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After 400 Years, Scientists Have Discovered A New Class of Shape

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By Akshat Rathi, The Conversation

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The work of the Greek polymath Plato has kept millions of people busy for millennia. A few among them have been mathematicians who have obsessed about Platonic solids, a class of geometric forms that are highly regular and are commonly found in nature.

Since Plato’s work, two other classes of regular convex polyhedra, as the collective of these shapes are called, have been found: Archimedian solids and Kepler solids. Nearly 400 years after the last class was described, researchers claim that they may have now invented a new, fourth class, which they call Goldberg polyhedra. Also, they believe that their rules show that an infinite number of such classes could exist.

Platonic love for geometry

Regular convex polyhedra need to have certain characteristics. First, each of the sides of the polyhedra needs to be of the same length. Second, the shape must be completely solid: that is, it must have a well-defined inside and outside that is separated by the shape itself. Third, any point on a line that connects two points in a shape must never fall outside the shape.

Platonic solids, the first class of such shapes, are well known. They consist of five different shapes: tetrahedron, cube, octahedron, dodecahedron and icosahedron. They have four, six, eight, twelve and twenty faces, respectively.

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These highly regular structures are commonly found in nature. For instance, the carbon atoms in a diamond are arranged in a tetrahedral shape. Common salt and fool’s gold (iron sulfide) form cubic crystals, and calcium fluoride forms octahedral crystals.

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The new discovery comes from researchers who were inspired by finding such interesting polyhedra in their own work that involved the human eye. Stan Schein at the University of California in Los Angeles was studying the retina of the eye when he became interested in the structure of protein called clathrin. Clathrin is involved in moving resources inside and outside cells, and in that process it forms only a handful number of shapes. These shapes intrigued Schein, who ended up coming up with a mathematical explanation for the phenomenon.

second lastDuring this work, Schein came across the work of 20th century mathematician Michael Goldberg who described a set of new shapes, which have been named after him, as Goldberg polyhedra. The easiest Goldberg polyhedron to imagine looks like a blown-up football, as the shape is made of many pentagons and hexagons connected to each other in a symmetrical manner (see image to the left).

However, Schein believes that Goldberg’s shapes – or cages, as geometers call them – are not polyhedra. “It may be confusing because Goldberg called them polyhedra, a perfectly sensible name to a graph theorist, but to a geometer, polyhedra require planar faces,” Schein said.

Instead, in a new paper in the Proceedings of the National Academy of Sciences, Schein and his colleague James Gayed have described that a fourth class of convex polyhedra, which given Goldberg’s influence they want to call Goldberg polyhedra, even at the cost of confusing others.

A crude way to describe Schein and Gayed’s work, according to David Craven at the University of Birmingham, “is to take a cube and blow it up like a balloon” – which would make its faces bulge (see image to the right). The point at which the new shapes breaks the third rule – which is, any point on a line that connects two points in that shape falls outside the shape – is what Schein and Gayed care about most.

fourth lastCraven said, “There are two problems: the bulging of the faces, whether it creates a shape like a saddle, and how you turn those bulging faces into multi-faceted shapes. The first is relatively easy to solve. The second is the main problem. Here one can draw hexagons on the side of the bulge, but these hexagons won’t be flat. The question is whether you can push and pull all these hexagons around to make each and everyone of them flat.”

During the imagined bulging process, even one that involves replacing the bulge with multiple hexagons, as Craven points out, there will be formation of internal angles. These angles formed between lines of the same faces – referred to as dihedral angle discrepancies – means that, according to Schein and Gayed, the shape is no longer a polyhedron. Instead they claimed to have found a way of making those angles zero, which makes all the faces flat, and what is left is a true convex polyhedron (see image below).

Their rules, they claim, can be applied to develop other classes of convex polyhedra. These shapes will be with more and more faces, and in that sense there should be an infinite variety of them.

Playing with shapes

Such mathematical discoveries don’t have immediate applications, but often many are found. For example, dome-shaped buildings are never circular in shape. Instead they are built like half-cut Goldberg polyhedra, consisting of many regular shapes that give more strength to the structure than using round-shaped construction material.

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However, there may be some immediate applications. The new rules create polyhedra that have structures similar to viruses or fullerenes, a carbon isotope. The fact that there has been no “cure” against influenza, or common flu, shows that stopping viruses is hard. But if we are able to describe the structure of a virus accurately, we get a step closer to finding a way of fighting them.

