text:
# manufacture

## Definitions

• a Workshop of Shoemakers Manufacturing Sandals
• WordNet 3.6
• v manufacture make up something artificial or untrue
• v manufacture put together out of artificial or natural components or parts; He manufactured a popular cereal" "the company fabricates plastic chairs","They manufacture small toys"
• v manufacture create or produce in a mechanical way "This novelist has been manufacturing his books following his initial success"
• v manufacture produce naturally "this gland manufactures a specific substance only"
• n manufacture the organized action of making of goods and services for sale "American industry is making increased use of computers to control production"
• n manufacture the act of making something (a product) from raw materials "the synthesis and fabrication of single crystals","an improvement in the manufacture of explosives","manufacturing is vital to Great Britain"
• ***

Manufacture of an Incandescent Lamp

Webster's Revised Unabridged Dictionary
• Interesting fact: 40 percent of the almonds in the world are used by manufacturers of chocolate
• Manufacture Anything made from raw materials by the hand, by machinery, or by art, as cloths, iron utensils, shoes, machinery, saddlery, etc.
• Manufacture The operation of making wares or any products by hand, by machinery, or by other agency.
• v. i Manufacture To be employed in manufacturing something.
• Manufacture To make (wares or other products) by hand, by machinery, or by other agency; as, to manufacture cloth, nails, glass, etc.
• Manufacture To work, as raw or partly wrought materials, into suitable forms for use; as, to manufacture wool, cotton, silk, or iron.
• ***
Century Dictionary and Cyclopedia
• Interesting fact: Draftsmen have to make 27,000 drawings for the manufacturing of a new car.
• n manufacture The operation of making goods or wares of any kind; the production of articles for use from raw or prepared materials by giving to these materials new forms, qualities, properties, or combinations, whether by hand-labor or by machinery: used more especially of production in a large way by machinery or by many hands working coöperatively.
• n manufacture Anything made for use from raw or prepared materials; collectively, manufactured articles; figuratively, anything formed or produced; a contrivance.
• n manufacture A place or building in which manufacturing operations are carried on; a factory.
• manufacture To make or fabricate, as anything for use, especially in considerable quantities or numbers, or by the aid of many hands or of machinery; work materials into the form of: as, to manufacture cloth, pottery, or hardware; to manufacture clothing, boots and shoes, or cigars.
• manufacture Figuratively, to produce artificially; elaborate or get up by contrivance or special effort; hence, to make a show of; simulate: as, to manufacture words or phrases; a manufactured public opinion; manufactured grief or emotion.
• manufacture To use as material for manufacture; work up into form for use; make something from: as, to manufacture wool into cloth.
• manufacture To be occupied in manufactures; fabricate or elaborate something.
• ***
Chambers's Twentieth Century Dictionary
• Interesting fact: Proctor & Gamble originally manufactured candles before moving on to soap.
• v.t Manufacture man-ū-fakt′ūr to make from raw materials by any means into a form suitable for use
• v.i Manufacture to be occupied in manufactures
• n Manufacture the process of manufacturing: anything manufactured
• ***

## Quotations

“We are all manufacturers. Making good, making trouble, or making excuses.”
• Woodrow T. Wilson
“Character is a by-product; it is produced in the great manufacture of daily duty.”
• Oliver Wendell Holmes
“Nature, when she invented, manufactured, and patented her authors, contrived to make critics out of the chips that were left.”
• Simone Weil
“Culture is an instrument wielded by teachers to manufacture teachers, who, in their turn, will manufacture still more teachers.”
• Watts Humprey
“INNOVATION is the process of turning ideas into manufacturable and marketable form.”
• Benjamin Ricketson Tucker
“We enact many laws that manufacture criminals, and then a few that punish them”

## Etymology

Webster's Revised Unabridged Dictionary
L. manus, the hand + factura, a making, fr. facere, to make: cf. F. manufacture,. See Manual, and Fact

## Usage

### In literature:

It is quite true that all the things she has bought from us were not produced or manufactured by us.
"Are we Ruined by the Germans?" by Harold Cox
What would become of the porcelain manufacture without it?
"Old and New London" by Walter Thornbury
Other important manufactures are automobiles (value, 1905, $4,256,979) and telescopes. "Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 5" by Various Coco-nut oil is also used in the manufacture of marine soap, which forms a lather with sea-water. "Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 6" by Various The poorer grades are employed in the manufacture of soap, candles and phonograph records. "Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 5" by Various There are few manufactures. "Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 6" by Various Manufactured primarily by Bennett in Chicago in 1859, it also may have been produced in the East, although no manufacturer's name can be found. "The Invention of the Sewing Machine" by Grace Rogers Cooper He is also indebted to many manufacturers who have furnished him with particulars and photographs of dredging plant. "Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 7" by Various The value of gross manufactured products increased 41.9% from 1890 to 1900. "Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 1" by Various The third importation was made by Sir Titus Salt, the English manufacturer of mohair, and arrived in South Africa in 1857. "Practical Angora Goat Raising" by C. P. Bailey Spirits are distilled from sugar-cane, and coarse sugar is manufactured. "Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 3" by Various American manufacturers in general copied the English styles, though they also developed several variations. "Colonial Homes and Their Furnishings" by Mary H. Northend It has a good harbour, fishing, trade in agricultural products, and manufactures of tobacco, salt and iron goods. "Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 10" by Various Foreign manufacturers, however, were able to standardize by reason of the large uniform demand which existed for their manufactures. "Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 2" by Various The firm that manufactures artillery and shells probably gets an order for half a dozen equipments and I suppose the contract time is liberal. "Over Here" by Hector MacQuarrie He took out a patent, but the manufacturers leagued themselves against them. "Triumphs of Invention and Discovery in Art and Science" by J. Hamilton Fyfe Then came many public trials and contests between rival manufacturers and inventors. "Inventions in the Century" by William Henry Doolittle Mr. Webster did not contest the constitutional right of Congress to lay duties for the protection of manufactures. "The Works of Daniel Webster, Volume 1" by Daniel Webster I'm in charge of the complete office organization of a brand-new manufacturing business that's to start up here. "Get-Rich-Quick Wallingford" by George Randolph Chester The principal manufactures are mining pumps and machinery, flour, woollen goods, lumber and furniture. "Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 4" by Various *** ### In poetry: The rear, in awful silence still, Trooped bravely up the hill, Led on by manufacture Dick, And George with umbrella stick. "The Watch And Ward." by Samuel Bamford The sound, without a pause between, Of foot, and wheel, and hoof ; The manufacture's loud machine From yonder lengthened roof. "A Town" by Jane Taylor "No — vile Manufacture! ne'er harbour A hope to be fed at our boards; — Base offspring of Arkwright the barber, What claim canst thou have upon Lords? "Cotton and Corn" by Thomas Moore He capped a flask and hissed a quiet curse — Bleakly smiling, tapped a switch to bleed A pressure vessel. (Clearly what he needs, To manufacture his own Universe, "The Alchemist" by Rainer Maria Rilke Therefore, good people, his goods are really grand, And manufactured at Weensforth Mill, Hawick, Scotland; Where there's always plenty of Tweeds on hand, For the ready cash at the people's command. "Lines in Praise of Mr. J. Graham Henderson, Hawick" by William Topaz McGonagall To think they have found a clever man indeed, That knows good wool and how to manufacture Scotch tweed, I wish you success for many a long day, Because your Scotch tweeds are the best, I venture to say. "A Tribute to Mr J. Graham Henderson, The World's Fair Judge" by William Topaz McGonagall ### In news: The National Institute of Standards and Technology (NIST) has announced that manufacturing industry executive Michael F Molnar has been appointed as the agency's first-ever chief manufacturing officer. The Rally Rails are manufactured from polished stainless steel for maximum rust protection, according to the manufacturer. We've reported before about various plans to improve the manufacturing of carbon fiber composites for use in mainstream automobile manufacturing. Plexus learned on Nov 5 that Juniper would stop using its manufacturing services by the end of the current fiscal year, the Neenah-based manufacturer said on a conference call Wednesday. Pfizer has two manufacturing facilities in Germany for high- potency manufacturing, respectively in Freiburg and Illertissen. Last year, Far East manufacturing centers experienced two high-profile natural disasters that highlighted for manufacturers and supply chain and operations managers the pressing need for risk mitigation strategies. Nearly every major computer manufacturer has one, and some manufacturers are explicitly targeting businesses that want a cheaper alternative for employees than full-blown laptops. Utility Trailer Manufacturing announced the expansion of its refrigerated trailer manufacturing plant in Marion, Va. American Axle & Manufacturing Holdings Inc.'s Detroit manufacturing complex may get new life as a plan is in the works for a new supplier to lease a portion of the plant. Zoned M15 (heavy manufacturing) and RP (auto parking), an existing manufacturing or warehousing operation could move to the site on a turn-key basis. The five buses were manufactured by Collins Bus Corp. And delivered to the district by the manufacturer's Oregon-based distributor, Western Bus Sales. Watlow, a designer and manufacturer of complete thermal systems with locations around the world, has moved its Mexican manufacturing operation in Queretaro to a larger facility, increasing the company's manufacturing capacity. Pfizer employs about 3,200 people in Kalamazoo County, many of whom work at its large manufacturing plant in Portage -- the company's largest manufacturing plant worldwide. George Rountree, 48, was charged with manufacturing methamphetamine , possession of methamphetamine and for children being present during the manufacture of methamphetamine . AMT--The Association for Manufacturing Technology has released the second generation of its Manufacturing Mandate, a plan that calls for a national, coordinated strategy to boost US manufacturing co mpetitiveness. *** ### In science: These speciﬁcations are among the most severe ever realised in radio telescopes and force the designer and manufacturer to push the boundaries of the technology. Study of the Dynamics of Large Reflector Antennas with Accelerometers Manufacturing and Service Operations Management, forthcoming. Martingale proofs of many-server heavy-traffic limits for Markovian queues Zero-inﬂated Poisson regression, with an application to defects in manufacturing. Accounting for self-protective responses in randomized response data from a social security survey using the zero-inflated Poisson model So we are investigating manufacturing another cell for the scientiﬁc instrument to avoid this problem which is only a limitation in the ﬁnal ﬂux (which may also be compensated by other actions). Laboratory performances of the solar multichannel resonant scattering spectrometer prototype of the GOLF-New Generation instrument The HPL developers recommended to HPL users willing to test matrices of size larger than 215 to not use power two. 2007 – numerical failure report – A large manufacturer observed a numerical failure with HPL and n = 2, 220, 032. The Problem with the Linpack Benchmark Matrix Generator Abstract —A monolithic pixel sensor in deep-submicron SiliconOn-Insulator (SOI) CMOS technology has been designed, manufactured and characterised. A Sensor with Analog and Digital Pixels in 0.15 micron SOI Technology If the path compensators do not step exactly in multiples of one delay step (due to manufacturing tolerances in the path compensators), there will be unsampled gaps in ∆τ. A spectral synthesis method to suppress aliasing and calibrate for delay errors in Fourier transform correlators However, it is certainly possible to adjust things to ”manufacture” supersymmetry by simply constructing Lagrangian that is written in non-supersymmetric form in regular coordinates (as opposed to superspace), but simply happens to satisfy supersymmetry transformations. Novel definition of Grassmann numbers and spinor fields In light of the fact that in this paper we have already ”manufactured” non-supersymmetric theory by adjusting measure, there is no reason to stop us from ”manufacturing” supersymmetric theories as well if we want to. Novel definition of Grassmann numbers and spinor fields In this work, for the ﬁrst step, we investigated the feasibility of manufacturing a large size gaseous photon detector with CsI photocathode and evaluated its performance. Development of a large area gas photomultiplier with GEM/$\mu\$PIC
Scintillator was manufactured at the scintillator workshop of IHEP with the use of molding technology.
Performance of a fine-sampling electromagnetic calorimeter prototype in the energy range from 1 to 19 GeV
The authors would like to thank the RIMST (Zelenograd) group for their help and sensors manufacturing.
Response of the CALICE Si-W Electromagnetic Calorimeter Physics Prototype to Electrons
Beyond background rejection capabilities, P-PC detectors also have potentially increased manufacturing speed, lower cost, simpler construction and data analysis, and decreased thermal load and photon path.
The Majorana Neutrinoless Double-Beta Decay Experiment
PC detectors are not difﬁcult to produce, the new detectors have validated ﬁeld calculation codes and simulations that allow us to determine the impurity gradient requirements and the dimensions to which such detectors can reliably be manufactured.
The Majorana Neutrinoless Double-Beta Decay Experiment
Our set of algorithms is a building block that can be immediately used by operators and manufacturers to block malicious trafﬁc in a cost-efﬁcient way.
Optimal Filtering of Malicious IP Sources
***


