there are numerous tasks in quantum information theory which involve the use of quantum channels .a quantum channel has many different capacities , depending on the task at hand , the nature of the information transmitted , and available resources .for example , the quantum capacity of a channel quantifies its potential for communication of quantum information , whereas its private capacity quantifies its potential for secure communication of classical information  . deciding whether a given quantum channel has a positive capacity is a non - trivial problem , e.g. there does not exist a unique criterion to determine whether the quantum capacity of a given channel is zero .classical channels with zero capacity are uninteresting in the information - theoretic sense .in contrast , quantum channels with zero capacity exhibit intriguing behavior as shown by the superactivation phenomenon  : there exist examples of pairs of channels with zero quantum capacity , which , when used in tandem , allow transmission of quantum information .one particular class of zero - capacity channels consists of _ antidegradable channels_. for such a channel , a post - processing of its environment can simulate the output of the channel  .the no - cloning theorem  ensures that such channels have zero quantum capacity .the simplest example of the latter is a 50% erasure channel which with equal probability either transmits the input state perfectly or replaces it with an erasure flag .however , there are other non - trivial examples of channels with zero quantum capacity , e.g. , the positive partial transpose ( ppt ) channels  . in addition , antidegradable channels also have zero private capacity ( unlike ppt channels ) , but whether they are the only non - trivial quantum channels with this property is an open question ( since there exist echo - correctable channels with arbitrarily small , but non - zero , private capacity  ) . therefore , the knowledge that a given channel has zero quantum and private capacity is not sufficient to conclude that it is antidegradable .this leads us to the following question :  ( q ) : is there a setting in which one can obtain a complete operational characterization of antidegradable channels ?  in this paperwe answer this question in the affirmative by constructing a game - theoretic framework which involves the noisy quantum channel ( which we wish to characterize ) , a quantum public side channel , and three parties : alice ( the sender ) , bob ( the receiver ) and eve ( the eavesdropper ) .alice sends classical information to bob through , whose environment is accessible to eve .alice also sends information through , which is accessible to both bob and eve .the game is constructed as follows ( formal definitions are given in section [ sec : main ] ) .alice chooses a letter at random from a given finite alphabet , and encodes it in a bipartite state , say .the part of the input is sent through , while the part is transmitted via .bob then obtains the output of while eve receives the information that is transmitted to the channel s environment . in other words , she receives the output of the _ complementary channel _ ( see section 2 for its definition ) .in addition , they both receive the output of .the task now , for both bob and eve , is to guess which letter alice chose .since bob and eve are competing , they both adopt the optimal guessing strategy they have available .correspondingly , the reliabilities of their guesses is measured by the optimal guessing probabilities of the ensembles of states they receive .bob wins the game whenever his guessing probability is _ strictly higher _ than that of eve ( i.e. in the case of a draw , eve wins ) .the situation is depicted in figure [ fig:1 ] below .( i.e. the one which we want to characterize ) and a quantum channel , which is public , in the sense that it conveys the same output to bob and eve .a natural example of such a public channel is a symmetric channel  .bob plays the guessing game against eve , who has access to the environment of ( labelled by ) and .,width=302 ]  to state our main result ( theorem [ theo : main ] ) which leads to the characterization of antidegradable channels , we first introduce the notion of _ extension _ of a quantum channel : for any pair of quantum channels we say that is an _ extension _ of if for some quantum channel .this is a generalization of the notion of _ degradable extension _ of the channel ( introduced in  ) which corresponds to the case in which the channel is degradable and is complementary to it .then our result can be stated as follows : for any given input ensemble of states , the guessing probability of the output ensemble of is higher than that of , if and only if is an extension of .we establish the above result by first proving its analogue for statistical comparison of bipartite states and then using choi isomorphism .consider the case in which is the quantum channel employed in the guessing game [ game ] , and is the channel which is complementary to it .for this choice , our result ( theorem [ theo : main ] ) implies that is antidegradable _ if and only if _ eve always wins , regardless of the choice of alice s encoding strategy . in other words, our result shows that , _ for any _ channel which is not antidegradable , there exists ( at least ) one encoding strategy which alice can choose to make bob win the guessing game .we note that even though the scenario of our guessing game is ` cryptographic ' in its nature ( since bob and eve compete ) , proving that bob is able to win against eve in the guessing game is insufficient to conclude that any _ information - theoretic secrecy _ can be established between alice and bob .this is because , in the guessing game , we only compare the guessing probabilities of bob and eve , and not the mutual informations between the random variables corresponding to their respective inferences and that of the random variable corresponding to alice s input . however , the game - theoretic scenario [ game ] has the particular advantage of singling out antidegradable channels as the only channels for which eve necessarily wins .in other words , a _ necessary and sufficient condition _ for the quantum channel to be antidegradable is that eve wins the guessing game , for any possible encoding strategy alice may choose .the paper is organized as follows . in section [ sec : main ] we introduce the necessary notation and definitions , and then state our main result ( theorem [ theo : main ] ) . in section[ sec : states ] we derive an analogue of theorem [ theo : main ] for partial orderings of bipartite quantum states . in section[ sec : back - to - channels ] we use this result , in conjunction with the choi isomorphism , to obtain a proof of theorem [ theo : main ]. some further implications of theorem [ theo : main ] for convex combinations of channels and their extensions are given in [ sec : further ] .we end with a brief summary and open questions in section [ sec : conclude ] .in what follows , we only consider quantum systems defined on finite dimensional hilbert spaces .we denote by the set of all linear operators acting on , and by the set of all density operators ( or _ states _ ) , with and =1 ] , for all and . therefore ,if is a channel , its adjoint is a completely positive , unital ( unit - preserving ) , i.e. , linear map ( and vice versa ) .  given a channel , its _ stinespring isometric dilation _ is given by a complementary ( ancillary ) quantum system ( the ` environment ' ) together with an isometry , , such that ,\quad\forall x\in\bound(\sh_a).\ ] ] the stinespring isometric dilation , which always exists , can be considered to be essentially unique , in the sense that it is unique up to isometric equivalences on .this leads us to define an essentially unique complementary channel as follows  : .