the emergence and popularity of personal mobile devices , such as smartphones and tablets , generates large amount of data traffic by accessing the internet and downloading applications , which imposes a huge burden for the cellular infrastructure and spectrum .device - to - device ( d2d ) communications have been introduced to offload the traffic burden from cellular infrastructure to personal devices .the d2d technology enables mobile device users directly establish wireless links between each other , without passing through the public cellular infrastructure or access points .many literatures have studied the application scenarios and possible technical solutions for d2d communications . in ,the authors propose d2d communications as an underlay to the cellular network , and present a mechanism for integrating d2d communications into lte - advanced network . discuss the power control issue for d2d communications , and derive an optimum power allocation for d2d links under cellular network control .the work in proposes to use wi - fi based d2d links among cellular users to improve the overall network performance in uplink transmission .wi - fi direct , initially called wi - fi p2p , is a wi - fi standard that enables devices to easily establish d2d connections using the wi - fi frequency band . gives a wide overview and experimental evaluation of the wi - fi direct protocol . considers the practical implementation challenges of wi - fi direct and shows that the wi - fi direct features allow deploying the d2d paradigm on top of the lte cellular infrastructure .though d2d communication has been a hot research topic in recent years , there is not much study focusing on the security aspect of d2d communications . and discuss the physical layer solutions for secure d2d communications , but their techniques are difficult to be implemented using devices on the market .in fact , due to the broadcast nature of wireless communication , wireless channels are considered vulnerable to a variety of attacks , and security is one of the major concerns for d2d communications . to secure the communication between two end users of a d2d link , establishing a shared secret key is the first and most significant step .however , lack of trusted third party and infrastructure under d2d connection environment makes this step a non - trivial task .the well - known diffie - hellman key agreement protocol enables two parties jointly establish a shared secret key without any prior knowledge .however , this protocol is vulnerable to the man - in - the - middle attack ( mitma) : an active adversary makes independent connections with the victims , making them believe that they are talking directly to each other . to address this issue ,researchers have come up with various diffie - hellman based cryptographic protocols , which can prevent the mitma by conducting mutual authentication .one simple protocol was suggested in , in which devices a and b exchange the hashes of their public keys over a secure channel , thus performing the mutual authentication .however , this protocol requires a large number of bits to be mutually authenticated .the mana protocol in reduces the size of the authentication message to bits , but requires a stronger notation of authentication channel . presents a protocol based on commitment schemes and requires 4-round communication over the wireless channel . in this paper, we propose a 3-round key agreement protocol based on commitment scheme .our proposed protocol is similar to the protocol in , but with less communication and computation overhead , meantime achieving the same level of security .major contributions of this paper are summarized as follows :  1 .we analyze the secure threats and challenges for d2d communications ; 2 .we design a secure and efficient diffie - hellman based key agreement protocol , and provide the security analysis ; 3 .we integrate our proposed key agreement protocol into the existing wi - fi direct protocol , and implement it on android smartphones .the rest of this paper is organized as follows : section ii introduces the security concerns and challenges for d2d communications ; section iii presents the details of the protocol design and security analysis ; section iv shows the implementation of our proposed protocol .we conclude this paper in section v.despite all the benefits of d2d communications , security is one of the major concerns that need to be well addressed before d2d technique gets widely accepted and implemented .it is well known that due to the broadcast nature of wireless channels , wireless communication such as wi - fi and bluetooth is vulnerable to a variety of attacks that challenges the three basic principles of security confidentiality , integrity and availability .some common attack vectors include surreptitious eavesdropping , message modification and node impersonation .for example , by stealthy listening to the communication between two devices , an attacker can gain critical or privacy information , such as trade secrets or identity related information .thus , the d2d communications between devices need to be properly secured .  to secure the d2d communications , cryptography solutions are needed to encrypt the messages while they are transmitted via wireless channels .numerous encryption algorithms have been well developed which can provide different security levels for the encrypted messages , but all of them require two devices agree on a shared secret ( either a shared secret key or each other s public keys ) . due to the large number of mobile devices ,the diversity of device manufacturers and lack of standards , preloading secure keys into mobile devices is neither efficient nor practical . on the other hand ,a trusted third party or infrastructure is not likely to be available in the d2d mobile environment .thus , how to establish a shared secret between devices is one of the main challenges for secure d2d communications .one straightforward way to establish a shared secret between two devices is that the two end users of the d2d link interactively set up a secret key via human negotiation ( such as making a phone call if they are in distance ) .the problem for this is that the shared secret established by human interaction will be too weak in most cases .the attackers do not even need to be smart to crack this weak secret via brute force method , considering current computation power . to deal with this issue ,cryptologists and researchers come up with two types of approaches which enable two individuals to establish a secure enough secret key : diffie - hellman key establishment protocol and secret key extraction from physical channel characteristics .physical layer based secret key generation methods have been proposed in recent years as alternative solutions for traditional diffie - hellman key agreement protocol . unlike diffie - hellman key agreement protocol , whose security is guaranteed by the computational hardness of discrete logarithms , these physical layer based methods rely on the randomness and uniqueness of wireless fading channel properties : temporal variation , spatial variation and reciprocity . generally , the two devices first send channel probing packets to measure the physical metrics of the wireless channel , then after using quantization and error correction technique , these two devices can yield the same secret key .the main problem for this type of methods is that the secret key generation rate is in most case very low .users have to send lots of channel probing packets to achieve a secret key with enough bits and randomness .the communication overhead and relatively longer key generation time are not quite desirable for the case of d2d communications .diffie - hellman cryptosystem is the oldest public key system still in use , which allows two individuals to agree on a shared secret key , even though they can only exchange messages over public channels .diffie - hellman key agreement protocol works as follows : assume and are publicly known to two devices a and b ( if not , a can put them into its message and send it to b ) , a and b both randomly generate a value and .a computes mod and sends it to b , correspondingly , b computes mod then sends it to a. at the last stage , a computes mod , b computes mod .both a and b will arrive at the same value , since and are equal mod . mod p will be the established shared secret between a and b , thus can be subsequently used as encryption key for future communication .the implementation of diffie - hellman key agreement protocol requires some extent of computation capacity , since , , and can be quite large numbers .however , mainstream mobile devices on today s market have achieved gigahertz level processor frequency , so generating a secure enough shared secret , say , 156 bits , can be conducted within seconds .as is well known , the above diffie - hellman key agreement protocol is vulnerable to the so called the man - in - the - middle attack . since and are transmitted over the public channel , there is no way for device a to know for sure whether comes from device b , vice versa .devices a will establish a shared secret with whoever transmits , and it certainly might not be device b. the essential reason that the mitma is possible is that there is no mutual authentication between these two devices . to provide the desired authentication ,one intuitive solution is both devices put the obtained secret key to a one - way hash function , e.g. md5 , to generate a hash value h(k ) , then compare the hash value via a trusted channel ( for example , output the computed hash code on device screens and perform visual or verbal comparison ) .if the mutual authentication process agrees , then both devices can confirm that they have established a shared secret key with each other .the main issue about the above mutual authentication procedure is that the number of bits needed to be checked by the user is too large .the output of a hash function is usually over 128 bits ( 32 hexadecimal digits ) , and visually or verbally checking them is a non - trivial task . using truncation of the hash codecan drastically reduce the number of digits needed to be checked , but doing this will introduce serious