A. Papoulis. Probability, Random Variables and Stochastic Processes. McGraw-Hill International Editions, 3rd Ed, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that some of the samples of f are known. Our task is to determine the remaining samples. Assume that the known samples are f i , i J . With the help of the matrix D defined by (1) the given data can be written Df . As we have seen before, the Papoulis Gerchberg iteration, originally introduced [15, 30, 31] as an extrapolation superresolution method for L 2 (R) signals, can be used to approach this problem. The algorithm consists of two steps, one of which is band limiting (application of the operator B) The other step enforces the time domain knowledge, that is, it resets the known part of the ....

A. Papoulis. Signal Analysis. McGraw-Hill International Editions, New York, 1987.

....phase; E5: the elected leader does not fail. Theorem 1 (Round success probabilities) a) The event [E3, E4, E5] in an election round in the protocol of Figure 2 implies that it is successful, that is, the election satisfies the Uniqueness and Agreement properties of Section 2.2. b) From [2, 16], the probability of success in an election round with parameter K can be lower bounded by Pr[E1, E2, E3, E4, E5] Pr[E1] Pr[E2 E1] Pr[E3 E1, E2] Pr[E4 E1, E2, E3] Pr[E5 E1, E2, E3, E4] e K1 8 e K2 8 ) e 2 (1 view prob) 2 1 ( 1 p ucastl ) ....

A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGrawHill International Edition, 3 edition, 1991.

....five terms. Pr[E1] can be bounded by assuming that N , the group size at the start of the round, is large enough (# K) so that, from the fairness of H, the number of members entering the Relay phase can be approximated by a normal distribution with mean (1 K = K 1 and variance K 1 (1 K 1 [20]. The (1 p mcastl ) term comes from the expected fraction of members receiving the initial multicast message. Similarly, the number of relay members that do not fail until their final multicast is a normal distribution with mean (1 p fail ) 1 p mcastl ) K = K 2 and variance K 2 (1 K 2 ....

....(1 p mcastl ) term comes from the expected fraction of members receiving the initial multicast message. Similarly, the number of relay members that do not fail until their final multicast is a normal distribution with mean (1 p fail ) 1 p mcastl ) K = K 2 and variance K 2 (1 K 2 . Thus [20], Pr[E1] say) Pr lb [E1] For a random graph with m members and edge probability view prob, 4] states that the probability of the graph having exactly one component is Pm # e m(1 view prob) m 1 , and this rises with m. Since E1 implies that there are at least K 2 2 relay ....

A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill International Edition, 3 edition, 1991.

....process does not exhibit local minima for sufficiently large numbers of realizations. Therefore we must show, that 1. the histogram is an asymptotic efficient estimate for the density function of an ARMA process, too. This is equivalent to showing that ARMA processes are ergodic in distribution [12], 2. the process governing the differences of two consecutive points of an ARMA process is ARMA too, 3. the probability density functions for ARMA processes produced by certain types of input noise do not exhibit any local minima, 4. deterministic signals superimposed to the ARMA process give ....

Athanasios Papoulis. Probability, Random Variables and Stochastic Processes. McGraw-Hill International Editions, 1989.

....inputs We present here preliminary results using this integrated input technique to analyze the case in which the inputs have a homogeneous Poisson distribution. We consider the case in which the (constant) rate on each bre is . The expressions for (t) t) and (t 2 ; t 1 ) take the forms [5] 5 (t) N a t Z 0 dt 0 u(t t 0 ) t) N a 2 t Z 0 dt 0 u 2 (t t 0 ) t 2 ; t 1 ) t 1 ) t 1 Z 0 dt 0 u(t 1 t 0 ) u(t 2 t 0 ) 16) For the perfect integrator model the method reproduces the well known analytical result [4] In the case of the Stein model ....

A. Papoulis. Probability, Random Variables, and Stochastic Processes. McGrawHill International Editions, Singapore, 1991. 3rd Edition.

....synchronization index [10] of the input spikes, with r in = 0:5 representing a highly modulated input and values of r in closer to zero representing inputs that contain less of the frequency dependent component. This input rate represents an inhomogeneous (i.e. nonstationary) Poisson process [16]. The probability density of the potential V (t) is denoted by p(v; t j v 0 ; which is the probability that the potential has the value v at time t, given that the previous spike occurred at time t = 0 when the potential is reset to the value v 0 , the frequency of the input is and the ....

.... 0 ; 1 Z 1 dx 2 exp i x (v v 0 (t; x 2 2 (t; 1 q 2 (t; exp ( v v 0 (t; 2 2 (t; 7) In the case of an inhomogeneous Poisson process with rate (t) on each bre, the expressions for (t; and (t; take the forms [16] 4 (t; N X k=1 a k E fs k (t)g ; N a t Z 0 (t 0 )u(t t 0 )dt 0 ; t; N X k=1 a 2 k E n s 2 k (t) o (E fs k (t)g) 2 =N a 2 t Z 0 (t 0 )u 2 (t t 0 )dt 0 ; 8) where the postsynaptic potentials from the inputs are all excitatory ....

A. Papoulis. Probability, Random Variables, and Stochastic Processes. McGrawHill International Editions, Singapore, 1991. 3rd Edition.

