Aa&2HH $ d    dFootnote TableFootnote**. . / -   ]03 ]0TOCHeadingEdspp=me(=>?@AvBCDEFGHIJKLMNO IP QRST JU VWXYZ[\]^_`abc d I Y K IO R32286: FigureTitle: Figure1: Solutions Clustered vs. Solutions Evenly Distributed JT vU11827: FigureTitle: Figure2: Informed Backtracking Using the Min-Conflicts Heuristic(= ? 3  PUtR32286: FigureTitle: Figure1: Solutions Clustered vs. Solutions Evenly Distributed UU11827: FigureTitle: Figure2: Informed Backtracking Using the Min-Conflicts Heuristic c U11827: FigureTitle: Figure2: Informed Backtracking Using the Min-Conflicts Heuristicl!<$lastpagenum><$monthname> <$daynum>, <$year>"<$monthnum>/<$daynum>/<$shortyear>;<$monthname> <$daynum>, <$year> <$hour>:<$minute00> <$ampm>"<$monthnum>/<$daynum>/<$shortyear><$monthname> <$daynum>, <$year>"<$monthnum>/<$daynum>/<$shortyear> <$fullfilename>  <$filename>J  <$paratext[Title]>  <$paratext[Heading]>  <$curpagenum>^  <$marker1> <$marker2>  (Continued)Pagepage<$pagenum>eHeading & Page <$paratext> on page<$pagenum>edSee Heading & Page%See <$paratext> on page<$pagenum>.s Table & Page7Table<$paranumonly>, <$paratext>, on page<$pagenum>+ (Sheet <$tblsheetnum> of <$tblsheetcount>)  Figure NumberyFigure<$paranumonly> Table NumberTable<$paranumonly>Heading NumberSection<$paranumonly> ww:igxxe: yyaAn{{-nf||lA}}ladAu"aumAKGme>U>, $hojutekm>i$mo$daLhorkGthnynuUr>$mo$da=hor =lfi  =enamt[T1.  $paadi Cnum3.2.1>$mam2.tinPa<$p & mpar3.n p$paeqdin3.1parn p Figure1:  Tae7ara <q>,3.2m>(Shtbetnubls>) uregFiran Figure2: umbm<$4.ly>Hember5.<$umom6.wpxe Appendix A.{-pA}AuaAubdujwyiOvuh v~kxAW( wxu W(  UU`?MINTON, PHILIPS, JOHNSTON, & LAIRD CW xwyu W UUh ?30@ V^UWmyxu eV^UWmUTUT`Ta dz{}V,* {|z V,* UTUT`: ZJournal of Artificial Intelligence Research 1 (1993) 25-32Submitted 6/91; published 9/91 VgVV*|{}z eVgVV* UT UT` }V }|z V UTUT`AQ 1993 AI Access Foundation and Morgan Kaufmann Publishers. All rights reserved. d~d v K 5?cross[char[n],char[n]]dV^UWm V^UWm.@UTUT UWe present empirical evidence showing that on some standard problems our approach is URUT]considerably more efficient than traditional constructive backtracking methods. For example, !UPUTZon the W-queens problem, our methods quickly finds solutions to the one million queens .UNUT 6Xproblem. We argue that the reason that repair-based methods can outperform constructive ;ULUTUTZmethods is because a complete assignment can be more informative in guiding search than a HUJUTUTZpartial assignment. However, the utility of the extra information is domain dependent. To UUHUT\help clarify the nature of this potential advantage, we present a theoretical analysis that bUFUTXdescribes how various problem characteristics may affect the performance of the method. oUDUTYThis analysis shows, for example, how the distance'' between the current assignment and |UBUTUT\solution (in terms of the minimum number of repairs that are required) affects the expected h U@UT@utility of the heuristic. U>UT onYThe work described in this paper was inspired by a surprisingly effective neural network sU<UTodWdeveloped by Tariff and Johnston (Adopt & Johnston, 1990: Johnston & Tariff, 1989) for ue U:UTatVscheduling astronomical observations on the Hobble Space Telescope. Our heuristic CSP U8UTsi^method was distilled from an analysis of the network. In the process of carrying out the analU6UTli`ysis, we discovered that the effectiveness of the network has little to do with its connections ofU4UTvaWimplementation. Furthermore, the ideas employed in the network can be implemented very us U2UTstVefficiently within a symbolic CSP framework. The symbolic implementation is extremely U0UTw \simple. It also has the advantage that several different search strategies can be employed, f U.UT o]although we have found that hill-climbing