We consider quantum systems driven by hamiltonians of the form H +W (t), where the spectrum of H consists in an innnite set of bands and W (t) depends arbitrarily on time. Let hHi ' (t) denote the expectation value of H with respect to the evolution at time t of an initial state '. We prove upper bounds of the type hHi ' (t) = O(t), > 0, under conditions on the strength of W (t) with respect to...

Our expectation of an event such as a visual stimulus clearly depends on previous experience, but how the brain computes this expectation is currently not fully understood. Because expectation influences the time to respond to a stimulus, we arranged for the probability of a visual target to suddenly change and found that the time taken to make an eye movement to it then changed continuously, e...

We present a mathematical solution to the insurance puzzle. Our solution only uses time-average growth rates and makes no reference to risk preferences. The insurance puzzle is this: according to the expectation value of wealth, buying insurance is only rational at a price that makes it irrational to sell insurance. There is no price that is beneficial to both the buyer and the seller of an ins...

An approach to reduce number of spurious symptoms in aircraft engine fault monitoring is investigated. Two strategies were utilized. A set of rules designed to filter spurious symptoms was created. Then a neural network was designed to generate expectation value for each of the sensors monitored. The neural net was trained for a specific engine during normal operation. After capturing patterns ...

We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a basic random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a great variety of distributions observed in nature, which can hardly be described by the conventional methods. As a simple example, we explicitly derive the...

• Distribution 2: Pr(0) = Pr(50) = Pr(100) = 1/3. Both have the same expectation: 50. But the first is much less “dispersed” than the second. We want a measure of dispersion. • One measure of dispersion is how far things are from the mean, on average. Given a random variable X , (X(s) − E(X)) measures how far the value of s is from the mean value (the expectation) of X . Define the variance of ...

We extend a result of Dubins (Ann Probab 3:89–99, 1975) from bounded to unbounded random variables. Dubins showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectat...

the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka's $d$-poset and prove the basic properties ofconditional expectation on this  structure.

In this paper, we firstly give a brief introduction of expectation maximization (EM) algorithm, and then discuss the initial value sensitivity of expectation maximization algorithm. Subsequently, we give a short proof of EM's convergence. Then, we implement experiments with the expectation maximization algorithm (We implement all the experiments on Gaussion mixture model (GMM) ). Our experiment...

Chern-Simons Theory with gauge group SU(N) is analyzed from a perturbation theory point of view. The vacuum expectation value of the unknot is computed up to order g6 and it is shown that agreement with the exact result by Witten implies no quantum correction at two loops for the two-point function. In addition, it is shown from a perturbation theory point of view that the framing dependence of...