smart power grids represent an important group of devices and applications within the umbrella of internet of things ( iot ) .especially , the large number of network - connected smart electricity meters that already are or will be located in all households and commercial / industrial locations are representative examples of iot devices . at present ,smart electricity meters are primarily used by electricity providers only for availability monitoring and billing . however , with the increasing number of distributed energy resources ( ders ) , such as wind turbines , solar panels , and electric vehicles , strong and sometimes unpredictable variations in the power quality are introduced , prompting for an increased need of monitoring and control .specifically , distribution system operators ( dsos ) need to be able to observe the circumstances in the low voltage ( lv ) power grid by introducing more frequently - sampled measurement points .such wide area measurement systems ( wams ) exist already in the transmission grid , whereas in the distribution grid the dsos rely mainly on open loop control beyond the substation level , i.e. , without real - time feedback from consumers .as the number of ders increases , this control loop must be closed by providing the feedback from measurements in the lv grid , enabling the state estimation and prediction of the grid behavior , and ultimately ensuring stable operation .it is expected that in the future lv grid , in addition to the traditional smart meter ( sm ) , which is so far primarily used for billing purposes with hourly or daily reports , another more advanced monitoring node will be needed , here referred to as enhanced smart meter ( esm ) .the esm is largely similar to a wide area measurement system ( wams ) node , as it integrates phasor measurement unit ( pmu)-like capabilities ; in other words , the esm measures power quality parameters ( such as power phasors ) more frequently and in more details compared to sms  . while it is generally expected that not all smart meter locations need to be equipped with esm devices , the fraction of esms needed in the distribution grid to achieve satisfactory state estimation is still an open research question .today , sm devices are typically connected to the dso backend system using either : 1 ) a concentrator that gathers the data from the sms in its neighborhood , via local wi - fi or plc connections , and then relays it via cellular or a wired connection to the dso backend ; or 2 ) direct connections from each sm through the cellular network to the dso backend [ 4 ] .while the concentrator based approaches reduce the load on the access networks by aggregating data locally , they are not suited for real - time monitoring from esms .the reason for this in plc is the limited bandwidth , reliability and the delays related to the daisy - chain topology .wi - fi is challenged due to the issues of the shared spectrum and uncontrollable interference .therefore , we assume that sms and esms are equipped with cellular interfaces , so as to eliminate the potential delays , ease deployment and reduce maintenance costs associated with the network connectivity .the traffic profile generated by smart meters falls into the category of machine - to - machine ( m2 m ) traffic .a main characteristic of m2 m traffic is that it consists of transmissions of small amounts of data from a very high number of devices , differing significantly from the bursty and high data rate traffic patterns in human - oriented services , and instead requiring network reliability and availability .further , m2 m traffic is more demanding in the uplink and less focused on downlink performance , as typical use cases encompass monitoring and control functions .with lte gaining an increasing market share , it is expected that within a number of years one of the existing 2 g or 3 g systems will be taken out of service in order to re - harvest the spectrum to use for newer technologies .current reports on the active m2 m cellular devices indicate that of them are gsm / gprs - only , both 3 g and gsm / gprs compatible , 3g - only , and only 1 % is lte capable .it is clear that gsm / gprs ( hereafter denoted gprs ) dominates the m2 m industry , therefore in this paper we analyze how well this technology can support the connectivity demands of sm and esm devices . given the promise of lte , we also investigate its potential use as the access network for esm devices .specifically , in this paper we have the following four contributions : 1 ) extraction and classification of smart meter traffic models from relevant specifications , as well as predicted future traffic growth ; 2 ) comprehensive simulation model of radio access systems that includes all phases in the access , in contrast to and the nist _pap2 guidelines for assessing wireless standards for smart grid application v1.0 _ that use simplified models ; 3 ) quantitative assessment of how many smart meter devices can be supported in cellular systems , comparing the simplified and comprehensive simulation model results ; and 4 ) recommendations for standardization and future roadmap of the radio access technologies .the rest of this paper is organized as follows . in section [ sec : smart_meter_traffic_model ] and[ sec : wams_traffic_model ] we characterize the traffic models of the sm and esm devices . in section [ sec : cellular_systems_performance ] we describe the access bottlenecks in the cellular access reservation protocol and provide numerical results that show how the proposed traffic models affect the performance of gprs and lte networks .then , in section [ sec : standardization_outlook ] we provide guidelines that the future cellular network standards should take in account when designing the network system . finally , we wrap - up the paper with the main take - home points .in the literature there are different examples of traffic models for traditional smart meters . of these , the opensg _ smart grid networks system requirements specification _ ( described in ) from the utilities communications architecture ( uca ) user group is the most coherent and detailed network requirement specification , and it has therefore been used in this paper as input for the sm traffic model . the uca opensg is a relevant consortium of 190 companies and the considered smart grid use cases are in line with those studied by other standardization organizations such as etsi and usef . since there are differences in which use cases and applications are offered by the dso or electricity retail company and which of those the individual customers are using , a one size fits all traffic model does not exist . in the following we consider a comprehensive configuration where all use cases that involve communication from the smart meters to the core network will be in operation andnote that actual deployments with different configurations may lead to different results . for calculating the message frequency in the uplink sm traffic model the event occurrence frequencies listed in table [ tab : event_assumptions ] have been used . besides the values listed in table [ tab : event_assumptions ] we assume that a commercial / industrial sm sends a 2400 bytes meter reading packet every hour , whereas a residential sm sends a 1200 bytes report every 4 hours ..assumptions for deriving traffic model . [ cols="<,<",options="header " , ]   table [ tab : ul - dl_ratio ] shows that the raw data rate requirements of sms with default reporting interval ( ri ) are quite modest , with an average uplink data rate of appr .13.4 kb per day per sm and an average downlink data rate of appr .40.4 kb per day per sm .while the total downlink data rate is actually higher than the uplink , it is constituted primarily of software updates , which are large low - priority data transfers that occur infrequently during the night , where it does not interfere with the day - to - day operation of the smart grid .given the modest traffic requirements , it is expected that gprs networks , that are deployed ubiquitously and offer a reliable coverage , but are gradually becoming less suitable for human - oriented traffic , can easily satisfy the default sm traffic requirements .further , an option to increase observability in the power grid is to reduce the meter reading reporting interval .we investigate how capable the current cellular systems are to support this in section [ sec : cellular_systems_performance ] , when the report packet sizes are respectively 300 bytes and 600 bytes for residential and commercial / industrial and reporting intervals range from 5 min , 1 min , 30 sec , to 15 sec .as shown in table [ tab : ul - dl_ratio ] , in case of these reduced ris , the uplink data rate requirements become much larger than in the downlink .the esm is a pmu - like device for the distribution grid , which is able to measure voltage and current phasors .however , it has less strict real - time requirements than transmission grid pmus , since it is used to increase observability rather than for protection purposes .being deployed not only in dso substations , but also in and close to prosumer homes , the esm reports measurements through cellular networks , since this allows a mobile network operator to prioritize and dedicate resources to esm traffic , thus achieving qos , which may not be possible 3rd party consumer - grade wired internet connections .phasor measurements can be used on different time scales , ranging from a few milliseconds ( e.g. , for protective relays ) up to several seconds ( e.g. , real - time monitoring and state estimation ) .the esms are intended to improve observability and enable state estimation and real - time control , with the suggested lower bound of 1 second for the reporting interval  .since the esms features and requirements are not yet standardized , the esm traffic model considered in this study is based on the requirements of the transmission grid pmu and wams related standards , ieee 1588 , ieee c37.118 and iec 68150 .specifically , we assume that every second an esm sends a measurement report that consist of concatenated pmu measurements ( 50 hz sample rate ) from the preceding 1 second measurement interval .the samples are , as specified in pmu standards