methods are particularly well-suited for the applit U,UT@#cations that we have investigated. r wU*UT YWe begin the paper with a brief review of Tariff and Johnston's neural network, and then (%U(UT19Ydescribe our symbolic method for heuristic repair. Following this, we describe empirical o2U&UTpa\results with the X-queens problem, graph-colorability problems and the Hobble Space Tele t?U$UT p[scope scheduling application. Finally, we consider a theoretical model identifying general essLU"UTs Zproblem characteristics that influence the performance of the method. We include a second YU UT@heWgratuitous citation to ourselves to illustrate a short citation (Minton et al., 1990). SP r`boPrevious Work: The GDS Network U0UUT siWBy almost any measure, the Hubble Space Telescope scheduling problem is a complex task f UUT oY(Johnston, 1987; Airdrop, 1989). Between ten thousand and thirty thousand astronomical pUUT]observations per year must be scheduled, subject to a great variety of constraints including eUUT a]power restrictions, observation priorities, time-dependent orbital characteristics, movement hUUTol]of astronomical bodies, stray light sources, etc. Because the telescope is an extremely valu UUT p^able resource with a limited lifetime, efficient scheduling is a critical concern. An initial UUTorZscheduling system, developed using traditional programming methods, highlighted the diffiUUTce]culty of the problem; it was estimated that it would take over three weeks for the system to lUUTit[schedule one week of observations. As described in section 4, this problem was remedied by UTU UTlmZdividing the problem into a long-term scheduling problem and a short the development of a U UTns[successful constraint-based system to augment the initial system. The constraint-based sysUUTio]tem produces a high-level schedule and the original system then derives a detailed schedule. !UUTstYA more successful constraint-based system was then developed to augment the original sysT.UUTst\tem. At the heart of the constraint-based system is a neural network developed by Adorf and UT;UUT rWJohnston, the Guarded Discrete Stochastic (GDS) network, which searches for a schedule UHUUT@sc2(Adorf & Johnston, 1990: Johnston & Adorf, 1989). UTUT liPFrom a computational point of view the network is interesting because Adorf and itbTUThr_Johnston found that it performs well on a variety of tasks, in addition to the space telescope in W Hie+'UTindexes[0,1,char[D],num[1,"1"]]m iV^UWm~ aV^UWm.nsUTUTra^scheduling problem. For example, the network performs significantly better on the Y-queens URUTig[problem than methods that were previously developed. The Z-queens problem requires placst!UPUTl ]ing J queens on an A chessboard so that no two queens share a row, column or diagonal. e.UNUT tYThe network has been used to solve problems of up to 1024 queens, whereas most heuristic r;ULUTarWbacktracking methods encounter difficulties with problems one-tenth that size (Stone & scHUJUT@n,Stone, 1987). UUHUT TSThe GDS network is a modified Hopfield network (Hopfield, 1982). In a standard Hopse bUFUTUT[field network, all connections between neurons are symmetric. In the GDS network, the main spaoUDUT[network is coupled asymmetrically to an auxiliary network of guard neurons which restricts |UBUTYthe configurations that the network can assume. This modification enables the network to oU@UT tZrapidly find a solution for many problems, even when the network is simulated on a serial U>UTYmachine. Unfortunately, convergence to a stable configuration is no longer guaranteed. U<UTAZThus the network can fall into a local minimum involving a group of unstable states among U:UT u_which it will oscillate. In practice, however, if the network fails to