even a quick look at the set of known proteins ( pdb database ) reveals a striking feature . while there are tens of thousands of protein sequences , they only assume some thousands folds . in other words , proteins are highly designable .this concept can be quantified by measuring the number of sequences that fold uniquely into a particular structure .  with the use of a simple 20 letter lattice model of protein folding ithas been shown that the whole issue of estimating the number of sequences that fold to the same conformation is reduced to enumerate how many of them have native energy lying below a threshold , the energy which any sequence with the same composition displays in the conformation structurally dissimilar to the native conformation .the aim of the present paper is to provide a reliable , analytic expression for , which we shall show increases exponentially with the gap between the native energy of the optimal sequence and the threshold energy .this functional form is found to be universal , as it emerges from the central limit theorem .we have furthermore found that while the parameters defining depend on the interaction matrix , they are independent of the particular choice made for the native structure or for the optimal sequence .  in sections 2 and 3 we briefly review the 20 letters lattice model of proteins in general and the question of protein designability in particular .the quantitative , analytic answer to the question of how many mutations a designed protein tolerates is given in section 4 .the conclusions are collected in section 5 .a useful theoretical approach to study protein folding is provided by a simplified lattice model , where the protein is a string of beads that is arranged on a cubic lattice .the configurational energy of a chain of n monomers is given by where is the effective interaction potential between monomers and , and denote their lattice positions and is the contact function . in eq .( 1 ) the pairwise interaction is different from zero when and occupy nearest neighbour sites , i.e. , and for , where indicates the step length of the lattice .in addition to these interactions , it is assumed that on site repulsive forces prevent two amino acids to occupy the same site simultaneously , so that .we shall consider throughout a 20letters representation of protein sequence where is a matrix .a possible realization of this matrix is given in ref . ( table 5 and 6 ) , where it was derived from frequencies of contacts between different amino acids in protein structures .the employment of a matrix ensures that the threshold energy is well defined , depending only on the interaction matrix elements and on the composition of the protein in terms of amino acids .the model we study here is a generic heteropolymer model which has been shown to reproduce important generic features of protein folding thermodynamics and kinetics , independent on the particular potential chosen .however , in using such an approach , one should keep in mind that the labelling of amino acids ( spherical beads all of the same size and with no side chain ) is generic too and may be no obvious relation between those labels and labels for real amino acids .good folder sequences are characterized by a large gap ( compared to the standard deviation of the contact energies ) between the energy of the designed sequence in the native conformation , and the lowest energy of the conformations structurally dissimilar to the native conformation . in other words ,good folders are associated with a normalized gap , quantity closely related to the z score .for example , the 36mer sequence listed in the caption to fig . 1 and called s in the literature , designed by minimizing the energy in the target ( native ) conformation with respect to amino acid sequence for fixed composition has , in the units considered here (  ) , an energy gap and thus a sufficiently large value of ( ) so as to ensure fast folding .in fact , monte carlo simulations carried out at the temperature of 3000 36mers with energies , in the native conformation , lying inside the gap fold in times mc steps ( for caveats see ref . ) . in particulars folds in mc steps .it has been also shown that most of the thermodynamical and dynamical behaviour of designed proteins is controlled by only of the sites . as a consequence , making mutations in these sites , which are called `` hot '' in ref . , one destroys , as a rule , the ability the protein has to fold ( denaturation ) . on the other hand ,the effects of substitutions in any other site ( that can be regarded as `` cold '' ) are small , leading to neutral mutations .while twenty letters heteropolymers capture the essential components of real proteins , it is hardly possible to enumerate all sequences which have a given conformation as their non degenerate ground state .accordingly , it is not possible to calculate the exact designability of protein conformations . to bypass this problem, we shall determine designability from energetic considerations , using a strategy which relies on the fact that all sequences which have an energy lower than fold on short call , in any case in times which are much shorter than that associated with the random search .any sequence of a given length ( e.g. ) can be obtained making mutations ( i.e. substitution of a amino acid in a given site with a different one ) in the minimum energy sequence ( e.g. s in the case of fig .1(a ) ) . consequently, the designability of a conformation can be found starting from the minimum energy sequence , counting how many mutations lay within the gap .if is the change in the energy of the native state produced by a mutation , the energy distribution probability associated with mutations and the total number of sequences that can be produced by introducing mutations in the minimum energy sequence , designability can be defined as so far , we have done nothing more than expressing the problem in another way , since to know the spectrum of mutation energies of the optimal sequence one has again to enumerate all sequences .in fact , it looks like as if we have made things even worse , in that now one has to find the optimal sequence , which is a non trivial problem , and also has to ensure that does not change with mutations .we shall show in the following that the distribution of mutation energies does not depend on the particular structure or on the particular sequence chosen ( provided that ) nor on the contact energy matrix used to design the protein , but only on its composition and on the number of contacts ( or the length , if it is fully compact ) .this observation leaves room to approximations .in fact , if one is able to find an approximate expression for , such an expression will hold for all model proteins of the same length .furthermore , the knowledge of the sequence associated with the global minimum of energy is not necessary ( because all sequences have the same spectrum of mutations ) , only the value of is required .consequently , even if the optimal sequence can not be known without a full enumeration of all sequences , it is allowed to use any other sequence with energy , introducing in this way only an error in the integration boundaries ( and not on the function to be integrated ) .it is then possible to calculate designability of a structure from eq .( 23 ) using an approximate distribution and an approximate value of .the most conservative way to calculate the number of sequences which fold to a conformation is then to use a distribution found only by swappings between the residues of the optimal sequence , as in such a way the composition is conserved and does not change . on the other hand ,since there are also sequences with different composition folding to the same conformation , one is also forced , in principle , to calculate the number associated with pointlike mutations .the values found from swapping of amino acids and from pointlike mutations can be viewed as the lower and the upper limit to designability , respectively .  in figs .2(a ) and 2(b ) we display the unnormalized energy distribution probabilities associated with two composition conserving and with two pointlike mutations of s ( the integral of these distributions being the total number of sequences ) .each of these curves can be well fitted by the sum of two gaussians , whose means are and ( fig .2(a ) , composition conserving case ) and and ( fig .2(b ) , pointlike mutations case ) .standard deviations are and ( fig .2(a ) ) and and ( fig . 2(b ) ) .the behaviour of these two distributions seems very alike , except for the fact that the area below the composition conserving curve is much smaller than that below the pointlike mutations curve .this is because much fewer mutations can be made in the first than in the second case and , consequently , the associated gaussian behaviour is less well defined .  the overall structure of the curves shown in fig .2 can be understood from the fact that the average value of for `` cold '' sites is and for `` hot '' sites is  .accordingly , the low energy peak can be associated with two mutations in `` cold '' sites , while the high energy peak can be associated with a mutation in a `` cold '' site and a mutation in a `` hot '' site .the contribution from mutations in two `` hot '' sites leads to an enhancement of the high energy tail of the curve . concerning the gaussian behaviour, we note that the energies associated with the 19 possible mutations on a given `` cold '' site are uncorrelated .in other words , one has to pay an energy ( concerning the factor one is reminded of the fact that gets contributions from two mutations ) to remove the wild type residue , reflecting the fact that it has been optimized .second , one has to introduce a new residue in the _ niche _ left by the wild type residue .the gaussian shape of the distribution suggests that the _ niche _ is neutral with respect to the new residue and that the new interactions are merely random . to be more precise , the change in energy upon mutations is the difference between the energy needed to remove the original residue ( which is roughly constant and assumes two different values for cold and for hot sites ) and the sum of a number of contact energies associated with the new residue , energies which can be considered as random numbers .being the sum of random numbers , the energy associated with the new residue is forced to respect the central limit theorem , and consequently its distribution approaches a gaussian function .of course , an exact gaussian distribution could be reached only if the number of nearest neighbours of each site were infinite ( while in a cubic lattice this is , at most , five ) . on the other hand , the fact that can be accurately fitted by gaussian distributions ( cf ., e.g. , fig .2(b ) ) testifies to the fact that we are not far from the conditions in which the central limit theorem holds .  while the hypothesis that `` cold '' mutations give raise to gaussian like peaks is quite grounded , due to the uncorrelateness of the energy contributions of `` cold '' sites , it is unlikely that the central limit theorem works properly for `` hot '' sites , whose energy contributions are correlated . in order to calculate the degree of designability of a protein conformation, we only need to know the contributions from cold sites and , consequently , we don not need to better characterize the peaks associated to `` hot '' sites .  we have found that the distribution of mutation energies are rather universal functions .examples of such a behaviour are shown in fig .3 , where 2pointlikes mutations spectra associated with low energy 36mer sequences optimized ( making use of the mj elements of table 6 ) on three different conformation ( cf . figs .1(a)1(c ) ) and with three sequences designed on the same conformation ( fig .1(a ) ) are displayed .similar results have been obtained for chains of different lengths .furthermore , using different interaction matrices lead to the same gaussian behaviour of , although the mean values and the standard deviations are different .this is again a consequence of the central limit theorem .this can be seen from fig .4 , where we display the function associated with two pointlike mutations on s ( cf .1 ) , but making use this time of the interaction matrix elements listed in table 5 of ref . . because the average change in energy upon mutations in cold sites is zero ,while that in hot sites is , it is easy to identify the peaks associated with two cold mutations ( and ) , with one cold and one hot mutations ( and ) , and with two hot mutations ( and ) .  summing up , the function associated with chains of different length and sequence as well as designed on different native conformations overlap quite nicely , suggesting that the spectrum of both composition conserving and non conserving mutations is universal . on the other hand , the actual value of and characterizing the different peaks of the energy distribution probability depend on the matrix used to describe the contact energies among the amino acids .the univerality of the energy distribution probability is in agreement with the interpretation of the main peaks of the spectrum of mutations of a designed protein in term of `` cold '' and `` hot '' sites .in fact , the properties of the `` hot '' sites are rather homogeneous , their contribution to the mutation spectrum being universal . assuming furthermore that the interactions associated to the mutations in `` cold '' sites are random, the resulting energy distribution is gaussian ( and so universal ) , and its standard deviation depends only on the interaction matrix , while its average value depends on the degree of optimization of the wild type monomer .this , in turn , can be approximated by the degree of optimization of the whole chain ( measured by the energy gap ) divided by its length , a quantity which is essentially constant for long chains ( for example , in the case of s this number is ) .the basic idea to calculate the designability of a model protein , as we have discussed above , is to find a simple approximation to the universal distribution of energies associated with mutations onto the optimal sequence , integrate this distribution up to the gap and normalize this result to the total number of mutations that one can make ( cf .( 23 ) ) . as a consequence of this, designability turns out to depend only on the length of the protein ( through the total number of mutations ) and on the gap . in order to calculate using eq .( 23 ) we have first to know the total number of sequences that can be obtained by making sequence conserving mutations ( swappings ) in the optimal sequence .this number can be obtained by counting the number of ways one can select sites , multiplied by the number of permutations of these sites which move all the residues .that is where is the number of ways one can permute m sites in such a way that only positions are kept fixed . from the relation it is possible to extract the expression for , for large , one can use the stirling approximation for the factorials in eqs .( 46 ) , and keep only the largest exponent term in the sum ( saddle point approximation ) , obtaining .the constant can be determined from the relation , which for leads to .  to proceed further in the calculation of , one needs to find a simple approximation to . for this purpose, we shall express the energy distribution of an arbitrary number of mutations as a convolution of functions associated with the swapping of two amino acids .the validity of this approximation rests on the ansatz that every couple of mutations affect the energy of the native state independently of the other couple of mutations .this approximation is expected to work also for large values of , where the probability of mutating neighbouring sites is not negligible , because the contact energy associated with the mutated residues are in any case random quantities with average zero ( cf .the discussion in the previous section ) . within this scenario ,the number of folding sequences displaying mutations and whose energy in the native conformation lies inside the energy gap can be written as making use of the energy distribution probability associated with an amino acid swapping ( composition conserving mutations ) or with two point like mutations ( composition non conserving mutations ) one obtains the lower and the upper limit of the designability of a conformation .  in what followswe shall essentially discuss the case of composition conserving mutations . if is lower than the peak associated with mutations in `` hot '' sites ( as in the case of the sequence s where , cf .2 ) , one should convolute only the peak of associated with mutations in `` cold '' sites . exploiting the fact that the convolution of gaussian distributions , of the form is a gaussian distribution with average and standard deviation ,it is possible to write for ( in the case of s this condition means ) one can neglect the first exponential factor in the integral , in which case the integration can be carried out analytically , leading to - 1\right ) \label{eq6}\ ] ] where the substitution has been made .this equation tells us that designability increases exponentially with the gap . in other words ,the number of sequences folding to a ( compact ) conformation is determined only by the gap associated with the minimum energy sequence .we have shown that the concepts of designability ( i.e. number of sequences folding to a given conformation ) and foldability ( i.e. , thermodinamical stability of the sequences with low energy on the given conformation , expressed by the gap ) are intimately connected by eq .( [ eq6 ] ) . if a protein is stable in its native conformation , such native conformation is necessarilly highly designable .vice versa , if a conformation is highly designable , there exist sequences with a large gap folding to it .  to give a numerical evaluation of protein conformations , we make use of eq .( [ eq5 ] ) ) in the form ,\ ] ] where does not depend on and , for the case of the structure displayed in fig .1(a ) , assumes the value ( in keeping with the fact that , and ) . in the case in which , which in the case of the 36mer under discussion implies , one can keep only the largest term in the above sum . within this approximation one can write , a number to be compared with .one can mention , for the sake of completeness , that the number of sequences within the gap obtained by pointlike mutations ( which is the upper limit to designability ) , is well fitted by the function , while the total number of sequences is .the degree of designability of a given conformation depends exponentially on the energy gap .since the number of folding sequences is given by the integral of a universal function ( the mutation energy distribution ) carried up to , a quantity which also determines the thermal stability of the designed protein , one can conclude that designability and thermal stability are strongly interconnected .in other words , sequences displaying large gaps are both thermally stable and highly designable . even sequences displaying , in the native conformation , a small gap fold on short call and share ( in the compaction process ) the conserved contacts leading to local elementary structures and to the ( post critical ) folding nucleus .consequently , it is possible to obtain from them , through composition conserving mutations , other sequences folding to the same native conformation and displaying a large gap . in other words ,any sequence able to fold fast , folds to a highly designable conformation .we have estimated that there are of the order of sequences folding to a compact 36mer conformation , over a total of .this is only the lower limit , but let us assume that it describes well the typical degree of designability of the designed protein .is this number small or big ?the answer to this question has , of course , important implications from the evolutionary point of view . if good folders were distributed homogeneously in the space of sequences ( like in the case of rna ) the important parameter would be their density , that is .this number would be very low , preventing sequences from moving along neutral pathways ( which are collections of sequences folding to the same conformation and differing by single mutations ) .such a scenario is very unfavourable for evolution .the situation is however quite different for proteins .in fact , it has been shown that good folders group themselves in clusters and superclusters , giving rise to a quite an inhomogeneous landscape .consequently , the relevant parameter which measures the designability of a conformation is the total number of sequences which conserve , in any way , the energy gap .this number ( ) is very large in particular in keeping with the fact that over a life span of the order of 60 mutations occur in the genome of each person ) .99 e. i. shakhnovich , phys .lett . * 72 * , 3907 ( 1994 ) v. i. abkevich , a. m. gutin and e. i. shakhnovich , j. chem .phys * 101 * , 6052 ( 1994 ) r. goldstein , z. luthey schulten , p. wolynes , proc .usa * 89*. 4918 ( 1992 ) a. sali , e. shakhnovich and m. karplus , j. mol .* 235 * , 1614 ( 1994 ) r. a. broglia , g. tiana , h. e. roman , e. vigezzi and e. i. shakhnovich , phys .* 82 * , 4727 ( 1999 ) s. miyazawa and r. jernigan , macromolecules * 18 * , 534 ( 1985 ) n. go , int . j. peptide prot .res . * 7 * , 313 ( 1975 ) k. f. lau and k. dill , macromolecules * 22 * , 3986 ( 1989 ) e. i. shakhnovich , a. m. gutin , j. chem .phys . * 93 * 5967 ( 1989 ) e. i. shakhnovich , curr .struct . biol .* 7 * , 29 ( 1997 ) e. i. shakhnovich , folding and design * 1 * , r50 ( 1996 ) j. bowie , r. luthey schulten , d. eisenberg , science * 253 * , 164 ( 1991 ) g. tiana and r. a. broglia , j. chem .phys . * 114 * , 2503 ( 2001 ) v. i. abkevich , a. m. gutin and e. i. shakhnovich , j. chem . phys .* 101 * , 6052 ( 1994 ) v. abkevich , a. gutin and e. shakhnovich , biochemistry * 33 * , 10026 ( 1994 ) n. socci , w. bialek , j. onuchic , phys .e * 49 * ( 1994 ) 3440 d. klimov and d. thirumalai , phys .lett * 76 * ( 1996 ) 4070 g. tiana , r. a. broglia , h. e. roman , e. vigezzi and e. i. shakhnovich , j. chem . phys . * 108 * , 757 ( 1998 ) r. a. broglia and g. tiana , j. chem .( in press ) strictly speaking , the monte carlo algorithm was to designed to study equilibrium properties of systems with many degrees of freedom .nonetheless , it has been shown that , being equivalent to solving the fokker planck equation for diffusion in a potential , it can be helpful also in studying the kinetical properties of complex systems , provided that the fokker planck approximation is valid ( i.e. , moves are local and the potential changes smoothly on the diffusion lenght scale ) .furthermore , rey and skolnick have shown that the folding trajectories obtained with monte carlo simulations are consistent with those obtained with real molecular dynamics calculations .n. metropolis , a. w. rosenbluth , m. n. rosenbluth , a. h. teller and e. teller , j. chem . phys . * 21 * , 1087 ( 1953 ) k. kikuchi , m. yoshida , t. maekawa and h. watanabe , chem .196 , 57 ( 1992 ) j. rey and j. skolnick , chem . phys . * 158 * , 199 ( 1991 ) this is equivalent to assume that different degrees of optimization are mainly due to `` cold '' sites , while `` hot '' sites are always optimized at the same degree . in the case of pointlike mutationsthis can not be done , because the associated is not zero for negative values of the energy , so that energies within the gap can be obtained from mutations in `` hot '' sites , compensated by mutations with negative energy values in other sites .r. a. broglia , g. tiana , s. pasquali , h. e. roman , e. vigezzi , proc .usa * 95 * , 12930 ( 1998 ) p. schuster and w. fontana , physica d * 133 * , 427 ( 1999 ) g. tiana , r. a. broglia and e. shakhnovich , proteins * 39 * , 244 ( 2000 ) t. e. creighton , _ proteins _ , j. freeman and co. , new york ( 1993 )

Abstract: protein folds are highly designable , in the sense that many sequences fold to the same conformation . in the present work we derive an expression for the designability in a 20 letter lattice model of proteins which , relying only on the central limit theorem , has a generality which goes beyond the simple model used in its derivation . this expression displays an exponential dependence on the energy of the optimal sequence folding on the given conformation measured with respect to the lowest energy of the conformational dissimilar structures , energy difference which constitutes the only parameter controlling designability . accordingly , the designability of a native conformation is intimately connected to the stability of the sequences folding to them .


the current generation of earth - based interferometric gravitational wave ( gw ) detectors are sensitive to differential length variations with amplitude spectral densities as small as  m . the next generation of detectors are designed to be about a factor of ten more sensitive and in several cases they are either in the advanced planning stages  or have already begun construction  . in order to take full advantage of the scientific reach afforded by these detectors , continuous calibration with accuracy and precision approaching the 1% level will be required . thus , detector calibration is an active area of research for all gw projects , with a significant percentage of resources being devoted to calibration - related activities .these activities include amplitude and phase calibration in both the frequency domain  and in the time domain  .historically , the ligo project has relied on a calibration method that requires extrapolation from test mass displacements that are about twelve orders of magnitude larger than the expected apparent displacements that will be caused by gravitational waves . while the precision of this method has improved over the more than five years it has been employed , the possibility of a large systematic error has not been eliminated until now .  to search for systematic errors in the ligo calibration procedure ,we have employed three fundamentally different actuator calibration techniques : the _ free - swinging michelson _method  that relies on the wavelength of the laser light in the interferometer , the _ photon calibrator _method  that uses the recoil of photons from an auxiliary laser source to induce calibrated test mass displacements with amplitudes close to the detector sensitivity limit , and the _ frequency modulation _ method  that relies on the frequency - to - length transfer function for a fabry - perot optical cavity .our investigations have spanned the frequency range from 90 hz to 1 khz and the range of actuation amplitudes from m to m.  the closed - loop calibration of the ligo displacement actuators is described in the following section , and an overview of each of the three calibration methods is presented .measurement results and estimates of the uncertainties associated with each method are given in section [ sec : measresultsuncert ] .conclusions and implications for future calibration work are discussed in section [ sec : conclusions ] .the ligo detectors are power - recycled michelson interferometers with fabry - perot arm cavities . the interferometer optics are suspended as pendulums and actively controlled to maintain resonance conditions .changes in the difference between the lengths of the interferometer s arms , the degree of freedom most sensitive to gravitational waves , are sensed at the anti - symmetric port .the differential arm length ( darm ) control system uses a variation of the pound - drever - hall ( pdh ) radio - frequency locking technique  with electromagnetic displacement actuators consisting of voice coils interacting with magnets glued to the back surfaces of the mirrors .the idealized force - to - length transfer function is proportional to the inverse of the square of the excitation frequency .the darm control loop is shown schematically in figure [ fig : darm ] , and in the context of the interferometer in figure [ fig : ifo ] .the darm readout signal is amplified , filtered , and then directed to the voice coil actuators on the mirrors at the ends of the arm cavities .these mirrors , together with the input arm cavity mirrors , are the _ test masses _ for gravitational wave signals .reconstruction of differential length disturbances from the darm readout signal requires correcting for the darm closed - loop response .measurement of the overall darm loop transfer function is relatively straightforward .however , measurement of the transfer functions for components of the loop such as the sensing and actuation paths is more difficult .calibrating the response of the interferometer to differential length variations is directly dependent on the characterization of the actuation function .in addition to the voice coil actuators and the suspended test masses , the actuation path includes actuation electronics that convert the drive voltages to coil currents . these electronics have two modes of operation , a low - noise _ run _ mode , and an _ acquire _ mode that allows larger drive amplitudes .calibration of this actuation chain is the focus of this article .the technique that has been the traditional calibration method employed by ligo is referred to as the free - swinging michelson method because it relies on measurement of michelson interference fringes when the suspended optics are swinging freely .it thus uses the wavelength of the interferometer s laser light as a length reference , and to calibrate the end test mass ( etm ) actuation function via a series of measurements made with both the interferometer and the actuation path electronics in various configurations .the required drive amplitudes are on the order of m. this process is described in detail in ; an overview of the procedure is given here .the first step in this process is to misalign the etms and the power recycling mirror , then align the input test masses ( itms ) and beam splitter to form a simple michelson interferometer as shown in figure [ fig : fsm]a .the length control servo electronics are configured to lock this setup on a dark fringe , i.e. with destructive interference of the light from each arm at the anti - symmetric port where the photodetector is located .two transfer function measurements are made in this configuration , the overall open - loop transfer function ( exc . 1 in figure [ fig : fsm ] ) and the transfer function from actuation of an itm ( exc. 2 ) to the michelson readout signal .the second measurement is repeated for the other itm .then , the feedback control is switched off , allowing the optics to swing freely in response to the seismic motion filtered by the vibration isolation systems . withthe loop unlocked , the time series of the photodetector output is recorded as the michelson length difference changes , causing the output to vary between the bright - fringe and dark - fringe levels .the difference between the maximum and minimum outputs corresponds to relative itm motion of one - fourth of the wavelength of the laser light , thus providing a calibration of the anti - symmetric photodetector output signal in this michelson configuration . combining this result with the transfer functions resulting from itm actuation and the overall open - loop transfer function yields a calibrated actuation function for the itms .the next step in the process is to misalign one of the itms and realign the etm on the opposite arm .the servo electronics are then configured to feed back to the position of the etm forming a resonant fabry - perot arm cavity as shown in figure [ fig : fsm]b .transfer functions from itm and etm actuations ( exc .3 and 4 ) to the single - arm readout are then measured .their ratio , combined with the calibration of the itm actuation function yields the etm actuation function . making similar measurement with only the other interferometer arm cavity aligned yields the calibrated actuation function for the other etm .the swept - sine measurements that are performed in the single - arm configuration require the actuation path electronics to be in the acquire mode .however , in the acquire mode the coupling of electronics noise to test mass displacement is 3 - 4 orders of magnitude larger than in the run mode , which is used for gw searches .there are four parallel paths for the four voice coil actuators on each etm and several components in each path .measuring and combining the electronics transfer functions with overall precision approaching 1% is a task that has proved difficult to achieve . converting calibrations performed using the free - swinging michelson method to the high - sensitivity , fully - locked interferometer configuration requires correcting for differences between the acquire and run mode actuation paths .the photon calibrator method uses an auxiliary , power - modulated laser to induce calibrated displacements via the recoil of photons from the surface of the etm .photon calibrators have been used before  and are currently being employed at several gw observatories  .a detailed description of the ligo photon calibrators can be found in .  to avoid sensing the region of the etm that is elastically deformed by the photon pressure  ,the ligo photon calibrators have evolved to a two - beam configuration with the beams symmetrically displaced about the center of the etm as shown in figure [ fig : pcalandvacuumchamber ] .the spot locations and powers in the two beams are balanced to minimize induced rotations which , for a mis - centered interferometer beam , would cause apparent length variations .the total sensed test mass motion is given by \ ] ] where is the excitation frequency , is the modulated laser power reflecting from the etm , is the angle of incidence , is the mass of the etm , is the speed of light , and are the weighted - average photon calibrator and interferometer beam centering offsets and is the moment of inertia of the etm . in ligo ,the typical power - modulation amplitude is about 100 mw , the laser wavelength is 1047 nm , the angle of incidence is about 10 degrees , and the mass of the etm is about 10.3 kg .typical beam offsets are less than a few cm , so the rotation - induced apparent displacement is more than 100 times smaller than the longitudinal displacement . to minimize bulk elastic deformation caused by the photon calibrator beams , they are displaced from the etm center by about 0.65 times the radius of the etm , where finite - element modeling indicates that the coupling to bulk deformation sensed by a centered interferometer beam is minimized    accuracy of calibration using the photon calibrators is directly dependent on estimates of the absolute power reflecting from the etm .temperature - stabilized ingaas photodetectors mounted on integrating spheres and calibrated at nist ( national institute of standards and technology ) are employed to calibrate an internal power sensor .they are also used to measure the transmissivities of the vacuum windows and the reflectivities of the etms .the internal sensor provides a continuous monitor of the photon calibrator output power .calibration of the etm actuation coefficient at a given frequency is achieved by modulating the etm position using the voice coil actuators at the desired frequency and simultaneously modulating the laser power at a nearby frequency , typically offset by about 0.1 hz. the ratios of the amplitudes of the lines induced in the amplitude spectral density of the darm readout signal combined with the calculated etm motion caused by the photon calibrator yields a calibration of the voice coil actuation path .this calibration is to first order insensitive to changes in the interferometer operating conditions because the frequencies of the excitations are closely spaced and the measurements are made simultaneously .these measurements are performed with the interferometer locked in the configuration that is used during gw searches and with actuation forces inducing displacements that are close to the sensitivity limit .frequency modulation provides a force - free method for calibrating the etm voice coil actuators . by modulating the frequency of the laser light in a single - arm configuration, we create an effective length modulation detected by the pdh sensor .the magnitude of the induced effective length modulation is given by the dynamic resonance condition for a fabry - perot cavity  , where is the normalized frequency - to - length transfer function , is the laser frequency , is the length of the arm cavity , and is the frequency of the modulations , and . for the frequencies considered in our measurements , much lower than the cavity free spectral range , such that   as described in more detail in and shown schematically in figure [ fig : vco ] , the frequency modulation is applied via a frequency shifter that is embedded in the frequency stabilization servo that is used to lock the laser frequency to a reference cavity .the frequency shifter uses a voltage - controlled oscillator ( vco ) that drives a double - passed acousto - optic modulator to modulate the frequency of the laser light directed to a three - mirror suspended mode cleaner .calibrating the frequency shift induced by a sinusoidally - varying control voltage is a key step in applying this technique . in practice, we calibrate the vco by locking it to a frequency synthesizer that is itself locked to a frequency standard .the frequency modulation induced by an applied offset is determined by measuring the frequency modulation sideband - to - carrier ratio using a spectrum analyzer .the frequency - modulated light passes through the mode cleaner , which acts as a low - pass filter for frequency fluctuations .the mode cleaner filtering is measured via a power - modulation transfer function using photodetectors located both upstream and downstream of the mode cleaner cavity .this filtering is well approximated by a single pole at a frequency of about 4 khz .as with the photon calibrator technique , we generate two peaks in the spectrum of the single - arm readout signal , in this case by simultaneously modulating the position of the etm using the voice coil actuators while applying the frequency modulation at a frequency separated by about 0.1 hz .excitation amplitudes are on the order of to m , with the lower bound for frequency modulation dictated by the mode cleaner control signal background at the input to the vco and the upper bound for length modulation governed by saturation concerns in the run mode actuation path electronics .comparing the heights of the peaks induced in the single - arm readout signal and multiplying by the vco calibration yields the calibration of the voice coil actuation . unlike the free - swinging michelson transfer functions which are typically measured at many frequencies with large drive amplitudes , the frequency modulation measurements use long integration times at a single frequency with the voice coil actuation electronics in the run mode .the difficult step of precise compensation for the differences in run versus acquire electronics paths is therefore not required .the measurements reported here were performed at the ligo hanford observatory ( lho ) during a period dedicated to calibration - related activities at the end of the s5 science run  in october and november of 2007 .two interferometers were operating at lho , the h1 interferometer with 4-km - long arm cavities and the h2 interferometer with 2-km - long arms .the photon calibrators for three of the four etms had already been converted to two - beam configurations . only the h1 y - arm system was still in a one - beam configuration with the beam centered on the etm .the photon calibrator and frequency modulation measurements were similar in that they were made at a few discrete frequencies .long integration times ( seconds ) and multiple averages enabled assessment of the statistics for the measurements and reduction of the standard errors . on the other hand ,swept - sine measurements with approximately fifty measurement frequencies between 90 hz and 1 khz were used for the free - swinging michelson technique .this is not a fundamental requirement for this method , rather it is the type of measurement found to be most useful for estimating the actuation function over the relevant band of frequencies . we thus compare swept - sine measurements for the free - swinging michelson method with single - frequency measurements at a few discrete frequencies for the other two methods .  the results of measurements carried out with all three techniques are plotted together in figure [ fig : compare ] . for each datum ,the calculated actuation coefficient is multiplied by the square of the measurement frequency to facilitate comparison with a simple functional dependence .the free - swinging michelson data , plotted without error estimates , are from two separate calibration sequences that were carried out on consecutive days . for better visibility, the error bars for the photon calibrator and frequency modulation data are estimates of statistical uncertainties only , with a representative standard error for the averaged measurements .estimates of systematic uncertainties for each calibration method  have intentionally been omitted so that the overall systematic uncertainty can be evaluated by comparing the results of the three methods with statistical precision indicated by the error bars , or the scatter in the data for the free - swinging michelson results . for each etm ,the dashed horizontal lines indicate the simple mean value for the free - swinging michelson method and the weighted mean values for the photon calibrator and frequency modulation methods .all data are normalized to the average of the mean values for the three methods , .the h1 y - arm photon calibrator is in a single - arm configuration , therefore local elastic deformation caused by the photon calibrator forces and sensed by the interferometer beam causes the overall actuation function to rise dramatically with increasing frequency . we thus fit a curve with the functional form predicted by hild , et al . to the data in figure [ fig : compare ] instead of averaging over frequencies .the low frequency asymptote is the actuation coefficient we would expect for a two - beam photon calibrator operating on this mass .  .the free - swinging michelson data are plotted without error bars ; for visibility , statistical error bars are plotted for the other two methods .the single - beam h1 y - arm photon calibrator data show the influence of local elastic deformation by photon radiation pressure.,scaledwidth=100.0% ]  the data for all three measurement methods exhibit variations with frequency that appear to be inconsistent with a simple frequency dependence .this is likely due to either frequency - dependent systematic errors in the calibration methods or frequency - dependent variations in the actuation path electronics in run mode . for the free - swinging michelson data , the sensing function and errors in making the run / acquire correction can also introduce frequency - dependent variations .potential sources of systematic errors for the free - swinging michelson technique include time - dependent alignment variations during sequential measurements , measuring in different interferometer and electronics configurations , and extrapolation over nearly 12 orders of magnitude in actuation range .overall systematic uncertainty , estimated from the observed spread in the data and from propagating errors through the many steps of the technique , is approximately 10% . the primary identified sources of systematic uncertainty for the photon calibrator method are rotation due to beam centering offsets and absolute power calibration . with reasonable centering tolerances and the demonstrated power calibration accuracy ,the estimated total systematic uncertainty can be reduced to the order of 1% . for the frequency modulation method , the dominant sources of potential systematic errors are the calibration of the vco which relies on accurate measurement of the sideband - to - carrier ratios and extrapolation over approximately 5 orders of magnitude in actuation range . in practice , the overall estimated uncertainty for this method due to known sources of systematic errors can also be reduced to the 1% level .  all calculated actuation coefficients for all frequencies , for all masses , and for all three techniques fall within the % ranges plotted in figure [ fig : compare ] .the maximum difference between the mean values over all frequencies of any two methods for any etm is less than 8% .the maximum difference between the mean value for any method and the average of the mean values for all three methods , , for any etm , is 3.7% ; the standard deviation of the twelve differences ( all four etms ) is 2.4% .errors in the measurement of the actuation functions directly translate into errors in the inferred responses of the ligo detectors to length variations .potential errors in the determination of the actuation functions have been the principal concern regarding overall detector amplitude calibration uncertainty .we have presented the results of measurements made to compare three intrinsically different test mass actuator calibration methods in order to bound potential systematic errors in the free - swinging michelson method , the main calibration technique traditionally used by ligo .the observed level of consistency , in light of the differences in the techniques from fitting interference fringes in a michelson configuration to photon pressure actuation to laser frequency modulation , in the methods of application from michelson and single - arm configurations to the fully - locked configuration used during gw searches , and in the range of actuation from m to m , indicates that the actual voice coil actuation functions are within the bounds of these measurement results .this , together with the independent measurement of detector displacement sensitivity afforded by the photon calibrator , gives us confidence that the ligo detector calibration is within the stated uncertainty estimates .  as we have described above , calibration of the displacement actuators of an interferometric gw detector can be a tedious and complicated enterprise .future gw detectors will have even more sophisticated actuation and readout chains .with optimal signal extraction requiring overall calibration accuracies of 1% in amplitude , plus constraints on phase and timing , continued improvement of calibration methods and procedures will be imperative .for instance , ongoing finite - element modeling of actuation forces interacting with ligo - style test masses indicates that calibration at the 1% level will require correcting for the bulk deformation induced by the actuation forces .this is particularly relevant at frequencies near and above 1 khz .techniques such as the photon calibrator method that can provide on - line calibration of the darm readout signal during gw searches will be particularly attractive .multiple parallel calibration efforts will likely be required to achieve these goals .our experience has exposed the benefits of employing several different methods to search for and mitigate potential sources of systematic errors .the need for precise and accurate on - line calibration dictates that calibration requirements must be an integral part of the design of gravitational - wave detectors to achieve their full scientific potential .we gratefully acknowledge the support of the ligo scientific collaboration and the ligo laboratory for construction and operation of the ligo detectors .we also thank the national science foundation for support under grant phy-0555406 .ligo was constructed by the california institute of technology and the massachusetts institute of technology with funding from the national science foundation and operates under cooperative agreement phy-0107417 .this document has been assigned ligo laboratory document number p0900155 .99 abbott b , 2009 _ _ * 72 * 076901 acernese f , 2006 _ _ * 23 * s63542 lck h , 2006 _ _ * 23 * s718 takahashi r and the tama collaboration 2004 _ _ * 21 * s4038 the virgo collaboration 2008 _ virgo doc ._ vir-0089a-08 ( https://tds.ego-gw.it ) kuroda k and the lcgt collaboration 2006 _ _ * 23 * s21521 harry g for the ligo scientific collaboration 2009 to be submitted to _amaldi 8 conf ._ lck h , 2009 submitted to __ lindblom l 2009 , _ _ d * 80 * 042005 - 17 landry m for the ligo scientific collaboration 2005 _ _ * 22 *s98594 rolland l 2009 to be submitted to _ amaldi 8 conf ._ hewitson m for the ligo scientific collaboration 2007 _ _ * 24 * s44555 tatsumi d and tsunesada y and the tama collaboration 2004 _ _ * 21 * s4516 siemens x , allen b , creighton j , hewitson m and landry m 2004 _ _ * 21 * s172336 aso y , 2009 _ _ * 26 * 055010 ( 13pp ) marion f , mours b and rolland l 2008 _ virgo doc . _ vir-078a-08 ( https://tds.ego-gw.it ) hewitson m , grote h , hild s , lck h , ajith p , smith j r , strain k a , willke b and woan g 2005 _ _ * 22 * 425361 telada s , tatsumi d , akutsu t , ando m , kanda n and the tama collaboration 2005 _ _ * 22 * s97584 adhikari r , gonzalez g , landry m and oreilly b ( for the ligo scientific collaboration ) 2003 _ _ * 20 * s90314 goetz e , 2009 accepted for publication in _ _ ( _ preprint _ gr - qc/0910.5591 ) goetz e and savage jr r l 2009 , in preparation for submission to _ _drever r w p , hall j l , kowalski f v , hough j , ford g m , munley a j and ward h 1983 _ appl . phys . _b : _ lasers opt ._ * 31 * 97105 regehr m w , raab f j and whitcomb s e 1995 _ opt ._ * 20 * 15079 clubley d a , newton g p , skeldon k and hough j 2001 _ _ a * 283 * 858 mossavi k , 2005 _ _ a * 353 * 13 rolland l , marion f and mours b 2008 _ virgo doc . _ vir-053a-08 ( https://pub3.ego-gw.it ) hild s 2007 , phd thesis university of hannover hild s , 2007 _ _ * 24 * 56818 badan m a , landry m , savage r and willems p 2009 _ ligo doc ._ t0900401 ( https://dcc.ligo.org ) rakhmanov m , savage jr r l , reitze d h and tanner d b 2002 _ _ a * 305 * 23944 kissel j , in preparation

Abstract: we describe three fundamentally different methods we have applied to calibrate the test mass displacement actuators to search for systematic errors in the calibration of the ligo gravitational - wave detectors . the actuation frequencies tested range from 90 hz to 1 khz and the actuation amplitudes range from m to m. for each of the four test mass actuators measured , the weighted mean coefficient over all frequencies for each technique deviates from the average actuation coefficient for all three techniques by less than 4% . this result indicates that systematic errors in the calibration of the responses of the ligo detectors to differential length variations are within the stated uncertainties .


when the boards of different organizations have members in common when their boards _ interlock_they can synchronize both their values and behaviors in the absence of explicit central control  .organizations that share key personnel in this fashion can reap the benefits of network connections and solve coordination problems  .board interlock is widespread in free - market societies , where it emerges in the business sector as a response to decentralization  .board interlock is also seen in the donation - based charity sector , where it helps coordinate of efforts and share of information  , and enhances both a nonprofit s perceived legitimacy and its capacity to acquire resources  . in the united states , board interlock spans multiple sectors , and links together the nonprofit , commercial , and political worlds  .much less is known about how interlock emerges as a response to the problem of decentralization within authoritarian governments .an authoritarian government that decentralizes may do so in part to take advantage of the benefits that accrue when many different problem - solvers operate with limited communication  . as in the non - authoritarian case, organizations may respond to decentralization by sharing board members in order to coordinate .  for a governmentconcerned with the dangers of independent agents , this interlock may be a benefit . the coordination induced by the resultant board interlock may reduce the independence between organizations and make the system easier to control .however , these benefits exist only if the government maintains control of the most central organizations in the resulting network .if it does not , board interlock may shift from an opportunity to a threat : organizations may not only reap the benefits of coordination , but now do so by coordinating around an independent agent .board interlock is crucial to understanding `` infrastructural '' forms of state power  .infrastructural power refers to the capacity of the state to act through civil society , by penetrating , and thereby influencing , its institutions .infrastructural power is often contrasted with despotic power : the ability of state elites to act without formal negotiations with civil society , through top - down , unilateral action .the coordination enabled by board interlock provides an important means by which a state might amplify infrastructural power or , conversely , a means by which non - governmental actors may reduce it . to study how these tensions play out in the state - society relationship in the real world , we present here the first network - based study of the rapidly - growing nonprofit sector in mainland china .while charities and `` social organizations '' appear early in china s history , the majority were closed down during the cultural revolution in the 1960s and 1970s  .the nonprofit sector only re - emerged during the reform era of the 1980s , as part of the government s push to decentralize and devolve power away from direct state control  .  because the sector has expanded so rapidly , many scholars today ask whether or not it represents the rise of a chinese civil society : a dense network of groups that bring together citizens to accomplish activities outside of government control .the concept of civil society has its origin in the 19th century , when alexis de tocqueville connected the early stages of american democracy to the growth of voluntary associations of ordinary citizens for everything from the promotion of temperance to the founding of schools  .ever since , political theorists and sociologists have tried to understand the role that these associations might play in the liberalization of authoritarian regimes and the early stages of democratic rule  .the concept of civil society has continued to evolve ; in a recent study of the illegal ngo sector within china , ref . quotes ref . to describe a neo - tocquevillian concept of civil society as `` an autonomous sphere of social power within which citizens can pressure authoritarians for change , protect themselves from tyranny , and democratize from below '' . for these reasons ,hard - line members of the chinese government are liable to view the very concept of civil society as a `` trap ''  .  yetthe existence of non - governmental associations does not necessarily imply a civil society in the tocquevillian mode or even a threat to authoritarian rule .while countries in the west have accepted nonprofits that operate independent of government control , foundations in china must contend with a one - party system potentially intolerant of organizations that might hold it accountable or draw attention to its deficiencies  .concerns about the lack of autonomy in the nonprofit sector have led many observers to talk in terms of _ state - corporatism _ , where the nonprofit sector is an auxiliary and dependent system of the state . in the classic definition of ref . , the relevant organizations in state - corporatism parallel those of government agencies , being `` singular , noncompetitive , hierarchically ordered , sectorally compartmentalized , interest associations exercising representational monopolies '' .   for these reasons , a central theme of research into the chinese nonprofit world is how much autonomy exists in the presence of state control  .previous studies have documented the strategies and tactics of individual nonprofits , either through case studies or the identification of qualitative patterns of behavior across multiple cases  .  civil society , however , is more than just the existence , and even the autonomy , of non - governmental organizations .it is how these organizations connect together , in a horizontal fashion , to form something more than a catalog of distinct endeavors  : organized `` multiple , overlapping , and intersecting sociospatial networks of power ''  .  to understand civil society in china , in other words, we must study not only how the state acts on individual foundations , but also how it interacts with the networks through which these foundations share personnel , information , and resources .the infrastructural power the state exercises may be both enhanced , and dissipated , by the horizontal connections between the organizations it penetrates .board interlock is one of the primary mechanisms for this self - organization to take place , and yet we know next to nothing about how this process has unfolded , and the results of this evolution in twenty - first century china .we will study the chinese state - society relationship by looking at the evolution of the non - profit board interlock network . to do this , we draw on a large dataset of officially - registered nonprofit foundations. this dataset records not only important information about each foundation , but also the list of board members , enabling us to construct the board interlock network .our analysis can then operate at two levels simultaneously : ( 1 ) at the level of the individual foundation , and ( 2 ) at the level of the network , where edges between foundations are defined by the sharing of board members .  at the level of individual foundations ,our data show the high level of presence of state officials on foundation boards .examination of how the number of government officials varies by working areas and foundation type shows how the presence of state officials correlates with activities , and legal statuses , that the government is expected to be most concerned to control .  at the network level, we find that board appointments connect together a significant fraction of legal chinese foundations into a single network .our results show the existence of network elites , associated with business entrepreneurs and their foundations , that form preferential ties to each other .this subnetwork appears to preferentially exclude government officials from its most central nodes , providing evidence that the network acts in part to frustrate the magnification of individual - level penetration that might be expected to arise in the presence of board interlock .our findings suggest the emergence of a form of network autonomy that exists despite high levels of individual - level government appointments to nonprofit boards . at the same time , the association of this network autonomy with the business elite rather than `` ordinary '' citizens means that this autonomy may not lead to the kind of pluralism associated with a tocquevillian civil society .our primary dataset is the research infrastructure of china foundations ( ricf  ) , a database containing the records of the 3,344 legally - registered foundations within mainland china between 1981 and 2013 .information about each foundation is drawn from six different sources , including both official government reports and information submitted to the government , or reported on websites , by the foundations themselves . comparing ricf s counts to other reference sources, the ricf s data appears to be at least 90% complete .the data is restricted to foundations allowed to conduct fundraising ; while these foundations are outnumbered by the much larger number of less formal `` associations '' , they are the most developed form of non - profit institution , and control just over 76% of all non - profit funding in the nation . ) ; this amounts to a large fraction of the 45.9 b of non - profit funding , tracked by the ministry of civil affairs of china in 2013 , for all `` associations '' and related classifications  . ]ricf strives to be as comprehensive as possible ; it includes foundations that may , for example , may be essentially defunct . within ricf datais a subset of foundations that have undergone an evaluation process , which rates the foundations according to standard criteria ; foundations who receive a `` 3a '' or above ( 3a+ ) are considered to have passed this evaluation .  for each foundation, ricf logs the names , gender , and date of birth of the board members .this allows us to resolve name collision and therefore construct the board interlock network : two foundations are connected when they share one ( or more ) board members . for simplicity in this analysis , our network is unweighted : we consider only the presence or absence of at least one shared member , and do not distinguish whether links are created by sharing presidents , secretaries , or ordinary members .the ricf data also contains the date of incorporation for each foundation , allowing us to study how the final network assembles over time .three critical variables help us characterize foundations at the individual level .  _public fundraising _ vs. _ non - public fundraising_. the main legal distinctions in the chinese nonprofit sector governs the scope of fundraising .`` public fundraising '' foundations are allowed to raise money from the general public for example , through fund drives and advertising while `` non - public fundraising '' foundations may not ( as shorthand , we refer to these as `` public '' and `` non - public '' hereafter ) . moreover , public foundations are further constrained by geography ; `` central - level '' foundations may raise funds at the national scale , while province - level and city - level foundations are restricted geographically .the chinese charity law , effective from 1 september 2016 , will nullify the distinction between public and non - public fundraising ; however , the ability of organizations to raise funds from general public will still be controlled by license issued from the state .  _ politically sensitive _vs. _ politically non - sensitive_. we supplement the ricf by hand - coding the foundations mission statements by whether or not they are involved in a potentially controversial or politically sensitive area ( `` sensitive '' vs. `` non - sensitive '' ) .tracking this variable allows us to look for systematic attempts to selectively control certain topics .if a foundation has one or more of the following characteristics it is coded as sensitive , " otherwise it is coded as non - sensitive " :  1 .  involving advocacy , _e.g. _ , human rights , labor issues , and environmental policy .2 .  involving international affairs , _ e.g. _ , programs promoting international cultural exchanges .3 .  involving religious or ethnic issues , _ e.g. _ , christian activities and tibet issues .4 .  involving the police or the legal system , or related `` social stability '' ( _ weiwen _ ) issues .  in order to control the researchers bias toward coding ,two assistants , who were unaware of the research purpose , were asked to independently classify foundations , solely according to the information provided in their mission statements .discrepancies between the two assistants were finalized by a third person who is a doctoral candidate in china studies .  _ state power_. our main tracker of state penetration into the non - profit sector is the number of government officials in senior management positions .the presence of state officials on a foundation board is a clear mechanism by which the state can exercise control ; at the same time the state , at least explicitly , forbids government officials from serving on these boards .official law ( article 23 ) is that `` principals '' ( the board chair ( president ) , deputy chair , or secretary general ) should not be currently employed by the state .law against direct government involvement are commonly violated .the standard annual reporting forms even asks foundations to report the number of principals who are government staff ; a non - negligible fraction ( 18% ) report non - zero numbers of current government officials . as a different measure of state influence ,we hand - coded the 3a+ foundations , noting whether or not the board president is a current or retired government official .hand - coding is a difficult and laborious task ; because it can be difficult to ascertain the current status of individual , our 3a hand - coding includes both retired and currently - serving government officials , and is thus not directly comparable to the self - reporting set .we thus count the number of government officials in three different ways .the ricf counts the number of _ current _ government officials who serve as principals ; it also counts the number of simultaneously _ retired _ and _ senior _ government officials who serve as principals ; and ( for a hand - coded subset ) it counts the number of either current or retired government officials who serve as the board president .note that the article 23 law does not forbid retired government officials from serving as board principals , and these people may well still represent government influence  .table [ counts ] shows the breakdown of the foundations in the ricf data .collectively , the 3,344 foundations in our data have a combined income of 35.3 billion rmb ; approximately 5.5 billion usd at current exchange rates . paralleling tocqueville s accounts of the diverse initiatives of citizens in 19th century america , foundations in contemporary china range in activity in everything from the promotion of the board game ( go ) to legal aid for the indigent .the majority are restricted to non - public fundraising , and work in non - sensitive areas .these non - public foundations control just over half of the total yearly nonprofit revenue in the country . despite laws to the contrary ,our results confirm persistent and high levels of state involvement in the governance of foundations .table [ control ] shows the relationship between fundraising scope and activity , relying on both the hand - coded 3a subsample that tracks the affiliations of board presidents , and official self - reports in the full database .because the 3a hand - coding includes retired officials , the two methods track slightly different phenomena .both methods also confirm that the presence of government officials is less for non - public foundations .the government is most involved in foundations that are able to raise funds from the general public .( self - reports , but not our hand - coding , show additional supervision when the foundation itself is associated with sensitive activities . because this signal does not appear in the hand - coded subset , it may be best - explained by differing incentives : public foundations involved with sensitive activities may be more willing to report government officials on their boards , despite the fact that this violates article 23 . )board interlock is widespread .a significant fraction of the foundations are integrated into the network : of the 3,344 foundations , 1,411 ( 42% ) share board members with at least one other foundation . as shown in table [ integration ] ,foundations at the central level are the most likely to be connected .both public and private foundations show significant network integration .a large fraction of this network is connects together , into a single giant component that contains 1,022 foundations ( see fig . [ bi ] ) .  while the existence of board interlock parallels the corporate cases studied in the west , there are significant differences .most notably , the network is not small world : the average path length between nodes in the giant component is , and the network diameter is ; in both cases much larger than the corporate board interlock seen in the united states  .  the board interlock network in chinese foundations , in other words , has a tendency to isolate nodes from each other . even if we restrict to the 77 central - level foundations in the giant component , the diameter remains large ( 9 steps ) ; by comparison , the network of fortune 800 firms in the 1970s , nearly ten times larger , had a diameter of five  .chinese foundations connect to each other , but the existence of these long paths shows that board interlocks are fundamentally limited in their ability to coordinate action on the very largest scales .  while the network has few shortcuts and hubs that connect otherwise distant nodes , it is also the case that a small number of foundations have very high degree they share an unusually large number of board members with other foundations .we show the network degree distribution in fig .[ degree ] .the existence of these `` super - connectors '' can be empirically confirmed by testing for heavy - tailed degree distributions ; standard methods strongly prefer a log - normal distribution to both an exponential ( _ i.e. _ , random - graph ) and power - law fit  .these super - connectors appear to preferentially connect to each other , suggesting the existence of highly connected elite groups ( the rich - club phenomenon " , first noted by ref .[ rc ] shows the rich - club coefficient in the full , the public , and the non - public subnetworks . in all cases , nodes with higher degreeare more likely to connect to each other than in a null model that preserves the node degree distribution but otherwise shuffled connections .note that the -core for the public network is much smaller than the non - public ; if a public foundation has high - degree in the full network , it is usually because it connects to non - public foundations .  if we code nodes by the board president s profession , we find that the highest degree nodes include both the government and the business elite .of the ten highest - degree foundations , six are associated with businesses , four with government .for example , the most connected foundation is the youchange china social entrepreneurs foundation , set up to encourage philanthropic giving by wealthy entrepreneurs ; the second is the forbidden city cultural heritage conservation foundation , which manages the state - owned historical treasure .the top ten most connected board members are also a mixture of both government and business elites ; three are business elites , six are current government officials , including members of the national people s congress , the cppcc , and the guangzhou people s congress ; and one is a retired government official .considering the public and non - public networks separately allows us to see how different groups dominate . in the public network ,the highest - degree nodes are nearly all associated with the government : of the top ten highest degree foundations , only two have a president with a non - governmental background ( a television celebrity , and the head of a hospital ) .by contrast , six of the ten highest degree nodes in the non - public network are associated with business elites .the highest degree node , for example , the youchange foundation , is run by the businesswoman ping wang , whose background is in international finance and law .board interlock is influenced by both geography and registration level ; see table [ geography ] , paralleling classic results for corporate networks , co - located foundations are far more likely to connect  .we also find evidence for preferential connections between sensitive foundations ; there are more links between sensitive foundations than found in the null .however , public- and non - public foundations appear to intermix freely and preferences ( though detectable ) are weak ; public foundations are only more likely to link to each other than null , and only less likely to link to non - public foundations .we next consider how the presence or absence of government officials predicts node degree .we use a multiple linear regression model , with node degree as the dependent variable and nine independent variables : three variables describing the node s legal status ( public vs. non - public ; registration level ; evaluation level ) , four `` nuisance '' variables describing the intrinsic properties of the foundation ( board size , income , sensitive area , and age ) , and two variables operationalizing the state power : ( 1 ) current government officials , and ( 2 ) retired , senior - level government officials , the two fields in the main ricf database .we consider both the full network , and the two public and non - public networks separately .the results are shown in table [ all ] .the most surprising results concern the relationship between the presence or absence of government officials , and node degree. foundation degree is ( weakly ) positively correlated with government presence in the public foundations : nodes with higher degree are more likely to have government officials . however , in the non - public network , high degree is strongly ( and significantly , ) correlated with reduced government presence .when the two networks are joined together , the two effects compete against each other , partially canceling out .significantly , we find no correlation for the presence or absence of retired senior officials ; only the absence of currently - serving officials is predicted by node degree . to allow comparisons between different networks , we use -score transformed data ; for example , in table [ all ] , the presence of a current official as board principal in the non - public network shifts node degree down by roughly standard deviations ( controlling for other factors ) , where a standard deviation is measured for all the nodes in the non - public degree distribution .  because table [ all ] s results rely on self - reports, it is possible that these effects may be driven in part due to differences in self - reporting .we can check for this effect by using the hand - coded 3a subset ; these results are shown in table [ 3a ] ; because the 3a hand - coding tracks only presidents , and includes both current and retired officials , our results here are not strictly comparable to the table [ all ] case .the smaller size of this set also means that our signal - to - noise is lower . in this subset ,the weaker correlation in the public data is no longer detectable , but we still see the negative correlation between network position and state presence .   how did these network effects evolve over time ?[ emergence ] shows the three critical metrics for the network evolution : the size of the public and non - public network over time ; the changing levels of government presence on boards ; and the evolution of the node degree government presence relationship .overlaid on these panels are five critical dates in the recent history of the non - profit sector : ( 1 ) 4 june 1989 , the tiananmen square protests , and the emergence of civil society in china  ; ( 2 ) 15 september 1995 , the fourth world conference on women , associated with the accelerating development of civil society in china  ; ( 3 ) 1 june 2004 , the day the regulations on the management of foundations , including the above - discussed article 23 , took effect ; ( 4 ) the sichuan earthquake of 12 may 2008 , according to ref . , a critical date in the expansion of the non - profit sector s horizontal linkages ; and ( 5 ) the 12th five - year plan for 20112015 , introduced march 2011 , which devoted a full chapter to `` social management innovation '' as a key government target .[ emergence_3a ] shows the same plots , but now for the 3a+ hand - coded subset , as discussed above .significant numbers of non - public foundations appear soon after the tiananmen square protests , though none of the foundations from that year retain 3a+ status today .the effect of the 2004 regulations on the growth rate is clear : for at least the next five years , it led to literally exponential growth in the number of both public and non - public foundations .the growth rate in the non - public sector was significantly stronger , so that , by 2011 , the non - public sector was larger than the public one .the effect of these same regulations on the levels of government supervision is more complex .the 2004 regulations led to a sudden decline in reported levels of government principals in the non - public network .this is consistent with foundations becoming aware of , and responding to , the restrictions of article 23 .this decline does not appear as strongly in the 3a+ hand - coded subset , however , which suggests one of two explanations : that new foundations are continuing to include government officials , but staying within the letter of the law by including only retired officials , or , that new foundations are continuing to include currently - serving government officials , but under - reporting their presence in official paperwork .the effects of article 23 are inconsistent : the decline in reported government presence does not occur in the public network ; indeed , after 2008 , reported government presence starts to rise .most interesting are the effects of network growth on the relationship between node degree and government presence . in both the full network , and the 3a+ hand coded subset , we see that the negative relationship between degree and government presence emerges only late in the network history .today the non - public network acts to systematically exclude government officials from high degree nodes . in the full network ,the negative relationship becomes strong enough to detect soon after the sichuan earthquake . in the 3a hand - coded subset ,the downward trend towards increasingly negative relationships between degree and government presence becomes detectable only after the 2011 five year plan .our results show high levels of state presence throughout the chinese non - profit world .the appointment of government officials to high - level positions on foundation boards throughout the sector means that the chinese government continues to hold significant levels of infrastructural power . in tocqueville s account of civil society in the 19th century united states ,citizens formed voluntary associations independent of the government itself .whatever they are doing , the non - profits of 21st century china are far from this 19th century model , and far from models of post - soviet democratization in eastern europe  .our quantitative results fit with what is widely seen in case studies and fieldwork in china itself : state power may not be complete , but it can not be ignored .our results , however , also show significant differences in the level of governmental penetration of the non - profit sector .this is most apparent among the non - public foundations where , at least officially , only one in ten foundations have a current government official as board principal .the government s relationship to its foundations is bimodal , with public foundations showing the highest levels of government involvement ; not surprisingly , of this more supervised group , the public foundations engaged in politically - sensitive topics receive the greatest levels of supervision of all .the unusual nature of the non - public foundations becomes apparent at the network level .a set of network elites are at the center of the non - public network .it is the linking patterns of the non - public networks that drives the creation of public node elites as well : high - degree nodes are , in general , high degree because they serve as hubs for the non - public nodes .these elites not only serve as hubs for large numbers of other foundations , but preferentially connect to each other .qualitative study of the highest degree nodes shows that , in a parallel to the united states  , the nodes responsible for these interconnections are , when they are not members of the government , the business elites .detection of this rich club effect provides a new view on the development of horizontal relationships that can enable communication and cooperation a process captured in fieldwork studies of horizontal connections during the 2008 sichuan earthquake  , and a missing piece for understanding the development of state that increasingly devolves government functions to non - government agencies  .our network analysis reveals an unexpected negative relationship between node degree and government presence in the non - public network . not only is government penetration much lower overall in the non - public foundations , it appears to have even less penetration to the foundations at the network s center .horizontal relationships between foundations appear to selectively exclude the top - down `` vertical '' control of the state in a form of structural autonomy .a dynamical analysis of network formation , shows how recent the creation of this partially autonomous sphere has been .it becomes detectable in the full network soon after the 2008 earthquake ( the downward trend in the 3a subset appears around this time as well , but only becomes statistically significant in 2011 ) .this result lends new support to the qualitative studies of ref . , which associated the earthquake to lasting cultural , political , and social changes in the non - profit world that led to new forms of autonomous civil society . ref . supports these results from a different angle , suggesting the increasing importance of private , as opposed to state - controlled , organizations in non - profit relief . in a comparative of study of how government - controlled and private firms responded to the 2008 earthquake, they found that private firms donated to relief more rapidly , and at greater levels of financial assistance , that state - owned firms .even many years after the 2008 earthquake , these effects persist .one more recent political change comes from the government : the promotion of `` social management innovation '' ( _ chuangxin shehui guanli _ ) , a core concept of state policy first introduced in the 4th plenum of the 16th ccp congress in 2004  ; the 12th five - year plan for 20112015 elaborated the policy as a governance target , proposing `` party leadership , government responsibility , societal cooperation , public participation '' as key principles  , the use of civil society to provide social services , and a correspondingly less rigid approach to controlling it  .our results confirm the impact of these further reforms : in the post - plan era , the negative relationship between government presence and node degree has persisted .network connectivity is associated with the ability to form common knowledge  , and both simulations and theory suggest that nodes of high degree play a crucial role when common knowledge is required for joint action  . the negative relationship between node degree and government presence observed in our data then amounts to a form of structural autonomy . taken at face value , these results seem to suggest that foundations within this non - public subset may be part of the emergence of a new civil society , whose interlocks occur increasingly independently of the state , and whose resultant capacity for independent coordination might even be seen as a threat to authoritarian control .  the identification of these links with a tocquevillian civil society is complicated , however , by the fact that when the most connected of the non - public foundations are not government in origin , they appear , instead , to be drawn from the business elite . the extensive ties between the state and business then suggest that this civil society is something less than might be expected ; ever since the reforms of the 1980s , scholars have suggested that the business elite act as an agent of the government itself  .  indeed , this provides a clear alternate explanation : if the highest degree nodes are sufficiently aligned with the government to begin with , they can be allowed to operate without direct supervision precisely as we see in our data . whether or not the elite are truly independent of the government , their special position in society , and their ability to influence the government financially  suggests that this civil society , such as it is , is far from the pluralist tocquevillian world of the ordinary citizen.  understood in the context of the qualitative literature on chinese foundations , our results are perhaps more consistent with the theory of `` consultative authoritarianism '' , argued for by ref . , in which the government tolerates increasing levels of autonomy among non - governmental organizations while developing new strategies of indirect control .networks of state power may overlap with ones defined by economic exchange , but need not be coextensive  .our results show that the government has come to tolerate communities of interlocking associations that operate with lower levels of direct government presence .today , the total number of these organizations is small .the new charity law , effective from 1 september 2016 , will allow a far greater number of associations potentially in the hundreds of thousands to raise funds from the general public .we expect the rapid expansion in both the size and scale of the chinese non - profit sector will radically increase its impact on the state - society relationship .our results here provide important clues for the effects of this further development .the relationship we find between government presence and network position suggest intriguing possibilities for the emergence of new coordinating hubs independent of government influence .closer examination of the nature of the highest degree nodes , however , suggests that our results provide at best ambiguous support for the bottom - up organization of truly autonomous non - government actors .j.m . thanks dr . zhaonanzhu , assistant professor of public administration at beijing university of chemical technology , and bin chen , ph.d .  student at renmin university of china , for assistance with coding ; qun wang , ph.d .candidate at indiana university , and the ricf data quality team members , for data collection and data quality control ; dr . peter frumkin at the university of pennsylvania , the 2016 penn summer doctoral fellows program fellows .we thank bradi heaberlin and torrin liddell for their valuable comments .the ricf project is supported in part by the dunhe foundation . s.d .thanks the santa fe institute for their hospitality while this work was completed .   .foundation status , activity , and yearly budgets ( in billions of _ yuan _ ; in 2016 ) for the 3,344 foundations in our database .the majority of the foundations are concerned with neutral ( non - sensitive ) activities , and the majority are restricted to private fundraising . despite the fact that non - public foundations can not raise money from the general public , they actually control the majority of nonprofit revenue in the network.[counts ] [ cols="<,<,<",options="header " , ]   , but for the 3a+ hand - coded subset .differences in overall levels of supervision are do both to reporting effects , and the necessary inclusion of retired officials in this set . despite these coding differences ,we see the same emergence of elite autonomy signal ( bottom panel ) as in the full network ; here the signal becomes detectably negative after the introduction of the 2011 `` five year plan '' .[ emergence_3a],title="fig:",height=192 ] , but for the 3a+ hand - coded subset .differences in overall levels of supervision are do both to reporting effects , and the necessary inclusion of retired officials in this set . despite these coding differences ,we see the same emergence of elite autonomy signal ( bottom panel ) as in the full network ; here the signal becomes detectably negative after the introduction of the 2011 `` five year plan '' .[ emergence_3a],title="fig:",height=192 ] , but for the 3a+ hand - coded subset .differences in overall levels of supervision are do both to reporting effects , and the necessary inclusion of retired officials in this set . despite these coding differences ,we see the same emergence of elite autonomy signal ( bottom panel ) as in the full network ; here the signal becomes detectably negative after the introduction of the 2011 `` five year plan '' .[ emergence_3a],title="fig:",height=192 ]

Abstract: in response to failures of central planning , the chinese government has experimented not only with free - market trade zones , but with allowing non - profit foundations to operate in a decentralized fashion . a network study shows how these foundations have connected together by sharing board members , in a structural parallel to what is seen in corporations in the united states . this board interlock leads to the emergence of an elite group with privileged network positions . while the presence of government officials on non - profit boards is widespread , state officials are much less common in a subgroup of foundations that control just over half of all revenue in the network . this subgroup , associated with business elites , not only enjoys higher levels of within - elite links , but even preferentially excludes government officials from the nodes with higher degree . the emergence of this structurally autonomous sphere is associated with major political and social events in the state - society relationship .   board interlock , ngo , civil society , elites , state corporatism , state power , state - society relationship , social network , people s republic of china , non - profit foundations , common knowledge