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Tag Archives: video
From Vimeo to Periscope. Do we really need another video app?
First, there was Vimeo, the first video sharing website.
Vimeo allowed users to upload, share and search for videos online, and life was good.
Then there was YouTube.
YouTube gave us our fill of all the videos we could no longer see on cable or broadcast TV, all with a quick search.
Vevo popped up after that.
Vevo was a great alternative to YouTube because it had higher quality videos, without all the associated riffraff of user generated content.
Suddenly UStream appeared, and not only could you watch video replays, but you could tap into live video streams.
Couldn't be there, but want to experience it live?
UStream let you do just that.
We had achieved video Nirvana.
Not to be left out of the fray, Facebook offered its own native video player, giving its millions of users an easy way to upload and share videos on its platform.
All of your low res, hi def, canned or live streaming video options were covered.
Because then came SnapChat with it's expiring videos.
Wait, that's a thing?
And then Meerkat, the app that lets you broadcast yourself doing whatever to whoever wants to tune in.
And finally (and I say "finally" loosely) Periscope, which let you do the same thing.
So, what's with all the video apps and services?
Well, video is a big thing.
No, I'm not talking about the bandwidth it requires.
I'm talking about the appetite folks have for it.
And they money that can be made.
Instagram has added video, so that its not just still photos anymore.
YouTube now offers "premium" channels.
Content companies, like HBO, are cutting ties with Cable companies and offering their content directly to consumers through apps and consoles.
Netflix and Hulu let you watch television and movies on the go.
Virtually everywhere you look – elevators, cabs, subways, planes, trains – video is offered.
And regular people are getting in on the action.
"YouTubers" is a thing.
Shooting a video of a melee and yelling "WorldStar!" is a thing.
People try to make "viral" videos as a way of getting their 15 minutes.
Folks earn bookoo bucks as YouTube broadcasters, creating often funny, niche content, attracting tens of thousands of viewers, and earning income as well.
Buzzfeed, FunnyOrDie, College Humor and many others' business models are built exclusively off producing and marketing video content.
So while I think the current 'fight' between the creators of apps like Periscope and Meerkat is stupid, because…well just because, there is clearly an insatiable appetite for virtually any kind of video.
Have you ever watched a sensory video – the kind that's supposed to give you tingles just by watching?
I digress.
To answer the question posed in the title of this post, "do we really need another video app?"
No. We don't.
Are Meerkat or Periscope the last of the video apps we've seen?
No. Not by a long shot.
There's a war for eyeballs currently being waged.
With billions of dollars to be made.
And folks out here seeking fame by turning their cameras on and streaming themselves doing whatever.
And with all of our shiny, powerful, always-on mobile devices clutched in our collective sweaty palms, we're all in the crosshairs.
Filed under mobile, opinion
Tagged as Instagram, live steaming app, Meerkat, Prridcope, Snapchat, streaming video, Ustream, Vevo, video, video player, video sharing website, Vimoe, Worldstar, YouTube, YouTubers
Is Google Glass the future of computing (or a passing fad)?
My colleagues and I are a bunch of (admitted) geeks.
Every day, we share links from Engadget, Gizmodo, TechCrunch and the like.
About interesting apps, techie news, digital trends or hot topics.
A few days ago, someone passed around a link to a promo video for Google Glass.
For the uninformed, Google Glass is Google's foray into developing a wearable computer.
Unlike the alleged smart watch being developed by Apple, Google Glass is a frame you wear on your face, like a pair of glasses.
There are no lenses, per se.
Just a small rectangular surface, sitting an inch or so away from the eye, within which sits the Google Glass display.
Google Glass is very limited in its functionality.
From the video demonstration, Google Glass lets you record and playback video, video chat, get turn-by-turn directions, or send a message.
The What It Does part of the Google Glass site seems to suggest that it does a little more than this.
But not much more.
Since there is no keyboard, you're limited to voice controlled functions.
Now, we can talk to our computers, Star Trek- like, and have them perform increasingly complex functions.
There is a little button on the side, presumably to allow the user to switch between functions.
But beyond that, it's totally hands free.
When I first watched the video, it reminded me of a GoPro commercial.
It was all about the visuals.
But unlike GoPro, Google Glass allows you to do more than just record video.
You almost forget about the little screen in the top right corner, because your field of vision is right in front of you.
And that got me wondering…
When you're wearing a pair of Google Glasses, are you always staring up and to the right?
Like you're thinking about something?
"Do I look like a dork?" perhaps?
My curiosity got the best of me, and I signed up to try out the damn things.
But a happy black chick on the sign up page told me that the applications to try Google Glass were closed.
If you weren't so cute, I'd be mad atcha.
I signed up anyway.
I doubt I'll see a pair in the wild before they're available for sale.
But one can always hope.
In any instance, it's definitely got me intrigued.
Is Google Glass the way of the future?
Tagged as digital trends, Engadget, Gizmodo, Google, Google Glass, playback, TechCrunch, video, video chat, voice commands
Superbowl XLVI and Social Media: A Wish List
Which brands will freak social media this year?
Tomorrow night, the New York Giants will play the New England Patriots in Superbowl XLVI.
While most will be focusing on the game, for marketers, talk always turns to the commercials that air during the game.
With an estimated audience of 111 million, advertisers are queued up to spend $3 million for a thirty second spot, all in hopes of making an impact on that audience.
A well executed commercial can leave an impression on viewers that will last for months afterward and translate into money well spent by the brand(s) that get it right.
Volkswagon's Young Vader commercial, which aired during Superbowl XLV has garnered over 50 million views to date, and was by far, one of the most popular commercials of the game.
While talk usually revolves around what Superbowl commercials the big brands are planning, I'm more interested in seeing how (and whether) these same brands integrate social media into their campaigns.
Aside from making their commercials available on YouTube (which is valuable), I'm curious as to how many have planned more comprehensive social media campaigns.
I'd imagine that we're going see a number of calls-to-action involving 'liking' this brand or that on Facebook.
Quite passe, if you ask me.
But aside from the standards, like this or follow that, are any of these brands thinking outside of the box?
My wish list for this year's Superbowl is to see brands utilizing social media in new and innovative ways.
I, for one, am going to be keeping a watchful eye for anything extraordinary tomorrow.
I'm also going to be looking out for which commercials create the biggest buzz during the game.
Which commercials are trending on Twitter?
Which brands get people updating their status with 'LMFAO's?
Which commercials get shared the most?
SMS. SnapTags. QR Codes. Spoof videos. Mobile-only content. I'm expecting it all!
Since my Cowboys were unceremoniously drummed out of Superbowl contention by the Giants (damn you Eli!), I've got no skin in the game.
So, don't worry. I won't be distracted rooting for any team. I know you were concerned.
I'll keep a scorecard of who did what, paying special attention to the campaigns that tricked out their social media components.
Check in Monday for my post-game survey.
Go <fill in the name of your team here>!
Filed under branding, digital advocacy, social media
Tagged as commercials, Dallas Cowboys, Facebook, follow, interactive, like, links, media campaigns, mobile-only content, New England Patriots, New York Giants, post, QR codes, SMS, SnapTags, social media, superbowl commercials, Superbowl XLV, Superbowl XLVI, video, Volkswagon Young Vader, YouTube
President Obama channels Al Green at the Apollo
I was going to give you an elaborate post about mobile engagement tools, but I saw this last night, and had to share:
Only President Obama could pull off (a few lines) of Al Green's Let's Stay Together.
Apparently on a dare!
It's this sense of spontaneity that makes Obama the President that he is.
And why he raised $3.6 million yesterday on his latest jaunt through New York city.
Haven't heard back from team Obama (remember I sent a resume online?), but I'll still rep for the Big 0.
Especially when he's coming with all that swagger!
With the heavy news coverage on his little song, I wouldn't be surprised if this video is viral by this weekend.
Filed under Smack talking, social media
Tagged as Al Green, Apollo, Let's Stay Together, New York, President Obama, singing, swagger, video, viral, YouTube
SoLoMo Profile: Wyst
The second company I'm going to profile for the Starters+Startups: The Future of SoLoMo & You panel I'm moderating is Wyst.
The Wyst app allows you to share geo-tagged photographs, with family, friends and members of your Facebook and Twitter social networks.
Wyst's homepage is spare.
In the header of the page, there are three icons next to a phone which offer:
Share experiences. As they happen, where they happen.
Discover new stories around you.
It's a new kind of message in a bottle.
Since there was a video, I watched.
It's a 3:13 minute commercial, that I think does a really good job of telling you what Wyst's all about, without a single line of dialogue.
You simply follow this bloke around NY as he use the app and a companion screen of his iPhone shows you his Wyst thread.
Nicely done Wyst.
From what I gleaned from watching the video alone, you can take a picture, tag it with different emoticons and post it to your Wyst profile.
I'll know more when I take the app for a test-drive.
The bottom of the page offers links to the App store, their social media profiles (Facebook and Twitter), the Latest News, Blog and About Us pages.
You can also sign up for the Wyst newsletter on the page.
The Latest News includes the fact that Wyst is now out of Beta and available in the iTunes App store.
The Blog takes you to a page which offers various Wysts of the Day.
It's essentially a blog roll of different pictures taken by Wyst users all over the globe.
Wyst of the Day
Wyst's About Us page is fairly irreverent.
It pays homage to the Brooklyn roots of the app, as well as the following:
"Wyst is a like a new kind of message in a bottle: it's a fun app that enables you to share cool moments, random musings, unique tidbits and interesting experiences by capturing them on a photo or text note and tagging them to a location for others to find. The idea came to us from a simple question:
"Wouldn't it be awesome to freeze this moment in time, in this place, so that when someone else passes by this same spot they can find it and experience it themselves?"
As the Wyst site is light on pages, I checked out their Facebook and Twitter pages too (let's get those numbers up fellas – okay?) while downloading the app from the App Store.
Wysts are a tad scarce, huh? Gimme a chance why dontcha!
I'm going to play around with their app this week too, so stay tuned for any updates.
Again, if you've used Wyst, like it or have an opinion, please share!
Filed under apps, branding, mobile
Tagged as App Store, beta, blog, Brooklyn, discover, Facebook, iPhone, message, share, Starters+Startups: The Future of SoLoMo & You, Twitter, video, Wyst, Wyst of the Day, YouTube
Digital Stewardship: PAL Digital U.N.I.Verse.City
A PAL Digital U.N.I.Verse.City workstation.
If you're a forty-something like me, computer classes in high school involved learning to program in ASCII or DOS on a monochrome screen.
If you attended college, there may have been more advanced computer classes, for which you likely moved and stored content on floppy disks.
After college, you used a PC running some version of Windows at the job, and computer proficiency meant that you knew how to use Microsoft's Office Suite.
You're up on the latest gadgets, even if you don't own an iPad or mobile tablet.
You probably have a smartphone, a laptop and an mp3 player.
And you probably consider yourself pretty savvy when it comes to digital technology.
We are dinosaurs!
Present company excluded, of course.
Today's youth are exposed to technology, not as a stiff class taught by some bored out-of-touch professor, but as a natural extension of their everyday existence.
Their access to and adoption of technological gadgets, is second nature to them, almost intuitive.
And unlike us, who came into the 'technological age' of massive building-size 'super computers,' today's youth have microprocessors in virtually every device they touch.
The Macbook Pros, Xboxes, Playstations, Wiis, Leapsters of today are tens of thousand times more powerful than anything we ever used growing up.
With Facebook, Twitter, texting, etc., kids are more immersed in interactive technology and applications than we ever were.
They can access and touch virtually any part of the digital universe, and regularly use technology to communicate, socialize and interact with one-another and others.
This intimacy, however, has it's consequences, though.
Cyber-bullying, internet plagiarism, and the regular posting of questionable (and often inappropriate) content are norms, that we didn't experience when we were using computers and cell phones.
Social media, as we know it today, didn't even exist.
It's no wonder that kids are acting…like kids, when they use them these different tools.
I think it's important that we take stock of what our children are exposed to (from a digital, content and technological perspective), and give them real guidance on the appropriate and responsible use of technology.
To that end, I want to share a project that I've been working on with the Police Athletic League of New York City (PALNYC).
It's called the PAL Digital Digital U.N.I.Verse.City and its a class being offered as part of an apprenticeship program.
The apprenticeship program is the initiative of Marcel Braithwaite, the Director of Centers for PALNYC.
Marcel manages PALNYC's eleven (11) centers, located in the five boroughs of New York City.
And he wanted to develop a program that exposed kids to technology as a means of both skills/workforce development and keeping them off the streets.
The curriculum we are using for the program was developed by Mark Hines, a graduate of Princeton University, and the CEO and Founder of Marksmen Productions, Inc., a New York city-based creative agency.
Mark has designed a program that teaches real life skills to the youth, using live scenarios which give the students active participation in projects with real time results.
The Digital U.N.I.Verse.City (DU) is a six (6) month intensive audio, video and technology training program, tailored to students of varying degrees of technical proficiency.
Digital U.N.I.Verse.City classes meet two (2) times a week to provide students instruction in digital media production, it's cultural impacts and ethical and moral responsibilities that accompany the use of these tools.
The program officially launches next Wednesday at the Harlem Center on 119th Street, and Digital Uni.Verse.City students will study media (news, tv, movies, music, art), how it is produced, and begin rudimentary hands-on manipulation of video and audio (DU101/102) in preparation for the Advanced Studio Workshop (DU201).
The Time Warner Center in the Harlem Center has been converted into the PAL Digital U.N.I.Verse.City classroom.
Students who successfully complete the intro courses will be invited to participate in the Advanced Studio Workshop, focusing on professional skill development in (one of the following) music production, audio/visual engineering, video production and direction, video editing, motion effects, journalism and musicianship.
Digital U.N.I.Verse.City instructors include many of our professional colleagues, who are experts in their respective fields.
From Grammy-winning musicians, to New York Times best-selling authors, the Digital U.N.I.Verse.City instructors will offer students hands-on training and skill development on live projects.
The Digital U.N.I.Verse.City curriculum starts with a review of the DU Acceptable Use Policy, which lays out the foundation for every student's participation in the program.
Most people have never seen (much less read) an acceptable use policy.
But it is the most important thing, for people living in a highly interconnected digital world – and the point of this rambling post.
I helped to develop (read: wrote) our acceptable use policy, which came together after many long sessions, during which we worked diligently to draft something that actually made sense.
For the majority of people who have ever read (read: scanned) an AU Policy, you know its a statement by the owners, administrators or other gatekeepers of any digital or online environment, which provides a code of conduct that users must observe while utilizing (or as a member of) a particular system.
As an advocate for technology, the Digital U.N.I.Verse.City program, gives me a constructive way to address the issue of responsible use of technology by our youth.
More importantly, working on this project has forced me to address the fact that most of us operate without a set of guiding digital principles.
Obviously, I always promote best practices with my clients, and have helped draft numerous Terms of Use, Privacy Policies and various other online instruments governing the use of certain online programs or environs.
But that's not quite the same thing, when the audience for my usual written verbosity is the youth.
Next Wednesday is our first class (did I say that already?) and I'm excited.
The pictures above were from our dry-run, when we set up the local Moodle we're using for the class.
Be sure to look out for future posts about how the program is coming along.
Also, feel free to donate to or volunteer at your local PAL!
Filed under opinion, technology
Tagged as acceptable use policy, ASCII, audio, audio/visual engineering, cell phone, communicate, cyber-bullying, digital apprenticeship, digital universe, DOS, Facebook, floppy disk, Harlem Center, interact, internet plagiarism, intimacy, iPad, journalism, laptop, Leapster, life skills, Marcel Braithwaite, Mark Hines, Microsoft Office, mobile tablet, motion effects, music production, musicianship, New York City, PALNYC, Playstation, Princeton University, smartphone, socialize, technology, texting, training, Twitter, video, video editing, video production and direction, Wii, Windows, workforce development, XBOX