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# Private Load Shape Algorithm Design¶

A common visualization in the energy efficiency sector is the “average load shape”, like this one from the California ISO (CAISO):

A load shape is the trace of energy usage over a given time period. It is useful at a number of timescales (hourly, daily, weekly). An average load shape averages the load shapes of a number of buildings together to understand overall energy usage patterns for a population.

What differential privacy mechanism is best suited for average load shapes?

[1]:

# Preamble: imports and figure settings

from eeprivacy import (
PrivateVectorClampedMeanLaplace,
PrivateVectorClampedMeanGaussian,
)

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import matplotlib as mpl
from scipy import stats

np.random.seed(1234) # Fix seed for deterministic documentation

mpl.style.use("seaborn-whitegrid")

MD = 28
LG = 36
plt.rcParams.update({
"figure.figsize": [25, 25],
"legend.fontsize": MD,
"axes.labelsize": LG,
"axes.titlesize": LG,
"xtick.labelsize": LG,
"ytick.labelsize": LG,
})

## A Semantic Model for Load Shapes¶

The first challenge that private load shapes presents is determining an appropriate sematic model of privacy. That is, since each figure contains multiple data points per individual building, how should privacy budget be allocated per data point?

If data points in a time series figure are not correlated, then privacy budget can be reset between each data point. For an overall $$\epsilon_G$$, each data point’s $$\epsilon_i = \epsilon_G$$.

However, if data points are correlated, then the value from one point in time in the figure could be used to undermine the privacy protection of another. The privacy budget $$\epsilon_G$$ must be shared over the entire set of points in the figure.

Perhaps at some time resolutions, data are highly correlated, but, at others, they are not. Minutely energy data would exhibit high correlation, while annual average consumption would exhibit much less.

In this example, we adopt a strict semantic model: privacy budget is never reset.

A few examples of privacy harms from energy data suggest that this is necessary:

• Occupancy is highly correlated across days

• Average energy consumption is highly correlated across days

In a previous example, we considered the case of a high profile environmentalist being embarrassed by secretly high energy consumption. This high energy consumption would be apparent at almost any hour of the day.

Therefore, we must bound privacy loss to the entire time series.

## Candidate Mechanisms¶

We will compare two mechanisms for private load shapes:

1. Laplace Mechanism

2. Gaussian Mechanism

The Laplace Mechanism adds less noise per data point than the Gaussian Mechanism, but the noise is scaled to the L1 norm of the dataset rather than the L2 norm.

For a small number of points per building per figure, the Laplace Mechanism will outperform the Gaussian Mechanism. As the number of points increases, the Gaussian Mechanism’s L2 scaling will overtake the accuracy benefit of the Laplace Mechanism.

## Sample Data Set¶

We will consider queries against a residential energy consumption dataset.

A reasonable upper bound for household energy consumption is 2 kWh, which translates into a sensitivity $$\Delta$$ = 2.

We are interested in average load shapes across a variety of time ranges – hourly, weekly, and daily – at the hourly resolution.

• Daily: An average day’s energy consumption, 24 points per building

• Weekly: An average week’s energy consumption, 168 points per building

• Monthly: An average houry’s energy consumption, 672 points per building

We will consider a variety of population sizes from 100 to 100,000 buildings.

Finally, we will seek an error of +/- 0.1 kWh per hour at 95% confidence.

[2]:

x = np.linspace(100, 100000, num=300)

def epsilons(points_per_building=0):
ret = []
for N in x:
private_mean_op = PrivateVectorClampedMeanLaplace(
lower_bound = 0,
upper_bound = 2,
k = points_per_building,
N = N
)
ci = private_mean_op.epsilon_for_confidence_interval(
target_ci = 0.1,
confidence = 0.95
)
ret.append(ci)
return ret

daily_epsilons_laplace = epsilons(points_per_building=24)
weekly_epsilons_laplace = epsilons(points_per_building=168)
monthly_epsilons_laplace = epsilons(points_per_building=672)

def epsilons(points_per_building=0):
ret = []
for N in x:
private_mean_op = PrivateVectorClampedMeanGaussian(
lower_bound = 0,
upper_bound = 2,
k = points_per_building,
N = N
)
ci = private_mean_op.epsilon_for_confidence_interval(
target_ci = 0.1,
confidence = 0.95,
delta = 1/(N**2)
)
ret.append(ci)
return ret

daily_epsilons_gaussian = epsilons(points_per_building=24)
weekly_epsilons_gaussian = epsilons(points_per_building=168)
monthly_epsilons_gaussian = epsilons(points_per_building=672)

fig, ax = plt.subplots()

ax.plot(x, daily_epsilons_laplace,
label="Daily - Laplace", color="r", linestyle="dashed", linewidth=3)
ax.plot(x, weekly_epsilons_laplace,
label="Weekly - Laplace", color="r", linestyle="solid", linewidth=3)
ax.plot(x, monthly_epsilons_laplace,
label="Monthly - Laplace", color="r", linestyle="dashdot", linewidth=3)
ax.plot(x, daily_epsilons_gaussian,
label="Daily - Gaussian", color="k", linestyle="dashed", linewidth=3)
ax.plot(x, weekly_epsilons_gaussian,
label="Weekly - Gaussian", color="k", linestyle="solid", linewidth=3)
ax.plot(x, monthly_epsilons_gaussian,
label="Monthly - Gaussian", color="k", linestyle="dashdot", linewidth=3)

ax.set_xscale("log")
ax.set_yscale("log")
plt.xlabel("Population Size (log scale)")
plt.ylabel("Required ε (log scale)")
plt.legend()

from matplotlib.ticker import ScalarFormatter, FormatStrFormatter
for axis in [ax.xaxis, ax.yaxis]:
axis.set_major_formatter(FormatStrFormatter("%.0f"))

ax.xaxis.grid(True, which='minor')
ax.yaxis.grid(True, which='minor')

plt.show()

format: plain


text:
 math handbook calculator - Fractional Calculus Computer Algebra System software
+ + =

