Across the company, machine learning and artificial intelligence (AI) are increasingly driving many of our latest innovations. Within Google, our investments in machine learning over a decade have enabled us to build products that are smarter and more useful -- it's what allows you to use your voice to ask the Google Assistant for information, to translate the web from one language to another, to see better YouTube recommendations, and to search for people and events in Google Photos. Our advertising tools also use machine learning to help marketers find the right audience, deliver the right creative, and optimize their campaigns through better auto-bidding and measurement tools. Machine learning is also showing great promise in helping us tackle big issues, like dramatically improving the energy efficiency of our data centers.

We continue to make significant R&D investments in areas of strategic focus such as advertising, cloud, machine learning, and search, as well as in new products and services.

The number of people who access the Internet through devices other than desktop computers, including mobile phones, smartphones, laptops and tablets, video game consoles, voice-activated speakers, wearables, automobiles, and television set-top devices, is increasing dramatically.

Our product innovations have made our services widely used, and our brand one of the most recognized in the world. Google's core products and platforms such as Android, Chrome, Gmail, Google Drive, Google Maps, Google Play, Search, and YouTube each have over one billion monthly active users. But most important, we believe we are just beginning to scratch the surface

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since the convents where some had been educated had been disbamlcd long ago by Henry Vlll,

the scalar curvatureRofds2is given byR= (1−u−2)Rρ+u−2n−1∑i,jR0ijij+ 2n−1∑i=1Rnini= (1−u−2)Rρ+u−2R0−2u−1∆ρu+ 2u−3∂u∂ρH0whereR0is the scalar curvature ofNwith respect tods20andRρis the scalar curvatureof Σρwith the induced metric.

Theoretically, positive thinkingworks because the individual alters the personal meaning ofan event so the new meaning is less threatening (Beck, 1967).Indeed, some of the women emphasized their personaldecision making:I’m not going to sit down and feel sorry for myself and get boggeddown and start thinking about those [depressing] things. Soon [as]it comes into my thought—I, I change it, I replace it with somethingpositive, something good. You know what I mean? I can choose.Now I can choose to be sad or I can choose to be happy. It’s noteasy, but it’s something that, um, can be achieved by continuedpracticing.

Programs that are well designed and take into consideration children's developmental stages are more likely to have educational merit than shows not geared toward their healthy growth. Even more important than the content and construction of a show, however, is the role a caregiver can play. By watching with the child, a parent can find ways to interact during the viewing and take advantage of learning opportunities embedded in a program.

Despite marketing claims that some television programs and DVDs help infants and toddlers learn, recent studies show that TV provides only empty calories for a child’s growing brain. The following research brief reviews the evidence that parents and caregivers of young children should take television off the menu.

In particular, the FCC’s action today has restored the jurisdiction of the Federal Trade Commission to act when broadband providers engage in anticompetitive, unfair, or deceptive acts or practices.

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Let Σ0be a compact strictly convex hypersurface inRn,Xbe the position vector ofa point on Σ0, and letNbe the unit outward normal of Σ0atX. Let Σrbe the convexhypersurface described byY=X+rN, withr≥0. The Euclidean space outside Σ0canbe represented by(Σ0×(0,∞),dr2+gr)wheregris the induced metric on Σr. Consider the following initial value problem(2.1)2H0∂u∂r= 2u2∆ru+ (u−u3)Rron Σ0×[0,∞)u(x,0) =u0(x)whereu0(x)>0 is a smooth function on Σ0,H0andRrare the mean curvature and scalarcurvature of Σrrespectively, and ∆ris the Laplacian operator on Σr.

Given a functionRonN, we want to find the equation forusuch that(1.2)ds2=u2dρ2+gρhas scalar curvatureR.

Let Σ be a smooth compact manifold without boundary with dimensionn−1 and letN= [a,∞)×Σ equipped with a Riemannian metric of the form(1.1)ds20=dρ2+gρfor a point (ρ,x)∈N. Heregρis the induced metric on Σρwhich is the level surfaceρ=constant

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One wonders what the obvious "positive modification" ofthe military-industrial complex is

Educators must work together to ensure that every American young person has access to theskills and experiences needed to become a full participant, can articulate their understanding of

Think of all the hard work and the sweat you put in to the things that your proudest of.

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But there’s, I think there is a question of how you interpret the data, even ... ifthe experiments are very well designed. And, in terms of advice—not that I’mgoing to say that it’s shocking—but one of my mentors, whom I very muchrespect as a scientist—I think he’s extraordinarily good—advised me to alwaysput the most positive spin you can on your data. And if you try to present, like,present your data objectively, like in a job seminar, you’re guaranteed tonotgetthe job

You are. And you know what the problems are in doing the experiments. And ifyou, in your mind, think that there should be one more control—because youknow this stuff better than anybody else because you’re doing it, you know—you decided not to do that, not to bring up what the potential difficulties are, youhave a better chance of getting that paper published. But it’s—I don’t think it’sthe right thing to do.

Lemma 2.3.(2.1) has a unique solutionufor allrwhich satisfies the estimates in Lemma2.2.

Let Σ0be a smooth compact strictly convex hypersurface inRn. Letrbe the distance function from Σ0. Then the metric on the exteriorNof Σ0is given bydr2+gr, wheregris the induced metric on Σr, which is the hypersurface with distancerfrom Σ0. The functionuwith prescribed scalar curvatureR= 0 is given by2H0∂u∂r= 2u2∆ru+ (u−u3)RrwhereH0is the mean curvature of Σr,Rris the scalar curvature of ΣrandR0is the scalarcurvature of Σrwith the induced metric fromRnand ∆ris the Laplacian on Σr.

The bias was first identified by the statistician Theodore Sterling, in 1959, after he noticed that ninety-seven per cent of all published psychological studies with statistically significant data found the effect they were looking for.