What is the difference between theoretical and experimental values

Asked by: Rhiannon Valdovinos asked in category: General Last Updated: 4th April, What is the difference between theoretical and experimental values? Theoretical value is the value a scientist expects from an equation, assuming perfect or near-perfect conditions. Experimental value , on the other hand, is what is actually measured from an experiment. Therefore, I might measure only This is my experimental value. What are some examples of experimental probability?

What is the formula for experimental probability? What is better theoretical or experimental physics? All physicists study the physical properties of the universe. Theoretical physicists develop mathematical models while experimental physicists perform tests on specific physical phenomena.

Solution: Now, we are looking for the theoretical probability. Question 1d: What can we do to reduce the difference between the experimental probability and theoretical probability? Do better in math today Get Started Now.

Introduction to probability 2. Organizing outcomes 3. Probability of independent events 4. Comparing experimental and theoretical probability 5. Determining probabilities using tree diagrams and tables 6.

Probability of independent events 7. Probability 8. Addition rule for "OR" 9. Multiplication rule for "AND" Conditional probability Laws of total probability Bayes' rule Probability with Venn diagrams Back to Course Index.

Don't just watch, practice makes perfect. Experimental probability VS. Theoretical probability. Bon rolled a 6-sided dice 16 times and recorded the outcomes shown. Does the chart provide information about experimental or theoretical probability?

Mutual information in bits can be calculated with the expression a measure that gives the average bits that can be predicted in given the state [ 21 ]. The calculation of mutual information includes the calculation of probabilities and joint probabilities of any estate and. To apply to the Kuramoto model described in the previous section, we divided the 66 regions of the original network into 6 clusters proposed by Hagmann et al.

In addition, and following [ 22 ], time series for each cluster were calculated as the synchrony between the oscillators belonging to that cluster. Then, we characterized these series as synchronized or not synchronized by constructing new binary time series from each. We selected this value because it was the median of , and using the median for thresholding eliminates the possible influence of extreme values, due to its robust properties. In addition, there was a theoretical reason for this election.

Finally, was calculated to these binary series and the result was taken as the complexity value of the Kuramoto model. In order to calculate an estimation of the PCI in the Kuramoto model, it was necessary to solve two problems in the simulation process. The first one was to perturb or stimulate the system from an external source to emulate the effects of TMS , and the second difficulty we found was to calculate reliable ERPs for the final PCI calculation.

The problem of the stimulation was easily solved since it has been done in other studies. For example, Hellyer et al. Hence, in our study we followed these studies and perturbed the system by transient increases in the connectivity between six oscillators located in the parietal cortex see Figure 1.

We randomly repeated this stimulation 15 times for each numerical integration of the model. The next step was to build reliable ERPs with the resulting phases from the oscillators.

To achieve this goal we simulated EEG series, and then, ERPs were calculated for each model by averaging the segments associated with each period of stimulation.

We explain this procedure in detail in the next two sections. The EEG activity from 32 sensors was simulated for each condition in agreement with the following weighted sum of the activity in each oscillator: where is the time series from sensor th and is the weighted contribution of source th in sensor th.

Each was calculated using a standard forward model algorithm [ 25 ] applied according to the Talairach coordinates of the oscillators. After that, each oscillator was considered a cortical source. Second, the weights of these sources were normalized to a maximum value of 1.

Because in the ERPs the interesting information is in the amplitude, we calculated the envelope of with the Hilbert transform.

Envelopes of the signal were then used to construct the ERPs with the average of all segments in each realization of the model. Formally, ERPs were built with the analytical signal in the complex plane of which is where is the original signal and represents the real part of the new complex series and is the imaginary part from the Hilbert transform with as the imaginary operator. The modulus is the amplitude or the analytic power of the signal and can be easily calculated with.

These new series were considered the activity from each sensor and the ERPs were built with segments extracted from them. PCI was obtained following the original algorithm in Casali et al. The signals were downsampled ten times to obtain a sampling rate similar to real data. SS was used as input for the Lempel-Ziv measure [ 26 ] to estimate the algorithmic complexity. The algorithm seeks for the minimal number of patterns necessary to describe the sequence.

PCI is defined as the normalized value of :. The results for the Kuramoto simulations are characterized in the first place to understand the basic dynamics of the model. In addition, we include graphical descriptions of the ERPs to visualize the structure of the averaged waves at each sensor from simulated perturbations. In Figure 3 a we show a diagram with the behavior in the baseline condition at several values of its coupling parameter. The most important property in the evolution of is the metastability that can be estimated by the variability of.

In addition, it is important to note that the frequency structure in is not fixed for all s. One can observe in Figure 3 a that the frequency of seems to increase with the increase of. To better understand this phenomenon, we include a spectral decomposition of the evolution of in Figure 3 b. Surprisingly, we found a complex landscape in the oscillatory structure of.

The general structure of the spectral diagram showed a resemblance with the bifurcation diagram of the classical logistic map.

This similarity appeared because it showed a bifurcation-like proliferation of frequency components as the parameter increased. The nature of this spectral structure, however, was not explored and goes beyond the goals of this study.

If we inspect Figure 3 b , it can be stated that the end of slow oscillatory properties of high metastability was evident at. As increases further, larger and larger synchronized clusters are formed, resulting in a reduced number of components, until approaches 1, with ultimately only a single component as tens to infinity [ 27 ]. Accordingly, in Figure 3 b , the main frequency of the signal slowly increased with , and the components of seemed to increase with as well following a complicated pattern.

It is also noteworthy that in Figure 3 b another bifurcation-like region for can be perceived that consists in a reduction in the number of components. Hence, by the end of the landscape, seems to be more simpler with less oscillatory properties and probably this could lead to low values of and PCI.

The shape of this diagrams led us to consider that and PCI could be sensitive to the bifurcation region in. If metastability is a necessary condition for brain functioning [ 16 ] it would be reasonable to think that should diminish in the low metastability region.

The same should be true for PCI if this measure is closely related to. As we will show in the next sections, the reduction after metastability was only found for.

The relation between and PCI was assessed using Pearson product-moment coefficient between the values of obtained for each of the -levels from. Thus, apparently, and PCI are linearly independent. A graphical description of the evolution of and PCI and the metastability of the model can be observed in Figure 4. Values were calculated with. However, the PCI did not show a significant decrease in this region of.

In fact, the PCI evolution seems to progressively increase with. The fact that there is no decrease in PCI does not mean that this measure is not related to ; as seen before, a closer exploration of both measures indicated a positive relation between them.

Under the assumption that conscious states come from integrated information in a system, various metrics have been proposed to try to quantify consciousness. In the present work, we tested two of them using a neurocomputational model. On the other hand, the PCI distinguishes conscious versus unconscious states at a single patient precision [ 10 ].

Sometimes, an error that is acceptable at one step can get multiplied into a larger error by the end. Experimental error is defined as the difference between an experimental value and the actual value of a quantity. This difference indicates the accuracy of the measurement. A random error is related to the precision of the instrument. If the experimental value is less than the accepted value, the error is negative.

If the experimental value is larger than the accepted value, the error is positive. In experiments, it is always possible to get values that are way greater or lesser than the true value due to human or experimental errors.

To identify a random error, the measurement must be repeated a small number of times. If the observed value changes apparently randomly with each repeated measurement, then there is probably a random error.

The random error is often quantified by the standard deviation of the measurements. The term defect rate designates the portion of defective elements in relation to all items produced. The rate is deduced by dividing the number of defective elements by the number of non-defective elements.