User Association for Offloading in Heterogeneous Network Based on Matern Cluster Process

User Association for Of floading in Heterogeneous Netw ork Based on Matern Cluster Process Y uxuan Xie ∗ , Xue fei Zhang ∗ , Qimei Cui ∗ and Y anyan Lu ∗ ∗ Ke y Laborato ry of Uni versal W ireless Communication , Ministry of Education Beijing University of Posts and T elecomm unications, Beijing, 1008 7 6, China Email: ∗ { cuiqimei, zhan g xuefei } @bupt.edu.cn Abstract —Future mobile networks are con v erging toward het- eroge neous multi-tier networks, where various classes of base stations (BS) ar e deployed b ased on user demand. So it is quite necessary to ut i lize the BSs resourc es rationally wh en BSs are sufficient. In th is paper , we develop a more realistic model that fully considering the inter-tier depen dence and the depend en ce between users and BS s, where the macro b ase stations (MBSs) are distributed according t o a homogeneous Poisson p oint process (PPP) and the small base stations ( S BSs) fo llows a Matern cluster process (M CP) whose parent point s are located in the positions of the M B Ss in order to offload the users from the over -l oaded MBSs. W e also assume the users are just randomly located in the circles centered at the MBS s. Under this model, we d eriv e the association probability and the a vera ge ergo dic rate by stochastic geometry . A n i nteresting result that the density of MBS and the radius of the clu sters jointly affect the association p robabilities in a joint form is obtained. W e also observ e that using the clu st ered SBSs results in aggr essiv e offloading compar ed with previo us cellular networks. Index T erms —Heterogeneous cellular networks, cell associa- tion, offloading, Matern cluster process, stochastic geometry . I . I N T R O D U C T I O N The fact th at wireless m o bile n etworks are facing explosive data traffics, es pecially video streams, pushes us to find compleme n tary altern ativ es to ease the pr essure of MBSs. Under this backgro u nd, heterogeneous network came into being with the deployment of multiple classes of BSs that differ in terms o f maximum tran smit power , phy sical size, ease-of-d e ployment and cost [1] . Th e deploymen t of multi- class BSs can no t only co m pensate for the coverage lo opho les of th e ma c r oBSs, but also tran sfer the over-load traffic fro m MBSs to o ther low-power BSs, named cellular o ffloading, in order to relie ve the macro BSs’ serv ic e p r essure coming fr om the increasing user demands [2 ] . Fro m the per spectiv e of users in such h eterogen eous network, u ser association play s a piv otal role in cellula r offloading and enhanc in g the lo a d ba la n cing, the spectrum efficiency , and the energy efficiency of networks [3][4] [5]. Recently , many works have been done to analyz e per for- mance metr ics (such as SINR distribution, the coverag e /outage probab ility and a verage ra te) in HetNet using the typical u ser methodo logy in stochastic geo metry [6-10] in comparison with traditional cellu lar network . Further, resear c hers derive the association proba bility in HetNet, a key metric on o ffloading [6], [9] repr esenting the pr obability that a typ ical user is associated with a certain tier . Specifically , literature [1 ], [6], [9] derived d ifferent perf ormanc e metr ics ( e.g., the coverage probab ility , av erage rate) under th eir resp ectiv e system m odel. There are subtle differences a mong these mod els, but they all assume that the locations of BS follow a hom o geneo u s Poisson poin t pro cess(PPP) fo r sing le - tier n etwork, o r m ul- tiple tiers of m utually indepen d ent PPPs for heterog e neous cellular networks (HCNs). In ad diction, in depend ent o f the BSs’ deploymen t, the users distribution also f ollow HPPP . Practically , hum an acti vities are hard ly c o mpletely random and tren d to be clustered. Alth o ugh the assumption of PPP makes the analysis tractab le, it do se not seem rea listic in the case of non-un iform user distributions. And the n etwork operator s trend to deploy the SBSs at where mor e peo ple aggregate ( in order to offload th e p ressure of M BS), we expect tha t the locations of SBSs to be clustered. Several models of cluster pro c ess are d escribed in detail in [8]. Poisson cluster processes (PCP) result from homogen eous independ ent clustering ap plied to a h omog e neous Poisson p r ocess. T he parent po ints f orm a homo geneou s Poisson process wh ile the daug hter points of a rep resentative cluster are random in number and are scattered in depend ently with identical spatial probab ility density aro und the origin. W e further focus o n one of mo r e specific models fo r the representative clu ster, namely Matern cluster pro c esses (MCP). In MCP , the num ber of points in the repr esentative cluster has a Poisson distribution with the mean c . The points of the repr esentativ e cluster are indep endently unifo rmly scattered in th e ba ll where R is the r adius. So the fact that BS d eployment is stro ngly associated with user activities leads to depen dence between MBSs an d SBSs an d dep e n dence between the BSs and the users. In [1 0], it pro poses a HCN model in which the MBSs and the SBSs following a PPP and an independ ent Matern cluster proce ss respectively , aiming at in creasing capacity in hotspots. Altho ugh the mo del consider s the clustering p roperty of SBSs, but do esn’t take th e depen dence between MBSs an d SBSs into con sid eration. L iter ature [1 1] further extends the model by using Poisson cluster pro c ess ( PCP) but PCPs a r e indepen d ent in different tiers witho ut co nsidering intra-tier depend ence. Moreover , nearly all work s assum e that the users are un iformly distributed in the whole region , so they d o no t consider the depen dence be twe e n the users and the BSs either . Thus, the inter-tier d epend e n ce (b e tween MBSs and SBSs) and the dep e ndence between BSs and user s have no t been studied intensively . However , w e kn ow that the original pu rpose of HetNet is to satisfy the non -unifo r m user demand, the two kinds of depende nce above mentioned shouldn’t be neglected. Therefo re, we fo c us on the association and offloading in the two-tier depe n dent HetNet to ease the p ressure of heavily loaded MBSs. The con tribution of this p aper ca n b e sum ma- rized as: 1. A novel a n alytical two-tier HetNet mod el is prop osed where MBSs follow a ho mogen eous PPP and SBSs follow a Matern cluster p r ocess w h ose parent points are exactly the locations of MBS. T he users follow uneven d istribution in the whole study region, but they a re uniform ly distributed in the circles center ed at MBSs. Unde r this model, we derive the association pro bability an d the av erage ergodic rate u sing stochastic ge o metry . Our difficulty lies in the d istribution of desired distance between the clustered SBSs and the typical user con stra int in the union o f the clusters com pared with the previous works. Furth ermore, we obtain some interesting results by exper iment evaluation. 2. On the above basis, we prop ose a cluster in g offloading scheme by deploying SBSs aroun d the he avily load ed MBSs. W e also interestingly discover that th e density of MBS and the ra d ius of the cluster can jointly control th e association probab ilities. I I . S Y S T E M M O D E L The system mode l in this paper con sid e rs u p to a two-tier deployment of th e BSs. The loca tio ns of the first-tier MBSs follow a homog eneous PPP Φ m = { x 1 , x 2 , · · ·} ⊂ R 2 of density λ m , and the locations of the second-tier SBSs follow a Matern cluster p rocess ( MCP) Φ s = { y 1 , y 2 , · · ·} ⊂ R 2 whose parent point process is exactly the first-tier homogen eous PPP Φ m , and the daughter p oints are uniform ly scatter ed on the ball of rad ius R center ed at each parent poin t, assuming that the average numb ers of SBS in each cluster is c , then th e density of the SBSs in the w h ole p lane is λ s = λ m c . Each tier has a d ifferent tran smit power P i , i = m o r s . For the user distribution, the user s in the network ar e assumed to be distributed with density λ u within the circles of radiu s R cente r ed at each location of th e MBSs an d with density λ u ′ outside the circ le s λ u > λ u ′ . But we ju st focu s on the users in th e circles. W ithout loss o f g enerality , we random ly cho o se a typical user lo cated in th e origin. For the notationa l simp licity , we d enote k ∈ { m, s } as the index o f the tier with which a ty pical user associated . Th e downlink desired and interference signals b o th experience p ath loss, and each tier we allow different pa th loss exp o nents { α j } j = m,s , α > 2 , an d Rayleigh fading ch aracterize th e channel fading, i.e., h i,j ∼ e xp(1) . Every BS in the same tier u ses th e same transmit power . W e thus denote X k as the distance between the serving BS and the typical u ser . W e denote { D j } j = m,s as th e distanc e of the typical user from the nearest BS in the j th tier . I n th e scenario, a user is allowed to access any tier’ s BSs b ecause of o pen acce ss. W e con sid e r a ce ll association po licy b ased on ma ximum averaged biased received p ower(ABRP), with B j denoting the associatio n bias correspo n ding to the j th tier . A user will associate with the BS that results in the h ighest biased averaged received signal strength. As the BSs b e longing to the same tier have th e same tran smit power, it means a user will choose its closest MBS or SBS as its serv ing BS. T hen we will use association probab ility to m easure the traffic offloading. Fig. 1. Example of the two-tier HetNet comprising a m ixture of m acro and small BSs: a high-po wer MBS is overlai d with denser and lower po wer SBSs (black dot). The radius of the cluster is R and the black square represent the typica l user . I I I . A N A LY S I S P RO C E S S As mentio ned above, we consider a cell association based on maxim um biased-received-power , where a mobile user is associated with the strong est BS providing th e high est lon g - term averaged biased received power at the user . The ABRP is P r,j = P j ( D j ) − α j B j (1) This is a lon g-term av eraged result and fading is averaged out, so the f ormula ( 1) doesn’t contain fading h . Howe ver , no te that the SINR mo d el of the user associated with a BS in cludes fading a n d it will effect th e distribution fun ction of the SINR. Therefo re th e SI NR of a ty pical user at a random d istance x from the serv ing BS in k th- tier is SINR k ( x ) = P k h k x − α k I + N 0 I = X i = m,s I i = X i = m,s X j ∈ Φ i \ B S k P j h j | Y j i | − α j (2) Where | Y j i | is the distance fro m the BS in tier i to the origin . N 0 is the thermal noise which is usually a co nstant a nd it can be n eglected compared with the ag gregated interference in the interferen ce limited system. A. Distribution of the Desir ed Distan c e When the locatio n o f the typical user is randomly ch osen from the e ntire plane, the CCDF of the desired distance o f an MCP was presen ted in [11] as P[ D s > r ] = exp( − π λ p cr 2 ) (3) The CCDF o f the desired distan c e in a PPP w ith the den sity λ m is given by P[ D m > r ] = exp( − π λ m r 2 ) (4) While in the mod el we prop osed, the location of the ty pical user is ran domly chosen from the un io n regions of the balls of radius R centered at the par ent points of th e MCP . Th erefore , we shou ld calculate the CCDF of the desired distance con di- tioning on the event that the typical user is loc ated within the union r egions of the b alls. First, the pro bability that the typ ical user is in the circles is as following based on Null Prob ability Theorem : P[ D m ≤ R ] = 1 − P[ D m > R ] = 1 − exp( − π λ m R 2 ) (5) And the cond itioned CCDF of the desired distance in the first- tier PPP is P[ D m > r | D m ≤ R ] = P[r < D m ≤ R ] P[ D m ≤ R ] = 1 − exp( − π λ m ( R 2 − r 2 )) 1 − exp( − π λ m R 2 ) (6) The PDF and CDF o f the distance between any two po ints in a circle are [12] f L ( l ) = 2 l R 2 ( 2 π cos − 1 ( l 2 R ) − l π R r 1 − l 2 4 R 2 ) , 0 < l < 2 R F L ( l ) = 1 + 2 π ( l 2 R 2 − 1)co s − 1 ( l 2 R ) − l π R (1 + l 2 2 R 2 ) r 1 − l 2 4 R 2 The near est distance between two points in a circle can b e expressed as L min = min( L 1 , L 2 , · · · , L N − 1 ) Moreover , the CDF of the minim um values of multip le inde- penden t iden tically distributed ra n dom variables is F L min = 1 − [1 − F L ( l )] N − 1 Then takin g the d eriv ati ve of F L min , we can ob tain PDF of L min f L min = ( N − 1)[1 − F L ( l )] N − 2 f L ( l ) (7) In our prop o sed model, there are c + 1 poin ts scattering in a clu ster unifo rmly . So the m apping relation is N = c + 1 , L min = D s , l = r . Therefo re, PDF of the desired distance is d erived as following: f D m ( r ) = d { 1 − P [ D m > r | D m ≤ R ] } d r = 2 π λ m r exp( − π λ m ( R 2 − r 2 )) 1 − exp( − π λ m R 2 ) (8) f D s ( r ) = c 2 r R 2 ( 2 π cos − 1 ( r 2 R ) − r π R q 1 − r 2 4 R 2 ) × [ r π R (1 + r 2 2 R 2 ) q 1 − r 2 4 R 2 − 2 π ( r 2 R 2 − 1)co s − 1 ( r 2 R )] c − 1 (9) B. Association Pr obability Based o n our assumption,ea c h u ser will connect to the BS that provides the hig hest ABRP . Lemma 1. The macr o-tier association pr obability can be expr essed as A m = P n P m ( D m ) − α m B m > P s ( D s ) − α s B s o = E D m [P { P m ( D m ) − α m B m > P s ( D s ) − α s B s } ] = E D m [P { D s > ( P m P s · B m B s ) − 1 α s · ( D m ) α m α s } ] = R R 0 P n D s > ( P m P s · B m B s ) − 1 α s · r α m α s o · f D m ( r ) dr = 2 π λ m 1 − exp( − π λ m R 2 ) × R R 0 r exp {− πλ p c ( P m P s · B m B s ) − 2 α s · r 2 α m α s − π λ m ( R 2 − r 2 ) } d r = 2 π λ m exp( − π λ m R 2 ) 1 − exp( − π λ m R 2 ) × R R 0 r exp {− πλ p c ( P m P s · B m B s ) − 2 α s · r 2 α m α s + π λ m r 2 ) } d r (10) A s = P  P s ( D s ) − α s B s > P m ( D m ) − α m B m  = Z 2R 0 P  D m > ( P s P m · B s B m ) − 1 α m · r α s α m  · f D s ( r ) dr = c Z 2 R 0 exp {− π λ m ( P s P m · B s B m ) − 2 α m · r 2 α s α m }× [ r π R (1 + r 2 2 R 2 ) r 1 − r 2 4 R 2 − 2 π ( r 2 R 2 − 1)cos − 1 ( r 2 R )] c − 1 × 2 r R 2 ( 2 π cos − 1 ( r 2 R ) − r π R r 1 − r 2 4 R 2 ) dr (11) If { α m , α s } = α , the association pr obability o f ma cr o-tier and smallBS-tier is simplified to A m = { 1 − exp[ − π λ m R 2 ( c ( P m P s · B m B s ) − 2 α − 1)] } · exp( − π λ m R 2 ) [ c ( P m P s · B m B s ) − 2 α − 1] · [1 − exp( − π λ m R 2 )] (12) A s = c R 2 R 0 exp {− π λ m ( P s P m · B s B m ) − 2 α · r 2 } × [ r πR (1 + r 2 2 R 2 ) q 1 − r 2 4 R 2 − 2 π ( r 2 R 2 − 1)cos − 1 ( r 2 R )] c − 1 × 2 r R 2 ( 2 π cos − 1 ( r 2 R ) − r πR q 1 − r 2 4 R 2 ) dr (13) From Lemma 1, we obser ve that the den sity of the MBSs λ m (also th e den sity of the par ent point pr ocess λ p due to the loc ation coinc idence of the MBSs and the parent po ints of the MCP ) an d the radius of the clu ster R alw ays ap pear in the same for m of λ m R 2 . No matter how λ m or R varies, if the value of λ m maintain constant, A m remains unchang ed as far as the typical user co n cerned . In the section o f nu m erical results, we will d iscuss the specific relationship of th ese parameters. W e f urther observe th at th e BS d ensity is more dominan t in de ter mining A k than BS tr ansmit power or b ias factor(when α > 2 ). The association p r obability of each tier is a very usefu l index in analyzing the network perfo rmance. It can dir e ctly represent the pe r centage of the users served by cer ta in tier from the total users. So the average n umber of users associated with a BS in the k th tier is g i ven a s N k = A k λ u λ k , k = m, s (14) Lemma 2. The P DF of th e distan ce X k between a typ ical user and its serving BS is f X m ( x ) = 2 π λ m exp( − π λ m R 2 ) A m (1 − exp( − π λ m R 2 )) x × exp {− π λ p c ( P m P s · B m B s ) − 2 α s · x 2 α m α s + π λ m x 2 } (15) f X s ( x ) = c A s exp {− π λ m ( P s P m · B s B m ) − 2 α m · x 2 α s α m }× [ x π R (1 + x 2 2 R 2 ) r 1 − x 2 4 R 2 − 2 π ( x 2 R 2 − 1)cos − 1 ( x 2 R )] c − 1 × 2 x R 2 ( 2 π cos − 1 ( x 2 R ) − x π R r 1 − x 2 4 R 2 ) (16) Pr o of: W e utilize the similar pr ocedur e of der i vation as the Lemma 3 in [9 ], an d the difference b etween the two der ivation proced u res is the in tegral up per limits. Our integral upper limits ar e R and 2 R corre sp onding to the m acro-tier an d smallcell-tier r espectiv ely , while in [9] it is po siti ve infinity . So the fo rmulas also present similar form. C. A vera ge Er godic R ate W e d erive the av erage ergodic r ate of a ty p ical ran domly located user, and it is given as [13][1 4 ] ℜ = X k A k ℜ k , k = m, s (17) W e d enote ℜ k as the av erage ergodic rate of a typical user associated with the k th- tier , A k is the association pr obability of the k th-tier wh ich is deriv ed in Lemma 1. And we ign ore th e thermal noise in th e SINR mod el in the following deriv ation. Theorem 1 . The average ergodic rates of overall network is ℜ = 2 π λ m exp( − π λ m R 2 ) (1 − exp( − πλ m R 2 )) × Z R 0 Z ∞ 0 x · exp {− π ( X j = m,s x 2 / ˆ α j C j ( t ) + λ s ( ˆ P s ˆ B s ) 2 /α s x 2 / ˆ α s − λ m x 2 } dtdx + c Z 2 R 0 Z ∞ 0 exp {− π ( X j = m,s x 2 / ˆ α j C j ( t ) + λ m ( ˆ P m ˆ B m ) 2 /α m x 2 / ˆ α m ) } × [ x π R (1 + x 2 2 R 2 ) q 1 − x 2 4 R 2 − 2 π ( x 2 R 2 − 1)cos − 1 ( x 2 R )] c − 1 × 2 x R 2 ( 2 π cos − 1 ( x 2 R ) − x π R q 1 − x 2 4 R 2 ) dtdx (18) where λ s = λ p c, λ p = λ m and C j ( t ) = λ j ˆ P 2 /α j j ( ˆ B 2 /α j j + Z ( e t − 1 , α j , ˆ B j )) (19) Pr o of: the average ergodic rate of the macro -tier is ℜ m = E x [ E S I N R m [ln(1 + S I N R m ( x ))]] = Z R 0 E S I N R m [ln(1 + S I N R m ( x ))] · f X m ( x )d x = Z R 0 Z ∞ 0 P[ln(1 + S I N R m ( x )) > t ]d t · f X m ( x )d x = Z R 0 Z ∞ 0 P[ h m > ( e t − 1) · I P m − 1 x α m ]d t · f X m ( x )d x = Z R 0 Z ∞ 0 L I m (( e t − 1) P m − 1 x α m ) · L I s (( e t − 1) P m − 1 x α m )d t · f X m ( x )d x (20) W ith the similar me thod, we can o btain the as ℜ s = Z 2 R 0 Z ∞ 0 L I m (( e t − 1) P s − 1 x α s ) · L I s (( e t − 1) P s − 1 x α s )d t · f X s ( x )d x (21) Where L I i ( z ) is the laplace transfor m of I i . For clarity of exposition, we define ˆ P i = P i P k , ˆ α i = α i α k , ˆ B i = B i B k (22) Which re sp ectiv ely repre sen t transmit power ratio, path lo ss exponent ratio and b ias ratio of intererin g BS to th e serving BS. And the laplace transfor m is L I i (( e t − 1) P k − 1 x α k ) = exp {− π λ i ˆ P 2 /α i i x 2 / ˆ α i Z ( e t − 1 , α i , ˆ B i ) } (23) with Z ( e t − 1 , α i , ˆ B i ) = ( e t − 1) 2 α i Z ∞ ( ˆ B i / ( e t − 1)) 2 /α i 1 1 + u α i / 2 du (24) Plugging (2 3) in to ( 20) an d (2 1), we obtain the average ergodic rate o f ea ch tier . Furth ermore, plu gging( 10)(1 1)(20) and (21) into (17) , we achieve the a verage ergodic r ate of entire network. I V . N U M E R I C A L R E S U LT S A N D D I S C U S S I O N In Fig. 2 , we obtain the average ergodic rate usin g Mo nte Carlo simulations for comparing the two-tier PPPs and o ur propo sed hybr id mo del ( PPP+MCP). Our simulatio n pa r am- eters are as follows : ( P m , P s ) = (53 , 33 ) dBm, α = 4 , B m /B s = 1 , λ m = 1 / ( π 5 00 2 ) . It shows the average ergodic rate versus the intensities of SBS λ s . The blu e line and red line are the av erage ergo dic rate of PPPs and our propo sed model, respectiv ely . From the numerical r esults f rom the observations that for M CP , a large n umber of dau g hter nodes within each cluster achieve a h igher ergodic rate than PPP because of th e non -unifo rm distribution o f users. In Fig. 3, we explore the re latio n betwee n a ssocia tio n probab ility and b ias ratio wh ere the inc r easing ratio means SBS Density 4 6 8 10 12 14 16 18 20 Average Ergodic Rate[nats/sec/Hz] 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 PPP+PPP PPP+MCP Fig. 2. A verage ergodic rate compari- son for va rying SBS density B1/B2 5 10 15 20 25 30 35 40 45 50 Association probability 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 Macro-tier Smallcell-tier Fig. 3. E ff ect of association bias ratio on associatio n probabili ty Radius 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Association probability with macro-tier 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 LamdaMBS=1/(2*pi*500 2 ) LamdaMBS=1/(pi*500 2 ) LamdaMBS=2/(pi*500 2 ) Fig. 4. E f fect of radius of cluster on MBS associatio n probabili ty Radius 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Association probability with smallcell-tier 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LamdaMBS=1/(2*pi*500 2 ) LamdaMBS=1/(pi*500 2 ) LamdaMBS=2/(pi*500 2 ) Fig. 5. E f fect of radius of cluster on SBS association probabilit y the power a m plification of MBS is larger than tha t of SBS. Higher bias r atio leads to the co nsequenc e tha t more user ar e offloaded from SBS to MBS. W e can flexibly con trol the load of e ach tier by tun e the b iases. From the above figur e, we also can see th e association prob a b ility with SBS-tier is much higher than that with macro- tier . Th is means the typical user is mor e likely to conn ect to a SBS instead of a MBS, i.e., the users can b e o ffloaded fr om MBSs to SBSs. In Fig. 4 and Fig. 5, we can see that when the de nsity of M BS is fixed, th e association p r obabilities incr ease with increasing r adius of clusters. This is because the SBSs and the u ser s ar e distributed un iformly thro ugho u t the entire plane with the increasing r a dius. Whe n the radiu s incre a ses to a certain value, the u ser s can ach iev e an equivalent u niform distribution, and the association pr obabilities will be constant. Moreover , they also show that the association prob a bilities under larger de nsity reach a stable value at a faster speed , which validates th e formu la (12 ) in which the den sity o f the MBS and the ra d ius R always occur in the integrated fo rm of λ m R 2 . V . C O N C L U S I O N In this paper, we p resented a model considering both the inter-tier and u ser-BS depend ence to analy ze the ef fects o f offloading in HetNet. The association prob abilities and average ergodic rate were deriv ed. A n interesting result that the d ensity of MBS an d the radius of the clusters jointly affect the associa- tion p robab ilities is obtained . Simulation a n d n umerical results showed that the pro posed mo d el can aggressively offload the mobile users fro m MBSs by bias adjustment. V I . A C K N O W L E D G E M E N T The work was supp orted b y Nationa l Natur e Scienc e Foun- dation of China Project (Grant No. 6147 1058 ) , Hong Kong, Macao and T aiw an Science and T ech nology Coo peration Projects (2014D FT 1 0320 2016YFE0122900), the 111 Project of China (B1600 6) and Beijing Training Pr o ject f or The Leading T alents in S&T (No. Z141 1010 01514 026). 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