Somerset has many local services, support groups and activities for people with Dementia and their carers, such as memory cafes and singing for the brain.
For information on the local services provided by the Alzheimer's Society please go to their website. You can also find information on other activities in your local area by using our 'Find services' directory.
Worried someone has dementia? If someone you know is becoming increasingly forgetful, encourage them to see their GP.
Staying independent with dementia People with dementia can remain independent for some time, but will need support from family and friends.
Activities for dementia Keeping up an active social life is key to helping someone with dementia feel happy and motivated.
Communicating with people with dementia Dementia will gradually affect the way the person communicates. Learn more about their ability to present rational ideas and to reason clearly will change.
Coping with behaviour changes in dementia Advice on what to do if the behavior of someone with dementia become aggressive, suspicious or difficult to deal with.
Looking after someone with dementia If you have dementia, or you are looking after someone who does, you will experience a range of practical issues. You can find information and advice to help you on the Alzheimer's Society and AgeUK websites.


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Lyric Robot was approved to set up a national post-doctoral research station
Lyric Robot Posted 12/20/2018
In order to implement the notice of the National Postdoctoral Management Committee of the Ministry of Human Resources and Social Security on approving the establishment of postdoctoral scientific research stations by 399 units including Guangdong Lyric Robot Automation Co.,Ltd., the Party's 19th National Congress on the strategy of accelerating the construction of an innovative country was thoroughly implemented. The deployment will further strengthen the support for post-doctoral work to improve the innovation capability of enterprises and institutions, and promote the in-depth integration of industry, academia and research. After evaluation by experts, the Ministry of Human Resources and Social Security and the National Postdoctoral Management Committee decided to approve Guangdong Lyric Robot Automation Co.,Ltd. After 399 units set up post-doctoral research stations to carry out postdoctoral work.
Scientific and technological innovation is an important driving force for the development of the automation industry and a core element to ensure the core competitiveness of enterprises. High-level innovative scientific and technological talents are the key strength of enterprise science and technology innovation, and post-doctoral talents are an important part of high-level innovative talents. In the increasingly fierce economic globalization competition, the development of post-doctoral workstations and post-doctoral talents of enterprises has played an increasingly important role in promoting enterprises to become the mainstay of innovation.
Partially approved to set up a postdoctoral research station
Lyric Robot adheres to the "people-oriented" scientific development concept, attaches importance to the cultivation and use of scientific and technological talents, establishes and improves the high-level talent welfare system, and has a strong radiation effect of talents, which has led Lyric Robot to introduce more than ten doctors who are committed to research and development. Innovative technologies in the fields of auto parts, lithium batteries, precision electronics, rail transit, medical care, fire protection, etc., constantly broaden the company's technical vision, improve the company's scientific research level, actively promote the transformation of scientific and technological achievements, and realize the company's leap-forward development. On the
other hand, the company gives full play to its advantages in professional literacy, research fields, and disciplinary systems, actively explores and adopts various measures that are consistent with post-doctoral characteristics, and forms a mechanism for nurturing talents and talents that is conducive to high-level talents.
The importance of establishing a post-doctoral research station
The post-doctoral research station of the enterprise is an effective way to combine production, study and research;
The post-doctoral research station of the enterprise is an effective platform for the research institutes and the transfer stations of scientific and technological achievements in universities and the technological innovation of enterprises;
The post-doctoral research station of the enterprise is an incubator for scientific research achievements and an intermediary organization for the industrialization of scientific research results;
Post-doctoral research stations make information more effective and facilitate the flow of talent.
In the future, Lyric Robot will keep up with the development trend of the world, keep a close eye on the company's development goals, keep a close eye on the frontiers of science and technology development, and stand on the overall and strategic perspectives, continuously optimize the talent allocation of high-level people, and accelerate the cultivation of complex and strategic strategies with independent innovation capabilities. Type of post-doctoral talent team.
Father of Robotics Joseph F. Engelberger Dies at Age 9012/01/2015
Weekly Bot Brief on Robotic Research and Investment Review 11-2-201811/04/2018
What's the Best Reach for an Industrial Robot?01/07/2020
Weekly Bot Brief on Robotic Research and Investment Review 12-21-201812/23/2018
Germany's Hanover Fair is Coming to Ann Arbor – Join Phoenix Contact04/12/2018
Association for Advancing Automation White Paper Links Increasing Robotics Shipments to U.S. Job Growth10/02/2015
Project Management Process05/19/2015
Yaskawa America, Inc. Names New CEO04/18/2016
PIA AT AHTE 201908/12/2019

redpajama_set_name: RedPajamaCommonCrawl


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\section{Introduction}\label{sec:intro}
\begin{abstract}
\emph{Over-the-air federated edge learning} (Air-FEEL) is a communication-efficient solution for privacy-preserving distributed learning over wireless networks. Air-FEEL allows ``one-shot" over-the-air aggregation of gradient/model-updates by exploiting the waveform superposition property of wireless channels, and thus promises an extremely low aggregation latency that is independent of the network size. However, such communication efficiency may come at a cost of learning performance degradation due to the aggregation error caused by the non-uniform channel fading over devices and noise perturbation. Prior work adopted channel inversion power control (or its variants) to reduce the aggregation error by aligning the channel gains, which, however, could be highly suboptimal in deep fading scenarios due to the noise amplification. To overcome this issue, we investigate the power control optimization for enhancing the learning performance of Air-FEEL. Towards this end, we first analyze the convergence behavior of the Air-FEEL by deriving the optimality gap of the loss-function under any given power control policy. Then we optimize the power control to minimize the optimality gap for accelerating convergence, subject to a set of average and maximum power constraints at edge devices. The problem is generally non-convex and challenging to solve due to the coupling of power control variables over different devices and iterations. To tackle this challenge, we develop an efficient algorithm by jointly exploiting the \emph{successive convex approximation} (SCA) and trust region methods. Numerical results show that the optimized power control policy achieves significantly faster convergence than the benchmark policies such as channel inversion and uniform power transmission.
\end{abstract}

\section{Introduction}\label{sec:intro}
In the pursuit of ubiquitous intelligence envisioned in the future 6G networks, recent years have witnessed the spreading of {\it artificial intelligence} (AI) algorithms from the cloud to the network edge, resulting in an active area called {\it edge intelligence} \cite{Survey_FEEl,Debbah19}.
The core research issue therein is to allow low-latency and privacy-aware access to rich mobile data for intelligence distillation. To this end, a popular framework called {\it federated edge learning} (FEEL) is proposed recently, which distributes the task of model training over edge devices so as to reduce the communication overhead and keep the data-use locally \cite{Konecny2016aa_FL,Chen20FL}.
Essentially, the FEEL framework is a distributed implementation of {\it stochastic gradient decent} (SGD)  over wireless networks. A typical training process involves iterations between 1)  broadcasting of the global model under training from edge server to devices for local SGD execution using local data, and 2) local models/gradients uploading from devices to edge server for aggregation and global model updating. Although the uploading of high-volume raw data is avoided, the updates aggregation process in FEEL may still suffer from a communication bottleneck due to the high-dimensionality of each updates and the multiple access by many devices over wireless links. To tackle this issue, one promising solution called {\it over-the-air} FEEL (Air-FEEL) has been proposed, which exploits the {\it over-the-air computation} (AirComp) for ``one-shot" aggregation via concurrent update transmission, such that communication and computation are integrated in a joint design by exploiting  the superposition property of a {\it multiple access channel} (MAC)  \cite{Survey_FEEl,nomo_function_Nazer,Gastpar08}.

The idea of AirComp was first proposed in \cite{nomo_function_Nazer} in the context of data aggregation in sensor networks, where it is surprisingly found that ``interference" can be harnessed by structured codes to help functional computation over a MAC. Inspired by the finding, it was shown in the subsequent work \cite{Gastpar08} that for Gaussian {\it independent and identically distributed} (i.i.d.) data sources, the uncoded transmission is optimal in terms of distortion minimization. Besides the information-theoretic studies, various practical issues faced by AirComp implementation were also considered in \cite{Abari15,Cao_PowerTWC,Cao_2020aa}. In particular, the synchronization issue in AirComp was addressed in \cite{Abari15} via an innovative idea of shared clock broadcasting from edge server to devices. The optimal power control policies for AirComp over fading channels were derived in \cite{Cao_PowerTWC} to minimize the average computation distortion, and the cooperative interference management framework for coordinating coexisting AirComp tasks over multi-cell networks was developed in \cite{Cao_2020aa}.

More recently, AirComp found its merits in the new context of FEEL, known as Air-FEEL, for communication-efficient update aggregation as demonstrated in a rich set of prior works \cite{GZhu2020TWC,Amiri2020TSP,KYang2020TWC,NZhang2020Ar,GZhu2020Ar,DLiu2020Ar}. Specifically, a broadband Air-FEEL solution was proposed in \cite{GZhu2020TWC}, where several communication-learning tradeoffs were derived to guide the design of device scheduling. Around the same time, a source-coding algorithm exploiting gradient sparsification was proposed in \cite{Amiri2020TSP} to implement Air-FEEL with compressed updates for higher communication efficiency. In parallel, a joint design of device scheduling and beamforming in a multi-antenna system was presented in \cite{KYang2020TWC} to accelerate Air-FEEL. Subsequently, the gradient statistics aware power control was investigated in \cite{NZhang2020Ar} to further enhance the performance of Air-FEEL. Furthermore, to allow Air-FEEL compatible with digital chips embedded in modern edge devices, Air-FEEL based on digital modulation was proposed in \cite{GZhu2020Ar} featuring one-bit quantization and modulation at the edge devices and majority-vote based decoding at the edge server. Besides the benefit of low latency, Air-FEEL was also found to be beneficial in data privacy enhancement as individual updates are not accessible by edge server, eliminating the risk of model inversion attack  \cite{DLiu2020Ar}.

Despite the promise in high communication efficiency, Air-FEEL may suffer from severe learning performance degradation due to the aggregation error caused by the non-uniform channel fading over devices and noise perturbation. Prior work in this field mostly assumed channel inversion power control (or its variants) \cite{GZhu2020TWC,Amiri2020TSP,KYang2020TWC,DLiu2020Ar} in an effort to reducing the aggregation error by aligning the channel gains, which could be highly suboptimal in deep fading scenarios due to the noise amplification.  Although there exists one relevant study on power control for Air-FEEL system in \cite{NZhang2020Ar}, it focused on the minimization of the intermediate aggregation distortion (e.g., mean squared error) instead of the ultimate learning performance (e.g., the general loss function). Therefore, there still leaves a research gap in learning performance optimization of Air-FEEL by judicious power control, motivating the current work. To close the gap, we first analyze the convergence behavior of the Air-FEEL by deriving the optimality gap of the loss-function under arbitrary power control policy. Then the power control problem is formulated to minimize the optimality gap for convergence acceleration, subject to a set of average and maximum power constraints at edge devices. The problem is generally non-convex and challenging to solve due to the coupling of power control variables over different devices and iterations. The challenge is tackled by the joint use of {\it successive convex approximation} (SCA) and trust region methods in the optimized power control algorithm derivation. Numerical results show that the optimized power control policy achieves significantly faster convergence than the benchmark policies such as channel inversion and uniform power transmission, thus opening up a new degree-of-freedom for regulating the performance of Air-FEEL by power control.

\section{System Model}\label{sec:system}
\begin{figure}
\centering

 \setlength{\abovecaptionskip}{-4mm}
\setlength{\belowcaptionskip}{-4mm}
    \includegraphics[width=3.5in]{Sys_model.eps}
\caption{Illustration of over-the-air federated edge learning. } \label{fig:model}
\end{figure}

We consider an Air-FEEL system consisting of an edge server and $K\ge 0$ edge devices, as shown in Fig.~\ref{fig:model}. With the coordination of the edge server, the edge devices cooperatively train a shared machine learning model via over-the-air update aggregation as elaborated in the sequel.

\subsection{Learning Model}
We assume that the learning model is represented by the parameter vector ${\bf w}\in\mathbb{R}^q$ with $q$ denoting the model size.
Let ${\mathcal D}_k$ denote the local dataset at edge device $k$, in which the $i$-th sample and its ground-true label are denoted by ${\bf x}_i$ and $y_i$, respectively.
Then the local loss function of the model vector $\bf w$ on ${\mathcal D}_k$ is
\begin{align}\label{LocalLossFunction}
F_k({\bf w})=\frac{1}{|{\mathcal D}_k|} \sum \limits_{({\bf x}_i,y_i)\in{\mathcal D}_k} f({\bf w},{\bf x}_i,y_i)+\rho R({\bf w}),
\end{align}
where $f({\bf w},{\bf x}_i,y_i)$ denotes the sample-wise loss function quantifying the prediction error of the model $\bf w$ on the sample ${\bf x}_i$ {\it with respect to} (w.r.t.) its ground-true label $y_i$, and $R({\bf w})$ denotes the strongly convex regularization function scaled by a hyperparameter $\rho\geq 0$.
For notational convenience, we simplify $f({\bf w},{\bf x}_i,y_i)$ as $f_i({\bf w})$.
Then, the global loss function on all the distributed datasets is given by
\begin{align}\label{GlobalLossFunction}
F({\bf w})=\frac{1}{K}\sum\limits_{k\in\mathcal K} D_k F_k({\bf w}),
\end{align}
where ${\mathcal D}=\cup_{k\in\mathcal K} {\mathcal D}_k$ with $D_{\rm tot}=|{\mathcal D} |$, and the sizes of datasets in all edge devices are assumed to be uniform for notation simplicity, i.e., $|{\mathcal D}_k|=\bar D,\forall k\in\mathcal K$.

The objective of the training process is to minimize the global loss function $F({\bf w})$:
 \begin{align}\label{OptimalParameter}
 {\bf w}^{\star}=\arg \min_ {\bf w} F({\bf w}).
\end{align}
Instead of directly uploading all the local data to the edge server for centralized training, the learning process in \eqref{OptimalParameter} can be implemented iteratively in a distributed manner based on gradient-averaging approach as illustrated in Fig.~\ref{fig:model}.

At each communication round $n$, the machine learning model is denoted by ${\bf w} ^{(n)}$. Then each edge device can compute the local gradient denoted by ${\bf g}_{k}^{(n)}$ using the local dataset ${\mathcal D}_k$:
\begin{align}\label{sys_LocalGradient}
{\bf g}_{k}^{(n)}=	\frac{1}{|{\mathcal D}_k|} \sum \limits_{({\bf x}_i,y_i)\in{\mathcal D}_k} \nabla f_i({\bf w}^{(n)})+\rho \nabla R({\bf w}),
\end{align}
where $\nabla$ is the gradient operator and we assume that the whole local dataset is used to estimate the local gradients.
Next, the edge devices upload all local gradients to the edge server, which are further averaged to obtain the global gradient:
\begin{align}\label{sys_GlobalGradient}
\bar{\bf g}^{(n)}=	\frac{1}{K}\sum\limits_{k\in\mathcal K} {\bf g}_{k}^{(n)}.
\end{align}
Then, the global gradient estimate is broadcast from edge server to edge devices, based on which edge device can update its own model under training via
\begin{align}\label{sys_ModelUpdate}
{\bf w}^{(n+1)}={\bf w}^{(n)}-\eta\cdot \bar{\bf g}^{(n)},
\end{align}
where $\eta$ is the learning rate. Notice that the above procedure continues  until convergence criteria is met or the maximum number of iterations is achieved.

 \subsection{Basic Assumptions on Learning Model}
 To facilitate the convergence analysis next, we make several standard assumptions on the loss function and gradient estimates.

 \begin{assumption}[Smoothness]\label{Assump_Smooth}\emph{
Let ${\bf g}=\nabla F({\bf w})$ denote the gradient of the loss function evaluated at point ${\bf w}$. Then there exists a non-negative constant vector  ${\bf L}\in\mathbb{R}^q$, such that
\begin{align*}
F({\bf w})\!-\!\left[ F({\bf w}^{\prime})\! +\! {\bf g}^T (\!{\bf w}\!\!-\! {\bf w}^{\prime})\right] \le \frac{1}{2}\sum_{i=1}^{q}\! L_i({{ w}_i\!-\!{w}^{\prime}_i}\!)^2, \forall {\bf w}, {\bf w}^{\prime},
\end{align*}
where the superscript $T$ denotes the transpose operation.}
\end{assumption}

\begin{assumption}[Polyak-Lojasiewicz Inequality]\label{Assump_PL}\emph{
Let $F^{\star}$ denote the optimal loss function value to problem \eqref{OptimalParameter}. There exists a constant $\mu\ge 0$ such that the global loss function $F({\bf w})$ satisfies the following Polyak-Lojasiewicz (PL) condition:
\begin{align*}
	\| {\bf g}\|_2^2 \ge 2\mu(F({\bf w})-F^{\star}).
\end{align*}
	}
\end{assumption}
 Notice that the above assumption is more general than the standard assumption of strong convexity \cite{Karimi2016}. Typical loss functions that satisfy the above two assumptions include logistic regression, linear regression and least squares.

 \begin{assumption}[Variance Bound]\emph{
The local gradient estimates $\{{\bf g}_k\}$, defined in \eqref{sys_LocalGradient}, where the index $(n)$ is omitted for simplicity, are assumed to be independent and unbiased estimates of the batch gradient ${\bf g}$ with coordinate bounded variance, i.e.,
\begin{align}
	&\mathbb{E}[{\bf g}_k]={\bf g}, \forall k\in\mathcal K,\\
	&\mathbb{E}[ ({g}_{k,i}-g_i)^2]\le \sigma_i^2, \forall k\in\mathcal K, \forall i,
\end{align}
where ${g}_{k,i}$ and $g_i$ are defined as the $i$-th element of $\{{\bf g}_k\}$ and ${\bf g}$, respectively, and ${\bm\sigma}=[\sigma_1,\cdots,\sigma_q]$ is a vector of non-negative constants.
 }
\end{assumption}

\vspace{-0.45cm}
\subsection{Communication Model}
\vspace{-0.2cm}

The distributed training latency is dominated by the update aggregation process, especially when the number of devices becomes large. Therefore, we focus on the aggregation process over a MAC. Instead of treating different devices' update as interference, we consider AirComp for fast update aggregation by exploiting the superposition property of MAC.
We assume that the channel coefficients remain unchanged within a communication round, and may change over different communication rounds.
Besides, the channel state information (CSI) is assumed to be available at all edge devices, so that they can perfectly compensate for the phases introduced by the wireless channels.

