modern and demanding application of radial velocities , like those associated with the search for extra - solar planets , have promoted the introduction of new methods of wavelength calibration .the key to success has been recording of the reference wavelength grid for to the whole duration of the science exposure and through the same optical train and path .two approaches have been followed : the _ parallel _ ( where thorium lines going through telescope optics are recoded on the ccd close and parallel to the science spectrum with an exposure lasting as long as the science observation ) , and the _ iodine - cell _ one ( the stellar spectrum passes through and is absorbed by a cell filled with iodine vapors , that mark the stellar spectrum with a huge number of sharp and equally intense absorption lines ) .both approaches require delicate instrumentation , careful maintenance and dedicated spectrographs .as such they are not easily manageable on small , all - purpose telescopes .we propose here a third , independent way to mark with reference wavelengths the science spectrum as it is recorded , through exactly the same optical train and path .it consists of using optical fibers with recorded in them bragg gratings that allows undisturbed passage of all wavelengths except a selection of few ones that will appear in the spectrum as sharp , deep absorption lines of constant and pre - selected wavelengths .the latter are then used as a reference grid to accurately wavelength calibrate the science spectrum .the system is easy and fast , allows to decouple the spectrograph from the telescope and operate it in a controlled environment , requires minimal mechanical work to be adapted to existing spectrographs , the marking absorption lines can be placed at any preferred wavelength , and the fibers can be mass - produced at low cost for distribution to interested observatories .fbgs can be easily installed on spectrographs already designed to operate in multiple fiber mode .the rave project ( steinmetz 2003 ) , with its fixed wavelength range , would represent an ideal case for the application of fbgs .the fbgs ( fiber bragg grating ) appear of potential interest also to gaia .the latter s spectrograph operates in tdi , slit - less mode with thousands of spectra simultaneously crossing the field of view as the satellite spins .no conventional calibration lamp can be used , obviously .the base - lined wavelength calibration procedure foresees using stars of recognized constant radial velocity as they travel across the spectrograph focal plane , by accurately linking their astrometric position on the sky to the wavelength of their absorption lines on the pixels of the ccds .  a bundle of fbgs properly introduced in the gaia spectrograph optical train would mark with a set of properly placed reference absorption lines the spectra of all stars entering the field of view .the fbgs could become the prime wavelength calibration mean of gaia spectra ( particularly for preliminary solutions while the mission is still flying ) , or a backup for the method based on standard radial velocity stars in case this would not satisfactorily operate for whatever reason once the satellite will reach l .the fbgs dissipate no power and have no movable parts .they should also stand the low operating temperatures of the satellite in l and should do not degrade with time , and thus looking ideal for use in space .no fbg has ever been used as proposed in this paper , and thus confirmatory tests are required . at the astronomical observatory of padovawe plan to manufacture and test prototype fibers for the gaia / rave wavelength range to check their performance with actual observations at the telescope .fiber gratings are made by laterally exposing the core of the fiber to a periodic pattern of intense ultraviolet light .the exposure produces a permanent increase in the refractive index of the fiber s core , creating a fixed index modulation according to the exposure pattern : this fixed pattern is called a grating . at each periodic change of refraction , a small amount of light is reflected ( bragg diffraction ) .all the reflected light signals combine coherently to one large reflection at a particular wavelength when the grating period is approximately half the input light wavelength .this is referred as the bragg condition and the wavelength at which this reflection occurs is called the bragg wavelength ( ) .light at wavelengths different from , which are not phase matched , will pass unabsorbed through the fiber . thus , light propagates through the grating with negligible attenuation and only those wavelengths that satisfy the bragg condition are affected and strongly back - reflected .application of this technology to astronomical spectra at gaia wavelengths is attractive for two basic reasons : ( ) the technology is already mature with the tele - communication industry that operate it in the near - ir , down to 1  m , and ( ) the limited range observed by gaia and rave requires only a limited number of reference lines to be properly calibrated ( see discussion in desidera and munari 2003 ) , which in turn means an easier fbgs production .exposing a photosensitive fiber , usually germanium - doped ( yuen , 1982 ) , to an intensity pattern of ultraviolet radiation ( at wavelengths between 240 and 255 nm , where the germanium has an absorption band ) is used to produce ( i.e. write ) a fiber bragg grating . in its basic formthe grating selectively reflects light at the bragg wavelength , where is the grating spacing and is the effective index of refraction .both and depend on fabrication parameters : depend on the modal dispersion characteristics of the fiber and lies , for each mode , between the core and cladding indices .the functional form of the normalized frequency ( ) parameter is given by : where is the diameter of the fiber core , is the free space wavelength , the core index and the clad index .note that the difference between the two squared index is also the numerical aperture of the fiber . for low enough valuesthe fiber is single mode and only one bragg reflection is observed at wavelength given above . at a certain value of the fiber become two moded with two separated bragg wavelengths , and for larger values many more modes begin to appear in the fiber grating spectrum .the lowest order or fundamental mode has the longest , and the higher order modes have progressively shorter with the cladding index giving the limit on the shortest .the peak reflectivity is an increasing function of the grating length and of the difference between and ( lam & garside , 1981 ) .  recording fbgs inside a fiber usually involves interference between two coherent uv laser beams that precisely define the spacing between the grating planes . for symmetric incidence and an angle between the uv beams ,the pitch of the recorded grating is 0.5 , where is the illumination wavelength .the basic interferometric setup splits the laser beam to create an interference pattern on the fiber ( morey et al ., 1989 ) as shown in figure 2 ( left panel ) .because the beams travel different paths , the laser must have sufficient temporal coherence to account for path - length mismatch , and good spatial coherence .the sensitivity to mechanical instabilities of this method of fbg production can make difficult to produce identical replicas .the other way for writing fbgs is to use phase mask to generate multiple beams ( hill et al . , 1993 ) .two of the beams carry approximately 40% of the total energy and closely overlap the phase mask surface to create an interference pattern at the desired bragg wavelength .the fiber - phase mask assembly can be illuminated either by a large beam to cover the full fiber bragg grating length or by a small scanning beam . because the fiber is usually in proximity to the phase mask , the assembly is a very stable mechanical system , suitable for mass - production of identical fbg replicas .the pattern recorded into the fiber is a copy of the phase mask ( pitch and chirp ) scaled by about 50% .desidera , s. , munari , u. , 2003 , this volume , pag .xxx hill k. , malo b. , bilodeau f. , johnson d. 1993 , appl.phys.lett .62 ( 10 ) , 1035 lam d.k.w . ,garside 1981 , appl .optics , 20 ( 3 ) , 440 morey w.w . , meltz g. , glenn w.h .1989 , proc .spie , 1169 , 98 steinmetz m. , 2003 , this volume , pag .xxx ( and http://www.aip.de./rave/ ) yuen m.j .1982 , appl .optics , 21 ( 1 ) , 136

Abstract: we propose a new technique , the use of fbgs ( fiber bragg gratings ) , for accurate , easy and low cost wavelength calibration of gaia , rave and follow - ups spectra at local observatories . fbgs mark the spectra with absorption lines , freely defined in number and position during the fibers manufacturing . the process goes in parallel with the science exposure and through the same optical train and path , thus ensuring the maximum return in wavelength calibration accuracy . plans to manufacture and test fbgs for the caii / paschen region are underway at the astronomical observatory of padova .   # 1_#1 _ # 1_#1 _ =  # 1 1.25 in .125 in .25 in


different from other countries , korea is known to have relatively small number of family names .for example , the nationwide survey in 2000 has shown that the population of the family name kim is about 10 millions , which means that about one among four koreans is kim .in general , the family names have been devised to distinguish one family from others . accordingly ,if the number of family names is too small , or family sizes are too big , the distinction with other families becomes very inefficient . from this reasoning ,it is natural that koreans have developed additional way to give a kind of sub - system by using the information of the birthplace of the family name , i.e. , where the ancestor of the family came from .for example , one of the authors of the present paper has the family name kim from gimhae , a region in southern korea .the family name kim in 2000 survey has been found to have 348 different regional origins .almost all koreans know the regional origins of their family names from their births and the state keeps this information in the population registration .  in korean culture , having an unfamiliar family name is not common at all , and most people hesitate to invent new names . for 15 years from 1985 to 2000 ( table [ mytable ] ) ,the number of family names in korea increased only by 11 ( increase ) .in contrast , the number of the family names with regional origins ( e.g. , kim from gimhae is taken as different than kim from gyeongju ) , is increased in the same period by 829 ( increase ) ( see table [ mytable ] ) .consequently , this shows that most koreans consider inventing new family name as a taboo , while branching out by using new regional origins ( but with the same family name ) is totally acceptable in korean culture .  in this work , we study the distributions of the korean family names with and without regional origins . from the above observations ,one expects that the distributions look very different with and without the regional origins , and that the latter distribution is similar to other countries , where having new family name is not a taboo as in korea .  .date sets : korea00 and korea85 are for the total populations in korea in the years 2000 and 1985  .seongnam98 , osan04 , and hwaseong04 are extracted from telephone books , and ajou03 is obtained from the list of registered students in ajou university . and are numbers of family names with and without the regional origins , and is the population . [ cols="^,^,^,^",options="header " , ]   [ mytable ]  the data sets analyzed in this work are as follows ( table [ mytable ] ) : korea85 and korea00 are for the total population of korea in the years 1985 and 2000 , which were downloaded from korean national statistical office  .the set ajou03 is from the list of registered students in ajou university in 2003 , and the other sets seongnam98 , osan04 , and hwaseong04 are extracted from telephone books published in the corresponding cities at years 1998 , 2004 , and 2004 , respectively .we have information of the regional origins only in korea85 and korea00 . throughout the paper , is the size of populations , and are the numbers of family names with and without regional origins , respectively . for the family name ( when the family name is arranged from the biggest family to smallest one in descending order ) , is the number of people who have that name , leading to .we also use the integrated probability distribution function , which measures the proportion of the families with the size greater than .the paper is organized as follows : in sec .[ sec : name ] , which contains the main results of the present work , we study various aspects of family name distributions without regional origins .the relationships among the three basic quantities , , , and are analytically found and compared with empirical results .the distributions for various sizes of populations in table [ mytable ] are compared with previous results in other countries .the empirically obtained growth rate as a function of the family size is also discussed . in sec .[ sec : regionname ] , we perform analysis on the distributions of family names with regional origin ( e.g. , kim s from different regional origins are considered to be different names ) .finally sec .[ sec : conculsion ] is devoted to discussions and conclusions .we first present in fig . [fig : nfn ] the number of family names versus the population . as the population is increased , the number of family names is shown to increase logarithmically .this observation is in a sharp contrast to ref . , where has been observed in japan , instead of . due to the lack of information, we are not able to study versus .  in fig .[ fig : pintfk](a ) , the integrated distribution function , measuring the proportion of the family names with the populations greater than or equal to is displayed .since every family has at least one person as its member , one gets . as is increased , is a monotonically decreasing function of until is reached for . the logarithmic decay form in fig . [ fig : pintfk](a ) is again very much different from the corresponding results for other countries , where the power - law form has been observed with for u.s.a and brazil  , and for japan  .the probability distribution function , which is simply the normalized histogram , is easily obtained from the derivative of with respect to from , i.e. , . in a practical point of view , is more convenient than , since some practical issues like the bin size in are not needed to be taken care of . as will be clearly shown below the same logarithmic form in figs .[ fig : nfn ] and [ fig : pintfk](a ) is not accidental .another convenient and frequently used way of showing the distribution is the so - called zipf s plot  , where the population of the family name is plotted in terms of the rank .figure [ fig : pintfk](b ) is the zipf s plot of obtained from the data set korea00 ( see table [ mytable ] ) .clearly exhibited is that decays exponentially with , again in contrast to ref . where the power - law decay has been observed .  the zipf s plot of in fig .[ fig : pintfk](b ) and are easily related since is simply the number of family names of the size greater than : draw the horizontal line at the vertical position in fig .[ fig : pintfk](b ) and the value of at the crossing point is simply multiplied by . in other words ,once the functional form is given , we obtain the relation connecting the zipf s plot and the integrated probability function and are of the power - law form has been discussed in ref . . ] .the function is always a monotonically decreasing function of by definition , which confirms the existence of the inverse function . via eq .( [ eq : pint ] ) the logarithmic form of in fig .[ fig : pintfk](a ) implies the exponential form of in fig .[ fig : pintfk](b ) and vice versa .we next establish the simple mathematical relation between obtained for the total population and obtained for various sizes of population . the only one assumption we makeis that the set of ( with individuals is taken at random without any bias . in other words ,the family at the rank has members in total , and thus in the subset of the size , there are members of the same name .consequently , once for the total population is given , for the subset of the size is simply the number of family names that has more than one individual , [ , which leads to where is the heaviside step function with for and otherwise . from the definition of , the right - hand side of eq .( [ eq : nfx ] ) equals to the value of at the crossing point of the two curves and , yielding where and the identity in eq .( [ eq : pint ] ) have been used .it should be noted that the relation between the zipf s plot of and the family name distribution function in eq .( [ eq : pint ] ) should hold in any case , while the relation between and holds only when the assumption of unbiased random sampling of population is valid . as a specific example , for the power - law form , is expected .it is not clear whether or not this relation has been violated in ref . , where somehow self - contradictory results and have been concluded from the same unbiased random sampling of population .however , if the proper size of errorbars are taken , we strongly believe that the discrepancy should vanish .  in fig .[ fig : nfnpk](a ) , from for korea00 and korea85 are displayed together with the values in table [ mytable ] .although all curves show the logarithmic dependence , i.e. , , from computed by using eq .( [ eq : nfn ] ) shows a systematic difference that it lies higher than the empirical results at any .this makes us to conclude that the assumption of unbiased random sampling of population is not entirely valid for data sets in table [ mytable ] .nevertheless , the logarithmic dependence persists for all three different curves in fig .[ fig : nfnpk](a ) , which appears to justify the unbiased sampling assumption as a reasonable approximation .the substantial difference in fig .[ fig : nfnpk](a ) can be interpreted as follows : significant number of families exist in localized area .for example , in some villages in rural area , most of people in the community have the same family name .another possibility is that new names originate from foreigners who just became koreans with new korean names .the latter case can be probably found only in the biggest city , seoul .those non - uniformly distributed names in a geographic sense are captured in nationwide survey but one can not find them in the telephone book in cities we are investigating in this work .accordingly , actual values of can be different and lie lower than the expected values from eq .( [ eq : nfn ] ) based on the assumption of the unbiased random sampling .we then elaborate the above explanation further by introducing the probability that the name of the rank is chosen .the unbiased random sampling corresponds to .the extension of the above derivation of is straightforward : the number of people of the name in the subset of population is now given by and the is the number of family names satisfying . from the same reasoning as before , with now reads .consequently , one gets the expression of the probability that the name at the rank is chosen as we then use the values and from the empirical values in table [ mytable ] and then take from the zipf s plot for korea00 to compute in fig .[ fig : nfnpk](b ) , where seongnam98 , osan04 , ajou03 , hwaseong04 have been used .the data point ( marked as filled square ) for ajou03 is somehow special since ajou03 is not based on the residential location of individuals ( table [ mytable ] ) .it is interesting to note that is a decreasing function of , suggesting that a randomly chosen individual in urban cities is more probable to have top rank names than for the whole nation .this appears to be consistent with the expectation that rare names ( with lower ranks ) are not distributed uniformly across the whole country .we also sampled randomly individuals ( ) from ajou03 and count how many names ( ) are found in the set .we then compute in the same way [ filled circles in fig .[ fig : nfnpk](b ) ] .   in this section ,we investigate the distributions of family names for various data sets in table [ mytable ] . in fig .[ fig : zipfall ] , all data sets in table [ mytable ] are shown to have qualitatively the same distribution : zipf s plots of for all data sets show exponential decay form , implying that the integrated probability distribution follows the logarithmic form ( see discussions in sec .[ subsec : relations ] ) .the unanimously found logarithmic form for then suggests that the probability distribution , which measures how many family names have the size , follows the following form with in korea , in a sharp contrast to other countries where have been concluded .this somehow unique family name distribution in korea can be understood from the birth - death model in ref . , where it has been shown that occurs in a stationary state if the total population does not grow ( or the death rate ) and the rate of new name generation is very small .the latter condition appears to be fulfilled in korea since only very small number of new names were generated between 1985 and 2000 ( see table [ mytable ] ) .furthermore , the family names in korea have been introduced to korean societies very long time ago ( at least one thousand years ago ) , and therefore one can assume that the korean family name distribution is very close to the one at stationary state although the population is still growing .although new name generation is also very rare in japan like korea , family names in japan , on the contrary , have a short history ( most names were created about 120 years ago  ) .the qualitatively different family name distribution in japan appears to imply that the distribution is still far from its stationary state as pointed out in ref . . from this perspective, it is very plausible that as time proceeds the family name distributions in other countries also should approach to eventually , in the condition that the rate of new name generation becomes sufficiently small .when the family name was introduced in human history , it is expected that the larger the family , the more probable the family s survival , since the size of the family was the measure of its strength in many respects such as the labor power and the number of warriors . in other words ,the population growth rate of a family must have been an increasing function of the size of the family long time ago . however , in a modern society , the population growth rate is not necessarily an increasing function of the family size since the size is no longer a matter of life and death .we use two data sets korea85 and korea00 to compute the growth rate of the family size for each family name in 15 years .the growth rate of the total population is 0.1377 during this period as shown in table [ mytable ] .it is found that no name actually disappeared between 1985 and 2000 , but 11 new names were created . in fig .[ fig : rnf ] , we plot the growth rate as a function of ( a ) the rank and ( b ) the size of the family .there are several very interesting features .the growth rate of some family is huge .for example , one family at very low rank had only one individual as its member in 1985 while the family size became 462 in 2000 , with the growth rate 461 in 15 years .this can never be explained from any biological reason ( no one can have several hundreds of children in 15 years ) , but rather must be a reflection of some sociological or psychological forces .relatively high growth rates are mostly observed in families at lower ranks , and in fig .[ fig : rnf](a ) is roughly an increasing function of .such a nonuniform growth rate can be explained from the assumption that ( 1 ) the family name with a high growth rate was recently invented and that ( 2 ) the family of a smaller size tries harder to increase the number of its members by e.g. , recruiting new members from relatives who still keep the old name .the above assumptions look reasonable since most people , especially who have small family sizes , probably want to see their names flourishing , not disappearing in the future .  in fig .[ fig : rnf](b ) , we display the growth rate as a function of the family size . as expected from fig .[ fig : rnf](a ) , is a roughly decreasing function of , saturating towards the total growth rate .it is interesting to see that is significantly higher than when .the size can be interpreted as the size scale beyond which the nonbiological growth is dominated by the biological growth .one can also associate with a psychological turning point in people s mind separating small and big families .as an additional way to distinguish families in korea , the regional origins of families are simultaneously used in korea . in this section , we regard the family name with different regional origins as distinctive names , e.g. , kim from gimhae and kim from gyeongju are considered to be different names , and study various aspects of the distribution .figure [ fig : pintnr ] shows the integrated probability function measuring the proportion of families which have more than family members .the distribution in fig .[ fig : pintnr ] , with the broad intermediate range described by the power - law behavior , is very different from the corresponding plot in fig .[ fig : pintfk ] . in other words ,the family name distributions are completely different with and without the regional origins .furthermore , although the distribution of the family names without information of regional origins in korea is very different from other countries , if the regional origins are used to distinguish one family from others the distribution shows the qualitatively similar behavior to that in other countries .more specifically , the power - law behavior [ i.e. ] is observed in a broad range of .figure [ fig : nrall ] is for the subsets of ( a ) korea00 and ( b ) korea85 .for example , kim00 is a subset of korea00 that contains only the name kim but from different regional origins .the three biggest families kim , lee , and park have 348 , 283 , and 159 different regional origins in korea00 , and 281 , 244 , and 127 in korea85 , implying that new regional origins have been branching out quite rapidly within a family . all curves in fig .[ fig : nrall ] have similar power - law decay behaviors as in fig . [fig : pintnr ] .we finally investigate in fig .[ fig : rnr ] the growth rate for the family name with regional origin as a function of the family size for ( a ) the whole dataset korea , and for three major family names ( b ) kim , ( c ) lee , and ( d ) park ; all show qualitatively the same behaviors as in fig .[ fig : rnf ] in sec .[ subsec : growth ] , i.e. , very high growth rate for small families , and saturation to average growth rate beyond around .it is interesting to note that as long as the growth rate is concerned , the behavior does not depend much on whether the regional origins are taken into account or not .this implies that a family with very common family name but with a very rare regional origin still considers itself as small and thus makes tremendous nonbiological efforts to increase its members .we in this paper have studied the distributions of korean family names extracted from various sources : from nationwide surveys in 1985 and 2000 , from telephone books published in three cities , and from the list of registered student in a university .family name with and without regional origins have been found to show quite different distributions : integrated probability distribution is logarithmic without regional origins ( kim from gimhae and kim for gyeongju are regarded as the same name ) , while it is power - law behavior with regional origins ( kim from gimhae is considered to be different name than kim from gyeongju ) .the difference is also reflected in the zipf s plot of family size with the family rank : exponential versus power - law .relation between and have been established , and ( how many family names are found in population ) has been shown to have simple relation with ( and thus with ) by using the assumption of random unbiased sampling .the empirical observations show systematic deviations from the expected values , which was then used to compute the probability that the family at the rank is selected if we pick one individual at random .interestingly , has been found to be decreasing function of , implying that small family names are hard to find in general .growth rate for the family of the size has been computed from empirical data ( with and without regional origins ) .all show very interesting behaviors : huge growth rate [ in 15 years ] for small families implying nonbiological growth , and saturation towards average growth rate starting from around , which has been interpreted as the sociological / psychological separation point of big and small family .we thank s.h .jeon , s.h .lee , and d.m .lee for useful discussions and acknowledge ajou university for providing us the list of registered students .this work has been supported by the korea science and engineering foundation through grant no .r14 - 2002 - 062 - 01000 - 0 .

Abstract: the family name distribution in korea is investigated in comparison with previous studies in other countries . in korea , both the family name and its birthplace , where the ancestor of the family originated , are commonly used to distinguish one family name from the others . the family name distributions with and without the information of the regional origins are analyzed by using different data sets of various sizes , and compared with previous studies performed in other countries . the growth rate of the family is empirically obtained . contrary to commonly used assumptions , the growth rate is found to be higher for the smaller family .   family name distribution , zipf s law , growth rate , population  89.65.-s , 89.65.cd , 89.20.-a , 87.23.ge


with the advent of the web 2.0 , social tagging has become an essential tool to collaboratively annotate content with freely chosen _ tags _( i.e. , keywords ) .the result of a social tagging process is a network connecting users , content resources and tags , which is referred to as _folksonomy _ .since tags can be used to search for , browse and share content , they facilitate discovery and navigation in the social web .many social networks such as medium , twitter , instagram and facebook have adopted tagging in the form of hashtags as well . therefore , previous work has proposed tag recommendation algorithms with the aim to assist users in finding descriptive tags and to control the shared tag vocabulary . in this respect ,recent research has shown that a substantial amount of tag assignments can be explained by analyzing the information access in human memory , which is mainly influenced by past usage frequency , recency and the current semantic context .  even though there is already a large body of research available , which proposes algorithms for recommending tags , none of these approaches incorporate all three aforementioned factors .for example , folkrank solely utilizes tag frequency and the current semantic context , whereas girp solely builds on tag frequency and recency .typically these methods have been evaluated as integrated models and thus , it remains unclear to what extent the individual factors of the approaches contribute to the final algorithmic performance .* the present work : factors that influence tag reuse . * in this work , we study factors that potentially influence the tag reuse behavior in social tagging systems .specifically , we analyze the influence of frequency , recency and semantic context on the reuse of tags .hence , it is our goal to better understand to what extent these factors can be exploited to predict the reuse of tags given a specific _folksonomy type_. this should lead to a guideline for designing and implementing tag prediction algorithms for given environments .to that end , we integrate and extend our previous work on tag recommender systems , where we adapted the activation equation from the cognitive architecture act - r to develop a model termed _ bll. this model enables the prediction of future tag assignments for a user by modeling the usefulness of a piece of information  in our case , a tag in s memory based on three factors : ( i ) how _ frequent _ was used by in the past , ( ii ) how _ recent _( i.e. , the time since the last usage ) was used by in the past , and ( iii ) how useful is for in the current _ semantic context_.  this is achieved by the two components of the activation equation : first , the base - level learning component ( _ bll _ ) , which integrates the factors of frequency and recency via a power function for reflecting the time - depended decay of tag reuse and second , the associated component ( _ ac _ ) , which models the current semantic context as the similarity of tag to tags already associated with the currently tagged resource .however , since bll utilizes the three factors , ( i ) frequency , ( ii ) recency , and ( iii ) semantic context , as an integrated model , it is still unclear to what extent these factors individually contribute to the efficacy of the model . besides , we assume that the influence of these factors on predicting tag reuse depends on the folksonomy type , i.e. , _ narrow _ ( e.g. , flickr ) , _ _ mixed _ _ ( e.g. , bibsonomy ) or _ broad _ ( e.g. , movielens ) , of the given social tagging system .this leads to the following two research questions of our work :  * _ rq1 : _ how are the factors of frequency , recency and semantic context influencing a tag s probability of being reused in social tagging systems ? * _ rq2 : _ can the factors of frequency , recency and semantic context be exploited to efficiently predict a user s tag reuse given a specific folksonomy type ?  * methods and findings . * in order to address _, we conducted an empirical study on six social tagging datasets ( i.e. , flickr , citeulike , bibsonomy , delicious , lastfm and movielens ) , in which we analyzed the influence of the three factors frequency , recency and semantic context on the reuse probability of tags ( see section [ sec : emp ] ) .next , to answer _ rq2 _ , we carried out a prediction study on the same datasets , in which we not only compared algorithms that reflect these factors individually but also approaches that combine these factors or incorporate social influences , e.g. , by suggesting related tags of other users ( see section [ sec : pred ] ) .we find that frequency , recency and semantic context positively influence the reuse probability of tags in all systems ( _ rq1 _ ) and that the efficacy of these factors for predicting a user s tags depends on the folksonomy type of the given system ( _ rq2 _ ) .  to the best of our knowledge ,this is the first study of its kind , which analyzes the reuse of tags to provide a transparent overview of the factors that influence the prediction of tags and , at the same time , relates these factors to the folksonomy type of the given system .our findings may serve as a guideline for researchers and developers of tag - based recommender systems with regard to choosing the right prediction and recommendation methods for given environments .in this section , we present the datasets , methodology and results of our empirical study carried out to address _ rq1_.   for the sake of this study , we turn to publicly available , real - world datasets gathered from the six social tagging systems flickr , citeulike , bibsonomy , delicious , lastfm and movielens . to make our results comparable and to ensure reproducibility , we utilize the exact same dataset samples that were used in the study of .a major advantage of these dataset samples is that they were created without any -core pruning technique to ensure an unbiased evaluation .additionally , these datasets represent social tagging systems of various domains ( i.e. , images , web links , references , music and movies ) , and differ in size and narrowness degree .the narrowness degree is defined as the average number of posts per resource , which allows to distinguish between narrow ( flickr ) , mixed ( citeulike , bibsonomy , delicious ) and broad ( lastfm , movielens ) folksonomies .the final statistics of our datasets are shown in table [ tab : datasets ] .   in order to analyze the tag reuse behavior of users , we split our datasets into training and test sets via an evaluation protocol , which persists the chronological order of the data .thus , for each user , we sorted his / her posts by time , allocated the ( i.e. , the most recent ) post to the test set and the first posts to the training set .next , in order to quantify the influence of frequency , recency and semantic context on the reuse of tags , we compared the tag assignments of the first posts in the training set ( i.e. , reflecting the past ) of user with the tag assignments of s post in the test set ( i.e. , reflecting the future ) .more specifically , for each tag of , we counted the number of times was used by in the training set and determined if was also reused by in the test set . finally , to obtain a statistically reliable value, we pooled together the tags of all users with the same frequency value and calculated the proportion of reused tags to determine the influence of tag frequency on the reuse probability .we followed a similar procedure to study the influence of recency and semantic context . in the case of tagrecency , we calculated the days elapsed since the last use of by . in the case of the semantic context , we determined the tag co - occurrence value between and the tags already assigned to the currently tagged resource ( i.e. , the second component of the activation equation ) .then , as in the case of tag frequency , we pooled together the tags of all users with the same recency or semantic context values and calculated the tag reuse probability for both factors .l||cccc|c dataset & & & & & + flickr & 9,590 & 856,755 & 125,119 & 856,755 & 1.000 + citeulike & 18,474 & 811,175 & 273,883 & 900,794 & 1.110 + bibsonomy & 10,179 & 683,478 & 201,254 & 772,108 & 1.129 + delicious & 15,980 & 963,741 & 184,012 & 1,447,267 & 1.501 + lastfm & 1,892 & 12,522 & 9,748 & 71,062 & 5.674 + movielens & 4,009 & 7,601 & 15,238 & 55,484 & 7.299 +   +  +  +  +  +  c|ll||ccc|ccc|cc & & & & & + folksonomy type & dataset & metric & frequency & recency & semcon & girp & bll & bll & fr & pitf + & & & .371 & .464 & - & .455 & * .470 * & .470 & .365 & .350 + & & ndcg & .569 & .702 & - & .686 & * .711 * & .711 & .561 & .535 + & & & .231 & .236 & .041 & .243 & .254 & * .259 * & .250 & .178 + & & ndcg & .367 & .385 & .069 & .394 & .413 & * .422 * & .392 & .294 + & & & .253 & .252 & .063 & .262 & .269 & * .280 * & .279 & .215 + & & ndcg & .371 & .368 & .090 & .386 & .396 & * .409 * & .408 & .327 + & & & .173 & .179 & .108 & .190 & .203 & * .243 * & .196 & .199 + & & ndcg & .267 & .287 & .158 & .298 & .318 & * .374 * & .292 & .302 + & & & .193 & .189 & .202 & .198 & .202 & .251 & .270 & * .276 * + & & ndcg & .292 & .293 & .302 & .303 & .313 & .375 & .399 & * .414 * + & & & .077 & .076 & .077 & .077 & .079 & .086 & .153 & * .156 * + & & ndcg & .177 & .183 & .176 & .177 & .187 & .203 & .319 & * .324 * +   in figure [ fig : analysis ] , we plotted the tag reuse probability over ( i ) tag frequency , ( ii ) tag recency ( in days ) , and ( iii ) tag similarity with the current semantic context on a log - log scale for our six datasets .we also provided the ( i.e. , the slope ) and ( i.e. , the determination coefficient ) estimates of the linear regression on the data .specifically , we use the sign of to determine how tag reuse is influenced by the factors and to check if the data follows a power function . across all six datasets , we can make three main observations :  1 .the _ more frequently _ a tag was used in the past ( > 0 ) , the higher its reuse probability isthe _ more recently _ a tag was used in the past ( < 0 ) , the higher its reuse probability is . 3 .the _ more similar _ a tag is to tags in the _ current semantic context _( > 0 ) , the higher its reuse probability is .  as such, all three factors ( i.e. , frequency , recency and semantic context ) have a positive influence on a tag s probability of being reused .furthermore , the generally high estimates in the log - log scaled plots indicate that large amounts of the data can be explained by a power function , as also indicated by the first component of the activation equation .thus , the first research question of our work ( _ rq1 _ ) can be answered affirmatively . in order to better understand the ( individual ) influence of each of the factors for predicting tags given a specific folksonomy type ( _ rq2 _ ), we conducted a prediction study described in the next section .in this section , we present the algorithms , methodology and results of our prediction study , which was conducted to address our second research question ( _ rq2 _ ) .specifically , we want to establish to what extent the factors of frequency , recency and semantic context can be exploited individually to efficiently predict a user s tag reuse given a specific folksonomy type of a social tagging system .   in terms of the compared algorithms ,we utilize approaches that reflect the three factors individually , approaches that combine these factors and approaches that incorporate social influences ( e.g. , via related tags of other users ).  * individual factors . * to account for tag frequency , we utilize the most popular tags ( mp ) approach , which ranks the tags of a user based on their usage frequency . to predict tags solely based on tag recency , we rank the tags of a user by the timestamp of their last usage . since the third factor of interest , the semantic context _ semcon _ , is represented by the second component of the activation equation , we recommend the tags that highly co - occurred with tags already assigned to the currently tagged resource .* combination of factors . *we utilize three algorithms based on combinations of the factors , which enables us to analyze if the performance of the individual factors can be improved when they are combined in the form of hybrid approaches . the first one , _ girp _ , integrates frequency and recency using an approach that models the effect of time ( i.e. , recency ) via an exponential function .the second one , _ bll _ , implements the first component of the activation equation and models the effect of time via a power function as suggested by . the third algorithm in this respect , _ bll _ , is the full implementation of the model , accounting for all three factors ( frequency , recency and semantic context ) .* social influences . * to compare these methods that aim to predict a user s individual tag reuse with approaches that also integrate social influences ( e.g. , related tags of other users ) , we incorporate two well - known algorithms from tag recommender research in our study .the first one , folkrank ( _ fr _ ) , is an extension of google s pagerank approach to iteratively rank the entities in folksonomies .the second one , pairwise interaction tensor factorization ( _ pitf _ ) , is based on factorization machines and has become one of the most successful methods for recommending tags . for both algorithms, we use the same parameter settings as in ( i.e. , we set the preference vector weighting for fr to .7 and the dimension of factorization for pitf to 256 ) .we conducted our prediction study on the same datasets and training / test set splits as in our empirical study ( see section [ sec : emp_meth ] ) .this allowed us to train the algorithms based on the posts in the training set and compare the top- tags that an algorithm predicted for user and resource of a post in the test set with the set of relevant tags in this test set post .based on that , we computed two prediction accuracy metrics known from research on information retrieval and recommender systems. specifically , we report the f1-score ( ) for the top- predicted tags was also used as the main metric in pkdd09 : http://www.kde.cs.uni-kassel.de/ws/dc09/evaluation ] and the ranking - aware metric normalized discounted cumulative gain ( ndcg ) for the top- predicted tags .to ensure the reproducibility of our results , we conducted this study via the open - source tag recommender evaluation and benchmarking framework _ , which can be freely downloaded from github for scientific purposes .   in table[ tab : results ] , we present the results of our prediction study indicated by the and ndcg metrics . across all six datasets and both metrics ,we observe three patterns of results based on the folksonomy type of the tagging systems .* in the narrow folksonomy flickr , the semantic context has no influence since users are solely tagging their own images .the results show that frequency and especially recency can be exploited to efficiently predict a user s tag reuse in this narrow setting .furthermore , these factors even outperform fr and pitf , the two algorithms that also utilize social influences by means of other users tags .when combining frequency and recency , we see that the accuracy of the strong recency factor can only be slightly improved in the case of bll , which models the time component via a power function , and even decreases in the case of girp , which builds on an exponential temporal decay function .* for the mixed folksonomies citeulike , bibsonomy and delicious , we observe a good performance for the factors of frequency and recency , and an average one for the semantic context . additionally , the results suggest that a combination of all three factors in the form of bll provides the highest accuracy estimates and outperforms fr and pitf . again , bll ( and thus , the power function ) is apparently better suited to combine frequency and recency than girp ( and thus , the exponential function ) .* interestingly , the algorithms in the broad folksonomies lastfm and movielens had a completely different behavior . in these datasets , since there are a lot of tags assigned by other users to the currently tagged resource , the semantic context is a much more important factor for predicting tags than in the narrow and mixed settings .similarly to the narrow case , the combination of the factors only slightly improves the accuracy of the individual factors . due to a high number of average posts per resource ( 5.674 for lastfm and 7.299 for movielens see table [ tab : datasets ] ) , fr and pitf , which utilize related tags of other users as well , provide the best results in the broad setting .* summary . * our results are summarized in table [ tab : discussion ] .overall , they confirm that the factors of frequency , recency and semantic context can be exploited to efficiently predict a user s tag reuse .which factor to consider , however , strongly depends on the folksonomy type of the given social tagging system . as such , the second research question of our work ( _ rq2 _ ) can also be answered affirmatively .in this paper , we analyzed the influence of frequency , recency and semantic context on the reuse of tags in social tagging systems . to that end, we conducted an empirical study and a prediction study on datasets gathered from the six social tagging systems flickr , citeulike , bibsonomy , lastfm and movielens .the empirical study aimed to answer our first research question of this work ( _ rq1 _ ) and determine how the factors of frequency , recency and semantic context influence a tag s probability of being reused .the three main findings of this analysis are : ( i ) the _ more frequently _ a tag was used in the past , the higher its reuse probability is , ( ii ) the _ more recently _ a tag was used in the past , the higher its reuse probability is , and ( iii ) the _ more similar _ a tag is to tags in the _ current semantic context _ , the higher its reuse probability is .this confirms that all three factors ( i.e. , frequency , recency and semantic context ) have a positive influence on a tag s probability of being reused .our prediction study was designed to determine to what extent these three factors can be exploited to efficiently predict a user s tag reuse given a specific folksonomy type ( _ rq2 _ ) . with that regard , we applied not only algorithms that reflect these three factors individually ( _ frequency _ , _ recency _ and _ semcon _ ) but also algorithms that combine these factors ( _ girp _ , _ bll _ and _ bll _ ) and incorporate social influences , i.e. , related tags of other users ( _ fr _ and _ pitf _ ) .we observed three patterns of results based on the folksonomy type of the datasets , which are summarized in table [ tab : discussion ] . in the narrow case ,the factor of recency is the most important one , whereas in the mixed case all three factors highly contribute to the prediction accuracy and thus , the combination of these factors ( _ comb _ ) provides the best results . finally , in case of the broad folksonomies , the semantic context becomes a much more important factor than in the other two settings .furthermore , the best results in this setting are obtained for pitf , which utilizes social influences ( _ social _ ) , such as related tags of other users , as well .overall , our results show that frequency , recency and semantic context positively influence the reuse probability of tags in all six datasets ( _ rq1 _ ) and that the efficacy of these factors in terms of predicting a user s tags depends on the folksonomy type of the given social tagging system ( _ rq2 _ ) .additionally , with our findings summarized in table [ tab : discussion ] , we provide a transparent overview of the factors that influence the prediction of tags based on the given folksonomy type .we believe that our findings may be a guideline for researchers and developers in the area of tag - based recommender systems , helping them to choose the correct prediction method for a given social tagging environment .* limitations and future work .* one limitation of this study is that it is mainly focused on the factors that influence the _ individual _ reuse of tags .thus , for future work , we would like to extend this by also analyzing the influence of the reuse ( i.e. , imitation ) of other users tags and study how this _ social influence _effects tag predictions .furthermore , we plan to expand our model of the _ semantic context _ , since to date , we have analyzed it solely based on the tags that were already assigned to the currently tagged resource . in this respect , we want to incorporate other resource - dependent information , such as the resource title or content , as well .  finally , we plan to enhance our guideline with results for other types of social systems that utilize the concept of tags . to that end, we would like to determine the influence of frequency , recency and semantic context in systems that incorporate _ hashtags _ such as twitter , facebook and instagram . at the same time , this would allow us to verify that our findings can be generalized to various types of tags .  * acknowledgments . *the authors would like to thank paul seitlinger , tobias ley , ilire hasani - mavriqi and emanuel lacic for valuable comments on this work .this work is funded by the know - center and the eu - ip learning layers .d. kowald , s. kopeinik , p. seitlinger , t. ley , d. albert , and c. trattner . refining frequency - based tag reuse predictions by means of time and semantic context . in _ mining , modeling , and recommendingthings in social media _ ,pages 5574 .springer , 2015 .d. kowald , p. seitlinger , c. trattner , and t. ley .long time no see : the probability of reusing tags as a function of frequency and recency . in _ proc . of www14 companion _ , pages 463468 .international world wide web conferences steering committee , 2014 .d. m. romero , b. meeder , and j. kleinberg .differences in the mechanics of information diffusion across topics : idioms , political hashtags , and complex contagion on twitter . in _ proc . of www11_ , pages 695704 .acm , 2011 .

Abstract: in this paper , we study factors that influence tag reuse behavior in social tagging systems . our work is guided by the activation equation of the cognitive model act - r , which states that the usefulness of information in human memory depends on the three factors usage frequency , recency and semantic context . it is our aim to shed light on the influence of these factors on tag reuse . in our experiments , we utilize six datasets from the social tagging systems flickr , citeulike , bibsonomy , delicious , lastfm and movielens , covering a range of various tagging settings . our results confirm that frequency , recency and semantic context positively influence the reuse probability of tags . however , the extent to which each factor individually influences tag reuse strongly depends on the _ type of folksonomy _ present in a social tagging system . our work can serve as guideline for researchers and developers of tag - based recommender systems when designing algorithms for social tagging environments .


the prisoner s dilemma game , consisting of cooperation and defection as the two competing strategies , is considered a paradigm for studying the emergence of cooperation between selfish individuals . since the game promises a defecting individual the highest income if facing a cooperator the prevalence of cooperation within this theoretical framework presents a formidable challenge .indeed , the classical well - mixed prisoner s dilemma game completely fails to sustain cooperation , which is often at odds with reality where mutual cooperation may also be the final outcome of the game .a seminal theoretical mechanism for cooperation within the prisoner s dilemma game was introduced by nowak and may , who showed that the spatial structure and nearest neighbor interactions enable cooperators to form clusters on the spatial grid and so protect themselves against exploitation by defectors . a decade later , this theoretical prediction has been confirmed by biological experiments .nonetheless , the somewhat fragile ability of the spatial structure to support cooperation , along with the difficulties associated with payoff rankings in experimental and field work , has made it a common starting point for further refinements of cooperation facilitating mechanisms .in particular , the specific topology of networks defining the interactions among players has recently received substantial attention , and specifically scale - free graphs have been recognized as extremely potent promoters of cooperative behavior in the prisoner s dilemma as well as the snowdrift game .although the promotion of cooperation by the scale - free topology has been found robust on several factors , the mechanism has recently been contested via the introduction of normalized payoffs or so - called participation costs . moreover ,the interplay between the evolution of cooperation as well as that of the interaction network has also been studied , and it has been discovered that intentional rewiring in accordance with the preference and fitness of each individual as well as simple random rewiring of the interaction network might both have a beneficial effect on the evolution of cooperation in the prisoner s dilemma and the snowdrift game . for a comprehensive review of this field of research see .  besides studies addressing network complexity as a somewhat direct extension of ,several approaches have also been proposed that warrant the promotion of cooperation within nearest neighbor interactions .examples include strategic complexity , direct and indirect reciprocity , asymmetry of learning and teaching activities , random diffusion of agents on the grid , as well as fine - tuning of noise and uncertainties by strategy adoption .the impact of asymmetric influence , introduced via a special player with a finite density of directed random links to others , on the dynamics of the prisoner s dilemma game on small - world networks has also been studied .it is worth noting that stochasticity in general , either being introduced directly or emerging spontaneously due to finite population sizes , has been found crucial by several aspects of various evolutionary processes .  in this paper , we wish to extend the scope of stochastic effects on the evolution of cooperation in the spatial prisoner s dilemma game by introducing the social diversity of players as their extrinsically determined property .this is realized by introducing scaling factors that determine the mapping from game payoffs to the fitness of each individual .the scaling factors represent extrinsic differences amongst players , and as such determine their social status and the overall social diversity on the spatial grid .importantly , the scaling factors are drawn randomly from different distributions and are determined only once at the beginning of the game .positive scaling factors increase the magnitude of payoffs a particular player is able to exchange , while negative factors have the opposite effect .it is important to note that the average of all scaling factors is exactly zero , so that there is no net contribution of social diversity to the total payoff of the population .presently , we consider scaling factors drawn from the uniform , exponential , and scale - free distribution , and thus distinguish three different cases of social diversity .we investigate how the introduction of social diversity , and in particular its distribution and amplitude , affect the evolution of cooperation amongst players on the spatial grid .we report below that the cooperation is enhanced markedly as the amplitude of social diversity increases , and moreover , that the biggest enhancement is obtained if the social diversity follows a power - law distribution .we attribute the enhancement of cooperation to the emergence of cooperative clusters , which are controlled by high - ranking players that are able to prevail against the defectors even if the temptation to defect is large . indeed , the role of these clusters is similar to the role of pure cooperator neighborhoods around hubs on scale - free networks , or to the part of imitating followers surrounding master players in the enhanced teaching activity model , as will be clarified later . to highlight the importance of the strongly diverse social rank , we also study the impact of spatially correlated social diversity , and find that the facilitation of the cooperative strategy deteriorates as the correlation length increases .thus , a finite spatial correlation of social diversity hinders the formation of strong cooperative clusters , in turn lending support to the validity of the reported cooperation - facilitating mechanism in the spatial prisoner s dilemma game .the remainder of this paper is structured as follows .section ii is devoted to the description of the spatial prisoner s dilemma game and the properties of scaling factors determining social diversity of players on the spatial grid . in sectioniii we present the results of numerical simulations , and in section iv we summarize the results and outline some biological implications of our findings .we consider an evolutionary two - strategy prisoner s dilemma game with players located on vertices of a two - dimensional square lattice of size with periodic boundary conditions .each individual is allowed to interact only with its four nearest neighbors , and self - interactions are excluded . a player located on the lattice site can change its strategy after each full iteration cycle of the game .the performance of player is compared with that of a randomly chosen neighbor and the probability that its strategy changes to is given by  } \,\, , \label{eq : prob}\ ] ] where characterizes the uncertainty related to the strategy adoption process , serving to avoid trapped conditions and enabling smooth transitions towards stationary states .the payoffs and of both players acquired during each iteration cycle are calculated in accordance with the standard prisoner s dilemma scheme , according to which the temptation to defect , reward for mutual cooperation , punishment for mutual defection , and the sucker spayoff .importantly , throughout this work the original prisoner s dilemma payoff ranking ( ) is applicable since the introduction of social diversity via scaling factors only acts as a mapping of the original payoffs to individual fitness , as will be described next .  )originating from the uniformly distributed random variable ( ) .the three functions correspond to uniform ( u ) , exponential ( e ) , and power - law ( p ) distribution when . for easier comparison only the  ] .an efficient algorithm for the generation of spatially correlated random numbers with a prescribed correlation length is given in .the effect of different values of on the scaling factors determining social diversity is demonstrated in fig .[ fig : fig3 ] . clearly , the random undulations become more and more correlated across neighbors on the spatial grid as increases .  before the start of each game simulation , both strategies populate the spatial grid uniformly and the scaling factors are drawn randomly from a given distribution to determine the social diversity of participating players .after these initial conditions are set , the spatial prisoner s dilemma game is iterated forward in time using a synchronous update scheme , thus letting all individuals interact pairwise with their four nearest neighbors . after every iteration cycle of the game , all players simultaneously update their strategy according to eq .[ eq : prob ] . to avoid finite - size effects ,the simulations were carried out for a population of players , and the equilibrium frequencies of cooperators were obtained by averaging over iterations after a transient of iteration cycles of the game .the figures showing values of cooperator densities on the spatial grid ( ) resulted from an average over simulations with different realizations of social diversity as specified by the appropriate parameters .these simulation parameters yield at least % accurate values of in all figures .   and spatial correlation length ( bottom ) , ( middle ) , and ( top ) .lines show an exemplary cross - section of the two - dimensional grid.,width=321 ]next , we study how different distributions of social diversity affect the evolution of cooperation via numerical simulations of the above - described spatial prisoner s dilemma game .figure [ fig : fig4 ] features color - coded for all three types of social diversity in the relevant parameter space .evidently , regardless of the distribution , increasing values of clearly promote cooperation as the threshold of cooperation extinction increases from in the absence of social diversity to ( uniformly distributed social diversity ) , ( exponentially distributed social diversity ) , and ( power - law distributed social diversity ) .moreover , there always exists a broad range in the parameter space within which cooperators rule completely ; a non - existent feature if .we argue that the above - reported facilitation of cooperation is due to the induced inhomogeneous social state of players that fosters cooperative clusters around players with the largest values of . indeed, as soon as cooperators overtake these prime spots of the grid they start to spread due to their cluster - forming nature .note that the latter feature is not associated with defectors who therefore fail to take the same advantage out of social diversity , and are thus defeated .a similar behavior underlies also the cooperation - facilitating mechanism reported for the scale - free networks , where the players with the largest connectivity dominate the game .since cooperators are much better equipped for permanently sustaining the occupation of hubs , the scale - free networks provide a unifying framework for the evolution of cooperation .an even better similarity can be established with the model incorporating the inhomogeneous teaching activity . in the latter ,some players are blocked and therefore unable to donate their strategies , which results in homogeneous cooperative domains around players with full teaching capabilities .in the presently studied model , the introduction of social diversity partly results in a similar suppression of selected players , especially so for the power - law distributed case where the majority of players are low - ranking , as demonstrated in fig .[ fig : fig1 ] .these players can form an obedient domain around a high - ranking player and so prevail against defectors . on the other hand ,a high - ranking defector will be weakened by the low - ranking players who follow its destructive strategy .the above - described feedback works only if the high - ranking defectors can be linked solely by their follower neighborhoods ; namely there must not be a strong connection with other high - ranking players . in the opposite case, the heterogeneous strategy distribution supports the survival of defectors . to support our explanation, we study the impact of spatially correlated social diversity on the evolution of cooperation . according to our argument, the transition from uncorrelated to spatially correlated diversity should be marked with the deterioration of cooperation .we thus introduce spatially correlated social diversity as described in section ii , and study the effect of different on the evolution of cooperation .figure [ fig : fig5 ] features the results . in agreement with our conjecture ,the facilitation of cooperation deteriorates fast as increases .indeed , a near linear decrease of the critical marking the extinction of cooperators can be established , and moreover , by large the cooperators can outperform defectors only for slightly higher values of than in the absence of social diversity ( ) .this result supports the validity of the reported cooperation - facilitating mechanism , and hopefully paves the way for additional studies incorporating social diversity into the theoretical framework of evolutionary game theory .in this paper , we show that social diversity is an efficient promoter of cooperation in the spatial prisoner s dilemma game .the facilitative effect increases with the dispersion of social diversity and deteriorates with the increase of its spatial correlation .accordingly , spatially uncorrelated power - law distributed social diversity provides the biggest boost to the cooperative strategy .we argue that the facilitative effect is conceptually similar to the one reported previously for inhomogeneous teaching activities , and also has the same root as the mechanism applicable by scale - free networks , namely : akin to hubs or players with enhanced teaching activity , in this model , high - ranking players can form robust cooperative clusters with low - ranking obedient neighbors .the presented results suggest that the distribution of wealth plays a crucial role by the evolution of cooperation amongst egoistic individuals , and it seems reasonable to investigate further whether a co - evolution of both might yield new insights and foster the understanding of the formation of complex societies .this work was supported by the slovenian research agency ( z1 - 9629 ) ( m. p. ) and the hungarian national research fund ( t-47003 ) ( a. s. ) .discussions with gyrgy szab are gratefully acknowledged .we also thank girish nathan for useful comments .

Abstract: the diversity in wealth and social status is present not only among humans , but throughout the animal world . we account for this observation by generating random variables that determine the social diversity of players engaging in the prisoner s dilemma game . here the term social diversity is used to address extrinsic factors that determine the mapping of game payoffs to individual fitness . these factors may increase or decrease the fitness of a player depending on its location on the spatial grid . we consider different distributions of extrinsic factors that determine the social diversity of players , and find that the power - law distribution enables the best promotion of cooperation . the facilitation of the cooperative strategy relies mostly on the inhomogeneous social state of players , resulting in the formation of cooperative clusters which are ruled by socially high - ranking players that are able to prevail against the defectors even when there is a large temptation to defect . to confirm this , we also study the impact of spatially correlated social diversity and find that cooperation deteriorates as the spatial correlation length increases . our results suggest that the distribution of wealth and social status might have played a crucial role by the evolution of cooperation amongst egoistic individuals .


ecc is an approach to public - key cryptography based on the algebraic structure of elliptic curves over finite fields .the use of elliptic curves in cryptography was suggested independently by neal koblitz and victor s. miller in 1985 .elliptic curve cryptography , in essence , entails using the group of points on an elliptic curve as the underlying number system for public key cryptography .the primary reason for using elliptic curves as a basis for public key crypto - systems is that elliptic curve based crypto - systems appear to provide better security than traditional crypto - systems for a given key size , thereby reducing the process overhead .one can take advantage of this fact to increase security , or ( more often ) to increase performance by reducing the key size while keeping the same security .designers are now working on designing dedicated hardware accelerator blocks along with the main processor to increase the throughput of the design .ecc algorithm is used for secured communication in smart cards and also in gsm security .so , high speed , resource constrained environment is required . using a dual - core instead of a dedicated co- processor enables the user to operate from the application layer without entering the subordinate layers . also , the thread - level parallelism , used by the dual - core ensures higher throughput without increasing the much power , which is an important issue for low - power communication devices like smart cards .implementations can be made in different platforms namely , fpga or asic or can be done using micro - controllers .fpgas provides reconfigurability and lesser design time , while asic provides better throughput though the design time is large and expensive .we propose the design and implementation of elliptic curve cryptography ( ecc ) encryption algorithm by developing suitable single core and dual core design on xilinx virtex 4 ( ml403 ) device .the system is optimized in terms of execution speed .we perform a trade - off between throughput , power and resource requirements for our dual core implementation . to the best of our knowledge ,dual - soft core processor based implementation of ecc in an fpga is not yet available in related literatures and hence it is first of its kind .the paper is organized as follows : section 2 details the overview of ecc , the encryption and decryption process .the design and implementation details for single and dual - core processor architectures are described in section 3 .the experimental results are summarized in section 4 .conclusion and references are briefed in section 5 .this section provides some background on elliptic curves and ecc and then the hardness of decrypting the elliptic curve ciphers is also discussed .the idea of a multi processor system , establishment of communication between the processors using shared memory and the needed data synchronization is also briefed in the later part of this section .elliptic curves are described by curves , which are similar to cubic equations , used for calculating the circumference of an ellipse . in general , cubic equations for elliptic curvestake the following form known as weierstrass equation : where _ a _ , _ b_,_c _ , _ d _ , _ e _, _ p _ are real numbers and _ x _ and _ y _ take on any values in the real numbers . for our purpose , it is sufficient to limit ourselves to equation of the form given in equation[eqn : reduced weierstrass equation ] for appropriate curve parameters of ecc . figure [ fig : elliptic curve(a ) ] shows an example of elliptic curve .ecc can be used to encrypt a plain text message _m _ into cipher text for secured communication .firstly , the plain text message _m _ is converted into a set of finite points p(_x _ , _ y _ ) , which lie in the elliptic curve e(_a _ , _ b _ ) .a generator point , _ g _e(_a _ , _ b _ ) , is chosen next such that the smallest value of _ n _ for which _ ng _ = _ o _ is a very large prime number .the elliptic curve e(_a _ , _ b _ ) and the generator point _g _ are then made public .let there be two parties a and b who wish to communicate using ecc .each user selects a private key , user a s private key is n , while n is the private key for user b such that n , n < _ _n__. then they compute their public keys .the public key of a is p = n _ , while for b the public key is p = n. to send the secret message to b , a encrypts the message point p by choosing a random number _k _ and computes the cipher text points c using b s public key . the cipher text is given by :  \label{ciphertext}\ ] ] on receiving the cipher text ( pair of points ) _ c _ , b multiplies the first pair of points ( _ kg _ ) with his private key _n _ , and then adds the result to the second point of the cipher text ( _ p + kp _ )i.e. , = \;\;(p_{m } + kn_{b}g ) - [ n_{b}(kg ) ] = \;\;p_{m } \label{palintext}\ ] ] plain text message point p , corresponds to the message _ m_.it is to be observed here that only b can remove n(_kg _ ) from the second part of the cipher text .no , third party or intruder can know the message except b. thus , ecc is very secured and can be relied for confidential communication .+ breaking of ecc is a `` hard problem '' , which requires computing of discreet logarithm .a multi processor system consists of two or more processors working concurrently and capable of communicating with each other .such a design tends to double the throughput , with two processors running independently , but with an extra cost of resource and power . on the other hand ,a multi core system is one in which more than one processor is build on the same die .in fpga we have on - chip soft processor cores , which has been utilized in our design to multi core design .there are some basic conditions required for the execution of a design in a multi core system .the primary being concurrency in the design i.e. , no data dependency must be present in processes that run in different processors and also the two processors must have some handshaking for synchronization of data .multi core processors often use a shared memory system or a mailbox system as a interprocessor communication mechanism , that operates very quickly .   in a multi core environment , mailbox and shared memory are the two mechanisms , provided by xilinx .out of these two mechanisms , shared memory is the most common and most intuitive way of passing information between processing subsystems and we have used it in our design .  a shared memory system has the following properties : + any processor can refer any location in the shared memory directly by some system call .+ location of data in memory is transparent to the programmer .data could be distributed across multiple processors , with the help of some proper api , data can be handled at program level .+ a synchronization is a must for accessing the shared memory segment by some hardware / software protocol between the two processors .+ shared memory is typically the fastest asynchronous mode of communication , especially when the information to be shared is large .shared memory gives another approach of `` in - place '' message processing schemes .shared memory can be built out of on - chip local memory like bram or on external memory like ddr sdram .the region in which the shared data is stored is known as a critical region in operating system terminology . unless there is some sort of well - defined non - conflicting way in which each processor accesses the shared data , the multi core system can not work properly . a synchronization protocol or constructis usually required to serialize accesses to the shared resource .the xps mutex synchronization primitive is used in this work , which is provided by xilinx as a separate ip - core . when using shared memory as a method of data communication , the pseudo code should look like this to ensure proper synchronization , + _ /* shared tasks * / _ + _ xmutex_lock ( ) ; _ + _ / * critical region - perform shared memory access * / _ + _ xmutex_unlock ( ) ; _ + by calling the _ xmutex_lock ( ) _ it must be ensured that one processor is accessing the critical region and other processor should not be allowed to access the same until _ xmutex_lock ( ) _ is called by that processor .this section highlights the key components of our proposed design . at first, we describe the processor that is used and then we brief the design innovations made to enhance the throughput .the microblaze embedded processor soft core is a 32-bit reduced instruction set computer ( risc ) optimized for implementation in fpgas . as a soft - core processor , microblazeis implemented entirely in the general - purpose memory and logic fabric of xilinx fpgas . the embedded development kit ( edk )platform from xilinx has been used to build a complete processor system on fpga .   in a single processor architecture ,the fpga receives the input via the rs-232 port through uart and then the input plaintext message is encrypted using ecc algorithm , which is running in the microblaze processor of the the fpga . after encryption ,the cipher text is send back to the host pc and is seen in the hyper terminal using serial communication between the board and the pc .figure [ single ] shows the flow of steps in the design .processor working at 100mhz clock frequency is used to encrypt 8-bits of message using ecc .scalar multiplication constitutes the main operation in ecc .it is seen that the processor takes 19.01 msec to perform the total encryption . the resource utilized i.e. , the number of luts and slices required by the design as well as the power requirements are summarized in the table [ table : resource and power calculation ] .     after evaluating the performance of ecc in single processor architecture by using microblaze soft - core processor ,another approach is taken to implement it in dual processor architecture by considering the fact discussed in section [ mps ] for higher throughput and efficiency .xilinx virtex4 ml403 is taken as a platform for design .shared memory is used for creating a handshaking between the two processors as described in section [ shared ] and the synchronization for communication is achieved using the process described in section [ sync ] .[ dual ] shows the architecture of dual microblaze design ,    in addition , multiple port memory controller ( ddr_sdram ) and inter - processor communication - xps mutex hardware ip is also incorporated in the test bed to facilitate the memory sharing and inter processor synchronization and communication .  in the experiment ,the two processors are equally engaged to execute ecc in parallel fashion and in between the consequent steps , the two processors communicate with each other via shared memory with proper synchronization .the message to be encrypted is transferred to the fpga from a computer using rs232 serial port communication .the two multiplications are executed concurrently in two processors and the resulting data is assembled in the shared memory .the addition operation is then performed by the 1st processor and the resultant cipher text is generated .the resultant cipher text is send back to the pc using the rs232 interface and is viewed at the hyper terminal of the computer .[ dual - mb ] shows the mechanism in which the two processors communicate using the shared memory and using mutex locking and unlocking .it is seen that the encryption engine speeds up by 3.3 times as the proposed architecture takes only 5.72 msec to perform the encryption.the resource estimation , power required and throughput measurements for both the designs are shown in table [ table : throughput calculation ] and table [ table : resource and power calculation ] below . the design improves the throughput of execution , but utilizes more resources due to the dual cores .it is to be noted here that the throughput of the design can be improved further by enabling the cache memory . but due to the resource constraints of our implementation board the cache memory of the two processorscould not be enabled ..for an encryption process [ cols="^,^,^,^,^ " , ]   [ table : resource and power calculation ]this work is an exploration of ecc implementation for fpga based embedded systems .two specific designs have been addressed , the first one is simpler involving a single microblaze core whereas the other one utilizes two microblaze cores and thus enables multi - 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Abstract: cryptographic algorithms are computationally costly and the challenge is more if we need to execute them in resource constrained embedded systems . field programmable gate arrays ( fpgas ) having programmable logic devices and processing cores , have proven to be highly feasible implementation platforms for embedded systems providing lesser design time and reconfigurability . design parameters like throughput , resource utilization and power requirements are the key issues . the popular elliptic curve cryptography ( ecc ) , which is superior over other public - key crypto - systems like rsa in many ways , such as providing greater security for a smaller key size , is chosen in this work and the possibilities of its implementation in fpga based embedded systems for both single and dual processor core architectures involving task parallelization have been explored . this exploration , which is first of its kind considering the other existing works , is a needed activity for evaluating the best possible architectural environment for ecc implementation on fpga ( virtex4 xc4vfx12 , ff668 , -10 ) based embedded platform .   fpga , ecc , single - core , dual - core , microblaze , shared memory