we find that this can lead to phases of decay - rate maxima in the range 0 to 0.183 or 0.683 to 1 ( september 6 to march 8) but that , according to this hypothesis , phases in the range 0.183 to 0.683 ( march 8 to september 6 ) are `` forbidden . '' we find that phases of the three datasets here analyzed fall in the allowed range .


thanks to the progress of telescope technology and the detection technique of recent years , it is expected that we will meet with a situation where a large scale of high - quality data is continuously generated by such as subaru telescope , sloan digital sky survey an so on . the way of traditional analysis , however , appears to be insufficient for using the large amount of data effectively and efficiently and getting the maximum scientific results .although many people recognize the importance of research that uses the multi - wavelength data , such research actually needs considerable effort .one reason is that , for each data set , one needs to learn how to reduce and analyze the data , and even needs to know where the analysis tools are available .to overcome such situation and maximize the scientific return from a big project like subaru and alma , it is important to construct an environment where user can access to the science - ready data with very few effort .national astronomical observatory of japan ( naoj ) started its vo project ( japanese virtual observatory jvo ) in 2002 .the objectives of the jvo project are to provide a seamless access to the distributed data service in the vo , and to provide user - friendly analysis environment .this paper describes our recent progress on the second objective ., is an optical - infrared 8.2 m telescope operated by national astronomical observatory of japan ( naoj ) at mt .mauna kea hawai .subaru has seven open use instruments : ciao , comics , focus , ircs , suprimecam , hds and moircs .cisco is no longer available for open - use . using these instruments ,observation can be made for wavelengths from optical ( 300 nm ) to infrared ( 20 m ) with spectrum resolution up to ( hds ) .the total amount of public data for each instrument is shown in figure [ fig : totalamount ] .as of october 2006 , 8 tb of data is archived in the public area .more than 70% of the data are from the suprimecam , which is a mosaic of ten 2048 4096 ccds and covers a 34 x 27 field of view with a pixel scale of 0.20 .more than 90% of all the data requests are for the suprimecam , so our current priority issue is how to improve the usability of the suprimecam data .figure [ fig : subaruarchive ] shows the flow of data taken by the subaru .the data are registered in the subaru telescope archive system ( starts ) as soon as the data are acquired by the instruments , so an observer retrieves his data from stars during and/or after the observation .the data of stars is mirrored to the mitaka advanced stars ( mastars ) , so the observer can retrieve the data also from the mastars .starts and mastars are not public data archive . to use the system , you need to get an account on the subaru computing system for stars or an account on the mitaka computing system for mastars .the data that passed 18 months of a proprietary period becomes publicly available through the , and system .the smoka system provides various query modes for the subaru archive , and it is described in enoki et al .the jvo system provides a vo standard access interface to the subaru archive .currently only the data of suprimecam is available from the jvo .the amount of data , especially of suprimecam , is very large , so it is important to provide a way to analyze the data without moving the data to a remote users machine .one of the ways to do so is to login to the subaru or mitaka computing system and analyze the data on the machine .it is , however , not practical to use the visualization tool from a remote machine , especially when accessing through a slow network .another solution is to provide a web service , through which one can access to the data analysis software and visualize the data in a compact graphical format such as gif , jpeg and png . recentlya lot of open source framework are available for making such a service , and it has been realized that interactivity of the web based service can be improved by using ajax technique as demonstrated by the google map service . another important point is to provide the data in a form that detector and environment dependencies are removed .those dependencies are usually not known by an archive user , so it should be properly reduced by a data provider .the quality of the data reduction is improved as the experience is accumulated and the reduction software is also evolves continuously , so it is adequate to reduce the data on demand with the most developed algorithm .it is also important to provide the way to reduce the data with older version software for assuring data reproducibility to enable later same analysis . by providing the data in such a manner ,a data provider can control the quality of data by putting a tag representing a version of reduction software in the fits header .the reduction process is hidden from a user , and the user does not need to take care about most of part of data reduction .so , we have decided to provide such a service on the japanese virtual observatory ( jvo ) web portal .the data reduction processes are concentrated on the jvo servers , so computing resources need to be integrated in a scalable manner to the jvo .we have developed a web service based grid computing system .this system is composed of four services : monitoring and discovering service ( mds ) , data analysis service ( das ) , data search service ( dss ) and storage service ( srs ) . figure [ fig : subarupipeline ] shows an example of suprimecam response ( flat frame ) calculation system , which is showing how each service interacts each other .the mds manages the status of each das , and schedules the job submission requested by a grid client .each das server periodically report its status , such as load average , number of running job and job status , and the status is stored on an mds database .a grid client queries to the mds to ask which server is free for a job submission .the mds returns a service endpoint url that is appropriate for the job submission .the client submit the job , and wait it to finish .while waiting , the client periodically polling to the mds for querying the job status .the das sends a query to the dss to get subaru raw data , the dss returns the urls for the data , the das retrieves the data and starts analysis .when a job status is changed to `` finish '' , the client queries the das for an url to retrieve the result .the url is passed to the srs , the result is stored on the storage of the srs , and the metadata of the result is registered on the dss .the interactions between each service and client are made by exchanged a soap message .the interface of each service is defined in the web service description language ( wsdl ) .several examples of the defined interfaces are described in java interface as follows :  .... mds interface   void reportstatus(string hostid , double load , int njob )   serviceinfo resolveservice(string serviceid )   void reportjobstatus(string hostid , int jobid , string status )   string getjobstatus(string hostid , int jobid )   ...  