Let $\hat h_k^{(n)}$ denote the complex channel coefficient from device $k$ to the edge server at communication round $n$, and $h_k^{(n)}$ denote its magnitude with $h_k^{(n)}=|\hat h_k^{(n)}|$.
During the gradient-uploading phase, all the devices transmit simultaneously over the same time-frequency block, and thus the received aggregate signal is given by
 \begin{align}\label{sys_ReceivedSignal}
 	{\bf y}^{(n)}=\sum\limits_{k\in\mathcal K}h_k^{(n)}\sqrt{p_k^{(n)}}{\bf g}_{k}^{(n)}+{\bf z}^{(n)},
 \end{align}
 in which $p_k^{(n)}$ denotes the transmit power at device $k$, and ${\bf z}^{(n)}\in\mathbb{R}^q$ denotes the additive white Gaussian noise with ${\bf z}^{(n)}\sim{\mathcal CN}(0,N_0\bf I)$, where $N_0$ is the noise power density and $\bf I$ is an identity matrix. Therefore, the global gradient estimate at the edge server is given by
\begin{align}\label{sys_GlobalGradient}
	\hat{\bf g}^{(n)}=\frac{{\bf y}^{(n)}}{K}.
\end{align}
The devices can adaptively adjust their transmit powers for enhancing the learning performance.
In practice, the transmit power of each edge device $k\in\mathcal K$ at each communication round is constrained by a maximum power budget $\bar P_{k}$:
\begin{align}
p_{k}^{(n)}  \leq \bar{P}_{k},~\forall k\in{\mathcal K}, ~\forall n.\label{sys_bar_P_max}
\end{align}
In addition, each device $k\in\mathcal K$ is also constrained by an average power budget denoted by $\tilde{P}_{k}$ over the whole training period as expressed below:\begin{align}
\frac{1}{N}\sum \limits_{n\in\mathcal{N}}p_{k}^{(n)}  \leq \tilde{P}_{k},~\forall k\in{\mathcal K}.\label{sys_bar_P_ave}
\end{align}
Here, we generally have $\tilde{P}_{k} \le \bar{P}_{k},~\forall k\in{\mathcal K}$.

 \section{Convergence Analysis for Air-FEEL with Adaptive Power Control}

 In this section, we formally characterize the learning performance of Air-FEEL system, which is derived to be a function of transmit powers of all devices.

Let $N$ denote the number of needed communication rounds and $L\triangleq \|\bf L\|_{\infty}$. For notational convenience,  we use $F^{(n+1)}$ to represent $F({\bf w}^{(n+1)})$.
The optimality gap after $N$ communication rounds defined by $F^{(N+1)}-F^{\star}$ is derived in the following theorem, from which we can understand the convergence behavior of Air-FEEL.

\begin{theorem}[Optimality Gap]\label{ConvergenceRate}\emph{
The optimality gap for Air-FEEL, with arbitrary transmit power control policy $\{p_k^{(n)}\}$, is given as
\begin{align}
&\mathbb{E}\left[F^{(N+1)} \right]-F^{\star}\leq {\Phi}(\{p_k^{(n)}\},\eta)\notag\\
&\!\!\triangleq\!\prod_{n=1}^{N}\!A^{(n)}\!\!\left(F^{(1)}\!-\!F^{\star}\!\right) \!+\!\sum_{n=1}^{N-1}\!\left(\!\prod_{i=n+1}^{N}\!A^{(i)}\!\right)\!B^{(n)}\!+\!B^{(N)},\label{Conv_F_Gap}\!
\end{align}
with $A^{(n)}=1-\frac{2\mu\eta}{K}\sum\limits_{k\in\mathcal K}\left(h_k^{(n)}\sqrt{p_k^{(n)}}-\frac{ \eta L}{2K}(h_k^{(n)})^2p_k^{(n)}\right) $ and $B^{(n)}=\frac{ \eta^2L\|{\bm \sigma}\|_2^2}{2K^2}\left(\sum\limits_{k\in\mathcal K}(h_k^{(n)})^2p_k^{(n)}\right)+\frac{ \eta^2LN_0q}{2K^2}$.
	}
\end{theorem}
\begin{IEEEproof}
The proof follows the widely-adopted strategy of relating the norm of the gradient to the expected improvement made in a single algorithmic step, and comparing this with the total possible improvement.
\begin{footnotesize}
\begin{align*}
	&F^{(n+1)}- F^{(n)}\\
&\overset{(a)}{\leq}   ({\bf g}^{(n)})^T ({\bf w}^{(n+1)}- {\bf w}^{(n)}) + \frac{1}{2}\sum_{i=1}^{q} L_i({{ w}_i^{(n+1)}-{w}^{(n)}_i})^2,\\
	&\overset{(b)}{\leq} ({\bf g}^{(n)})^T ({\bf w}^{(n)}-\eta\cdot \hat{\bf g}^{(n)}- {\bf w}^{(n)}) + \frac{L}{2}\|{\bf w}^{(n)}-\eta\cdot \hat{\bf g}^{(n)}- {\bf w}^{(n)}\|_2^2\\
	&=-\eta ({\bf g}^{(n)})^T \hat{\bf g}^{(n)}+ \eta^2\frac{L}{2}\|\hat{\bf g}^{(n)}\|_2^2\\
	&\!\!=\!\!-\!\frac{\eta}{K} ({\bf g}^{(\!n\!)}\!)^T\!\!\left(\!\sum\limits_{k\in\mathcal K}\!h_k^{(\!n\!)}\sqrt{p_k^{(\!n\!)}}\!{\bf g}_{k}^{(\!n\!)}\!\!+\!\!{\bf z}^{(\!n\!)}\!\right)\!\!\!+\!\frac{ \eta^2L}{2K^2}\!\!\left\|\!\sum\limits_{k\in\mathcal K}\!\!h_k^{(\!n\!)}\sqrt{p_k^{(\!n\!)}}{\bf g}_{k}^{(\!n\!)}\!+\!{\bf z}^{(\!n\!)}\!\right\|_2^2\!,\!
\end{align*}
\end{footnotesize}
where the inequalities (a) and (b) follows the Assumption~\ref{Assump_Smooth} and $L\triangleq \|\bf L\|_{\infty}$.
By subtracting $F^{\star}$ and taking expectation at both sides, the convergence rate of each communication round is given by \eqref{App_Con_expectation}.
Next, \eqref{App_Con_gap} is obtained by applying the PL condition in the Assumption~\ref{Assump_PL}.
Then, by applying above inequality repeatedly through $N$ iterations, after some simple algebraic manipulation we have \eqref{Conv_F_Gap}, which completes the proof.

\begin{figure*}[t]
\begin{align}
&\mathbb{E}\left[F^{(n+1)} \right]-F^{\star}\notag\\
	&\le F^{(n)}-F^{\star}-\frac{\eta}{K}\left(\sum\limits_{k\in\mathcal K}h_k^{(n)}\sqrt{p_k^{(n)}}\right)\|{\bf g}^{(n)}\|_2^2 +\frac{ \eta^2L}{2K^2}\left(\sum\limits_{k\in\mathcal K}(h_k^{(n)})^2p_k^{(n)}\right)\left(\left\|{\bf g}^{(n)}\right\|_2^2+\left\|{\bm \sigma}\right\|_2^2\right)+\frac{ \eta^2LN_0q}{2K^2}\notag\\
		&= F^{(n)}-F^{\star}-\left[\sum\limits_{k\in\mathcal K}\left(\frac{\eta}{K}h_k^{(n)}\sqrt{p_k^{(n)}}-\frac{ \eta^2L}{2K^2}(h_k^{(n)})^2p_k^{(n)}\right)\right]\|{\bf g}^{(n)}\|_2^2 +\frac{ \eta^2L}{2K^2}\left(\sum\limits_{k\in\mathcal K}(h_k^{(n)})^2p_k^{(n)}\right)\left\|{\bm \sigma}\right\|_2^2+\frac{ \eta^2LN_0q}{2K^2}.\label{App_Con_expectation}
\end{align}
\vspace*{-0.2\baselineskip}
\end{figure*}

\begin{figure*}
\begin{align}
\!\!\mathbb{E}\!\left[\!F^{(n+\!1)} \!\right]\!\!-\!F^{\star}\!\!\le\! \! \underbrace{ \left[\!1\!-\!2\mu \! \! \left(\! \sum\limits_{k\in\mathcal K}\!\!\left(\!\frac{\eta}{K}h_k^{(n)}\sqrt{p_k^{(n)}}\!-\!\frac{ \eta^2L}{2K^2}(h_k^{(n)})^2p_k^{(n)}\right)\! \! \right)\!  \right]\! }_{A^{(n)}}\left(\!F^{(n)}-F^{\star}\!\right) 	\! +\underbrace{\frac{ \eta^2L\left\|{\bm \sigma}\right\|_2^2}{2K^2}\sum\limits_{k\in\mathcal K}(h_k^{(n)})^2p_k^{(n)}\!+\!\frac{ \eta^2LN_0q}{2K^2}}_{B^{(n)}}.\label{App_Con_gap}
\end{align}\!
\vspace*{-1\baselineskip}
\end{figure*}
\end{IEEEproof}

Further applying the mean inequality $(a_1a_2\cdots a_m)\leq(\frac{a_1+a_2+\cdots +a_m}{m})^m$, we can derive a more elegant upper bound for the expression in \eqref{Conv_F_Gap} to attain more insights as follows
\begin{align}
& {\Phi}(\{p_k^{(n)}\},\eta)\leq\!\!\alpha^N\left(\!F^{(\!1\!)}\!-\!F^{\star}\!\right) \!\!+\!\!\sum_{n=1}^{N}\!\!B^{(n)}\beta_{(n)}^{N-n},\label{Conv_F_Gap_bound}
\end{align}
where $\alpha=\frac{\sum_{i=1}^{N}\!\!A^{(i)}}{N}$ and $\beta_{(n)}=\frac{\sum_{i=n+1}^{N}A^{(i)}}{N-n}$ for $n=1,\cdots,N-1$ while $\beta_{(N)}=1$.
\begin{remark}\emph{
	The first term on the right hand side of \eqref{Conv_F_Gap_bound} suggests that the effect of initial optimality gap vanishes as the number of communication round $N$ increases. The second term reflects the impact of the power control and additive noise power on the convergence process, that is, transmission with more power in the initial learning iterations is more beneficial in decreasing the optimality gap. This is because that the contribution of power control at iteration $n$ is discounted by a factor $\beta_{(n)}^{N-n}$.}
\end{remark}