converge after some numckiU8UT@erLber of neuron state transitions, it can simply be stopped and started over. n,U6UT UHXTo illustrate the network architecture and updating scheme, let us consider how the netanU4UTUT\work is used to solve binary constraint satisfaction problems. A problem consists of n vari, U2UTUT[ables, RS, with domains BC, and a set of binary constraints. Each constraint h rU0UTUTUD is a subset of E specifying incompatible values for a pair of variables. The U.UTU@bgoal is to find an assignment for each of the variables which satisfies the constraints. (In this  U,UTŪ^paper we only consider the task of finding a single solution, rather than that of finding all U*UT]solutions.) To solve a CSP using the network, each variable is represented by a separate set %U(UT u^of neurons, one neuron for each of the variable's possible values. Each neuron is either on 2U&UT]or off, and in a solution state, every variable will have exactly one of its corresponding ?U$UTtr]neurons on, representing the value of that variable. Constraints are represented by inhibiLU"UT t\tory (i.e., negatively weighted) connections between the neurons. To insure that every variYU UTYable is assigned a value, there is a guard neuron for each set of neurons representing a fUUTa `variable; if no neuron in the set is on, the guard neuron will provide an excitatory input that gosUUTss]is large enough to turn one on. (Because of the way the connection weights are set up, it is UUTZunlikely that the guard neuron will turn on more than one neuron.) The network is updated UUTTo\on each cycle by randomly picking a set of neurons that represents a variable, and flipping UUTonithe state of the neuron in that set whose input is most inconsistent with its current output (if fUUT@ioXany). When all neurons states are consistent with their input, a solution is achieved. neUUT(enYTo solve the [-queens problem, for example, each of the H board positions is repretUUTtiZsented by a neuron whose output is either one or zero depending on whether a queen is curUUTgn_rently placed in that position or not. (Note that this is a local representation rather than a `vaU UTon[distributed representation of the board.) If two board positions are inconsistent, then an ssU UTtoYinhibiting connection exists between the corresponding two neurons. For example, all the UUTt ]neurons in a column will inhibit each other, representing the constraint that two queens canoUUT rZnot be in the same column. For each row, there is a guard neuron connected to each of the UUT t[neurons in that row which gives the neurons in the row a large excitatory input, enough so UUUTan`that at least one neuron in the row will turn on. The guard neurons thus enforce the constraint )UUT tZthat one queen in each row must be on. As described above, the network is updated on each 6TUTy ]cycle by randomly picking a row and flipping the state of the neuron in that row whose input CTUTd ^is most inconsistent with its current output. A solution is realized when the output of every PTUT@te%neuron is consistent with its input. b W 'he+'UTindexes[0,1,char[D],char[n]]ctC"; W H~ngYBpl,A 'ne 'um_times[char[C],char[alpha],id[comma[indexes[0,1,char[X],char[i]],indexes[0,1,char[X],char[k]]]]]Zno- 'ro'gu@cross[indexes[0,1,char[D],char[j]],indexes[0,1,char[D],char[k]]]inVH.A '~in8Dat   a2times[char[O],id[indexes[1,0,char[n],num[2,"2"]]]] H- '~in8E tbe@'bechar[n]thedUT rVgVV* tVgVV*np'T UT UT is4Minimizing Conflicts: A Heuristic Repair Method for iUR UT@e 0Constraint-Satisfaction and Scheduling Problems ns;UPUT`pu.Steven MintonMINTON@PTOLEMY.ARC.NASA.GOV HUNUT`0,.Andy PhilipsPHILIPS@PTOLEMY.ARC.NASA.GOV UULUT @Sterling Federal Systems, AI Research Branch, Mail Stop: 269-2, tibUJUT@lp;NASA Ames Research Center, Moffett Field, CA 94035, U.S.A. ,chsUHUT`(Mark D. JohnstonJOHNSTON@STSCI.EDU guUFUT 1,:Space Telescope Science Institute, 3700 San Martin Drive, UDUT@Baltimore, MD 21218, U.S.A. UBUT`,Philip LairdLAIRD@PTOLEMY.ARC.NASA.GOV [iU@UT ,nANASA Ames Research Center, AI Research Branch, Mail Stop: 269-2, U>UT@ Moffett Field, CA 94035, U.S.A. beUU WThis paper describes a simple heuristic approach to solving large-scale constraint satVUUTisfaction and scheduling problems. In this approach one starts with an inconsistent paUUURZassignment for a set of variables and searches through the space of possible repairs. The UUNTgsearch can be guided by a value-ordering heuristic, the min-conflicts heuristic, that attempts UUUT[to minimize the number of constraint violations after each step. The heuristic can be used Cen*UU, [with a variety of different search strategies. We demonstrate empirically that on the b-6UUleWqueens problem, a technique based on this approach performs orders of magnitude better , UBUU⪪Zthan traditional backtracking techniques. We also describe a scheduling application where NUUse]the approach has been used successfully. A theoretical analysis is presented both to explain ZUU p\why this method works well on certain types of problems and to predict when it is likely to UUfUU@n be most effective. ms.`on Introduction nU1UT ŪZOne of the most promising general approaches for solving combinatorial search problems is U/UTŪdto generate an initial, suboptimal solution and then to apply local repair heuristics. TechU-UTYniques based on this approach have met with empirical success on many combinatorial probhU+UTedQlems, including the traveling salesman and graph partitioning problems (Johnson, rU)UTatZPapadimitrou, & Yannakakis, 1988). Such techniques also have a long tradition in AI, most U'UTgnYnotably in problem-solving systems that operate by debugging initial solutions (Simmons, cU%UTap]1988; Sussman, 1975). In this paper, we describe how this idea can be extended to constraint aU#UT@ b2satisfaction problems (CSPs) in a natural manner. U!UT rtVMost of the previous work on CSP algorithms has assumed a constructive backtracking UUTZapproach in which a partial assignment to the variables is incrementally extended. In conUUT c[trast, our method (Minton, Johnston, Philips, & Laird, 1990) creates a complete, but incontio!UUTy [sistent assignment and then repairs constraint violations until a consistent assignment is ave.UUTl ]achieved. The method is guided by a simple ordering heuristic for repairing constraint violan;UUTon_tions: identify a variable that is currently in conflict and select a new value that minimizes alsHUUT@it1the number of outstanding constraint violations. odbyutV'  apV' de hUU`e TMINIMIZING CONFLICTS: A HEURISTIC REPAIR METHOD l V  oV asa UUhkt =29> UTV^UWm paV^UWmme eUTUT`U TZ3N `@ inZ!_<Z!_< Footnote99Zr@ `@ ioZ{_<Z{_<i Single LineentZ'tiFootnoteen ev. ordZD@ `@ trZ_<Z_< Double Linens:Z nt Double LinealuitraiutZ ap Single Linee M ZZ M TableFootnoteZER `@ ZN_<ZN_< TableFootnoteUZAbstract Title   `@`_< Abstract Z0 `@ Z_<Z_<<Abstract  ;F  2times[char[O],id[indexes[1,0,char[n],num[2,"2"]]]]ڄO trڟGvhl u* ~xH  K 5?cross[char[n],char[n]]  2times[char[O],id[indexes[1,0,char[n],num[3,"3"]]]]c ap;ISidV^UWm V^UWmTa`*Why does the GDS Network Perform So Well? UTUT tnWOur analysis of the GDS network was motivated by the following question: Why does the 'URUT\network perform so much better than traditional backtracking methods on certain tasks''? In 4UPUT`particular, we were intrigued by the results on the \-queens problem, since this problem has AUNUTareceived considerable attention from previous researchers. For ]-queens, Adorf and Johnston NULUTtr^found empirically that the network requires a linear number of transitions to converge. Since [UJUT^each transition requires linear time, the expected (empirical) time for the network to find a hUHUT[i_solution is F. To check this behavior, Johnston and Adorf ran experiments with G as high uUFUTH@as 1024,Kat which point memory limitations became a problem. UDUT` Nonsystematic Search Hypothesis UBUT Wh[Initially, we hypothesized that the network's advantage came from the nonsystematic nature waU@UT f`of its search, as compared to the systematic organization inherent in depth-first backtracking. itU>UT m[There are two potential problems associated with systematic depth-first search. First, the sulU<UTen[search space may be organized in such a way that poorer choices are explored first at each m pU:UTs.`branch point. For instance, in the ^-queens problem, depth-first search tends to find a solueqU8UTbe_tion more quickly when the first queen is placed in the center of the first row rather than in he U6UTl)^the corner; apparently this occurs because there are more solutions with the queen in the cenU4UT r`ter than with the queen in the corner. Nevertheless, most naive algorithms tend to start in the tiU2UTemZcorner simply because humans find it more natural to program that way. However, this fact U0UThaZby itself does not explain why nonsystematic search would work so well for _-queens. A  U.UTedWbacktracking program that randomly orders rows (and columns within rows) performs much m-U,UT@teUbetter than the naive method, but still performs poorly relative to the GDS network. :U*UThpaN bU(UThh 9OSolutions Clustered vs. Solutions Evenly Distributed :U&UT brZThe second potential problem with depth-first search is more significant and more subtle. #U$UTfAs illustrated by PFigure1Q, a depth-first search can be a disadvantage when solutions are not ap@'occhar[n]useVUX, qVUX,K(thh  orjThe network, which is programmed in Lisp, requires approximately 11 minutes to solve the 1024 queens probe llem on a TI Explorer II. For larger problems, memory becomes a limiting factor because the network requires atrkeapproximately I space. (Although the number of connections is actually L, some connections are o'@ p*computed dynamically rather than stored). h(Cx v~peڟJ tdc ;LtrV^UWm seV^UWmar0moUTUT m^chooses a variable that is currently in conflict and reassigns its value, until a solution is URUTheXfound. The system thus searches the space of possible assignments, favoring assignments UX!UPUT_with fewer total conflicts. Of course, the hill-climbing system can become stuck'' in a local ich.UNUTLiXmaximum, in the same way that the network may become stuck in a local minimum. In the le;ULUT IWnext section we present empirical evidence to support our claim that the min-conflicts HUJUT@ap6approach can account for the network's effectiveness. UUHUT LYThere are two aspects of the min-conflicts hill-climbing method that distinguish it from CbUFUTv[standard CSP algorithms. First, instead of incrementally constructing a consistent partial oUDUTWassignment, the min-conflicts method repairs a complete but inconsistent assignment by m|UBUT^reducing inconsistencies. Thus, it uses information about the current assignment to guide its U@UTti]search that is not available to a standard backtracking algorithm. Second, the use of a hill-iU>UT@as\climbing strategy rather than a backtracking strategy produces a different style of search. teU<UT k'YExtracting the method from the network enables us to tease apart and experiment with its U:UTmi]different components. In particular, the idea of repairing an inconsistent assignment can be U8UT-c^used with a variety of different search strategies in addition to hill climbing. For example, U6UTe Zwe can backtrack through the space of possible repairs, rather than using a hill-climbing U4UTda]strategy, as follows. Given an initial assignment generated in a preprocessing phase, we can TU2UT_employ the min-conflicts heuristic to order the choice of variables and values to consider, as U0UTonhdescribed in UFigure2V. Initially, the variables are all on a list of VARS-LEFT, and as they are chU.UTabUrepaired, they are pushed onto a list of VARS-DONE. The algorithm attempts to find a s U,UTy ]sequence of repairs, such that no variable is repaired more than once. If there is no way to 'U*UTetZrepair a variable in without violating a previously repaired variable (a variable in VARS %U(UT@en!DONE), the algorithm backtracks. i; nt3Procedure INFORMED-BACKTRACK (VARS-LEFT VARS-DONE) vaF s=If all variables are consistent, then solution found, STOP. 6Qwe8Let VAR = a variable in VARS-LEFT that is in conflict. er\-cRemove VAR from VARS-LEFT. stg. Push VAR onto VARS-DONE. rprILet VALUES = list of possible values for VAR ordered in ascending order i}chGaccording to number of conflicts with variables in VARS-LEFT. cri21For each VALUE in VALUES, until solution found: VheEIf VALUE does not conflict with any variable that is in VARS-DONE, Vrithen Assign VALUE to VAR. UTen0Call INFORMED-BACKTRACK(VARS-LEFT VARS-DONE) orer end if  end for rhoend procedure  v a VBegin program heHLet VARS-LEFT = list of all variables, each assigned an initial value. (E)Let VARS-DONE = nil ss .Call INFORMED-BACKTRACK(VARS-LEFT VARS-DONE)  @L End program ia$U&UThha<TInformed Backtracking Using the Min-Conflicts Heuristic S-UTreafrom the root to a leaf. To select a path, the algorithm starts at the root node and chooses one eU<UT. [of its children with equal probability. This process continues recursively until a leaf is inU:UTveaencountered. If the leaf is a solution the algorithm terminates, if not, it starts over again at eU8UT aXthe root and selects a path. The same path may be examined more than once, since no meminU6UT@90-ory is maintained between successive trials. oU4UT  sXThe Las Vegas algorithm does, in fact, perform better than simple depth-first search on U2UTon]a-queens (Brassard & Bratley, 1988). In fact, this result was already known. However, the aU0UTmaZperformance of the Las Vegas algorithm is still not nearly as good as that of the GDS netU.UTriYwork, and so we concluded that the systematicity hypothesis alone cannot explain the neto U,UT@lework's behavior. >#U*UT`frInformedness Hypothesis se4U(UT lg[Our second hypothesis was that the network's search process uses information about the curualAU&UT p_rent assignment that is not available to a constructive backtracking program's use of an itera a NU$UTitZtive improvement strategy guides the search in a way that is not possible with a standard [U"UTth_backtracking algorithm. We now believe this hypothesis is correct, in that it explains why the ucchU UTU4^network works so well. In particular, the key to the network's performance appears to be that uUUTUT\state transitions are made so as to reduce the number of outstanding inconsistencies in the HoUUTUT_network; specifically, each state transition involves flipping the neuron whose output is most DS UUTainconsistent with its current input. From a constraint satisfaction perspective, it is as if the ,UUTwo\network reassigns a value for a variable by choosing the value that violates the fewest conndUUT@atUTl aare all on a list of VARS-LEFT, and as they are repaired, they are pushed onto a list of tU<UTsi^VARS-DONE. The algorithm attempts to find a sequence of repairs, such that no variable is U:UTrdbrepaired more than once. If there is no way to repair a variable in VARS-LEFT without vioU8UT@ wclating a previously repaired variable (a variable in VARS-DONE), the algorithm backtracks. ist` bExperimental Results fU6UT`st[Section Omitted] `ddA Theoretical Model . $U4UT`[Section Omitted] =`e Discussion PU2UT`he[Section Omitted] i` aAcknowledgments n |U0UT  ZThe authors wish to thank Hans-Martin Tariff, Don Rosenthal, Richard Fernier, Peter CheesU.UTrmXman and Monte Zwieback for their assistance and advice. We also thank Ron Music and our reU,UT tZanonymous reviewers for their comments. The Space Telescope Science Institute is operated U*UT@reGby the Association of Universities for Research in Astronomy for NASA. m a`se'Probability Distributions for N-Queens is U(UT`rd[Appendix Omitted] onc`wa References vaU&UT`-L[Interbred, M. (1973). Cluster analysis for applications. New York: Academic Press. n U$UT  t[Blaming, D., & Hit, E. (1988). 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Information, uncertainty and the utility of categories. ProUDUTnoXceedings of the Seventh Annual Conference of the Cognitive Science Society (pp. 2830.UBUT@$287). Irvine, CA: Lawrence Erlbaum. U@UT YIba, W., & Gennari, J. H. (in press). Learning to recognize movements. In D. Fisher & M. oU>UT).ZPazzani (Eds.), Computational approaches to concept formation. San Mateo, CA: MorU<UT@, gan Kaufmann. U:UT [Michalski, R. S., & Stepp, R. (1983). Learning from observation: Conceptual clustering. In serU8UTŪ\R. S. Michalski, J. G. Carbonell, & T. M. Mitchell (Ends.), Machine learning: An artifiaU6UT@UT@cial intelligence approach. San Mateo, CA: Morgan Kaufmann. H.U4UT`isaQuinlan, J. R. (1986). Induction of decision trees. Machine Learning, 1, 81106. i1U2UT YSchneider, W., Dames, S. T., & Shivering, R. M. (1984). Automatic and control processing a>U0UTca^and attention. In R. Parathormone & D. R. Davies (Ends.), Varieties of attention. San KU.UT@tyDiego, CA: Academic Press. @rl@'UTchar[n]es@'o char[n] mozx UTڟW(E t@'atchar[n]Sank , ڟXUTSt@'. char[n]froJ^ ~ngڟYne@'tcchar[n]s.)p+k ~aڟZciMa@'n char[n] H. z ~R.ڟ[de@' 8char[n]1U2Dun amڟ\, l @'U0char[n]z rmڟ]ds. @'char[n]DiF) ڟ^@'char[n]|j ڟ_@'char[n]>ӂ kڟ`@'char[n]V; JڟaW ڟb! ned[nLeftduRightd Referenced'TitlechdzTitled~ddddddl =D5@=@ . AddressAbstractf>E fch| EnumerateE:\t f?@ k$-6?H@QZ[ncluJ~ڟWCodeBody @@TQ f$Hre     lh z TableTitleT:Table: Body fAHQ 1Heading H:.\t FirstBodyl @B@ AddressAbstract$ fCHQ $ch3HeadingH:..\t FirstBodyfE f CellHeading fFPڟTitleAuthorsode@G Header@H n+> TitleFooter fIP Hea 2Heading*i FirstBody fJP res 1Heading* FirstBodyffK f TableFootnotetyfL Abstract Title@M@ fAuthorsrAddress fN f Reference fOHQ 2Heading H:.\t FirstBody@P HeaderfQ fing Itemizef\tfRDf fotn FirstBodyBody@S t TFooter$ fTP $th 3Heading* FirstBody@U ereFooter fV fFootnote fW f Quotation$ fYHQ $3HeadingH:..\t FirstBody@Zf otntB TitleHeadero @[Fa fFo$H     h  FigureTitleF:Figure: Bodyf] f$Bodyf^ f CellBody f_AQ f HfAppendixA:Appendix .\tBody fe fFootnote fg@ $-6? tlHroQZcl@u~CodeBody$ @hD =< :dy    fh  AbstractAbstract TitleHeading@i  TitleFooter@jf  TitleHeader fkPTitleAuthors fmHQ 1Heading H:.\t FirstBody fpP l 1Heading* FirstBody fqHQ 2Heading H:.\t FirstBody$ @Dt =     h  AbstractAbstract TitleHeadingff f$Bodyf fBody fAQ fHAppendixA:Appendix .\tBody@@ fAuthorsAddressingf fCellBodyf f CellHeading  @Fa ftra$ctitH e    fh  FigureTitleF:Figure: BodyfD f FirstBodyBody f f Reference @TQ f$H  f   h th  TableTitleT:Table: Body f f Quotation1 Emphasis lHe Subscript @  Superscript Bold   figuemail: ff email  stBy f   f Code fCode   Ta  f = =Emphasis fEmphasis flHeSu f f f f f/fBold f0fEmphasis ; Z ZeujeThinfMediumgDoublehThick@i Very Thin eeeeeeeeegHHHHHFormat A efeeeeefHmHfHeHHFormat B-=.-Comment Courier HelveticaTimesRegular RomanMediumBold RegularItalic X59bJ!S `|FV>*4Z%gcbQ=f 3E2<guX"pNg%< W4*cQ: 1 (d4_Vv]W >${>mb+xK|2䖳Cji0~>f^$E2/$,PV5 2H,9B^]/~clR