Tag: Data

Daily Data Dump: Chicago homicides are decreasing, while homicide clusters still persist

 

2016 and 2017 Homicides in Chicago per Month

 

Homicides of Neighborhood/Homicides of Chicago

 

Number of Homicides per Neighborhood

 

 

Matt has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University. He is also a professional member of the Society of Industrial and Applied Mathematics and the International Society for the Systems Sciences and a scholarly member of Omicron Delta Epsilon, which is an International Honors Society for Economics. 

You can connect with him directly in the comments section, and follow him on Facebook

You can also follow The Systems Scientist on Twitter or Facebook.

 

Photo Credit: Pixabay

 

 

 

 

 

 

Copyright ©2017 – The Systems Scientist

Data Dump Saturday: United States Earnings by Education and Sex, 2015

In today’s data dump, there are three observations to keep in mind while sifting through the data. First, Graph 1 through Graph 4 illustrate that as education increases, earnings increase. This is the case for both men and women. Mathematically these observations are confirmed by a positive slope.

Graph 1

Second, there is an obvious earnings discrepancy between men and women at each level of the education ladder. As an example, the earnings of “Some College or associate’s degree” for men, $41,407, is slightly lower than the earnings of a “Bachelor’s degree” for women, $41,763. This is a fascinating statistic.

It should be noted that the purpose of this data dump is to provide information; the purpose of this data dump is not to take a side on earnings differences between men and women, nor is it to examine why it is so.

With that said, it should be noted that these discrepancies will change, increase or decrease, at different levels of the Super-system, which is the United States. For example, earnings differences between men and women will vary at the regional, the state level, the county, level, the city level, the zip code level, and so and so forth. And these earnings differences will change depending on geography, education (obviously), and industry and type of job, just to name a few parameters.

Lastly, Graph 2, Graph 3, and Graph 4 are simply partitions of Graph 1. That is, the three following graphs have been created to help the reader parse out the data a bit more clearly, i.e., make the data less busy. And it provides the reader with the opportunity to see the earnings behavior of the United States from different perspectives, while also providing the capability of comparing data in Graph 1.

Here’s Saturday’s data dump on 2015 earnings by education and sex in the United States.

Total Earnings by Education and Sex

 

Graph 2

Male Earnings by Education and Sex

 

Graph 3

Female Earnings by Education and Sex

 

Graph 4

 

Matt Johnson is a blogger/writer for The Systems Scientist and the Urban Dynamics blog. He has also contributed to the Iowa State Daily and Our Black News.

Matt has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University. He is also a professional member of the Society of Industrial and Applied Mathematics and the International Society for the Systems Sciences and a scholarly member of Omicron Delta Epsilon, which is an International Honors Society for Economics. 

You can connect with him directly in the comments section, and follow him on Facebook

You can also follow The Systems Scientist on Twitter or Facebook.

 

Photo Credit: Flickr

 

 

 

 

 

 

Copyright ©2017 – The Systems Scientist

Minneapolis crime pattern since 2013

With the Minneapolis mayoral and city council elections only a few weeks away, crime is still a top issue. How will the mayoral candidates fair and will crime continue to remain a top issue?

Graph 1

As Graph 1 illustrates, crime is seasonal as it goes through its peaks during the summer months and valleys during the winter months. What is also interesting about this graphical representation, besides the fact that it’s dynamical, is that it shows how crime decreased each year from 2013 through 2015.

You can check for yourself by aligning a ruler with the peak crime months of 2013, 2014, and 2015. As you’ll notice, the ruler is tipping downward, i.e., a downward (negative) slop.

But 2016 illustrates an increase when compared to the previous months and years; and it appears 2017 will maintain that trend of increasing crime.

Thus, you can perform the same exercise with the ruler with the peak months of 2015, 2016, and 2017. You’ll notice an increasing slope with this set of months, i.e., increasing crime rates.