 \section{Power Control Optimization}
 In this section, we focus on speeding up the convergence rate by minimizing the optimality gap in Theorem~\ref{ConvergenceRate}, under the power constraints stated in \eqref{sys_bar_P_max} and \eqref{sys_bar_P_ave}.
The optimization problem is thus formulated as
 \begin{align}
 	\mathbf{P1:} \min_{\{p_k^{(n)}\ge 0\},\eta\ge 0} ~~&{\Phi}(\{p_k^{(n)},\eta\})\notag\\
 {\rm s.t.}~~~~~&\eqref{sys_bar_P_max}~\text{and}~\eqref{sys_bar_P_ave}.\notag
 \end{align}
Due to the coupling between the power control $\{p_k^{(n)}\}$ and learning rate $\eta$, problem (P1) is non-convex and hard to solve. We resort to the alternating optimization technique for efficiently solving this problem. In particular, we first solve problem (P1) under any given $\eta$, and then apply a one-dimension search to find the optimal $\eta$ that achieves the minimum objective value.

Let $\tilde{\Phi}(\{p_k^{(n)}\})={\Phi}(\{p_k^{(n)},\eta\})$ under any given $\eta$.
 Note that the transmit powers at different devices and different communication rounds are coupled with each other in the objective function in \eqref{Conv_F_Gap} under given learning rate $\eta$, leading to a highly non-convex problem:
  \begin{align}
 	\mathbf{P2:} \min_{\{p_k^{(n)}\ge 0\}} ~~& \tilde{\Phi}(\{p_k^{(n)}\})\notag\\
 {\rm s.t.}~~~~~&\eqref{sys_bar_P_max}~\text{and}~\eqref{sys_bar_P_ave}.\notag
 \end{align}
To tackle this problem, we propose an iterative algorithm to obtain an efficient solution using the SCA technique. The key idea is that under any given local point at each iteration, we can approximate the non-convex objective as a constructed convex one. Therefore, after solving a series of approximate convex problems iteratively, we can obtain a high-quality suboptimal solution to problem (P2).

Let $\{p_k^{(n)}[i]\}$ denote the local point at the $i$-th iteration with $i\ge 0$, and ${\mathcal N}\triangleq \{1,\cdots,N\}$ the set of communication rounds. Notice that by checking the first-order Taylor expansion of $\tilde{\Phi}(\{p_k^{(n)}\})$ w.r.t. $\{p_k^{(n)}\}$ at the local point $\{p_k^{(n)}[i]\}$, it follows that
\begin{align*}
	&\tilde{\Phi}(\{p_k^{(n)}\})\approx \bar{\Phi}(\{p_k^{(n)}\})\notag\\
	&~~ \triangleq \!\tilde{\Phi}(\{p_k^{(n)}[i]\})\!+\!\sum\limits_{n\in{\mathcal N}} \!\sum\limits_{k\in{\mathcal K}}\!\left(p_k^{(n)}-p_k^{(n)}[i]\right)\nabla \tilde{\Phi}(\{p_k^{(n)}[i]\}),
\end{align*}
where $\nabla \tilde{\Phi}(\{p_k^{(n)}[i]\})$ represents the first-order derivative w.r.t. $p_k^{(n)}[i]$, given in \eqref{Derivation_1} and \eqref{Derivation_2}.
\begin{figure*}[t]
\begin{align}
	\nabla \tilde{\Phi}(p_k^{(n)}[n])&=-\frac{\mu\eta h_k^{(n)}\left(F^{(1)}-F^{\star}\right)}{K}\left(\frac{1}{\sqrt{p_k^{(n)}}}-\frac{\eta L h_k^{(n)}}{K}\right)\prod_{i\in{\mathcal N}\setminus \{n\}}A^{(i)}+\frac{\eta^2L \left\|{\bm \sigma}\right\|_2^2 (h_k^{(n)})^2\prod_{j=n}^{N}A^{(j)}}{2K^2A^{(n)}}\notag\\
	&~~-\frac{\mu\eta h_k^{(n)}}{K}\left(\frac{1}{\sqrt{p_k^{(n)}}}-\frac{\eta L h_k^{(n)}}{K}\right)\sum_{\ell=1}^{n-1} B_{(\ell)}\frac{\prod_{j=\ell}^{N}A^{(j)}}{A^{(n)}A^{(\ell)}},\forall n\in\mathcal{N}\setminus \{1\}\label{Derivation_1}\\
	\nabla \tilde{\Phi}(p_k^{(1)}[i])&=-\frac{\mu\eta h_k^{(1)}\left(F^{(1)}-F^{\star}\right)}{K}\left(\frac{1}{\sqrt{p_k^{(1)}}}-\frac{\eta L h_k^{(1)}}{K}\right)\prod_{i\in{\mathcal N}\setminus \{1\}}A^{(i)}+\frac{\eta^2L \left\|{\bm \sigma}\right\|_2^2 (h_k^{(1)})^2}{2K^2}\prod_{i\in{\mathcal N}\setminus \{1\}}A^{(i)}.\label{Derivation_2}
\end{align}
\vspace*{-1\baselineskip}
\end{figure*}\!

In this case, $\bar{\Phi}(\{p_k^{(n)}\})$ is linear w.r.t. $\{p_k^{(n)}\}$.
To ensure the approximation accuracy, a series of trust region constraints are imposed as \cite{YLiu_Trust}
\begin{align}
	|p_{k}^{(n)}[i]-p_{k}^{(n)}[i-1]|\le \Gamma[i], ~\forall k\in\mathcal{K}, \forall n\in\mathcal{N},\label{TrustRegion}
\end{align}
where $\Gamma[i]$ denotes the radius of the trust region.
By replacing $\bar{\Phi}(\{p_k^{(n)}\})$ as the approximation of $\tilde{\Phi}(\{p_k^{(n)}\})$ and introducing an auxiliary variable $\gamma$, the approximated problem at the $i$-th iteration is derived as a convex problem:
 \begin{align}
 	\mathbf{P2.1:} \min_{\{p_k^{(n)}[i]\},\gamma\ge 0} ~~&\gamma \notag\\
{\rm s.t.}~~~~~&\bar{\Phi}(\{p_k^{(n)}[i]\})\le \gamma\\
&\eqref{sys_bar_P_max},~\eqref{sys_bar_P_ave},~\text{and}~\eqref{TrustRegion},\notag
 \end{align}
which can be directly solved by CVX \cite{cvx}.

Let $\{p_k^{(n)*}[i]\}$ denote the optimal power control policy to problem (P2.1) at local point $\{p_k^{(n)}[i]\}$. Then, we can obtain an efficient iterative algorithm to solve problem (P2) as follows. In each iteration $i \ge 1$, the power control is updated as $\{p_k^{(n)*}[i]\}$ by solving problem (P2.1) at local point $\{p_k^{(n)}[i]\}$, i.e. $p_k^{(n)}[i+1]=p_k^{(n)*}[i],\forall n\in\mathcal N, \forall k\in\cal K$, where $\{p_k^{(n)}[0]\}$ denotes the initial power control.
At the $i$-th iteration, we compute the objective value in problem (P2) by replacing $\{\hat{p}_k^{(n)*}[i]\}$ as $\{p_k^{(n)*}\}$. If the objective value decreases, we then replace the current point by the obtained solution and go to the next iteration; otherwise, we update $\Gamma[i]=\Gamma[i]/2$ and continue to solve problem (P2.1). This algorithm would stop until that $\Gamma[i]$ is lower than a given threshold denoted by $\epsilon$.
In summary, the proposed algorithm is presented in Algorithm 1.

\begin{table}[htp]
\begin{center}\vspace{-0.1cm}
\hrule
\vspace{0.2cm} \textbf{Algorithm 1 for Solving Problem (P2)}\vspace{0.2cm}
\hrule \vspace{0.1cm}
\begin{itemize}
    \item[1]  Initialization: Given the initial power control $\{p_k^{(n)}[0]\}$; let $i=0$.
    \item[2]  {\bf Repeat:}
                \begin{itemize}
                \item[a)]  Solve problem (P1.1) under given $\{p_k^{(n)}[i]\}$ to obtain the optimal solution as $\{p_k^{(n)*}[i]\}$;
                 \item[b)]  If the objective value of problem (P2) $\tilde{\Phi}(\{p_k^{(n)}\})$ decreases, then update $p_k^{(n)}[i+1]=p_k^{(n)*}[i],\forall n\in\mathcal N$ with $i=i+1$; otherwise $\Gamma[i]=\Gamma[i]/2$;
                \end{itemize}
     \item[3] {\bf Until} $\Gamma[i]\le \epsilon$.
    \end{itemize}
\hrule \vspace{0cm}
\end{center}\vspace{-0.5cm}
\end{table}

With the obtained power control in Algorithm 1, we can find the optimal $\eta$ accordingly via a one-dimensional search.

   \vspace{-0.1cm}
\section{Simulation Results}\label{sec_simu}

In this section, we provide simulation results to validate the performance of the proposed power control policy for Air-FEEL.
In the simulation, the wireless channels from each device to the edge server over fading states follow i.i.d. Rayleigh fading, such that $h_k$'s are modeled as i.i.d. {\it circularly symmetric complex Gaussian} (CSCG) random variables with zero mean and unit variance.
The dataset with size $D_{\rm tot}=600$ at all device are randomly generated, where part of the data, namely $100$ pairs (${\bf x}$, $y$), are left for prediction, and the remaining ones are used for model training. The generated data sample vector ${\bf x}$ follow i.i.d. Gaussian distribution as $\mathcal{N}(0,{\bf I})$ and the label $y$ is obtained as $y=x(2)+3x(5)+0.2z$, where $x(t)$ represents the $t$-entry in vector ${\bf x}$ and $z$ is the observation noise with i.i.d. Gaussian distribution, i.e., $z\sim\mathcal{N}(0,1)$.
Unless stated otherwise, the data samples are evenly distributed among the $K=20$ devices, and thus it follows $D_k=25$.
Moreover, we apply ridge regression with the sample-wise loss function $f({\bf w},{\bf x},y)=\frac{1}{2}\| {\bf x}^T{\bf w}-y\|^2$ and the regularization function $R({\bf w})=\|{\bf w}\|^2$ with $\rho=5\times 10^{-5}$ in this paper.
Furthermore, recall that $D_{\rm tot}=\sum_{k\in \mathcal{K}}D_k$ and then we can obtain the smoothness parameter $L$ and PL parameter $\mu$ as the largest and smallest eigenvalues of the data Gramian matrix ${\bf X}^T{\bf X}/D_{\rm tot}+10^{-4}{\bf I}$, in which ${\bf X}=[{\bf x}_1,\cdots,{\bf x}_{D_{\rm tot}}]^T$ is the data matrix. The optimal loss function $F^{\star}$ is computed according to the optimal parameter vector $\bf w^{\star}$ to the learning problem \eqref{OptimalParameter}, where ${\bf w}^{\star}=({\bf X}^T{\bf X}+\rho{\bf I})^{-1}{\bf X}^T{\bf y}$ with ${\bf y}=[y_1,\cdots,y_{D_{\rm tot}}]^T$.
We set the initial parameter vector as an all-zero vector and the noise variance $N_0=0.1$.

We consider two benchmark schemes for performance comparison, namely the {\it uniform power transmission} that transmits with uniform power over different communication round under the constraint of average power budget, and the {\it channel inversion} adopted in \cite{DLiu2020Ar}.
As for the performance metric for comparison, we consider the optimality gap and prediction error to evaluate the learning performance.

\begin{figure}[htbp]  \vspace{-0.05cm}
  \centering
  \subfigure[Optimality gap versus varying number of devices.]
  {\label{fig:FL_v_K1}\includegraphics[width=8cm]{K1028_OG.eps}}
  \subfigure[Prediction error versus varying number of devices.]
  {\label{fig:FL_v_K2}
\includegraphics[width=8cm]{K1028_PE.eps}}
  \caption{Effect of number of devices on the learning performance of  Air-FEEL.}
  \label{Fig:FL_v_K}
\end{figure}

The effect of device population on learning performance is illustrated in Fig.~\ref{Fig:FL_v_K}  with $N=30$, where the power budgets at all devices are identically set to be  $\tilde P=1$ W and $\bar P=5$ W.
Notice that the increasing of device population may introduce both the  positive and negative effects on the learning performance. The positive effect is that the training process can exploit more data, while the negative effect is the increased aggregation error raised by AirComp over more devices. As observed in Fig.~\ref{Fig:FL_v_K}, the positive effect can be cancelled or even overweighed by the negative effect when applying the channel inversion or uniform power control. The blessing of including more devices in Air-FEEL can dominate the curse it brings only when the power control is judiciously optimized, showing the crucial role of power control in determining the the learning performance of Air-FEEL.

\begin{figure}[htbp] \vspace{-0.05cm}
  \centering
  \subfigure[Tendency of loss function.]
  {\label{fig:MSE_v_Con1}\includegraphics[width=8cm]{GO1026_N80.eps}}
  \subfigure[Tendency of prediction error.]
  {\label{fig:MSE_v_Con2}
\includegraphics[width=8cm]{PE1026_N80.eps}}
  \caption{Learning performance of Air-FEEL over iterations, where $\eta^*$ denotes the optimized learning rate after one-dimensional search.}
  \label{Fig:MSE_v_Con}
\end{figure}

Fig.~\ref{Fig:MSE_v_Con} shows the learning performance during the learning process under the optimized learning rate, where we set $K=20$, $\tilde P=1$ W, $\bar P=5$ W, and $N=80$.
It is observed that the proposed power control scheme can achieve faster convergence than both the channel-inversion and uniform-power-control schemes. This is attributed to the power control optimization directly targeting convergence acceleration.

\begin{figure}   \vspace{-0.1cm}
\centering

 \setlength{\abovecaptionskip}{-1mm}
\setlength{\belowcaptionskip}{-1mm}
    \includegraphics[width=3.5in]{PA1029.eps}
\caption{The optimized power allocation over iterations under static channels.} \label{fig:MSE_V_PA}
\end{figure}

Fig.~\ref{fig:MSE_V_PA} shows the power allocation over a static channel with uniform channel gain during the learning process, where we set $K=20$, $\tilde P=1$ W, $\bar P=5$ W, and $N=30$.
It is observed that the power allocation over a static channel follows a stair-wise monotonously decreasing function.
The behavior of power control coincides the analysis on Remark 1.

\section{Conclusion}\vspace{-0.2cm}
In this paper, we exploit power control as a new degree of freedom to optimize the learning performance of Air-FEEL, a promising communication-efficient solution towards edge intelligence. To this end, we first analyzed the convergence rate of the Air-FEEL by deriving the optimality gap of the loss-function under arbitrary power control policy. Then the formulated power control problem aimed to minimize the optimality gap for accelerating convergence, subject to a set of average and maximum power constraints at edge devices. Due to the coupling of power control variables over different devices and iterations, the challenge of the formulated power control problem was tackled by the joint use of SCA and trust region methods. Numerical results demonstrated that the optimized power control policy can achieve significantly faster convergence than the benchmark policies such as channel inversion and uniform power transmission.

\vspace{-0.1cm}

redpajama_set_name: RedPajamaArXiv


text:
Органджи ( или Κύρια, Кирия, до 1953 година Οργαντζή, Органдзи) е село в Гърция, част от дем Доксат на област Източна Македония и Тракия. Населението му е 1714 души (2001).

География
Селото се намира на 150 m надморска височина в Драмското поле на 15 km източно от град Драма, в западното подножие на Ярум Кая.

История
В XIX век Органджи е турско село в Драмската каза на Османската империя.

След Междусъюзническата война в 1913 година, селото попада в Гърция. В 1923 година по силата на Лозанския договор жителите му като мюсюлмани са изселени в Турция и на тяхно място са заселени гърци бежанци. В 1928 година Органджи е чисто бежанско село със 133 бежански семейства и 565 души бежанци. В 1953 година е прекръстено на Кирия. Църквата "Свети Димитър и Свети Георги" е изградена от 1962 до 1968 година.

Населението се занимава с отглеждане на тютюн, жито и други земеделски култури, както и със скотовъдство.

Бележки

Села в дем Доксат

redpajama_set_name: RedPajamaWikipedia


text:
MARKET WRAP: Rand, JSE weaker as focus shifts to central bank rates decisions
NUM tells Gordhan there are solutions available to end intensified rolling blackouts
Eskom crisis triggers water cuts across Joburg
South Africa Finance News
Business, Markets, Money & Technology
TDC opens 2023 call for Ascenders competition, jurors announced
January 25, 2023 Juanita Slabbert
Tourism and hospitality professionals from around the world can now register to attend Arabian Travel Market (ATM) 2023, which will take place at Dubai World Trade Centre (DWTC) from 1-4 May.
Source: Supplied
In line with its theme of Working Towards Net Zero, the 30th edition of ATM will offer a forum for industry leaders and policymakers from across the Middle East and beyond to explore challenges and opportunities related to the future of sustainable travel.
Danielle Curtis, exhibition director ME, Arabian Travel Market, says: "We are excited to officially open registration for the 30th edition of ATM, which will shine a spotlight on sustainability within our sector and how regional decision-makers are driving decarbonisation while maximising profitability and enhancing customer experiences.
Sustainability across the travel and tourism industry
"This year's conference programme will feature a huge range of sessions that will explore innovation and best practices related to environmental, social and governance (ESG)," Curtis adds. "We expect to welcome more than 34,000 public and private sector travel, tourism and hospitality experts from around the world to ATM 2023 – including over 1,500 exhibitors and representatives from over 150 destinations – making it the perfect platform for relationship-building and knowledge-sharing that will drive tangible, sustainable change."
The ATM 2023 conference programme is being specifically developed to address sustainability issues across the travel and tourism industry, with commentary from leadership figures representing a variety of sectors such as Destinations, Travel Technology, Aviation, Cruise, Investment, Recruitment, Hotels and Hospitality.
There will also be a number of sessions dedicated to key source markets, including India and Saudi Arabia. In addition, ATM will see the return of the ATM Start-up competition where this year, seven innovative travel start-ups will pitch battle on stage to expert judges and audiences as they look to showcase their solutions impacting travel sustainability and recovery.
The conference programme will also explore how innovative sustainable travel trends are likely to evolve, allowing delegates to identify growth strategies within key vertical sectors while providing a platform for regional experts to explore a sustainable future ahead of COP28, which will take place in November 2023 at Expo City Dubai.
To mark its 30th annual event, ATM and its organiser RX Global will unveil a dedicated sustainability pledge comprising 30 goals that will inform the show's journey towards decarbonisation. In conjunction with sustainability guidelines developed for exhibitors and delegates, this pledge will also help to ensure that this year's edition of ATM is the most sustainable in history.
The Best Stand Awards will also feature a sustainability category for the first time. Exhibiting organisations will be recognised based on the extent to which they have considered the environmental impact of their stands, as well as their efforts to reduce their carbon footprint.
Source: bizcommunity.com
← High Court orders RAF CEO to pay legal costs 'out of his own pocket'
Global Microsoft outage hits Teams, Office users →
Football influencer superstars: Increasing brands' reach of the Fifa World Cup
October 13, 2022 Juanita Slabbert
#BehindtheSelfie: Rena Engelbrecht, head of marketing at The Crazy Store
August 25, 2022 Juanita Slabbert
#SONA2019: Accelerated rural, urban land reform key to growth
June 21, 2019 Juanita Slabbert
Copyright © 2023 South Africa Finance News. All rights reserved.


The Lincolnshire Bombers Roller Girls took to the track for the final time this season when they travelled to Peterborough to take on Suffolk Roller Derby at the weekend.
Peterborough went into half time with a 62-53 points lead despite the best efforts of the Lincolnshire outfit to end the campaign with a win.
Things improved after the break when the Bruisers picked up points in a couple of timely power jams.
In what turned out to be a close-fought match it was Suffolk who took the honours with a 136-132 victory after a lead charge in the very last jam.
Lincolnshire Bombers captain Christy 'Razzo' Robinson said: "It was an end to the season the girls should be proud of.
"Each and every skater gave everything and we all worked hard as a team.
Brandon 'Papa Grande' Eby, Lincoln's coach reflected on the game. She said:"Everything was left on that track.
"I could see all the hard work and training being used out there.


Banking & Finance Associate Attorney-LSA1239 – Legal Search Associates, Inc.
The Kansas City office of a large law firm is searching for a Banking & Finance Associate with two to five years of experience. Relevant and desired experience would include all aspects of commercial lending work, including cash flow lending, acquisition finance, asset based loan transactions, real estate loan transactions and floor plan financing; preparation and review of documents; familiarity with most types of security issues, particularly lien perfection issues and filing requirements; and familiarity with most types of loan related documents, including credit agreements, security agreements, deeds of trust, indemnities, UCC's, guaranties, subordination agreements, and inter-creditor agreements.
The candidate must have a strong academic record, strong interpersonal skills with the ability to work well with a team, superior judgment, the ability to effectively handle multiple projects, and the ability to articulate legal strategies and courses of action.
Candidates should have a Missouri bar license, depending on the office to which they are applying, or commit to obtaining one as soon as possible.
Qualified applicants should submit their resume to Chuck Loose (cloose@jdhunter.com or Terry Bashor (tbashor@jdhunter.com) of Legal Search Associates, Inc. Please refer to LSA1239 when doing so.


text:
You are here Tuesday
Silencing The Country Girls: Edna O'Brien and the Censor
This event revisits Edna O'Briens interview and the issues it raised, which continue to resonate today, both within and far beyond the literary world.
Edmund Burke Theatre, Arts Building
In 1988, Edna O'Brien gave an interview to Julia Carlson for her seminal book, Banned in Ireland: Censorship & the Irish Writer, which examined the personal, social, and literary impacts of censorship in twentieth-century Ireland. The School of Law and the School of English present a programme of events investigating the history and impact of censorship in Ireland and to celebrate the selection of Edna O'Brien's The Country Girls Trilogy as Dublin One City One Book 2019, Silencing The Country Girls: Edna O'Brien and the Censor revisits O'Brien's interview and the issues it raised which continue to resonate today, both within and far beyond the literary world. Julia Carlson joins us to speak about her work on Banned in Ireland, which also featured interviews with John McGahern, Benedict Kiely, and Brian Moore, and the question of gender and censorship. She will also discuss these issues, and their contexts, in conversation with Eoin O'Dell, Associate Professor of Law at Trinity and a leading expert on freedom of expression and copyright. Finally, we welcome the acclaimed actor and writer Noni Stapleton (Penny Dreadful, Charolais)who will bring Edna O'Brien's witty, candid, and serious interview to life in a special performance.
Event Participants:
Julia Carlson (NUIG) joins us to speak about her work on Banned in Ireland, which also featured interviews with John McGahern, Benedict Kiely, and Brian Moore, and about the question of gender and censorship.
Eoin O'Dell, Associate Professor of Law at Trinity and a leading expert on freedom of expression and copyright, will discuss the legal and historical significance of Banned in Ireland.
Acclaimed actor and writer Noni Stapleton (Penny Dreadful, Charolais), brings Edna O'Brien's witty, candid, and serious interview to life in a special performance.
Trinity Week > Tuesday


text:
Ron Paul Would Beat Obama: Why Romney Must Be Replaced If the GOP Hopes to Win in 2012
By Joseph Beck
Throughout the Republican primaries, the Mitt Romney campaign did a fairly decent job at keeping Romney above the fray. He made the occassional $10,000 bet on national television and agreed with Obama's signing of the NDAA, but for the most part, he remained low key. It was his front-runner position to lose after all, right? Instead of critiquing the assumed front-runner, the mainstream media hyped up the "anti-Mitt" candidate. Newt Gingirch, Rick Perry, and Rick Santorum — who claimed "Romney was the worst Republican in the country to put up against Barack Obama,"then later endorsed Romney — were all considered top contenders. Now that the spotlight is focused on the presumptive nominee, his flaws are all too apparent. Is Romney really the best choice for conservatives?
The most recent gaffe by the Romney campaign involved spokeswoman Andrea Saul, who made the mistake of a lifetime by touting Romneycare in response to the recent controversial attack ad from a pro-Obama super PAC. "Conservatives" are freaking out. Both Rush Limbaugh and Ann Coulter have condemned Saul's impromptu response, even demanding the Romney campaign fire Saul. This just adds to Romney's troubles. His 40% favorability mark for presumptive presidential nominees is the worst since 1948. Even the conservative group "Jews and Christians Together" released a memo advising delegates to abstain from voting for Romney on the crucial first ballot. Time is running short, and momentum is not in his favor. In order to defeat President Obama this November, the GOP must nominate the consistent conservative Ron Paul instead of the Goldman Sachs warmonger Mitt Romney.
Think about it. Does Mitt Romney have a base? And if he does, isn't it mostly those "anyone but Obama" voters? Without the support of the Paul faithful, the already-weak Romney faces a difficult challenge against the campaigner-in-chief Barack Obama, who will have plenty of ammunition to use against Romney in the debates. With so little difference between Romney and Obama, its hard to imagine Romney being able to gain the upper hand against the incumbent. The GOP needs to make a decision fast: continue with a struggling Romney, or choose an idealogically consistent champion of liberty to defeat Obama.
As I mentioned in a previous article, Barack Obama's promise of hope and change in 2008 did not deceive everyone. Even then Ron Paul asserted that Obama offered no change, and would only reinforce the status quo.
Dr. Paul would have an incredible advantage over President Obama in a debate. Obama's continuation of the same failed Keynesian policies that more often than not benefit campaign contributors hasn't revived the American economy. The wasteful spending overseas and the outright ignorance of the coming fiscal cliff, not to mention an impending dollar crisis, have put our country on a course to financial ruin. Doom and gloom, yes. But economic law cannot be repealed by Federal Reserve Chairman Ben Bernanke's magical printing press. Obama would be forced to defend his assault on civil liberties, his unconstitutional war on Libya, his defense of the banking establishment, his attacks on medicinal marijuana users and his overall involvement in the same type of crony capitalism that has resulted in a massive transfer of wealth to the politically connected.
Ron Paul has already won six states, and potentially more. This means he will be on the ballot at the Republican Convention later this month. If the GOP can be convinced to nominate Paul, he could go on to combine the full support of the GOP with those disallusioned Obama supporters and Independents, who are tired of the wars and the failing economy, and become the 45th president of the United States.


text:
Q: Solve the differential equation using power series. $\displaystyle y^{'} = {\frac{y}{x}} + 1$
cannot be solved for $y$ as a power series $x$. Solve this equation for $y$ as a power series in powers for $ x-1 $.: Introduce $t=x-1$ as a new independent variable and solve the resulting equation for y as a power series in $t$.)
So far I have proved that it cannot be solved for y as power series in terms of x because you get negative exponents. I did solve for x, which equal t+1.
So, the equation looks like $\displaystyle y^{'} = {\frac{y}{t+1}} + 1$.
Can I multiply both sides by $(t+1)$ so the equation looks like $ \displaystyle (t+1)y^{'} = y + (t+1)$?
My solution so far:
$y^{'} = \displaystyle \sum^{\infty}_{n=1}{n}{c_n}{(t+1)^{n-1}}$
$y = \displaystyle \sum^{\infty}_{n=0}{c_n}{(t+1)^{n}}$
$ \displaystyle (t+1)y^{'} = y + (t+1)$
$(t+1)\displaystyle \sum^{\infty}_{n=1}{n}{c_n}{(t+1)^{n-1}} = \displaystyle \sum^{\infty}_{n=0}{c_n}{(t+1)^{n}} + (t+1)$
$\displaystyle \sum^{\infty}_{n=1}{n}{c_n}{(t+1)^{n}} - \displaystyle \sum^{\infty}_{n=0}{c_n}{(t+1)^{n}} =(t+1)$
$\displaystyle \sum^{\infty}_{n=0}{n}{c_n}{(t+1)^{n}} - \displaystyle \sum^{\infty}_{n=0}{c_n}{(t+1)^{n}} =(t+1)$
$\displaystyle \sum^{\infty}_{n=0}[nc_n-c_n]*(t+1)^n = (t+1)$
$\displaystyle nc_n-c_n = (t+1)$
$\displaystyle c_n(n-1) = (t+1)$
$\displaystyle c_n = \frac {(t+1)}{n-1} $
Substituing x back in we get:
$\displaystyle c_n = \frac {(x)}{n-1} $
Did I do this correctly?

A:
$\displaystyle \sum^{\infty}_{n=0}[nc_n-c_n]*(t+1)^n = (t+1)$
$\displaystyle nc_n-c_n = (t+1)$
$\displaystyle c_n(n-1) = (t+1)$
$\displaystyle c_n = \frac {(t+1)}{n-1} $
Substituing x back in we get:
$\displaystyle c_n = \frac {(x)}{n-1} $
Did I do this correctly?

From this line is is not.
$$
 \sum^{\infty}_{n=0}[nc_n-c_n]*(t+1)^n = (t+1)
\implies \forall n\neq 1\ \ \ nc_n-c_n = 0
$$
At the end, $c_n$ should not depend on $x$!
Note that you can solve the equation directly with the substitution
$$
y(x) = r(x)x
$$

redpajama_set_name: RedPajamaStackExchange


text:
Home / Celebrity /
'This Is Us' Star Milo Ventimiglia's Favorite Food Explains 1 Jack Pearson Moment
Elizabeth Randolph
Milo Ventimiglia stars in This Is Us as Jack Pearson. The Pearson family patriarch entices fans through his touching moments with his wife Rebecca (Mandy Moore) and children Kevin (Justin Hartley), Kate (Chrissy Metz), and Randall (Sterling K Brown). Additionally, the actor became a heartthrob through his role. In Nov. 2018, Ventimiglia revealed what he eats to make sure Jack looks good.
Mandy Moore as Rebecca, Milo Ventimiglia as Jack on 'This Is Us'| Vivian Zink/NBCU Photo Bank/NBCUniversal via Getty Images
'This Is Us' star Milo Ventimiglia has different eating habits than Jack Pearson
Ventimiglia, 39, landed the role of Jack around 2016. He was best known for playing Jess Mariano in Gilmore Girls and Peter Petrelli in Heroes. Although he initially didn't think he would get the job, the actor agreed to play the character.
RELATED: 'This Is Us': Milo Ventimiglia and Mandy Moore Share an Adorable 'Tradition' After a New Episode
In Sept. 2016, This Is Us debuted on NBC. Some fans fell in love with Jack's long hair, scruffy beard, and sculpted physique instantly. The Opposite Sex alum even became one of People's Sexiest Men Alive in 2017. His co-stars and TV sons, Brown and Hartley, were also celebrated.
During Ventimiglia's Nov. 2018 cover story for Men's Journal, the actor shared one of the secrets to his rock-hard abs. The NBC star said his mantra when it comes to food is to "be healthy and eat good stuff." When asked what he enjoys eating, Ventimiglia said he mostly eats "beans and rice, or different kinds of pasta" at home. Unlike his character, who ate big, family meals, the actor revealed he prefers snacking on foods like almonds rather than cooking.
"I feel like I'm more of a snack guy than a big meal guy," he said.
How Milo Ventimiglia's diet benefitted him on 'This Is Us'
On the pilot episode of This Is Us, fans watched as Rebecca gave birth to the Big Three on Jack's birthday. However, before she gave birth, Jack decided to wear nothing but a Pittsburgh Steelers towel in honor of his special day. The scene was something Ventimiglia didn't see coming, per Entertainment Weekly.
"To be honest, I was like; it's NBC, they're not going to show anything," he said.
RELATED: 'This Is Us': Why Milo Ventimiglia Says He's the 'Most Isolated on the Show'
Ventimiglia ended up showing his bare butt on screen. However, the actor's physical trainer, Jason Walsh, said they didn't need to do any extra workouts for him to get camera-ready. Additionally, Ventimiglia's eating habits helped keep his physique intact.
"We really didn't change much; we just kept doing our normal routine," Walsh told People. "Milo has always been dedicated to his workouts."
The Jack Pearson actor flaunted his body again in 'This Is Us' season 4
Following the pilot episode of This Is Us, Ventimiglia's career skyrocketed. The Jack Pearson actor landed other roles while on the show, including playing Jennifer Lopez's love interest in Second Act. Ventimiglia also has a net worth of $12 million. In 2018, his salary per episode on This Is Us reportedly jumped from $125,000 to $250,000.
RELATED: 'This Is Us': Milo Ventimiglia Says There's More to 'Unpack' Between Jack and Nicky
The actor's new payday didn't stop him from dropping down to a towel once more. During season 4 of This Is Us, he replicated Jack's nude scene from the pilot episode. However, he and Rebecca were interrupted by the Big Three, who were toddlers in the flashback scene.


