sadat2307/MSciNLI huggingface dataset:
Domain: Networks
Sentence 1: Thus, Np v provides an unbiased estimate of v. However, as discussed in section 2, the sample count of each entry is Ne = Nv + cmin,with cmin the smallest amount by which the m counters corresponding to a .ow have been raised by other .ows when detection occurs.
Sentence 2: by estimating .ow Nv+cmin sizes on the basis of Ne,wehave that v = p ,which translates into a mean square error (MSE) given by 2v(1 - p) E[c 2 min] E[(v - v )]= + 2 .
Relationship: reasoning
Domain: Networks
Sentence 1: Indeed, while the traditional tier-structure of the Internet is still recognizable and can be largely recovered, the observed rich peering fabric at this IXP enables connectivity among networks of all different types and is essentially agnostic of any tier structure.
Sentence 2: at least as far as connectivity for the part of the Internet that involves this IXP is concerned, the observed IXP-related peerings provide a myriad of shortcuts and essentially complement any perceived or real hierarchical structure.
Relationship: reasoning
Domain: Networks
Sentence 1: This is because, with multi-threading, the number of memory accesses made during the time taken to serve one grows linearly with the number of threads in use and saturates at Penalt y/(C + Cont ext Swit chOverhead) where C denotes the number of compute operations performed per context­switch, and Penalt y denotes the memory access latency.
Sentence 2: pro­cessor utilization achieved by multi-threading is limited not only by C but also by the available memory bandwidth.
Relationship: reasoning
Domain: Networks
Sentence 1: Compared to the centralized TDMA scheme, the CSMA protocol has two distinguishing characteristics: i) CSMA is an ACK-based protocol, such that the re­ceivers are required to reply an ACK packet for each successful transmission.
Sentence 2: bi-directional commu­nications need to be explicitly considered when for­mulating the constraints on simultaneous transmission imposed by CSMA.
Relationship: reasoning
Domain: Networks
Sentence 1: As the assumed probability of false alarm is PFA=0.2, we approach an average of the expected number of clutters for each snapshot of the sensor node as in Equation 1. .
Sentence 2: = PFA · V (1) for normal cluttered scenarios, we assume that we have on the average .=2 false alarm detections uniformly distributed inside the sensing region of each sensor.
Relationship: reasoning
Domain: Networks
Sentence 1: APPENDIX Deriving z-Transform of Pr{M =0,U = u} Given M =0, we have Pr{N = n|M =0} Pr{M =0|N = n}Pr{N = n} = Pr{M =0} (19) [1 - pg(h, t)]nPN (n) = .
Sentence 2: pr{M =0} the probability generating function of N given M =0 is * PN|M=0 (z) 8 n =n=0[1 - pg(h, t)]nPN (n)z Pr{M =0} (20) PN * [(1 - pg(h, t))z] = .
Relationship: reasoning
Domain: Networks
Sentence 1: If we take Interval equal to L.T T I and RT T equal to R.T T I, the sum of Interval and the dead time is (L+R)×TTI.
Sentence 2: bmini can be formulated as following: { .Ai×TTI × (L + R)., ifAi > 0; Bmini = S (3) L + R, ifAi =0.
Relationship: reasoning
Domain: Networks
Sentence 1: From the following Lemma 2, we know that the payment to link ek is the same for cost pro.le d and d .
Sentence 2: the utility of link ek under pro.le d by payment scheme p becomes p k(d ) - ck = p k(d) - ck = p k(d) - (pk(d) - d 2 ) = - d 2 < 0.
Relationship: reasoning
Domain: Networks
Sentence 1: cause that reliable transmission is used.
Sentence 2: in SS+RT, the We de.ne the state space as S={(n,8)}, where 0:n:N is the number of consistent hops, and 8is a special variable taking transition rate from state (i-1,1)to state (i,0)becomes on values of 0 or 1 to indicate whether the Markov chain is in a fast path Markov state (8=0)ora slow path (8=1) Markov state.
