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The blockchain network lives in a state of consensus, one that automatically checks in with itself every ten minutes. A kind of self-auditing ecosystem of a digital value, the network reconciles every transaction that happens in ten-minute intervals. Each group of these transactions is referred to as a “block”. Two important properties result from this:

Transparency It cannot be corrupted

In theory, this could be possible. In practice, it’s unlikely to happen. Taking control of the system to capture Bitcoins, for instance, would also have the effect of destroying their value.

Blockchain solves the problem of manipulation . When I speak about it in the West, people say they trust Google, Facebook, or their banks. But the rest of the world doesn’t trust organizations and corporations that much — I mean Africa, India, the Eastern Europe, or Russia. It’s not about the places where people are really rich. Blockchain’s opportunities are the highest in the countries that haven’t reached that level yet.” Vitalik Buterin, inventor of Ethereum


(computer connected to the blockchain network using a client that performs the task of validating and relaying transactions) gets a copy of the blockchain, which gets downloaded automatically upon joining the blockchain network.

Together they create a powerful second-level network, a wholly different vision for how the internet can function.

Every node is an “administrator” of the blockchain , and joins the network voluntarily (in this sense, the network is decentralized). However, each one has an incentive for participating in the network: the chance of winning Bitcoins .

Nodes are said to be “mining” Bitcoin, but the term is something of a misnomer. In fact, each one is competing to win Bitcoins by solving computational puzzles. Bitcoin was the raison d’etre of the blockchain as it was originally conceived. It’s now recognized to be only the first of many potential applications of the technology.

There are an estimated 700 Bitcoin-like cryptocurrencies (exchangeable value tokens) already available. As well, a range of other potential adaptations of the original blockchain concept are currently active, or in development.

“Bitcoin has the same character a fax machine had. A single fax machine is a doorstop. The world where everyone has a fax machine is an immensely valuable thing.” Larry Summers, Former US Secretary of the Treasury

By design, the blockchain is a decentralized technology.

Anything that happens on it is a function of the network as a whole. Some important implications stem from this. By creating a new way to verify transactions aspects of traditional commerce could become unnecessary. Stock market trades become almost simultaneous on the blockchain, for instance — or it could make types of record keeping, like a land registry, fully public. And decentralization is already a reality.

Electron tomography studies of thin sections of the DEB at the secretory stage of enamel formation were performed using a Tecnai 12 transmission electron microscope (FEI, Hillsboro, OR, USA), equipped with an LaB6 filament, at 120 kV. Tomography tilt series of thin-sectioned samples were acquired at nominal magnifications of ×23,000 to ×26,000. The micrographs were recorded automatically using a bottom-mounted Gatan 2000 charge-coupled device (CCD) camera (Gatan, Warrendale, PA, USA). The micrographs were taken in a tilt range from –60° to 60°, with a 1° increment from –45° to 45°, and a 0.5° increment from –60° to –45° and from 45° to 60°. Because of the strong contrast of mineralized samples, the images were aligned using fiducial-less procedure in the IMOD 3.9 reconstruction package (University of Colorado, Boulder, CO, USA). Three-dimensional density maps were reconstructed from the tilt-series images using C himera software (University of California, San Francisco, CA, USA).

HR-TEM of the DEB was performed using a Tecnai F20 (FEI) microscope equipped with a field-emission gun at 200-kV accelerating voltage. The images were recorded using a Gatan 4k × 4k CCD camera. The power spectra of the lattice images of mineral crystals at the DEB were created and analyzed using imagej 1.44 image-processing software (NIH, Bethesda, MD, USA).

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The TEM image of the DEB at the secretory stage revealed that the von Korff fibrils of mantle dentin were intimately associated with enamel mineral particles ( Great Deals Online Miko Butter Shoes For Cheap Sale Online 100% Guaranteed For Sale QneoinC
). The mineral crystallites in the mineralized von Korff fibrils, as well as the ribbon-like 10- to 20-nm-thick enamel mineral particles in the aprismatic enamel layer were found to be oriented normal to the DEB plane, indicating the continuity of the crystal orientation between dentin and enamel. Higher-magnification micrographs showed that the enamel crystals directly interface with dentin crystallites, and many of them are ‘embedded’ into the mineralized von Korff fibrils ( POMPON Mules blu Prices Cheap Online Get To Buy Shopping Online With Mastercard DTlTgTNrRa

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Fig. 1

Transmission electron microscopy (TEM) micrographs of the dentino–enamel boundary (DEB) in non-demineralized sections of the midsecretory stage of enamel formation at low magnification (A) and high magnifications (B–D). Note that the dentin and enamel mineral are tightly integrated at the DEB. Arrowheads point to the adjacent dentin crystallites in the mineralized von Korff fibrils and enamel crystals (*).

To gain a better understanding of the relationships between the mineralized collagen fibrils in mantle dentin and the mineral particles of secretory enamel, we carried out a series of ET studies of areas of the DEB, located at different distances from the cervical loop. In the region of initial enamel mineral deposition we observed a number of enamel mineral particles intimately attached to the mineralized von Korff fibrils ( Fig. 2 , Video S1 ). The three-dimensional (3D) reconstruction of the area shown in Fig. 2A revealed a long ribbon-like enamel mineral particle that was closely associated with a mineralized collagen fibril ( Fig. 2B,C ) and with the mineral crystals within the fibril, and that its long axis was co-aligned with the crystallites in the fibril ( Fig. 2 , Video S1 ). Figure 3 and Video S2 represent a tomographic reconstruction of the area of the DEB at the late secretory/transitional phase of enamel formation. At this stage the enamel crystals are much more numerous; however, they are similarly intertwined with the crystallites of the mineralized collagen fibrils of mantle dentin. Overall, the tomography studies indicate that the enamel mineral at the DEB is integrated into the mineralized von Korff fibrils and exists in very close physical contact with dentin crystallites at the nanoscale level.

Other ideas aren’t so lucky. Do we instinctively see the growth of e, or is it an abstract definition? Do we realize the rotation of i, or is it an artificial, useless idea?

I still have to remind myself about the deeper meaning of e and i — which seems as absurd as “remembering” that a circle is round or what a cat looks like! It should be the natural insight we start with.

Missing the big picture drives me crazy: math is about ideas — formulas are just a way to express them. Once the central concept is clear, the equations snap into place. Here’s a strategy that has helped me:

Step 1: Find the central theme of a math concept. Step 2: Explain a property/fact using the theme. Step 3: Explore related properties using the same theme

Let’s try it out.

Understanding the number e has been a major battle. e appears all of science, and has numerous definitions, yet rarely clicks in a natural way. Let’s build some insight around this idea. The following section will have several equations, which are simply ways to describe ideas . Even if the equation is gibberish, there’s a plain-english idea behind it.

Here’s a few popular definitions of e:

The first step is to find a theme. Looking at e’s history , it seems it has something to do with growth or interest rates. e was discovered when performing business calculations (not abstract mathematical conjectures) so “interest” (growth) is a possible theme.

Let’s look at the first definition, in the upper left. The key jump, for me, was to realize how much this looked like the formula for compound interest. In fact, it is the interest formula when you compound 100% interest for 1 unit of time, compounding as fast as possible.

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describes this interpretation.

Let’s look at the second definition: an infinite series of terms, getting smaller and smaller. What could this be?

After noodling this over using the theme of “interest” we see this definitions shows the components of compound interest . Now, insights don’t come instantly — this insight might strike after brainstorming “What could 1 + 1 + 1/2 + 1/6 + …” represent when talking about growth?”

Well, the first term (1 = 1/0!, remembering that 0! is 1) is your principal, the original amount. The next term (1 = 1/1!) is the “direct” interest you earned — 100% of 1. The next term (0.5 = 1/2!) is the amount of money your interest made (“2nd level interest”). The following term (.1666 = 1/3!) is your “3rd-level interest” — how much money your interest’s interest earned!

Money earns money, which earns money, which earns money, and so on — the sequence separates out these contributions (read the article on e to see how Mr. Blue, Mr. Green Mr. Red grow independently). There’s much more to say, but that’s the “growth-focused” understanding of that idea.

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