\ ] ]  given a channel , let be its complementary channel . is called _ antidegradable _ if and only if there exists another channel such that ( it is easy to verify that the property of being antidegradable does not depend on the particular stinespring isometric dilation chosen to construct the complementary channel . ) [ def : degradable ]  in other words , an eavesdropper , eve , who has access to the environment of an antidegradable channel , can perfectly simulate the output of the channel by means of a fixed post - processing which is independent of the input . in this sense ,eve always receives _ more information _ than the receiver bob . as a straightforward consequence ,antidegradable channels turn out to have zero capacity for any information - theoretic protocol that aims to put bob in a position of advantage over eavesdropper .another notion we need is the following  :  [ def : symmetric ] for a given finite integer , let be a -dimensional hilbert space , and be -dimensional hilbert spaces ; moreover , let be any isometry embedding into the symmetric subspace ; the channel , defined by its action  ] via the relation : conversely , any bipartite state with =d^{-1}\openone_a ] , contains linearly independent elements .suppose that there exists a povm on such that the set , where  ] . clearly , all belong to , and they are linearly independent if and only if the are. therefore contains linearly independent elements , i.e. is -complete .conversely , suppose that is -complete .then , there exist positive operators such that all \in\ss_b(\rho_{ab}) ] . since the first elements of are linearly independent if and only if the are , we have that the set surely contains linearly independent elements .[ theo : equiv ] given two bipartite quantum states and with , the following are equivalent :  1 . ; 2 .  for any , any , and any auxiliary bipartite state , 3 .  for some -complete state , with ,  we begin by noticing that the implication ( 1)(2 ) is a trivial consequence of the fact that , if for some channel , the action of any povm on can be exactly simulated on by using the povm , where we denoted by the heisenberg dual of .also the implication ( 2)(3 ) is trivial .we are then left to prove that ( 3)(1 ) . in order to do so , we consider two auxiliary hilbert spaces and , such that , and a -complete state ( see def .[ def : complete ] ) .we then consider , in particular , the following measurement on the composite state : ,\ ] ] where  * is an informationally complete povm on ( i.e. any operator in can be written as a linear combination of its elements ) ; * is the povm on , whose existence is guaranteed by lemma [ lemma : complete ] , inducing a complete set of linearly independent reduced ( subnormalised ) states  ] , where and is a maximally entangled state in .therefore , for any given channel , its choi state is constructed so that , for any input state , there exists an operator such that  ] spans the whole , i.e. the bipartite state is complete , according to definition [ def : complete ] .conversely , suppose that the choi state , associated with a channel , is ( -)complete , in the sense of definition [ def : complete ] .then , by definition , there exist operators such that the states defined as  ] , where  ] are possible outputs of , i.e. , is complete .therefore , its associated choi state  ] for all .it is therefore clear that point ( 3 ) in theorem [ theo : equiv ] is completely equivalent ( in fact , just a reformulation ) of point ( 3 ) in theorem [ theo : main ] . since point ( 3 ) in theorem[ theo : equiv ] is also equivalent to point ( 1 ) in theorem [ theo : equiv ] , we are left to show that point ( 1 ) in theorem [ theo : equiv ] is just a reformulation of point ( 1 ) in theorem [ theo : main ] .the logical steps are summarized as follows : where the first equivalence has been proved above , the second equivalence is in the statement of theorem [ theo : equiv ] , and only the last equivalence is left to be proved . butthis is a simple consequence of the fact that choi s correspondence is one - to - one , therefore two channels and are such that there exists a third channel with , if and only if .one can extend the results of theorem [ theo : main ] to convex combinations of channels .it was shown in  that degradable channels and degradable extensions have especially nice properties which prove to be useful when evaluating their quantum and private capacities .these properties are also reflected in the game - theoretic framework . in particular , the following two corollaries show how to compare and combine convex combinations of degradable channels and their extensions in this framework .consider a channel , and a sequence of channels , , such that .assume that each is degradable , with the corresponding degrading map is given by .define the flagged version of the convex combination of as .then , is strongly more informative than , i.e. .it was proven in  that is a degradable extension of . then the corollary follows after applying theorem [ theo : main ] .consider two channels , , for each of which there exist and such that for .then , for and we have that is strongly more informative than : .it is sufficient to observe that is a degradable extension of  . then the corollary follows after applying theorem [ theo : main ] .we introduced a game - theoretic framework [ game ] which allowed us to derive a necessary and sufficient condition for a channel to be antidegradable .we showed that for any channel which is not antidegradable , there exists an encoding strategy for which such a channel provides a strict advantage for the two players over the adversary in the guessing game that we defined .the key ingredients in the proof of this result are the tools of statistical comparison of bipartite quantum states , and the choi isomorphism .the exact relationship between our game - theoretic framework and the standard information - theoretic framework remains to be explored .it would be interesting to see whether any inference about the quantum or private capacity of a quantum channel could be made from results obtained in our game - theoretic framework .another direction worth pursuing is one which involves devising game - theoretic characterizations of other classes of quantum channels , since this might lead to a better understanding of the structure of zero - capacity channels. it would also be interesting to explore the connections between our game - theoretic approach and other incapacity tests  for quantum channels .the authors are grateful to michele dallarno for suggesting an improvement to their previous proof of lemma [ lemma : complete ] .s.s . acknowledges the support of sidney sussex college .i. devetak and p. w. shor , _ the capacity of a quantum channel for simultaneous transmission of classical and quantum information_. communications in mathematical physics * 256 * , issue 2 , pp 287 - 303 ( june 2005 ) .e shmaya , _ comparison of information structures and completely positive maps_. j. phys . a : math . and gen .* 38 * , 9717 - 9727 ( 2005 ) .a chefles , _ the quantum blackwell theorem and minimum error state discrimination_. arxiv:0907.0866v4 [ quant - ph ] .g m dariano and p lo presti , _ imprinting a complete information about a quantum channel on its output state_. phys .lett . * 91 * , 047902 ( 2003 ) .f buscemi , _ comparison of quantum statistical models : equivalent conditions for sufficiency_. comm .* 310 * , 625647 ( 2012 ) .f buscemi , _ all entangled states are nonlocal_. physlett . * 108 * , 200401 ( 2012 ) .g smith , j a smolin , and a winter , _ the quantum capacity with symmetric side channels_. ieee trans .theory * 54 * , 9 , 4208 - 4217 ( 2008 ) .f g s l brando and j oppenheim , _ the quantum one - time pad in the presence of an eavesdropper_. phys . rev . lett . * 108 * , 040504 ( 2012 ) . f g s l brando and j oppenheim , _ public quantum communication and superactivation_. ieee transtheo . * 59 * , 2517 ( 2013 ) .note , however , that there exist channels which convey the same information to both bob and eve , but which can not be written as -dimensional symmetric channels .an example is given by the 50% erasure channel mentioned in the introduction , which maps -dimensional inputs into -dimensional outputs .graeme smith , john a. smolin , _ additive extensions of a quantum channel_. proc . of the ieee inf .workshop 2008 , pp 368 - 372 .

Abstract: we introduce a guessing game involving a quantum channel , three parties the sender , the receiver and an eavesdropper , eve and a quantum public side channel . we prove that a necessary and sufficient condition for the quantum channel to be antidegradable , is that eve wins the game . we thus obtain a complete operational characterization of antidegradable channels in a game - theoretic framework .


