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Search Results: 1 - 10 of 4688 matches for " Neil Lutz "
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Algorithmic information and plane Kakeya sets
Jack H. Lutz,Neil Lutz
Computer Science , 2015,
Abstract: We formulate the conditional Kolmogorov complexity of x given y at precision r, where x and y are points in Euclidean spaces and r is a natural number. We demonstrate the utility of this notion in two 1. We prove a point-to-set principle that enables one to use the (relativized, constructive) dimension of a single point in a set E in a Euclidean space to establish a lower bound on the (classical) Hausdorff dimension of E. We then use this principle, together with conditional Kolmogorov complexity in Euclidean spaces, to give a new proof of the known, two-dimensional case of the Kakeya conjecture. This theorem of geometric measure theory, proved by Davies in 1971, says that every plane set containing a unit line segment in every direction has Hausdorff dimension 2. 2. We use conditional Kolmogorov complexity in Euclidean spaces to develop the lower and upper conditional dimensions dim(x|y) and Dim(x|y) of x given y, where x and y are points in Euclidean spaces. Intuitively these are the lower and upper asymptotic algorithmic information densities of x conditioned on the information in y. We prove that these conditional dimensions are robust and that they have the correct information-theoretic relationships with the well studied dimensions dim(x) and Dim(x) and mutual dimensions mdim(x:y) and Mdim(x:y).
Lines Missing Every Random Point
Jack H. Lutz,Neil Lutz
Computer Science , 2014,
Abstract: We prove that there is, in every direction in Euclidean space, a line that misses every computably random point. We also prove that there exist, in every direction in Euclidean space, arbitrarily long line segments missing every double exponential time random point.
Examining the Reuse of Open Textbooks
John Hilton III,David A. Wiley,Neil Lutz
International Review of Research in Open and Distance Learning , 2012,
Abstract: An important element of open educational resources (OER) is the permission to use the materials in new ways, including revising and remixing them. Prior research has shown that the revision and remix rates for OER are relatively low. In this study we examined the extent to which the openly licensed Flat World Knowledge textbooks were being revised and remixed. We found that the levels of revision and remix were similar to those of other OER collections. We discuss the possible significance and implication of these findings.
Self-stabilizing uncoupled dynamics
Aaron D. Jaggard,Neil Lutz,Michael Schapira,Rebecca N. Wright
Computer Science , 2014,
Abstract: Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player's behavior is independent of the other players' preferences. Recognizing an equilibrium in this setting is a distributed computational task. Self-stabilizing uncoupled dynamics, then, have both resilience to arbitrary initial states and distribution of knowledge. We study these dynamics by analyzing their behavior in a bounded-recall synchronous environment. We determine, for every "size" of game, the minimum number of periods of play that stochastic (randomized) players must recall in order for uncoupled dynamics to be self-stabilizing. We also do this for the special case when the game is guaranteed to have unique best replies. For deterministic players, we demonstrate two self-stabilizing uncoupled protocols. One applies to all games and uses three steps of recall. The other uses two steps of recall and applies to games where each player has at least four available actions. For uncoupled deterministic players, we prove that a single step of recall is insufficient to achieve self-stabilization, regardless of the number of available actions.
Dynamics at the Boundary of Game Theory and Distributed Computing
Aaron D. Jaggard,Neil Lutz,Michael Schapira,Rebecca N. Wright
Computer Science , 2015,
Abstract: We use ideas from distributed computing and game theory to study dynamic and decentralized environments in which computational nodes, or decision makers, interact strategically and with limited information. In such environments, which arise in many real-world settings, the participants act as both economic and computational entities. We exhibit a general non-convergence result for a broad class of dynamics in asynchronous settings. We consider implications of our result across a wide variety of interesting and timely applications: circuit design, social networks, Internet routing, and congestion control. We also study the computational and communication complexity of testing the convergence of asynchronous dynamics, as well as the effects of limited asynchrony. For uncoupled game dynamics, in which preferences are private inputs, we give new bounds on the recall necessary for self stabilization to an equilibrium. Our work opens a new avenue for research at the intersection of distributed computing and game theory.
Is it Rational to Minimize Tax Payments?  [PDF]
Andreas L?ffler, Lutz Kruschwitz
Modern Economy (ME) , 2010, DOI: 10.4236/me.2010.11004
Abstract: The opinion is occasionally voiced that investors should avoid paying tax at all costs. In this paper it is being investigated, using a simple portfolio model with taxes, whether avoiding tax really leads to more µ-σ-efficient solutions. It is demonstrated for four different concepts of tax-minimising policy that they are a far cry from an efficient solution.
Transversality and the Stochastic Nature of Cash Flows  [PDF]
Lutz Kruschwitz, Andreas L?ffler
Modern Economy (ME) , 2015, DOI: 10.4236/me.2015.66072
Abstract: We show that a transversality condition is necessary when it comes to valuing a company with an infinite lifespan. Without transversality the firm value cannot be uniquely determined. Also, an assumption on a lower bound of cash flows is necessary to achieve the desired result. We discuss four different stochastic cash flow processes and analyze to what extent the processes associated with these enterprise values satisfy the transversality condition.
The Globalization-Deglobalization Policy Conundrum  [PDF]
Neil Dias Karunaratne
Modern Economy (ME) , 2012, DOI: 10.4236/me.2012.34048
Abstract: The dynamic process of economic globalization and deglobalization has been occurring in “waves” over the past 250 years. Diffusion models reveal how globalization policies occupy the policy-centre stage when the global economy is booming and is cast on the back-burner when the global economy nose-dives into a slump. According to the diffusion models, when the global economy is booming the nodes that establish crucial linkages in the economy exceed the social optimum generating negative externalities thereby eroding social welfare in such a context policy intervention is justified to reduce the linkages that facilitate the spread of negative shocks or contagion that reduce the capacity for risk- sharing. The globalization-deglobalization policy conundrum also resurfaces in relation to trade flows, cross-border capital mobility, current account sustainability and technology diffusion. The latter has exacerbate the “digital divide” that has accompanied the revolutionary changes in information and communication technology (ICT) revolution by overcoming the “tyranny of distance”. The recurrent global financial crises and speculative attacks on the currency peg have ignited the debate for reshaping the international financial architecture in order to reduce the vulnerability of the domestic economy to the disruptive effects of the global financial crises.
The Economic Value of Public Goods  [PDF]
Thaddeus Neil Cummins
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.518272
Abstract: This paper explores US entrepreneurial history and public budgets from President Eisenhower’s election in 1952 until the beginning of the Obama administration 2008. A mix of market forces, structural changes and a tendency toward unfettered capitalism [1] challenge diagnosis. This analysis examines these complexities with 216 business quarters of economic history. It also provides a mathematical model to characterize in broad strokes positive governance modeling for business. This work is important as economic growth ensures a nation’s ability to protect its citizens.
Child Murder in Nazi Germany: The Memory of Nazi Medical Crimes and Commemoration of “Children’s Euthanasia” Victims at Two Facilities (Eichberg, Kalmenhof)
Lutz Kaelber
Societies , 2012, DOI: 10.3390/soc2030157
Abstract: Nazi Germany’s “children’s euthanasia” was a unique program in the history of mankind, seeking to realize a social Darwinist vision of a society by means of the systematic murder of disabled children and youths. Perpetrators extinguished “unworthy life” during childhood and adolescence by establishing killing stations, misleadingly labeled Kinderfachabteilungen (“special children’s wards”), in existing medical or other care facilities. Part of a research project on Nazi “euthanasia” crimes and their victims, this paper uses a comparative historical perspective to trace memories of the crimes and the memorialization of their victims at the sites of two of these wards (Eichberg and Kalmenhof in Hesse, Germany). It also discusses the implications of the findings for theorizing mnemonic practices and analyzing ways in which memorials and other sites of memory deal with past trauma and atrocity.
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