ieee 1588 and c37.118 , timestamped using gps time precision . assuming that the floating point pmu frame format from ieee 1588 is used and that each sample covers 6 phasors , 1 analog value and 1 digital value , each pmu frame accounts to 76 bytes .adding udp header ( 8 bytes ) and ipv6 header ( 40 bytes ) to each report of 50 pmu samples , an esm packet is 3848 bytes , and a bit rate of 30.8 kbit / s . since it may be an exaggeration to send all 50 pmu samples per measurement interval , we also consider in our performance analysis the case of esm reduced report sizes .from the communications perspective , it is important to investigate which cellular technologies can support the current billing - only smart meter use cases , but also the use cases / services that go beyond the current ones . in and nist_ pap2 guidelines for assessing wireless standards for smart grid application v1.0 _ performance analyses were carried out to determine the number of smart grid devices supported by different wireless technologies , however , they only evaluated the data capacity of the systems and neglected to account for the bottlenecks in the access reservation protocol used in cellular systems . as it is shown in ,the access reservation bottlenecks are particularly prone to exposure with m2 m traffic such as smart grid traffic , meaning that a pure data capacity based analysis may lead to overly optimistic results .therefore , our analysis will include all aspects of the access reservation procedure and compare those results to a data capacity only analysis .for the analysis we will consider the traffic patterns for sm and esm devices described in sections [ sec : smart_meter_traffic_model ] and [ sec : wams_traffic_model ] . from those traffic modelsit is clear that the communication requirements of these two device types are orders of magnitudes apart in terms of message frequency and bandwidth , meaning that for esm deployment a more capable technology than gprs is needed . with its integrated pmu unit ,the esm is already a more complex and expensive device than the sm , and since fewer esms than sm will be needed , a higher unit price can be better tolerated , and thus we will assume that the esm uses lte .   in cellular networks , a device with no active connection to the network first has to establish one , in order to perform a data transmission .this is accomplished via an access reservation protocol , which in general consists of three main stages : random access , granting access and data access . in the first stage ,the cellular devices perform a random access request in one of the random access opportunities ( raos ) . in the second stage ,the base station grants access to the network if : ( i ) the random access request is received without error by the base station ; ( ii ) no other device has transmitted in the same rao ( i.e. , collision free ) ; and ( iii ) there are data resources available to the device .otherwise , the access reservation procedure must be restarted and the device will transmit a new random access request until it is granted by the base station or until the maximum number of retransmissions is reached and the request fails .in gprs there are 217 raos / s per carrier while in lte there are 10.8k raos / s . on the other hand , only 32 grants / s and 3k grants / s are offered in gprs and lte , respectively  .therefore , when the random access stage is heavily loaded , the grant stage becomes a decisive limitation in cellular networks .furthermore , in gprs and lte the data stage is not only limited by the amount of the actual data resources , but also by the amount of the uplink identifiers used to coordinate transmissions from active devices , which limit the amount of simultaneously active m2 m communication links .   to evaluate the performance of the cellular access, we used the outage rate , i.e. , the probability of a device failing to deliver a report before the report deadline expires , while accounting for the access reservation protocol .this can be regarded as a measure of the cellular access reliability , which is the paramount performance indicator for the wide - area distribution supervision and control applications . to evaluate the outage we used event - driven simulators developed in matlab , which cover the complete access reservation protocol , as defined in 3gpp release 12 .particularly , the gprs simulator considers the amount of available access granted messages in the access granted channel ( agch ) , with a typical configuration of 28 agch / s , the limited number of the identifiers used to coordinate the uplink transmissions , i.e. , the uplink stage flag ( usf ) , and the amount of data resources available .the lte simulator considers the restricted amount of access grant messages ( rar messages ) due to the physical downlink control channel ( pdcch ) limitations  .finally , both in the gprs and the lte simulator , the data resources are shared with the signaling required in the access reservation procedure and the actual data transmissions .the evaluation scenario is set in a single cell with 1000 m radius , which includes 4500 smart meters  , from which % correspond to residential customers and the remaining % to commercial / industrial customers . in the case of gprs , we consider a single carrier corresponding to a 200 khz system .the considered lte bandwidth is  mhz ( 6 prbs ) , in line with the reduced capabilities for lte devices  .in addition , the control channel and data channel probability of error , are respectively and  . in both systems , we assume the devices always transmit with the highest modulation scheme available , in order to focus the evaluation on the performance of the access reservation protocol . in these conditions, we observed that the sm traffic , provided in section [ sec : smart_meter_traffic_model ] , is supported by both gprs and lte with near 0% outage , as the total number of messages per hour from each sm only amounts to approximately 125 .we start by considering for gprs the scenario of reducing sm report intervals ( ri ) , as described in section [ sec : smart_meter_traffic_model ] .[ fig : gprsplot ] depicts the outage probability for increasing number of sms and different ris . taking as reference a cell population of sms, we can see that for ri 5 min , gprs can provide a significant increase on the distribution network observability from hourly intervals to every 5 minutes . for smaller report intervals to be supported in gprs , then the options are either to reduce the cell size and/or increase the number of carriers .we proceed by considering in fig .[ fig : lte_and_gprsplot ] the cellular network outage as a function of the esm penetration , i.e. , of how many esms are deployed per every 100 smart meter locations . as described in section [ sec : wams_traffic_model ] , each esm report contains 50 samples of the power phasors measured since the last report with an expected payload of  bytes . since this large payload has severe implications on the cellular network performance , we also consider the impact of smaller payloads on system performance , which can be motivated by the introduction of pre - processing to extract statistics , data compression and/or reduced number of samples .specifically , we consider reduced report sizes ( rs ) of 3848 , 400 , and 115 bytes , where the last two values correspond respectively to a payload reduction of approximately 10% and 3% of the original payload size . the outage results for lte and gprs are shown in fig .[ fig : lte_and_gprsplot ] .we note that gprs is not able to support esm traffic irrespective of the chosen rs , while lte for rs of 3848 bytes only supports up to 2% esm penetration .when a 10 mhz bandwidth is completely dedicated in lte to serve the esm traffic then it is possible to reach 30% of penetration with less than 10% of outage , which means a large amount of resources dedicated to a potentially low profit application . on the other hand , if we assume lower rs , already at 400 bytes lte supports up to 20% of esms .further , when comparing the results that correspond to the case when only data phase is taken into account with the results obtained by considering the access reservation phase as well , it can be observed that the access reservation protocol impacts the number of supported esms . particularly , the limitations of the access reservation protocol become substantial as the report size decreases and it could shown that this is mainly due to the lack of access grant messages required to complete the access reservation procedure .note that this effect has been overlooked in the previous works .the presented results allow us to conclude that the rs of the esm nodes must be small to support a high percentage of nodes .in addition , we emphasize that small data traffic can not be analyzed only in terms of the system data capacity , but that the bottlenecks of the access reservation protocol itself must be considered , as observed in the gap between the two types of analysis depicted in fig .[ fig : lte_and_gprsplot ] .we conclude by noting that in practice , when deploying esms , due to the required communication reliability , good coverage should be ensured , e.g. , by careful selection of the placement location and/or by adding an external antenna if needed . in the above presented study, it is assumed that all sms and esms are under a cellular coverage .although the traffic resulting from smart meters can be easily accommodated into current cellular systems , the same is not observed for the traffic generated by the esm . in the following , we discuss the challenges and possible solutions that need to be tackled by standardization bodies to ensure that the observability of the distribution network can be improved efficiently .the inclusion of additional phasor measurement units into the distribution grid , so as to increase its observability , is being discussed specifically at the last mile to the customer premises  .currently , it is not yet clear if that will imply the same level of detail ( in number of samples and report frequency ) as in the transmission grid pmus , where the reporting is done by scada over dedicated wired links .  as discussed in section [ sec : cellular_systems_performance ] , if the esms generate the same amount of traffic as transmission grid pmus , then the cellular networks will require an extensive overhaul to be able to support both esm and human centric traffic , leading to substantial investment in the cellular infrastructure .on the other hand , esms will most likely be lighter versions of pmus , both sampling and reporting less frequently .therefore , if local processing and compression of the monitoring data is allowed and/or the required level of detail lowered , then the amount of generated traffic will be much lower .another viable option , as discussed in section [ sec : cellular_systems_performance ] , is to increase the report frequency of current smart meters without introducing local pmu functionality .the generated small packets could then be handled by the network , as long as the bottlenecks at the access protocol level are addressed .it seems likely that the standardization for the esm s pmu functionality falls within the scope of the ieee c37.118 and iec 68150 standards , since these specify the measurement and communications requirements for traditional pmu units .therefore , it is of paramount importance that standardization bodies reach a consensus on the esm communication requirements allowing the affected stakeholders to take informed actions .   in 3gpp ,the standardization body responsible for the cellular air interface and core network functionality , there are two activities that will affect how the traffic from sm and esm will be handled  .we start by noting that , although grps is seen as an outdated communication technology  , there is an ongoing effort to continue to reengineer gprs to serve m2 m applications , in which the sm traffic can be classified .one of the goals of this initiative is to achieve 160 bit / s .concurrently , there is a push from the industry ( both utilities and vendors ) to keep gprs networks and their associated resources active , while facing the pressure to re - harvest the gprs spectrum to be used in the next cellular network generation .a viable solution to keep the gprs connectivity , is to _ virtualize _ its air interface into the next generation cellular systems .the second effort is to define a low complexity lte user equipment category with respect to the cellular interface , which supports reduced bandwidth and transmit power while extending coverage operation  .specifically , the goal of reduced bandwidth is to specify 1.4 mhz operation within any lte system bandwidth , allowing operators to multiplex reduced bandwidth mtc devices and regular devices within their existing lte deployments . in terms of extended coveragethe goal is to improve the coverage of delay - tolerant mtc devices by 15 db , thereby allowing operators to reach mtc devices in poor coverage conditions , such as smart meters located in basements  .  to further improve the support of the traffic generated by sm and esm with very low duty cycle and latency requirements in the order of seconds, the inclusion of _ periodic reporting and discontinuous transmission _ functionality into cellular standards should be considered . in here , the network provides periodic communication resources so that devices can perform their short data transmission .this allows devices to go to sleep and save energy , since they have prior knowledge of when the next transmission time slot can occur .a solution based on this concept has been proposed through the reengineering of the lte access protocol  .  to cope with the esm traffic demands and increase the network capacity , _ localized aggregation of traffic _ should be considered . in this solutionthe traffic generated by multiple sms and esms in a geographical area could be aggregated , at esms or cellular relays , and then trunked to the cellular network  .the use of aggregation and relaying would then allow to decrease the contention pressure at the base station , as well as to improve the single link connection , providing connectivity and coverage enhancements to sms and esms with poor propagation conditions .  finally , to support _ massive asynchronous access of small packet transmissions _, access reservation protocols in cellular systems are just the first step of the asynchronous access to the network .after it has been completed , then the device starts exchanging signaling information via the higher layers with the entities in the core network , which leads to a high signaling overhead and possible air interface and core network congestion .although there are already efforts to reduce the signaling exchanges with the core network  , when the payloads are small enough , the facility to perform the data transmission already in the third step of the access reservation protocol should be in place .in this paper we have evaluated two approaches to increase the observability of the network : ( 1 ) decreasing the report interval of the meter reading and ( 2 ) introduction of enhanced smart meters with phasor measurement units ( pmus ) .we provided details on the characteristics of the traffic generated by smart meters and enhanced smart meters and have highlighted the associated challenges in supporting it from a cellular network point of view .the obtained results show that gprs can support traditional smart meter traffic , as well as more frequent measurements down to 5 min report intervals .further , it is shown that lte can support distribution grid pmus , if the report payloads are appropriately dimensioned .these results can be used as input for both smart meter and cellular system standardization bodies to enable the introduction of current and future smart grid devices into the cellular networks .the current main open issue is the uncertainty associated with the esm communication requirements , which will lead to different cellular systems optimizations .this work is partially funded by eu , under grant agreement no .619437 sunseed .the sunseed project is a joint undertaking of 9 partner institutions and their contributions are fully acknowledged . the work of .stefanovi was supported by the danish council for independent research , grant no .dff-4005 - 00281 .j. sexauer , p. javanbakht , and s. mohagheghi , `` phasor measurement units for the distribution grid : necessity and benefits , '' in _ innovative smart grid technologies ( isgt ) , 2013 ieee pes_.1em plus 0.5em minus 0.4emieee , 2013 , pp .huang , s. werner , j. huang , n. kashyap , and v. gupta , `` state estimation in electric power grids : meeting new challenges presented by the requirements of the future grid , '' _ signal processing magazine , ieee _ , vol .29 , no . 5 , pp . 3343 , 2012 .c. hagerling , c. ide , and c. wietfeld , `` coverage and capacity analysis of wireless m2 m technologies for smart distribution grid services , '' in _ smart grid communications ( smartgridcomm ) , 2014 ieee international conference on_.1em plus 0.5em minus 0.4emieee , 2014 , pp . 368373 .    g. c. madueno , c. stefanovic , and p. popovski , `` reengineering gsm / gprs towards a dedicated network for massive smart metering , '' in _ smart grid communications ( smartgridcomm ) , 2014 ieee international conference on _ , nov 2014 , pp . 338343 .g. madueno , c. stefanovic , and p. popovski , `` reliable reporting for massive m2 m communications with periodic resource pooling , '' _ wireless communications letters , ieee _ , vol . 3 , no . 4 ,429432 , aug 2014 .p. osti , p. lassila , s. aalto , a. larmo , and t. tirronen , `` analysis of pdcch performance for m2 m traffic in lte , '' _ vehicular technology , ieee transactions on _ , vol .63 , no . 9 , pp .43574371 , nov 2014 .

Abstract: the introduction of smart electricity meters with cellular radio interface puts an additional load on the wireless cellular networks . currently , these meters are designed for low duty cycle billing and occasional system check , which generates a low - rate sporadic traffic . as the number of distributed energy resources increases , the household power will become more variable and thus unpredictable from the viewpoint of the distribution system operator ( dso ) . it is therefore expected , in the near future , to have an increased number of wide area measurement system ( wams ) devices with phasor measurement unit ( pmu)-like capabilities in the distribution grid , thus allowing the utilities to monitor the low voltage grid quality while providing information required for tighter grid control . from a communication standpoint , the traffic profile will change drastically towards higher data volumes and higher rates per device . in this paper , we characterize the current traffic generated by smart electricity meters and supplement it with the potential traffic requirements brought by introducing enhanced smart meters , i.e. , meters with pmu - like capabilities . our study shows how gsm / gprs and lte cellular system performance behaves with the current and next generation smart meters traffic , where it is clearly seen that the pmu data will seriously challenge these wireless systems . we conclude by highlighting the possible solutions for upgrading the cellular standards , in order to cope with the upcoming smart metering traffic .