.... (w n b) Gamma 1 w n2 ln e w n b 1 e b 1 p(w n ) dw n (14) ff AE fh(w n )g (15) with h(y) 1 y (y b) Gamma 1 y 2 ln e y b 1 e b 1 (16) Keeping in mind that the first order approximation of E fh(w n )g is given by h(E fw n g) [5], equation (15) can be approximated by E Phi w n 1 Psi Gamma E fw n g = ff Ah(E fw n g) 17) which is a nonlinear difference equation for the expected value of w n . Its continuous time equivalent is given by W = ff Ah(W ) 18) where W denotes E fw(t)g. To gain an approximate ....

Athanasios Papoulis. Probability, Random Variables and Stochastic Processes. McGraw-Hill International Editions, 1989.

....that some of the samples of f are known. Our task is to determine the remaining samples. Assume that the known samples are f i , i 2 J . With the help of the matrix D defined by (1) the given data can be written Df . As we have seen before, the PapoulisGerchberg iteration, originally introduced [15, 30, 31] as an extrapolation superresolution method for L 2 #R# signals, can be used to approach this problem. The algorithm consists of two steps, one of which is band limiting (application of the operator B) The other step enforces the time domain knowledge, that is, it resets the known part of the ....

A. Papoulis. Signal Analysis. McGraw-Hill International Editions, New York, 1987.

....di#er in the degree of invariance to the radiometric image distortion: The Sum of Square Di#erences averaged over image pairs assumes that only identity transformation of intensity values acts among the images. This may be too restrictive in certain applications. The Standard Correlation Coe#cient [3] is invariant to a linear transformation acting on image values. It is computed as a mean of all pairwise correlation coe#cients and has a range of [ 1, 1] It allows to suppress the influence of small deviations from surface non Lambertianity. A Rank Correlation [2] is more general since it ....

....as a mere average over all image pairs. The invariance to monotonic image transformations is paid for by the loss of discriminability. More general transformations of image values are possible to assume; the corresponding consistency measure would be based either on relative mutual information [3] invariant to all 1:1 mappings or by explicit parametric models. These choices will not be discussed in this paper. As will be seen in the next section, however, the actual verification procedure can be made independent on the choice of the measure. 4 The Statistical Decision Procedure The goal ....

A. Papoulis. Probability, Random Variables, and Stochastic Processes. McGraw-Hill International Editions, 3rd edition, 1991.

.... mean[i] mean[i] factor translation; peak[i] mean[i] rho; The C function normal distribution( oe) generates Gaussian random numbers with mean and standard deviation oe. On a computer, normal distributed random numbers can be generated (based on the central limit theorem (CLT) [Pap91]) with the help of equally distributed random numbers [Pei92] which are usually available on every computer. The parameter ae = m=R is used to calculate the peak rate from the mean rate. This value could theoretically be varied but for analysis purposes it is easier to generate different traces ....

Athanasios Papoulis. Probability, Random Variables, and Stochastic Processes. McGRAW-HILL INTERNATIONAL EDITIONS, 1991. ISBN 0-07-100870-5.

....video signal is multiplied with the PN sequence p having mean p = 0 and variance oe 2 p . The product has mean p v = 0 and variance oe 2 p v = oe 2 p Delta (oe 2 v 2 v ) In the sum Sigma 1 , the product p v is summed cr times. Thus, according to the central limit theorem [25], the probability density function of the sum approaches a normal distribution with mean Sigma 1 = cr p v = 0 and variance oe 2 Sigma 1 = cr Delta oe 2 p v = cr Delta oe 2 p Delta (oe 2 v 2 v ) A bit error occurs if the current information bit is a 1 and Sigma 1 ....

A. Papoulis. Probability, Random Variables, and Stochastic Processes. McGraw Hill International editions, 1991.

....and solving analytically problems arising in different domains, prevailed upon any metaphysical difficulty. Scientific concepts have a precise connection with the real world defined by the ability of making predictions and solving practical problems. This idea is clearly explained by Papoulis [11] through an example extracted from the discipline of circuit theory. In this domain, the typical practical problem that one wishes to solve consists in combining electrical devices in a circuit where the output (the potential of one point of the circuit) varies in time as a given function of the ....

....assume that the resistance R is a precise number satisfying [the relation R = v(t) i(t) and we develop a theory based on [such relation] and on Kirchhoff s laws. It would not be wise, we all agree, if at each stage of the development of the theory we were concerned with the true meaning of R [11]. Also in our every day life, we use working hypotheses in a very similar way, for example when, buying a new table for our kitchen, we measure a candidate for checking if it will fit into the available space. Measuring a table requires, at least implicitly, to assume a model in which the concept ....

A. Papoulis. Probability, Random Variables, and Stochastic Processes. McGraw-Hill International Editions, New York, NY, USA, 3rd edition, 1991.

No context found.

A. Papoulis. Probability, Random Variables and Stochastic Processes. McGraw-Hill International Editions, 3rd Ed, 1991.

No context found.

Athanasios Papoulis, Probabili randon; variables, and stochastic processes, p. 329, 3rd edition, McGraw-Hill International Editions, New York, 1991. 659

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC