Policeman, jewelry, and burglar

Suppose some dark night a policemanwalks down a street, apparently deserted. Suddenly he hears a burglar alarm, looks across the street, and sees a jewelry store with a broken window. Then a gentleman wearing a mask comes crawling out through...

Logical implication

Show via Venn diagrams that the logical implication ($A\Rightarrow B$) is equivalent to the following expressions, \[A\bar{B} ~ \text{is false} ~,\] \[\bar{A} + B ~ \text{is true} ~,\] \[A = AB ~,\]

Logic implication, denial, equivalence

We have learned that the logical implication ($C\Rightarrow D$) is equivalent to the following expressions, \[C\bar{D} ~ \text{is false} ~,\] \[\bar{C} + D ~ \text{is true} ~,\] \[C = CD ~,\] Now, using the above expressions, show that if, \[(B\Rightarrow...

Venn diagram representation of Boolean expressions

Consider the following Boolean algebraic expressions. Draw a Venn diagram corresponding to each one,

Regression: Predicting the bivariate distribution of the a dataset subjected to censorship (sample incompleteness)

Problem Supposed we have observed a dataset comprised of $4975$ events with two attributes variable1 and variable2 points in this file: data.csv. Plotting these points would yield a scatter plot like the red points in the following plot, The pale...

Regression: Predicting the distribution of the a dataset subjected to censorship (sample incompleteness)

Problem Supposed we have observed a dataset comprised of $15027$ events with one attribute variable in this file: data.csv. Plotting these points would yield a red-colored histogram like the following plot, The pale black shaded area represents the missing points...

Best visualization coloring

Problem Consider the following color palettes. Which one is more appropriate for effective visualization communications with humans?

Regression: Predicting the global land temperature of the Earth in 2050 from the past data via the maximum likelihood approach

Problem Consider this dataset, usaTemperatureHistory.txt, which contains the global land temperature of the earth from 1743 to 2013 at every monthly resolution. As stated in the file, temperatures are in Celsius and reported as anomalies relative to the average global...

Regression: Predicting the global land temperature of the Earth in 2050 from the past data: linear vs. exponential temperature increase

Problem Consider this dataset, 1880_2020.csv, which contains the global land and ocean temperature anomalies of the earth from January 1880 to June 2020 at every month. As stated in the file, temperatures are in Degrees Celsius and reported as anomalies...

The different faces of binned data via different transformations

Problem Consider this CSV dataset containing the durations of a set of astrophysical events (T50 and T90), their corresponding 1-sigma uncertainties (T590err, T90err), the event IDs (Trigger) and the starting time of the events (T90Start) with respect to some reference...

Coordinates transformation for better visualization

Problem Consider the following plot. Explain the types of $x-$ and $y-$ axes of this plot. What type of mathematical function would best describe the initial (seemingly linear) phases of the three blue, yellow, and red curves in this plot?...

Implementing an integration problem via an integrand object

Problem Integration by midpoint rule: The idea of the Midpoint rule for integration is to divide the area under a curve $f(x)$ into $n$ equal-sized rectangles. The height of the rectangle is determined by the value of $f$ at the...

Making and using multiple Dynamic-Link Libraries (DLL) from within a single executable using the Intel Fortran Compiler on Windows OS

Consider the following set of Fortran module files: Constants_mod.f90, JaggedArray_mod.f90, String_mod.f90, Math_mod.f90. (These files are actually part of the ParaMonte library). These modules depend on each other: Math_mod uses Constants_mod and String_mod, String_mod uses Constants_mod and JaggedArray_mod, JaggedArray_mod uses Constants_mod,...

Intel Parallel Studio installation on Windows Operating Systems

Problem How can I install Intel Parallel Studio on Windows? Solution The Intel Parallel Studio provides a wide variety of High-Performance numerical libraries and tools, most importantly, the Intel Fortran and C/C++ compilers. However, its installation on Windows systems, in...

Regression: obtaining the most likely mean of a set of Standard Normally Distributed Random Variables

Problem Consider this dataset, Drand.mat, which contains a set of random numbers. Write a sctipt that computes the mean of this sample via the Least-Sum-of-Squares method. For this, you will need to use a funtion minimizer in the language of...

Regression: obtaining the most likely mean of a set of Standard Normally Distributed Random Variables via the least absolute deviations method

Problem Consider this dataset, Drand.mat, which contains a set of random numbers. Write a sctipt that computes the mean of this sample via the Least-Sum-of-Squares method. For this, you will need to use a funtion minimizer in the language of...

Regression: obtaining the most likely mean of a set of Standard Normally Distributed Random Variables via the least absolute deviations method

Problem Consider this dataset, Drand.mat, which contains a set of random numbers. Write a sctipt that computes the mean of this sample via the Least-Sum-of-Squares method. For this, you will need to use a funtion minimizer in the language of...

Monte Carlo sampling of the sum of two Gaussian distributions

Problem Suppose that you wanted to generate points whose distribution follows the blue curve in the following curve, whose mathematical formulation is known (in the case here, the function is just the sum of two Gaussian distributions), The equation describing...

Kmeans clustering

Problem Consider this dataset points.txt. Write a script that reads this dataset and plots the second column of the dataset versus the first column as the following, Now write another script that applies Kmeans clustering technique to this data set...

Regression: Predicting the global land temperature of the Earth in 2050 from the past data

Problem Consider this dataset, usaTemperatureHistory.txt, which contains the global land temperature of the earth from 1743 to 2013 at every monthly resolution. As stated in the file, temperatures are in Celsius and reported as anomalies relative to the average global...