with more than 845 million facebook users at the end of 2011 and over 140 million tweets sent daily in 2011 users can take photos , videos , post their opinions , and report incidents as they happen .many of the posts and tweets are about quotidian events and their preservation is debatable .however , some of the posts and events are about culturally important events whose preservation is less controversial . in this paperwe shed light on the importance of archiving social media content about these events and estimate how much of this content is archived , still available , or lost with no possibility of recovery .+ to emphasize the culturally important commentary and sharing , we collected data about six events in the time period of june 2009 to march 2012 : the h1n1 virus outbreak , michael jackson s death , the iranian elections and protests , barack obama s nobel peace prize , the egyptian revolution , and the syrian uprising .to our knowledge , no prior study has analyzed the amount of shared resources in social media lost through time .there have been many studies analyzing the behavior of users within a social network , how they interact , and what content they share . as for twitter ,kwak et al . studied its nature and its topological characteristics and found a deviation from known characteristics of human social networks that were analyzed by newman and park .lee analyzed the reasons behind sharing news in social media and found that informativeness was the strongest motivation in predicting news sharing intention , followed by socializing and status seeking .also shared content in social media like twitter move and diffuse relatively fast as stated by yang et al .+ further more , many concerns were raised about the persistence of shared resources and web content in general .nelson and allen studied the persistence of objects in a digital library and found that , with just over a year , 3% of the sample they collected have appeared to no longer be available .sanderson et al . analyzed the persistence and availability of web resources referenced from papers in scholarly repositories using memento and found that 28% of these resources have been lost .memento is a collection of http extensions that enables uniform , inter - archive access .ainsworth et al . examined how much of the web is archived and found it ranges from 16% to 79% , depending on the starting seed uris .mccown et al .examined the factors affecting reconstructing websites ( using caches and archives ) and found that pagerank , age , and the number of hops from the top - level of the site were most influential .we compiled a list of uris that were shared in social media and correspond to specific culturally important events . in this sectionwe describe the data acquisition and sampling process we performed to extract six different datasets which will be tested and analyzed in the following sections .the stanford large network dataset is a collection of about 50 large network datasets having millions of nodes , edges and tuples .it was collected as a part of the stanford network analysis platform ( snap ) project .it includes social networks , web graphs , road networks , internet networks , citation networks , collaboration networks , and communication networks . for the purpose of our investigation , we selected their twitter posts dataset .this dataset was collected from june 1st , 2009 to december 31st , 2009 and contains nearly 476 million tweets posted by nearly 17 million users .the dataset is estimated to cover 20%-30% of all posts published on twitter during that time frame . to selectwhich events will be covered in this study , we examined cnn s 2009 events timeline .we wanted to select a small number of events that were diverse , with limited overlap , and relatively important to a large number of people . given that , we selected four events : the h1n1 virus outbreak , the iranian protests and elections , michael jackson s death , and barrack obama s nobel peace prize award .   a tweet is typically composed of text , hashtags , embedded resources or uris and usertags all spanning a maximum of 140 characters .here is an example of a tweet record in the snap dataset :  * t * 2009 - 07 - 31 23:57:18 + * u * http://twitter.com/nickgotch + * w * rt : december 21 , 2009 depopulation by food will begin + http://is.gd/1wmzb whoa .. better watch rt plz # pwa # tcot + -5pt  the line starting with the letter * t * indicates the date and time of the tweet creation . while the line starting with * u * shows a link to the user who authored this particular tweet .finally , the line starting with * w * shows the entire tweet including all the user - references `` '' , the embedded uris `` http://is.gd/1wmzb '' , and hashtags `` # pwa # tcot '' .we wanted to select tweets that we can say with high confidence are about a selected event . in this case, precision is more important than recall as collecting every single tweet published about a certain event is less important than making sure that the selected tweets are definitely about that event .several studies focused on estimating the aboutness of a certain web page or a resource in general . fortunately in twitter, hashtags incorporated within a tweet can help us estimate their `` _ _ aboutness _ _ '' .users normally add certain hashtags to their tweets to ease the search and discoverability in following a certain topic .these hashtags will be utilized in the event - centric filtration process . + for each event , we selected initial tags that describe it ( table [ tab : tags ] ) .those initial tags were derived empirically after examining some event - related tweets .next we extracted all the hashtags that co - occurred with our initial set of hashtags .for example , in class h1n1 we extracted all the other hashtags that appeared along with _# h1n1 _ within the same tweet and kept count of their frequency .those extracted hashtags were sorted in descending order of the frequency of their appearance in tweets .we removed all the general scope tags like _ # cnn _ , _ # health _ , _ # death _ , _ # war _ and others . in regards to aboutness , removing general tags will indeed decrease recall but will increase precision .finally we picked the top 8 - 10 hashtags to represent this event - class and be utilized in the filtration process .table [ tab : tags ] shows the final set of tags selected for each class .  -21pt.twitter hashtags generated for filtering and their frequency of occurring [ cols="<,<,<",options="header " , ]   +  -50pt  -15pt  -15pt  -20pt [ fig : thebigfigure ]  figure [ fig : thebigfigure ] shows the missing and archived values from table [ tab : split ] as a function of time since shared .equation [ missing ] shows the modeled estimate for the percentage of shared resources lost , where _ age _ is in days .while there is a less linear relationship between time and being archived , equation [ archived ] shows the modeled estimate for the percentage of shared resources archived in a public archive . given these observations and our curve fitting we estimate that after a year from publishing about 11% of content shared in social media will be gone .after this point , we are losing roughly 0.02% of this content per day .we can conclude that there is a nearly linear relationship between time of sharing in the social media and the percentage lost . although not as linear , there is a similar relationship between the time of sharing and the expected percentage of coverage in the archives . to reach this conclusion , we extracted collections of tweets and other social media content that was posted and shared in relation to six different events that occurred in the time period from june 2009 to march 2012 .next we extracted the embedded resources within this social media content and tested their existence on the live web and in the archives . after analyzing the percentages lost and archived in relation to time and plotting them we used a linear regression model to fit those points .finally we presented two linear models that can estimate the existence of a resource , that was posted or shared at one point of time in the social media , on the live web and in the archives as a function of age in the social media .+ in the next stage of our research we need to expand the datasets and import other similar datasets especially in the uncovered temporal areas ( e.g. , the year of 2010 and before 2009 ) .examining more datasets across extended points in time could enable us to better model these two functions of time .also several other factors beside time would be analyzed to understand their effect on persistence on the live web and archiving coverage like : publishing venue , rate of sharing , popularity of authors and the nature of the related event . -25ptthis work was supported in part by the library of congress and nsf iis-1009392 .-25pt   ainsworth , scott g. and alsum , ahmed and salaheldeen , hany and weigle , michele c. and nelson , michael l. : how much of the web is archived ? in _ proceedings of the 11th annual international acm / ieee joint conference on digital libraries , jcdl 11 _ , pages 133 - 136 , ( 2011 ) .bar - yossef , ziv and broder , andrei z. and kumar , ravi and tomkins , andrew .: sic transit gloria telae : towards an understanding of the web s decay . in _ proceedings of the 13th international conference on world wide web , www 04 _ , pages 328 - 337 , ( 2004 ) .f. benevenut , t. rodrigues , m. cha , and v. almeida . : characterizing user behavior in online social networks . in _ in proc . of acmsigcomm internet measurement conference , sigcomm 09 _ , pages 49 - 62 , ( 2009 ) .kwak , haewoon and lee , changhyun and park , hosung and moon , sue . : what is twitter , a social network or a news media ? in _ proceedings of the 19th international conference on world wide web , www 10 _ , pages 591 - 600 , ( 2010 ) .frank mccown and norou diawara and michael l. nelson . : factors affecting website reconstruction from the web infrastructure . in _ proceedings of the 7th acm / ieee - cs joint conference on digital libraries , jcdl 07 _ , pages 39 - 48 , ( 2007 ) .hany m. salaheldeen , michael l. nelson . : losing my revolution : a year after the egyptian revolution , 10% of the social media documentation is gone .http://ws-dl.blogspot.com/2012/02/2012-02-11-losing-my-revolution-year.html      wan , x. , yang , j. : wordrank - based lexical signatures for finding lost or related web pages . in _ proceedings of the 8th asia - pacific web conference on frontiers of www research and development , apweb06, pages 843 - 849 , ( 2006 ) .  c. wilson , b. boe , a. sala , k. p. puttaswamy , and b. y. zhao . :user interactions in social networks and their implications . in _ proceedings of the 4th acm european conference on computer systems ,eurosys 09 _ , pages 205 - 218 , ( 2009 ) .wu , shaomei and hofman , jake m. and mason , winter a. and watts , duncan j. : who says what to whom on twitter . in _ proceedings of the 20th international conference on world wide web , www 11 _ , pages 705 - 714 , ( 2011 ) .d. zhao and m. b. rosson . :how and why people twitter : the role that micro - blogging plays in informal communication at work . in _ proceedings of the acm 2009 international conference on supporting group work .group 09 _ , pages 243 - 252 , ( 2009 ) .

Abstract: social media content has grown exponentially in the recent years and the role of social media has evolved from just narrating life events to actually shaping them . in this paper we explore how many resources shared in social media are still available on the live web or in public web archives . by analyzing six different event - centric datasets of resources shared in social media in the period from june 2009 to march 2012 , we found about 11% lost and 20% archived after just a year and an average of 27% lost and 41% archived after two and a half years . furthermore , we found a nearly linear relationship between time of sharing of the resource and the percentage lost , with a slightly less linear relationship between time of sharing and archiving coverage of the resource . from this model we conclude that after the first year of publishing , nearly 11% of shared resources will be lost and after that we will continue to lose 0.02% per day .   archiving , social media , digital preservation


the support vector machine ( svm ) is a widely used modern classification method . in the standard binary classification problem ,training dataset consists of pairs , , where and .the linear svm seeks a hyperplane which maximizes the smallest margin of all data points : where is defined as the _ margin _ of the data point , s are slack variables introduced to ensure all margins non - negative , and is a tuning parameter controlling the overlap . by using a kernel trick , the svm can also produce nonlinear decision boundaries by fitting an optimal separating hyperplane in the extended kernel feature space .the readers are referred to for a more detailed explanation of the svm . noticed that when the svm is applied on some data with , many data points lie on two hyperplanes parallel to the decision boundary . referred to this phenomenon as _ data pilling _ and claimed that the data pilling can affect the generalization performance of svm " . to overcome this issue , proposed a new method called the distance weighted discrimination ( dwd ) , which finds a separating hyperplane minimizing the sum of the inverse margins of all data points : the initial version of also mentioned the sum of the inverse margins could be also replaced by , the power of the inverse margins , and this generalized version was used as the definition of the dwd in . asserted the dwd can avoid the data piling and thereby improve the generalizability .one example [ see the group 2 of figure 3 in ] shows that the dwd has about 5% prediction error whereas the svm does 15% .enhancement of the dwd over the svm can also be exemplified in through a novel geometric view . as for the computation of the dwd, observed that the dwd is an application of the second - order cone programming and thus can be solved by the primal - dual interior - point methods .the algorithm has been implemented in both matlab code http://www.unc.edu/~marron/marron_software.html and an r package ` dwd ` .  in this paperwe focus on classification with high - dimensional data where the number of covariates is much larger than the sample size .the standard svm and dwd are not suitable tools for high - dimensional classification for two reasons .first , based on the scientific hypothesis that only a few important variables affect the outcome , a good classifier for high - dimensional classification should have the ability to select important variables and discard irrelevant ones .however , the standard svm and dwd use all variables and do not conduct variable selection .second , because these two classifiers use all variables , they may have very poor classification performance .as explained in , the bad performance is caused by the error accumulation when estimating too many noise variables in the classifier .owing to these two considerations , sparse classifiers are generally preferred for high - dimensional classification . in the literature ,some penalties have been applied to the svm to produce sparse svms such as the svm , the scad svm , and the elastic - net penalized svm .  in this workwe consider sparse penalized dwd for high dimensional classification .the standard dwd uses the penalty and can be solved by the second - order cone programming .however , the sparse dwd is computationally more challenging and requires a different computing algorithm . to cope with the computational challenges associated with the sparse penalty and high - dimensionality, we derive an efficient algorithm to solve the sparse dwd by combining majorization - minimization principle and coordinate - descent .we have implemented the algorithm in an r package ` sdwd ` . to give a quick demonstration here, we use the prostate cancer data [ , 102 observations and 6033 genes ] as an example .the left panel of figure [ fig : solnpaths ] depicts the solution paths of the elastic - net penalized dwd , and ` sdwd ` only took 0.453 second to compute the whole solution path . as comparison, we also used the code in to compute the solution path of the elastic - net penalized svm .we observed that the timing of the sparse svm was about 290 times larger than that of the sparse dwd .  , ) using the elastic - net dwd and the elastic - net svm . in every method , is fixed to be 1 .the dashed vertical lines indicate the selected by the five - folder cross validation .both timings are averaged over 10 runs . ]  , ) using the elastic - net dwd and the elastic - net svm . in every method , is fixed to be 1 .the dashed vertical lines indicate the selected by the five - folder cross validation .both timings are averaged over 10 runs . ]in this section we present several sparse penalized dwds .our formulation follows the svm .thus , we first review the derivation process of the svm .the standard svm is often rephrased as the following quadratic programming problem : moreover , the above constrained minimization problem has an equivalent _ loss+penalty _formulation : {+ } + \dfrac{\lambda_2}{2}||{\boldsymbol}{\beta}||^2_2 .\label{eq : l2svmloss}\ ] ] the loss function {+}=\max(1-t,\ 0) ] . with the warm - start trick, we can use the solution at } ] .  specifically , to find } ] , where when and otherwise .all the other grid points are placed to uniformly distribute on a log scale .second , we follow the strong rule to improve the computational speed .suppose } ] are the solutions at } ] and } ] , i.e. , }=0 ] .we rephrase them as } ] .otherwise , any incorrectly discarded variable should be added to the survival set .we update by where after each update of , some incorrectly discarded variables are added back to the survival set .third , the active set is also used to boost the algorithm speed .after we apply algorithm [ algo1 ] on the survival set , we only apply the coordinate descent on a subset of till convergence , where .then another cycle of coordinate descent is run on to investigate if the active set changes .we finish the algorithm if no changes in ; otherwise , we update the active set and repeat the process .  in algorithm [ algo1 ] ,the margin can be updated conveniently : if is updated by , we update by .last , the default convergence rule in ` sdwd ` is for all . showed the gcd algorithm enjoys descent property . in this section ,we also show the gcd algorithm has a stronger statement , the strict descent property , when the gcd is used to solve the sparse dwd .we first elaborate the following majorization result , whose proof is deferred in the appendix . is the coordinate - wise update function defined in , and is the surrogate function defined in .we have and :    [ lemma : p5 ]  given , and assuming , and imply the strict descent property of the gcd algorithm : .it is because .note that the original gcd paper only showed .the arguments above prove that the objective function strictly decreases after updating all variables in a cycle , unless the solution does not change after each update .if this is the case , the algorithm stops .we show that the algorithm must stop at the right answer .assuming for all , implies : a straightforward algebra can show that for all , which is exactly the kkt conditions of the original objective function . in conclusion , if the objective function does not change after a cycle , the algorithm necessarily converges to the correct solution satisfying the kkt condition .the simulation in this section aims to support the following three points : ( 1 ) the sparse dwd has highly competitive prediction accuracy with the sparse svm and the sparse logistic regression ; ( 2 ) the adaptive elastic - net penalized dwd performs the best in variable selection ; ( 3 ) for the prediction accuracy , no single method among the , the elastic - net , and the adaptive elastic - net penalized dwds dominate the others in all situations .  in this section ,the response variables of all the data are binary .the dimension of the variables is always 3000 . within each example , our simulated data consist of a training set , an independent validation set , and an independent test set .the training set contains 50 observations : 25 of them are from the positive class and the other 25 from the negative class .models are fitted on the training data only , and we use an independent validation set of 50 observations to select the tuning parameters : is selected from , , , , 1 , 5 , and 10 ; is searched along the solution paths .we compared the prediction accuracy ( in percentage ) on another independent test data set of 20,000 observations .we followed to generate the first two examples .in example 1 , the positive class is a random sample from , where is the by identity matrix and has all zeros except for at the first dimension ; the negative class is from with .in example 2 , of the data are generated from the same distributions as example 1 ; for the other of the data , the positive class is drawn from and negative class where .we obtained the other three examples following .in example 3 , the positive class has a normal distribution with mean and covariance , where has 0.7 in the first five covariates and 0 in others ; the negative class has the same distribution except for a different mean . in example 4 and 5 , we consider the cases where the relevant variables are correlated .two classes have the same distributions except for the covariance , in example 4 , the diagonal elements of are 1 and the off - diagonal elements are all equal to . in example 5, the element of equals .we compared the sparse dwd with the sparse svm and the sparse logistic regression .both the dwd and the logistic regression use the , the elastic - net and the adaptive elastic - net penalties .we used r packages ` sdwd ` and ` gcdnet ` to compute the sparse dwds and the sparse logistic regressions respectively .the and the elastic - net svms were solved by using the code from which does not handle the adaptive elastic - net penalty .table [ tab : simu1 ] presents the prediction accuracy results . in the first two examples , the dwd and the logistic regressionperform the best .we attribute this good performance to the only one nonzero variable in the data , despite of outliers in example 2 . in example 3 , 4 , and 5 , we increase the number of nonzero variables to five . for all models ,the elastic - net and the adaptive elastic - net penalties have similar performance , and both of them dominate the penalties .the elastic - net dwd produces the least prediction error in example 4 and 5 .table 3 compares the variable selection . in all cases ,the adaptive elastic - net penalties address all relevant variables with relatively few mistakes .the penalties share similar performance in the first two examples .in this section we analyze four benchmark data .the data arcene was obtained from , the breast cancer data from , the lsvt data from , and the prostate cancer was from .we randomly split each data with a ratio 1:1 into a training set and a test set . on the training set, we fit the sparse dwd with imposing the elastic - net and the adaptive elastic - net penalties . with the same tuningparameter candidates in the simulation , we used a five folder cross validation to find the best pair of incurring the least mis - classification rate .then we investigated the prediction accuracy of the selected model on the test set .as comparisons , we considered the sparse svm and the sparse logistic regression .every method was trained and tuned in the same way as the sparse dwd .all numerical experiments were carried out on an intel core i7 - 3770 ( 3.40 ghz ) processor .  in table [ tab : realdata ] , we reported the average mis - classification percentage on the test set from 200 independent splits .we observe that the classifiers achieving the least error in these four datasets are the adaptive elastic - net logistic regression , the elastic - net svm , the elastic - net and the adaptive elastic - net dwds .we also find all the differences are not quite large .for the sparse dwd , we get the same message as concluded for the standard dwd : it very often is competitive with the best of the others and sometimes is better . "we also notice that the computation of the sparse dwd is the fastest in almost all cases .the timing of the svm is much longer than other methods .a possible explanation is that the svm uses the non - differentiable hinge loss function which makes the gcd algorithm not suitable for solving the sparse svm .so far , the best algorithm for the sparse svm is a lars type algorithm , which is very different from the gcd algorithm for the sparse dwd and logistic regression .it has been observed that coordinate descent may be faster than the lars algorithm for solving the lasso penalized least squares .in this article , we have proposed the sparse dwd for high - dimensional classification and developed an efficient algorithm to compute its solution path .we have shown that the sparse dwd has competitive prediction performance with the sparse svm and the sparse logistic regression and is often faster to compute with the help of our algorithm .thus , the sparse dwd is a valuable addition to the toolbox for high - dimensional classification .the generalized dwd defined in minimizes the power of the inverse margins .when , it reduces to the usual dwd . for computation considerations , choose to fix , because it leads to a second order cone programming problemwe have found that our algorithm can be readily used to solve the sparse generalized dwd with any positive . in our numerical studywe tried the generalized dwd with and also tried to use cross - validation to select a data - driven value .our numeric results indicated that using different values does not lead to significant differences in performance .we opt to leave those results to the technical report version of this paper .the authors thank the editor , the associate editor , and two referees for their helpful comments and suggestions .[ [ proof - of - lemmalemmap5 ] ] proof of lemma [ lemma : p5 ] + + + + + + + + + + + + + + + + + + + + + + + + +  is trivial . to prove , it suffices to show for any , first , it is not hard to check that the first - order derivative is lipschitz continuous , i.e. , for any , let , then shows is strictly increasing . therefore is a strictly convex function , and its first - order condition leads to directly .bradley , p. and mangasarian , o. ( 1998 ) , `` feature selection via concave minimization and support vector machines , '' in _ machine learning proceedings of the fifteenth international conference ( icml98 ) _ , citeseer , 8290 .graham , k. , de las morenas , a. , tripathi , a. , king , c. , kavanah , m. , mendez , j. , stone , m. , slama , j. , miller , m. , antoine , g. , willers , h. , sebastiani , p. , and rosenberg , c. ( 2010 ) , `` gene expression in histologically normal epithelium from breast cancer patients and from cancer - free lemmahylactic mastectomy patients shares a similar profile , '' _ british journal of cancer _ , 102(8 ) , 12841293 .singh , d. , febbo , p. , ross , k. , jackson , d. , manola , j. , ladd , c. , tamayo , p. , renshaw , a. , damico , a. , richie , j. ( 2002 ) , `` gene expression correlates of clinical prostate cancer behavior , '' _ cancer cell _ , 1(2 ) , 203209 .tibshirani , r. , bien , j. , friedman , j. hastie , t. , simon , n. , taylor , j. , and tibshirani , r. j. ( 2010 ) , `` strong rules for discarding predictors in lasso - type problems , '' _ journal of the royal statistical society , series b _ , 74(2 ) , 245266 .tsanas , a. , little , m. , fox , c. , and ramig , l. ( 2014 ) , `` objective automatic assessment of rehabilitative speech treatment in parkinson s disease , '' _ ieee transactions on neural systmes and rehabilitation engineering _ , 22(1 ) , 181190 .

Abstract: distance weighted discrimination ( dwd ) was originally proposed to handle the data piling issue in the support vector machine . in this paper , we consider the sparse penalized dwd for high - dimensional classification . the state - of - the - art algorithm for solving the standard dwd is based on second - order cone programming , however such an algorithm does not work well for the sparse penalized dwd with high - dimensional data . in order to overcome the challenging computation difficulty , we develop a very efficient algorithm to compute the solution path of the sparse dwd at a given fine grid of regularization parameters . we implement the algorithm in a publicly available r package ` sdwd ` . we conduct extensive numerical experiments to demonstrate the computational efficiency and classification performance of our method . + * key words : * high - dimensional classification , svm , dwd .


growth phenomena in non - equilibrium conditions  are an important subject of condensed matter physics . many properties of specific devices depend on rough surfaces that are produced under such non - equilibrium conditions .technological applications such as conducting - field emitter devices that operate in ultra high vacuum ( uhv ) conditions , require the control of several properties such as the surface morphology .it is well known that large values of the current intensity on field emitter devices are connected to extremely small values of the effective emitting area .one method to increase the effective area of emission is to use surfaces with an ending fractal boundary with self - affine scale invariance instead of considering structurally regular tips .in fact , the connection between the morphology of irregular surfaces including sharp conducting tips and the field emission properties has been a subject of intense research . in a recent work ,cabrera _ et al ._ measured experimentally the current - voltage ( i - v ) of a tunnel junction consisting of a sharp electron emitting metallic tip at a variable distance (  " ) from a planar collector and emitting electrons using electric field assisted emission .their results showed scale invariance of the tunnel junction with respect to changes in ( from few to several ) , which means that the physical laws governing the flow of current are invariant with respect the changes of the length scale .however , this behavior fails when was only a few nanometers as showed in reference .the reported scale invariance for a single tip can be regarded as a preliminary study of the more general problem of field emission by an irregular conducting interface that will be considered in this work .  in the statistical mechanics framework, macroscopic laws that emerge in surface growth can be explained at different spatial and temporal scales considering a theoretical microscopic description that involves simple probabilistic laws .an interesting related point is the possibility of modeling these systems so that in the large - scale limit ( i.e. , where the scale invariance arises ) , they do not depend on the corresponding details but only on symmetries and the corresponding conservation laws .previous theoretical works related to the emitting properties of rough surfaces have studied the behavior of the electric potential in a region bounded by a rough conducting profile / surface and a smooth conducting line / plane , which is held to a constant voltage bias . in particular , the references analyzed the roughness exponent of the equipotential lines ( surfaces ) in 2 ( 3)-dimensional systems . however , to our knowledge , no previous work discussed the properties of equipotential lines / surfaces under the perspective of its height distribution properties .  in this work, we investigate the height distribution properties of a family of equipotential lines in a region that is confined by a rough profile , which is regarded as an electron - emitting cathode , and a flat anode which is placed sufficiently away from it .the profile results from a numerical simulation of the deposition and growth surface models , whereas the cathode and the anode are subject to an electric potential difference .our results are mainly based on the model that was introduced by silva and moreira , which is compared to those obtained for the simpler family model in some limiting cases .we emphasize two consequences of our results for the following aspects : the height distribution presents a more detailed characterization of the equipotential lines than that provided by the roughness exponents and such investigation of equipotential lines offers a much more reliable method to characterize the surface . for particular applications , our work can contribute to elucidate the image distortions in probe microscopies such as electrostatic force microscopy ( efm ) , where the knowledge of the electric field distribution along the tip probe is relevant to extract morphological information about the real irregular surface .this main conclusion from our work is particularly useful to study surfaces under the influence of non - linear mechanisms in the growth phase , where the surface width is not expressed as a power law with a single growth exponent for a large number of deposited monolayers .this investigation is also motivated by the quoted experimental aspects related to the electronic properties of rough surfaces and the recent theoretical advances regarding the solution of the kardar - parisi - zhang ( kpz ) equation in d = 1 + 1 , where , in general , indicates that a system composed by a n - dimensional substrate ( here , 1-dimensional ) and an extra dimension to where an important effect produced by the substrate is propagated .the remainder of the paper is organized as follows . in sec .[ sec0 ] , we describe the main features of the used models and emphasize the conditions under which they reproduce the typical features of the kpz and edwards - wilkinson ( ew ) growth dynamics . in sec .[ seci ] , we describe the methodology to calculate and characterize of the equipotential lines . in sec .[ secii ] , we discuss our results for the morphological properties of equipotential lines and analyze the corresponding behavior of the skewness and kurtosis with the electric potential . in sec .[ conclusion ] , we summarize the results and present our conclusions .it is convenient to discuss the properties of the computational surface growth models that are used in this work with those of the kpz equation in dimensions    where represents the height of the profile in the direction with respect to the line , , that describes the flat profile at .. [ eq00 ] comprises several terms that consider the essential features of a stochastic surface growth .these features include irreversibility and locality , which enhance the surface roughness . in eq .] corresponds to a constant driving force , is the diffusion coefficient of the deposited atoms on the surface , and is a white gaussian noise that mimics the stochastic nature of the growth process . the non - linear term accounts for a considerable number of experimental results for the height distribution .many of them can not be described by a gaussian function , which is the solution of the linear ew equation , which corresponds to setting in eq .[ eq00 ] .the investigated model depends on a parameter , which describes the probability that the deposited particle follows the restricted solid on solid ( rsos ) local rule , whereas is the probability related to the ballistic deposition ( bd ) rule .both rsos and bd discrete models belong to the universality class that is defined by the kpz equation but are characterized by negative and positive values of the parameter , respectively .although the used model has not been proved to be equivalent to a kpz equation , recent numerical investigations suggest that a change in the probability changes the value of in a kpz equation , which may be suitable to describe the competitive model .for almost all ranges of , a growing profile first experiences a transient phase before attaining a stationary growth regime , where its width scales with the number of monolayers with the typical exponent of the kpz universality class . for finite profiles ,this regime is interrupted when exponentially relaxes to a saturation regime and becomes constant . in this work ,we analyze only rough interfaces in the growth regime , which corresponds to typical experimental conditions . in the first transient phase , depending on , the growth exponent can reach values close to those typical of ew dynamics . starting from , the length of the transient phase increases until a specific value , where the ew typical value is always valid . for ,the model reaches kpz scaling again after a decreasing transient time . because the condition is very special, we find it wise to compare the properties of the profiles and equipotential lines with those obtained when the cathode is represented by family - model produced profile , which shows the ew properties notably clearly .the interesting behavior of the competitive model makes it suitable to investigate how the equipotential lines change when is selected to reproduce either kpz or ew dynamics , and for a fixed value of , how the magnitude of the non - linear terms affects the ew - kpz crossover as a function of time , which is particularly important for experimental interests .indeed , the competition between physical mechanisms is present in many real processes in thin - film science. then , the actual study clearly advances on the previously one where single models were considered , and the roughness exponent of equipotential lines were evaluated without a perspective for height distribution properties .the distribution of height fluctuations of the kpz equation , for a flat initial condition , can be expressed by gaussian orthogonal ensemble ( goe ) tracy - widom ( tw ) distributions  .therefore our results can be better appreciated by comparing the skewness ( ) and kurtosis ( ) of the equipotential height distributions with the typical tw values for the corresponding quantities .both and depend on the average distance from the equipotential lines to the cathode and anode .such dependence has intrinsic features according to whether or .a third distinct behavior is observed at , when the profile falls into an ew universality class .we emphasize again that our investigation opens the possibility of analyzing the effects on the behavior of equipotential lines of distinct surfaces with growth exponents near those that feature an ew class .this possibility is important because of the emergence of local growth exponents in the first transient growth phase , which is near the phase that characterizes the ew dynamics when .as shown in sec .[ secii ] , our results indicate that the height distributions of equipotential lines for such transient patterns are clearly different from those obtained for an actual ew profile , no matter whether they are produced using the competitive model at or the family model .the current investigation starts by constructing the rough profile , which acts as the cathode and results from one of the quoted deposition models . here , and are integer numbers that represent distance measured in terms of some basic unit distance , the precise size of which is not important in a theory of the kind under discussion .the growth process along the direction of the considered system ( one - dimensional substrate + height , as mentioned in sec.[intro ] ) starts with a flat substrate , where is an integer number , and  ] and the flat anode , i.e :    as previously indicated , is evaluated at , except if explicitly indicated .  to compare the results for different rough profiles, we fixed the value of .as a consequence , which is measured with respect to the substrate where the film is grown , changes with . in this way , to select a proper and fixed value of , such that for any value of the anode is sufficiently away from the cathode , we first determined the value of for which the roughness ( defined in eq .[ eq2a ] ) attains its maximum , which is when .next , we identified the vertical coordinate of the highest peak for this value of and set , which result , using eq .[ eqe ] , in :    where corresponds to the distance defined on the second paragraph of sec.[intro ] . at this point ,let us comment on the reasons to choose the particular value of used in this work .for , the results are expected to be largely independent of the precise value of , but the computational work is largely increased .we have observed that , for all the rough profiles , the equipotential lines become flat and parallel to the axis very rapidly after the value of surpasses the highest peak .therefore , we choose the value , which corresponds to .we use this average distance for all , because it is already sufficient large to have very smooth equipotential lines ( with roughness exponent , , near to unity ) that are observed at the flat anode .if we consider the basic unit distance nm , we obtain nm for , and  m , which correspond to the typical scale used in the non - contact mode in atomic force microscopy ( like efm ) where the electrostatic force is probed .then , the results of this work can motivate experimental realizations in this regime .observed at this angle , the geometrical set up depends on two different scales ( expressed by and ) along the horizontal and vertical directions .however , the rough profile has its own length scale in the vertical direction , which is the roughness  ^{1/2 } \label{eq2a}\ ] ]  where  ] .this regime corresponds to typical experimental conditions , in contrast to the exponential relaxation that is observed in steady - state ( long - time ) properties .for  ] are used throughout this work . here , is a shorthand notation for , which is defined in eq .( [ eq2a ] ) .as function of probability . is the average distance between the anode and the irregular cathode ( see eq.[eqe ] ) while is the roughness of the irregular cathode ( see eq.[eq2a ] ) .the results are presented considering =198 , and it is possible to observe that the global roughness decreases at the interval and increases for .the global roughness is minimum at the point ),width=283 ]  .[ larg ]  before discussing the results for the family and the competitive models , we emphasize that in this last case , our results are based on a single profile for each distinct value of .this usage is justified by the following facts : for each profile , our procedure amounts to considering an entire set of equipotential lines , which demands a considerably numerical effort ; we have found that , in the interval and , at time , the height distribution of the cathode and the resulting equipotential lines are almost insensitive to , which can be observed by comparing the values of and .therefore , our procedure is equivalent to replacing several realizations for one value of with a set of independent realizations at slightly different values of this parameter .this method can also be justified when we move to the close neighborhood of . here , and vary smoothly even for the results that are produced using 1 profile realization .the first illustrated aspect in figure [ larg ] refers to the relative positions of the profile with respect to the anode , which can be expressed by the ratio ( ) as a function of . in units of the roughness , the curve in figure [ larg ]represents the height where the anode is maintained above the average height of the corresponding rough profile .it is possible to observe that the smoother rough profile occurs at , i.e. , near the critical point .moreover , it is expected that in the infinite - size limit , the peak becomes more pronounced .( a ) and kurtosis ( b ) for a family of equipotential lines as a function of for different values of .three distinct regimes can be identified : for  and ,  , and  and .the inset details the behavior in a region where the rough profile morphologies are blurred because of finite time effects .the horizontal dashed line defines and .( c ) scaled height distributions for the equipotential lines considering and for a rough conducting profile grown with .the vertical dashed line defines /w = 0 ] ., title="fig:",width=264 ]  ( a ) and kurtosis ( b ) for a family of equipotential lines as a function of for different values of .three distinct regimes can be identified : for  and ,  , and  and .the inset details the behavior in a region where the rough profile morphologies are blurred because of finite time effects .the horizontal dashed line defines and .( c ) scaled height distributions for the equipotential lines considering and for a rough conducting profile grown with .the vertical dashed line defines /w = 0 ] of the equipotential lines for and .in fact , our results show that the large deviations of for each equipotential line determine the behavior of . for ,the behavior of has similar but less pronounced features , which indicates a weaker dependence of at this value of .   for and .the dashed and solid lines indicate the exact ew and kpz values.,width=321 ]  for , becomes negative for near the rough conducting profiles . in this region ,the absolute value of is also near that typical of a goe tw distribution .the important aspect is that crosses the null value at , which coincides with the point where exhibits a minimum value ( see figure [ skew ] ( b ) ) .this result indicates that , for conducting surfaces where , there is an equipotential line near the surface that presents a symmetric asymptotic behavior at the tails of the height distributions .this result suggests that the height distribution of the equipotential lines changes in a different manner ( for positive and negative fluctuations ) with respect to that of the actual conducting profile .  in the insets of figures 3 ( a ) and 3 ( b ), we focus on the behavior of and for p = , , and , where for and , the system presents morphologic features in the crossover ew - kpz .interestingly , the results indicate that similar features do not appear for the values of and .we notice no appreciable differences for , in the values of and for  [ 0 , 0.75 ] and  ( 0.75 , 0.83 ) or  ( 0.83 , 0.9 ) and  [ 0.9 , 1 ] .our results suggest that the potential variation does not feel the consequences of these finite time effects ( kpz - ew crossover ) , following the typical values for models that obey the kpz statistics .the analysis of equipotential lines appears as a better estimator to uncover the actual geometric features of the growing system .let us proceed with a closer discussion of our results for and at times where the ew features are believed to exist .it is well known that in this region , the duration of the transient phase ew - kpz increases quickly .more specifically , it is claimed that the time to reach the asymptotic limit ( i.e. the kpz class ) scales with  . in competitive models , grows at least linearly with the difference  , and the crossover time is expect to depend on with .this result is corroborated by evaluating the local growth exponent ( or effective growth exponent ) illustrated in figure [ local ] .let us first recall that , for any growing profile , a single growth exponent can only be defined if a strict linear dependence between and is observed .because this dependence is not verified for a large interval of values of when , we analyze the behavior of , which is computed by numerically evaluating the local slope of this curve .we consider two conditions for which linear features should prevail in the morphology of conducting rough profiles as and .figure [ local ] shows the time evolution of , which indicates the presence of a minimum that hints the value of where the profile should be closer to one grown using a pure ew dynamics ( this minimum was estimated at the times and for and , respectively ) .to show that the analysis of equipotential lines helps elucidating the fine differences between profiles , we also explicitly consider a rough profile that is grown using the well - know linear family model .then , we compare the resulting behavior of the corresponding equipotential lines with those for the competitive model for and ( and at times and , respectively ) . in figure [ skewfm1 ] ( a ) and ( b ) , we observe a similar behavior for and , respectively , as a function of for the family model and as .this result is interesting because modeling the condition provides vacancies in the volume , but these features are not reflected in the behavior of the equipotential lines , as we can observe by directly comparing with the results obtained using the family model .however , for , we do not observe a similar behavior for the equipotential lines , which now exhibit different morphologies from the previous ones .this result indicates that of the competitive model close to those that characterize the ew dynamic ( minimum of ) , is not a reliable measure to confirm the electrical features of the rough devices that are similar to that grown using the ew dynamics .moreover , we observe that for , exhibits low values for far equipotential lines , compared with the other models ( for ) . finally we can observe that a notable convergence for the limit and for values of that correspond to the minimum of , to the behavior of and of equipotential lines , which are associated to ew features . at these values of , the misinterpretations of small differences in compared to can significantly affect the design of electrical devices , where roughness is an important tool .   and ( b ) kurtosis of equipotential lines as functions of the electric potential for the rough profiles that were grown according to the family model and the competitive model at , and . for and ,the rough cathode surfaces were considered at times when the is minimum ( see figure [ local ] ) .this minimum was estimated when and for and , respectively .it is possible to observe the convergence to ew behavior in the limit.,title="fig:",width=283 ]  and ( b ) kurtosis of equipotential lines as functions of the electric potential for the rough profiles that were grown according to the family model and the competitive model at , and . for and ,the rough cathode surfaces were considered at times when the is minimum ( see figure [ local ] ) .this minimum was estimated when and for and , respectively .it is possible to observe the convergence to ew behavior in the limit.,title="fig:",width=283 ]  at this point , let us remark that the height distribution of the equipotential lines becomes a reliable criterion to analyze the morphological differences that are produced by distinct rough cathodes . indeed , the previous results , which were only based on the local roughness exponent ( see reference ) , have not produced such clear - cut differences in the local roughness exponent of the equipotential lines that are produced by rough cathodes generated by a ballistic ( ) and random deposition with surface relaxation ( rdsr ) ( ) . in the current work , such differences become clear when we consider the height distributions of equipotential lines for all three regimes , which are characterized by ( ) and ( ) .further morphological aspects of the profile have been revealed by our results .let us define the set of peaks in an equipotential line .a point , where its associated vertical coordinate is larger than those of its first lateral neighbors , i.e. , . in a similar way ,let us define , the set of peaks of an equipotential line that are also characterized by positive fluctuations .a point when and .finally , let us define as the fraction of the number of points that also satisfy .it is possible to show that a relation should be valid , where is the average value of that was restricted to points .this regime identifies the regions for equipotential lines where the small fluctuations quickly disappear and large fluctuations with lower wavelengths prevail when the electric potential grows .in fact , for equipotential lines that are far from the rough profile , we find that ( for example , the main peaks in figure [ figure1 ] ( a ) for and ) .therefore , the corresponding global roughness can be written as    additionally , should depend on as :    so that for equipotential lines that are far from the cathode .this result is observed in figure [ skew ] ( a ) , where as for .it is worth noting that such behavior is observed in the large roughness limit ( ) of the conducting profile . in figure[ skew1 ] , we show that these theoretical predictions are confirmed by numerical calculations for the rough conducting profile that were generated for and .it is clearly observed that in the regime where , the exponent of tends to . in this region, quickly grows for immediately before the inflexion point ( see figure [ skew ] ( a ) ) .   and .in the inset , we show a magnified region where the scale relation holds.,width=283 ]  if we only consider the cases where the equipotential lines have , the predictions by eqs .( [ eq4 m ] ) and ( [ eq4n ] ) fail for , i.e. , in the case of smooth surfaces , where the values of the skewness of distant equipotential lines are as ( for example , see figure [ skew ] ( a ) for ) . in that case, grows slowly before the inflexion point mainly because of the variations of fluctuations , which are associated to longer wavelengths ( see figure [ figure1 ] ( b ) ) . for , the region before the inflection point corresponds to .however , figure [ skew1 ] shows that , in this region , the absolute value of the exponent of is greater than .this result explains the rapid disappearance of roughness with lower wavelengths ( which do not corresponds to pronounced peaks ) .then , we encounter another regime with the absolute value of the exponent of less than , which explains the limit in figure [ skew ] ( a ) for .in this paper , we study the behavior of the height distributions of the equipotential lines and focus the behavior of their skewness and kurtosis .we used rough profiles that were grown following a competitive model with kpz components , which show opposite signals of .our results show a non - trivial behavior of and as a function of .we conducted our investigation for profiles with a lateral extension grown until a time , which considerably reduces ( but not eliminate ) the presence of finite time effects for any 0.83 .for all kpz profiles with , an almost invariant behavior of and on was found .the same behavior occurs to families for which , where and for the height distribution of the equipotential lines have an invariant behavior with respect to , although they are different from the previous families with . for families with ,our results show a third distinct behavior for and .these results suggest that the electric potential variation can identify the signal of , which provides the signal of the skewness of the rough conducting profile .however , the height distribution statistics of equipotential lines far from the conducting profile were shown as being notably different .  the particular behavior of and as a function of when motivated the comparison of these parameters with the corresponding ones that were obtained for substrates that are characterized by identical ew values of growth exponents .this comparison was conducted considering the equipotential lines of rough profiles : ( i ) which are defined by , ( ii ) for the case of a family model , and ( iii ) at the time in the competitive model ( for =0.80 and =0.825 ) where the effective growth exponent nearly .the results show similar behaviors for and the family model but clearly different results when the effective growth exponent is nearly . at these values of , where thin - film technology arises , the misinterpretations of small differences in (if experimentally reliable ) compared with can significantly affect the design of the electrical devices .finally , our results can provide new insights for cases where the rough morphologies are an important tool to construct devices where electrical properties play a fundamental role .for example in the design of devices for the flexible stacked resistive random access memory ( rram ) applications the rough surface leads to a local electric field enhancement which accelerates the oxygen ion back - drift by the external positive bias ( reset process ) .radio - frequency absorption and electric field enhancements due to surface roughness are also subjects of theoretical research . however , there are situations where high roughness is an important tool , such as when the deposited surface is combined with metallic and nonmetallic materials . in that case , understanding the evolution of the surface morphology and the electric potential distribution along an irregular shape during electrodeposition phenomena is greatly significant .moreover , in our viewpoint , the current study has called the attention to interesting characteristics that help one more systematically interpret of images from probe microscopies , such as the electrostatic force microscopy . in that case, the tip must be maintained far enough from the rough surface to avoid unwanted short - range interactions ( which may result from van der waals forces ) and close enough to not loose important morphologic information about the real profile .this work has the financial support of cnpq and fapesb ( brazilian agencies ) .c. p. de castro acknowledges specific support from fundao capes .

Abstract: this work considers the behavior of the height distributions of the equipotential lines in a region confined by two interfaces : a cathode with an irregular interface and a distant flat anode . both boundaries , which are maintained at distinct and constant potential values , are assumed to be conductors . the morphology of the cathode interface results from the deposit of monolayers that are produced using a single competitive growth model based on the rules of the restricted solid on solid and ballistic deposition models , both of which belong to the kadar - parisi - zhang ( kpz ) universality class . at each time step , these rules are selected with probability and . for several irregular profiles that depend on , a family of equipotential lines is evaluated . the lines are characterized by the skewness and kurtosis of the height distribution . the results indicate that the skewness of the equipotential line increases when they approach the flat anode , and this increase has a non - trivial convergence to a delta distribution that characterizes the equipotential line in a uniform electric field . the morphology of the equipotential lines is discussed ; the discussion emphasizes their features for different ranges of that correspond to positive , null and negative values of the coefficient of the non - linear term in the kpz equation .