The golden ticket Fortnow, Lance
2013., 20130327, 2013, 2013-03-27, c2013
eBook
The P-NP problem is the most important open problem in computer science, if not all of mathematics.The Golden Ticketprovides a nontechnical introduction to P-NP, its rich history, and its algorithmic ...implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives.
The Golden Ticketexplores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of the P-NP problem.
The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community ...conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.
Since 1984, Geophysical Data Analysis has filled the need for a short, concise reference on inverse theory for individuals who have an intermediate background in science and mathematics. The new ...edition maintains the accessible and succinct manner for which it is known, with the addition of: MATLAB examples and problem setsAdvanced color graphicsCoverage of new topics, including Adjoint Methods; Inversion by Steepest Descent, Monte Carlo and Simulated Annealing methods; and Bootstrap algorithm for determining empirical confidence intervalsOnline data sets and MATLAB scripts that can be used as an inverse theory tutorial.
Additional material on probability, including Bayesian influence, probability density function, and metropolis algorithmDetailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studiesNumerous examples and end-of-chapter homework problems help you explore and further understand the ideas presentedUse as classroom text facilitated by a complete set of exemplary lectures in Microsoft PowerPoint format and homework problem solutions for instructorsCheck out the companion website: http://www.elsevierdirect.com/companion.jsp?ISBN=9780123971609 and the Instructor website: http://textbooks.elsevier.com/web/manuals.aspx?isbn=9780123971609
These articles, written by leading experts, address important analytic, numerical, and physical issues of the newly developing imaging modalities (photoacoustics, current impedance imaging, hybrid ...imaging techniques, elasticity imaging), as well as the recent progress in resolving outstanding problems of more traditional modalities, such as SPECT, ultrasound imaging, and inverse transport theory. Related topics of invisibility cloaking are also addressed.
Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important ...applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory.
Activated Gradients for Deep Neural Networks Liu, Mei; Chen, Liangming; Du, Xiaohao ...
IEEE transaction on neural networks and learning systems,
2023-April, 2023-Apr, 2023-4-00, 20230401, Letnik:
34, Številka:
4
Journal Article
Odprti dostop
Deep neural networks often suffer from poor performance or even training failure due to the ill-conditioned problem, the vanishing/exploding gradient problem, and the saddle point problem. In this ...article, a novel method by acting the gradient activation function (GAF) on the gradient is proposed to handle these challenges. Intuitively, the GAF enlarges the tiny gradients and restricts the large gradient. Theoretically, this article gives conditions that the GAF needs to meet and, on this basis, proves that the GAF alleviates the problems mentioned above. In addition, this article proves that the convergence rate of SGD with the GAF is faster than that without the GAF under some assumptions. Furthermore, experiments on CIFAR, ImageNet, and PASCAL visual object classes confirm the GAF's effectiveness. The experimental results also demonstrate that the proposed method is able to be adopted in various deep neural networks to improve their performance. The source code is publicly available at https://github.com/LongJin-lab/Activated-Gradients-for-Deep-Neural-Networks .
The main purpose of this study was to test the effects of word-problem (WP) intervention, with versus without embedded language comprehension (LC) instruction, on at-risk 1st graders' WP performance. ...We also isolated the need for a structured approach to WP intervention and tested the efficacy of schema-based instruction at 1st grade. Children (n = 391; Msubscript age = 6.53, SD = 0.32) were randomly assigned to 4 conditions: schema-based WP intervention with embedded language instruction, the same WP intervention but without LC instruction, structured number knowledge (NK) intervention without a structured WP component, and a control group. Each intervention included 45 sessions, each 30 min long. Multilevel models, accounting for classroom and school effects, revealed the efficacy of schema-based WP intervention at 1st grade, with both WP conditions outperforming the NK condition and the control group. Yet, WP performance was significantly stronger for the schema-based condition with embedded LC instruction compared to the schema-based condition without LC instruction. NK intervention conveyed no WP advantage over the control group, even though all 3 intervention conditions outperformed the control group on arithmetic. Results demonstrate the importance of a structured approach to WP intervention, the efficacy of schema-based instruction at 1st grade, and the added value of LC instruction within WP intervention. Results also provide causal evidence on the role of LC in WP solving.
