The degree sequence of a scale
... most basic properties of a graph or network is its degree sequence. For the standard random graph model n m of all graphs with m edges on a fixed set of n vertices, introduced by Erdős and Rényi in [8] and studied in detail in [9], there is a “characteristic” degree 2m/n: the vertex degrees hav ...
... most basic properties of a graph or network is its degree sequence. For the standard random graph model n m of all graphs with m edges on a fixed set of n vertices, introduced by Erdős and Rényi in [8] and studied in detail in [9], there is a “characteristic” degree 2m/n: the vertex degrees hav ...
Disjoint Paths in Expander Graphs via Random Walks
... number of paths that use any one edge, the edge congestion, by some value in place of one. Bounds on the number of routable pairs in this case are given in Theorem 5. Dynamic problem In the dynamic version of the problem each vertex receives an infinite stream of requests for paths starting at tha ...
... number of paths that use any one edge, the edge congestion, by some value in place of one. Bounds on the number of routable pairs in this case are given in Theorem 5. Dynamic problem In the dynamic version of the problem each vertex receives an infinite stream of requests for paths starting at tha ...
The start of a script for the course
... 50 %. Where did this come from ? You made a model, reasoning as follows: 1. there are two possible outcomes (lets ignore the possibility of the coin landing on its side); 2. I have no reason to prefer one outcome over the other (Laplace’s rule of insufficient reason), so I assign the same probabilit ...
... 50 %. Where did this come from ? You made a model, reasoning as follows: 1. there are two possible outcomes (lets ignore the possibility of the coin landing on its side); 2. I have no reason to prefer one outcome over the other (Laplace’s rule of insufficient reason), so I assign the same probabilit ...
Theoretical Analyses of Cross-Validation Error and
... Section 5 discusses the practical application of this theory. It is shown how it is possible to estimate the expected cross-validation error from the training set. This section presents estimators that can indicate whether voting will increase or decrease stability for a particular set of data. This ...
... Section 5 discusses the practical application of this theory. It is shown how it is possible to estimate the expected cross-validation error from the training set. This section presents estimators that can indicate whether voting will increase or decrease stability for a particular set of data. This ...
Cryptography and Network Security - Text of NPTEL IIT Video Lectures
... based on the value of f x, so Bob essentially has got the information of f x, but now what Bob needs to do, is that Bob needs to tell Alice his guess of whether x is odd or even. I will come to the properties, but first of all just try to understand the protocol. Then Alice what she does is that Ali ...
... based on the value of f x, so Bob essentially has got the information of f x, but now what Bob needs to do, is that Bob needs to tell Alice his guess of whether x is odd or even. I will come to the properties, but first of all just try to understand the protocol. Then Alice what she does is that Ali ...
Notes on Spinner Learning Task 3 - Georgia Department of Education
... Sometimes when studying probability, it is easier to understand how to find an answer by examining a smaller sample space. The wheel used on Wheel of Fortune has many different sections. It also has “lose a turn” and “bankrupt” which turns a simple probability problem into one that is much more comp ...
... Sometimes when studying probability, it is easier to understand how to find an answer by examining a smaller sample space. The wheel used on Wheel of Fortune has many different sections. It also has “lose a turn” and “bankrupt” which turns a simple probability problem into one that is much more comp ...
organizational behavior and human decision processes
... the origin of the response styles themselves would remain the mystery it has always been.) Fischhoff, Slovic, and Lichtenstein (1977) provided an excellent model for how one might approach an issue like the present one. In two experiments, these investigators set out to determine whether their (pres ...
... the origin of the response styles themselves would remain the mystery it has always been.) Fischhoff, Slovic, and Lichtenstein (1977) provided an excellent model for how one might approach an issue like the present one. In two experiments, these investigators set out to determine whether their (pres ...
When Did Bayesian Inference Become “Bayesian”? Stephen E. Fienberg
... detailed discussion of what all of these authors meant by these terms). This focus on the meaning of probability quickly spread to other countries as well. The links between France and Russia were especially strong as Seneta (152) notes and, while the work in Russia influenced the formal development ...
... detailed discussion of what all of these authors meant by these terms). This focus on the meaning of probability quickly spread to other countries as well. The links between France and Russia were especially strong as Seneta (152) notes and, while the work in Russia influenced the formal development ...
doc - John L. Pollock
... It is convenient to be able to write proportions in the same logical form as probabilities, so where and are open formulas with free variable x, let x ( / ) ({x | & },{x | }) . Note that x is a variable-binding operator, binding the variable x. When there is no danger of confusi ...
... It is convenient to be able to write proportions in the same logical form as probabilities, so where and are open formulas with free variable x, let x ( / ) ({x | & },{x | }) . Note that x is a variable-binding operator, binding the variable x. When there is no danger of confusi ...
Misspecified Recovery Jaroslav Boroviˇcka Lars Peter Hansen Jos´e A. Scheinkman
... Arrow, that asset prices reflect a combination of investors’ risk aversion and the probability distributions used to assess risk. In dynamic models, investors’ risk aversion is expressed by stochastic discount factors that include compensations for risk exposures. In this paper, we ask what can be l ...
... Arrow, that asset prices reflect a combination of investors’ risk aversion and the probability distributions used to assess risk. In dynamic models, investors’ risk aversion is expressed by stochastic discount factors that include compensations for risk exposures. In this paper, we ask what can be l ...
Ars Conjectandi
Ars Conjectandi (Latin for The Art of Conjecturing) is a book on combinatorics and mathematical probability written by Jakob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way, and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations—the aforementioned problems from the twelvefold way—as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.