Algorithm. We now describe the basic step of the reconciliation mechanism, i.e., the reconcili- ation between two sites on a given object. Section 8 describes when to invoke the reconciliation mechanism, and the options that exist in its use. The basic step is as follows.
Algorithm. Prior to GEMS commencing --------- discussions with the Institutional Review Board ("IRB"), R2 shall confirm in writing to GEMS that the R2 Product algorithm can process the PMA (pre-market approval) cases which are done in feasibility format and that R2 can use them for the PMA submission. In the event that the FDA does not accept these cases for R2's FDA submission, then GEMS and R2 shall negotiate in good faith to determine how to acquire additional cases as outlined in Section 2.8.3.
Algorithm. The K-medians algorithm is simply the K-means algorithm, using cityblock distance and me- dian in place of squared Euclidean distance and mean. Thus, any of the K-means algorithm variations pre- sented (individual-reassignment, batch, or combined) can be used with K-medians. Median definition. If the number of observations (N) is odd, the sample median is the observation in the middle of an ordered list of observations. If the number of observations is even, the sample median is the mean of the two middle observations (Weiss, 2002). A cluster median is the vector of the cluster-wise medians for each variable (attribute). For a group of observations with more than one variable, the cluster median is a vector of the group-wise medians for each variable (attribute).
Algorithm. Mutual information I(X; Y) computes the amount of information a random variable includes about another random variable, or in terms of entropy it is the decrease of uncertainty in a random variable due to existing knowledge about the other. For example, suppose discrete random variable X represents the roll of a fair six-sided dice, whereas Y shows whether the roll is odd or even. Then, it is clear that the two random variables share information, as by observing one we receive knowledge about the other. On the other hand, if we have a third discrete random variable Z denoting the role of another dice, then variables X and Z or Y and Z do not share mutual information. More formally, for a pair of discrete random variables X, Y with joint probability function p(x,y) and marginal probability functions p(x)and p(y) respectively, the mutual information I(X;Y) is the relative entropy between the joint distribution and the product distribution:
Algorithm. Transfer entropy is a non-parametric statistic measuring the amount of directed (time-asymmetric) transfer of information between two random processes. Transfer entropy from a process X to another process Y is the amount of uncertainty reduced in future values of Y by knowing the past values of X given past values of Y. The transfer entropy can be written as: = , , +1 , , (2) → +1 , , +1 +1 , , Transfer Entropy from Y to X is written as: = , , +1 , , (2) → +1 , , +1 +1 , , Transfer Entropy is able to distinguish effectively driving and responding elements and to detect asymmetry in the interaction of subsystems. Transfer entropy is conditional Mutual Information  with the history of the influenced variable in the condition. Transfer entropy reduces to Granger causality for vector auto-regressive processes. Hence, it is advantageous when the model assumption of Granger causality doesn't hold, for example, analysis of non-linear signals. However, it usually requires more samples for accurate estimation. While it was originally defined for bivariate analysis, transfer entropy has been extended to multivariate forms, either conditioning on other potential source variables or considering transfer from a collection of sources, although these forms require more samples again.. The flowchart that corresponds to the TE calculation is shown on the following figure. First the pdf estimation is done and the TE is calculated. Input Data NO pdf created pdf Estimation YES NO MI calculated MI Calculation YES MI Result Figure 11: Transfer Entropy basic flowchart
Algorithm. The ECM-sketch combines the well-known Count-Min sketch structure , which is used for conventional streams, with a state-of-the-art tool for sliding-window statistics, i.e. the Exponential Histograms .The input of the ECM-sketch data structure is a number of distributed data streams. The output of the ECM-sketch algorithm is a sliding window sketch synopsis that can provide provable, guaranteed error performance for queries, and can be employed to address a broad range of problems, such as maintaining frequency statistics, finding heavy hitters, and computing quintiles in the sliding-window model.
Algorithm. This algorithm is named as the MOV reduction. Later, it was shown that the MOV reduction can be applied to ordinary curves as well when the embedding degree (see the definition in Section 2.5.2) is sufficiently small . Hence, in practice one is advised to avoid using curves with small embedding degrees when implementing ECCs1. However, recent developments on the pairing-based cryptography created another “twist”. Although the MOV reduction implies faster algorithms to solve the ECDLP when the em- bedding degree is small, certain security levels for practical use can still be achieved if the ground field size and the embedding degree are chosen properly. Moreover, in this con- text efficient pairings can be applied in very constructive ways to build novel cryptographic schemes. For example, Joux  observed that the pairing can be used to construct a round-efficient tripartite key agreement protocol. By using the pairing computation and a Diffie-Hellman-like message exchange, the Joux protocol requires each party to broadcast only a single message to establish an agreed session key among three parties. An even more striking development is that in 2001 Boneh and Franklin  using pairing constructed the first practical identity-based encryption (IBE) scheme with provable security based on a reasonable pairing-based intractability assumption. This work has solved the long-standing cryptographic problem of constructing a secure and practical IBE as proposed by Shamir in 1984 . After these pioneering works, many novel cryptographic systems have been constructed with pairings. This thesis is devoted to the study of pairing-based cryptography. In the last three decades, we have learned an important lesson that ad hoc approaches to construct cryptographic schemes are a dangerous way to go. Numerous security schemes with only ad hoc security analysis were later broken. As an alternative, many researchers have been seeking to build cryptography on firm foundations by borrowing methods from the theory of complexity. Rigorous approaches to treat cryptography have then prevailed. Now it has become more or less a standard process to solve a cryptographic problem with 1It was also shown that for abnormal curves, there exist polynomial-time algorithms for the DLP [142, 148, 141] and the Weil descent attack is applicable to certain normal curves . two phases: a definitional phase and a constructive phase . In the definitional phase, one identifies th...
Algorithm. The time of arrival information shall be determined using a predictive algorithm that utilizes the current AVL information for the approaching buses to a bus stop. AIM shall calculate the arrival times for all buses up to the next 60 minutes and display up to the next five buses that will arrive at each stop. If more than five buses, the user can scroll to see the additional bus arrivals. The time of arrival information shall be updated at least every thirty seconds and made available to the systems using such information within one second after the AIM server receives a location update. AIM shall also calculate time of departure information which shall be used for announcements for the first stop for each bus route trip. The accuracy of the predictive algorithm shall be such that the predicted error shall be less than 75 seconds when a bus is five minutes or less from a stop; and less than two minutes when a bus is between six and 10 minutes from a stop. The AIM predictive algorithm shall be a learning algorithm that is based on historical data for the stop location, route, and the time of day, day of week, and week of year.
Algorithm. Hall This algorithm is designed to emulate the effect of reverberation in real concert halls. Unsurprisingly, this makes it particularly suited to acoustically recorded material, though it is also ideal for any sort of multitracked music, to provide a common sense of space. The algorithm comprises two distinct elements: early reflections and reverberation.