sadat2307/MSciNLI huggingface dataset:
Domain: Networks
Sentence 1: i=1 ri) k min i=1 ri 15 d when n =16 d =5 d =9 d =13 d =17 10 BCCC 512 262144 6 × 166 8 × 168 SW C ube 5000 52488 165888 524288 Diameter 5 order, di.erent networks accommodate di.erent numbers of servers.
Sentence 2: again we use the average bandwidth allocated to each server for a fair comparison.
Relationship: reasoning
Domain: Networks
Sentence 1: Within a pair, the following effect is important to understand.
Sentence 2: assume that the probe and its pacesetter are back-to-back and that the latter has just arrived at an empty queue on hop h. Be- cause of the store and forward router behaviour, the probe will not enter the queue until after an interval x i h-1 controUed by the previous hop, whereas the pacesetter will leave the queue af- ter a time zi h controlled by hop h. as pointed out in [1], the ability of the pacesetter to guarantee that the probe queues behind it is bounded by the ratio of the probe and pacesetter ser- vice times, which depends on the ratio of the link rates.
Relationship: reasoning
Domain: Networks
Sentence 1: 5.3.1 Lowest Mobility (mobility pause = 800 seconds) Pause Time = 800 seconds By setting the pause period to 800 seconds, the packet loss in the 0.055  steady network was only due to channel error and network congestion, 0.05 not mobility.
Sentence 2: since AODV+SBA distributes routes and traffic overall network, we expected that AODV+SBA would offer the best delay and throughput.
Relationship: reasoning
Domain: Networks
Sentence 1: The reaction time of the driver treact is the time interval between the instant of hazard recognition and the instant of actually applying the brakes.
Sentence 2: a complete stopping distance is given as:  dstop = dbrake + dreact (3) In kinematics the distance traveled while performing a braking maneuver according to equations of uniformly ac­celerated motion is given as: 2 v 0 dbrake = (4) 2 × µ × g where v0 is the vehicle speed in m/s; µ is the coe.cient of friction between the tires of the vehicle and the roadway; g is the acceleration due to gravity of the Earth in m/s2 .
Relationship: reasoning
Domain: Networks
Sentence 1: Inthislight, condition(D) can be read as: for any type i, the arrival rate of corresponding clients, .i,isstrictlylessthanthetotal arrivalrateofservers that can serve such clients, that is j=i .j.
Sentence 2: formally, condition (D) is related to the classical stability condition of single server queues, which reads .< 1, where the load .
Relationship: reasoning
Domain: Networks
Sentence 1: As far as synthetic trace-based approaches are concerned, sem­inal studies have focused on the impact of microscopic mobilitymodels that describe the acceleration or deceleration behavior of each car with respect to the surrounding driving conditions [14,15].These works unveiled the high bias that unrealistic random andpseudo-random driver behaviors can induce on the network topol­ogy, and the importance of properly modeling road signalization.However, they did not consider the impact of macroscopic traf.cparameters, such as the vehicular density, the arrival rates and theroutes traveled by drivers.
Sentence 2: later works focused on the macroscopic dimension,built on top of validated microscopic mobility models.
Relationship: reasoning
Domain: Networks
Sentence 1: In this case, it is desirable to discard a min­imal number of .ows while satisfying the deadline of the remaining .ows.
Sentence 2: unfortunately, minimizing the number of tardy .ows in a dynamic setting is an NP-complete prob­lem.2 we use a simple heuristic, called Early Termi­nation, to terminate a .ow when it cannot meet its deadline.
Relationship: reasoning
Domain: Networks
Sentence 1: To defend against this attack, a community node (e.g., X in this example) should perform a secure neighbor detection right after its .ag is set to 1.
Sentence 2: in the exchanged messages, the node must tell each of its neighbor that it just heard RREP C.B and B s ACK to C. since RREP C.B is authenticated by C (according to network security assumption) and unforgeable, this effectively triggers Y s execution of Algorithm B. Packet modi.cation attacks CBS adds one upstream .eld in RREQ and one hop count .eld in RREP.
Relationship: reasoning
Domain: Networks
Sentence 1: This can be true for a number of reasons: for instance, not all DCs may provide the speci.c kind of hyper­visor or computing/storage resources required by the given VM; or maybe the speci.c kind of services provided by the VM has some latency requirement that cannot be satis.ed if they are migrated to a DC located too far from their .nal users; also, not all DCs in a cloud federation are equivalent in terms of energy savings or maintenance schedules; last but not least, load balancing reasons may force to choose some DCs instead of others.
Sentence 2: this model assumes that the request of migrat­ing a given VM z can be satis.ed by m(z) computing re­sources, which are available in a subset of the n + 1 DCs that constitute the cloud federation.
Relationship: reasoning
Domain: Networks
Sentence 1: If x¯i is true, the power value of Si,2 is 1; otherwise, the power value of Si,2 is 2.
Sentence 2: in addition, there is a node Xi which will be used to determine whether either xi is true or x¯i is true, and the transmission power of Xi is zero, 1 = i = n. (3) For each 3-CNF Cj = yj,1 .yj,2 .yj,3,there is a corresponding node SCj with a transmission power 0, 1 = j = m. the node set N = {S0,0}.
Relationship: reasoning
Domain: Networks
Sentence 1: The delay in wired communication is common without depending on any packet distribution in wireless access network because the wired communica­tion is out of scope of wireless access network.
Sentence 2: the delay in wired communication can be assumed to be constant to any packet distribution in wireless access net­  2.5 4x107 FTP file size 350 Kbytes session interval 10 sec FTP file size 350 Kbytes session interval 10 sec FTP file size 350 Kbytes session interval 10 sec 8x106 2 VC video rate 32 Kbps frame rate 10 fps VC video rate 32 Kbps frame rate 10 fps  VC video rate 32 Kbps frame rate 10 fps 7x106 3.5x107 Proposal 6x106 RR SL TR 5x106 3x107 4x106 IP Average Delay (sec/packet) IP Throughput (bps) IP Out-of-Order Packets (bps) 11a Load (bps) 3x106 2.5x107 Proposal RR Proposal RR SL SL 2x106 TR TR 1x106 300 400 500 600 700 800 900 1000 300 400 500 600 700 800 900 1000 300 400 500 600 700 800 900 1000 0 2x107 Simulation Time (sec) Simulation Time (sec) Simulation Time (sec) Figure 7: IP average delay.
Relationship: reasoning
Domain: Networks
Sentence 1: For instance, a DAG could have paths for CCN [10] and a source route over IP addresses, with edges permitting intermediate routers to pick either means of reaching the data.
Sentence 2: xIA s main approach to partial deployment (which is a key step in enabling evolution) is to allow transitions between architectures at network elements that understand both (i.e., an element that understands CCN and source­routed IP could take a request sent on one architecture and pass it to the other).
Relationship: reasoning
Domain: Networks
Sentence 1: Gn,p)= P(ej (i)) j=1 for the independent core Gn,p, implying rki () EN(Q,Gn,p)= P(ej (i)).
Sentence 2: i=1 j=1 by making a term by term comparison using (2), we obtain ()() EN(Q,G.,f )= EN(Q,Gn,p), completing the proof.
Relationship: reasoning
Domain: Networks
Sentence 1: By induction, we can assume the bound holds for r(ßPk,ß), yielding k r(ßPk+1,ß) = r(ßPk+1,ßPk)+ r(aPi,ai).
Sentence 2: i=1 to prove the bound for k+ 1,weneedtoshow r(ßPk+1,ßPk) = r(aPk+1,ak+1).
Relationship: reasoning
Domain: Networks
Sentence 1: Then user i s utility function can be described as the di.erence of its achievable rate and payment for () gi band wi: ui(p, wi)= wi log - pwi, which im­ wi plies that the optimal spectrum demand is achieved * as w (p) = arg maxwi =0 ui(p, wi)= gi exp(-(1 + p)).
Sentence 2: i n * the total users demand is(p)= i=1 wi n G exp(-(1 + p)), where G =This optimal i=1 gi.
Relationship: reasoning
Domain: Networks
Sentence 1: (3) In all other cases where t moves tThe FPi t i t i t it i is updated, the FPin LPLPin LPis implicitly At thetimewhen LPto from one square to another in ( * LP t i +2)8, we replace the old with a temporary forwarding pointer to the new Li rent lookup request as when a LP tthe FPi could cause similar racing conditions with a concur­ t i +1 instead of removing the and update FP t i is removed.