das interface   int submitjob(string command , string argv )   string getresulturl(int jobid )   string query(int jobid )   string finalize(int jobid )   ...  srs interface   int copyasync(string src , string dest )   void copy(string src , string dest )   void finalize(int jobid )   ...  dss interface   vodata performquery(select select )   ... ....  the ` reportstatus ` interface is used by a das server to report its load average and the number of submitted jobs .the ` resolveservice ` interface is used by a grid client to decide which server to submit a job .the returned ` serviceinfo ` contains an endpoint url .the ` submitjob ` interface is used to submit a job to the das server , which returns a job i d and it is used for polling the job status .the ` getresulturl ` interface returns an access url for retrieving the result .the ` copyasync ` and ` copy ` interface are used to transfer data between two servers or just to copy the data inside the same server .the former interface is used for data transfer that is expected to take long time .the ` performquery ` interface is used for querying the data by astronomical data query language ( ) , and return the result in format .  a web form based gui for calculating a response frame of suprimecam ccd is made for easy job submission as shown in figure [ fig : subaruflat ] .the * observation * section of the gui is used for browsing the number of exposures for each filter on each day . the observation period for calculating a response frameis determined here . usually select a period of successive suprimecam observations , which typically lasts one week . at the section of *create flat calibration frames * , one can select a filter and/or a chip for which a flat calibration frame is calculated . after submitting the jobs, the job status can be viewed at the section of * job status*. the status changes from `` running '' to `` data transfer '' and then to `` finished '' if an error does not happen .the mds server manages a database that contains static information ( host name , ip address , cpu type , memory size ) and status ( load average , number of submitted jobs , living and enabled flags ) of each das server , which can been seen on the mds web page as shown in figure [ fig : mds ] .the living flag stays `` true '' while the mds are receiving a hear beat message from the das server .when a successive five minutes of disconnection happens , the flag changes to `` false '' , and the server is recognized as `` unavailable '' .the `` enabled '' flag is used to prohibit the job submission to the server . when the flag is `` false '' , a job is not submitted to the server .the japanese virtual observatory ( ) is a vo portal service , which federates the distributed vo services and provides data analysis environment through a web browser .jvo is especially going to provide analysis environment utilizing the subaru data .the subaru data currently available on the jvo are : subaru deep field catalog ( sds , sxds ) , suprimecam chip image , and suprimecam mosaic image .we are preparing to provide reduced data of the other subaru instruments .we are also going to implement the data analysis interface for : reduction of raw data with user specified parameters , image manipulation , spectrum fitting , catalog creation from a image , and so on .these data analysis will be executed on the server side , so any plugin tools are required to be installed on the user s machine .we are going to integrate the grid computing system described above to the jvo portal so that enough amount of computing resource is provided to a user .an overview of the jvo system is shown in figure [ fig : overviewjvo ] .the details of the jvo system were described in elsewhere ( shirasaki et al .2006 , shirasaki et al .2006b , tanaka et al .2006 , ohishi et al .figure [ fig : searchresult ] shows the result of cross match query between the catalogs of subaru suprimecam ( optical ) and spitzer ( infrared ) .the jvo provides several visualization tools such as jvo data viewer , jvoplot , by vo india and by cds .the voplot and aladin are java applets .the jvo data viewer and jvoplot are server side web applications , so the data itself are not transfered to the local machine ; they are converted to compact - sized graphics and transfered to the user s web browser .it is especially convenient to view the large data set .figure [ fig : subarudataservice ] shows the result of query for reduced suprimecam data .the service returns a link to the reduced data , the link invokes the on - the - fly data reduction web application , and then a fits file the reduced image is returned .the search result includes also the links to the raw and response frames .the reduction procedure consists of bias subtraction , flat fielding , distortion correction , and astrometric calibration .the flat frames are calculated in advance by the response calculation service described above , and registered on the database .the typical time to execute the reduction is about 10 sec .once the reduced data are generated , it is stored on a cash area to avoid repetitions of the same reduction on the same data .the construction of the subaru advanced data and analysis service has just started this year ( 2006 ) .currently the data of suprimecam is a primary target of the development , but data of other instruments will be available from the jvo .the grid computing system are constructed to obtain enough computing resource to analyze all the suprimecam data in reasonably short time .the jvo portal service is available for everyone at ` http://jvo.nao.ac.jp/portal ` , where currently only the limited functionality is publicly available . to use all the jvo functionality ,user registration will be required .this work was supported by the jsps core - to - core program , grant - in - aid for information science ( 15017289 and 18049074 ) and young scientists ( b ) ( 17700085 ) carried out by the ministry of education , culture , sports , science and technology of japan .

Abstract: we present our activity on making the subaru data archive accessible through the japanese virtual observatory ( jvo ) system . there are a lot of demand to use the archived subaru data from various fields of astronomers . to be used by those who are not familiar with the way to reduce the subaru data , the data reduction should be made before providing for them , or at least it should be easily done without precise knowledge about instrument s characteristic and environment where data are taken . for those purposes , data quality assessment system naqata is developed , which is presented in this meeting by nakata et al . ( 2006 ) , and the science - ready image data are provided for some of the suprimecam data at smoka data service which is presented by enoki et al ( 2006 ) . jvo portal will provide the way to access the reduce data , and also provides the way to reduce from raw data with very few efforts through the user - friendly web browser i / f . to provide such a cpu - intensive service , we have developed a grid computing system . the architecture of this subaru data and analysis system are discussed .