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Course Allocation
Course allocation is the problem of allocating seats in Course (education), university courses among students. Many universities impose an upper bound on the number of students allowed to register to each course, in order to ensure that the teachers can give sufficient attention to each individual student. Since the demand for some courses is higher than the upper bound, a natural question is which students should be allowed to register to each course. Many institutions allow students to register on a first come, first served basis. However, this may lead to unfair outcomes: a student who happens to be near his/her computer when registration starts can manage to register to all the most wanted courses, while a student who comes too late might find that all wanted courses are already full and be able to register only to less-wanted courses. To mitigate this unfairness, many institutions use more sophisticated allocation mechanisms. Draft mechanisms In a draft mechanism (also called ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Course (education)
In higher education, a course is a unit of teaching that typically lasts one academic term, is led by one or more instructors (teachers or professors), and has a fixed roster of students. A course usually covers an individual subject. Courses generally have a fixed program of sessions every week during the term, called lessons or classes. Students may receive a Grading in education, grade and academic Credit (education), credit after completion of the course."course" in ''Merriam-Webster Online Dictionary''. Retrieved 15 August 2008. Courses can either be compulsory material or "elective". An elective is usually not a required course, but there are a certain number of non-specific electives that are required for certain academic major, majors. The entire collection of courses required to complete an academic degree is called a ''undergraduat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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First-price Sealed-bid Auction
A first-price sealed-bid auction (FPSBA) is a common type of auction. It is also known as blind auction. In this type of auction, all bidders simultaneously submit sealed bids so that no bidder knows the bid of any other participant. The highest bidder pays the price that was submitted. Strategic analysis In a FPSBA, each bidder is characterized by their monetary valuation of the item for sale. Suppose Alice is a bidder and her valuation is a. Then, if Alice is rational: *She will never bid more than a, because bidding more than a can only make her lose net value. *If she bids exactly a, then she will not lose but also not gain any positive value. *If she bids less than a, then she ''may'' have some positive gain, but the exact gain depends on the bids of the others. Alice would like to bid the smallest amount that can make her win the item, as long as this amount is less than a. For example, if there is another bidder Bob and he bids y and y [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Stable Matching
In mathematics, economics, and computer science, the stable matching problem is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of the other set. A matching is ''not'' stable if: In other words, a matching is stable when there does not exist any pair (''A'', ''B'') which both prefer each other to their current partner under the matching. The stable marriage problem has been stated as follows: The existence of two classes that need to be paired with each other (heterosexual men and women in this example) distinguishes this problem from the stable roommates problem. Applications Algorithms for finding solutions to the stable marriage problem have applications in a variety of real-world situations, perhaps the best known of these being in the assignment of graduating medical students to their first hospital appointments. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Two-sided Market
In mathematics, specifically in topology of manifolds, a compact codimension-one submanifold F of a manifold M is said to be 2-sided in M when there is an embedding ::h\colon F\times 1,1to M with h(x,0)=x for each x\in F and ::h(F\times 1,1\cap \partial M=h(\partial F\times 1,1. In other words, if its normal bundle is trivial. This means, for example that a curve in a surface is 2-sided if it has a tubular neighborhood which is a cartesian product of the curve times an interval. A submanifold which is not 2-sided is called 1-sided. Examples Surfaces For curves on surfaces, a curve is 2-sided if and only if it preserves orientation, and 1-sided if and only if it reverses orientation: a tubular neighborhood is then a Möbius strip. This can be determined from the class of the curve in the fundamental group of the surface and the orientation character on the fundamental group, which identifies which curves reverse orientation. * An embedded circle in the plane is 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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One-sided Matching
In economics and computer science, the house allocation problem is the problem of assigning objects to people with different preferences, such that each person receives exactly one object. The name "house allocation" comes from the main motivating application, which is assigning dormitory houses to students. Other commonly used terms are assignment problem and one-sided matching. When agents already own houses (and may trade them with other agents), the problem is often called a housing market. In house allocation problems, it is assumed that monetary transfers are not allowed; the variant in which monetary transfers are allowed is known as rental harmony. Definitions There are ''n'' people (also called: ''agents''), and m objects (also called: ''houses''). The agents may have different preferences over the houses. They may express their preferences in various ways: * ''Binary valuations'': each agent values each house at either 1 (which means that the agent likes the house), or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek alphabet, Greek letter Sigma, σ (sigma), for the population standard deviation, or the Latin script, Latin letter ''s'', for the sample standard deviation. The standard deviation of a random variable, Sample (statistics), sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Second-price Auction
A Vickrey auction or sealed-bid second-price auction (SBSPA) is a type of sealed-bid auction. Bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins but the price paid is the second-highest bid. This type of auction is strategically similar to an English auction and gives bidders an incentive to bid their true value. The auction was first described academically by Columbia University professor William Vickrey in 1961 though it had been used by stamp collectors since 1893. In 1797 Johann Wolfgang von Goethe sold a manuscript using a sealed-bid, second-price auction. Vickrey's original paper mainly considered auctions where only a single, indivisible good is being sold. The terms ''Vickrey auction'' and ''second-price sealed-bid auction'' are, in this case only, equivalent and used interchangeably. In the case of multiple identical goods, the bidders submit inverse demand curves and pay the opportunity cost. Vickrey auctions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Top Trading Cycles
Top trading cycle (TTC) is an algorithm for trading indivisible items without using money. It was developed by David Gale and published by Herbert Scarf and Lloyd Shapley. Housing market The basic TTC algorithm is illustrated by the following house allocation problem. There are n students living in the student dormitories. Each student lives in a single house. Each student has a preference relation on the houses, and some students prefer the houses assigned to other students. This may lead to mutually-beneficial exchanges. For example, if student 1 prefers the house allocated to student 2 and vice versa, both of them will benefit by exchanging their houses. The goal is to find a core-stable allocation – a re-allocation of houses to students, such that all mutually-beneficial exchanges have been realized (i.e., no group of students can together improve their situation by exchanging their houses). The algorithm works as follows. # Ask each agent to indicate his "top" (most prefe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Machine Learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task (computing), tasks without explicit Machine code, instructions. Within a subdiscipline in machine learning, advances in the field of deep learning have allowed Neural network (machine learning), neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. ML finds application in many fields, including natural language processing, computer vision, speech recognition, email filtering, agriculture, and medicine. The application of ML to business problems is known as predictive analytics. Statistics and mathematical optimisation (mathematical programming) methods comprise the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Substitute Good
In microeconomics, substitute goods are two goods that can be used for the same purpose by consumers. That is, a consumer perceives both goods as similar or comparable, so that having more of one good causes the consumer to desire less of the other good. Contrary to complementary goods and independent goods, substitute goods may replace each other in use due to changing economic conditions. An example of substitute goods is Coca-Cola and Pepsi; the interchangeable aspect of these goods is due to the similarity of the purpose they serve, i.e. fulfilling customers' desire for a soft drink. These types of substitutes can be referred to as close substitutes. Substitute goods are commodity which the consumer demanded to be used in place of another good. Economic theory describes two goods as being close substitutes if three conditions hold: # products have the same or similar performance characteristics # products have the same or similar occasion for use and # products are sold in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Complementary Good
In economics, a complementary good is a good whose appeal increases with the popularity of its complement. Technically, it displays a negative cross elasticity of demand and that demand for it increases when the price of another good decreases. If A is a complement to B, an increase in the price of A will result in a negative movement along the demand curve of A and cause the demand curve for B to shift inward; less of each good will be demanded. Conversely, a decrease in the price of A will result in a positive movement along the demand curve of A and cause the demand curve of B to shift outward; more of each good will be demanded. This is in contrast to a substitute good, whose demand decreases when its substitute's price decreases. When two goods are complements, they experience ''joint demand'' - the demand of one good is linked to the demand for another good. Therefore, if a higher quantity is demanded of one good, a higher quantity will also be demanded of the other, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Independent Goods
Independent goods are goods that have a zero cross elasticity of demand. Changes in the price of one good will have no effect on the demand for an independent good. Thus independent goods are neither complements nor substitutes. For example, a person's demand for nails is usually independent of his or her demand for bread, since they are two unrelated types of goods. Note that this concept is subjective and depends on the consumer's personal utility function. A Cobb-Douglas utility function implies that goods are independent. For goods in quantities ''X''1 and ''X''2, prices ''p''1 and ''p''2, income ''m'', and utility function parameter ''a'', the utility function : u(X_1, X_2) = X_1^a X_2^, when optimized subject to the budget constraint that expenditure on the two goods cannot exceed income, gives rise to this demand function for good 1: X_1= am/p_1, which does not depend on ''p''2. See also * Consumer theory * Good (economics and accounting) In economics, goods are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |