Unconventional section headings in computing and robotics research articles
New heuristics for packing unequal circles into circular container

New Heuristics for Packing Unequal Circles into a CircularContainer∗WenQi HUANG1,Yu LI2,ChuMin LI2,RuChu XU1(1)College of Computer Science,HuaZhong Univ.of Science and Technology,Wuhan430074,China,email:wqhuang@(2)LaRIA,Universitéde Picardie Jules Verne,33Rue Saint Leu,80039Amiens cedex1,France,email:{yli,cli}@laria.u-picardie.frAbstractWe propose two new heuristics to pack unequal circles into a two dimensional circular con-tainer.Thefirst one,denoted by A1.0,is a basic heurisitc which selects the next circle to placeaccording to the maximal hole degree rule.The second one,denoted by A1.5,uses a self look-ahead strategy to improve A1.0.We evaluate A1.0and A1.5on a series of instances up to100cir-cles from the literature and compare them with existing approaches.We also study the behaviourof our approach for packing equal circles comparing with a specified approach in the literature.Experimental results show that our approach has a good performance in terms of solution qualityand computational time for packing unequal circles.Keywords:circle packing problem;combinatorial optimization;heuristic1IntroductionThe two dimensional(2D)circle packing problem is a famous packing problem[14],encountered in some industries(textile,glass,wood,paper,etc).It consists in placing a set of circles in a container without overlap.The usual objective is to maximize the material utilization and hence to minimize the wasted area.There are various options in the problem,e.g.the container can be circle,rectangle or polygon,the radii of circles to be placed can be equal or unequal.In this paper,we investigate the problem of packing unequal circles into a circular container.The problem is known to be NP-hard[7].Most published research on circle packing focused on packing equal circles into a container[2,3, 5,15].The proposed approaches were heavily influenced by the congruence of the circles.Several authors addressed the problem of packing unequal circles into a rectangular or a strip container.George et al.[4]proposed a set of heuristic rules and different combinations of these rules to pack unequal circles into a rectangle and the best ones were a quasi-random algorithm and a genetic algorithm.Stoyan and Yaskov[16,17]proposed a mathematical model and a solution method basedon a combination of the branch-and-bound algorithm and the reduced gradient method to pack unequal circles into a strip.Hifiand M’Hallah[6]presented a Bottom-Left(BL)based genetic algorithm to solve a dual of circle packing problem:cutting unequal circles on a rectangular plate.But to our knowledge,no significant published research addresses the problem of packing unequal circles into a circular container,except a simulation approach based on an elasticity physics model, proposed by Huang et al.[9,10]and Wang et al.[18].This approach can obtain good enough solutions for packing unequal circles and very good solutions for packing equal circles,but the computational time greatly increases for large instances.In this paper,we propose two new heuristics to solve the problem.A preliminary version of this work appeared in[12,13],and then extended to solve the problem of packing unequal circles into a rectangular container[11].The basic idea of our approach is a quantified measure,called hole degree, to evaluate the benefit of placing a circle in the container,which gives thefirst algorithm,denoted by A1.0.Another feature of our approach is the use of a self look-ahead strategy to improve A1.0and gives the second algorithm,denoted by A1.5.We evaluate our approach on a series of instances up to100circles from the literature[10,12,13,16,17,18,20]and compare it with existing approaches. We also study the behaviour of our approach when it is applied to pack equal circles.Experimental results show that our approach has a good performance in terms of solution quality and computational time for packing unequal circles.The paper is organized as follows.In Section2,we give a formal definition of the circle packing problem.In Section3,we present the two heuristics A1.0and A1.5.In Section4,we present and analyze the experimental results.Section5concludes the paper.2Circle Packing ProblemWe consider the following circle packing optimization problem:given a set of unequal circles,find the minimal radius of a circular container so that all the circles can be packed into the container without overlap.The associated decision problem is formally stated as follows.Given a circular container of radius r0and a set of n circles c1,...,c n of radii r1,...,r n.There may be several circles with the same radius.Let(0,0)be the coordinate of the container center,and (x i,y i)the coordinate of the center of the circle c i,the problem is to determine if there exist2n real numbers x1,y1,...,x n,y n such thatr0−r i−(x i−x j)2+(y i−y j)2−r i−r j≥0,i=j∈{1,...,n}(2)Constraint(1)states that circle c i placed in the container should not extend outside the container, i.e.,the distance from c i to the container,denoted by d i0,should not be negative:d i0=r0−r i−Figure1:Circle packing problemProcedure DichotomousSearch(I, ,A)Beginr0= r i;while(A(I,r0/2)return“success”)dor0=r0/2;r 0=r0/2;repeatif(A(I,(r0+r 0)/2)return“success”)then r0=(r0+r 0)/2;else r 0=(r0+r 0)/2;until r0−r 0< ;r min=r0;End.Figure2:Dichotomous searchConstraint(2)requires that circles placed in the container cannot overlap each other.For such two circles c i et c j,the distance between them,denoted by d ij,should not be negative:d ij=3Algorithms A1.0and A1.5Inspired from human experiences in packing,we propose a quantified measure,called hole degree, to evaluate the benefit of placing a circle in the container.The selection of the next circle to pack is guided by the Maximal Hole Degree(MHD)rule,which gives our basic packing algorithm A1.0.Following the same line,we propose a self look-ahead strategy to improve A1.0,which consists in using A1.0itself to evaluate the benefit of placing a circle in the container,which gives our second packing algorithm A1.5.First,we explain the basic notions,corner placement and hole degree.Then,we present the MHD rule and A1.0,and the self look-ahead strategy and A1.5.3.1Corner placement and hole degreeWe give some preliminaries before presenting the corner placement and the hole degree.Definition(Configuration)A configuration C is a partial pattern(layout)where m≥2circles have been already placed inside the container without overlap,and n−m circles remain to be packed into the container.A configuration is said to be successful if m=n,i.e.,all circles have been placed inside the container without overlap.A configuration is said to be failure if m<n and none of the circles outside the container can be placed into the container to satisfy constraints(1)and(2).Let M be the set of circles already placed in the container.Assume in addition that the container is itself in M.3.1.1Corner placementHuman experiences in packing show that the placements of a circle at some particular positions, like corner regions formed by the container and circles already placed,are worth to be examined to generate a successful configuration[11].The notion corner placement in our approach is inspired from these experiences,which refers to placing a circle at a corner region formed by the container and circles already placed,so that the circle touches at least two circles.Definition(corner placement)Given a configuration C,a corner placement is the placement of a circle c i inside the container,so that c i does not overlap any other circle in M and is tangent at least with two circles in M(note that the two circles are not necessarily tangent each other, and one of them may be the container itself).A corner placement is represented by a triplet p(c i,x,y),meaning that c i is to be placed at position(x,y).Figure3illustrates an instance of7circles,c1,c2,c3,c4,c5,c6and c7,to be placed into a circular container with radius r0,where c2and c4are of the same size,i.e.r2=r4.Note that,(a)Corner placements to put circle c5(b)A successful configuration obtained by A1.0Figure3:An instance of7circles1.Let p(c i,x,y)be a corner placement,the two circles tangent with c i if c i is placed at(x,y)areuniquely determined.Reciprocally,if c i is placed in the container and tangent with two circlesc u and c v,then the center of c i is also uniquely determined.So a corner placement might alsobe denoted by p(c i,c u,c v).2.There may be several corner placements to put a circle in the container.Figure3(a)illustratesfour possible corner placements to put circle c5:p1,p2,p3and p4,where circles c1,c2,c3and c4are already placed in the container(in this order),p1places c5at the position tangent with c1 and the container,p2places c5at the position tangent with c1and c2,p3places c5at the position tangent with c2and c4,p4places c5at the position tangent with c4and the container.3.For circles of the same radius,the corresponding corner placements are identical.For example,the placements to put circles c2and c4are the same.3.1.2Hole degreeHuman experiences also tell us that a good placement may be a region of a good“hole”form so that the wasted area after placing the circle is as small as possible.To evaluate the benefit of a corner placement,we propose a quantified measureλ,called hole degree,to describe how the circle to be placed at a corner placement is close to the nearest circle already inside the container.Definition(Hole degree)Let p(c i,x,y)be a corner placement,c u and c v be the two circles in M and tangent with circle c i if c i is placed at(x,y).The degreeλof the corner placement p(c i,x,y) is defined asd minλ=(1−occupies a complete“hole”,and the wasted area after placing this circle is the minimal.For example, the degreeλof the corner placement putting c3at the position tangent with c1,c2and the container in Figure3(a)is equal to1,since the corresponding d min=0.Figure3(a)also indicates the minimal distance d min of the four corner placements to put circle c5.3.2Maximal Hole Degree(MHD)rule and Algorithm A1.0We use the hole degreeλas the benefit of a corner placement.Intuitively,since one should place a circle as close as possible to the circles already inside the container,a packing procedure should select a corner placement having the maximal hole degree to put the next circle into the container.Definition(MHD rule)By the MHD rule,the corner placement p(c i,x,y)having the maximal hole degreeλis selected to place c i at position(x,y).The MHD rule directly results in our basic packing algorithm A1.0.Given a circle packing instance I,A1.0proceeds as follows.It starts by placing a pair of un-equal circles into the empty container,so that the two circles are tangent each other and also to the container,generating an initial configuration.Under the current configuration,for each circle outside the container,A1.0examines every corner placement by calculating its degree.Among all possible placements,A1.0selects the placement p(c i,x,y)with the maximal degreeλ,and places c i at(x,y).If all circles are placed in the container so that constraints(1)and(2)are satisfied,A1.0stops with success.If a failure configuration is reached,A1.0tries the next pair of circles.If all pairs of circles have been tried but no successful configuration is found,A1.0stops with failure.Figure3(b)illustrates a successful configuration obtained by A1.0to pack seven circles into the container,where circles c1and c2arefirst placed in the container to generate an initial configuration, then c3,c4,c5,c6and c7are successively placed according to the MHD rule.Figure4(a)shows a successful configuration obtained by A1.0for packing26circles into a container(instance NR26-1in Table1).Algorithm A1.0is described in Figure5.Given a configuration C,we always associate to C the list L of all possible corner placements. Note that L is empty for a successful configuration or a failure configuration.After placing circle c i, the list L of corner placements is modified as follows.•Remove all invalid corner placements.A corner placement becomes invalid because the in-volved circle would overlap c i if it was placed;•Re-calculate the degreeλof the remaining corner placements;•If a circle outside the container can be placed inside the container without overlap so that it is tangent with c i and another circle inside the container(including the container),create a new corner placement and put it into L,and compute its degree.Algorithm A1.0was tested on the instances presented in Section4.Experimental results show that A1.0is effective enough to solve some instances.(a)Solution by A1.0,r 0=249.93(b)Solution by A1.5,r 0=249.93Figure 4:Two successful configurations for instances NR26-1obtained by A1.0and A1.5,where the number of each circle is the order to place.The same configurations with the order of circles in Table 1are shown in Figure 8(a),(b).Procedure A1.0(I )Beginfor k :=1to n −1dofor l :=k +1to n dogenerate an initial configuration C using circles k and l ;generate the corner placement list L ;if (A1.0Core(C,L )returns a successful configuration)then stop with success;stop with failure;End.Procedure A1.0Core(C,L )Beginwhile (there are corner placements in L )dofor every corner placement p (c i ,x,y )dobenefit(p (c i ,x,y )):=λ;select the corner placement p (c i ,x,y )with the maximum benefit;modify C by placing c i at (x,y );modify L ;return C ;End.Figure 5:Algorithm A1.0Procedure A1.5(I)Beginfor k:=1to n−1dofor l:=k+1to n dogenerate an initial configuration C using circles k and l;generate the corner placement list L;if(A1.5Core(C,L)returns a successful configuration)then stop with success;stop with failure;End.Procedure A1.5Core(C,L)Beginwhile(there are corner placements in L)dofor(every corner placement p(c i,x,y)dolet C and L be copies of C and L;modify C by placing circle c i at(x,y);modify L ;C =A1.0Core(C ,L );if(C is successful)then return C ;else benefit(p(c i,x,y)):=density(C );select the corner placement p(c i,x,y)with the maximum benefit;modify C by placing circle c i at(x,y);modify L;return C;End.Figure6:Algorithm A1.53.3Self look-ahead strategy and Algorithm A1.5Given a configuration,A1.0only looks at the relation between the circles already inside the container and the circle to be packed.It doesn’t examine the relation between the circles outside the container.In order to more globally evaluate the benefit of a corner placement and to improve A1.0,we propose a self look-ahead strategy which consists in using the result obtained by A1.0(A1.0Core more precisely)to measure the benefit of a corner placement,which gives our second packing algorithmA1.5which is presented below.Given a configuration C,A1.5examines every corner placement using procedure A1.0Core on a copy of C.It places the circle of the examined placement in the container and then applies A1.0Coreto reach afinal configuration.If thefinal configuration is successful,A1.5stops;otherwise,the density of thefinal configuration is used to define the benefit of the examined placement,where theconfiguration density is the ratio of the total surfaces of the circles inside the container to the surfaceof the container.After examining all placements,A1.5takes the corner placement with the maximal benefit to really change the configuration C.Like A1.0,A1.5tries all pairs of unequal circles before stopping with failure.A1.5is described in Figure6.Obviously,A1.5looks further forward and evaluates the benefit of a corner placement by examin-ing the relation between all circles(inside and outside the container).Figure4(b)shows a successful configuration obtained by A1.5to solve NR26-1in Table1.3.4Complexity of A1.0and A1.5The analysis of the real computational time of A1.0and A1.5is difficult,because it not only depends on the number of circles and the container radius,but also the diversity of circle radii,as well as the implementation.Here,we analyze the upper bound of the complexity of A1.0and A1.5in the worse case,i.e.,when they do notfind a successful configuration,and discuss the real computational time to find a successful configuration.3.4.1Upper bound of A1.0’s complexityGiven a configuration C where m circles are already placed in the container and it remains n−m circles outside the container.Let|L|be the number of corner placements in the list L of corner place-ments.After placing a new circle c i into the container,the modification of L is done by removing all invalid corner placements,re-calculating the degreeλfor remaining ones and computing new corner placements.To remove invalid placements,we must check each placement in L to verify if it over-laps the new placed circle c i,which is done in O(|L|).To re-calculate the degreeλfor remaining placements,we must compute the distance between c i and the circles involved in the remaining place-ments,which is done in O(|L|).New corner placements for n−m circles outside the container are generated by using c i and m circles in the current configuration,which is done in O(m(n−m)).So the complexity for placing a circle is O(|L|+m(n−m)).Then the complexity for placing n circles, i.e.,the complexity of A1.0Core,is O(n(|L|+m(n−m)))=O(n|L|+n3).A1.0calls A1.0Core for every pair of circles,its complexity is bounded by O(n3|L|+n5).3.4.2Upper bound of A1.5’s complexityA1.5Core uses a powerful self look-ahead strategy in which the consequences of each possible place-ment in L is evaluated by applying A1.0Core in full,which allows to examine the relation between all circles(inside and outside the container).So,the complexity of A1.5Core for placing a circle is O(|L|(n|L|+n3))=O(n|L|2+n3|L|).The complexity of A1.5Core for placing n circles is bounded by O(n(n|L|2+n3|L|))=O(n2|L|2+n4|L|).A1.5calls A1.5Core for every pair of circles,its com-plexity is bounded by O(n4|L|2+n6|L|).In theory,since every pair(there are m(m−1)/2pairs)of circles(including the container)can give two possible corner placements for n−m circles outside the container,|L|is bounded by O(n3). But in practice,most corner placements are infeasible and the real number of corner placements in L is much smaller than the theoretical upper bound O(n3).In Tables4and5,the rows max(|L|)record the maximal number of placements to be examined for placing a circle by A1.0and A1.5to solve an instance.These numbers vary from32to360for A1.0,and from52to571for A1.5,for solving24 instances of up to60circles in Table4;and from70to750for A1.0,and from135to792for A1.5, for solving6instances of up to100circles in Table5.The real computational time of A1.0and A1.5tofind a successful configuration is still much smaller than the above upper bounds.When a successful configuration is found,A1.0does not con-tinue to try other pairs of circles,nor A1.5to exhaust the search space.In fact,every call to A1.0Corein A1.5Core may lead to a successful configuration and stop the execution.Then,the real computa-tional cost of A1.0and A1.5essentially depends on the real number of corner placements in L and the distribution of successful configurations.4Experimental results and analysisIn this section,we evaluate our approach on a series of instances up to100circles from the literature [10,12,13,16,17,18,20],and compare our approach with the simulation approach proposed by Huang et al.and Wang et al.[9,10,18]in terms of solution quality and running time.We also study the behaviours of our approach when it is applied to pack equal circles.The simulation approach in[9,10,18]is practically a Local Search based on an elasticity physics model,denoted by LS.We briefly present it below:the n circles are considered as elastic disks and squeezed inside the container.Due to elastic forces between the disks,the n disks will move to restore their original shapes.The objective function to minimize is thus defined as the sum of the potential energies of the disks in the system.Such movements continue until the potential energy of the system reaches a local minimum.Then a strategy inspired from human behaviour is used to make the system escape from local minima.A more detailed description of the approach can be found in[10,18,20]. Though LS can obtain enough good solutions for packing unequal circles and very good solutions for packing equal circles,the computational time greatly increases for large instances,as shown by the following experimental results.A1.0,A1.5and LS were all implemented in C language,and executed on a PC with an Athlon XP2000+processor and256Mo of RAM.4.1Test instancesUnequal circle packing instances can be classfied into two categories:irregular instances and regular instances.For an irregular instance,the successful configurations have an irregular form(see Figures 7and8)and the optimal container radius is unknown;while for a regular instance,the successful configurations are of regular form and the optimal container radius can be obtained by geometrical calculation.Regular instances are in general easier to solve than irregular ones[12].We concentrate thus the following discussion on irregular instances.We evaluate our approach on two groups of irregular instances which are intended to represent a large spectrum of the difference between the radii of circles to be placed.Thefirst group includes24 irregular instances from10to60circles listed in Table1.The radii of the circles to be packed are of discrete values and some of them are identical.The column Inst gives the identifier of an instance, the columns n and r i respectively provide the number and the radii of the circles to be placed,and the column r∗0gives the minimal container radii obtained by A1.5.The5instances marked by“*”were used to test LS:NR10-1*,NR11-1*,NR14-1*and NR17-1*used in[10];NR15-2*in[18];NR15-2* and NR17-1*also in[20].The19other instances are taken from a preliminary version of the present work in[12,13].We also use the6irregular instances of20to100circles proposed by Stoyan and Yaskov[16,17], in such a way that we place the cirlces into a circular container instead of a rectangular one.The6instances,denoted by SY1,...,SY6,constitute the second group.The radii of the circles to be packed are random real numbers and all different,available from[19].In addition,we made these instances and their solutions publicly available from[19],including the successful configurations and the corresponding circle center coordinates,hoping to help further study on this problem.4.2Results and analysisWe apply A1.0and A1.5to solve the above instances and analyze the obtained results in terms of solution quality and running time,i.e.the obtained minimal container radius and the running time to get a successful configuration with this minimal container radius.We also evaluate LS in the same way for the comparison purpose.The results obtained by A1.0,A1.5and LS for thefirst group of the instances are reported in Table2and Table4,and for the second group in Table3and Table5.Table2and Table3provide the solution quality results of A1.0,A1.5and LS.The columns r0 give the obtained minimal container radii.The columns density(%)are the corresponding successful configuration densities.We summerize,in the columns gain(%),the density gains made by A1.5over A1.0,A1.5over LS,and A1.0over LS respectively,which are calculated as100×density1−density2Inst r i1099.89 1160.71 1265.30 14113.84 1538.97 1538.85 16143.44 16128.29 1849.25 18197.40 20125.53 20122.21 21148.82 23175.47 24138.38 25190.4726246.7526303.3827222.5830178.6630173.7040357.0050380.00 60522.93 Table1:24irregular instances of thefirst groupInst A1.5r0density(%)r0density(%)gain(%)gain(%)gain(%)NR10-1*99.8981.27961.5879.55560.7981.636 2.810.26-2.62NR12-165.3079.970114.8380.396114.3981.016 1.720.96-0.77NR15-138.9783.13239.1580.90239.0681.275 1.53 1.07-0.46NR16-1143.4484.530129.2679.817129.3579.706 1.50 1.630.14NR17-1*49.2583.486198.8882.512199.6781.860 1.48 2.260.79NR20-1125.5384.022123.5582.708123.6782.547 2.16 2.350.19NR21-1148.8283.694176.6583.092177.8581.974 1.33 2.66 1.35NR24-1138.3886.234192.6881.327192.3381.623 2.28 1.92-0.36NR26-1246.7583.207306.2580.906306.0081.038 1.87 1.71-0.16NR27-1222.5883.961178.9085.217180.9083.3440.27 2.46 2.20NR30-2173.7085.627360.7582.480361.7582.025 2.07 2.610.55NR50-1380.0085.648525.5783.602528.9782.531 1.00 2.27 1.2881.97781.961 1.83 1.830.02Table2:Solution quality results obtained by A1.0,A1.5and LS for thefirst group of instances.For each algorithm,r0indicates the obtained minimal container radius,density(%)the density of the corresponding successful configuration,gain(%)the density gain obtained by one algorithm over another one.Inst n A1.0LS A1.5/A1.0r0density(%)gain(%)gain(%)density(%) SY1307.3082.5647.3282.114 2.456.2783.689 2.200.0081.638SY325 6.4584.242 6.4983.2070.939.0585.106 3.65 1.3081.738SY510013.2085.72213.3883.4310.4514.9486.123 3.39 3.2682.24385.117 2.91 1.5082.161 Table3:Solution quality results obtained by A1.0,A1.5and LS for the second group of instances.For eachalgorithm,r0indicates the obtained minimal container radius,density(%)the density of the corresponding successful configuration,gain(%)is the density gain obtained by one algorithm over another one.Column S.Y.gives the density of a successful configuration obtained by Stoyan and Yaskov’s approach[17,16]to pack these circles into a rectangular container.Inst A1.5r0time(s)time(s)r0time(s)time(s)max(|L|)max(|L|) NR10-1*99.89<161.58<1<160.7948<12836NR12-165.306114.83<13114.39115034050 NR15-138.972539.15<1<139.0652737375NR16-1143.4471129.26<110129.35121385284 NR17-1*49.2530198.88<16199.671080378112 NR20-1125.5339123.55<1<1123.673029280118 NR21-1148.82683176.65<15177.853******** NR24-1138.382339192.68336192.33107761395158 NR26-1246.751019306.255185306.009981557108193 NR27-1222.584436178.906200180.9026219154229 NR30-2173.701078360.751058361.754152314192324 NR50-1380.009717525.571031219528.9774574272360571 Table4:Running time results of A1.0,A1.5and LS for thefirst group of instances.For each algorithm,r0indicates the obtained minimal container radius;time(s)is the running time(in second)tofind a successfulconfiguration under r0.The last two columns max(|L|)give the maximum number of corner placements to be examined for placing a circle by A1.0and A1.5for an instance.Inst n A1.0A1.5LS A1.5A1.0A1.5r0time(s)time(s)r0time(s)time(s)max(|L|)max(|L|) SY1307.30157.3297332126183SY220 6.34<1<1 6.344671<170135SY325 6.45319 6.4916119<1112222SY4359.16429.224749<1156323SY510013.20364261613.38327563710741SY610014.958445601415.20415133750792Table5:Running time results of A1.0,A1.5and LS for the second group of instances.For each algorithm,r0indicates the obtained minimal container radius;time(s)is the running time(in second)tofind a successfulconfiguration under r0.The last two columns max(|L|)give the maximum number of corner placements to be examined for placing a circle by A1.0and A1.5for an instance.(a)Solution for NR50-1,r 0=380.00(b)Solution for NR60-1,r 0=522.93(c)Solution for SY5,r 0=13.17Figure 7:Three successful configurations obtained by A1.5,where the number of circles for NR50-1and NR60-1is theorder in Table 1,and for SY5the order in Stoyan and Yaskov’s files [19]•The running time of A1.0to get a successful configuration under its minimal container radius for an instance is reasonable,but that of A1.5is considerable for large instances.On the one hand,this fact can be explained by the computational complexity analysis in the sub-section 3.4,and on the other hand we can also give some practical analyses as follows:•The real computational time of A1.0and A1.5essentially depends on the number |L|of corner placements for placing a circle and the distribution of successful configurations.|L|is related to the size of the instance and the structure of the instance (radii of the circles).In general,the larger the instance,the more the number of corner placements (see the column max(|L|)in Table 4and 5).Concerning the distribution of successful configurations,when the container radius is not close to the optimal one,there exist many successful configurations,A1.0and A1.5can quickly find such one (see Table 4and 5).However,when the container radius is very close to the optimal one,few successful configurations exist in the search space,A1.0and A1.5may need more time to find a successful configuration in this case.The minimal container radii found by A1.5are guessed to be very close to the optimal values,even though the optimal ones are not known.•Our main objective in this paper is to study the behaviours of the proposed algorithms A1.0and A1.5,so we did not make a big effort to optimize our implementation.The further improvement to the implementation might considerably reduce the real run time of A1.0and A1.5.Figure 7gives three successful configurations for NR50-1,NR60-1and SY5obtained by A1.5with its minimal container radius r 0.Figure 8(a)and (b)give two successful configurations for NR26-1obtained by A1.0and A1.5with r 0=249.93.The corresponding circle center coordiantes for these configurations are available from [19].4.2.2Comparison of A1.0and A1.5with LS We observe that:。
asia uncensored section

Asia Uncensored SectionIntroductionThe Asia Uncensored Section is a platform that aims to promote and share uncensored content from various countries in Asia. With the rapid growth of internet usage and the increasing demand for diverse perspectives and uncensored information, this platform serves as a valuable resource for individuals seeking a deeper understanding and alternative viewpoints on Asian cultures, politics, and social issues.ContentThe Asia Uncensored Section provides a wide range of content, including articles, opinion pieces, and interviews with individuals from different walks of life. The platform covers a diverse range of topics, such as government policies, human rights issues, cultural traditions, environmental challenges, and economic developments. By featuring uncensored content, the platform seeks to provide a fresh and unfiltered perspective on these topics, allowing readers to form their own opinions based on facts and alternative viewpoints.ObjectiveThe main objective of the Asia Uncensored Section is to empower individuals with reliable and uncensored information about Asian countries and their cultures. By providing a platform for voices that are often unheard or suppressed due to political and cultural constraints, the platform promotes freedom of speech and democratizes access to information. It allows readers to gain a more comprehensive understanding of Asian countries beyond the mainstream narratives often presented by media outlets.FeaturesUncensored ArticlesThe Asia Uncensored Section publishes articles written by independent journalists and experts who have firsthand experience and knowledge of the topics they cover. These articles are meticulously researched, ensuring accuracy and reliability. By avoiding censorship and self-censorship, the authors can express their opinions and present alternative perspectives without fear of reprisal or suppression.Opinion PiecesOpinion pieces are a distinctive feature of the Asia Uncensored Section. The platform encourages individuals from various backgrounds to share their thoughts and opinions on various subjects. These pieces provide a platform for constructive discussions and debates, encouraging readers to think critically and form their own perspectives.InterviewsThe Asia Uncensored Section conducts interviews with notable individuals, including activists, artists, academics, and community leaders. These interviews provide readers with unique insights into the personal experiences, struggles, and aspirations of these individuals. By amplifying their voices, the platform aims to inspire and empower readers to take action and make positive changes in their own communities.User-generated ContentThe Asia Uncensored Section also welcomes user-generated content, allowing individuals to share their experiences, stories, and opinions. By providing a space for users to contribute, the platform creates a community where diverse voices are heard and valued.ConclusionThe Asia Uncensored Section is a valuable platform for individuals seeking uncensored information, alternative perspectives, and an understanding of Asian cultures beyond mainstream narratives. Through its uncensored articles, opinion pieces, interviews, and user-generated content, the platform promotes freedom of speech and empowers individuals to form their own informed opinions. By bridging the gap between different cultures and promoting dialogue, the Asia Uncensored Section plays a crucial role in fostering a more inclusive and democratic society.。
美国陪审团的一致裁决原则

美国陪审团的一致裁决原则:历史与当下关键词: 美国,陪审团,一致裁决原则内容提要: 陪审团的一致裁决原则起源于14世纪的英国,作为一项普通法的传统,它在美国确立后经历了一个联邦强制适用与各州选择适用并存这一局面被明确和强化的过程。
虽然饱受质疑,但是从一致裁决原则对陪审团司法工具价值和政治民主价值的发挥及对审判成本控制的影响这三个角度出发综合考虑,其在一定时间内还将继续存在下去。
“你为什么会认为他无罪?”“虽然你们11个都认为他有罪,但我想先和你们好好谈谈,否则我很难说服自己举手认同你们的观点,送这个男孩去死。
”[1]作为美国司法体系的核心组成部分,陪审团制度曾为其赢得了广泛的赞[2]。
陪审团审理案件时,在就相关情况进行充分的“秘密评议”[3]后,无论要做出有罪还是无罪裁决,均需首先在其内部达成一致意见,否则会导致无效审判(mistrial)的出现(此时陪审团相应地被称作“悬置陪审团”(hung ju-ry)—这就是美国陪审团的一致裁决原则[4]。
这项原则起源于英国,作为普通法的传统为美国所接受后,长期以来被视为一项“神圣不可侵犯的”[5]、“统治性的规则”[6],并作为陪审团制度的“基石”[7]、裁决规则的“底线”[8]在美国联邦法院系统和州法院系统被严格遵行。
然而,随着一系列具有争议的陪审团裁决的出现[9],美国民众对陪审团审判“不准确、不公正”的印象日益滋生,对其进行根本性改革的呼声也越来越高[10]。
在这种整体性的不满之中,指向一致裁决原则的自然也占有相当大的比重。
有学者认为这是一个“过时的传统”[11],甚至认为它所带来的危害正是现在陪审团面临的“最严重的问题之一”[12]。
与民众的呼声和学界的议论相伴,在司法实践中,这一原则也已有所松动。
虽然在联邦层面,依然继续严格要求使用一致裁决,但是在各州,情况则发生了变化。
就刑事案件而言,路易斯安那州和俄勒冈州已经在州宪法中明确规定,除死刑案件外,其他案件允许非一致裁决。
不通存 不通兑范英文术语

不通存不通兑范英文术语The term "notional" in English financial terminology refers to a fictitious or theoretical amount of money. It is commonly used in derivatives contracts, such as options and swaps, to determine the value of the contract and to calculate payments between parties.In simple terms, the notional amount is the face value or principal of the contract, which determines the size of the financial obligation or exposure. It does not represent the actual amount of money that is exchanged between the parties but is used as a reference point for pricing and settlement.For example, in an interest rate swap, the notional amount is the principal balance on which the interest payments are calculated. If two parties agree to exchange fixed and floating interest rate payments on a notional amount of $1 million, they are not actually exchanging $1 million, but the contractual payments are based on this theoretical amount.The notional amount is important because it affects the cash flows and risks associated with the contract. For instance, in a currency swap, the notional amount determines the size of the foreign currency payments exchanged between the parties. A larger notional amount would result in larger cash flows and potentially higher risks.It's worth noting that the notional amount is not the same as the market value or the actual exposure of the contract. The market value represents the current worth of the contract, which can fluctuate with changes in market conditions. The notional amount, on the other hand, remains constant throughout the life of the contract, unless there is a specific agreement to change it.The concept of notional amounts is also used in other financial contexts. For example, in insurance contracts, the notional amount is the maximum potential payout or coverage amount. In this case, it represents the hypothetical value of the insured property or the potential liability of the insurer.In conclusion, the term "notional" in English financial terminology refers to a theoretical or fictitious amount of money used as a reference point in derivatives contracts and other financial agreements. It is an important factor in determining the size of financial obligations and exposures. However, it should be distinguished from the actual market value or exposure, which can vary over time.。
不方便鉴合同英语

不方便鉴合同英语In the realm of contract law, the intricacies of language play a pivotal role. The ability to comprehend and interpret the legal jargon in contracts is paramount, especially when dealing with international agreements where English is the lingua franca. The challenge arises when parties to a contract are not equally proficient in English, leading to potential misunderstandings and disputes.Contracts are the backbone of commercial transactions, providing a framework for the rights and obligations of the parties involved. They are legally binding and enforceable by law, which is why clarity and precision in language are essential. When one party is not comfortable with English, it becomes crucial to ensure that the contract is still accessible and understandable to them.The use of plain language in contracts can significantly reduce the risk of misinterpretation. Legal documents traditionally filled with archaic terms and lengthy sentences can be transformed into clear and concise agreements. This approach not only benefits those who are not native English speakers but also streamlines the contract review process for all parties.Moreover, the translation of contracts into other languages is a common practice to accommodate the needs of all signatories. However, translation must be done meticulously to preserve the original intent and meaning of the contract terms. Any discrepancy between the English version and its translation can lead to legal complications.In addition to language barriers, cultural differences can also impact contract negotiations and execution. Legal concepts that are standard in one jurisdiction may be foreign in another. Therefore, it is crucial to have a cross-cultural understanding and to seek legal advice when drafting contracts that cross international borders.Furthermore, the rise of technology has introduced new tools to assist in contract drafting and review. Software solutions can help identify potential issues in contractlanguage and suggest improvements. These tools are particularly beneficial for those who may not have a strong command of English, as they provide an additional layer of scrutiny.In conclusion, the importance of language in contracts cannot be overstated. It is the medium through which legal rights and duties are communicated and understood. For parties not comfortable with English, it is essential to employ strategies such as using plain language, accurate translation, and leveraging technology to ensure that contracts are clear, fair, and enforceable. By doing so, we can foster trust and cooperation in international commerce, paving the way for successful business relationships.This article has explored the significance of language in contracts, particularly for those who are not at ease with English. It has highlighted the need for clarity, the role of translation, the influence of cultural differences, and the support of technology in making contracts accessible to all parties involved. Through these measures, we can achieve a balance between legal formality and practical understanding, ensuring that contracts serve their intended purpose without excluding those who are less familiar with the English language. 。
地域歧视英文介绍作文

地域歧视英文介绍作文Title: Combating Regional Discrimination: Understanding and Addressing a Global Issue。
Regional discrimination is a pervasive societal problem that manifests in various forms across the globe. Definedas prejudice or bias against individuals based on their geographical origin, it undermines social cohesion, perpetuates inequality, and stifles progress. In this essay, we delve into the complexities of regional discrimination, examining its root causes, consequences, and strategies for mitigation.At its core, regional discrimination stems from deep-seated stereotypes, misconceptions, and historical animosities towards specific geographic regions or communities. Whether it manifests as xenophobia towards immigrants from certain countries, prejudice against individuals with regional accents, or unequal treatment based on residential address, its effects are profoundlydamaging. Not only does it hinder individuals'opportunities for advancement and social inclusion, but it also fosters divisiveness and undermines efforts to build diverse and inclusive societies.One of the primary challenges in addressing regional discrimination lies in its subtle and often implicit nature. Unlike overt forms of discrimination, such as racial slursor hate crimes, regional discrimination can be more insidious, manifesting through subtle biases in hiring practices, educational opportunities, or access toessential services. These systemic inequalities perpetuate cycles of disadvantage, trapping individuals in socio-economic marginalization based on their geographic origin.Moreover, regional discrimination intersects with other forms of prejudice, exacerbating its impact on marginalized communities. For example, individuals from historically marginalized regions may face compounded discrimination based on their race, ethnicity, or socio-economic status, further limiting their opportunities for advancement. This intersectionality underscores the need for comprehensiveapproaches to address the root causes of discrimination and promote equity and inclusion for all.To combat regional discrimination effectively, it is essential to adopt a multi-faceted approach that encompasses legislative measures, educational initiatives, and community engagement efforts. Firstly, governments and policymakers must enact laws and policies that explicitly prohibit discrimination based on geographic origin and enforce strict penalties for offenders. Additionally, educational institutions should implement curriculum reforms that promote cultural sensitivity, diversity appreciation, and empathy towards individuals fromdifferent regions.Furthermore, fostering dialogue and understanding between communities is crucial in dismantling stereotypes and fostering mutual respect and solidarity. Initiatives such as intercultural exchanges, community forums, and awareness campaigns can facilitate constructive conversations about the impact of regional discrimination and promote empathy and understanding across diversepopulations. By engaging individuals from all walks of life in these efforts, we can cultivate a culture of inclusivity and respect that transcends geographical boundaries.In conclusion, regional discrimination poses a significant barrier to social cohesion, equality, and human dignity. Addressing this complex issue requires a concerted effort from all sectors of society, including governments, civil society organizations, educational institutions, and individuals. By acknowledging the harmful effects of regional discrimination, challenging stereotypes, and promoting inclusive policies and practices, we can work towards a more just and equitable world where everyone, regardless of their geographic origin, can thrive and contribute to society.。
涉外合同英语争议点

涉外合同英语争议点Dispute Points in International Contracts.International contracts, by their nature, are complex and often fraught with potential disputes. These disputes can arise from a wide range of issues, including but not limited to language barriers, differences in legal systems, cultural misunderstandings, and varying interpretations of contract terms. In this article, we will explore some of the key dispute points that commonly arise in international contracts.1. Language Barriers.One of the most significant dispute points in international contracts is language barriers. When parties to a contract come from different countries, they may use different languages as their primary mode of communication. This can lead to misunderstandings and misinterpretations of contract terms, which can, in turn, lead to disputes.To address this issue, it is crucial for parties to ensure that the contract is drafted in a language that is mutually understood by all parties. If necessary, they should consider using a neutral language such as English, which is widely spoken and understood internationally. Additionally, parties should ensure that any translations of the contract are accurate and complete, to avoid any potential misunderstandings.2. Differences in Legal Systems.Another common dispute point in international contracts arises from differences in legal systems. Each country has its own unique legal system, with its own rules, regulations, and interpretations of the law. This can lead to differences in how contract terms are interpreted and enforced by the courts of different countries.To mitigate this risk, parties should conduct thorough research on the legal systems of the countries involved in the contract. They should also consider including disputeresolution clauses in the contract, such as arbitration clauses or choice of law clauses, which can help to resolve disputes in a more efficient and cost-effective manner.3. Cultural Misunderstandings.Cultural misunderstandings can also be a significant dispute point in international contracts. Differences in culture, values, and business practices can lead to misunderstandings and conflicts between parties. For example, certain cultural norms may consider certain business practices acceptable, while others may consider them unethical or illegal.To avoid these misunderstandings, parties should make an effort to understand the cultures and business practices of the other party involved in the contract. They should also ensure that the contract is drafted in a way that is culturally sensitive and respectful of the other party's values and norms.4. Varying Interpretations of Contract Terms.Finally, varying interpretations of contract terms can also lead to disputes. Different parties may interpret the same contract term differently, depending on their own understanding and interpretation of the law and business practices. This can lead to conflict and disputes over the meaning and intent of the contract.To address this issue, parties should ensure that the contract is drafted in a clear and unambiguous manner. They should also consider including definitions andclarifications of key terms to help avoid any potential misunderstandings. Additionally, parties should strive to negotiate and agree on a common interpretation of the contract terms before signing the contract.In conclusion, international contracts can be complex and fraught with potential disputes. To avoid these disputes, parties should take the necessary steps to ensure that the contract is drafted in a clear, unambiguous, and culturally sensitive manner. They should also conduct thorough research on the legal systems and cultures of thecountries involved in the contract, and strive to negotiate and agree on a common interpretation of the contract terms. By doing so, they can help to minimize the risk of disputes and ensure a successful and beneficial outcome for all parties involved.。
法律英语翻译:涉外公正书

法律英语翻译:涉外公正书和其他法律文书一样,涉外公证书的结构也是有首部、正文和尾部三个部分组成。
第一、公证书首部(标题)的翻译。
( Heading ) 公证书可译作“ Notarization ”或“ NotarialCertificate ”,一般不应做改动。
具体的,比如‘ 毕业公证书’ 、‘ 收养公证书’ 等可以译成‘Notarization of Diploma’ 和‘Notarization of Adoption’ ,也可以就直接译成“ Notarization ”或“ Notarial Certificate ”标题翻译过程中应特别注意以下四个问题:1. 标题字母必须全部大写( Capitalize All Letters ) 或大写标题中每个单词的第一个字母( Capitalize the VeryFirst Letter of Each Word );但2. 标题中的冠词( Articles )及少于5个字母的连词( Conjunctions )、介词( Prepositions )不应大写,除非位于句首;3. 标题中不用引号( Quotation Marks )及句号( Periods );4. 标题要在公证书上方中央位置( Center Top );受公证书类型限制,在公证书标题中一般不会出现象“ Between”这样长的连词或介词。
二、公证书正文的翻译( Body)1. “兹证明”的翻译:我国公证书公证词多以“兹证明…… ”开头,其英文翻译( English Equivalent )应该是:“ This is to certify that… ”2. 公证词翻译应忠实于原文( Conformity )。
- 1、下载文档前请自行甄别文档内容的完整性,平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益,请联系客服反馈,我们会尽快为您处理(人工客服工作时间:9:00-18:30)。
Unconventional section headings in computing and robotics research articlesCarmen Soler MonrealLuz Gil SalomMaría Carbonell OlivaresUniversidad Politécnica de ValenciaAbstractThis paper describes the macro-structure of 28 RAs in computing and robotics through the analysis of section headings and subheadings. Our analysis shows that the IMRD framework is a rhetorical model typically followed by RA writers. But this does not imply that all the RAs have the same organisational characteristics and unified section headings. Authors combine generic and partially generic titles with topic-specific headings, particularly when describing methods and presenting results.Key words: genre analysis, section headings, rhetorical models, research articlemacrostructureIntroductionThe most generally analysed genre of academic writing has been the research article (RA) and much research has been done on its organisational pattern. A number of studies have been devoted to validate and complete the Introduction-Method-Results- Discussion (IMRD) model, either dealing with the overall organisation of RAs from different disciplines and its lexicogrammatical features (Posteguillo, 1999), or focusing on specific RA sections, such as introductions (Swales, 1990; Samraj, 2002), results sections (Brett, 1994), discussions (Hopkins & Dudley-Evans, 1988; Ruiying & Allison, 2003). But there is little research on the connection among the different sections and the importance of the section headings in guiding the reader on the organisation of complete RAs.This paper seeks to describe a set of RAs written in English through the analysis of the terminology employed in the titles of sections and subsections. Our study will show that the standard IMRD model cannot account for all the specific choices regarding organisation and headings of individual RAs. Unconventional section headings and subheadings convey information both on the rhetorical and conceptual levels.MethodIn order to carry out our study, we created a corpus of 28 RAs selected from leading scientific journals in the fields of computing and robotics. The corpus comprises articles written between 2002 and 2003, 13 articles in the specific discipline of computing and 15 texts from journals in the field of robotics. The main reasons for choosing the journals in our corpus were that they are cited in the Science Citation Index (SCI®), they are read by university lecturers and students, and it is in these journals where our lecturers and postgraduate students try to publish their research. In the appendix, a full reference list of the texts analysed is included.Our first task was to extract the macro-organisation of each text. Then we analysed the terminology employed in the section headings and subheadings with reference to the widely accepted IMRD framework. When the titles were explicit about their rhetorical functions, it was easy to establish the correspondence with the IMRD model. But when the titles were content-based, i.e. they related to some aspect of the research topic, the function of a section and subsection was identified by consulting the abstract or the introduction and studying the overall purpose of the RA.Results and discussionSections tell us how the writer sees the structure of his/her text. For this reason, the terminology employed in the title of each section should serve as a guide to the reader through the text.We found that the 28 RAs in our corpus were organised into sections whose number varied from 4 to 12 different sections: 2 RAs presented a 4-section structure; 4 RAs presented a 5-section structure; 11 RAs were organised in 6 sections; 5 RAs had 7 sections; 1 RA had 8 sections; 2 RAs 9 sections, and 3 other RAs had respectively 10, 11 and 12 sections. The conventional section headings in the 4-section RAs reproduce the IMRD structure, although they do not coincide as regards terminology. They share the opening section heading “Introduction”. However, RAS3 presents the next sections with the titles “Materials and Methods”, “Results” and “Discussion”, while AI3 entitles them “Model”, “Results and Discussion” and “Conclusion”. The function of the generic heading “Materials and Methods” in RAS3 is evident and we can consider that “Model” in AI3 is equally clear as to the communicative purpose of the section. This term is not unusual in the field of Artificial Intelligence as improvements of models are often proposed. Moreover, according to the conventional organisational pattern, the “Results” section of a RA is devoted to the exposition of the findings, while the “Discussion” section includes comments on the specific data obtained in the study and the implications for the field. The purpose of sections III and IV in RAS3 is clearly signalled again with the headings “Results” and “Discussion”. The title of the third section of AI3, “Results and Discussion”, indicates that the report of the results will be accompanied with comments. And the closing section, “Conclusion” leads us to infer that it will contain a more general view of the study.But the fact that 26 RAs in our corpus had more than 4 sections revealed that it is customary to find some deviation from the standard division, although it was still possible to identify the underlying IMRD structure.Table 1 indicates that all the 28 RAs in the corpus present either 1 or 2 introductory sections. The most usual first section heading is the conventional term “Introduction”(24 RAs). But, maybe because of the relevance of the information (Bhatia, 1993), 17 RAs add an independent section focusing either on the background or the literature review. Their function coincides with steps 2 and 3 in Move 1 of Swales’s Create a Research Space (CARS) model1 and they appear under generic headings (9 RAs), partially generic headings (2 RAs) and topic-specific headings (4 RAs) (see Table 1).T ABLE 1. Headings for introductory sections-Number of instances1st section headingIntroduction -24Motivation -2Background -1Topic-specific heading -12nd section headingRelated work-2Review of existing methods-1Literature review-1Previous work-1Applications-1Background-1State of the art-1Key technical concept-1Definition of X-1Related X research-1Topic-specific heading-4As Table 2 shows, the 28 RAs in the corpus devote one or more sections to the description of the elements taken into account and the procedures followed in the study. Although 11 RAs dedicate only 1 section to aspects dealing with the materials and methods used in the study, 7 RAs have 2 sections, 7RAs present 3 sections, 2 RA have 4 sections and 1 has 7 sections. 14 RAs entitle the first section using the two generic words “method/s” and “model/s” or partially generic headings in combination with them. 8 RAs employ other partially generic headings and 6 RAs use topic-specific headings. However, the headings used in subsequent sections are mainly partially generic.T ABLE 2. Headings for methods sections-Number of instances1st section headingMethod-1Methods-2Materials and methods-1Model-1Mechanistic models-1Model and notation-1Testbed and experimental task-1A model for X-1X model-5X models-1X process-1X approach-1X revision-1X algorithm-1Arquitecture of X-1Quantification of X-1Evaluating X-1Topic-specific heading-62nd section headingAnalytical evaluation-1Evaluation methodology-1Learning the model-1X model-1X method-2X algorithm-2Equations for X-1Design of X-1Scheduling rules for X-1Quantification of X-1Character of X-1X visualizations of X-1Topic-specific-53rd section headingNumerical method-1Analysis of the method-1Equations of X-1X architecture-1X design-1Procedure of X-1Topic-specific heading-14th section headingTopic-specific heading-15th section headingTopic-specific heading-16th section headingTopic-specific heading-17th section headingTopic-specific heading-1The tendency when exposing results seems to be similar. In our corpus, results appear generally in only one independent section (16 RAs), although we can mention that in IEETRA2 and ACMTCS3 experimental results appear as a subsection of the method/results section. The function of this section is transparent because of generic or partially generic headings containing the words “results” and “experiments”. But, when more than one section is devoted to the exposition of results, authors prefer topic-specific headings (see Table 3).T ABLE 3. Headings for results sections-Number of instances1st section headingResults-3Overall results-1Simulation and results-1Simulation and experimental results-1Experiments-1Experimental results-4Experiments and applications-1Simulation studies-1Physical demonstrations-1Numerical results obtained from X-1X experiments-2Experiment X-1Implementation of X-1Findings from X-1Topic-specific heading-52nd section headingAn example-1Experiment X-1Findings from X-1Topic-specific heading-43rd section headingExperiment X-1Topic-specific heading-2Table 4 reveals that the main functions of the final sections of RAs are either to comment on findings, to come to more generalised conclusions, or to suggest areas of future research. The 28 RAs include 1 final section generally entitled “Discussion/s” (13 RAs) or “Conclusion/s” (7 RAs). Moreover, 11 out of 28 RAs in our corpus have 2 sections with a closing role and 1 RA has 3 sections,which indicates the importance the writer sees they play.Their generic headings reflect the moves and steps that were identified in the discussion section by Swales (1990) and by Ruiying and Allison (2003), indicating a specific-to-general movement. The first moves refer directly to the study and its findings while the following ones focus more generally on the importance of the study in the field and suggest future investigation. According to this, it is easy to understand why the writers of IEEETRA3, CVIUV2 and CVIUV3, have devoted sections 4 (“Discussion”) and 5 (“Conclusion”/“Concluding Remarks”) to deal with the specific-to-general movement convention. Even more clearly, sections 4 (“Discussion”), 5 (“Future work”) and 6 (“Conclusion”) in IJHCS1 deal independently with information conveyed through moves identified for the discussion section.T ABLE 4. Headings for discussion sections-Number of instances1st section headingDiscussion-12Discussions-1General discussion-1Conclusion-4Conclusions-3Discussion and conclusion-1Conclusions and discussions-1Future work-1Discussion and future work-1Conclusion and future work-2Comparison of X-12nd section headingFuture work-1Conclusion-3Conclusions-5Concluding remarks-23rd section headingConclusion-1Only 2 RAs include the discussion in a subsection of the section where findings are presented. However, IJRR3, AI3 and IEEETRA1 combine both results and discussion in the same section using respectively the following generic titles: “Discussion of results”, “Results and discussion” and “Experimental results and discussion”. In all these cases, a closing section is entitled “Conclusion”.Another relevant characteristic present in26 out of the 28 RAs in the corpus is that they incorporate subsections and sub-subsections. Although we found subsections in the introduction (8 RAs) and in the discussion sections (6 RAs), the subsections and even the sub-subsections appear mainly in the method and results sections. In contrast with the section headings, the majority of the titles used for the subsections and sub-subsections are partially generic or topic-specific, thus relating to some aspect of the research. This reflects explicitly not only the rhetoric typical of the genre but also specific contents.Partially generic headings make the reader aware of the current move or step and, at the same time, guide him/her through the research carried out and the concepts and issues dealt with. Headings with words like “problems”, “previous knowledge” or “hypothesis” announce steps within the introduction. “System”, “participants”, “device”, “model”, “apparatus and materials”, “description of models” indicate we are dealing with materials. “Application”, “design”, “procedure”, “analysis”, “practice” make reference to the method. “Performance”, “analysis”, “effect”, “behaviour”, “experiments” are related to results. “Comparison”, “methodological issues”, “guidelines”, “performance”, “perspective”, correspond to the moves for the Discussion section. They are premodified or postmodified by clauses referring to a particular topic of study (for example, “Results for the visual search task” in JHCS1).But it was difficult to identify the standard pattern with topic-specific terminology: although the RAs had introductory and concluding sections, the headings in central sections did not help to understand the writer’s purpose. However,we observed that some cyclicity, repetitive or symmetrical pattern of the terminology and syntactic structure of subheadings in many sections is often helpful for understanding the rhetorical and the contents organisation of the sections. In IJHCS3a MRD pattern is systematically repeated inside 3 sections which explain in detail the procedure, results and comments on 3 different experiments. Here, the coherence is kept by repeating the same generic headings. In ACMTCS3 it is the repetition of the same subheadings in two different sections presenting results that allows coherence. In AI1 subheadings sharing the terms “approximation” and “linear response” contribute to guiding the reader in the presentation of three different approximations dealt with in different sections (“3.1. The mean field approximation–linear response”/ “5.1. The Onsager approximation–linear response”/“6.3. The Bethe approximation–linear response”), while in IEEETRA3 the section on experimental results contains subheadings where lexical opposition points to the design of the experiments carried out (“In vitro experiments of drilling”/“In vivo experiment”). But inner coherence in the subheadings within a section is frequently manifested in the form of lexical variations in postmodifiers of the same noun, as in “Minkowski sum based on CH”/“Minkowski sum based on slope diagram” (CAD1). ConclusionThe IMRD framework is a rhetorical model typically followed by RA writers in computing and robotics. But this does not imply that all the RAs have the same organisational characteristics and conventional section headings. Authors combine generic and partially generic titles with topic-specific headings, particularly in the sections and subsections devoted to describing methods and presenting results. Their purpose when organising information in their RAs seems to be to indicate not only their communicative function but also the key elements in the different RA sections (as pointed out by Anthony, 1999: 38) so as to limit the scope of the research. One explanation to this may be that the reader does not usually read the text thoroughly unless he/she is specially interested in it. A way of helping him/her decide whether the contents of the RA will be of any use to him/her is to indicate clearly what every section is about, not only what its role is. However, a certain cyclical or symmetrical structure is usually kept. A more detailed study of the means of maintaining coherence could be investigated with a larger corpus.ReferencesAnthony, L. (1999). “Writing research article introductions in software engineering: how accurate is a standard model?” IEEE Transactions on Professional Communication 42, 1: 38-46.Bhatia, V.K. (1993). Analysing Genre: Language Use in Professional Settings. London: Longman. Brett, P. (1994). “A genre analysis of the Results section of sociology articles.” English for Specific Purposes 13, 1: 47-59.Hopkins, A. & T. Dudley-Evans (1988). “A genre-based investigation of the discussion sections in articles and dissertations.” English for Specific Purposes 7, 2: 113-122.Posteguillo, S. (1999). “The scientific structure of computer science research articles.” English for Specific Purposes 18, 2: 139-160.Ruiying, Y. & D. Allison (2003). “Research articles in applied linguistics: Moving from results to conclusions.” English for Specific Purposes 22, 4:365-385.Samraj, B. (2002). “Introductions in research articles: variations across disciplines.” English for Specific Purposes 21, 1: 1-17.Swales, J. M. (1990). Genre analysis: English in academic and research settings. Cambridge: Cambridge University Press.AppendixJournals and RAs in ComputingACMTransactions on Computer Systems (ACMTCS)ACMTCS1 “Design and Evaluation of a Conit-Based Continuous Consistency Model for Replicated Services”. Vol. 20 No3 August (2002) 239-282.ACMTCS2 “Run-Time Support for Distributed Sharing in Safe Languages”. Vol. 21 No1 February (2003) 1-35.ACMTCS3 “Lightweight Probabilistic Broadcast”. Vol. 21 No4 November (2003) 341-374.Computer-Aided Design (CAD)CAD1 “Improvements to algorithms for computing the Minkowski sum of 3-polytopes”. Vol. 35 (2003) 1181-1193.CAD2 “A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining”. Vol. 35 (2003) 1249-1259.CAD3 “Mechanistic modelling of the milling process using an adaptive depth buffer”. Vol. 35 (2003) 1287-1303.Computer Vision and Image Understanding (CVIU)CVIU1“Robust parameterized component analysis: theory and applications to 2D facial appearance models”. Vol. 91 (2003) 53-71.CVIU2 “Facial asymmetry quantification for expression invariant human identification”. Vol. 91 (2003) 138-159.CVIU3 “Locating human faces within images”. Vol. 91 (2003) 247-279.International Journal of Human-Computer Studies (IJHCS)IJHCS1 “The effect of spatial layout of and link colour in web pages on performance in a visual search task and an interactive search task”. Vol. 59 (2003) 327-353.IJHCS2 “Internet attitudes and Internet use: some surprising findings from the HomeNetToo project”. Vol. 59 (2003) 355-382.IJHCS3 “Visualizations of binary data: A comparative evaluation”. Vol. 59 (2003) 569-602.Journals and RAs in RoboticsArtificial Intelligence (AI)AI1 “Approximate inference in Boltzmann machines”. Vol. 143 (2003) 19-50.AI2 “Towards an analytic framework for analysing the computation time of evolutionary algorithms”. Vol. 145 (2003) 59-97.AI3 “Object-based visual attention for computer vision”. Vol. 146 (2003) 77-123.AI4 “Dynamic belief revision operators”. Vol. 146 (2003) 193-228.IEEE Transactions on Robotics and Automation (IEEETRA)IEEETRA1 “Visually Guided Landing of an Unmanned Aerial Vehicle”. Vol. 19 No3 June 2003. 371-380.IEEETRA2 “Toward Active Tremor Canceling in Handheld Microsurgical Instruments”. Vol. 19 No5 October 2003. 793-800.IEEETRA3 “Stem Cell Harvesting Device With Passive Flexible Drilling Unit for Bone Marrow Transplantation”. Vol. 19 No5 October 2003. 810-817.International Journal of Robotics Research (IJRR)IJRR1 “Artificial Muscles: Actuators for Biorobotic Systems”. Vol. 21 No4 April 2002. 295-309.IJRR2 “Persistent Passive Hopping and Juggling is Possible Even With Plastic Collisions”. Vol. 21 No7 July 2002. 621-634.IJRR3 “Isotropic Design of Spatial Parallel Manipulators”. Vol. 21 No9 September 2002. 811-824. Robotics and Autonomous Systems (RAS)RAS1 “Real time gait generation for autonomous humanoid robots: A case study for walking”. Vol. 42 (2003) 107-116.RAS2 “A multisine approach for trajectory optimization based on information gain”. Vol. 43 (2003) 231-243.RAS3 “Developing a robot visual system using a biologically inspired model of neuronal development”. Vol. 45 (2003) 111-130.Robotics and Computer Integrated Manufacturing (RCIM)RCIM1 “Implementation of concurrent engineering: A survey in Italy and Belgium”. Vol. 19 (2003) 225-238.RCIM2 “Modeling, scheduling and simulation of product development process by extended stochastic high-level evaluation Petri nets”. Vol. 19 (2003) 329-342.RCIM3 “Algorithmic selection of a disassembly sequence of a component by a wave propagation method”. Vol. 19 (2003) 439-448.Notes1. Move 1. Establishing a TerritoryStep 1: Claiming centrality, and/orStep 2: Making topic generalisation(s), and/orStep 3: Reviewing items of previous research Move 2: Establishing a NicheStep 1A: Counter-claiming, orStep 1B: Indicating a gap, orStep 1C: Question-raising, orStep 1D: Continuing a traditionMove 3: Occupying the NicheStep 1A: Outlining purposes, orStep 1B: Announcing present researchStep 2: Announcing principal findingsStep 3: Indicating RA structure(Swales 1990: 141)。