# acot(x)

The circular cotangent differs from the hyperbolic cotangent in having imaginary units in the exponential, plus an extra factor from the sine. Solving for the exponential gives

$cotw=i eiw +e−iw eiw -e−iw =z (i-z) e2iw +i+z =0 eiw =z+i z-i w=cot−1z =12i ln(z+i z-i)$

Applying the behavior of the logarithm, the inverse circular cotangent on an arbitrary branch is

$cot−1z =12i ln(z+i z-i) +πn$

The individual branches look like this:

The imaginary part of this function retains the same numerical value between branches, while the real part moves up and down in value. Visualize the real part of several branches simultaneously:


text:
# Prove that $a^4+b^4+c^4+a^3(b+c)+b^3(a+c)+c^3(a+c)-3a^2bc-3ab^2c-3abc^2 \geq 0.$

For every three real numbers $a,b,c$ prove that $$a^4+b^4+c^4+a^3(b+c)+b^3(a+c)+c^3(a+c)-3a^2bc-3ab^2c-3abc^2 \geq 0.$$

Attempt

I was thinking of using AM-GM but that seems like it would make it worse. I rewrote it as $$a^4+b^4+c^4+a^3(b+c)+b^3(a+c)+c^3(a+c)-3a^2bc-3ab^2c-3abc^2 = a^4+b^4+c^4+(b+c)(a^3+(a+c)(b^2-bc+c^2)+(b^3+c^3)(a+c)-3a^2bc-3ab^2c-3abc^2$$ Then I don't see how this helps to show it is greater than or equal to 0.

• Shouldn't that $c^3(a+c)$ be $c^3(a+b)$ given the pattern of others? – user64066 Jan 2 '16 at 20:23
• According to my book no, but it could be a typo. – Jacob Willis Jan 2 '16 at 20:43
• @JacobWillis: It is a typo, or else it would be false for $a=20$, $b=20$, $c=19$. – darij grinberg Jan 2 '16 at 21:16

Assuming the correction suggested by user64066, the left hand side factors as $\left(a+b+c\right)^2\left(a^2+b^2+c^2-bc-ca-ab\right)$. While $\left(a+b+c\right)^2$ is clearly nonnegative, the nonnegativity of $a^2+b^2+c^2-bc-ca-ab$ is well-known (for example, it follows from $2\left(a^2+b^2+c^2-bc-ca-ab\right)=\left(b-c\right)^2+\left(c-a\right)^2+\left(a-b\right)^2 \geq 0$). So the left hand side is nonnegative, qed.


text:
# Book: CategoryDuality

See: Math Notebook

Investigation: Explore how duality is broken by comparing a category and its opposite category?

• What are categories related to logic?
• What are examples in math where a category is isomorphic to its opposite category?
• When is a category actually equal (not merely isomorphic) to its opposite category?

Examples to study:

• Set (and the tiniest versions)
• Top (and the tiniest versions)
Parsiųstas iš http://www.ms.lt/sodas/Book/CategoryDuality
Puslapis paskutinį kartą pakeistas 2019 vasario 13 d., 15:20


text:
# Glossary

List of terms and definitions to help you get started in Web3.

## 0-9

### 51% attack

A condition in which more than half the computing power of a cryptocurrency network is controlled by a single malicious miner or group of miners. If he controls 51% of the network that makes him the authority on the network, giving him the power to spend the same coins multiple times, issue transactions that conflict with someone else’s or stop someone else’s transaction from being confirmed

## A

### Abstract

An abstract is defined as a summary of a larger written written document. Abstracts are common in the beginning cryptocurrency technical documents to briefly describe the entire document.

### Account

An account is access to a computer, website or software that allows users to use the tools located within. Access is usually gained through a username and password but with cryptocurrencies, it is often done with what is known as a private key.

Used to receive and send transactions on the network. An address is a string of alphanumeric characters, but can also be represented as a scannable QR code.

### Agreement ledgers

Distributed ledgers used by two or more parties to negotiate and reach agreement.

### Airdrop

An airdrop is the process of freely distributing a new cryptocurrency to people hopefully creating more demand. When a new cryptocurrency is created, it needs to gain users. One way of doing this through an airdrop. The group issuing the airdrop hopes new users will begin researching and sharing the coin creating more demand. To start an airdrop, the crypto group will often find people who already have another cryptocurrency and identify them as being equipped with wallets that can accept these airdropped coins. Their other option is to have people voluntarily complete a form where they will then receive their coins. NOTE: Beware of any website that asks for your private keys. DO NOT share your private keys with anyone unless you trust them with your money!

### Algorithm

An algorithm is a series of steps that will solve a problem. In cryptocurrencies, algorithms are used to hide and reveal information.

### Alphanumeric

Alphanumeric is something made up of both letters and numbers. Alpha- comes from the word “alphabet” and -numeric comes from the word “numerical” meaning relating to numbers.

### Altcoin

An abbreviation of “Bitcoin alternative”. Currently, the majority of altcoins are forks of Bitcoin with usually minor changes to the proof of work (POW) algorithm of the Bitcoin blockchain. The most prominent altcoin is Litecoin. Litecoin introduces changes to the original Bitcoin protocol such as decreased block generation time, increased maximum number of coins and different hashing algorithm

### Anonymous

Anonymous is something made or done by an unknown person or group. Compare this definition with “pseudonymous” which means acting or done under a false name.

### Anti-Money Laundering (AML)

Anti-Money Laundering or AML is a set of laws designed to prevent the conversion of illegally earned money into what appears to be legally earned money. Money laundering is the process of making illegally earned money appear to be legally earned.

### Application-Specific Integrated Circuit

Application-Specific Integrated Circuit is commonly known as ASIC. “Integrated circuit” is just a computer chip. “Application-specific” means it was built for one specific purpose or computer application. An ASIC is used in cryptocurrencies to help record transactions on the digital record or blockchain. This process is known as mining.

### Arbitrage

Arbitrage is the business of making money by buying something for a low price in one market and selling it in another for a profit. Arbitrage can be done with virtually any product including cryptocurrencies.

### ASIC

An acronym for “Application Specific Integrated Circuit”. ASICs are silicon chips specifically designed to do a single task. In the case of bitcoin, they are designed to process SHA-256 hashing problems to mine new bitcoins.

### ASIC Miner

ASIC is short for “Application-Specific Integrated Circuit”. And that’s a computer chip or “integrated circuit” which was built for the single purpose of mining cryptocurrencies. Mining is the process of recording on a digital record, known as the blockchain, money being received and spent. All of this is requires computer power and is done in return for money. Because an ASIC is built specifically for mining, it does the job faster than other computers and can earn more digital money.

### ATH

ATH is short for All Time High. ATH is the highest price an investment has ever reached in its history. Whenever a cryptocurrency price passes its ATH, things can get crazy. While many leading investors thought bitcoin would hit an ATH of $10,000 by the end of 2018, it actually did so on December 6th, 2017. The price continued to rocket upward hitting$18,000 on the 8th. Time will tell if bitcoin can pass that and hit an even higher cost.

### Atomic Swap

Atomic Swap is technology that allows two different people to exchange different cryptocurrencies directly. Right now, if you wanted to exchange bitcoin for ethereum, with another, you couldn’t. However, any coin using Atomic Swap can be exchanged for any other coin also using Atomic Swap.

### Attestation Ledgers

Distributed ledgers that provide a durable record of agreements, commitments or statements, providing evidence (attestation) that these agreements, commitments or statements were made.