Relationship: reasoning
Domain: Networks
Sentence 1: The probability of a successful transmission in a time slot of epoch i isgiven by: « n-i-1 ps(i)= pi(1- pi)n-i-1 =1 1- 1 n - in - i It is easy to see that each Wi is a geometrically distributed random variable withparameter(n - i)ps(i).
Sentence 2: n-1 n XX 1 E[W]= E[Wi]= ` = ne (4) ´i-1 1- 1 i=0 i=1 i wherethelastinequalityfollowsfrom Lemma1inAppendixA.
Relationship: reasoning
Domain: Networks
Sentence 1: While focusing on trace properties of a packet (or .ow), i.e., the invariants related to the hop­by-hop journey of a single packet (or .ow) in the network [11,12,18,20], is invaluable in preventing certain classes of in­correct network behaviors such as loops, black-holes, or con­gestion, it is far from su.cient for today s networks.
Sentence 2: there is a need for de.ning a new notion of correctness that takes into account the sequence of observations made by the  controller and end-hosts, with potential interdependencies.
Relationship: reasoning
Domain: Networks
Sentence 1: On(i ) consists of On(i)/d(i ) intervals of length d(i), and according to the 79 lemma, in each of these intervals the overall average latency is equal to hu(i)d(i)2/2.
Sentence 2: the overall average latency accumulated to retrieve item i during the n-th cycle is given by: Ln(i) = ~'-~) (rn(i)2 + On(i)d(i)) (8) and the long-term overall average latency to retrieve item i is ~ven by: N(i.T)   In(i) L(i)= lira n-I (9) T-,o* T The following theorem gives lower and upper bounds forL(i).
Relationship: reasoning
Domain: Networks
Sentence 1: Given a counter epoch CX of length n at observation point X where each counter subvector is of length m, let tX denote the sum of all counters in CX, the estimate t f,X of the sum of all time stamps of the packets in .ow f is calculated as follows {m } L f t f,X = 1 n SX[j]-mtX (4) n -m j=1 Proof.
Sentence 2: given CX and .ow f, we can easily obtain the values of every counter in the counter subvector Sf of f. 1 Lm Sf we can calculate E[C]as E[C]= [j].
Relationship: reasoning
Domain: Networks
Sentence 1: Diagram of an OFDMA system model 2.2 Channel Allocation Methods 2.2.1 OFDMA-FDMA statistical allocation In the fixed allocation method of OFDM-FDMA for multiple user interfaces, different users will be assigned to different subcarriers and the subcarriers are assigned to each user during user operation [13].
Sentence 2: this method is known for poor adaptability as well as no anti-interference mechanism.
Relationship: reasoning
Domain: Networks
Sentence 1: However, observe that t t t t 2 i( .k-.l) 2 2 E{|A(t)|}= E{RkRle }= E{Rk}= st k,l=1 k=1 from E{e i.
Sentence 2: }= 0 and the independence of the random vari­ables for k = l. its standard deviation or the average v displacement of node A during time t scales as O( t).7 In other words, after a duration of time t, a node will typically v travel a distance of O( t) from its original position.
Relationship: reasoning
Domain: Networks
Sentence 1: By an almost identical argument, w.h.p., Alice does not exceed her budget of Cn 1/2 lnn.
Sentence 2: for C suf.ciently large, Alice and the correct nodes are guaranteed to reach a round where there are no blocked phases and, therefore, Lemma11guarantees thatatleast (1-o)n nodes areinformed and terminate; the o-fraction that might terminate without m follows from our observations about an n-uniform adversary.
Relationship: reasoning
Domain: Networks
Sentence 1: We observed that a large number of replies of Refused error are sent to 1,275 local resolvers from two authoritative nameservers at 4-5am.
Sentence 2: .uctuations in the entropies of the authoritative nameservers in Refused errors decreased and those of increased due to the skew of sending queries from two authoritative nameservers to many local resolvers in the academic network.
Relationship: reasoning
Domain: Networks
Sentence 1: IPv6 introduces some additional features (like flow label) and the current support for QoS mechanisms in IPv6 implementations approaches the corresponding QoS support in IPv4.
Sentence 2: a number of tests with DiffServ QoS mechanisms applied on IPv6 traffic have been carried out on a testbed created specifically for this purpose, in order to validate the mechanisms and evaluate the router s overall performance.
Relationship: reasoning
Domain: Networks
Sentence 1: Currently, we do not actually use multi-hop transmissions in mobile k-hop clustered networks because multi-hop trans­missions require signi.cantly higher overhead due to the need to discover cluster heads at a further distance away and to establish multi-hop paths on demand.
Sentence 2: we proposed a simpli.ed routing strategy to avoid the technicalities of a more complicated one which may obscure our main target.
Relationship: reasoning
Domain: Networks
Sentence 1: ..(HSMS L + H AR1) ×tout + (L + 2) ×tin .. ×2 (10) i CN1 SMSiL (11) (HSMS L + H ) ×tout + (L + 2) ×tin AR1 i As shown in Figure 4, SIP+HCoP-B omits the SIP URI allocation, SIP REGISTER and 200 OK messages.
Sentence 2: the total number of messages for session initialization is the sum of (h)+(i)+(j)+(k)+(l)+(m) and equal to (5×2L+1-6).
Relationship: reasoning
Domain: Networks
Sentence 1: Denote the packet scheduled by ALG by p. By the de.nition of ADV , it waits one time unit, sets used = in(p), increases i by one and the iteration ends.
Sentence 2: at the end of iteration K -1 the claim holds, since i = 2, used = in(p) and p has remaining length of 2K-1 - 1.
Relationship: reasoning
Domain: Networks
Sentence 1: But this will not take obvious in.uence on the whole mechanism because of the fading factor which can gradually recovery this kind of small error with the elapsed time.
Sentence 2: the ATVal can be calculated as:  ATV al(s)t (t-t ) latestlatest =0.5+(ATV al(s)t " - 0.5) × ß" ARV al(o)tlatest - dsus (t-t ) latest +( ) × (1 - ß" )(5) drev Where, 0.5isan initialvalue of ATVal for each node.
Relationship: reasoning
Domain: Networks
Sentence 1: The function delete deletes the region and removes its key from the key set.
Sentence 2: to allocate an object in a region, Vault pro- vides a primitive new operation taking the following form: new(rgn) T [init] Given a tracked region rgn with key R, the new construct returns an object of type R:T, that is, an object guarded by key R. 7 this object is accessible as long as the region is accessible.
Relationship: reasoning
Domain: Networks
Sentence 1: The expected value of the average run size of 1s is a monotonic function of the number of tags, which means that a unique inverse of this function exists.
Sentence 2: given the observed average run size of 1s, using the inverse function, we can get the estimated value t of tag population size t. Similar to other tag esti­mation schemes, ART also uses multiple frames obtained from multiple rounds of the framed slotted Aloha protocol to reduce its estimation variance and therefore increase its estimation reliability.
Relationship: reasoning
Domain: Networks
Sentence 1: Note that the state evolution of a path is a continuous-time process, while different .ows can be considered as sampling this process at different time granularities.
Sentence 2: we can .rst use a probing .ow (with relatively large probing interval to reduce probing overhead) to sample the path, and then a discrete-time HMM representing the loss process expe­rienced by the application .ow can be obtained given the sampling intervals of both the probing .ow and the application .ow.
Relationship: reasoning
Domain: Networks
Sentence 1: (t(ei)= ' d(ei)) holds, the weights of these edges ei in H are the same as their weights w(ei)in H (by givingin.nite weights to edge not in H).
Sentence 2: for every node u in H ' , the following two facts hold: (1) the distance d ' (u) from u to s in H ' is the same as the distance d(u) from u to s in H, and(2) the time t ' (u)at which node u receives the message from s inthe.oodingprotocol restricted totheedgesof H ' is the same as the time t ' (u) at which node u receives the message from s in S. As a consequence, t ' (u)= d ' (u) for every node in H ' .
Relationship: reasoning
Domain: Networks
Sentence 1: In this case the MSE criterion is given by E = EVp u + HTc u - Qf u 2(18) where Qf contains the phase-corrected correlation elements.
Sentence 2: f [Q ]m,r = .m,r fm,r (19) The precoding matrix at CBS is then given by Tc,IRLP = HH (HHH )-1(Qf - Vp) (20) the received signals vector at primary and cognitive users is given by Qf u y = v + n (21) ßIRLP The average transmitted power normalization factor ßIRLP is given by HH ßIRLP = tr(Tc,IRLP Tc,IRLP ) + tr(Tp Tp ) (22)  5.
Relationship: reasoning
Domain: Networks
Sentence 1: That is, once it .nds some coordinates that bring its queries to the current home node (even though they may not be ex­actly the same coordinates produced using the parameter s in the hash function), the attacker already knows a quite close position to the exact coordinates.
Sentence 2: when the home node runs out of battery and the next closest node to the hash output coordinates becomes the home node, the at­tacker will need very few queries to .nd the new home node.
Relationship: reasoning
Domain: Networks
Sentence 1: Speci.cally, since wireless signals are electromagnetic waves that prop­agate at the speed of light (c m/sec), a human moving at aspeed of v m/sec, results in a maximum Doppler shift of 2c f v,where f is the frequency of the wireless transmission [3].
Sentence 2: a 0.5 m/sec gesture results in a 17 Hz Doppler shift on a 5 GHz Wi-Fi transmission.
Relationship: reasoning
Domain: Networks
Sentence 1: However, to resist against time varying misbehaviors, intermittent link availability, network congestion and most importantly misbehaving nodes when they comprise a con­siderable percentage of the network members and compro­mise most of the paths, a closed loop feedback system is proposed to react to these behaviors based on Path State Information (PSI) concept.
Sentence 2: our proposed mech­anism is able to tune itself for the best performance in each situation.
Relationship: reasoning
Domain: Networks
Sentence 1: More impor­tantly, the fact that the interception signature used here can also result from valid scenarios in the Internet implies that we have to rely on the pre.x owners for conclusive evidence of interception.
Sentence 2: for the remaining anomalies, we conducted an e-mail survey asking the pre.x owner if they had a peering relation with the next-hop AS suspected of interception.
Relationship: reasoning
Domain: Networks
Sentence 1: Overall, our results indicate two key observations: (1) Channel hopping de-correlates packet losses both across time and frequency domain, thus reducing the number of consec­utive packet losses compared to the corresponding individ­ual channels.
Sentence 2: in single-hop communication, or on .xed topologies where adaptive routing is not an option (such as preplanned WirelessHART deployments) frequency diversity can yield signi.cant reliability improvements.
Relationship: reasoning
Domain: Networks
Sentence 1: The performance of fOFDM compares with FBMC only in the case of 10 nodes, as in this case, the amount of tra.c is relatively low and as a consequence, the e.ect of mutual interference among di.erent nodes is minimum even with fOFDM.
Sentence 2: when there are more nodes, FBMC will en­able upper layer applications to exchange data at a very high rate.
Relationship: reasoning
Domain: Networks
Sentence 1: The trustworthiness associated with a pair (t, c) is de.ned as q (t-1)2 (c-1)2 + 2 2 xy T (t, c) 6 1 - q , (3) 1 1 + 2 2 xy where x and y are parameters that determine the relative importance of the trust value t vs. the con.dence value c. The default value of trustworthiness is de.ned as Tdef 6 T (0.5, 0), which represents the trustworthiness value assigned to a node when its assigned trust and con.dence values are t = 0.5and c = 0, respectively.
Sentence 2: the value Tdef represents ignorance about the trustworthiness of a node.
Relationship: reasoning
Domain: Networks
Sentence 1: Ai = f Bl Bi i=1 l=1 K N v Ai pi × li i=1 i=1 =.
Sentence 2: f = v = v K K l=1 Bl l=1 Bl MCAED is minimized when J v v N j=1 pj × lj Ai = Bi × f = Bi × v K Bll=1 and N v * K i=1 pi × li 2 MCAED = × ( K v ) 2 l=1 Bl D  According to Theorem 1, MCAED is optimized only when vAi the instances of each item are equally spaced and is a Bi constant f. Obviously, these two conditions cannot always be satis.ed.
