Memory-less

Non-linearity with Memory. The AR-MNL model is clearly somewhat restrictive in that most distortion mechanisms will involve memory. For example an amplifier with a non-linear output stage will probably have feedback so that the memoryless non-linearity will be included within a feedback loop and the overall system could not be modelled as a memory less non-linearity. The general NARMA model incorporates memory but its use imposes a number of analytical problems. A special case of the NARMA model is the NAR (Non-linear AutoRegressive) model in which the current output x[w] is a non-linear function of only past values of output and the present input s [n ]. Under these conditions equation 4.27 becomes ... 

It would seem tempting to obtain a memory-less equation from (62) by writing... 

This is the Markovian memory-less approximation to the Master Equation. In this approximation, the effective time evolution operator becomes independent of t and the integral may be extended to infinity. It is also consistent to assume that the system lost memory of the initial state of the reservoir, whatever this was. In the limit when Uq is calculated in perturbation theory and pq(0) = 0, we obtain the conventional Born-Markov time evolution which has a long and successful history. 

This is the memory-less exact time evolution equation. In the limit when the Markovian property is expected to hold, we should obtain by comparison with (64) the result... 

This is the exact memory-less equation of motion. Its solution should be identical with the original solution. We can see that after a time t 7-1 we loose the influence of the initial value for v but it is needed if the exact solution is required. 

We have derived exact memory-less differential equations by eliminating w(0) in terms of the value lift). This has been carried out analytically, and this has given formally correct equations. However, this process is not unique, because we get the same w(t) for several w(0). As long as 7 < fi, the inversion from (114)... 

Figure 3 Time evolution for two different initial conditions for over-damped situation with 7 = 3 and 0 = 1. Now w(t) i=- 0 for all finite t and the memory-less Master Equation has a unique solution.

The Markovian limit. The correct memory-less Markovian limit is the following... 

As an alternative to Master Equations with memory, many authors suggest memory-less equations with time dependent coefficients. This approach seems... 

The term memory-less signing (from [Gold87]) does not mean that the entity of a signer does not need any memory Even between transactions, some secret information has to be stored. Instead, it means that this memory is read-only after initialization in particular, no information about authentication transactions needs to be stored. In this case, the constant secret information is called the secret key. 

Although memory-less signing has been given some importance, e.g., in [Gold87, G0MR88], the only qualitative advantage I see is that it implies that the signer s access point can easily be duplicated (see Section 5.2.11, Local... 

Entities of recipients cannot be memory-less in the same sense as entities of signers, because they must store some information about each authenticated message they have received in case of disputes. Hence, memory-less receiving is used to denote that the actions of the recipient s entity in authentication do not depend on previous authentications and disputes. 

Schemes with more than one recipient per initialization (see Section 5.2.10, Dependence of Authentication on the Recipients ) are almost always memoryless at least, testing a new message must work no matter whether the earlier messages from the same signer had the same recipient or not. Similarly, courts are almost always memory-less . In contrast, the efficiency of schemes with fixed recipient or one recipient per initialization can often be improved by giving up memory-less receiving (see [FoPf91] or Section 10.6).

No dependence on the recipient. As mentioned in Section 5.3.2, such schemes are usually with memory-less receiving, but not always. A related structural property, however, is common to all existing schemes in this class The court s entity in a dispute acts as follows. 

If receiving is memory-less , in addition to all the conventions made so far, the special structure sketched in Section 3.2 has been reached. 

Test. The conventional definition is only formalized for the case where test is deterministic and receiving is memory-less (restriction restr2). 

The structure of disputes in standard fail-stop signature schemes was almost completely described in Section 6.1.2 (Subsection Number of Recipients and Complexity of Tests ) by the actions of the court s entity In Step 1, the court s entity tests the signature with the algorithm test defined above. (Now test is memory-less anyway, i.e., no special case is needed.) In Step 2, this signature is sent to the signer s entity, which can answer with a string called a proof of forgery. In Step 3, the court s entity verifies this proof... 

External verifiability of authentication is easy to achieve because authentication is non-interactive, public keys exist, and test is deterministic and memory-less restr If the message exchange during authentication, i.e., sending the signature, takes place on a reliable broadcast channel (as it is standard when external verifiability is considered), all entities that took part in initialization can test the signature with the same public key. 

Assume that J stmctures Mj are received, with j e 0,. J-1. The vectors pd and ij of length Lxj are derived as described above from each received stmcture. Further, we assume that the attack on the embedded watermark is memory less, that is all demodulated watermark letters are statistically independent. Thus, the probability p uc,i = 1) that the /th coded watermark bit Uc,i is 1, is given by... 

If sufficient high frequency components are present, then the mass of the memory kernel is typically found to be localized around 0 in such a situation of rapid decay it is found that one may replace the function by a Dirac delta function scaled by a positive coefficient y we say that the system is Markovian or memory-less in this situation and we replace the delay-differential equation (6.29) by the SDEs... 

A Markov system is defined as a "memory-less" system where the probability of moving from one state to another is dependent only upon the current state and not past history of getting to the state. This is the primary characteristic of a Markov model. Markov models are well suited to problems where a state naturally indicates the situation of interest. In some models (characteristic of reliability and safety models) a variable follows a sequence of states. These problems are called Markov chains. 

The second environmental factor is the attacker population. [18] shows that the exploit creation may occur according to a Pareto probabilistic distribution. However, knowing the exact date of Slammer worm creation, we modeled the worm creation event by a deterministically. To model system attacks, we assume exponential probabilistic distributions. This choice was motivated by the need of having a density function with a high decrease and not by the need of the memory less property of this density distribution. The data published in [29,30] help us to calculate the attack rate. Nevertheless, the SAN model developed in our study can be run using other types of distributions. 

In metallic systems, another important constitutive linear relationship has to be taken into account the free current density ] f which is generated by the electric field E. The free current density is added to the external current density in Eq. (1.4). For linear, memory-less, and isotropic media we have... 

Memory A suture s ability to return to its original shape after deformation. Similar to pliability (more memory = less pliability and less knot security)... 

The most prominent phosphoms polymers are nucleic acid (NA) and teichoic acid (TA) these naturally occurring polymers are not covered in this chapter. Backbones of NA and TA are composed of hydrolytically stable diesters of phosphoric acids. The major functions of DNA (and several types of RNA) are related to storing and transferring information, genetic code, synthesis of proteins with a given microstmcture, and contribution to the funaion of memory. Less known TA (mainly polyphosphates of glycerol or ribitol) with molar mass up to 2.5 x 10 are present in cell walls in Gram-positive baaeria. The main function of TAs is to provide... 

To make matters worse, this scenario is memory less, i.e., once the pressures revert to normal there is no indication as to what happened. Identification of the source of the contamination can be particularly difficult if the process chemical that has entered the utility header is used in many parts of the overall process. 

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