Sentence 2: lP * , which is located in LP+1t i .
Relationship: reasoning
Domain: Networks
Sentence 1: Number of APs required: In general, if there are N clients in the network, then BBN needs to align (N - 1) packets at the .rst AP, (N - 2) packets at the second AP and so on.
Sentence 2: a total of at least (N -1)+(N -2)+· · ·+2 = N2-N-2 2 variables are required to satisfy all the constraints.
Relationship: reasoning
Domain: Networks
Sentence 1: Assuming symmetric RF channels, this also acts as a probe to provide the client s SNR to the AP.
Sentence 2: it is simple for the AP to choose the client with the best SNR and send  Table 1: Rate coupling functions (k vehicles) rateC ouple (r1,r2,...,rk) User Rate System Rate 802.11 1 k X j=1 1 rj k ×U ser Rate Time Fairness MV-MAX 8 >  : ru 0 ru k if ru = max(r1,...,rk) otherwise 1 k k X j=1 rj max(r1,...,rk) it an ACK, denying access to all other clients.
Relationship: reasoning
Domain: Networks
Sentence 1: e ` X ´ We calculate E e next as follows: X' E e X = E e nsl !
Sentence 2: x kl-kk = kp (1 - p)nse nsl i=0 =(1+(e - 1)p)nsl (1 + (e - 1)p)nsl P(X = W max(., 1)) = eW max(.,1) (1) nsl(e-1)p e = 2 W max(.,1) e (e-1).
Relationship: reasoning
Domain: Networks
Sentence 1: This eliminates the need for RtSolPr/PrRtAdv messages which in turn reduces the long anticipation time imposed by FMIPv6 by reducing signalling overheads.
Sentence 2: when our proposed mechanism is applied to FMIPv6, it can increase the probability predictive mode of operation and also reduces overall (both L2 and L3) handover latency.
Relationship: reasoning
Domain: Networks
Sentence 1: Note that if we randomly se­lect one of the landmarks as target s location estimate, the mean error obtained is 7.62 miles for Comcast network and 8.76 miles for Verizon network.
Sentence 2: existing techniques perform worse than random selection , while PBG geolo­cates the target to within 2 - 4 miles of its actual location.
Relationship: reasoning
Domain: Networks
Sentence 1: Since the server part of the speci.cation is relatively simple it mostly de.nes reply codes and implementation­speci.c responsestrings ,weopted to useandcomplement only the FTP speci.cation related to the messages trans­mitted by the clients.
Sentence 2: all automata and network traces concern the client-side of the protocol speci.cation.
Relationship: reasoning
Domain: Networks
Sentence 1: Even though it is ef.cient to detect whethera looped walk contains a cross-link using a CLDP probe, itcan be more costly to determine whether this looped walkwas caused by a cross-link or a destination not in the graph,as the example in Figure 13 illustrates.
Sentence 2: lCR is not ef.cient for data centric storage, butdoes provide highly scalable, low overhead any-to-any rout­ing.
Relationship: reasoning
Domain: Networks
Sentence 1: For example, if we consider the connectivity degree coupled with a hop-count as the indicator of a node s location, then sojourn time is defined as the span of time in which this aggregated metric of location is maintained.
Sentence 2: to ground sojourn time to an anchor, we define it as  Definition 3: Sojourn time of a transient node nT is the duration in which it resides in the vicinity of the current governing arbitrator.
Relationship: reasoning
Domain: Networks
Sentence 1: slots is uniformly chosen in the range [0, C Wmin 2i - 1] after the station has failed transmission for i times.
Sentence 2: accumulatively, the station will wait j i CWmin 2-1 for total oftime slots on average from the j=0 2 time a packet is ready for transmission to the time of the successful transmission of its .rst bit, at the (i + 1)th at­tempt.
Relationship: reasoning
Domain: Networks
Sentence 1: It appears that the nature of the system is such, that, independently of our initial guess, the iteration converges in a few steps (depending on the param­eters of the system after 2 to 5 iteration steps), a fact that makes the method computationally e.cient.
Sentence 2: knowing the transition probabilities pcc,psc, we evaluate, from (14), the value of p ., and substituting it to (13), we .nally obtain the conditional collision probability p.  4.
Relationship: reasoning
Domain: Networks
Sentence 1: The kth area of the concentric circular band is 2 )2 × (k × d ) - × ((k -1) × d .
Sentence 2: the expected total min min kth number of candidate proxy forwarders in the CBB with regard to the wedge with angle ia is ( )( 2 min )/ 2( dki ××××× a.
Relationship: reasoning
Domain: Networks
Sentence 1: However, in SCADA interconnected by computers/communication elements with or without Internet access, it is possible that intruders can induce attacks that would not have been considered by the system designer.
Sentence 2: the major challenge for SCADA security lies in arriving at methods of control of the plant that shall overcome such plausible attacks and maintain the stability and the trustworthiness of the system  thus, making the system robust.
Relationship: reasoning
Domain: Networks
Sentence 1: These selection rules except rule (1) must be implemented in all border routers as the standard and should not be changed in designing the routing control architecture.
Sentence 2: the VR architecture that modi.es local pref and next hop at­tributes can control the forwarding addresses of the next hop in the path to the destination, and therefore can control conventional routers externally without any protocol exten­sions.
Relationship: reasoning
Domain: Networks
Sentence 1: Recall that we have derived the spanning angle of G, denoted by a,in Equation4.
Sentence 2: based on Equation 3, we know that the node stores one key for each cell in G with a probability of d .the R number of veri.able cell keys stored by the node is propor­tional to the number of cells within G. That is, [28] S. Zhu, S. Setia, S. Jajodia, and P. Ning.
Relationship: reasoning
Domain: Networks
Sentence 1: T do if u = s then transmit message j at time 3(j - 1)k +1 else after receiving message j,delay transmission of j by delay(u) time units return all transmit times Figure 4: Single Source Multiple Message (SSMM) with each other.
Sentence 2: it su.ces to separate two di.er­ent messages by three levels in order to allow simultaneous collision-free transmissions of these messages.
Relationship: reasoning
Domain: Networks
Sentence 1: t-1Pi(r) = 1,i=1,...,K (18)  ri-1ri -1 <1,i=1,...,K  rK = D. An examination of (18) reveals that its objective function is a monomial , the inequality constraints are signomials, and the equality constraint is a monomial of the variables (r,t) (refer to the appendix for the concepts of monomial, posynomial, and signomial).
Sentence 2: (18) is a signomial optimization problem of the standard form [22].
Relationship: reasoning
Domain: Networks
Sentence 1: It is achieved for a 1D symmetric network as described in Fig­ure 3 with a large number N of nodes, when the throughput Many of the NC strategies proposed in the literature (e.g., COPE) require that packets are decoded at each node.
Sentence 2: each node has to maintain the packets received and trans­mitted successfully in the past in order to decode the pack­ets that will arrive in the future.
Relationship: reasoning
Domain: Networks
Sentence 1: TheostinurredbyalgorithmAzoninputIlis Proof:LetG.denotetheexpetedostinurredbythe algorithmA.CombiningthealulationbelowwithCorol­uifu:z G(AzIl) lary5yieldsthetheorem.
Sentence 2: z+1ifu>z G.: TheoptimalofineostPToninputIlis l PT(Il)min(u1) :GOPT -nOPT+P(z)(nz+znOPT -Ez)dz o fromEquation(1)  :GOPT -nOPT+ G(AzIl)1ifu:z z+l ll PTifu>z (Il)l P(z)(nz+znOPT -nwdW+(1-z)nOPT)dz o z WemayassumewithoutlossofgeneralitythatanyonlinefromLemma4 ll w algorithm(deterministiorrandomized)willbuybytime1, GOPT+P(z)nzdz-nwP(z)dzdWsinethereafter,theoptimalofinedoesnotinrease,but oo theonlineostdoes.Thus,inourdisussion,weassume o byhangingtheorderofintegrationthatbothuandzarebetween0and1.
Relationship: reasoning
Domain: Networks
Sentence 1: However such a link would necessarily cause again route .uttering, because Pi1 and Pi2 would meet at this link and at link eb2 , buttheywould needto separatebetween themselvesbecause they do not share eb1 nor eb3 (see Figure 4).
