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Newcomb’s paradox is the name usually given to the following problem. You are playing a game against another player, often called Omega, who claims to be omniscient; in particular, Omega claims to be able to predict how you will pl...
Newcomb’s paradox is the name usually given to the following problem. You are playing a game against another player, often called Omega, who claims to be omniscient; in particular, Omega claims to be able to predict how you will play in the game. Assume that Omega has convinced you in some way that it is, if not omniscient, at least remarkably accurate: for example, perhaps it has accurately predicted your behavior many times in the past. Omega places before you two opaque boxes. Box A, it informs you, contains $1,000. Box B, it informs you, contains either $1,000,000 or nothing. You must decide whether to take only Box B or to take both Box A and Box B, with the following caveat: Omega filled Box B with $1,000,000 if and only if it predicted that you would take only Box B. What do you do? (If you haven’t heard this problem before, please take a minute to decide on an option before continuing.) The paradox The paradox is that there appear to be two reasonable arguments about which option to take, but unfortunately the two arguments support opposite conclusions. The two-box argument is that you should clearly take both boxes. You take Box B either way, so the only decision you’re making is whether to also take Box A. No matter what Omega did before offering the boxes to you, Box A is guaranteed to contain $1,000, so taking it is guaranteed to make you $1,000 richer. The one-box argument is that you should clearly take only Box B. By hypothesis, if you take only Box B, Omega will predict that and will fill Box B, so you get $1,000,000; if you take both boxes, Omega will predict that and won’t fill Box B, so you only get $1,000. The two-boxer might respond to the one-boxer as follows: “it sounds like you think a decision you make in the present, at the moment Omega offers you the boxes, will affect what Omega did in the past, at the moment Omega filled the boxes. That’s absurd.” The one-boxer might respond to the two-boxer as follows: “it sounds like you think you can just make decisions without Omega predicting them. But by hypothesis he can predict them. That’s absurd.” Now what do you do? (Again, please take a minute to reassess your original choice before continuing.) The von Neumann-Morgenstern theorem Let’s avoid the above question entirely by asking some other questions instead. For example, a question one might want to ask after having thought about Newcomb’s paradox for a bit is “in general, how should I think about the process of making decisions?” This is the subject of decision theory, which is roughly about decisions in the same sense that game theory is about games. The things that make decisions in decision theory are abstractions that we will refer to as agents. Agents have some preferences about the world and are making decisions in an attempt to satisfy their preferences. One model of preferences is as follows: there is a set of (mutually exclusive) outcomes, and we will model preferences by a binary relation on outcomes describing pairs of outcomes such that the agent weakly prefers to . This means either that in a decision between the two the agent would pick over (the agent strictly prefers to ; we write this as ) or that the agent is indifferent between them. The weak preference relation should be a total preorder; that is, it should satisfy the following axioms: Reflexivity: . (The agent is indifferent between an outcome and itself.) Transitivity: If and , then . (The agent’s preferences are transitive.) Totality: Either or . (The agent has a preference about every pair of outcomes.) If and then this means that the agent is indifferent between the two outcomes; we write this as . The axioms above imply that indifference is an equivalence relation. The strong assumptions here are transitivity and totality. One reason to
about 1 hour ago
In this lesson, we will discover a special rule that can be applied when you square a binomial.
In this lesson, we will discover a special rule that can be applied when you square a binomial.
about 5 hours ago
Learn to multiply binomials by using the foil method
Learn to multiply binomials by using the foil method
about 6 hours ago
Copyright © 2013 http://jtonedm.com James TaylorI got an update on Red Hat JBoss BRMS recently. I last wrote about them with release 5.2 back in 2011 and JBoss BRMS 5.3 is the current release and includes their support for business rules...
Copyright © 2013 http://jtonedm.com James TaylorI got an update on Red Hat JBoss BRMS recently. I last wrote about them with release 5.2 back in 2011 and JBoss BRMS 5.3 is the current release and includes their support for business rules, business process and event processing (based on the Drools and jBPM open source community projects) with a repository, runtime engines, web-based authoring, governance and a set of Eclipse-based development tools. With release 6.0, Red Hat is planning to integrate Polymita (a BPM suite acquired last year) and JBoss BRMS. This will allow them to release a separate Business Rules Management System – JBoss BRMS 6 – that supports business rules and event processing as well as a new combined product supporting BPMS/BRMS called Red Hat JBoss BPM Suite 6. With release 6.0 Red Hat JBoss BRMS will continue to provide “classic” BRMS capabilities: It will support business and developer authoring tools that share a repository. Support deployment for event processing and rules execution. Consumes business data and real-time event feeds at runtime Provides decisions to client applications. There are also plans to add new capabilities, including: Inclusion of the JBoss Drools 6.0 project runtime which includes lots of work on performance and execution tuning. OptaPlanner for resource scheduling problems is now included as a technology preview (the evolution of the Drools Planner project). New repository architecture based on git for source control (in place of JCR) to allow easier integration of rules development with general IT development as well as providing new features. UberFire to allow authoring tools to be shared between Eclipse and the web while also improving the user interface for business users and increasing collaboration. From a go-to-market perspective Red Hat is focusing on automating decisions (Decision Management), empowering business users, accelerating application development and transitioning to the cloud (as part of the new xPaaS) announcements. Their targets are business-focused Decision Management projects, more general application development where complex logic is a big issue and real-time data analysis focused on event processing. JBoss BPM Suite 6.0 includes all the BRMS 6.0 as well as new features from Polymita such as dashboards/reporting (including Business Activity Monitoring), data modeling, a forms designer, simulation based on the BPSim standard and improved authoring tools for business users. The xPaaS announcement will include the option to buy the BRMS (and BPM Suite) products through OpenShift service provisioning. It is not clear how this will change the pricing but the clear intent is to move to consumption pricing v core-based pricing for on-premise. Red Hat is one of the vendors in our Decision Management Systems Platform Technologies Report and you can get more information on Red Hat JBoss BRMS at redhat.com/brms
about 6 hours ago
Multiplying Polynomials - Step by step examples using the foil method to help you multiply polynomials.
Multiplying Polynomials - Step by step examples using the foil method to help you multiply polynomials.
about 6 hours ago
Subtracting Polynomials -Use these clear, step by step examples to help you subtract polynomials!
Subtracting Polynomials -Use these clear, step by step examples to help you subtract polynomials!
about 6 hours ago
Adding polynomials - step by step examples!
Adding polynomials - step by step examples!
about 7 hours ago
This unit is a brief introduction to the world of Polynomials. We will add, subtract, multiply, and even start factoring a polynomial.
This unit is a brief introduction to the world of Polynomials. We will add, subtract, multiply, and even start factoring a polynomial.
about 7 hours ago
When writing this entry on Compressive Sensing and Uncertainty Quantification a while ago, the following slide was telling me a different story than the one we should be expecting. Yes, a CS approach to uncertainty quantification ...
When writing this entry on Compressive Sensing and Uncertainty Quantification a while ago, the following slide was telling me a different story than the one we should be expecting. Yes, a CS approach to uncertainty quantification does provide some relief in allowing you to have access to the largest coefficients. However, this finding has to be tempered with the fact that lower level coefficients do have an impact (in effect the norm used to evaluate the error is not the real norm that which one uses to evaluate a technique) In fact, I was not overly surprised to see some of the slides in yesterday's entry. The post featured the slides of the second edition of the International Workshop on Compressed Sensing applied to Radar (CoSeRa 2013), where few presentations tell a story as to why Radar is not directly applicable to actual data. The reason the work of Yonina and collaborators is more successful is because of their focus on the analog based sensing. In MRI, the most advanced field using some of the concepts of compressive sensing, there is a focus on less than random sampling especially for low frequency items, there is not a well theoretically understood reason as to why This is not exactly true, some of these reasons are featured in the following paper (previous coverage and Q&A with some of the authors is also listed below). On a personal level, my mind races through these arguments and wonder how we should change some of the phase transitions we have been accustomed to use and ultimately how sensors should be changed as a result. Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum by Ben Adcock, Anders Hansen, Bogdan Roman, Gerd Teschke The purpose of this paper is to report on recent approaches to reconstruction problems based on analog, or in other words, infinite-dimensional, image and signal models. We describe three main contributions to this problem. First, linear reconstructions from sampled measurements via so-called generalized sampling (GS). Second, the extension of generalized sampling to inverse and ill-posed problems. And third, the combination of generalized sampling with sparse recovery techniques. This final contribution leads to a theory and set of methods for infinite-dimensional compressed sensing, or as we shall also refer to it, compressed sensing over the continuum. Previously, Infinity Matters: Generalized Sampling and Infinite Dimensional Compressed Sensing Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing Additional insights on the Q&A with Ben Adcock and Anders Hansen A Q&A with Ben Adcock and Anders Hansen: Infinite Dimensional Compressive Sensing, Generalized Sampling, Wavelet Crimes, Safe Zones and the Incoherence Barrier. CS: Recovering Lost Sensor Data through CS, A Question to Anders Hansen Join the CompressiveSensing subreddit or the Google+ Community and post there ! Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.
about 10 hours ago
(Click on the cartoon to see the full image.) (C)Copyright 2013, C. Burke.Imagine if the pins were number like Pascal's Triangle. This should be the last of the "The Number of the" for a while. And surprisingly, it seems to be only my...
(Click on the cartoon to see the full image.) (C)Copyright 2013, C. Burke.Imagine if the pins were number like Pascal's Triangle. This should be the last of the "The Number of the" for a while. And surprisingly, it seems to be only my second bowling comic, and the first in over 500 strips, since my 300th comic.
about 16 hours ago