Relationship: reasoning
Domain: Networks
Sentence 1: By studying the properties of the K1,k-matching, the outage probability of each user is given by () dk dk pout = ps + O ps , (7) lJ L+1 where dk = L - k +1 for k =1,...,M+1 ,and dk = M(L- kM + 1) otherwise.
Sentence 2: the optimal DMT is a piece-wised linear function by connecting (1 - r/k) dk.
Relationship: reasoning
Domain: Networks
Sentence 1: iterator) over the .ows set, which is physically represented by gi­ant two-dimensional arrays1, with one row per each .ow2 .
Sentence 2: when the agents iterate over the Flows, they actually use a single Flow instance for all .ows in the set, greatly reducing the object creation/destruction overhead, while maintaining the same programmatic interface as with individual object instances.
Relationship: reasoning
Domain: Networks
Sentence 1: We start by assuming that pm = 0 and establish The .rst derivative test can be used to establish that a contradiction to the equilibrium requirement xi = when sm = 1, the objective is monotonically decreas­ i 1-xi 1 ing in x1 over the range listed in the case assumption.
Sentence 2: .sm nxi the objective is minimized when x1 = 1 , If pm =0, xi = 1.
Relationship: reasoning
Domain: Networks
Sentence 1: Algorithm 2 Sending rate adaptation mechanisms OpenConnection(flowi) if flowi.Rate == 0 and flowi.T ype == deadline then CloseConnection(flowi) end if while IsOpenConnection(flowj ) do if flowi.T ype == elastic then if NeedtoincreaseTCP CWND then if Bytes sent within T < flowi.Rate then T CWND ++ end if end if else if Bytes sent within T = flowi.Rate then T Queue packet else Send P acket end if end if end while  4.3 Evaluation In reality, given the high network loads and as a result the num­ber of .ows each forwarder must handle per unit time, .ow allo­cation must be ef.ciently computed.
Sentence 2: we have evaluated the performance (duration in microseconds) of Algorithm 1 (for a single switch) on an old 700MHz computer.
Relationship: reasoning
Domain: Networks
Sentence 1: 2.1 Deferred Malicious URLs We measured whether shortening services retroactively analyze malicious URLs, that is, we determined if these services perform any repeated veri.cation of the safety of the long URLs to which their existing short URLs point to.
Sentence 2: we set up a web page that served benign HTML content for a period of three days; this page s URL contained 32 random characters to ensure that no legitimate users accidentally stumbled upon the URL.
Relationship: reasoning
Domain: Networks
Sentence 1: We establish a correspondencebetween thetwo networks N and N ' as follows: Let Aj(t) denote the number of ar­rivals of .ow j, j=1,2,...,J, occurring at node sj in time slot t. Let .j(t) denote the number of packets departing from the external bu.er for .ow j, in time slot t. By con­struction, .j(t) =0 for t =.ks, for some integer k and Ps .j(t)= i=1 Aj((k-1)s+i)fort = ks.The arrival process to N ' is denoted by A ' j(t)and is de.ned as A ' j(t)=.j(st).
Sentence 2: the arrival rate to network N ' is ss1 .
Relationship: reasoning
Domain: Networks
Sentence 1: For multicast .ows, TransCom s in­tegrated .ssion+fusion allows multi-tree distribution wherein fu­sion creates individual trees and .ssion .sses trees into multiple trees.
Sentence 2: even though we speak of .ssion and fusion as the two primitive transformations, in practical terms, the transfor- Figure 2: Program view and network view of fusion Table 2: ILP formulation for fusion+.ssion Constraints C1 .i, .j, .v = si,v /.
Relationship: reasoning
Domain: Networks
Sentence 1: -0.64 -0.52 -0.62 -0.87  -0.94 -0.47 -0.79 -0.75 (c) IM in a medium-congested environment -0.80 -0.97   (d) IM in a low-congested environment Figure 3: Dynamic Interference Map mand depends largely on F3 and vice versa.
Sentence 2: only the throughputs of theirs appear to have the interference patterns that VOID looks for.
Relationship: reasoning
Domain: Networks
Sentence 1: De.nition 4 (Path assignment) A path assignment for the routing system (N, .1 ,..., .N , F1 ,..., FN ) is a vector of paths P = (P1 ,...,PN ) such that, for all i, Pi EFi.
Sentence 2: a path assignment is an assignment of a feasible path to each node i, where feasibility is determined by the set of paths Fi.
Relationship: reasoning
Domain: Networks
Sentence 1: Since each bit of the key can be 1 or 0 with the same prob­ability, the probability for correctly guessing the key in one attempt is 21 L , and the computational complexity for .nd­ ing out the key is O(2L).
Sentence 2: as long as the size of a key is large enough (e.g., 80 bits), the time complexity is prohibitively high.
Relationship: reasoning
Domain: Networks
Sentence 1: InWirelessLANs,wheretheDomRepsarehubs,allframes fromthenetwork(downstreamevents)arereeivedbyall hubs,whihtransodethemfortransferoverthewireless medium.TheMEisthusrequiredtoflteroutdupliated frames.Fortheupstreamevents,MEtransmitstheframes onthewirelessmedium,andanyhubthatisabletodistin­guishitfromnoise,relaysthemtothewiredmedium.
Sentence 2: thisisatypialaseoftheNon­CoordinatedRedun­dantServieapproah,wheretheDomRepsdonothaveto oordinateanyations(andhene,stritlyspeaking,there isnohandoverprotool).
Relationship: reasoning
Domain: Networks
Sentence 1: The di.culty with variable­length .elds is that protocols can use di.erent elements to mark the .eldboundary such as1) direction .elds, that store information about the location of another target .eld in the message,forexamplelength .eldsandpointer .elds,and2) separators, i.e., constant values that mark the boundary of the .eld.
Sentence 2: we .rst need to locate those elements to identify the .eld boundaries.
Relationship: reasoning
Domain: Networks
Sentence 1: The next step in the bootstrap process is to discover and interact with other NetS core peers reachable via the avail­able networks.
Sentence 2: for everyFB x providingnetwork­ingfunctionality, the coreNetSfunctionalblock will execute the two following commands : resolve(x, "*", "net share", r) : where x is tobe subsequently replaced by the IDP labels of the previ­ously discovered FBs.
Relationship: reasoning
Domain: Networks
Sentence 1: We assume that each new nodejoins withdegree m, hence the mean number of nodes ofdegree k thatgains an edgefrom theincoming node and moves to degree k +1 can be expressed as djo = k.(k+1) m × Ak = mkpk .
Sentence 2: the net change in the number zf of k degree nodesduetojoining of a new node jo jo jo m((k - 1)pk-1 - kpk) d= d- d= (3) k (k-1).kk.
Relationship: reasoning
Domain: Networks
Sentence 1: As the transmitter requires only beamforming vectors to op­erate, it is not necessary to transmit more feedback than that required to inform the transmitter of the beamforming vectors.
Sentence 2: it is easier to consider the time-varying channel at the receiver side than at the transmitter side, as then it is possible to enjoy the stationary property of the channel at the receiver.
Relationship: reasoning
Domain: Networks
Sentence 1: From (3) and (2), we have w,(e)- Z > 0 (4) e6p I eEp Based on (2) and (4), we know that the right-hand side and the left-hand side of the inequality (3) are positive.
Sentence 2: it can be implied that e6Io I e6p e~p e6p t from which we conclude that  + w (e) > rw,(e) + w (e) eEp t eEp This, in turn, implies that p' will not be selected by the algorithm, which concludes the proof.
Relationship: reasoning
Domain: Networks
Sentence 1: When RTTs over paths available to a user are di.erent, satisfying goals 1 and 2 of the RFC [10] can lead to sending tra.c on paths that are not the least congested but have a small round trip times.
Sentence 2: using a TCP-compatible algorithm, it is not pos­sible to avoid problems P1 and P2 in all possible settings.
Relationship: reasoning