Of course, the increasing slope of crime doesn’t appear to be as pronounced as the decreasing slop of crime, but the decrease and increase are obvious nonetheless. Something to think about with city elections on the horizon.

 

Matt Johnson is a blogger/writer for The Systems Scientist and the Urban Dynamics blog. He has also contributed to the Iowa State Daily and Our Black News.

Matt has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University. He is also a professional member of the Society of Industrial and Applied Mathematics and the International Society for the Systems Sciences and a scholarly member of Omicron Delta Epsilon, which is an International Honors Society for Economics. 

You can connect with him directly in the comments section, and follow him on Facebook

You can also follow The Systems Scientist on Twitter or Facebook.

 

Photo Credit: Wikimedia Commons

 

 

 

 

 

 

Copyright ©2017 – The Systems Scientist

 

Minneapolis: July’s Top 7 Neighborhoods for Crime in 2017

There are few things to consider when sifting through this data set. First, the highest number of reported crimes in Minneapolis are not in the Jordan neighborhood in North Minneapolis, or any  other neighborhood in North Minneapolis for that matter. To the contrary, Downtown West has the highest number of reported crimes. In fact, it has had the highest number of reported crimes in each month this year, and it generally does year after year.

Second, 6 of the 7 neighborhoods in the top 7 are not in North Minneapolis. Of course, this doesn’t mean there aren’t other North Minneapolis neighborhoods that don’t experience a relatively high number of crimes. As a group of neighborhoods, the north side definitely illustrates a concentration of reported crimes. This will be illustrated in a future blog.

Crime: Top 7 Neighborhoods 

Neighborhood Homicide Rape Robbery Aggravated Assault Burglary Larceny Auto Theft Arson Total
Downtown West 1 4 30 18 8 195 6 0 262
Whittier 0 1 6 5 12 59 5 0 88
Loring Park 0 2 7 3 2 55 3 0 72
Longfellow 0 1 6 2 12 46 3 0 70
Lowry Hills East 0 3 3 6 11 43 3 0 69
Marcy Holmes 0 1 5 2 6 40 12 0 66
Jordan 0 0 8 17 10 22 5 1 63
Total 1 12 65 53 61 460 37 1 690
(Crime/Total) x 100% 0.14 1.74 9.42 7.68 8.84 66.7 5.36 0.14 100

(Source: City of Minneapolis)

And lastly, 66.7 percent of the of the reported crimes of the top 7 neighborhoods are Larceny. Matter of fact, Larceny is between 65 and 75 percent of the reported crime each month in Minneapolis. Of course this statistic varies from neighborhood to neighborhood, but it’s a fairly consistent statistic for Minneapolis.

 

Matt Johnson is a blogger/writer for The Systems Scientist and the Urban Dynamics blog. He has also contributed to the Iowa State Daily and Our Black News.

Matt has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University. He is also a professional member of the Society of Industrial and Applied Mathematics and the International Society for the Systems Sciences and a scholarly member of Omicron Delta Epsilon, which is an International Honors Society for Economics. 

You can connect with him directly in the comments section, and follow him on Facebook

You can also follow The Systems Scientist on Twitter or Facebook.

 

Photo Credit: Tony Webster, Flickr

 

 

 

 

 

 

Copyright ©2017 – The Systems Scientist

Has the number of business establishments in Minneapolis increased since 2006?

Analyzing data always provides interesting insights. For example, a simple analysis of establishment (business) data from the Minnesota Department of Employment and Economic Development (DEED) reveals some fascinating insights into the systems dynamics – a system changing over time – of the Minneapolis marketplace with respect to business firms.

As the data, Graph 1, reveals, the number of establishments, or businesses, in Minneapolis has been decreasing for at least the past 10 years. Why is this so? This blog will not venture into such speculation. This is because the system’s perspective is limited to only establishment data. A multivariate perspective (multiple perspectives) is needed to find such possible reasons.

 

Graph 1

As Graph 1 illustrates, the number of firms per quarter has been decreasing since at least 2006. And although this rate has been variable, which is to be expected because the marketplace is probabilistic, the overall trend has been negative.

Furthermore, this overall negative trend can be shown in a couple of different ways. First, it can be illustrated via linearization. As Graph 2 shows, the overall trend is negative. That is, the Minneapolis marketplace decreased in the total number of establishments between the 1st Quarter of 2006 and the 3rd Quarter of 2016.

Graph 2

It should be noted that the linearization seen here is not the same linearization as in dynamical systems. In dynamical systems, linearization is an approximation “to a function at a given point.” Obviously this is not the case here.

Again, the main idea to take away from linearization, in the way it is used here, is the overall trend of the graph – did the marketplace gain businesses over the period stated in Graph 2, did the marketplace lose businesses over the period stated in Graph 2, or did the marketplace remain about the same over the period stated in Graph 2?

And finally, the marketplace behavior of business establishments in Minneapolis can be illustrated through Vector Algebra. Yes! That’s right – Vector Algebra. In this case, there will be no math included, just an illustration of direction via Graph 3, so there is no reason to be alarmed.

Graph 3

As Graph 3 shows, the overall dynamics, or vector, of the marketplace is negative in regards to the number of establishments from the 1st Quarter of 2006 through the 3rd Quarter of 2016. And the vectors, those letter “a’s” with the hats over them, further illustrate a greater decrease in total establishment between the 1st Quarter of 2006 and the 3rd Quarter of 2010 than between the 3rd Quarter of 2010 and the 3rd Quarter of 2016.

Of course, these vectors could further be broken into smaller vectors. But the way the algebra works, each vector that is computed in this system should add up to the overall vector, which is negative. Thus, this decomposition of the system behavior provides a more conclusive way of viewing the dynamics of this particular system than how linearization is being used here. And the vector idea, along with the math, supports the initial observation. That is, the total number of establishments in the Minneapolis marketplace has decreased since at least the 1st Quarter of 2006.

So how does this market behavior compare to the county or state level? How does Minneapolis compare to the zip codes that reside within it?

And another interesting question to ask one’s self is, has employment increased, decreased, or stayed the same in Minneapolis? And what does this mean for the number of employees per establishment?

 

Matt Johnson is a writer for the Urban Dynamics blog; and is a mathematical scientist. He has also contributed to the Iowa State Daily and Our Black News.

You can connect with him directly in the comments section, and follow him on LinkedIn or Facebook

Photo credit: The Systems Scientist

 

 

 

 

 

Copyright ©2017 – The Systems Scientist

 

A quick view of an economic system

By Matt Johnson

In this short blog, I will illustrate one way an urban dynamicist, i.e., systems scientist, looks at an economic system and its data.

Diagram 1

Diagram 1 is hierarchical, derives from the U.S. Census Bureau, and represents a few of the many levels of an economic system. Moreover, each level of the economic system in Diagram 1 is further a sub-system, or sub-economy, of the general United States economy.

This means that a zip code, for example, can be examined as an economic system, and then it can be compared and contrasted with a city’s economic system. And this examination will illustrate similarities and differences between a sub-system, a zip code, and a general system, a city, for instance.

Thus, an urban dynamicist can partition out each level of the economic system and analyze each level as a distinct entity, although one system is still a sub-system of the one superior to it in the hierarchy. Within each level, differences, relationships, perspectives, dynamics, and models can be examined through data.

As stated before, each level of the system can be analyzed against the other levels of the system through data, because data provides a picture at each level of the system. For example, the State can be illustrated and compared to the Division, Zip Code, or Census Tract via crime densities, demographic comparisons and migration patterns, and economic variables such as median household incomes, unemployment rates, the labor force and labor participation rates.

Here is the stochastic (probabilistic) behavior of the labor force in Minneapolis over the past 10 years as seen here in Graph 1.

Graph 1

And here is the stochastic (probabilistic) behavior of the Minnesota labor force over the past 10 years as illustrated in Graph 2.

Future articles will delve deeper into the specifics of the behavior and dynamics of these two systems and their respective data sets. For now, the main point is that data can provide a picture of the economic systems at their respective levels of the system.

One last thought, Diagram 1 does not illustrate the interactions or dynamics that take place within each level of the system by itself, nor does it account for a lot of things. This is why the data is needed. So assumptions and conclusions should be limited.

As this focus on data continues, I will be utilizing the hierarchical model and other systems models to help illustrate and explain how economic systems can be better understood. In addition, I will be using systems theory along with applied mathematics to explore the complexity of systems. But I will also be working diligently and meticulously to convey this information to you the best I can.

As I get better at explaining this stuff to you, I hope your knowledge of systems, mathematics, and economics increases as well.

 

Matt Johnson is a writer for the Urban Dynamics blog; and is a mathematical scientist. He has also contributed to the Iowa State Daily and Our Black News.

You can connect with him directly in the comments section, and follow him on Facebook

Photo credit: Pixabay

 

 

 

 

 

Copyright ©2017 – The Systems Scientist

 

 

With new technology, mathematicians turn numbers into art

Once upon a time, mathematicians imagined their job was to discover new mathematics and then let others explain it.

Today, digital tools like 3-D printing, animation, and virtual reality are more affordable than ever, allowing mathematicians to investigate and illustrate their work at the same time. Instead of drawing a complicated surface on a chalkboard, we can now hand students a physical model to feel or invite them to fly over it in virtual reality.

Last year, a workshop called “Illustrating Mathematics” at the Institute for Computational and Experimental Research in Mathematics (ICERM) brought together an eclectic group of mathematicians and digital art practitioners to celebrate what seems to be a golden age of mathematical visualization. Of course, visualization has been central to mathematics since Pythagoras, but this seems to be the first time it had a workshop of its own.

The atmosphere was electric. Talks ran the gamut, from wildly creative thinkers who apply mathematics in the world of design to examples of pure mathematical results discovered through computer experimentation and visualization. It shed light on how powerful visualization has become for studying and sharing mathematics.

Reimagining math

Visualization plays a growing role in mathematical research. According to John Sullivan at the Technical University of Berlin, mathematical thinking styles can be roughly categorized into three groups: “the philosopher,” who thinks purely in abstract concepts; “the analyst,” who thinks in formulas; and “the geometer,” who thinks in pictures.

Mathematical research is stimulated by collaboration between all three types of thinkers. Many practitioners believe teaching should be calibrated to connect with different thinking styles.


Borromean Rings, the logo of the International Mathematical Union.
John Sullivan

Sullivan’s own work has benefited from images. He studies geometric knot theory, which involves finding “best” configurations. For example, consider his Borromean rings, which won the logo contest of the International Mathematical Union several years ago. The rings are linked together, but if one of them is cut, the others fall apart, which makes it a nice symbol of unity.

The “bubble” version of the configuration, shown below, is minimal, in the sense that it is the shortest possible shape where the tubes around the rings do not overlap. It’s as if you were to blow a soap bubble around each of the rings in the configuration. Techniques for proving that configurations like this are optimal often involve concepts of flow: If a given configuration is not the best, there are often ways to tell it to move in a direction that will make it better. This topic has great potential for visualization.

At the workshop, Sullivan dazzled us with a video of the three bands flowing into their optimal position. This animation allowed the researchers to see their ideas in action. It would never be considered as a substitute for a proof, but if an animation showed the wrong thing happening, people would realize that they must have made an error in their mathematics.


In this version of the Borromean Rings, a virtual ‘soap bubble’ is blown around the wire-frame configuration.
John Sullivan

The digital artists

Visualization tools have helped mathematicians share their work in creative and surprising ways – even to rethink what the job of a mathematician might entail.

Take mathematician Fabienne Serrière, who raised US$124,306 through Kickstarter in 2015 to buy an industrial knitting machine. Her dream was to make custom-knit scarves that demonstrate cellular automata, mathematical models of cells on a grid. To realize her algorithmic design instructions, Serrière hacked the code that controls the machine. She now works full-time on custom textiles from a Seattle studio.

Edmund Harriss of the University of Arkansas hacked an architectural drilling machine, which he now uses to make mathematical sculptures from wood. The control process involves some deep ideas from differential geometry. Since his ideas are basically about controlling a robot arm, they have wide application beyond art. According to his website, Harriss is “driven by a passion to communicate the beauty and utility of mathematical thinking.”

Mathematical algorithms power the products made by Nervous System, a studio in Massachusetts that was founded in 2007 by Jessica Rosenkrantz, a biologist, and architect, and Jess Louis-Rosenberg, a mathematician. Many of their designs, for things like custom jewelry and lampshades, look like naturally occurring structures from biology or geology.

Their first 3-D printed dress consists of thousands of interlocking pieces designed to fit a particular model. In order to print the dress, the designers folded up their virtual version, using protein-folding algorithms. A selective laser sintering process fused together parts of a block of powder to make the dress, then let all the unwanted powder fall away to reveal its shape.

Meanwhile, a delightful collection called Geometry Games can help everyone, from elementary school students to professional mathematicians, explore the concept of space. The project was founded by mathematician Jeff Weeks, one of the rock stars of the mathematical world. The iOS version of his “Torus Games” teaches children about multiply-connected spaces through interactive animation. According to Weeks, the app is verging on one million downloads.

Mathematical wallpaper

My own work, described in my book “Creating Symmetry: The Artful Mathematics of Wallpaper Patterns,” starts with a visualization technique called the domain coloring algorithm.

I developed this algorithm in the 1990s to visualize mathematical ideas that have one dimension too many to see in 3-D space. The algorithm offers a way to use color to visualize something seemingly impossible to visualize in one diagram: a complex-valued function in the plane. This is a formula that takes one complex number (an expression of the form a+_b_i, which has two coordinates) and returns another. Seeing both the 2-D input and the 2-D output is one dimension more than ordinary eyes can see, hence the need for my algorithm. Now, I use it to create patterns and mathematical art.


A curve with pleasing 5-fold symmetry, constructed using Fourier techniques.
Frank A Farris

My main pattern-making strategy relies on a branch of mathematics called Fourier theory, which involves the superposition of waves. Many people are familiar with the idea that the sound of a violin string can be broken down into its fundamental frequencies. My “wallpaper functions” break down plane patterns in just the same way.

My book starts with a lesson in making symmetric curves. Taking the same idea into a new dimension, I figured out how to weave polyhedral solids – think cube, dodecahedron, and so on – from symmetric bands made from these waves. I staged three of these new shapes, using Photoshop’s 3-D ray-tracing capacity, in the “Platonic Regatta” shown below. The three windsails display the symmetries of Platonic solids: the icosahedron/dodecahedron, cube/octahedron and tetrahedron.


A Platonic Regatta. Mathematical art by Frank A. Farris shows off three types of polyhedral symmetry: icosahedral/dodecahedral, cube/octaheral and tetrahedral.
Frank Farris

About an hour after I spoke at the workshop, mathematician Mikael Vejdemo-Johansson had posted a Twitter bot to animate a new set of curves every day!

Mathematics in the 21st century has entered a new phase. Whether you want to crack an unsolved problem, teach known results to students, design unique apparel or just make beautiful art, new tools for visualization can help you do it better.

This article was updated on April 5, 2017 with the full name of Mikael Vejdemo-Johansson.

Frank A. Farris, Associate Professor of Mathematics, Santa Clara University

Photo Credit:  Frank Farris

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This article was originally published on The Conversation. Read the original article.