The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded prealgebraic reasoning instruction, improved word-problem performance. Students ...with mathematics difficulty (MD; n = 304) were randomly assigned to a business-as-usual condition or 1 of 2 variants of word-problem intervention. The prealgebraic reasoning component targeted relational understanding of the equal sign as well as standard and nonstandard equation solving. Intervention occurred for 16 weeks, 3 times per week, 30 min per session. Sequential mediation models revealed main effects, in which each intervention condition significantly and substantially outperformed the business-as-usual condition, corroborating prior research on the efficacy of schema word-problem intervention. Yet despite comparable effects on word-problem outcomes between the two word-problem conditions, the process by which effects accrued differed: An indirect path via equal-sign understanding and then equation solving was significant only for the word-problem intervention condition with embedded prealgebraic reasoning instruction. Additionally, the effect of this condition on equal-sign reasoning was strong. Given the link between equal-sign reasoning for success with algebra and the importance of algebra for success with advanced mathematics, results suggest an advantage for embedding prealgebraic reasoning instruction within word-problem intervention.
Educational Impact and Implications Statement
This study suggests prealgebraic reasoning is important within math word-problem instruction for third-grade students who experience difficulty with math. Prealgebraic reasoning involves interpreting the equal sign as "the same as" and solving equations (e.g., 3 + __ = 9 or 7 = 13 − __). As students develop strong prealgebraic reasoning, they are better equipped to solve word problems.
The case for a modern democratic humane socialism typically has two parts. The first is that capitalism is bad, at or least not very good. In reaching this conclusion, most have either analyzed a ...theoretical ideal-type of capitalism or used a single country, often the United States, as a stand-in for capitalism. To fully and fairly assess democratic socialism’s desirability, we need to compare it to the best version of capitalism that humans have devised: social democratic capitalism, or what is often called the Nordic model. Each chapter in this book examines one of the things that we should want in a good society, that contemporary democratic socialists typically say they want, and that socialism might, conceivably, improve our ability to achieve: an end to poverty in rich countries, an end to poverty everywhere, more jobs, decent jobs, faster economic growth, inclusive growth, more public goods and services, affordable healthcare for all, helpful finance, truly democratic politics, economic democracy, less economic inequality, gender and racial equality, more community, and a livable planet. The book offers a close look at the evidence about how capitalist economies have performed on these outcomes, with particular attention to the performance of social democratic capitalism. The second part of the case for democratic socialism is the notion that it would be an improvement. For each of these outcomes, the book considers what, if anything, we can conclude about whether democratic socialism would do better than social democratic capitalism.
Investigations have found mothers’ adverse childhood experiences (ACEs) confer an intergenerational risk to their children's outcomes. However, mechanisms underlying this transmission have only been ...partially explained by maternal mental health. Adult attachment insecurity has been shown to mediate the association of ACEs and mental health outcomes, yet an extension of this research to children's behavioral problems has not been examined.
To examine the cascade from maternal ACEs to risk for child behavioral problems at five years of age, via mothers’ attachment insecurity and mental health.
Participants in the current study were 1994 mother-child dyads from a prospective longitudinal cohort collected from January 2011 to October 2014.
Mothers retrospectively reported their ACEs when children were 36 months of age. When children were 60 months of age, mothers completed measures of their attachment style, depression and anxiety symptoms, and their children's behavior problems.
Path analysis demonstrated maternal ACEs were associated with children's internalizing problems indirectly via maternal attachment avoidance, attachment anxiety, and depression symptoms, but not directly (β = .05, 95% CI −.001, .10). Maternal ACEs indirectly predicted children's externalizing problems via maternal attachment avoidance, attachment anxiety, and depression. A direct effect was also observed from maternal ACEs to child externalizing problems (β = .06, 95% CI .01, .11).
Maternal ACEs influenced children's risk for poor behavioral outcomes via direct and indirect intermediary pathways. Addressing maternal insecure attachment style and depression symptoms as intervention targets for mothers with histories of ACEs may help to mitigate the intergenerational transmission of risk.
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