## B

### Initial Coin Offering (ICO)

ICOs are types of crowdfunding mechanisms conducted on the blockchain. Originally, the main idea of an ICO was to fund new projects by pre-selling coins/tokens to investors interested in the project. Entrepreneurs present a whitepaper describing the business model and the technical specifications of a project before the ICO. They lay out a timeline for the project and set a target budget where they describe the future funds spending (marketing, R&D, etc.) as well as coin distribution (how many coins are they going to keep for themselves, token supply, etc.). During the crowdfunding campaign, investors purchase tokens with already established cryptocurrencies like Bitcoin and Ethereum.

### Input

Input describes digital money coming into your digital wallet. When you want to spend your money, your inputs are later used as proof to show that you have X amount of money. That is known as an “output”.

### Instamine

Instamining means new cryptocurrencies, for a short time after launch, are very easy to create. The purpose of instamining is to accumulate a large quantity of the available supply early on and later sell it for a big profit. Mining is a computer process of recording and verifying information on the digital record known as the blockchain. Mining usually also involves computers working very hard at solving a math problem. The first computer to solve this problem would discover a new block and could record information on the blockchain. This earned them a reward in brand new digital money plus fees paid for each transaction.

### Invest

Invest is the process of spending money on something with the expectation that it will increase in value later and can be sold for more money.

### IPFS

The InterPlanetary File System (IPFS) is a hypermedia distribution protocol, addressed by content and identities. IPFS enables the creation of completely distributed applications. It aims to make the web faster, safer, and more open. IPFS is an open source project developed by the team at Interplanetary Networks and many contributors from the open source community. It is a peer-to-peer distributed file system that seeks to connect all computing devices with the same system of files. In some ways, IPFS is similar to the Web, but IPFS could be seen as a single BitTorrent swarm, exchanging objects within one Git repository. In other words, IPFS provides a high throughput content-addressed block storage model, with content-addressed hyperlinks. This forms a generalized Merkle DAG, a data structure upon which one can build versioned file systems, blockchains, and even a Permanent Web. IPFS combines a distributed hash table, an incentivized block exchange, and a self-certifying namespace. IPFS has no single point of failure, and nodes do not need to trust each other

## J

### JOMO

JOMO is short for Joy of Missing Out. This is the pleasure of doing what you are doing and not worrying about anything worthwhile you might be missing out on.

## K

### Key

A key is a secret string of letters and numbers that must be used to make hidden, unreadable information readable.

Know Your Customer or KYC is a set of laws where financial organizations must request government issued identification from their customers before allowing them to use their services. KYC was established to prevent criminals from converting their illegally earned money into digital money to hide it from the police.

## L

### Ledger

A ledger is a book or other collection of records in which a person, business, or other group records how much money it receives and spends.

### Leverage

Leverage is increased investment power through margin. Margin is a borrowed asset (stocks or cryptocurrencies), usually from the financial services company you are investing with, that allows you to make larger investments in the hopes of making even more money. Leverage allows the investor to control much more assets than he actually owns giving him the opportunity to make or lose more money.

### Light Node

A computer on a blockchain network that only verifies a limited number of transactions relevant to its dealings, making use of the simplified payment verification (SPV) mode

### Lightning Network

The Lightning Network is technology that allows near-instant and low fee transactions of cryptocurrencies using bitcoin’s technology. With cryptocurrencies like bitcoin, it can take an average of 10 minutes for your transaction to be registered in the digital recording known as the blockchain. The Lightning Network will make those transactions instant.

## M

Margin trading describes a way of investing where you use margin. Margin increases your investment power. Margin is a borrowed asset (stocks or cryptocurrencies), usually from the financial services company you are investing with, that allows you to make larger investments in the hopes of making even more money. This advantage is known as leverage. The borrowed assets aren’t free, you must pay back interest on each transaction involving margins. Margin allows the investor to control much more assets than he actually owns giving him the opportunity to make or lose more money.

### Tokenless ledger

A distributed ledger that doesn’t require a native currency to operate.

### Total Supply

Total supply is the complete amount of coins currently available for a cryptocurrency not including any coins that were burnt. Burning coins is the action of sending cryptocurrency to an address which is unspendable.

### Transaction (TX)

Transaction or TX, is the transfer of money from one person to another for a business deal.

### Transaction block

A collection of transactions on the bitcoin network, gathered into a block that can then be hashed and added to the blockchain.

### Transaction fees (TX Fee)

Small fees imposed on some transactions sent across the bitcoin network. The transaction fee is awarded to the miner that successfully hashes the block containing the relevant transaction.

### Trustless

Trustless is a positive quality where you are not required to trust the person you’re doing the transaction with. A trustless system or technology is so secure and smooth in handling your transactions, that both people in a transaction can safely hand over money and other valuables without the risk of being cheated.

### Turing completeness

A machine is Turing complete if it can perform any calculation that any other programmable computer is capable of. All modern computers are Turing-complete in this sense. The Ethereum Virtual Machine (EVM) which runs on the Ethereum blockchain is Turing complete. Thus it can process any “computable function”. It is, in short, able to do what you could do with any conventional computer and programming language

## U

### Unpermissioned ledgers

Have no single owner (Ex. Bitcoin) — indeed, they cannot be owned. The purpose of an unpermissioned ledger is to allow anyone to contribute data to the ledger and for everyone in possession of the ledger to have identical copies.

### Unregulated

Unregualted describes something that is not managed and controlled according to rules. Cryptocurrencies remain unregulated by many governments.

### Unspent Transaction Output (UTXO)

Unspent Transaction Output or UTXO, is a list of money received that has not yet been spent. In other words, if you were to total up the UTXO, you would get the user’s available balance. Bitcoin and other cryptocurrencies based on its technology use UTXO in their blockchain technology to verify that a person has unspent crypto available for spending.

## V

A vanity address starts is a string of letters and numbers that is publicly available and starts with a customized set of letters and numbers. Your address allows cryptocurrency to be received, held and sent.

### Venture

A venture is a business that has a large risk of failure.

### Venture Capital

Venture capital is money provided to new companies that hold a promise of long-term growth. In exchange for the money, the companies will share ownership. Because they are new companies and have no history of success, they usually have a higher risk of failure.

### Volatility

Volatility is the measurement of how much the price of an asset is likely to change over a period of time. Stocks for established companies like Apple and Google have a much lower volatility than cryptocurrencies which may change a lot in one day.

## W

### Wallet

A wallet is software that interacts with the network of recordings (blockchain) and lets users receive, store, and send their digital money. The wallet doesn’t actually store the money, instead it locks away access to the money. The only way to get access to it is by providing a key, a string of letters and numbers like a password.

### Weak Hands

Weak hands describes an investor who doesn’t have the confidence in his investment to continue holding while the price falls so he sells it.

### Wei

Wei is the smallest amount of ethereum coin. One ethereum coin is worth 1 quintillion (1,000,000,000,000,000,000) wei.

### Whales

Whales are people or organizations that hold large quantities of cryptocurrency or stocks in a company. Because they can move buy and sell large quantities, they can greatly affect the price based on whether they buy or sell.

### Whisper

Whisper is a part of the Ethereum p2p protocol suite that allows for messaging between users via the same network that the blockchain runs on. The main task of whisper will be the provision of a communication protocol between dapps

### White Paper

A white paper is a document that explains the purpose and technology used in a cryptocurrency. Usually a white paper is used when a cryptocurrency is just starting to help people understand what it has to offer. A clear, simple white paper is a good sign for a new cryptocurrency.

## Z

### Zero Confirmation Transaction

A zero confirmation transaction, means a seller who is receiving cryptocurrency as part of a deal doesn’t wait for verification that the money was sent and instead immediately delivers what was sold.


text:
## Introduction

Stroke is a leading cause of death worldwide and the leading cause of permanent disability1,2. About 80% of stroke cases are of ischaemic origin3. The risk of ischaemic stroke (IS) is determined by a complex interplay of genetic and environmental factors partly acting through modifiable risk factors such as hypertension and diabetes. Roughly thirty-five genomic loci have been robustly associated with stroke4,5,6,7, and many more genetic associations have been reported for stroke-related risk factors8,9,10,11,12,13,14, e.g., over 1000 loci have been associated with blood pressure (BP)11,15,16,17,18,19 and >100 with atrial fibrillation (AF)10,20. These data are now beginning to be harnessed to aid risk prediction.

Recent work has highlighted the potential of genomic risk scores (GRS) for risk prediction of common diseases21,22,23,24. Genomic risk prediction has a notable advantage over established risk factors as it could be used to infer risk of disease from birth, thus allowing the initiation of preventive strategies before conventional risk factors manifest and their discriminative capacity begins to emerge.

For stroke, a recent 90-SNP GRS derived from the MEGASTROKE GWAS meta-analysis4 showed that genetic and lifestyle factors are independently associated with incident stroke24, and that even among individuals with high GRS, lifestyle factors had a large impact on risk, implying that risk could be reduced in those with high genetic predisposition for stroke. However, in contrast to GRSs for other cardiovascular diseases like coronary artery disease (CAD)21,22,23, the predictive power of previous GRS for stroke has been limited25,26,27, likely because of limited genetic data for stroke and the well-known heterogeneity of the stroke phenotype4,7. Recent analytical advances have enabled more powerful GRS construction, such as those leveraging multiple sets of GWAS summary statistics21,28, potentially allowing for power and heterogeneity limitations to be overcome. Specifically, for CAD, an approach where multiple GRSs are combined into one meta-score (metaGRS) was found to improve risk prediction over any one of the individual CAD GRS21. Such an approach may be widened to provide substantively improved genomic prediction of stroke.

Here, we extend the metaGRS strategy to predict IS by incorporating GWAS summary statistics for stroke and its aetiological subtypes along with GWAS summary statistics for risk factors and co-morbidities of IS. This new IS metaGRS is validated and compared with previously published GRS using UK Biobank29,30. We next compare the predictive capacity of the IS metaGRS to established non-genetic risk factors for IS. Finally, we assess the additional information provided by the metaGRS in combination with current guidelines for the treatment of established IS risk factors and create joint models which predict absolute risk of incident IS.

## Results

### Derivation of a metaGRS for ischaemic stroke

To create the GRSs we randomly split the UK Biobank (UKB) British white dataset (n = 407,388) into a derivation (n = 11,995) and validation set (n = 395,393; “Methods” section Fig. 1, Table 1). In order to increase statistical power in the derivation phase, we enriched the derivation set (n = 11,995) with IS events (n = 888, 7.4%). A schematic of the overall study design is given in Fig. 1.

We used GWAS summary statistics that did not include the UKB for five stroke outcomes and 14 stroke-related phenotypes (Supplementary Table 1) to generate 19 GRSs associated with IS (Fig. 1). As expected, the 19 individual GRSs were correlated with each other in several distinct clusters: (i) any stroke (AS), IS, cardioembolic stroke (CES), large artery stroke (LAS), and small vessel stroke (SVS); (ii) the three CAD scores (1KGCAD, 46K, and FDR202); (iii) total cholesterol (TC), triglycerides (TG), low-density lipoprotein cholesterol (LDL), and high-density lipoprotein cholesterol (HDL); (iv) systolic BP (SBP) and diastolic BP (DBP); and (v) body mass index (BMI) and type 2 diabetes (T2D) (Fig. 2). From the 19 distinct GRSs, we constructed the metaGRS using elastic-net logistic regression with 10-fold cross-validation on the derivation set (Fig. 1; metaGRS; model weights are shown in Supplementary Fig. 1), and subsequently converted the model to a set of 3.2 million SNP weights, which are freely available (https://doi.org/10.6084/m9.figshare.8202233).

We performed a sensitivity analysis to assess whether the estimation of the metaGRS weights on the UKB derivation set led to over-fitting (upwards bias in apparent performance) of the score in the validation set. We developed a metaGRS based on four component GRSs (AS, IS, BMI, and SBP) in cross-validation on the derivation set. We compared this metaGRS with a score derived using smtPred28, which relies on the chip heritabilities and genetic correlations estimated from the GWAS summary statistics via LD score regression31,32, independently of the UKB (Supplementary Fig. 2). Overall, the two scores were highly correlated (Pearson r = 0.98), and had indistinguishable associations with IS in the UKB validation set, indicating that our metaGRS procedure did not lead to overfitting in the validation set.

### The metaGRS improves risk prediction of ischaemic stroke compared with other genetic scores

Using the independent UKB validation set, we next quantified the risk prediction performance of the metaGRS, and evaluated its association with IS via survival analysis. The metaGRS was associated with IS with a hazard ratio (HR) of 1.26 (95% CI 1.22–1.31) per standard deviation of metaGRS, which was stronger than any individual GRS comprising the metaGRS (including the IS GRS [HR = 1.18, 95% CI 1.15–1.22]) and was twice the effect size of the previously published 90-SNP IS score24 (HR = 1.13 [95% CI 1.10–1.17]; Supplementary Fig. 3a). The metaGRS also increased the C-index by 0.029 over the 90-SNP GRS (Supplementary Fig. 3b). We also assessed the performance of the IS metaGRS for predicting the AS outcome. We found the associations were consistently weaker for AS than for IS, however, as with IS, the metaGRS was a stronger predictor of AS than the 90-SNP GRS score (Supplementary Fig. 3).

In a Kaplan–Meier analysis of IS, the top and bottom 10% of the metaGRS showed substantial differences in cumulative incidence of IS (Supplementary Fig. 4; log-rank test between the top decile and the 45–55% decile: P = 3 × 10−6); these results were consistent with a Cox proportional hazards model of the metaGRS assessing the HRs for the top 10% decile vs the middle 45–55% decile (Supplementary Fig. 5). The top 0.25% of the population were at a threefold increased risk of IS vs. the middle decile (45–55%), with HR = 3.0 (95% CI 1.96–4.59) (Fig. 3).

There was no evidence for a statistical interaction of the metaGRS with sex on IS hazard (Wald test in Cox proportional hazard model, P = 0.614), indicating that the substantial differences in cumulative incidence between the sexes were driven by differences in baseline hazards rather than by any sex-specific effects of the metaGRS itself.

A small number of individuals (n = 45) had recorded haemorrhagic stroke before their primary IS event. We conducted two sensitivity analyses to assess the impact of this on our results: (i) excluding n = 45 individuals from the analysis; (ii) adjusting for haemorrhagic stroke status in the analysis. In both cases, there was essentially no difference in the association of the metaGRS with IS compared with the original analysis (HR = 1.27 per standard deviation of the metaGRS across the two analyses).

### The ischaemic stroke metaGRS has comparable or higher predictive power than established risk factors

We next compared the performance of the metaGRS with established risk factors33 for predicting IS. We examined seven risk factors at the first UKB assessment: LDL cholesterol, SBP, family history of stroke, BMI, diabetes diagnosed by a doctor, current smoking, and hypertension (an expanded definition based on SBP/DBP measurements, BP medication usage, self-reporting, and hospital records; “Methods” section).

As expected, established risk factors were positively associated with incident IS, with hypertension being the strongest risk factor (Supplementary Fig. 7). Notably, the HR of the metaGRS (incident IS HR = 1.25 per s.d.) was similar to that of SBP (incident IS HR = 1.28 per s.d., where the s.d. of SBP was 21.7 mm Hg) and current smoking (incident IS HR = 1.25, s.d. = 0.3) (Supplementary Fig. 7).

Comparison of the C-index for time to incident IS revealed that BP phenotypes, hypertension and SBP (C = 0.590 [95% CI 0.577–0.603]; C = 0.584 [95% CI 0.570–0.598], respectively), had the largest C-indices, followed by the metaGRS (C = 0.580 [95% CI 0.566–0.593]) and the remaining established risk factors (Fig. 4). Notably, the metaGRS had a greater C-index than family history of stroke (C = 0.558, 95% CI 0.544–0.572; Fig. 4). The metaGRS and hypertension contained similar additional information on top of the other risk factors; adding either the metaGRS or hypertension to the six other risk factors yielded similar predictive power, C = 0.629 (95% CI 0.615–0.643) and C = 0.628 (95% 0.614–0.641), respectively. Finally, adding both the metaGRS and hypertension to the six risk factors yielded the model with the highest C-index, C = 0.637 (95% CI 0.623–0.650) (Fig. 4). Note that LDL-cholesterol was not included in this analysis as it had only weak associations with stroke and is not considered a major stroke risk factor.

### The metaGRS contributes to ischaemic stroke risk independent of established risk factors

Given that the metaGRS is composed of GRSs for stroke and stroke risk factors, we conducted several complementary analyses to assess the association of the metaGRS with these risk factors, and whether the metaGRS was associated with IS risk independently of these risk factors. As expected, the IS metaGRS was positively and significantly associated with all seven risk factors (Supplementary Table 2). Adjusting for these risk factors as well as BP-lowering and/or lipid-lowering medication status only modestly attenuated the association of the metaGRS with incident IS (Supplementary Fig. 8), indicating that the information contained in the metaGRS was only partially explained by these factors. On the other hand, adjusting for the metaGRS modestly but consistently attenuated the association of each risk factor itself with IS risk (Supplementary Fig. 7). There was no evidence for statistical interaction of the metaGRS effects on incident IS with medication status at assessment (Wald test in logistic regression, P = 0.23 and P = 0.82 for interaction of the metaGRS with BP medication and cholesterol-lowering medication, respectively).

### Predicting ischaemic stroke risk with established risk factors and the metaGRS

The clinical utility of a GRS depends on its performance in combination with established risk factors and risk models. To examine this, we conducted analyses integrating information on risk factor levels based on (i) recent ACC/AHA/AAPA/ABC/ACPM/AGS/APhA/ASH/ASPC/NMA/PCNA guidelines34 (SBP < 120 mm Hg); (ii) AHA/ASA guidelines for primary prevention of stroke33 (BMI < 25 kg m−2); (iii) smoking status and diabetes status. We used Cox models of these established risk factors and the metaGRS together with the estimated baseline cumulative hazards to predict cumulative incidence of IS for individuals with a high metaGRS (top 1%), average metaGRS (50%), and low metaGRS (bottom 1%) along with two levels of risk factors: (i) meeting guideline targets for the above risk factors34 and (ii) the following combination of risk factors representative of an individual at typical stroke risk: SBP = 140 mm Hg, BMI = 30 kg m−2, current smoking, and no diagnosed diabetes.

The predicted risk of IS for individuals with a high metaGRS (top 1%) and high levels of risk factors was maximal by age 75, reaching a cumulative incidence of 8.5% (95% CI 5.2–11.6%) for males and 5.1% (95% CI 3.1–7.1%) for females (Fig. 5a). Effective reduction in the levels of the modifiable risk factors (SBP, BMI, and smoking) to match guideline targets was predicted to result in a substantial reduction in risk, down to 2.8% (95% CI 1.7–3.9%) for males and 1.7% (95% CI 1.0–2.4%) for females by age 75, thus substantially compensating for the high genomic risk.

Conversely, for individuals matching the guidelines for established risk factors (Fig. 5b), there were notable differences in IS incidence for individuals in the top (1%) compared with the bottom (1%) of the metaGRS; with 2.8% (95% CI 1.7–3.9%) vs. 1.2% (95% CI 0.7–1.7%) in males and 1.7% (95% CI 1.0–2.4%) vs. 0.7% (95% CI 0.4–1.0%) in females, respectively, by age 75. These results further indicate that the metaGRS captures residual risk of stroke not quantified by existing risk factors.

## Discussion

In this study, we developed a genomic risk score for IS based on GWAS summary statistics for 19 stroke and stroke-related traits. We quantify the predictive power of the IS metaGRS by comparing it to previously published genetic scores and measures of established non-genetic risk factors, and demonstrate its added value in combination with established risk factors and in the context of current guidelines for primary stroke prevention. While GRS for stroke are not yet at the level necessary for clinical translation, our analyses constitute several significant advances.

First, we showed that the IS metaGRS had stronger association with IS than previously published genetic scores, doubling the effect size of the most recent genetic score. To put its performance in context, we estimated the IS metaGRS identified the 1 in 400 individuals who were at threefold increased risk of IS, a level of risk and frequency similar to common monogenic cardiovascular diseases, such as familial hypercholesterolaemia (FH), a risk factor for myocardial infarction35. Monogenic forms of stroke, such as CADASIL, are relatively rare36, thus the IS metaGRS may represent a potential new avenue to more common polygenic risk stratification, in combination with established risk factors.

Second, the IS metaGRS had comparable predictive power to SBP, higher predictive power than other established risk factors measured, apart from hypertension, and captured residual risk not quantified by the established risk factors. In anticipation of a potential role in early screening, we estimate the risk reduction through modifiable stroke risk factors across different metaGRS backgrounds, and further show that current guidelines for stroke risk factors may be insufficiently stringent for individuals at high metaGRS.

Third, we explicitly modelled how changes in modifiable risk factors, such as SBP and BMI, can compensate for high genomic risk. Previous research has demonstrated that intervening on modifiable risk factors can compensate for increased genetic risk of disease21,37. However, these analyses relied on simply counting the number of elevated risk factors, which does not account for the differences in effect size between various risk factors. Importantly, our approach was flexible in that various combinations of risk factor reductions can lead to the same outcome in terms of risk.

Our approach shows, for different genomic risk backgrounds, how modifiable risk factors could, in principle, be tailored to an individual’s ability to reduce an established risk factor(s) while maintaining an overall acceptable level of absolute risk. Similarly, this approach could potentially be used to guide early prevention of stroke: identifying individuals at increased risk early in life, who would then be targeted for more intensive lifestyle modifications, similar to the roles that have been proposed for genetics in cancer risk stratification38. Unlike most established risk factors which may vary over time and are typically not informative at an early age, the metaGRS remains stable and can be derived from birth. Later in life, when measurements of established risk factors are available, these can be further combined with the metaGRS to give the most accurate prediction of a person’s risk of incident stroke. Further research is required to determine what levels of risk factor reductions will be achievable and cost effective in practice.

Lastly, even for individuals within risk factor levels recommended by current guidelines (SBP < 120, BMI < 25, not currently smoking, no diagnosed diabetes), our models predict substantial differences in risk between different metaGRS levels. These results suggest that for individuals with high metaGRS, achieving currently recommended risk factor levels may not be sufficient and that it is time to contemplate whether future guidelines on primary and secondary stroke prevention should integrate genetic information when defining treatment goals for high-risk individuals. Ultimately, the practical implications of these results to stroke risk screening in the general population will require public health modelling, taking into account what is considered ‘high risk’ of stroke in the context of each country and health system, and the efficacy of interventions or treatments that are available for risk reduction.

Our study has several limitations. Compared with GRS for other common conditions, such as CAD21, the performance of our metaGRS for stroke is limited. A likely reason is that stroke is more heterogeneous and that GWAS sample sizes for mechanistically defined stroke subtypes are still limited in comparison with other diseases. As stroke GWAS progress, GRS will become more powerful39,40. We did not observe substantial advantage from incorporating GRSs based on GWAS summary statistics for specific IS subtypes (LAS, CES, SVS) over that of IS as a whole; however, we were not able to examine subtype-specific outcomes in the UKB due to the lack of such detailed information. There may still be benefit from developing subtype-specific scores that take advantage of the unique genetic architecture of each subtype41. The number of older individuals (>75 years) in UKB is limited at this stage, reducing our ability to model stroke risk in the age strata where the majority of events occur. Furthermore, the duration of follow-up in UKB is relatively limited and, because of the limited number of assessments, we could not model the cumulative effect of BP and smoking over time; however, we accounted for potential regression dilution bias in SBP measurements via the use of diagnosed hypertension, which showed stronger associations with stroke. Family history of stroke in UKB may be less comprehensive than in stroke-specific studies, limiting its predictive power, and overall the UKB study population is healthier than the general UK population42, which could have led to underestimation of some of the effects of risk factors. Further independent validation of the stroke metaGRS in other cohorts would be necessary before considering its clinical use; however, this is challenging given that the majority of available stroke GWAS studies have been included in MEGASTROKE. Nonetheless, recent successful validation of our previous CAD metaGRS21 in French-Canadian cohorts43 suggests that scores developed on the UK Biobank are generalisable to other cohorts of European ancestry. Our modelling assumes that risk factors, such as SBP and BMI, can be varied independently of each other. In practice, common lifestyle interventions such as exercise and diet will likely affect several risk factors at a time. Finally, this study focused on British white ancestry and it is yet unknown what performance is achievable in individuals of different ancestry;44 successful development of scores in non-Europeans will require both stroke GWAS summary statistics from non-Europeans as well as sufficiently large prospective studies of stroke on which to validate these scores.

Taken together, despite challenges in phenotypic heterogeneity and corresponding GWAS power, our study presents the most powerful IS genomic risk score to date and assesses its potential for risk stratification in the context of established risk factors and clinical guidelines. It lays the groundwork for larger GWAS of stroke and its multiple subtypes as well as analyses which leverage the totality of information available for stroke genomic risk prediction.

## Methods

### Study participants

This study was conducted under the UK Biobank project #26865, under the approval of the North West Multi-centre Research Ethics Committee (MREC) in the UK. All participants of UK Biobank provided written informed consent.

The UK Biobank (UKB) study29,30 included individuals from the general UK population, aged between 40–69 years at recruitment. Recruitment included a standardised socio-demographic questionnaire, as well as medical history, family history, and other lifestyle factors. Several physical measurements (e.g., height, weight, waist-hip ratio, systolic and diastolic BP) were taken at assessment.

Individual records were linked to the Hospital Episode Statistics (HES) records and the national death and cancer registries. The age of event was age at the primary stroke event (the diagnostic algorithm for stroke in UKB can be found at http://biobank.ndph.ox.ac.uk/showcase/docs/alg_outcome_stroke.pdf; last accessed 11/04/2019).

We defined stroke risk factors at the first assessment, including: diabetes diagnosed by a doctor (field #2443), BMI (field #21001), current smoking (field #20116), hypertension, family history of stroke, and LDL cholesterol. For hypertension we used an expanded definition including self-reported high BP (either on BP medication, data fields #6177, #6153; or SBP > 140 mm Hg, fields #4080, #93; or DBP > 90 mm Hg, data fields #4079, #94) as well as hospital records; for registry cases, we use HESIN (hospital admission) and death registry data including both primary and secondary diagnoses/causes of death (HESIN: ICD9 401–405, ICD10 I10–I15; death: ICD10 I10–I15, data fields #40001, #40002). For family history of stroke, we considered history in any first-degree relative (father, mother, sibling; fields #20107, #20110, and #20111, respectively).

For individuals on BP-lowering medication, we adjusted SBP by adding +15 mm Hg as per Evangelou et al.16,45. We used LDL-cholesterol from the UKB biomarker panel, measured at first UKB assessment. For individuals on lipid-lowering medication at the time of assessment (n = 66,737), we adjusted the measured LDL-cholesterol level by +1.5 mmol L−1.

We excluded individuals with withdrawn consent, self-reported stroke at age <20 years due the potential unreliability of these records, and those not of British white ancestry (identified via the UKB field ‘in.white.British.ancestry.subset’29), leaving a total of n = 407,388 individuals. We censored the age of stroke at 75 years.

### Genotyping quality control

The UKB v2 genotypes were genotyped on the UKB Axiom array, and imputed to the Haplotype Reference Consortium (HRC) by the UKB;29 SNPs on the UK10K/1000Genomes panel were excluded from the current analysis. Imputed genotypes were converted to PLINK hard calls. For the initial GRS analysis, we considered genotyped or HRC-imputed SNPs with imputation INFO > 0.01 and global MAF > 0.001 (14.5 M autosomal SNPs). A further QC step was performed on the final metaGRS (see below).

### Generation of the metaGRS

We randomly sampled n = 11,995 individuals from the UKB dataset, oversampling individuals with AS events, leading to 2065 individuals with AS (of which 889 were also IS events) and 9935 non-AS referents. This subset was used for developing GRSs, and was excluded from all further analysis. Five individuals were later removed due to withdrawn consent.

Using the UKB derivation set, we generated 19 GRSs for phenotypes associated with stroke (Supplementary Table 1). To minimise the risk of over-fitting due to overlap of individuals between the GWAS meta-analyses and the UKB validation dataset, we selected GWAS that did not include the UK Biobank in their meta-analysis.

The three CAD GRSs (46K, 1KGCAD, FDR202) were generated previously using an n = 3000 derivation subset of the UKB (included in the larger n = 11,995 subset employed here);21 briefly: (i) the 46K score was derived by LD thinning of the Metabochip summary statistics;46 (ii) the 1KGCAD was derived by LD thinning of the 1000Genomes CAD summary statistics;47 and (iii) the FDR202 score was from the 1000Genomes CAD summary statistics, consisting of SNPs with associations at false discovery rate < 0.05. The AF GRS was derived from a GWAS of AF48 using a pruning and thresholding approach. For the remaining GRSs, we used published summary statistics to generate a range of scores based on different r2 thresholds with PLINK49 LD thinning (–indep-pairwise), and selected one optimal model (in terms of the largest magnitude hazard ratio), resulting in one representative GRS for each set of summary statistics.

Each GRS was standardised (zero mean, unit standard deviation) over the entire dataset. Next, we employed elastic-net logistic regression50 using the R package ‘glmnet’51 to model the associations between the 19 GRSs and stroke, adjusting for sex, genotyping chip (UKB vs BiLEVE), and 10 genetic PCs. A range of models with different penalties was evaluated using 10-fold cross-validation. The best model, in terms of highest cross-validated AUC (area under receiving-operating characteristic curve), was selected as the final model and held fixed for validation in the rest of the UKB data. The final adjusted coefficients for each GRS (odds ratios) in the penalised logistic regression are shown in Supplementary Fig. 1, in comparison with the univariate estimates (based on one GRS at a time).

The final per-GRS log odds γ1, …, γ19 were converted to an equivalent per-SNP score via a weighted sum

$$\begin{array}{*{20}{c}} {{\mathrm{GRS}}_i^{{\mathrm{meta}}} \propto \mathop {\sum}\limits_{j = 1}^m {x_{ij}} \left( {\frac{{\gamma _1}}{{\sigma _1}}\alpha _{j1} + \ldots + \frac{{\gamma _{19}}}{{\sigma _{19}}}\alpha _{j19}} \right), } \end{array}$$
(1)

where m is the total number of SNPs, σ1, …, σ19 are the empirical standard deviations of each of the 19 GRSs in the derivation data, αj1, …, αj19 are the SNP effect sizes (from the GWAS summary statistics) for the jth SNP in each of the GRSs, respectively, and xij is the genotype {0, 1, 2} for the ith individual’s jth SNP. A SNP’s effect size αjk was considered to be zero for the kth score if the SNP was not included in that score. This resulted in 3.6 million SNPs for inclusion in the metaGRS.

We conducted a sensitivity analysis to evaluate whether stricter quality control filtering would impact the performance of the metaGRS; removing SNPs with imputation INFO < 0.4 and MAF < 0.01 did not substantially affect the association of the metaGRS with stroke, hence, we selected the metaGRS with stricter QC as the final score, bringing the total number of SNPs to 3.2 million.

### Evaluation of the metaGRS

The metaGRS developed using the derivation set was held fixed and evaluated in the UKB validation subset (n = 395,393) using a Cox proportional hazard model. We conducted complete case analysis due to the low proportion of participants with any missing values for the seven risk factor variables of interest (5.1% of participants).

Age was used as the time scale in the Cox proportional hazard regression. The regression was stratified by sex and weighted by the inverse probability of selection into the validation set, together with robust standard errors (R package ‘survival’52). All analyses were adjusted for chip (UKB vs BiLEVE) and 10 PCs of the genotypes (as provided by UKB29). For analyses of incident stroke, age at UKB assessment was taken as time of entry into the study. Cox models of the metaGRS did not show deviations from proportional hazard assumptions, based on the global test for scaled Schoenfeld residuals (P = 0.32).

The predicted cumulative risk curves (as a function of time t) were calculated using ‘survfit.coxph’ within each stratum of sex as

$$\begin{array}{*{20}{c}} {1 - \widehat S\left( t \right) = 1 - {\mathrm{exp}}\left( { - \widehat {H}_0\left( t \right){\mathrm{exp}}\left( {{\mathbf{x}}^{\mathrm{T}}\hat {\mathbf{\upbeta }}} \right)} \right),} \end{array}$$
(2)

where $$\widehat S\left( t \right)$$ is the cumulative survival at time t, $$\widehat {H_0}(t)$$ is the estimated baseline cumulative hazard at time t, x is the vector of the predictor variables set to the values of interest, and $$\widehat {\mathbf{\upbeta }}$$ is the vector of the estimated log hazard ratios for each predictor.

We performed a sensitivity analysis testing whether the association of the metaGRS with IS was affected by familial relatedness in the validation set. Relatedness analysis was done using KING53 v2.1.4, based on ~784,000 autosomal SNPs measured on the Axiom chip, identifying n = 336,643 participants in the UKB validation set with kinship more distant than that of 2nd degree. There was a negligible difference in the association between the metaGRS and stroke in the full UKB validation set and within this distantly related subset of individuals.

Calibration of the metaGRS risk score was evaluated by fitting logistic regression models of the metaGRS (adjusting for sex, chip, and 10 genetic PCs) in the derivation set, predicting the absolute risk of event in the test set (allowing for the 9.38-fold lower observed baseline rate of events between the testing set compared with the derivation set), and evaluating the proportion of test set individuals with stroke events within each decile of the predicted risks (Supplementary Fig. 9). Pointwise confidence intervals were obtained via the binomial test for proportions.

We estimated the heritability of IS explained by the metaGRS, on the liability scale, using the R2 and partial R2 obtained from linear regression of the stroke outcomes on metaGRS (partial R2 was from linear regression adjusted for sex, age of assessment, genotyping chip, and 10 PCs). The estimates were converted to the liability scale54, assuming that the IS prevalence in UKB represents that of the general population (K = 0.008). Due to a lack of robust estimates of the heritability of stroke, we examined a range of plausible h2 values from 0.1 to 0.4, yielding estimates of explained heritability ranging from 7.7 to 1.8%, respectively (Supplementary Fig. 10).

We performed sensitivity analysis to assess the effect of potential geographical stratification within the UKB55 on the metaGRS. We compared the original metaGRS with residuals of the metaGRS regressed on (i) the first 10 PCs, (ii) first 10 PCs and natural cubic splines of the geographical north-south coordinates and east-west coordinates (3 degrees of freedom each), (iii) the first 30 PCs and splines of the coordinates, (iv) first 10 PCs and a thin-plate regression spline (TPRS) representing smooth interactions between the two coordinates56, and finally (v) also adding the UKB assessment centre (Supplementary Fig. 11a). For the unadjusted score, we observed some variation across the north and east coordinates (up to 0.4 standard deviations), however, adjusting for PCs and the coordinates attenuated this variation substantially, with the TPRS method eliminating it completely. Despite the attenuation in geographical stratification, we observed negligible change in the association of the residuals of the scores with IS events (Supplementary Fig. 11b), indicating that any geographical stratification in UKB was not driving the metaGRS’s association with stroke.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.


text:
# Integrate xe^x dx

• Sep 3rd 2009, 02:16 PM
jebckr
Integrate xe^x dx
it is actually integrate from 0 to -infin, but I understand that part. When I see xe^x I integrate it and get (1/2x^2)(e^x). My solutions manuel says it is (x-1)(e^x). I don't get the same answer when using my work, what am I doing wrong?
• Sep 3rd 2009, 02:22 PM
Matt Westwood
Integrate by parts: $\int u dv = uv - \int v du$.

Here you set $u = x, dv = e^x$ and so $uv = x e^x$ and $\int v du = \int e^x = e^x$.

Hence, as they say, the result.
• Sep 3rd 2009, 02:29 PM
jebckr
So how does (xe^x)-(e^x) become (x-1)e^x? I'm sure I'm missing some simple rule here...
• Sep 3rd 2009, 02:35 PM
cgiulz
Yes:

(xe^x)-(e^x)

= xe^x - e^x

= e^x(x - 1)

= (x - 1)e^x


text:
# nLab measuring coalgebra

### Context

#### Algebra

higher algebra

universal algebra

# Measuring coalgebras

## Idea

Measuring coalgebras are an enrichment of the category of commutative rings (or commutative $\mathbb{Z}$-algebras) in the cartesian closed category $k$ Cocomm Coalg of cocommutative coalgebras (which we will write simply as $Coalg$), given a ground field $k$.

The starting point is the observation that the category $Coalg$ acts on the category Alg of commutative algebras: there is a functor

$\{-, -\}: Coalg^{op} \times Alg \to Alg$

where, given a coalgebra $C$ and an algebra $A$, $\{C, A\}$ is the abelian-group hom of additive homomorphisms $f: C \to A$, made into an algebra whose multiplication $f \cdot g$ is given by

$C \overset{d}{\to} C \otimes C \overset{f \otimes g}{\to} A \otimes A \overset{m}{\to} A$

where $d$ is the coalgebra comultiplication and $m$ is the algebra multiplication. That this is an “action” here means that there is a natural isomorphism

$\{C \otimes D, A\} \cong \{C, \{D, A\}\}$

of algebras; here $Alg$ is sometimes described as an actegory over $Coalg$.

## Definition

###### Definition

Given two algebras $A, B$, the measuring coalgebra $\mu(A, B)$ is by definition the representing object of the functor

$Alg(A, \{-, B\}): Coalg^{op} \to Set$

so that there is an isomorphism, natural for coalgebras $C$, of the form

$Coalg(C, \mu(A, B)) \cong Alg(A, \{C, B\})$

Assume the existence of equalizers in $Coalg$, and of a right adjoint

$Cof: Vect \to Coalg$

to the forgetful functor $U: Coalg \to Vect$ (the cofree cocommutative coalgebra construction). We let

$\pi: U \circ Cof \to 1_{Vect}$

denote the counit of the adjunction $U \dashv Cof$.

We construct $\mu(A, B)$ explicitly as the equalizer in $Coalg$ of a pair of maps of the form

$Cof(B^A) \overset{\to}{\to} Cof(B^{A \otimes A}) \times Cof(B^k)$

where we denote the internal hom in Vect by exponentiation (and we recall here that the cartesian product in $Coalg$ is given by tensor product at the level of $Vect$). The first of these maps is

$\langle Cof(B^{m_A}), Cof(B^{u_A}) \rangle: Cof(B^A) \to Cof(B^{A \otimes A}) \times Cof(B^k)$

where $m_A: A \otimes A \to A$ is the multiplication on $A$ and $u_A: k \to A$ is the unit. The second is given by a pair of maps

$\langle \Phi, \Psi \rangle$

which we now describe separately.

The map $\Phi: Cof(B^A) \to Cof(B^{A \otimes A})$ is the unique coalgebra map such that $U \Phi$ lifts the map

$U Cof(B^A) \overset{\delta}{\to} U Cof(B^A) \otimes U Cof(B^A) \overset{\pi \otimes \pi}{\to} B^A \otimes B^A \overset{\otimes_1}{\to} (B \otimes B)^{A \otimes A} \overset{m_{B}^{A \otimes A}}{\to} B^{A \otimes A}$

through $\pi: U Cof(B^{A \otimes A}) \to B^{A \otimes A}$. Here $\delta$ denotes the comultiplication (same as the diagonal map as seen in $Coalg$), and $\otimes_1$ indicates the structure of enriched functoriality for $\otimes$.

The map $\Psi: Cof(B^A) \to Cof(B^k)$ is the unique coalgebra map such that $U \Psi$ lifts the map

$U Cof(B^A) \overset{\varepsilon}{\to} k \overset{u_B}{\to} B \cong B^k$

through $\pi: U Cof(B^A) \to B^A$. Here $\varepsilon$ denotes the counit (same as the unique map to the terminal object as seen in $Coalg$).

## Enrichment of algebras in coalgebras

###### Proposition

The measure coalgebra $\mu(A, B)$ indeed gives an enrichment

$\mu(-, -): Alg^{op} \times Alg \to Coalg \,.$

Here the composition law in $Coalg$

$\mu(A_0, A_1) \times \mu(A_1, A_2) \to \mu(A_0, A_2)$

(recalling that the product in $Coalg$ is the tensor product of the underlying additive groups) is derived by universality from a composition of maps:

$\array{ Coalg(C, \mu(A_0, A_1) \times \mu(A_1, A_2)) & \cong & Coalg(C, \mu(A_0, A_1)) \times Coalg(C, \mu(A_1, A_2)) & (Coalg(C, -) preserves products)\\ & \cong & Alg(A_0, \{C, A_1\}) \times Alg(A_1, \{C, A_2\}) & (definition of \mu) \\ & \to & Alg(A_0, \{C, A_1\}) \times Alg(\{C, A_1\}, \{C, \{C, A_2\}\}) & (functoriality of \{C, -\})\\ & \to & Alg(A_0, \{C, \{C, A_2\}\}) & (composition law)\\ & \cong & Alg(A_0, \{C \otimes C, A_2\}) & (actegory constraint)\\ & \to & Alg(A_0, \{C, A_2\}) & (using d: C \to C \otimes C)\\ & \cong & Coalg(C, \mu(A_0, A_2)) & (definition of \mu) }$

Revised on March 5, 2012 03:30:42 by Todd Trimble (67.80.8.47)


text:
Eight minutes, an ordinary topic

neila9876

In Woody's leaning tower experiment, there are two kinds of interaction:
1. The interaction of gravity between the iron ball and the Earth. It is there long long ago;
2. The interaction of tension between Woody and the iron ball.
As soon as Woody let go of the bungee chord, the interaction of tension between Woody and the iron ball disappears. The interaction of gravity between the iron ball and the Earth demonstrates itself immediately.

benit13

In Woody's leaning tower experiment, there are two kinds of interaction:
1. The interaction of gravity between the iron ball and the Earth. It is there long long ago;
2. The interaction of tension between Woody and the iron ball.
As soon as Woody let go of the bungee chord, the interaction of tension between Woody and the iron ball disappears. The interaction of gravity between the iron ball and the Earth demonstrates itself immediately.
The time taken for a gravitational wave to propagate from the Earth to the iron ball is very, very small (let's call it $$\displaystyle \Delta t$$), so I don't know what you mean when you say that the interaction with gravity was from long, long ago. However, the interaction of gravity is continuously happening, so as soon as Woody let's go of the cord, the gravitational wave emitted at the time equal to the present time $$\displaystyle - \Delta t$$ will interact with the ball, causing it to drop.

Think of it like this... when a light bulb is turned on, the light is continuously shining. However, at any given moment, the light hitting you is light that was emitted from the light bulb at some very small time $$\displaystyle \Delta t$$ before it hit you. Since this light is the light you are using to understand what the light bulb looks like, the light bulb appears as if it were $$\displaystyle \Delta t$$ younger than the present time. If the light bulb changed colour, it would take $$\displaystyle \Delta t$$ seconds before you notice it. The same is true with all of the interaction mechanisms (gravity, electromagnetic, strong nuclear and weak nuclear).