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Function Points is a technique to measure the dimension of a software based on the functionalities that it has to offer. A weight is associated with each FP counts of different types; the total Unadjusted Function Points is computed by multiplying each “raw” c...

Architecture Java EE platform suggests a distributed multitiered architecture model for enterprise applications: Client Tier Application Clients: clients that run directly on the client machine. They are usuallyquite rich and they interact directly with th...

Identify every time a variable is defined (modified) and used with that version, for example: 1 int i, k = 0; 2 i = k; 3 while (i<10) 4 i++; The def-use pairs for k are <1, 2> while the ones for i are <2, 3>, <2, 4>, <4, 3>, <4, 4>. A more complex example: 0 ...

A Symbolic state is made by the tuple: <path-condition, symbolic bindings>. A simple example of a symbolic execution: read(a); read(b); x = a + b; write(x); We assign A to a and B to b, the printed result will be: A+B. When we have more than one path the exec...

Mean Time to Repair ($MTTR$): Average time between the occurrence of a fault and service recovery, also known as the downtime Mean Time To Failures ($MTTF$): Mean time between the recovery from one incident and the occurrence of the next incident, also kno...

Budget at completion ($BAC$): total budget for the project Planned value ($PV$): budgeted cost of work planned Earned value ($EV$): budgeted cost of work performed Actual cost ($AC$): actual cost for the completed work Schedule The project running behind...

It is used to estimate the minimum project duration. This schedule network analysis technique calculates the early start, early finish, late start, and late finish dates for all activities without delaying the project finish date or violating a schedule constr...

Complete course name: 051588 - MODEL IDENTIFICATION AND DATA ANALYSIS - 1ST MODULE (BITTANTI SERGIO) {051587 - MODEL IDENTIFICATION AND DATA ANALYSIS [sezione A]} Profesor: Simone Garatti Tutor: Marco Raffaele Rapizza Accademic year: 2021-2022 Recordings...

A signal is a function of time, usually symbolized $v(t,s)$. In a noisy signal, the exact value of the signal is random. Therefore, we will model noisy signals as a random function $v(t,s)$, where at each time $t$, $v(t,s)$ is a random variable. These “noisy s...

A stochastic process $v(t,s)$ is stationary if: $m_v(t)=m_v$ $\forall{t}$: the mean function is a constant $\gamma_v(t,\tau ) = \gamma_v(\tau )$ $\forall{t}$: the covariance is function only of the time lag $\tau$, not of the time $t$. In summary the partial ...

A white noise is a sequence of uncorrelated random variables with the same mean and the same variance. A stationary stochastic process is called white noise if: $\mathbb{E}[e(t,s)]=\mu$ $\forall t$ $Var[e(t,s)]=\mathbb{E}[(e(t,s)-\mu)^2]=\lambda^2$ $\forall t...

Given a zero mean white noise $e(t) \sim WN(0,\lambda^2)$ we define the moving average process of order $MA(n)$ as: $$y(t)=c_0e(t)+c_1e(t-1)+...+c_ne(t-n)$$ Which is a linear combination of the past values of $e(t)$ from $t$ to $t-n$ with real parameters $c_0...

AR processes Given a zero mean white noise $e(t) \sim WN(0, \lambda^2)$ then the stochastic process $y(t)$ is an auto regressive process if $y(t)$ is stationary and satisfies the recursive equation: $$y(t)=a_1y(t-1)+a_2y(t-2)+...+a_ny(t-n)+e(t)$$ which is a re...

The shift operators are: $z^{-1}$ backward shift operator $z^1$ forward shift operator Given a stochastic process $y(t,s)$ then $z^-1y(t,s)=y(t-1,s)$ which has the same realization shifted one time instant backwards. Properties The shift operators: are li...

A transfer function $W(z)=\frac{C(z)}{A(z)}$ is an operator that given a process $v(t)$ outputs the steady state solution of the recursive equation $y(t)$: $$y(t)=W(z)v(t) \iff A(z)y(t)=C(z)v(t)$$ We are particularry interested in the case when the proces $v(t...

Given the steady state output of the recursive equation defined by the transfer function $W(z)$ fed by the stochastic process $v(t)$: $$y(t)=W(z)v(t)$$ Then $y(t)$ is well defined iff: $v(t)$ is stationary $W(z)$ is assintotically stable So ARMA process $y(t...

If we consider a stationary stochastic process $v(t)$ and an assintotically stable transfer function $W(z)$ then the steady state solution of the recursive equation defined by the transfer function $W(z)$ is a well defined stationary stochastic process $y(t)$...

Given the ARMA process: $$y(t)=\frac{c_0+c_1z^{-1}+...+c_nz^{-n}}{1-a_1z^{-1}-...-a_mz^{-m}}e(t)=\frac{C(z)}{A(z)}e(t)$$ We can compute the weak (wide sense) characterization for a well defined $y(t)$ ($W(z)$ assintotically stable): $\mathbb{E}[y(t)]=m_y$ co...

Consider the ARMA process $y(t)=\frac{C(z)}{A(z)}e(t)$ where is a non zero mean white noise$e(t) \sim WN(\mu,\lambda^2)$. Gain theorem If $W(z)=\frac{C(z)}{A(z)}$ is assintotically stable, then: $$m_y=\mathbb{E}[y(t)]=\frac{C(1)}{A(1)}\mu$$ Unbiased processes ...

With ARMA we model time-series: we analize the output of a system without observing any input. In many application, however, we can observe an input process $u(t)$. $$ y(t)=a_1y(t-1)+...+a_my(t-m)+\newline b_0u(t-d)+b_1u(t-d-1)+...+b_pu(t-d-p)+\newline c_0e(t...