recent observations have generated new interest in understanding the sunspot fine structures like umbral dots , light bridges , and penumbral filaments .detailed spatial and temporal observations of these fine structures are crucial in understanding the physical mechanisms behind the formation of these structures . with the success of the solar adaptive optics ( ao ) ,it is now feasible to study structures close to the diffraction limit of modern telescopes .these small - scale structures harbour flows that are important for understanding the interaction between magnetic fields and plasma .observational study of these flows would provide constraints to the theoretical models and to the magnetohydrodynamic simulations of these flows and hence would lead to a better understanding of the overall structure .doppler shifts of spectral lines are regularly used to study the line of sight ( los ) velocity of solar features . they are observed either with a spectrograph - based instrument or with an instrument based on tunable narrow - band filter . in instruments based on a tunable narrow - band filter, doppler velocities are obtained using the red- and blue - wing intensity images of a chosen spectral line .intensity at a fixed wavelength point in the blue and/or red wing of any spectral line varies depending on the doppler shift . at a fixed wavelength point in the red wing of an absorption line , a red-(blue- )shift will reduce ( increase ) the intensity .similarly , at a fixed point in the blue wing of an absorption line , a red-(blue- ) shift will increase ( decrease ) the intensity .hence , the difference between the red- and blue - wing intensities obtained at a fixed wavelength point is used to estimate the doppler shift and hence the doppler velocity . a magnetic field and itsgradients may affect the magnetically sensitive spectral line profiles and hence the doppler velocities estimated from them .therefore , magnetically insensitive lines are preferred for a clean " velocity estimation .for example , 5434  or 5576  are typically used to estimate doppler velocities at the photosphere .systems based either on a tunable fabry - prot etalon or a universal birefringent filter ( ubf ) ( see , , , and references therein for details about these instruments ) are used to obtain the required spectral bandwidth ( _ e.g. _ , about 200m for photospheric spectral lines ) . in both schemes ,doppler velocities are estimated from the difference between intensities obtained at the blue and red wing of a chosen spectral line by using the following relation :    where and are the red- and blue - wing intensities and is a calibration constant which depends on the chosen spectral line and the spectral resolution . can be obtained using a well - known procedure briefly explained in section [ s - simul ] of this paper . with this definition ,positive ( negative ) velocity correspond to flows towards ( away from ) the observer .this sign convention is followed throughout this paper .  in such observations ,the blue- and red - wing images are not recorded simultaneously . the time difference between the two depends on the wavelength tuning time , required number of wavelength positions , andthe detector read - out time . in most casesthe detector read - out time , which is typically a few seconds , limits the cadence .hence , any appreciable change in the observing conditions within this time interval can introduce systematic errors in the velocity as well as spurious velocity structures .if these spurious velocities and these structures are comparable to those of the intrinsic velocities of photospheric structures , then the physical interpretation of the structures will be ambiguous .the typical intrinsic velocities in umbral dots are of the order of a few hundred m s , whereas the penumbral evershed flows and quiet - sun granular velocities are of the order of a few thousand m s .it is a well - known fact that ground - based observations are affected by the atmospheric turbulence which is often characterised by fried s parameter ( ) for long - exposure images . for this paper, a variable seeing condition refers to the time variation of the parameter .if the time variation is a few cm within the few seconds required for obtaining the red- and blue - wing images , then the variable seeing conditions can introduce spurious velocity signals . in ground - based observations ,an adaptive optics system is used to minimise the seeing effect .however , the performance of an adaptive optics system is a function of the seeing conditions at the time of observations .have shown that the sterhl ratio ( one of the metrics for evaluating ao performance ) of an ao corrected image is a function of fried s parameter ( ) .an example of the effect of variable seeing is shown in figure [ vel_image ] .the observations were obtained at the dunn solar telescope ( dst ) in sunspot , nm , usa using the ubf system .the images marked with r and b ( r1 , r2 , b1 , and b2 ) are the red- and blue - wing images whereas the images marked with v ( v1 and v2 ) are the estimated velocities from the respective r and b. the top row images were obtained under stable seeing conditions whereas the bottom row during variable seeing conditions .the velocity map clearly shows spurious velocity signals in the umbral and penumbral regions under variable seeing conditions .this is also true with quiet solar granulation ( not shown here ) but not so obvious to the eye due to the high intensity - velocity correlation at these regions .the aim of this paper is to quantitatively estimate the variable seeing - induced spurious velocity signals , through simulations and to compare them with observations . in section [ s - simul ] , the method used to simulate the variable seeing conditions is explained and the input data used for the simulation are also explained . in section [ s - results ] , results from the simulation using both space- andground - based data are discussed .the comparison of the simulation results with the observed data and a summary are given in section [ s - summary ] .we conclude with the result that there is a good correlation between seeing difference and spurious velocity signals , especially in the umbral region of the spots .our simulation indicates that spurious velocities can be as large as 1 km s and it is alarming to note that such high values are seen in the observed data .to simulate the effect of variable seeing on the doppler velocities , the red- and blue - wing images , initially unaffected by the atmospheric turbulence , were convolved with point spread functions ( psfs ) produced using different .the psfs were generated using the software tool adaptive optics performance evaluator ( aope ) , originally developed for performing simulations on the design needs of solar adaptive optics systems .a detailed description of the effect of the atmospheric turbulence on the quality of the images obtained with ground - based telescopes can be found in .the instantaneous wavefront perturbations induced by the atmosphere can be represented as a two - dimensional phase screen .aope generates such phase screens following the kolmogorov model of turbulence , for any given value of fried s parameter ( ) and derives a long - exposure psf from them for a chosen telescope diameter and observing wavelength .aope also simulates the effect of the adaptive optics correction by fitting a model phase screen with finite number of zernike polynomials ( which are generally used in characterising the aberrations in optical systems ) to the originally generated phase screen and subtracting the best fit model phase screen from the original phase screen .the long - exposure psfs after adaptive optics correction are then generated from a series of residual phase screens , again for a chosen telescope diameter and wavelength .thus , fried s parameter , telescope diameter , number of equivalent zernike modes corrected by the adaptive optics system and the observing wavelength are the input parameters to be selected by the users .long - exposure psfs with and without a finite number of zernike - mode correction , and ideal psf of the telescope are the output parameters .these output parameters are characterised with the strehl ratio , normalised strehl resolution and the strehl width which quantify the final image quality for a given set of input parameters . in our simulations , we used this tool to obtain the ideal psf of the telescope , and the psfs with and without the required zernike correction .the corrected psf depends on all the four input parameters , whereas uncorrected psfs do not depend on , the order of zernike correction .the ideal psfs depend only on telescope diameter and wavelength .the input data used for the simulation are obtained using the solar optical telescope ( sot ) on - board _ _ hinode _ _ - a satellite dedicated for solar observations ._ hinode _ is a joint mission between the space agencies of japan , united states , europe , and united kingdom .being a space - based instrument , the data obtained from sot are free from atmospheric turbulence .the narrow - band filter imager ( nfi ) on sot is used to observe wing images of magnetically insensitive ( ) line ( =5576 ) .the observations were carried out on 2007 july 14 , 11:34 ut of an active region noaa 10963 . a pair of images observed at the wings (  away from the line core ) of the line 5576.09  are used as the input images for this simulation .   60 m ; represented by asterisks ) and 5576  ( wing points at 136 m ; represented by pluses ) .solid and dashed lines are straight line fits to the respective curves . ]the input data for the simulation of ground - based images are obtained using ubf observation of a sunspot carried out at the dunn solar telescope ( dst ) , nso , nm , usa , on 2005 december 28 .the calibration constant ( _ cf ._ equation ( 1 ) ) , required for deriving the velocity from the observed normalised intensity difference ( = ) , is estimated using the spectral profile from the lige atlas .first , the atlas profile of the observed line is convolved with a gaussian filter profile of passband specific to the instrument used . in this paper ,data from the nfi on - board _ hinode _ as well as from the ubf at the dunn solar telescope are used .the passband is estimated to be 70 m in the case of nfi and 142 m for the ubf .the doppler shift of the spectral line for a defined velocity is calculated by using where is the speed of light . the convolved spectral line is then shifted by an amount of and the normalised intensity difference is calculated .this is repeated for a range of velocities .figure [ ubfcal ] shows the relation between and for both 5576  ( plus ) and 5434  ( asterisks ) spectral lines .the linear part of the curve is fitted with a straight line ( solid and dashed lines respectively ) and 1/slope provides the calibration constant value . for large velocity values , either the line core orthe continuum will cross one of the chosen wing wavelengths and hence the curve will deviate from the straight line .this sets the limit for the velocity range that can be measured using this method . the velocity range and the slope value ( or calibration constant ) depends on the spectral line and the chosen wing pair .this is clearly reflected in figure [ ubfcal ] in which the dynamic range achieved for 5576  is smaller compared to that of 5434  .the simulation is carried out for a telescope diameter of 50 cm ( commensurate with _ hinode _ ) and for different fried s parameter values ( starting from = 4 cm to 15 cm ) . in typical ground - based solar observations ,fried s parameter of 4 cm or below is considered as bad seeing and an of 12 cm or above is considered as an excellent seeing condition . for each values , psfs with and without zernike corrections ( of a particular order ) are generated . for the simulation , zernike order is varied from 11 to 55 depicting different amount of ao corrections .the psfs generated are then convolved with the input image to generate different observational conditions . in order to simulate the variable seeing effects, the blue- and red - wing images are convolved with different psfs generated using different as well as different zernike correction .the velocities are derived using equation ( [ eq1 ] ) for different simulated conditions .the generated velocity images are used to quantify the effect of variable seeing conditions .the umbra , penumbra , and quiet sun regions are analysed separately in order to quantify the effects in these different regions .  for quantifying such variable seeing conditions between blue- and red - wing images ,we define the normalised seeing difference by ,    where and are the seeing during the red- and blue - wing observations respectively .the top row of figure [ hinode_fig2 ] shows a pair of red- and blue - wing images and the velocity image used in our simulation .the velocity image in the top row shows the typical granular flows in the quiet region , evershed flows in the penumbral region and uniform or zero flows in the umbral region . the grey scale used for the velocity imagesare also marked as a colour bar on the right side of the velocity figures .the bottom row shows the best case scenario when the seeing is good , like with the case of = 15 cm and high order ao correction ( = 66 ) .the estimated velocity image looks similar to the original .the middle row shows a seeing - affected blue - wing image simulated for = 4 cm and without ao correction ( the worst case scenario ) , the original red - wing image ( convolved with ideal psf ) , and the resulting velocity image .note the change in the velocity values and the appearance of velocity structures in the umbra .these small - scale structures resemble umbral dots in the intensity image and hence are considered as cross - talk from intensity .this clearly shows the effect of the seeing difference inducing spurious velocity structures as well as modifying the velocity amplitudes .these effects are most notable in the umbral region .   except that it is simulated .the top row shows the original red- ( r1 ) , blue - wing ( b1 ) images and the corresponding velocity map ( v1 ) . the middle row shows the original red- ( r2 ) , convolved blue - wing ( b2 ) images and the corresponding velocity ( v2 ) .b2 is created by convolving original blue - wing image with a psf of = 4 cm and without ao correction . in the bottom row ,b3 is created by convolving original blue - wing image with the psf of = 15 cm and =66 .the colour bars on the right - hand side shows the grey scale range for the corresponding velocity images .dark and white contours in v1 are the regions selected for measuring and , respectively . ]  in order to quantitatively study the effect on the mean velocity ( ) , a core umbral region with minimal intensity structures ( like umbral dots ) is selected manually .this region is shown as a white contour in v1 of figure [ hinode_fig2 ] .the spurious velocity structures ( as seen in v2 of figure [ hinode_fig2 ] ) are quantified using the standard deviation of the velocity of an umbral region which includes the umbral structures ( like umbral dots ) and this is shown as a dark contour in v1 of figure [ hinode_fig2 ] .the two parameters ( and ) are plotted with normalised seeing difference ( cf .equation ( [ eq2 ] ) ) in figure [ hinode1 ] .the seeing difference is simulated by convolving one of the wing images ( either red or blue ) with a psf of a fixed fried s parameter ( called base seeing in this paper ) , and the other wing is convolved with psfs corresponding to variable fried s parameter ( = 4 to 15 cm ) .this is repeated by varying the base seeing values from 4 to 15 cm .the normalised seeing difference is calculated as per equation ( [ eq2 ] ) , and the mean velocity is calculated at the selected core umbral region . the same is also repeated with ao corrected psfs , with zernike correction order varying from =11 to =55 .  in figure [ hinode1 ] ,the normalised seeing difference versus umbral core mean velocity is plotted on the left column .the top plot is the case without ao correction , the middle plot is with a zernike correction of =11 and the bottom one is for =55 .all the plots have three types of symbols .squares are for base seeing , where either or is equal to 15 cm and the other varying from 15 to 4 cm .in other words , one of the wing images is affected by the best seeing condition and the other varies from best to worst .similarly , asterisks are for a base seeing of 4 cm and pluses are for 9 cm .each curve has two parts , separated by zero , and positive abscissa ( positive ) means .all the symbols are just connected by lines of different line types . as seen in the right column of figure [ hinode1 ] ,the standard deviation ( ) varies with seeing difference and hence can not be used as an error estimate for .the standard deviation of the velocity estimated in the selected umbral region of the original velocity image is used as the error in the velocity estimates for all simulated conditions .all the three plots show that spurious velocity values increase with normalised seeing difference . for a particular normalised seeing difference value, there is a range of velocity values depending on the base seeing condition .a poor base seeing , or the dashed line in the plot ( connecting asterisks , where either or is equal to 4 cm ) , represents the maximum limit , and a good base seeing , solid line ( connecting squares , where either or is equal to 15 cm ) is the minimum limit of these induced velocities .notice that the range comes to almost zero at zero normalised seeing difference , irrespective of the difference in the base seeing . as ao corrections are applied ( middle and bottom plots ) , both the maximum and minimum limit of the induced velocity decreases .   or = 15 cm and the solid line connects the symbols , pluses are for or = 9 cm , asterisks are for or = 0 cm and the dotted lines and dashed lines connect the symbols , respectively ., title="fig : " ]  or = 15 cm and the solid line connects the symbols , pluses are for or = 9 cm , asterisks are for or = 0 cm and the dotted lines and dashed lines connect the symbols , respectively ., title="fig : " ]  or = 15 cm and the solid line connects the symbols , pluses are for or = 9 cm , asterisks are for or = 0 cm and the dotted lines and dashed lines connect the symbols , respectively ., title="fig : " ]  or = 15 cm and the solid line connects the symbols , pluses are for or = 9 cm , asterisks are for or = 0 cm and the dotted lines and dashed lines connect the symbols , respectively ., title="fig : " ]  or = 15 cm and the solid line connects the symbols , pluses are for or = 9 cm , asterisks are for or = 0 cm and the dotted lines and dashed lines connect the symbols , respectively ., title="fig : " ]  or = 15 cm and the solid line connects the symbols , pluses are for or = 9 cm , asterisks are for or = 0 cm and the dotted lines and dashed lines connect the symbols , respectively ., title="fig : " ]  in the right column of figure [ hinode1 ] , the standard deviation of the selected umbral area is plotted with normalised seeing difference .the top plot is without ao correction , the middle one with a zernike correction of =11 and the bottom one with =55 .the horizontal line is the value of of the original velocity image .it is clear from the curves that the seeing difference introduces spurious velocity structures in the selected umbral region , and ao with higher order correction helps in minimising these induced spurious velocity structures .when both wing images are affected by similar bad seeing , the fine scale intensity structures are smeared in both .hence the intrinsic velocity contrast of these structures is reduced representing the points below the horizontal line .a similar study is carried out for the penumbral regions . however , due to the presence of evershed flows , the mean velocity ( ) was calculated separately for positive and negative velocities ( flows away from and towards the observer ) .the standard deviation of the selected penumbral area is a measure of penumbral structures .these two parameters are plotted in figure [ hinode2 ] for different zernike corrections .it is clear from the figure that ( left column ) in a penumbra increases very little ( 200 - 300 m s ) with normalised seeing difference , whereas ( right column ) increases significantly .similar to the umbral structures , with higher order ao correction falls off to original and also does not fall to zero due to the existence of penumbral velocity structures in the input image . in the case of the penumbra , of the input imagecan not be taken as the error in the velocity estimate due to the presence of evershed flow velocity structures , and hence the error bars are not displayed .horizontal lines show the value of estimated from the initial velocity image .the quiet sun - study showed a similar behaviour ( with weaker amplitudes ) like the penumbra and hence is not discussed in this paper .but for the penumbral region .the mean velocity is calculated separately for positive ( towards the observer ) and negative ( away from the observer ) cases .squares ( positive side ) and triangles ( negative side ) represent the best base seeing condition ( or = 15 cm ) .similarly , asterisks ( positive side ) and diamonds ( negative side ) represent the bad base seeing condition ( 4 cm ) , and pluses represent the medium seeing condition ( 9 cm ) .lines are just a connection of data points . , title="fig : " ]  but for the penumbral region .the mean velocity is calculated separately for positive ( towards the observer ) and negative ( away from the observer ) cases .squares ( positive side ) and triangles ( negative side ) represent the best base seeing condition ( or = 15 cm ) .similarly , asterisks ( positive side ) and diamonds ( negative side ) represent the bad base seeing condition ( 4 cm ) , and pluses represent the medium seeing condition ( 9 cm ) .lines are just a connection of data points . , title="fig : " ]  but for the penumbral region .the mean velocity is calculated separately for positive ( towards the observer ) and negative ( away from the observer ) cases .squares ( positive side ) and triangles ( negative side ) represent the best base seeing condition ( or = 15 cm ) .similarly , asterisks ( positive side ) and diamonds ( negative side ) represent the bad base seeing condition ( 4 cm ) , and pluses represent the medium seeing condition ( 9 cm ) .lines are just a connection of data points ., title="fig : " ]  but for the penumbral region .the mean velocity is calculated separately for positive ( towards the observer ) and negative ( away from the observer ) cases .squares ( positive side ) and triangles ( negative side ) represent the best base seeing condition ( or = 15 cm ) .similarly , asterisks ( positive side ) and diamonds ( negative side ) represent the bad base seeing condition ( 4 cm ) , and pluses represent the medium seeing condition ( 9 cm ) .lines are just a connection of data points ., title="fig : " ]  but for the penumbral region .the mean velocity is calculated separately for positive ( towards the observer ) and negative ( away from the observer ) cases .squares ( positive side ) and triangles ( negative side ) represent the best base seeing condition ( or = 15 cm ) .similarly , asterisks ( positive side ) and diamonds ( negative side ) represent the bad base seeing condition ( 4 cm ) , and pluses represent the medium seeing condition ( 9 cm ) .lines are just a connection of data points . , title="fig : " ]but for the penumbral region . the mean velocity is calculated separately for positive ( towards the observer ) and negative ( away from the observer ) cases .squares ( positive side ) and triangles ( negative side ) represent the best base seeing condition ( or = 15 cm ) .similarly , asterisks ( positive side ) and diamonds ( negative side ) represent the bad base seeing condition ( 4 cm ) , and pluses represent the medium seeing condition ( 9 cm ) .lines are just a connection of data points . , title="fig : " ]a similar study is carried out with images obtained from ground - based observation .the seeing was variable at the time of observation .about 3 s was required to tune ubf from one wing to the other wing . due to the variable seeing condition, there were many wing - pair images affected by the seeing difference in the observed data ( one such an example is shown in figure [ vel_image ] ) .from the observed data , a pair of best images were chosen as input for the simulations .differential seeing was simulated as explained in the previous section .the curves of and are very similar to the curves seen in figure [ hinode1 ] , and hence they are not reproduced here in this paper .the only notable difference was in the curves and that can be attributed to the difference in the umbral structures for these two different sunspot regions .in the velocity measurements from the ground using narrow - band filters , there is always a chance of systematic error in velocity estimates due to the seeing difference .if seeing changes within the time of wavelength tuning from one wing to the other , it will create spurious velocity values .we simulated such seeing difference conditions using the aope code , and we studied the induced velocity values in different areas of a solar active region ( like umbra , penumbra , and quiet sun ) .it is concluded that the seeing difference affects the velocity estimates more in the umbra than in the penumbral region of the sunspot .it is also seen that the effect is minimal in the quiet sun . under worst normalised seeing difference conditions , where one wing image is obtained under a good seeing condition ( = 15 cm ) and the other during worst condition ( = 4 cm ; =0.58 ), the induced velocity is as high as 1 km s .such a large variation in seeing may not occur often in real cases , but our sample observations ( _ e.g. _ figure [ vel_image ] ) using the ubf at the dst have shown velocities up to 600 m s .it is also clear that these induced velocity structures are due to cross - talk from intensity .a correlation analysis carried out between intensity and velocity shows a correlation coefficients up to 50% in the worst case scenario .these simulations also show that adaptive optics corrections can significantly reduce such induced velocities , and velocity structures .we used ubf observations carried out during variable seeing conditions to compare with the simulations .however , in order to compare with the real observations , contrast values are used as a measure of seeing , since there were no simultaneous measurements of fried s parameter .the contrast at the umbra - penumbra border was used as a measure of seeing rather than the quiet - sun contrast .this is because the lock point of ao was in the umbra - penumbra border .the ao correction away from the lock point was really variable due to the variable seeing condition and hence contrast obtained at these areas will not represent the seeing changes alone in the umbra .we have also taken care to choose the region which has a minimum velocity throughout the time sequence of roughly 2 hours , as velocity can also change the intensity contrast .we define contrast as the standard deviation of the selected region in the intensity image .the normalised contrast difference is defined as the ratio between the difference and total of the blue- and red - wing contrasts and hence is a proxy for the normalised seeing difference value .figure [ dcontra ] shows the relation between normalised seeing difference and normalised contrast difference from simulations with nso data as the input .it is clear from the plot that the spread in the curve will cause a degeneracy in the normalised contrast difference values for a particular normalised seeing difference .also , the zero normalised contrast difference does not fall on the zero normalised seeing difference and vice versa .this shift can be associated to the seeing difference in the input wing images and to the convective blue - shift .figure [ final_plot ] shows the scatter plot between the normalised contrast difference versus at the core umbra estimated for the nso data .squares are from observation and pluses are from simulation .the simulation was extended to include all combinations of seeing values varying from = 4 to 15 cm and a zernike correction from = 11 to 77 to mimic a real observation .the error bar of the original data points are three times the standard deviation ( ) of the velocity distribution in the selected umbral core region. the value of this will be a combination of the actual error in the velocity estimation and the standard deviation due to the induced structures because of the seeing difference .in general most of the data points ( 70% ) fall within the simulated velocity distribution . however , there are points well away from the simulated curve which may be due to ( 1 ) the observed data being a time sequence spanning approximately 2 hours , and hence any evolution can change both the velocity value and the contrast , ( 2 ) simulation assuming noiseless psf after perfect ao correction whereas in a real situation it will not be .we conclude the folloeing .( 1 ) a seeing difference introduces spurious velocity signals which are large in the umbra compared to the penumbra and the quiet sun due to the low intrinsic velocities inside the umbra .( 2 ) the spurious velocity also depends on the base seeing condition .if the general seeing conditions are very bad , then even a small seeing difference can cause large spurious velocity .( 3 ) the simulations have given a range of spurious velocity , for a particular seeing difference in very bad base seeing condition ( = 4 cm ) and for very good base seeing condition ( = 15 cm ) .for a normalised seeing difference condition of 0.5 this spurious velocity can range from 600 m s ( good base seeing ) to 1200 m s ( bad base seeing ) .a normalised seeing difference of 0.5 in the umbra occurs when the ratio of fried s parameter between the red- and blue - wing images is larger than 3 .a normalised seeing difference of 0.5 corresponds to a normalised contrast difference of approximately 0.2 and such values are seen in the observed data .( 4 ) with higher order ao corrections , the spurious velocities are reduced by a factor greater than 4 for a normalised seeing difference of 0.5 or less for a perfect ao system .we wish to caution the reader that this simulation is just to approximate the range of errors induced due to a seeing difference in velocity measurements based on a narrow - band filter .an error in the range of 1 km s is important in areas like the umbra and penumbra at the photospheric level .these results can not be used to remove the spurious velocities from the seeing - affected observed images . at the same time, we can not ignore all seeing - affected data , especially in the case of observation of transient phenomena like penumbral formation or a flare .in real observational situations , psfs can vary even when remains constant ( especially for exposures not long enough to average out the seeing fluctuations ) . in our simulation, it is assumed that the changes in psfs are only due to changes in . if psfs can be estimated using the ao data simultaneously along with the doppler measurements , then the variable seeing effects could be minimised by using deconvolution techniques . in the future , new methods and technologiesmay also be developed to observe the blue- and red - wing images simultaneously to avoid such effects .

Abstract: imaging systems based on a narrow - band tunable filter are used to obtain doppler velocity maps of solar features . these velocity maps are created by taking the difference between the blue- and red - wing intensity images of a chosen spectral line . this method has the inherent assumption that these two images are obtained under identical conditions . with the dynamical nature of the solar features as well as the earth s atmosphere , systematic errors can be introduced in such measurements . in this paper , a quantitative estimate of the errors introduced due to variable seeing conditions for ground - based observations is simulated and compared with real observational data for identifying their reliability . it is shown , under such conditions , that there is a strong cross - talk from the total intensity to the velocity estimates . these spurious velocities are larger in magnitude for the umbral regions compared to the penumbra or quiet - sun regions surrounding the sunspots . the variable seeing can induce spurious velocities up to about 1 km s . it is also shown that adaptive optics , in general , helps in minimising this effect .


complex networks have been studied intensively for more than a decade .the rapid development of network science has greatly helped us to understand and model real systems  .so far , many systems have been described by networks including the transportation system  , neural system  , social system  , power grid  and so on .some other systems coupled by two different elements are modeled by the bipartite networks .for example , the online commercial systems  and the scientific collaborative systems  are well represented by such networks .  with the help of the network structure , many novel methods have been proposed to improve the function of real systems .the online commercial system is a good example .nowadays , we can simply order books , movies , clothes from the online retailer even at home .however , like a coin has both sides , internet also brings us overabundant information so that we always have too many candidate products to compare . in order to solve the problem , many recommendation algorithms such as collaborative filtering  , content - based analysis , spectral analysis  and iterative self - consistent refinement  were developed to filter irrelevant information .recently , some physical dynamics on the bipartite networks , including mass diffusion  and heat conduction process  , have been applied to design recommendation algorithms .hybrid of these so - called network - based inference methods ( nbi ) is shown to have significant improvement in both recommendation accuracy and item diversity compared to the traditional methods  .  when studying the recommendation , most of the previous works are devoted to improve the performance of the recommendation algorithms by examining their methods on some standard datasets  .however , the network structure properties will inevitably affect the recommendation process  .for example , given a recommendation method , its the performance would change from one network to another .actually , how much do the recommendation method rely on typical data are still unclear . to answer such question ,it is useful to investigate the users online behaviors in different real systems .previous works have found that people s behavior are far different from random and obey certain predictable rules  .therefore , the users online behavior will emerge some typical statistical patterns on the network structure .consequently , these patterns will influence the recommendation process based on the networks .  in this paper , we focus on understanding online users statistical behavior pattern and the related effect on information filtering .we will compare the real bipartite networks with the randomized counterpart networks ( i. e. the reshuffled networks ) in which real users behavior pattern are destroyed .actually , some specific properties of the real networks has been discovered by the comparison to the reshuffled networks such as the loop distribution  , rich club  , community structure  , assortative  and motifs  . here , we find that online users have significant taste diversity and their interests for niche items highly overlap .additionally , recommendation process are investigated on both the real networks and the reshuffled networks .we find that the performance of popularity - based recommendation methods do nt rely on the real network structure while the performance of personalized recommendation methods is strongly related to it .detail study on the personalized methods indicate that recommendation accuracy for hot items is almost maximum and quite robust to the reshuffling process . on the contrary , niche itemscan not be accurately recommended without real users behavior properties .moreover , our work is meaningful in practical aspect since it reveals an effective direction to improve the accuracy and the robustness of the existing recommender systems .in real systems where is the average degree of selected items for each user.,title="fig:",width=340 ] +  .properties of the used datasets [ cols="<,^,^,^,<,^,^,^",options="header " , ]   in this paper , the datasets that we will use are the subsets of data obtained from four online systems : movielens ( http://www.grouplens.com/ ) , netflix ( http://www.netflixprize.com/ ) , delicious ( http://www.delicious.com/ ) and amazon ( http://www.amazon.com/ ) .these data are random samplings of the whole records of user activities in these websites , the descriptions of data are given in table i.  to investigate users behavior pattern , we will compare the real bipartite networks with the reshuffled networks . in each step of the reshuffling process , we first randomly pick two links from the real network , for example , one is from user to item and the other is from user to item ( throughout this paper we use greek and latin letters , respectively , for object- and user - related indices ) .then we rewire these two links by to and to .hence , the degree of the users and items would not be changed by this reshuffling process while the links in this reshuffled networks are randomized . denoting as the reshuffling times and as the total links in the networks, we fix in the following analysis .after the reshuffling process , users degree and items degree are preserved while the correlation between users and items are destroyed . to begin our comparison , we focus on the average degree of users selected items .suppose a user selects items with degree ( ) , we calculate the average degree of the items that he / she selected as .actually , the distribution of reflects the taste diversity of the users .when all the users prefer the same type of items , users will be the same to each other .consequently , the distribution of will be extremely narrow .on the contrary , the distribution of will be quite flat if all the users seek for different items .we then compare the distribution in real networks and their reshuffled networks . as shown in fig . 1 , in real networks indeed are much boarder than that in the reshuffled networks .obvious , users have obvious taste diversity in real systems .secondly , for each user we study the inter - similarity among all his / her selected items .the similarity of two items is calculated by the common neighbor here  .suppose a user selects items and the similarity between item and is denoted as , the inter - similarity among all these items can be obtained by .in fact , indicates the taste diversity for each single user .specifically , when a user always select for the same kind of items , for him / her will be high .on the other hand , if the interest of a user changes from time to time , his / her will be very low .as shown in fig .2 , compared to the reshuffled networks , the _ inactive users _ ( i.e. users with small degree ) in real systems show a higher while the _ active users _ ( i.e. users with large degree ) are with lower .actually , since the inactive users in real networks do not have much experience in seeking for their own interested objects , they tend to conservatively choose several most popular objects .hence , their selected items are very similar . on the contrary ,active users in real systems are more likely to explore and try different kinds of unpopular objects .therefore , their selected items are with low .   among all the selected items for each user vs user s degree .for a given , its corresponding is obtained by averaging over all the items whose degrees are in the range of $ ] , where is chosen as for a better illustration.,title="fig:",width=340 ] +   among all the selecting users for each item vs item s degree .the is averaged by the same process in fig.2.,title="fig:",width=340 ] +  similarly , for each item we investigate the inter - similarity among all the users who selected it .assume a item is chosen by users and the similarity between user and is denoted as , the inter - similarity among all these users can be calculated by .actually , reflects whether a specific item is selected by the same group of users . in fig.3, we study in the real networks and the reshuffled networks . for _ hot items _ ( i.e. item with large degree ) , their selectors in real networks have a lower than those in the reshuffled networks . however , the selectors of _ niche items _( i.e. item with small degree ) enjoy a higher inter - similarity in the real networks than those in the reshuffled networks .as we know , the personalized recommendation systems generally filter relevant information by cooperating the history of similar users , the overlap of users interests for niche items is very meaningful .it makes the limited historical information for these niche items valuable for the recommendation systems to refer to . in next section, we will detailedly investigate how these users online behavior patterns affect the recommendation process .in order to reveal the effect of users online behavior patterns on information filtering , we investigate the recommendation process on both the real networks and the reshuffled networks in which real users behavior patterns are destroied .we consider four conventional recommendation algorithms including mass diffusion ( md ) , heat conduction ( hc ) , collaborative filtering ( cf ) , popularity - based ( pr ) methods .we will study how the recommendation performance is influenced when we gradually remove users real behavior patterns .we first briefly describe these algorithms .consider a system of users and items represented by a bipartite network with adjacency matrix , where the element if user has collected object , and otherwise .for a target user , the md algorithm starts by assigning one unit of resources to objects collected by , and redistributes the resource through the user - item network .we denote the vector as the initial resources on items where is the resource possessed by object .the redistribution is represented by , where is the diffusion matrix , with and denoting the degree of object and user respectively  .technically , recommendations for a given user are obtained by setting the initial resource vector in accordance with the objects the user has already collected , that is , by setting . the resulting recommendation list of uncollected objectsis then sorted according to in descending order .physically , the diffusion is equivalent to a three - step random walk starting with units of resources on the target user .the recommendation score of an item is taken to be the amount of resources on it after the diffusion .the scores for objects that user have already collected are set to .the recommendation list for user is generated by ranking all his / her uncollected objects in descending order of their final resources .the hc algorithm works similar to the md algorithm , the only difference is the diffusion matrix is calculated as physically , the temperature of an object is considered to be the average temperature of its nearest neighborhood , i.e. its connected users .the higher the temperature of an item , the higher its recommendation score  .the cf algorithms provide recommendations based on user or item similarities . here , we consider the item - based cf which has been successfully applied to many online applications such as amazon ( one of the largest online product retailers ) . in the item - based cf method ,the recommendation score of an item is evaluated based on its similarity with the collected items of the target user .the final recommendation score for each item can be written as where is the similarity between item and  .the measure of similarities used in cf is subject to definition .here we simply define the similarity as the number of common neighbors in the bipartite networks .the pr algorithms is very simple and commonly used in many websites . in this method ,the recommendation score for each item is proportional to its popularity .actually , the difference of these recommendation methods has been studied in detail in ref . . in order to further understand these methods, we calculate the total recommendation score for each item as .the result is shown in fig .4 . in statistical sense ,the md , cf and pr methods assign high recommendation score to the high degree items . in hc method , the items with low degree are generally with high recommendation score . therefore , the md , cf and pr methods tend to recommend the popular items while the hc method inclines to recommend unpopular items .   vs item degree in different recommendation systems .the maximum for each method has been scaled to .,title="fig:",width=340 ] +  we then apply all these methods to the real networks and their reshuffled networks to see how users real behavior patterns affect the recommendation .similar to previous work  , to test the recommendation result we randomly remove of the links ( the probe set denoted as ) .we then apply the algorithms to the remainder ( the training set denoted as ) to produce a recommendation list for each user .  in order to measure the accuracy of the recommendation result , we make use of the ranking score index  . for a target user ,the recommender system will return a ranking list of all his uncollected objects to him according to the recommendation scores .for each hidden user - object relation ( i.e. , the link in probe set ) , we measure the rank of the object in the recommendation list of this user .for example , if there are uncollected objects for user , and object is at place , we say the position of this object is , denoted by .a successful recommendation result is expected to highly recommend the items in the probe set , and thus leading to small ranking score .averaging over all the hidden user - object relations , we obtain the mean value of ranking score to evaluate the recommendation accuracy , namely where denotes the probe link connecting user and object . clearly , the smaller the ranking score , the higher the algorithm s accuracy , and vice versa .  in fig . 5, we report how the ranking score of different recommendation methods will be influenced when we gradually remove real users behavior patterns .the results show that the ranking score of pr is hardly affected by the reshuffling process .it is reasonable because the pr method does nt rely on the detail bipartite network structure and gives the recommendation score for each item simply according to its popularity . on the contrary , the personalized recommendation such as the md , hc and cf methods are influenced . obviously , the ranking score of hc method increases most significantly when we reshuffle the networks .in fact , the hc method is considered as an effective method to enhance recommendation diversity by mainly predicting users preference for niche items .therefore , the result implies that without the real correlation between users and items , only the information of degree is insufficient for the recommendation systems accurately providing a diverse recommendation .more specifically , as we discussed in the previous section , users interests for niche items highly overlaps in real systems . hence , the recommendation systems can predict target user s potential niche items by cooperating the information from his / her similar users .however , in the reshuffled networks users interests for niche items only slightly overlap , so there is little information from the similar users for the recommendation engines to refer to. it finally leads to the serious increment in the ranking score of hc method .   of different recommendation methods when reshuffling the real networks . is the reshuffling steps and is the total links in the networks.,title="fig:",width=340 ] +  as recommendation algorithms which tend to recommend popular items , md and cf methods are not so sensitive to the reshuffling process as the hc method . in the dense networks like movielens and netflix ,the ranking scores of md and cf stay almost unchanged .however , in the sparse networks like delicious and amazon , the ranking score of md and cf methods show an observable increment . in order to see the effect of the reshuffling process on the md and cf methods in detail, we study the ranking score for each item , namely where denotes all the links in the probe set that connect to item .then we can see the relation between items degree and their ranking score , the result is reported in fig .6 . in real networks ,the hot items enjoy a low ranking score ( ) while the niche items are with high ranking score ( it can be even higher than the random recommendation whose ) .it suggests that the recommendation accuracy for the hot items is almost maximum and can not be improved anymore . however , niche items accuracy is quite low and has plenty of room for improvement .therefore , in order to design an more effective personalized recommendation method than current ones , it is crucial to solve the cold start problem  , i.e. to improve the recommendation for niche items .another interesting finding is that only the ranking scores for unpopular items are affected by the reshuffling process while the ranking score for popular items stays almost the same . since lots of items are with low degree in the sparse networks such as delicious and amazon , the average ranking score increases with the reshuffling process .in the movielens and netflix networks where the links are relatively dense , fewer items are with low degree in these networks .accordingly , the average ranking scores for md and cf do not increase much . from the practical point of view , if one want to enhance the robustness of the recommender system , the most effective way is to preserve the recommendation result for niche items since they are sensitive to randomness .   on the item degree .the is averaged by the same process in fig.2 .the main figures are the results of md method while the inserts are the results of cf method.,title="fig:",width=340 ] +  precious study reveals that hybrid of the md and hc methods can result in significant improvement in both recommendation accuracy and item diversity  . actually , this hybrid method is implementable because the hc method can effectively catch the users taste for niche items .as the recommendation accuracy for hc method in the reshuffled networks is almost the same as random recommendation ( ) , the hybrid method is impossible to be carried out in the systems where users randomly choose their items .it means that users behavior patterns in real systems are essential for solving the diversity - accuracy dilemma of recommender systems .the development for network science has greatly improved the function as well as our understanding to many real systems . in recommendation which is considered as a promising way to solve the problem of information overabundance, researchers have designed the network - based inference methods to improve the recommendation performance .for example , with the help of some typical physics dynamics on the bipartite networks , the mass diffusion and heat conduction algorithms have been proposed to improve the recommendation accuracy and diversity respectively .  in this paper, we investigate the users online behavior patterns and related effect on information filtering .we compare the real bipartite networks with the reshuffled networks in which users behavior patterns are gradually removed .we find that online users have significant taste diversity and their interests for niche items highly overlap .in addition , we find that the performance of popularity - based recommendation methods do nt rely on the real network structure while the performance of personalized recommendation methods is strongly related to it .detail study on the personalized methods indicates that recommendation accuracy for hot items is almost maximum and quite robust to the reshuffling process . on the contrary , niche itemscan not be accurately recommended without real users behavior properties .  from the practical point of view , in order to design a more accurate personalized recommendation method than current ones , our results suggest that it is crucial to improve the recommendation for niche items .if one wants to enhance the robustness of the recommender system , the most effective way is to preserve the recommendation result for niche items .therefore , our work may shed some light for developing a new recommender system with both higher accuracy and better reliability .we thank y .- c .zhang , m. medo and c. h. yeung for the useful suggestions .this work is supported by the swiss national science foundation under grant no .( 200020 - 121848 ) .

Abstract: understanding the structure and evolution of web - based user - object bipartite networks is an important task since they play a fundamental role in online information filtering . in this paper , we focus on investigating the patterns of online users behavior and the effect on recommendation process . empirical analysis on the e - commercial systems show that users have significant taste diversity and their interests for niche items highly overlap . additionally , recommendation process are investigated on both the real networks and the reshuffled networks in which real users behavior patterns can be gradually destroyed . our results shows that the performance of personalized recommendation methods is strongly related to the real network structure . detail study on each item shows that recommendation accuracy for hot items is almost maximum and quite robust to the reshuffling process . however , niche items can not be accurately recommended after removing users behavior patterns . our work also is meaningful in practical sense since it reveals an effective direction to improve the accuracy and the robustness of the existing recommender systems .   bipartite networks , reshuffling process , information filtering