If nothing else, Schein’s work will invoke mathematicians to find other interesting geometric shapes, now that regular convex polyhedra may have been done with.

This article was origianlly posted on The Conversation and can be read here.

Free Franco DeNicola Screening: The Shift In Consciousness

We interviewed Franco DeNicola about what is happening with the shift in consciousness. It turned out to be one of the deepest and most important information we pulled out within an interview.

We explored why things are moving a little more slowly with the shift at times, what is stopping certain solutions from coming forward and the important role we all play.

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Beijing Doctors Said 7 Coma Patients Would Not Wake Up — AI Predicted The Opposite, And Was Right

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In Brief

  • The Facts:

    AI technology has outsmarted doctors when it comes to coma patients. The lives of at least 7 individuals have been saved as a result.

  • Reflect On:

    Given the serious questions about AI, are there are ways that AI technology can aid our current systems on the planet? How do we decide when we have gone too far with AI?

Sometimes after tragic accidents, people lose their consciousness and enter a coma or unresponsive state. Doctors usually make the call as to whether or not there is any point in keeping these people alive or if the family should consider “pulling the plug.” Doctors know best, right?

Well, recently there were at least seven patients in Beijing who doctors said had no hope of being able to regain consciousness, they were then re-evaluated by an artificial intelligence system that predicted these patients would awaken within a year. Guess what? They did.

One of the awakened patients was a 19-year-old who spent six months with unresponsive wakefulness syndrome after an accident that left him with a severe injury to his left temple. Some of China’s top neurologists conducted numerous rounds of assessment to determine his potential for a recovery. They gave him seven out of a possible 23 points on the coma recovery scale, this score gave his family members the legal rights to take him off of life support if they chose to do so.

After going through his brain scans the computer software assessed him with over 20 points, which is much closer to the full score, which would mean a recovery.

Another patient was a 41-year-old female who was victim to a stroke; she had been in an unresponsive state for three months and had been assessed with a recovery score of six. The computers estimate? 20.23.

The two aforementioned individuals, in addition to five more patients who were also in an unresponsive state, who doctors had predicted would not recover or wake up, did within 12 months of the scan done by the artificial intelligence, just as predicted.

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The Machine Also Made Some Mistakes

Perhaps this is a good time to believe in the power of miracles, a 36-year-old man who had suffered bilateral brainstem damage after suffering from a stroke was given low scores by both the doctors and the AI. He still fully recovered in less than a year.

This AI system was developed after eight years of research, which was conducted by the Chinese Academy of Sciences and PLA General Hospital in Beijing and so far has achieved nearly 90 percent accuracy on all prognostic assessments.

Some of the results of this research were published in the journal, eLife.

“We have successfully predicted a number of patients who regained consciousness after being initially determined to have no hope of recovery,” the researchers said in a statement.

“At present, there are more than 500,000 patients with chronic disturbance of consciousness caused by brain trauma, stroke, and hypoexic encephalopathy with an annual increase of 70,000 to 100,000 patients in China, which brings great mental pain and a heavy burden to families and society,” they added.

“The possible prediction of the recovery of patient consciousness will directly affect the choice of clinical treatment strategies, and even the choice of life or death by the patient’s relatives.”

Associate researcher with the Institute of Automation, Chinese Academy of Sciences and the first author of this study, Dr. Song Ming, explained how the system they developed was different from other AI methods used in the diagnoses of diseases like cancer, “our machine can ‘see’ things invisible to the human eyes,” he said.

So How Does This Technology Work?

The patients are analyzed using a brain scan that includes functional magnetic resonance imaging, fMRI. This technology is able to chart the activity in the brain by measuring even the smallest changes in blood flow.

Because there are so many neural activities going on at once, they are not always directly visible to doctors, however the AI system is equipped with machine learning algorithms and is able to detect these changing details more accurately and recognize patterns that were previously unknown in past cases.

“The AI system assumes that every patient still has consciousness,” Song said. “Its job is to determine the likelihood they will come to within a certain period.

“It will never replace doctors. It is just a tool to help doctors and families make better decisions.”

The Positive Potential Of AI

Many, including myself for the most part, are generally under the impression that AI is something that we should be wary of, and I stand by that statement. But in instances such as these, we can see how this technology is developed and how when used by the right hands can actually be an amazing gift to humanity. There are many instances where AI and other forms of tech can drastically enhance our current models of doing things, with more precision and accuracy. It shouldn’t all be dismissed right away, and it shouldn’t all be given the green light either. We have to be able to use discernment and determine whether or not we are using this technology for the right reasons and what the potential implications of bringing in these new technological advancements to our lives and current system.

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Free Franco DeNicola Screening: The Shift In Consciousness

We interviewed Franco DeNicola about what is happening with the shift in consciousness. It turned out to be one of the deepest and most important information we pulled out within an interview.

We explored why things are moving a little more slowly with the shift at times, what is stopping certain solutions from coming forward and the important role we all play.

Watch the interview here.
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Scientists Discover A New & Efficient Way To Turn Sunlight Into Fuel

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In Brief

  • The Facts:

    A new process is able to effectively turn sunlight into fuel by combining natural processes and human made technologies.

  • Reflect On:

    With all of the emerging alternative energy sources that are becoming available to us, do we really need to be burning fossil fuels any longer?

The sun is a big burning ball of fire and thus, energy. Really, everything is energy. We already know that it is the light and warmth of the sun that gives life to every living thing on this planet. We have already seen an example of how the sun’s energy can be utilized to create power with the rapidly increasing use of solar panels, but researchers from St. John’s College, University of Cambridge, have now discovered a new way to utilize energy from the sun and turn it into fuel. Yes fuel — the type of fuel that could directly compete with fossil fuels.

The researchers used semi-artificial photosynthesis to explore new ways to produce and store solar energy. Using natural sunlight to separate hydrogen and oxygen including the use of a combination of biological components and human made technologies.

This research could revolutionize the way we are currently utilizing the sun for renewable energy production. Their method was able to absorb even more solar light than the natural process of photosynthesis. A paper, published in the journal Nature Energy described how the researchers were able to develop this process of unassisted, solar driven water splitting.

One of the authors of the study and PhD student at St. John’s college, Katarzyna Sokól said, “Natural photosynthesis is not efficient because it has evolved merely to survive so it makes the bare minimum amount of energy needed — around 1-2 percent of what it could potentially convert and store. “

One of the keys to this process is an ancient enzyme known as hydrogenase.

“Hydrogenase is an enzyme present in algae that is capable of reducing protons into hydrogen,” Sokól added.

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“During evolution this process has been deactivated because it was necessary for survival but we successfully managed to bypass the inactivity to achieve the reaction we wanted — splitting water into hydrogen and oxygen.”

The process of mimicking photosynthesis in order to collect and store energy is something that scientists have been experimenting with for years. However, according to Sokól, the earlier technologies are not capable of scaling up to industrial models for a myriad of different reasons — either they are too expensive, or inefficient of use materials could also pose a risk to the environment.

The team took the approach to create an electrochemical cell, similar to a traditional battery, but based on the light-collecting biochemistry of a process called photosystem II. This was able to provide the necessary voltage that is required for the hydrogenase enzyme to do do it’s job and reduce the amount of hydrogen in water so that it can separate from oxygen and become the gas it was born to be.

Although this process may sound simple, connecting artificial systems with natural and organic processes has proved to be quite challenging.

“This work overcomes many difficult challenges associated with the integration of biological and organic components into inorganic materials for the assembly of semi-artificial devices and opens up a toolbox for developing future systems for solar energy conversion,” says, Erwin Resner, author and laboratory head.

There is much more research that needs to be done, but this is a huge and important step towards being able to fully utilize this method for an alternate fuel source.

“This could be a great platform for developing solar technologies. The approach could be used to couple other reactions together to see what can be done, learn from these reactions and then build synthetic, more robust pieces of solar energy technology,” says Sokól.

“It’s exciting that we can selectively choose the processes we want, and achieve the reaction we want which is inaccessible in nature. This could be a great platform for developing solar technologies. The approach could be used to couple other reactions together to see what can be done, learn from these reactions and then build synthetic, more robust pieces of solar energy technology,” she added.

Final Note

While this is certainly a plus in the direction of moving toward new energy systems, these technologies have advanced counterparts in the realm of zero-point energy that can make an even greater impact on humanity, without the need for sunlight.

The challenge? It has often been said that if ‘free energy’ like technologies come out prior to humanity shifting their consciousness enough to truly handle these technologies, we will in essence use them in the exact same way we do now: patent them, limit them and then charge people extensively for energy. This does not help to free the population, but only keeps it enslaved, and abundance limited.

Much Love

 

 

Free Franco DeNicola Screening: The Shift In Consciousness

We interviewed Franco DeNicola about what is happening with the shift in consciousness. It turned out to be one of the deepest and most important information we pulled out within an interview.

We explored why things are moving a little more slowly with the shift at times, what is stopping certain solutions from coming forward and the important role we all play.

Watch the interview here.
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Wi-Fi Security – Measures to Prevent Technology Enabled Crimes

Every Wi-Fi user must know how to adopt security measures that will prevent them from becoming victims of wireless technology crimes.

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Considered as one of the greatest advancement since the Internet, Wi-Fi wireless networking technology has given mobility to computers. People use wireless technology in the office, at home, and in public places. Unless Wi-Fi users adopt some sort of security, various problems can result when computers transmit unsecured information to one another.

Bandwidth theft, exposed e-mail messages, password or user name theft, and hijacked online identity rank among the top problems brought about by unsecured Wi-Fi transmissions. Every Wi-Fi user must know how to secure their computer.

Use WPA Instead of WEP Encryption

Encryption protocols are used to make network traffic more secure by encoding data packets that are transmitted thereon. Unfortunately, some wireless routers don’t have encryption enable or use the weaker WEP (Wired Equivalency Privacy) security protocol.

It is well known that WEP security keys are easy to break and therefore network administrators should use the WPA or WPA2 protocols. Even if a router doesn’t support the more secure WPA or WPA2 protocols, WEP should be used; it is better than nothing.

Install a Firewall on Every Computer and Server

A firewall is the most basic and fundamental network security measure there is to secure wireless networks. While Wi-Fi routers can be used to extend the range of networks, they also make the network more vulnerable. A firewall will need to be installed on every computer to ward off security threats. This should be done even if the wireless router has a firewall installed on it.

Use Virtual Private Network (VPN)

B­asically, VPNs form a private network that uses a public network (usually the Internet) to connect remote sites or users together. VPNs use authenticated links to make sure that only authorized users can connect to a network. It also uses encryption to make sure that others can’t intercept and can’t use data that travels over the Internet. Numerous websites offer both free and paid VPN versions. VPNbase is one of them.

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Reduce the Transmitter Power of Network Access Points

Part of the convenience of using wireless networks is the ability to access services remotely. This strength also becomes a weakness, because others can see, and potentially use the network as well, especially when a powerful transmitter/antenna is being used.

To limit how far outside the premises the wireless signal travels, reduce the power output of wireless antennas. This requires some tweaking to find the right setting, because reducing the signal output of antennas also reduces the network’s service delivery and quality.

Disable Remote Administration

WLAN (wireless local area network) routers often come with the ability for a network administrator to remotely configure the router. By default, this feature is usually turned off and should stay that way if remote administration is not absolutely necessary. While network administrators can usually set passwords, to secure access to the router’s control panel, leaving the feature enabled could leave the network vulnerable as well.

Remove or Disable Weak Passwords and Access Codes

Ensure that all default passwords and access codes that come preset on network equipment are changed or disabled. Access the router’s web interface and update all settings that have a bearing on network security. Be sure the use strong passwords as well.

Physically Secure your Wireless Network Equipment

Hardware devices typically come with a hard reset button. Making network equipment readily available to be physically handled by anyone who wishes to do so puts the network at risk. Secure all critical and sensitive equipment in rooms or equipment racks.

Don’t Broadcast the Network’s SSID

To allow for the easy setup of wireless clients, most wireless access points will broadcast the SSID (Service Set IDentifier), or network name. While broadcasting the SSID makes setting up wireless clients easier, it also makes WLANs visible to wireless devices that are within range, including those that are malicious. Turn off SSID broadcast to make the network invisible and more secure.

Simple Wireless Network Security

Ensuring that a wireless network is secure is an ongoing responsibility. Wireless network threats, such as those posed by hackers and viruses can be thwarted by some common sense approaches such as physically securing network equipment and using strong encryption methods and technologies. However, the most effective security measures are those that seek to cover all the known security vulnerabilities.

Free Franco DeNicola Screening: The Shift In Consciousness

We interviewed Franco DeNicola about what is happening with the shift in consciousness. It turned out to be one of the deepest and most important information we pulled out within an interview.

We explored why things are moving a little more slowly with the shift at times, what is stopping certain solutions from coming forward and the important role we all play.

Watch the interview here.
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