security weakness . in ,the authors describe one possible way to attack the truncated hash code : an attacker with significant computing resources can crack a 32 bits truncated hash code in less than 1 second . through the analysis above , to secure the d2d communications, we need a key agreement protocol that enables two mobile devices to securely establish a shared secret key , at the meantime requires minimum amount of information to be mutually authenticated to prevent the mitma .we consider the following scenario .two mobile device users want to establish a shared secret key for their d2d communications . both of them are equipped with a smartphone or tablet which is capable of communicating over a wireless channel .both devices have the computation capacity to perform diffie - hellman key agreement protocol , and are capable of displaying sequence of digits .the two users do not have any pre - shared cryptographic information , and there is no trusted third party or infrastructure available .they can visually or verbally recognize each other for the purpose of mutually authenticate a short message .we assume devices a and b agree on a finite cyclic group , its generating element , and a large prime number .we assume to be a subgroup of of prime order q , where , is the multiplicative group consists of nonzero integers modulo .we consider the dolev - yao adversary model : the attacker has fully control over the wireless channel .it can overhear , intercept , and modify any message .the attacker can also initiate a conversation with any other user .we further assume that legitimate users will follow the protocol and are not compromised .a commitment scheme allows one user to commit to a chosen value or statement while keep it hidden to others , with the ability to reveal the commitment value latter .a commitment scheme has the following two main properties : 1 ) a user can not modify the value or statement after they have committed to it ; that is , the commitment scheme is binding and 2 ) the receiver can only know the committed value after the sender opens " it ; that is , the commitment scheme is hiding .a commitment scheme is defined by two algorithms * commit * and * open * :   transforms a value into a commitment / open pair . the commit value c reveals no information of m , but with decommit value together will reveal . output original value if is the commitment / open pare generated by .   herewe present our design of the key agreement protocol , which is based on the traditional diffie - hellman key agreement protocol and a commitment scheme . in out protocol ,two mobile users a and b respectively generate -bit random strings and , and as the short authentication string for mutual authentication .[ fig : protocol ] shows the message flow of our proposed protocol . at the initial stage , user a andb select their diffie - hellman parameter and , then compute and .a and b randomly generate their -bit strings and . and are formed by concatenation , in which and are human readable identifiers for user a and b , such as names or e - mail addresses .a also needs to calculates the commitment / opening for .after the initial stage , user a and user b perform the following message exchange over their d2d communications channel .user a sends the , the commitment value of to user b ; after receiving , user b sends to user a. in return , user a sends the decommit value to user b. user b opens the commitment and gets .  in the final stage ,user a and b generate the k bits authentication string by and , in which and are derived from messages received by a and b. then user a and b verify if via trusted channel ( visual or verbal comparison ) .if the authentication strings match , a and b accept each other s diffie - hellman parameters and calculate the shared secret key .the reason for comparing authentication string before generating diffie - hellman secret key is that if the strings do not match , both users can save the computation for secret key generation .   in our security analysis, we assume the commitment scheme we use to be an ideal commitment scheme .that is , no attacker can forge an which yields a commitment value such that ( is the commitment value of original message ) ; and no attacker can open a commitment with .we further assume that both and generated by devices a and b are perfectly random .notice that in our proposed protocol , any party has to commit on an before actually seeing ; and any party has to submit an before actually seeing .these statements directly follow from the binding and hiding properties of the commitment scheme .thus , no matter what attacking strategy the attacker applies , it has to first commit to or submit its own message .suppose the attacker e initiate a protocol with user b pretending itself to be a , it will first commit to an and send the commit value to b. after getting the reply message , the attacker can modify into and forward it to a. but when it comes to the final stage of the protocol , a and b will compare with .the only chance that a and b agree on the authentication string is . due to the binding property of the commitment scheme ,the attacker e can not modify after it sends out its commitment .the probability that e launch a successful attack is at most ( is the number of bits of the authentication string ) .if the attacker launch an attack by replying to a protocol initiator a , similar analysis follows .the bit length of authentication string can be tuned to balance the trade - off between security level and usability . with a larger ,users gain higher security level but need to compare a longer authentication string .usually we consider 20 bits ( 5 hexadecimal digits ) to be securely enough , this will give us a security level roughly equal to an atm machine .in this section , we integrate our proposed key agreement protocol into the existing wi - fi direct protocol .we call this enhanced version secure wi - fi direct " protocol , which provides secure key establishment functionality for the d2d connection between two mobile devices. we also implement the secure wi - fi direct protocol on two android smartphones .the implementation result shows that these two phones obtain a shared secret key at the meantime they establish a d2d connection .wi - fi direct protocol enables two devices to establish a d2d connection using wi - fi frequency without the help of access points .[ fig : fig2 ] shows the procedure for a d2d connection establishment using wi - fi direct .first , two devices perform the channel probing and discover each other .then the two devices will go through a 3 way handshake to determine the group owner ( works as an access point ) for this d2d connection .after the devices have agreed on their respective roles , a dhcp exchange will be conducted to set up the ip addresses for both devices .thus , the d2d connection between these two devices has been established .we add our proposed key agreement protocol on top of the existing wi - fi direct protocol , as is shown in fig .[ fig : fig3 ] .after the address configuring phase , the two devices will go through our proposed key agreement protocol as well as the mutual authentication process to agree on a shared secrete key .as long as the two devices have agreed on the authentication message , they can subsequently use their shared secret key for future communication .we implement the secure wi - fi direct protocol on two android smartphones .the model and operation system of the smartphones we use is nexus 5 and the newest androidos-4.4 kitkat .we build our application based on the wi - fi direct demo application in .our secure protocol is implemented by programming the android tcp socket .the result is shown in fig .[ fig : fig1 ] .we list some of the diffie - hellman parameters , as well as authentication strings in hexadecimal .we use a 40 digits value , which gives us a roughly 130 bits secret key .the authentication string length is set to be 20 bits ( 5 hexadecimal digits ) , which is easy to be compared by the two users and can achieve a strong security level . the overall running time for our security protocol , excluding the user - conducted mutual authentication part , including the computation time as well as the communication delay , is trivial on nexus 5 smartphone with its 2.26 ghz processor .in this paper , we analyzed the secure requirements and challenges for secret key establishment between two mobile devices .the proposed key agreement protocol enables two mobile users to securely set up a secret key with a small computation cost and low mutual authentication overhead .the security analysis of the proposed protocol shows that the probability for an attacker to launch a successful attack is at most , where is the number of bits used for authentication strings .we also integrated our key agreement protocol into the existing wi - fi direct protocol , and implemented it using real smartphones .the implementation result shows that our proposed protocol is efficient , and achieves high level of usability .this work was supported in part by the nsf under grants cns-1320736 and cns-1117687 .k. doppler , m. rinne , c. wijting , c.b .ribeiro , and k. hugl , `` device - to - device communication as an underlay to lte - advanced networks , '' _ ieee communications magazine _ , vol .42 - 49 , 2009 .   c. yu , k. doppler , c.b .ribeiro , and o. tirkkonen , `` resource sharing optimization for device - to - device communication underlaying cellular networks , '' _ ieee trans .wireless commun .10 , no . 8 , pp . 2752 - 2763 , 2011 .a. asadi and v. mancuso , `` energy efficient opportunistic uplink packet forwarding in hybrid wireless networks , '' in _ proceedings of the fourth international conference on future energy systems _ , acm pp .261 - 262 , 2013    d. balfanz , d.k .smetters , p. stewart , and h.c .wong , `` talking to strangers : authentication in ad - hoc wireless networks , '' in _ proc . network and distributed system security symposium conference _, 2002 .g. fodor , e. dahlman , g. mildh , s. parkvall , n. reider , g. miklos , and z. turanyi , `` design aspects of network assisted device - to - device communications , '' _ ieee communications magazine _ , vol .3 , pp . 170 - 177 , 2012 .

Abstract: with the rapid growth of smartphone and tablet users , device - to - device ( d2d ) communications have become an attractive solution for enhancing the performance of traditional cellular networks . however , relevant security issues involved in d2d communications have not been addressed yet . in this paper , we investigate the security requirements and challenges for d2d communications , and present a secure and efficient key agreement protocol , which enables two mobile devices to establish a shared secret key for d2d communications without prior knowledge . our approach is based on the diffie - hellman key agreement protocol and commitment schemes . compared to previous work , our proposed protocol introduces less communication and computation overhead . we present the design details and security analysis of the proposed protocol . we also integrate our proposed protocol into the existing wi - fi direct protocol , and implement it using android smartphones .   d2d communications ; diffie - hellman ; wi - fi direct ; key agreement protocol ; the man - in - the - middle attack


we are implementing a suite of software tools to aid gamma - ray burst ( grb ) researchers in working with the grb data .the major features of the tool shed a * sh*ell for * e*xpeditions using * d*atamining are a web - based data query facility , web - based data visualization capability , and a web - based interface to data mining software tools .the tool shed maintains a database of users allowing each user to store their own work at the tool shed site .each user s data will not be visible to other users of the system .our grb tool shed is populated with a standard set of preprocessed grb data such as the basic table data , flux / fluence data , and duration .these data are stored in tabular form as rows ( burst instances ) and columns ( attributes ) .each burst has the same attributes as all other bursts , with a provision for indicating `` missing '' attributes .users may augment this database by uploading their own table or performing sql database queries for data selection and calculations .the data mining tools can be given any of the queried data and produce either rules for classification of bursts or an identification of classes of bursts by identifying which bursts belong to which class . note that these `` identified '' classes are not necessarily classes based on physical properties of bursts ; they may be due to instrumental bias , or even statistical fluctuations from the small numbers of instances ( c.f .this step can lead to defining new data in new tables for further exploration .an example of applying these tools is given in .once a registered user has logged in , the data can be manipulated in a variety of ways .the user may simply query the existing data , selecting a subset of the bursts and/or attributes for later processing .they may augment the data by uploading their own attributes for existing bursts . or they may augment the data by uploading information for new bursts .  as an example database query ,consider selecting all bursts from the 4b catalog with high relative measurement errors on the channel 1 fluence measurement . to determine what might be considered `` high '', it may be necessary to see all of the bursts sorted by relative measurement error , easily done with this sql query :  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ select burstnum , channel1fluenceerror from 4bfluxtable where channel1fluence < > 0 order by ( channel1fluenceerror / channel1fluence ) ; _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  now , after viewing the results of this query , one may decide that a `` quality '' threshold of 1.0 standard deviations would be required on the fluence data .the quality data can be extracted using this query :  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ select burstnum , channel1fluence , channel1fluenceerror from 4bfluxtable where channel1fluence < > 0 and ( channel1fluenceerror / channel1fluence ) > 1.0 ; _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  for those users unfamiliar with sql , the web application will provide point - and - click , fill - in - the - box forms for generating a database query .these web pages should provide the user with most of the features they would be interested in .there will also be a blank form for users who may wish to enter the sql query directly .either way , the names of the tables and attributes will be shown on the web browser so the user need not memorize them .   at any timethe user may decide to invoke visualization tools to help `` see '' the data in their scratch area or in the system tables .the web application will send these requests to ion ( idl on the net ) to produce graphical views of the data .the display of these graphs will be done on the user s web browser window .several data mining tools will be available as part of the web application .initially , there will be the classic classification tool , c4.5 , a tool developed by a member of our group , esx , and at least one neural network package . these software packages run on the web server and the web application will guide the user , requesting information needed by the specific data mining tool being invoked .the output from the data mining tools differ from one tool to the next. our web application will be able to capture the output and transform it to an internal `` rule '' format .once captured , the user may view the rules , or go even one step further by applying the rules to a database in their scratch area .the application of the rules to the data is a significant feedback component of the tool shed .there will be extensive online help to guide the user through the data mining process .the help system will be written in a hyper - linked book format complete with a table of contents , an index , and a search engine .there will also be context - sensitive help in the sense of hyper - links from web forms to relevant pages of the help system .the help system will address how to use the tool .the grb data will be minimally documented , with pointers ( hyper - links ) to existing help in understanding the meaning of the data attributes .a tutorial will be provided that brings the user through a data mining session. this tutorial will provide ( scientific ) rationale for selecting options along with way .although the tool shed need will not be specific to grb data , the tutorial will be .the grb tool shed will initially run on a pentium - class computer system running redhat linux . to maximize portability , the java language will be used . sincethis tool is web - based , all of the java code will run as java servlets .the apache web server will be used along with its companion java servlet apache - jserv .the grb data will be stored in a postgresql database with access to the java code provided via jdbc .all of these software packages are available on many platforms , including unix , windows , and mac , and they are all freely available . the flow of information through these packages is shown in figure [ fig : infoflow ] .= 0.9 mm  ( 140,80 ) ( 55,0)_client browser request _( 110,0)(1,0)12 ( 110,4)(1,0)8 ( 118,4)(0,1)5 ( 122,0)(0,1)9 ( 122,9)(1,0)2 ( 118,9)(-1,0)2 ( 116,9)(1,1)4 ( 124,9)(-1,1)4 ( 100,10)(40,50)[ct](www.apache.org ) ( 103,13)(34,17)[cc ] ( 117,42)(27,14 ) ( 117,42)(0,0 ) ( 117,30)(0,1)5 ( 117,35)(0,-1)5 ( 62,32)(30,20)[cc ] ( 103,42)(-1,0)11 ( 92,42)(+1,0)11 ( 0,25)(56,29)[cb](www.postgresql.org ) ( 46,42)(16,12 ) ( 46,42)(0,0)jdbc ( 62,42)(-1,0)8 ( 54,42)(+1,0)8 ( 2,32)(30,20)[cc ] ( 38,42)(-1,0)6 ( 32,42)(+1,0)6 ( 17,52)(0,1)8 ( 17,60)(0,-1)8 ( 17,70)(30,20 ) ( 17,70)(0,0 )  this whole process is initiated by aiming a web browser at the appropriate url ( http://grb.mankato.msus.edu/ ) where the apache web server is configured to start a java servlet via apach jserv .the java servlet will then make requests to the postgresql database via the jdbc package that comes with postgresql .the major development effort for this application is in the creation of the java servlet code , which we call `` the web application . ''the java servlet application is a complex set of java code with many data structures and interfaces .there are two major data formats that will be used : standard user interface format ( suif ) and standard internal classifier format ( sicf ) .the suif will be used when presenting data to the user on the client machine ( web browser ) . andsicf will be used when presenting data to any of the supported classifiers ( data mining tools ) .the sicf format is proposed as a tool - independent representation format for holding all information necessary to conduct a classification / data mining run .we expect to provide a user interface on the web browser that looks very much like a spreadsheet program. this familiar view will allow the user to inspect and possibly update data easily .note that a `` donut '' object indicates a data format conversion is needed at that point .some of these data format conversions may require additional information , which would require the use of web pages to interact with the user . andthe wide arrows indicate data flowing across the internet from server to client ( browser ) .  the control of when and where the data flows is completely independent of this diagram .imagine a controller sitting above this page directing the data to flow along the various paths of the diagram .this controller is a web - based menu system under the direction of the user .the design of this perspective of the grb tool shed is least developed at this time .it is clear there needs to be a login menu screen .once that information has been verified , the user will be placed in a main menu / dispatcher web page .this page will allow the user to click on various functions on a menu bar either along the side , the top , or the bottom .the menu selections / actions might be :  [ cols= " < , < " , ]   each of these items constitutes a large implementation effort .for example , the `` work with the data '' selection initiates a sequence of web pages / forms where the user is required to make selection criteria for the various rows and columns of the data .the `` initiate classification '' selection will cause the user to be prompted for which classifier tool to invoke , then guide the user through selecting parameter values that are specific to that tool .with the creation of this software comes a powerful research tool capable of automating many aspects of manipulating grb data .our goal is to go beyond the tool creation and build up the collection of attributes about the grbs , emerging as a significant repository of grb information with a built - in efficient methodology .paciesas , w.s . , _et al . _ , 1999 , _ apj _ , 519 , 206 .hakkila , j. , _ et al ._ , submitted to _hakkila , j. , _ et al ._ , this conference .quinlan , j.r . , _c4.5 : programs for machine learning _, san francisco : morgan kaurmann , 1993 .roiger , r.j . , __ , `` esx a tool for knowledge discovery '' , in _ proc . of the federal data mining symp . & exposition 99 _ , edited by w.t .price , afcea international , publisher , fairfax va ., 1999 , pp . 109120 .

Abstract: we describe the design of a suite of software tools to allow users to query gamma ray burst ( grb ) data and perform data mining expeditions . we call this suite of tools a shed ( * sh*ell for * e*xpeditions using * d*atamining ) . our schedule is to have a completed prototype ( funded via the nasa aisrp ) by february , 2002 . meanwhile , interested users will find a partially functioning tool shed at http://grb.mankato.msus.edu .


it is generally surmised that microscopic chaos is a necessary condition for diffusive behavior of a system .microscopic chaos here means a positive kolmogorov - sinai ( ks ) entropy , or equivalently , at least one positive lyapunov exponent .while this seemed to be confirmed by an ingenious experiment with a brownian particle  , we showed that the same behavior on which the microscopic chaoticity of the brownian system was established also held for a manifestly nonchaotic system with zero ks entropy  , so that both systems exhibited diffusion ., a one dimensional hard rod model  and a heavy particle in a lattice of light particles  . in both casesthere are an infinite number of moving particles , so we expect that the ks entropy is infinite , as in the infinite ideal gas  . herewe have only one moving particle , and we argued in ref . that the ks entropy of our nonchaotic models is zero . ] in these works we used the mean square displacement ( eq . [ e : msd ] below ) , a two time distribution function , as our definition of diffusion .an anonymous referee of a ref . , alerted us to a definition of diffusion ( eq . [ e : multi ] ) which involved multitime distribution functions and the question arose whether those could distinguish between chaotic and nonchaotic models , in that all our chaotic models and none of our nonchaotic models would satisfy this definition . in this notewe show that this behavior does not occur : no difference has been found between the diffusive behavior of microscopically chaotic and nonchaotic models even in the multitime distribution functions we studied .  our models , a subset of those of ref . , consist of a point particle moving with unit speed in two dimensions , undergoing specular reflections ( collisions ) with fixed non - overlapping scatterers .the shapes , positions , and orientations of the scatterers in the various models are defined in the next section , and can be classified as lorentz or ( modified ) ehrenfest models . for each fixed configuration of scatterers ,the particle s position is determined numerically as a function of the time for random initial positions ( which are uniformly distributed over the plane , except that they can not lie inside a scatterer ) and random initial velocity directions ( also uniformly distributed ) of the particle .the probabilities below are defined with respect to this distribution of initial conditions .the definition of diffusion proposed by the referee and used in this paper is stated in terms of the probability of the particle initially at the origin visiting regions at different specified times .explicitly , a system is said to be diffusive , if , for all , the time ( including ) probability distributions satisfy the relation  : where are arbitrary times and the ( ) are arbitrary subsets of the plane . is the gaussian green s function of the ( generally anisotropic ) diffusion equation in two dimensions , and determines the probability density of a displacement in time in the limit .the scaling of the position and time by is based on the fact that for gaussian diffusion the mean square displacement of the particle is proportional to the time , and is a macroscopic limit . here , and are distances measured in the eigendirections of the diffusion tensor , while and are the corresponding eigenvalues . in the isotropic case andthe choice of orthogonal directions is arbitrary .the components of the diffusion tensor in an arbitrary orthonormal basis ( so that ) can be related to the mean square displacement : where .this expression involves the usual 2-time distribution function , that is , in eq .( [ e : multi ] ) .the mean square displacement is discussed in ref . , where we found numerically that both chaotic and nonchaotic models exhibited gaussian diffusion .it is conceivable that a system may have gaussian 2-time distribution functions but non - gaussian multi - time distribution functions , i.e. , for larger values of .the results of this note show that also for larger , both chaotic and nonchaotic models appear diffusive within the accuracy of the numerical methods .the models we consider are the same as some of those discussed in detail in ref . . , the periodic squares rp4 and the randomly positioned squares r. here , the l stands for the lorentz gas , r for the random orientations of the squares , p for periodic , 4 for the linear dimension of the unit cell ( there are also 4 scatterers per unit cell ) , and for the infinite `` unit cell '' . ] as mentioned above , they all contain a point particle colliding with fixed non - overlapping scatterers in two dimensions .the density is such that the scatterers cover exactly half of the available area .the microscopically chaotic models are lorentz models , consisting of circular scatterers distributed in position either periodically or randomly over the plane , such that they do not overlap .they are microscopically chaotic as they have a positive ks entropy .see fig .[ f : d ]  the microscopically nonchaotic models are ehrenfest - like models , consisting of square scatterers distributed in position either periodically or randomly over the plane , such that they do not overlap .they are microscopically nonchaotic , with zero ks entropy . unlike the original ehrenfest model , the squares in this paper are always oriented at random .see fig .[ f : d ] .( 400,200 ) ( -80,-530 )  in both the lorentz and ehrenfest periodic models , the elementary cell is square and contains four scatterers .the random models have no preferred directions , so the diffusion is isotropic . in contrast , the periodic models have a directionality defined by the elementary cell , and the diffusion is anisotropic as in eq .( [ e : gauss ] ) .we investigated eq .( [ e : multi ] ) for equally spaced times and two choices of the subsets of the plane :  a : :  the ( ) are all balls of  radius centered on the origin for   .b : :   , where and   are two balls of radius   centered on randomly chosen points   ; identifies the  different members of our sample of seven configurations of the   , see table [ t : conf ].  .positions defining the centers of the for case * b * , and corresponding symbols in fig . [ f : b ] below .[ t : conf ] [ cols="^,>,>,>,>,^",options="header " , ]   ( 400,500 ) ( -50,-300 )  ( 400,500 ) ( -50,-300 )  ( 400,500 ) ( -50,-300 )p. gaspard , m. e. briggs , m. k. francis , j. v. sengers , r. w. gammon , j. r. dorfman , and r. v. calabrese , nature * 394 * , 865 ( 1998 ) .c. p. dettmann , e. g. d. cohen and h. van beijeren , nature * 401 * , 875 ( 1999 ) . c. p. dettmann and e. g. d. cohen , j. stat .( in press ) ;nlin.cd/0001062 j. l. lebowitz and j. k. percus , phys . rev . *155 * , 122 ( 1967 ) ; j. l. lebowitz , j. k. percus and j. sykes , phys . rev . * 171 * , 224 ( 1968 ) .r. j. rubin , j. math . phys . * 1 * , 309 ( 1960 ) ; ibid * 2 * , 373 ( 1961 ) . s. goldstein , j. l. lebowitz , and m. aizenman , lecture notes in phys . * 38 * , 112 ( springer , berlin , 1975 ) .j. r. norris , `` markov chains '' ( cambridge university press , 1997 ) .

Abstract: using standard definitions of chaos ( as positive kolmogorov - sinai entropy ) and diffusion ( that multiple time distribution functions are gaussian ) , we show numerically that both chaotic and nonchaotic systems exhibit diffusion , and hence that there is no direct logical connection between the two properties . this extends a previous result for two time distribution functions .


optimization is a key goal in engineered systems and is traditionally assumed to be part of the intrinsic dynamics of natural evolving systems .the engineering perspective , associated to man - made objects and structures , is specially obvious when dealing with large - scale , interconnected units , as it occurs in very large integrated circuit design or spatially - extended infrastructures such as power grids and transportation or distribution networks . in these cases ,engineers cope with interfering constraints related to materials , space , packing , wiring , or dissipation costs .the staggering complexity of these designed systems can be addressed by algorithms that deal with multidimensional problems .  in biological systems , important network topologieshave been shown to result from optimality .these include transportation networks in living organisms where optimization is reached by means of fractal trees that guarantee a low cost and efficient location of resources .similarly , neural circuits display optimal features over a wide range of scales .the packing and interconnectivity in some cortical areas seem compatible with design principles shared by high - density electronic designs .  in all the previous examples tradeoffs between efficiency and costare present .packing many components in a given spatial domain is desirable because of cost minimization of connections , but dissipation of energy or wiring constraints will also be at work .what kinds of topologies result when considering multiple constraints ?this problem has been addressed by explicitly introducing efficiency measures ( such as average path length ) along with cost constraints ( such as number of connections of a given graph ) . a similar example in another field models languages as a network of associations between objects and words , and considers language evolution through a least effort process . here, the cost - efficiency conflict is mapped onto coding / decoding efforts for users of an economic ( while ambiguous ) language . both in the linguistic and the network examples , the tension between opposite demands leads to phase transition phenomena .we can wonder , in a more general note , when and how will phase transitions arise disregarding of the details of the problem in hand .  within the context of network optimization, we consider the set of all connected networks involving nodes and any number of links .latter on we will define an efficiency ( ) and a cost ( ) based on the structure of each network , so that a series of optimization problems can be posed . for each such graph , we can also introduce a global energy function that takes into account our optimization goals . the most straightforward way to dothis is through a linear combination : with  ] poses a different soo problem , potentially with a distinct global solution .we check now how solutions of this soo family are related .  by setting fix a value of choose a direction in the plane along which the minimization proceeds ( fig .[ fig:1](d ) ) . from eq .[ eq:5 ] , networks projected onto a straight line with slope have the same global energy . networks on straight lines _ pushed _ further against the front present lower energies , until one solution is singled out as global minimum of .it usually lays where the slope of the front is precisely .if the front is convex and its derivatives are well defined , we can smoothly sample the front by slowly tuning . any appropriate measurement that we perform on be a smooth , differentiable function of itself ., while those inside the cavity are not .( b ) this renders a gap in any adequate , measurable property of the global solutions .( c ) second order phase transition are associated to ill - defined derivatives i.e. sharp edges in the front. those designs at the edge are persistently optimal foe a range of the control parameter .( d ) hence , any property of the global solution is constant as a function of that same control parameter for the designated interval .( e ) second order phase transitions might also take place at the extremes of the pareto front .we say then that the front has an abrupt ending ( or that it ends in an abrupt manner ) as in the lower - right extreme of this front .( f ) any order parameter presents the well - known functional dependence of second order phase transitions ., width=8 ]  if a cavity exists in , the global solutions bypass those that lay inside ( fig .[ fig:2](a ) ) .for a certain value , two very different solutions ( and ) located far apart in the plane are simultaneously optimal .solutions between and ( inside the cavity ) never get to be global optima . for remain at one side of the cavity where a smooth sample of the pareto front is still possible .the same happens for at the other side of the cavity .but at the characteristic value there is a sudden jump between and and , consequently , in any order parameter that we can measure on when plotted as a function of ( fig . [ fig:2](b ) ) .this is a first order phase transition .a similar transition happens if the pareto front is a straight line ( then , where is the slope of the front ) with the singularity that all pareto optimal solutions are also global optima for .if the front is convex but its slope is ill - defined anywhere ( fig . [ fig:2](c ) ) there is a range of values for which the global optimum remains the same .because the optimum does not change within this singular range , if we plot any order parameter its derivative ( with respect to ) will be zero. the same derivative will be different from zero anywhere else .this results in a characteristic plot for any order parameter ( fig . [ fig:2](d ) ) associated to second order phase transitions .such non - differentiability of the front might be shifted all the way towards one of its extremes .for we seek global optima where the slope of the front is any .well - behaved pareto fronts should roll smoothly with slopes that completely span the interval ; otherwise the front will be exhausted while more soo problems can still be defined .if these slope values are not exhausted we say that the pareto front _ ends in an abrupt manner _ , meaning that its slope as we approach its leftmost end is some , or its slope as we approach its rightmost end is some other .these abrupt endings of the front will be optima already for some . we can still define soo problems for beyond these limits , for which the solutions at the corresponding extremes of the front will be persistently optimal ( fig . [fig:2](e ) ) .this implies again a discontinuity in the derivative of any order parameter , the fingerprint of second order transitions ( fig . [ fig:2](f ) ) .complex graphs are a great testbed to illustrate this theoretical framework .they allow us to define problems of increasing difficulty where first and second order transitions arise .seminal work on network optimization addressed the problem from an soo perspective , so some of our results can be put in context .another advantage of complex networks is that good optimizers can be produced in the computer , simplifying the empirical work .we propose three problems based on the conflict between the average path length between nodes and the density of edges , which roughly inform us about diffusion efficiency ( for which low average path length is desired ) and implementation costs ( lower for sparser networks ) .consider first the _ topological _ ( or standard ) average path length : where denotes the distance ( in number of edges ) between nodes along the shortest path that connects them ; and the topological ( or standard ) link density : where the adjacency matrix presents if two nodes are linked in and otherwise . and are normalization constants discussed below .  the superindices in , indicate that we deal with the topological ( or standard ) average path length and link density , in which edges cost unit .geometric costs can be included if nodes are distributed , e.g. , over a euclidean space .let be the euclidean length of the shortest path connecting and in network  i.e. the sum of the euclidean lengths of the edges in the shortest path between these nodes provided that is embedded in some geometric space .we introduce the geometric ( or weighted ) average path length : the shortest euclidean distance possible between two nodes only enters equation ( [ eq : app.02 ] ) if a direct link between and is present in ( in that case ) .this allows us to introduce the geometric ( or weighted ) link density :   just as before , and ( note the superindexes indicating their geometric dependence ) are normalized by and . a clique , or fully connected network ( ) ,has the shortest average path length possible always . as we will see later, this means that is pareto optimal _ always _ , so we base our normalization on it : , , and .+ we combine and as targets in different ways to generate three moo problems :  * fully topological problem , with and .note that the geometry does not play any role in this case .+ this version was originally studied in from an soo perspective . from that approach ,only the clique and star graphs appear relevant ( as discussed in ) as the representatives of two phases at either side of a discontinuous phase transition .we show how this fits parsimoniously within the framework presented in . but besides , we discuss now the whole pareto front its relevant shape and some of its constituents .this front includes non - trivial complexities well differentiated from the star and clique , and it presents connections to critical systems discussed elsewhere . * partly geometrical problem , with ( the same as above ) and .geometry , through , plays a relevant role now . since the disposition of the nodes in space matters , we study this moo in two different cases : i ) nodes scattered randomly over the \times[0,1] ] square in and ii ) nodes spaced evenly over a circle of radius .three relevant topologies indicate major feats of all our pareto fronts . the most prominent one is the clique : a fully connected network that presents the largest number of links possible ,thus maximizes edge density and minimizes the average path length always .this guarantees that the clique is always pareto optimal .it marks the top - left boundary of the pareto front , as illustrated in fig . [ fig:3](a ) .this is true for all problems considered in this paper .the star presents a hub to which all other nodes are connected , while non - hubs are not connected to each other .there are possible star graphs .if geometry is not considered , all of them are equivalent . when geometry intervenes and nodes are spaced over a circle all stars are equivalent as well .all possible trees consist of as many edges as the star but , if geometry matters , only the minimum spanning tree ( mst ) minimizes _ always _ the edge density ( ) .the mst is pareto optimal whenever geometry is relevant and it always indicates the end of the pareto front opposite to the clique ( at its bottom - right ) .determines that at a first order phase transition takes place .all networks laying on the front are global soo optima at that critical value . among themwe find networks produced by attaching links to a star and others radically different from the star and from the clique ( note the two graphs marked a and b : only one of them can be produced by attaching edges to the star ) .( b ) all _ core graphs _ for have been listed for . beyond that , it becomes increasingly difficult to count how many there are or even to tell apart two different ones ., width=8 ]  this case has been studied as an soo through equation ( [ eq:5 ] ) .that solution is incomplete from an moo perspective which was not the chosen paradigm in those works anyway .this problem has the advantage that its front ( fig . [fig:3](a ) ) can be found analytically and the phase transitions derived from it are independent of the number of nodes .we can not guarantee the same for the variations studied later .because we normalized both targets using the clique as a reference , this network is mapped into in the plane .any graph will have less edges than a clique , thus the set of all connected networks lays below in the target plane .the lower boundary of is achieved by connected networks with the minimum amount of edges possible ( ) .there are a collection of such graphs , from the star to a linear chain in between lay all possible trees .all them have , which tends to as goes to infinity .the average path length of these networks varies between that of the star ( ) and the linear chain ( ) .these minimally connected graphs lay on a horizontal stretch of the plane ( dashed line in fig .[ fig:3](a ) ) .  among these trees ( all with the same ) ,the star is the one with the lowest average path length , hence it is pareto optimal .any other network with a lower must have more links than the star , the clique setting the lower bound .thus the pareto front must lay on a curve connecting the clique and the star i.e. connecting and in the plane .we appreciate the following facts : i ) the edge density is a function of the number of links alone and it does not depend on the topology of the network .ii ) given a network that is pareto optimal , we generate new pareto optimal networks by simply adding new connections . as an instance, the star is pareto optimal and all its nodes are edge apart from the hub and edges apart from each other .then , new edges can only be added that connect directly two non - hub nodes , turning a distance into ; but not affecting the network in any other respect . put otherwise ,once a network is pareto optimal any addition of links has got only _ local _ effects in its average path length .adding new links to the star results in more pareto optimal networks , the number of which grows combinatorially ( that scaling saturates as we approach the clique ) .take apart the non - hub nodes of a star : any network that we implement on this subset of nodes ( connected or not ) , and which is subsequently embedded on the original star graph through the hub , is pareto optimal .it is a _ sufficient _ ( but not necessary ) condition for a network to be pareto optimal to contain a hub ( fig . [ fig:3](a ) ) .the _ necessary _ condition for pareto optimality is that every node is at maximum edges apart from each other .  from any pareto optimal network ( with or without a hub ) , adding new edges always generates new pareto optimal graphs . repeating this operation we always reach a clique , but this process is not reversible :take the clique and delete connections randomly with the condition that your network remains pareto optimal after every deletion .no rearrangement of the edges is allowed .let this process continue until we can not remove any link without violating the pareto - optimality condition .this algorithm might yield a star or any other graph from a collection of _ irreducible _ pareto optimal networks , which we call _ pareto core graphs_. the star is the core graph with less edges possible .we can only construct these networks as described , since other defining regularities are not apparent beyond the optimality condition that every node is at most hops away from each other .some of these graphs are represented in fig . [ fig:3](b ) for .the complexity scales from core graph for ; to two core graphs for ; to three for ; to an unknown number for . for larger also becomes increasingly difficult to determine whether two core graphs are the same , given their invariance under the labeling of the nodes .note that core graphs _ are _ pareto optimal .they are representative of the staggering complexity contained in the front ( which grows combinatorially ) and they can not be trivially composed as a mixture of stars and cliques . because of this they constitute pareto and global optima that have not been previously reported .even if we can not list down all pareto optimal networks , we can find where they live on the plane . adding one edge always modifies by an amount , thus is decreased .the same operation increases by . because does not depend on the number of edges , pareto optimal graphs thus generated lay on a straight line with slope ( fig . [ fig:3](a ) ) .such a front implies a first order phase transition at .the clique and the star are found at either phase ( correspondingly for and ) .right at the critical value any pareto optimal network is a global optimum .the degenerated complexity at , with so many and structurally different optimal solutions , presents interesting connections with critical phenomena and neutral theory that we explore in future work .the plot of any order parameter as a function of ( not shown ) just presents a gap between two constant values .figure [ fig:3](a ) provides an archetype for the pareto front that will be repeated ( with variations ) in the more elaborated moo problems .our fronts will present a first , stepped stretch that trades off between the clique ( top - left ) and some intermediate networks ( usually the star ) ; and a second , flat stretch with little variation in the vertical dimension ( ) and a broad variation in the horizontal axis ( ) . in the previous case , this second stretch ( dashed line in fig . [fig:3](a ) ) does not belong to the front , but it will in the following problems .figure [ fig:4](a ) shows the first example of this archetype . a very stepped stretch of the front trades off between the clique and the star just as before .however , this is a convex curve now , which we discuss below .the second archetypal stretch of the front trades off between the star and the mst , and is mapped onto an almost horizontal curve in the plane with a slight convexity .this pareto front ends up smoothly in its bottom - right extreme , so we dismiss any phenomenon associated to it . because the whole front is convex first order phase transitions are ruled out .the first , stepped stretch of the front ( fig .[ fig:4](a ) , inset ) presents a feature that appears in most subsequent cases .this stretch is a convex curve that ends abruptly ( with the notion of _ abruptness _ introduced before ) .this indicates that a second order phase transition takes place .this transition trades off between the clique ( persistent global optimum for ) and dense but incomplete graphs reached as we move below . because the clique is optimal for , anything that we measure on this global optimum stays constant as a function of until , for which our wandering over the pareto front yields a changing global optimum as decreases .then , any measurement performed on the soo optimum will vary steadily with a derivative ( with respect to ) different from .this discontinuity in the derivative indicates that a second order phase transition takes place ( fig .[ fig:4](c ) ) .  a sharp edge in the front ( fig .[ fig:4](b ) ) indicates yet another second order phase transition similar to that described in fig .[ fig:2](b ) : the slope of the front is well defined as we tend towards the sharp edge from the left ( yielding a slope such that ) , and as we tend to the sharp edge from the right ( now with such that ) . for any , soosare well defined through equation ( [ eq:5 ] ) ; but there are not any points of the front with a slope where to locate the optimum . instead , the same one network laying precisely at the sharp edge is consistently optimal for this range of .anything that we measure about this optimum will remain as a function of in , but samplings of the front run smoothly below and above , with well defined derivatives for any order parameter as a function of .hence , two discontinuities are evident in this derivative ( fig .[ fig:4](c ) , inset ) .qualitatively , browsing the front through is a continuous transition from the clique ( which is a global optima for a wide range of ) , through the star graph ( also a persistent optimum for a continuum of ) , to the mst .the weighted density of edges ( ) penalizes large connections first , which are dropped as we leave the clique . but enough of them survive among pareto optimal graphs so that the star can be reached continuously , without needing a drastic rewiring that would leave an imprint in the order parameters .note that these few long edges survive because they enable a low average path length ( ) , which is still measured as the number of hops between nodes . finally , to rearrange the star into the mst , the surviving long edges are replaced by winding branches that extend visiting many nodes on their way .alternative strategies , like hybrid msts that incorporate non - essential shortcuts between far - apart nodes , fall off the pareto front ( note the sub - optimal graph highlighted in fig .[ fig:4](a ) ) .it is very useful to consider the potential landscape introduced by equation ( [ eq:5 ] ) to stretch our intuition .for a fixed value of we compute the energy for every pareto optimal network .the result is a lower energy boundary ( fig .[ fig:4](d ) ) .not pareto - optimal networks must present yet higher energies .the soo solution becomes now very intuitive since the global optimum lays at the minimum of , which has got a vivid graphic representation .but this potential landscape changes as a function of , and consequently its minimum .the sharp edge of the pareto front is inherited by the potential landscape , which presents a persistent minimum for a range of the control parameter .   the front of this problem ( fig . [ fig:5](a)-(b ) ) again follows the archetype : i ) a stepped stretch to the left that trades - off between the clique and dense ( yet incomplete ) graphs and ii ) a flatter stretch that encompasses graphs with roughly the same edge density but a wide variation along the average path length dimension .this second stretch extends to large values of : a region populated by minimal , circlelike networks with little long - range connections .it seems a convex stretch that ends smoothly , so nothing remarkable happens there .again , the stepped stretch of the front is convex ( fig .[ fig:5](a ) , inset ) and ends abruptly revealing a second order phase transition .it is similar to the one encountered before by the clique and happens at a similar value ( fig .[ fig:5 ] ( c ) ) .the notable feature that this front introduces is a concavity at the junction between the two archetypal stretches of the front ( fig . [ fig:4](b ) ) .the cavity lays at the confluence between the three relevant network topologies : incomplete cliques , the star , and encircled nets ( the mst of the problem ) .as in the previous case , longer edges are dropped first .the scattered nodes managed to retain enough long - range links in that example , enabling a continuous transition through the star .this is not possible now , and the symmetry of the circle might be crucial therefore .earlier , the distribution of lengths were varied , while now all long - range edges are the same : the moment one is dropped , the others follow .as we leave the clique , we converge quickly to encircled graphs with little long range connections ; and these lay inside a cavity of the front ( fig . [fig:4](b ) ) . to reconstruct a star ( which remains pareto optimal due to its low average path length ) a drastic rewiring in unavoidable. this prompts a first order phase transition ( ) whose imprint is , indeed , that cavity .that transition is reflected in any order parameter that we plot as a function of ( fig .[ fig:4](c ) , inset ) .we can resort again to a potential landscape to visualize this transition .plotting for all pareto optimal networks we obtain the lower energy boundaries portrayed in fig . [ fig:5](d ) .this landscape changes as varies , producing two potential wells associated to local minimums . at ,both minimums present the same energy , thus both phases coexist .moving away from the transition point , one of the wells is unstabilized . note that moving back and forth could get us temporarily trapped in metastable states ( the most energetic local minimum ) and hysteresis loops would be observed .introducing geometry in both target functions has the effect of smoothing the pareto front , removing first order phase transitions .some relevant second order transitions disappear .others persist , but only at the extremes of the front . the picture becomes closer to a soft trading - off between the clique and the mst .poses an soo with a different solution .as we roll over the front , the clique gently leads to less connected networks , towards the mst .( b ) the absence of phase transitions renders smooth plots of any order parameters . ]this problem presents a quite uninteresting front ( fig . [ fig:6](a ) ) without phase transitions .the front spans all possible slopes , so that soos with different solutions can be posed for each .any order parameter renders a continuous plot ( fig . [ fig:6](b ) ) even when zooming in to tiny details ( inset ) .the first derivative of the order parameters also behaves properly .all phase transitions from previous cases have vanished . besides the geometric disposition of the nodes ( which has some obvious influence over what transitions are present ) , it is notable that choices of optimization targets exist for which previously existing transitions disappear .the fact that , given a same set of networks , a choice of targets erases previous transitions implies that a gentle evolution between radically different topologies ( clique and mst ) can happen , despite the drastic modifications that we might envision necessary _ a priori _ , and despite the phase transitions that do take place on the same graphs for other choices of targets .this stresses the role of target functions to frame phase transitions properly .    and ( inset ) .]  again , introducing geometry in both targets smooths the pareto front ( fig . [ fig:7](a ) ) .the first order transition found in the circle before has disappeared . there is no cavitynow and the tradeoff between clique and circle happens gradually as we roll over the front . that previous transition took place because the gradual drift from clique to circle was interrupted by the presence of the pareto optimal star , which kept the average path length low because it was measured as the number of hops between nodes .but now geometry also enters through and using only two links to get from one node to another is still costly if these are far reaching connections .it is more economic now to circle around even if that implies visiting many more nodes .thus the star is retracted from the pareto front and the transition from the clique to the mst proceeds smoothly .the bottom stretch of the front seems convex but abruptly terminated , suggesting a second order transition at that trades off between the mst ( an almost complete circle , which is persistently optimal for ) and other , more connected graphs .the characteristic plot of a second order transition is noted in any order parameter ( fig . [ fig:7](b ) ) . at the other end of the front we find the usual transition associated to the clique , which did not disappear buthas been moved to .the same characteristic order parameter plot can be appreciated ( fig .[ fig:7](b ) , inset ) . for order parameter is a smooth function of .in this paper we solve three moos defined on complex networks .these problems allow us to explore interesting aspects of pareto optimality . following recent contributions in biology ,our work is an exploration of a morphospace .a first approach to such spaces is to list all possible morphologies for a system and locate them quantitatively with respect to some relevant aspects here , complex networks are characterized in an average - path - length vs. edge - density two - dimensional space .we propose that a natural selection process based on pareto optimality shall constrain further such a morphospace and we study the effects of these conflictive restrictions . in doing so, we follow recent works that illustrate how pareto optimality reduces the effective dimensionality of certain complex systems .alternatively , a recent theoretical framework brings together statistical mechanics and moo , thus enriching the analysis of pareto optimal designs .this framework reveals universal features of pareto optimal systems that correspond to phase transitions or critical phenomena .first order phase transitions indicate that a system must undergo important structural changes despite little variation of some control parameter . in thermodynamics , this implies great investments of energy in reshaping matter , e.g. , as it transits from solid to fluid .similar demands might be requested of complex pareto optimal systems , specially if the parameters controlling the conditions for optimality may change over time .this underscores the importance of gathering knowledge about the pareto front before implementing solutions to any optimization problem .second order phase transitions can also be very informative about the nature of a system .they indicate that some solution is stable for a large range of the control parameters , thus making it more likely if evolution or design has taken place under many different scenarios . on the other hand ,if such stable solutions would not show up in an evolutionary setup , we would have strong evidence that a large set of possible circumstances do not occur naturally .we have found a variety of first and second order transitions .these depend very much on the precise mathematical expression of the optimization targets ( see , for example , how transitions disappear as we change the measure of average path length ) . hence , looking at the problem from an alternative perspective , the presence or absence of expected phase transitions in real systems could be informative about the nature of the optimization pressures that these systems might be subjected to .finally , the fully topological problem presents a quite singular case : a first order phase transition takes place between the star graph ( for ) and the clique ( ) , while all other pareto optimal networks are also global optima at .this would suggest that cliques and star graphs should happen overwhelmingly more often than any other topology when geometry is not relevant , unless every optimal network had evolved under the unlikely condition .this is notably at odds with the reality and a possible solution ( with connections to critical phenomena ) will be explored elsewhere .we thank the members of the csl for useful discussions .this work was supported by grants from the fundacin botn , the european research council ( erc advanced grant ) , and by the santa fe institute .we relied on genetic algorithms to locate the different pareto fronts .the fully topological case can be solved analytically , but the same genetic algorithm was used to check for good convergence showing very good results . in this appendixwe explain in detail the genetic algorithm . following that explanation ,a few disclaimers are in order about the numerical nature of the solutions found i.e. about the fact that convergence to the pareto front can not be guaranteed and the smoothing necessary to render a continuous approximation to the front .moo relays on the concept of pareto dominance . given two networks , both mapped into through and , we say that dominates ( and note it ) if is not worst than regarding any target and it is better than with respect to at least one target .we can visualize this : since we deal with minimizations in the plane , network has got a set of axes associated with their origin at and every network laying on the first quadrant of these axes is pareto dominated by .  following the literature on multiobjective genetic algorithms we computed a dominance score: we took the set of solutions from within a given _ population _ ( an arbitrary subset of ) that dominate .the size of this set ( , dubbed the _ dominance score _ ) , indicates how _ fit _ is in terms of pareto optimality .we proceeded then to minimize this score .we departed from an initial population of networks ( either random or designed , see below ) , selected of the population based on the dominance score , chose random pairs among the selected networks to produce new networks , and applied random mutations to all but a subset of _ elite _ networks .we iterated this scheme a fixed number of generations .mutations consisted in random appending or deleting edges or totally swapping the connections of two arbitrary nodes . for crossover , from each of the two mating nets we assigned each node and its connections randomly to each of the offspring graphs checking that the same node and connection was not assigned twice to the same _ child_. after crossover or edge deletion we checked that all networks remained connected all the time .we completed one missing link whenever connectedness failed and then checked for connectedness again .all we care about for the current research is good convergence towards the front .this justifies our using of crossover : this is a very good evolutionary operator , though unrealistic if we wanted to study some features of nature .for example , such an operator would not be adequate to study species that do not reproduce sexually .studying pareto optimality under constrained conditions e.g. without crossover also renders a set of non - dominated solutions .these might converge to the pareto front or not , and they might be subjected to geometrical constraints in that are similar to those studied in and in this paper for pareto optimal networks .such constrained evolutionary schemes pose interesting research questions , but here we are concerned with pareto optimal solutions .this justifies the crossover and a clever initialization of the algorithm .it might be difficult to converge towards some solutions that are highly non - trivial e.g. the mst . we know , though , that this solution belongs to the front of all physically grounded problems . if an algorithm would fail in finding this solution, this could hinder convergence towards an interesting ( though challenging ) region of the pareto front .once again , because we are concerned with pareto optimal solutions and would like to attain the closest convergence possible , it is also fully justified to _ seed _ the initial population with a few _ designed _ solutions .we did so by introducing since the very beginning cliques , star - graphs , msts , and circle networks ( these two are equivalent for the circle ) with very slight mutations .we produced of each such major topologies at the beginning .the crossover and mutation operators ensure fast exploration of hybrid topologies .  as noted above , we know that some of these networks are pareto optimal : the clique is always so , and the mst is pareto optimal in all physically grounded problems .however , and since we started with little variations upon these graphs , the algorithm did not always reach these solutions but it surely explored the region nearby .there might be other interesting regions of the front that might not have been fully explored and that are impossible to seed without foreknowledge .although we are concerned with pareto optimal solutions alone , our methods are numerical at the end and convergence of multiobjective genetic algorithms to the pareto front can not be guaranteed .we decided to report on the results of the simulations with as little reinterpretation and further speculation as possible .notwithstanding , the overall details of the pareto front seem to be recovered and the theory posed in is properly illustrated .+ as for the implementation of the algorithm , we used a population of connected networks with nodes with the initial population seeded as indicated above .the population was evolved during generations in every case .mutation happened with a probability of appending an extra link to each network , the same probability of deleting an existing edge , and the same probability of swapping the ends of each existing connection .the top networks of the population where considered _ elite _ and were spared any mutation .as the algorithm proceeds , many networks reach a dominance score of even if they are not pareto optimal .unluckily , this score is the best indicator of pareto optimality available ( not only in the current implementation , but generally ) .this results in elite members of the population not being objectively better than non - elite members in terms of pareto optimality . because the algorithm sorted the population consistently from one generation to the next ,what members of the population are considered elite is largely a matter of antiquity : early members that reach low dominance score and are not overthrown are likely to be preserved during the whole simulation .we repeated times the simulations with scattered nodes to check that the relevant features obtained were not artifacts of some lucky distributions of the nodes .the only speculation that we allowed ourselves is in choosing a relevant scale for analysis , which led to a smoothing of the pareto front . as noted in sec .[ sec:3 ] , we deal with a discrete set of networks whose front is necessarily discrete as well .accordingly , every shift in global optima is a first order phase transition at some scale and global optima remain so for a continuous range of , as in second order phase transitions .this does not further our understanding of the problem as much as a coarse - grained analysis that renders noteworthy phase transitions .since the genetic algorithm only produces a finite set of ( ideally ) pareto optimal solutions , we applied a bezier smoothing to their plot on the plane .we took care that the smoothing did not introduce alien concavities . because bezier curves can not present sharp edges ( thus ruling out second order phase transitions ) , when a sharp edge seemed the best description of the front ( sec .[ sec:3.02 ] , partly geometrical problem on nodes scattered over a plane ) , we decided to split the front in its two salient branches and apply two independent smoothing processes that allowed us to recover the transition in great detail .  to locate global optima, we calculated for the optimal solutions produced by the genetic algorithm , and for a large sample of points from the bezier curves introduced in the previous paragraph .we registered the global optimal for different values of .one of the problems pointed at earlier is that , because of the discreteness of the front , global optima are so for several values of .this would cause that the plots of order parameters look tiered . for a better illustration of the results , whenever order parameters are plotted we indicate only the first and last values of for which each global optima are indeed optima ( black crosses in all order parameter plots ) .the smoothing allows a finner grained sampling so that this is not an issue : the corresponding order parameters ( red curves in all order parameter plots ) look continuous always .+ following , anything _ well behaved _ that we measure upon global optima are accepted as order parameters . bywell behaved we imply that order parameters should not introduce alien divergences into the problem , and that solutions laying at different points over the front should score differently in this parameter . this way we ensure that any feature stemming from the optimization problem does not go unreported and that we do not introduce phase - transition like behaviors that originated , e.g. , on some function diverging to infinity for reasons of its own .taking these guidelines into account , the target functions themselves are always good order parameters .we use these ( in sec .[ sec:3.03 ] ) , or trivial transformations of them ( in sec .[ sec:3.02 ] ) .more drastic transformations such as would be banned : note that this function diverges for even if this is a perfectly 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Abstract: the organization of interactions in complex systems can be described by networks connecting different units . these graphs are useful representations of the local and global complexity of the underlying systems . the origin of their topological structure can be diverse , resulting from different mechanisms including multiplicative processes and optimization . in spatial networks or in graphs where cost constraints are at work , as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain , optimization plays an important part in shaping their organization . in this paper we study network designs resulting from a pareto optimization process , where different simultaneous constraints are the targets of selection . we analyze three variations on a problem finding phase transitions of different kinds . distinct phases are associated to different arrangements of the connections ; but the need of drastic topological changes does not determine the presence , nor the nature of the phase transitions encountered . instead , the functions under optimization do play a determinant role . this reinforces the view that phase transitions do not arise from intrinsic properties of a system alone , but from the interplay of that system with its external constraints .