My name is Cheyna (pronounced "Shayna") and my nickname is Cheyn or "Shane." I wanted to incorporate my name into the brand identity of my company. During my research, I found the word "chêne" meaning "oak" in French. My thought process lead me to create scents with woody top notes including, vetiver, cedar, sandalwood, and oud. The androgynous, woody scents are for both men and women and made from 100% natural ingredients sourced from the places where they grow the strongest. Cruelty-free, paraben-free, non-toxic.


JOURNEY's Steve Perry Opens Up on Abandoning Music: "I Had Lost That Deep Passion in My Heart"
Metal Wani's Carl O'Rourke recently sat down with guitar legend John Petrucci of Dream Theater. The two touched on a range of topics, including in-depth conversations on the band's upcoming new album, Distance Over Time', returning to the roots of Dream Theater, what keeps the band artistically brave in 2019 as well as shine some light on the debate surrounding the set up for drummer Mike Mangini.
On moving themselves into a country house to record their new album, John shared some of what that experience was like for the band and the influence it had on the record.
In the hope of ending the discussion as to why drummer Mike Mangini has his cymbals perched so high in the studio video of "Untethered Angel", John offered what he thinks the reason may be.
Active since 1985, Dream Theater remain artistically brave in 2019 and continue to motivate themselves to push the envelope. This results in adapting their core sound to their current incarnation upon each record. John shared his thoughts, stating.
"What keeps us going and motivated is that creative edge. It's that spark that just tries different and new things and explores that and it's part of being a progressive band, a prog band. We're fine labeling ourselves as a prog band, or a prog metal band, but its sort of in the nature of that is that you try different things. You try new things, new sounds and in the end, it's like, records are all an experience. To me, it's always been like watching a movie, like an even that you sit down for. And I remember doing that as a kid, as a teenager, as a young man just putting on a Yes record, or Rush record, or Pink Floyd record or whatever it is and just listening to the whole thing. You experience it in the way you experience a movie. When you think of things in broad strokes with that bigger picture mentality, it makes a little more open-minded to try a range of different things. So this way a record isn't just one dimensional. As you're listening you kind of get taken on this ride and you're not sure what's gonna be around the next corner. That unpredictability is really what makes it interesting and keeps us really motivated.


text:
Марієтта Дмитрівна Буневич (дівоче прізвище Іванова, сценічний псевдонім Marietta) ( , Черкаси, Україна);— українська співачка. Виконує пісні українською, російською та англійською мовами.
Брала участь у національному відборі на пісенний конкурс Євробачення у 2012 та 2013 роках.

Біографія
Marietta народилася 9 грудня 1995 року в Черкасах.

З дитинства брала участь в різних пісенних конкурсах.

У 10 років Marietta записала свій перший альбом у професійній студії. Ранній етап творчості співачки позначений двома яскравими дуетами — із Андрієм Кравчуком та Гайтаною. Загалом під час своєї ранньої професійної діяльності Marietta випустила у світ 3 альбоми, 5 кліпів та завоювала багато нагород на Всеукраїнських та Міжнародних вокальних конкурсах, серед яких «Дитяча нова хвиля», «Чорноморські ігри», «Відкрита Європа» та інші.

У 2007 та 2008 році Marietta стала фіналісткою Національного відбору до Дитячого Євробачення.

7 квітня 2012 року на Першому національному стартувало нове вокальне шоу «10+10», в якому Marietta брала участь в парі з грузинським співаком Ото Немсадзе.

В 2014 році завершила навчання в Київському інституті музики ім. Глієра, а в 2018 році стала випускницею Київского національного університету ім. Тараса Шевченка за спеціальністю «Журналістика (Реклама та PR)».

Marietta стає фіналісткою національного відбору на Євробачення в 2012 та 2013 роках.

У 2013 році Марієтта випускає альбом «Вкус тебя».

Нові треки: «Я тебе люблю», «Не відпускаю» і підготовка англомовного альбому «Heartbeat» остаточно сформували образ чуттєвої і енергійної співачки Marietta, яка не поспішає за модою, а намагається донести в своїй музиці гармонію, мелодійну основу і правдивість.

У 2015 році трек «Heartbeat» увійшов в десятку фіналістів міжнародного конкурсу «Unsigned Only» в США, вигравши право промоутування однойменного альбому в 60 країнах світу.

Сьогодні Marietta — це співачка яка стрімко набирає популярність і визнання публіки, за спиною якої великий творчий і концертний досвід. Співачка, разом зі своєю командою людей, закоханих в музику, готує нові роботи для своїх слухачів, які можна буде почути в найближчому часі.

Дискографія

Альбоми
 2006 — Дети — это золото
 2009 — Мечта-дорога
 2011 — Мои 16
 2014 — Вкус тебя
 2016 — Heartbeat

Сингли

Відеографія
 2006 «Тобі»
 2006 «Дети — это золото»
 2009 «Мечта-дорога» (разом з El Кравчук)
 2009 «Вконтакте »
 2010 «Пташечка»
 2010 «Кораблик Любви »
 2010 «Уходило Лето»
 2012 «Люди не острова »
 2013 «Далеко »
 2015 «Я тебе люблю»
 2016 «Не відпускаю»
 2017 «Мамо »
 2017 «Шалений світ»
 2017 «Буде все гаразд (Новорічна) »
 2019 «На крилах»
 2020 «Як не крути »

Нагороди

У 2010 році стала лауреатом Всеукраїнської премії «Жінка ІІІ тисячоліття» в номінації «Перспектива».

Цікаві факти
Marietta також є моделлю. Вона стала обличчям нової колекції «Широко крокуючи» Тетяни Островерхової сезону весна-літо 2010.

У 2013 році Marietta була ведучою українського музичного каналу Music Box UA. Вела авторську програму про прем'єри кіно під назвою MovieBox.

З 2018 року Marietta є ведучою української радіостанції Країна FM.

Посилання

Джерела
 Офіційний вебсайт співачки
 Канал на YouTube
 Сторінка у «ВКонтакті»
 Marietta — M1
 Сторінка у «Facebook»
 Сторінка в «Instagram»

Українські попспівачки
Українські телеведучі
Учасники національного відбору України на Євробачення 2012
Учасники національного відбору України на Євробачення 2013
Учасники національного відбору України на Євробачення 2014
Лавреатки премії Жінка III тисячоліття


4-7-2016 · Annie Proulx's latest novel is an epic masterpiece, spanning 300 years of history as two families make their way in the New World.
Analytical Essay of The Shipping News by Annie Proulx Admin | November 28, 2016 In The Shipping News, one will take notice of the author's central theme and plot.
Edna Annie Proulx was born in Connecticut in 1935 and before finishing her dissertation and embarked on a career as a freelance journalist.
© Best essays Essay writing | Essay examples Annie dissertation proulx.


text:
/*
 * @test
 * @bug 8026286
 * @summary This test previously forced an assertion to fail, due to
 *          TypeAnnotationPosition visiting a tree node prior to
 *          memberEnter.
 * @compile TestAnonInnerInstance1.java
 */

import java.lang.annotation.*;
import static java.lang.annotation.RetentionPolicy.*;
import static java.lang.annotation.ElementType.*;
import java.util.List;

class TestAnonInnerInstance1<T> {
    Object mtest(TestAnonInnerInstance1<T> t){ return null; }
    Object mmtest(TestAnonInnerInstance1<T> t){ return null; }

    public void test() {

        mtest(new TestAnonInnerInstance1<T>() {
                  class InnerAnon<U> { // Test1$1$InnerAnon.class
                      @A @B @C @D String ia_m1(){ return null; };
                  }
    //If this is commented out, annotations are attributed correctly
                  InnerAnon<String> IA = new InnerAnon< String>();
              });
   }
}

@Retention(RUNTIME) @Target({TYPE_USE,FIELD}) @interface A { }
@Retention(RUNTIME) @Target({TYPE_USE,METHOD}) @interface B { }
@Retention(CLASS) @Target({TYPE_USE,FIELD}) @interface C { }
@Retention(CLASS) @Target({TYPE_USE,METHOD}) @interface D { }

redpajama_set_name: RedPajamaGithub


My baby is sick, I'm sick, my daughter has the day off from school... Today's article just isn't coming together. So, I hope you don't mind, but I decided to repost a popular and timely article from a few years ago -- Halloween Costumes for the Last Minute Librarian.
Halloween, how do we love thee? Of course, when you're programming, weeding, ordering, organizing, doing statistics, and everything else in our daily lives, holidays can sneak up on you. In the interest of making this holiday fun without adding any extra stress, we present a variety of inexpensive, book-themed costume choices for the Last Minute Librarian, some of which cost no money at all!
It's our very own Kat!
Cat in the Hat - you need a black sweatsuit, a floppy hat, and a long piece of felt that you can tie into a bow tie. Add white or blue gloves and a little facepaint for a black nose and whiskers, and you're all set!
Where's Waldo - Waldo is easy as pie! You'll need a red and white striped shirt and hat, blue jeans, and glasses. Adding his accessories (binoculars, a cane, a camera, etc.) can be fun, and you might already have them! Waldo's girlfriend Wenda is similar - instead of jeans, you'll want a jean skirt and red and white striped stockings.
This one is from a school's Read Across America day!
Junie B. Jones - Much like Fancy Nancy, all you have to do here is wear a lot of loud patterns and colors at once, and tie a big, floppy bow on your head. Glasses are helpful but not mandatory. Sassy attitude is mandatory.
Fancy Nancy - This one is super easy. Put all your fancy clothes on at once! Bonus points for feather boas, fancy sunglasses, and any thing with lace, sparkles, or rhinestones.
Ms. Frizzle - Everyone's favorite teacher. This one is especially fun because you can pick any topic there is, and Ms. Frizzle has probably taught about it. Cut out some felt shapes and stick them to an existing dress (and shoes), and put some in your hair. Special kudos for adding Liz the lizard.
If You Give a Mouse A Cookie - overalls, a gray shirt, and a big, paper cookie! Mouse ears (which appear homemade here, and look fabulous) and a pink mouse nose with black whiskers complete the look.
I Spy - What a fun idea! Stick some stuff to the front of your shirt, and a list of what's there to the back! I love that the boy in the photos also has a book and a magnifying glass.
Olaf - Because everyone has been Elsa by now.
Lady MacBeth - for the adult librarians out there! Put on a long nightgown, mess up your hair, carry a candle, and have (fake) blood on your hands, face, and nightgown. (If you're feeling adventurous, you could have a dagger, too.) If anyone bothers you, you're allowed to tell them, "Out! Out!"
Of course, we'd love to see what other ideas you come up with! Please let us know (and show us pictures!) in the comments here, on our Facebook page or on Twitter.