Sentence 2: pi2 traverses eb3 , as well as eb4 ,because of(ii).
Relationship: reasoning
Domain: Networks
Sentence 1: Therefore, a new quasi-router b is created as an identical copy of the existing quasi-router a with the same neighbors as quasi-router a (see Figure 5(c)).
Sentence 2: quasi-router b will have a RIB-In match for a route with AS-path 1-5-4,but does not select it as best route (the AS-path 1-4 is shorter).
Relationship: reasoning
Domain: Networks
Sentence 1: For ex­ample, MPI/QMP[13] provides a M-VIA based communi­cation, however its low level communication performance is limited to 550 MB/s using six Gigabit Ethernet links on a 3-D mesh connection.
Sentence 2: we have developed a scal­able communication layer for the 3D-HXB network called PM/Ethernet-HXB.
Relationship: reasoning
Domain: Networks
Sentence 1: House Accuracy Error (sec) Experiment: FA% MD% Min Max Mean WiFi NORM 0.043 5.70 0.29 2.78 1.06 WiFi SEP 0.005 4.35 0.03 1.82 0.56 ZigBee 0.004 0.49 0.10 3.55 1.63 average missed detection rate of other groups (results pre­sented in Table 2 are averaged over the other three groups).
Sentence 2: we conclude that, although an MRW attack can pen­etrate concrete and brick walls, metallic structures in the line of sight path of the radio signals degrades the detection accuracy signi.cantly.
Relationship: reasoning
Domain: Networks
Sentence 1: For ease of exposition, we hereon refer to the fraction of other ASes whose tra.c is hijacked by the hijacking AS (averaged across all pre.xes) as the proba­bility of hijacking.The probability of interception is de.ned analogously.
Sentence 2: we were able to determine the probabil­ity of hijacking for each of the seven ASes.
Relationship: reasoning
Domain: Networks
Sentence 1: 6.3 Enhancements for Paths In the summation algorithm presented in Section 5.1, if a connected component of G1 is a path, the two nodes at both ends of the path will indicate it in the messages they send.
Sentence 2: there are two types of messages: (i) messages originating from the end of the path and (ii) messages origi­nating within the path.
Relationship: reasoning
Domain: Networks
Sentence 1: Then E[Yn+1 | Fn]= E[Xn+1 | Fn] T -1 +EE Bk Fn+1 Fn k=n+1 T -1 = Xn + E[Bn | Fn]+ E Bk Fn k=n+1 = Yn.
Sentence 2: thus, Yn is an Fn-adapted supermartingale; furthermore, by de.nition, Yn is non-negative for all n. by Theorem 7.2, []LT -1 E Bk * E[Y0] k=0 P(YT = a) = = .
Relationship: reasoning
Domain: Networks
Sentence 1: Assumethatattime0,thesystemhasaonfgurationof f(0)paketsinQ(f),g(0)paketsinQ(g)ande(0)pakets inQ(e).MakeMmax{f(0)g(0)e(0)}.Letusrunthe systemforMsteps,whihorrespondtothefrstpartof theperiod.
Sentence 2: letP(t)denotethenumberofpaketsinthesystemat timet,letPe(t),fe(t)andge(t)denoterespetivelythe numberofpaketsin/1,Q(f)andQ(g),thatwillpass throughe.ThenP(0)f(0)+g(0)+e(0)andPe(0) fe(0)+ge(0)+e(0).AstheprotoolisFIFO,attimeM, thenumberofpaketsfromPe(0)whihstillhavenotbeen servedbyQ(e)isatmostfe(0)+ge(0),andtheyarequeued inQ(e).Atthesametime,themaximumnumberofnew injetionsofpaketstargetedwitheisatmostrM.e(M):rM+fe(0)+ge(0).Let srM+fe(0)+ge(0)(1) thenattimeM+sallthePe(0)oldpaketswillhavebeen servedbyQ(e).
Relationship: reasoning
Domain: Networks
Sentence 1: (6) 32 Substituting (3) into (6), with .b = -23 ln P2 b ,the CR node transmit power Pt corresponds to: R/W a Pt = .b 2-1 ·I ·d.
Sentence 2: (7) we can write the problem of minimizing the average transmit power of CR nodes as: L 1 .
Relationship: reasoning
Domain: Networks
Sentence 1: As proven in Theorem A.2, face routing with small perturbations always works in the presence of collinear links.
Sentence 2: practical Collinear Link Robustness Even though small perturbations eliminate collinearity, they are dif.cult to implement in practice, for reasons including the poor numerical stability of representing small ei, &#38;c. we in­stead present an alternative modi.cation to the right-hand rule that clearly answers the two questions raised in Section 4.2.
Relationship: reasoning
Domain: Networks
Sentence 1: 3.1.1 Routing Protocols As the main subject of our evaluation is Chord, we wanted to factor out any artifacts of using a speci.c routing pro­tocol.
Sentence 2: we simulated Chord with three di.er­ent routing protocols: Ad hoc On-Demand Distance Vector (AODV) routing [16], Dynamic Source Routing (DSR) [14], and Optimized Link State Routing (OLSR) [13].
Relationship: reasoning
Domain: Networks
Sentence 1: We explain these independence assumption in more detail when we de.ne the model equations.
Sentence 2: for agivenset ofinputs,whichincludethetopology graph G =(V,E), the set of pathsP, the exogenous tra.c arrival rate for connections, fraction of tra.c that is trans­mitted over eachpath and thePHYlayer errorprobabilities, we .nd the average system performance.
Relationship: reasoning
Domain: Networks
Sentence 1: dW Ws2 + LnhT Then, (a) if CW = 1 then vP (W) is decreasing for positive W, (b) if CW < 1 then vP (W) is increasing on the interval  (v v ) 0,(1 - CW )ThnL/( CW s2)and it is decreasing on the (v v ) interval (1 - CW )ThnL/( CW s2),8.
Sentence 2: the optimal bandwidth W = W(CW ) which maxi­mizes the provider s revenue is given as follows: .
Relationship: reasoning
Domain: Networks
Sentence 1: V, ti · d(hi, (u, v)) · p(u, v) = (13) i=1 v.V k p(u, v) · d(hi, (u, v)) · ti, (14) v.V i=1 hence by (12), k p(u, v) · d(hi, (u, uv)) · ti = p(u, v) · tuv, (15) v.V i=1 v.V and by constraint (10), p(u, v) · tuv = b(u), (16) v.V  hence condition (7) holds.
Sentence 2: a is a legal broadcast scheme.
Relationship: reasoning
Domain: Networks
Sentence 1: Based on Equation (2), the probability of a random in­jected packet (e.g., Ri) connects to an authentic packet in R (e.g., Rj ) is equal to the probability of two random vec­tors in V (i.e., ui, wi) belong to the hyperplanes represented by the sanitization tags of the authentic packet (i.e., Hj and Gj ).
Sentence 2: it can be observed that an injected packet may connect to an authentic packet in R with the probability of at most ( 1 q )2 , where q is the .eld size.
Relationship: reasoning
Domain: Networks
Sentence 1: With this scaling, the length of the re­gion becomes s10,the width becomes 1/s0.1,and the radius that was 1/101hthat of the width becomes r (1/10)*(1/s)0.01.Let us suppose that the network is de­sired to last 10 times longer than the active lifetime of an in­dividual sensor, which implies a duty cycle of 10%.
Sentence 2: p0.1.We answer the following questions for this deploy­ment scenario from analysis as well as from simulation: 1.
Relationship: reasoning
Domain: Networks
Sentence 1: This probability depends on an operat­ing target SINR, ßi, or, correspondingly, a channel coding rate (determining the strength of channel coding), Ri, which are set with the QoS goal of limiting the relative contribution of Dc to Di below an acceptable limit [10].
Sentence 2: we consider cross-layer CR SUs that can jointly adapt both the source encoding rate and channel coding rate through CR parameter setting.
Relationship: reasoning
Domain: Networks
Sentence 1: Non-pipelined (i.e., non-scheduled) IP packets, i.e., packets that are not part of a SVP (e.g., IP best-effort packets), can be transmitted during any unused portion of a TF, whether it is not reserved or it is reserved (partially or completely) but currently unused.
Sentence 2: links can be fully utilized even if flows with reserved resources generate fewer packets than expected.
Relationship: reasoning