## 30.12.17

### SLAM Simultaneous Localization and Mapping

SLAM Simultaneous Localization and Mapping

In robotic mapping and navigationsimultaneous localization and mapping (SLAM) is the computational problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an agent's location within it.

Given a series of sensor observations  over discrete time steps , the SLAM problem is to compute an estimate of the agent's location  and a map of the environment . All quantities are usually probabilistic, so the objective is to compute:
${\displaystyle P(m_{t},x_{t}|o_{1:t})}$
Applying Bayes' rule gives a framework for sequentially updating the location posteriors, given a map and a transition function ${\displaystyle P(x_{t}|x_{t-1})}$,
${\displaystyle P(x_{t}|o_{1:t},m_{t})=\sum _{m_{t-1}}P(o_{t}|x_{t},m_{t})\sum _{x_{t-1}}P(x_{t}|x_{t-1})P(x_{t-1}|m_{t},o_{1:t-1})/Z}$
Similarly the map can be updated sequentially by
${\displaystyle P(m_{t}|x_{t},o_{1:t})=\sum _{x_{t}}\sum _{m_{t}}P(m_{t}|x_{t},m_{t-1},o_{t})P(m_{t-1},x_{t}|o_{1:t-1},m_{t-1})}$
Like many inference problems, the solutions to inferring the two variables together can be found, to a local optimum solution, by alternating updates of the two beliefs in a form of EM algorithm.

## 23.12.17

### Morse

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## 21.12.17

### Warren Buffett Partnership Letters

Warren Buffett Partnership Letters:
These letters are instrumental to informing the thought processes of many investors and are beneficial for anyone with a desire to increase their knowledge of the stock market.

The General Stock Market Picture 1957

### The Benefits of Mortgage-Backed Securities

The benefits of Mortgage-Backed Securities are wide and many. Among the reasons for the popularity of these products are their ability to increase Money Market Liquidity. The profitability and structure of these securities has allowed for ease of exchange and dissolution of risk otherwise encountered when trading securities that aren't backed by an asset. Government involvement and regulations has structured safety nets to increase the soundness of these financial tools. Pooling of assets creates the conditions that allow for greater likelihood of exchange due to decreased risk.

## 14.12.17

### Investment Terminology

Financial Terminology:

MC Market Capitalization: The aggregate value of a company or stock.
MC = (Number of Shares Outstanding)(Current Price Per Share)

P/E Ratio: Most common measure of how expensive a stock is.
P/E = MC/After-Tax Earnings During 12 Months

Preferred Stock: Capital Stock which provides a specific dividend that is paid before any dividends are paid to common stock holders, and which takes precedence over common stock in the event of a liquidation.

Book Value: A company's common stock equity as it appears on a balance sheet.
Book Value = Total Assets - Liabilities, Preferred Stock, and Intangible Assets Such as Goodwill

Equity: Ownership interest in a corporation in the form of common stock or preferred stock. Total assets minus total liabilities; here also called shareholders's equity or net worth or book value.

Hedge: An investment made in order to reduce the risk of adverse price movements in a security, by taking an offsetting position in a related security, such as an option or short sale.

Risk: The quantifiable likelihood of loss or less-than-expected returns.

Commodity: A physical substance which is interchangeable with another product of the same type and which investors buy or sell, usually through futures contracts.

Inflation: The overall general upward price movement of goods and serviced in an economy (often caused by an increase in the supply of money), usually as measured by the Consumer Price Index. As the price of goods and services increases, the value of the dollar falls and an individual has less purchasing power. The FED tried to maintain a 2-3% inflation rate.

Security: An investment instrument, other than an insurance policy or fixed annuity issued by a corporation, government, or other organization which offers evidence of debt or equity.

Annuity: A contract sold by an insurance company designed to provide payments to the holder at specified intervals, usually after retirement. The holder is taxed only when they start taking distributions or if they withdraw funds from the account. All annuities are tax-deferred.

Over-The-Counter (OTC): A decentralized market (as opposed to an exchange market) where geographically dispersed dealers are linked by telephones and computers. The market is for securities not listed on a stock or derivatives exchange.

Beta: The measure of an asset's risk in relation to the market.
Beta = [(n)(sum of [xy]]-[(sum of x)(sum of y)]/[(n)(sum of [xx]]-[(sum of x)(sum of x)]
where n = # of observations, usually 36 to 60 months
x = rate of return for the S&P 500
y = rate of return for the security

## 14.11.17

### Carmen Sandiego

Carmen Sandiego, A 90's Computer Game: