NOSTAGLIA INDEX Back to Main List E-Mail me!
This section,which is be added to regularly, contains ,as the title implies,memories of the past .Aviation has changed a lot since in the last 100 years and many of the airfields covered in Hampshire Airfields have either disappeared or changed beyond recognition.Much of the the material comes from various enthusiasts magazines of the time ,and my own records.
If you have any observations or pictures from the past that you would like contribute to this page,please contact me.Full credit will be given.
Portsmouth ,Southampton and Bournemouth Airports in 1962,Blackbushe in 1957and the Church Crookham Sabres.
Christchurch airfield Resident aircraft from the 30s till the late 60s.
Aircraft on board HMS Eagle in 1954,Bournemouth/Hurn visitors in April 1962,and overflights at Ibsley in April 1967.
Aircraft used by the U S Naval FASRON 200 at Blackbushe between 1956 and 1960.
Flight Refuelling at Tarrant Rushton.This page crosses over to the sister site "Dorset Airfields" and deals with the large numbers of Gloster Meteors that were refurbished for export at Tarrant Rushton.Also covered are those converted to unmanned configuration as U.16/16/21s .
A short history of Independent Air Transport,later known as Blue-Air,a charter airline based at Hurn in the late 50s.
The crash near Lee-on-Solent of Sunderland GR.V VB885 on 13th February 1946.
Photos kindly sent by Howard Haugh ,showing Simmonds Spartan(which were built in Southampton and on the Isle of Wight) aircraft in New Zealand in the thirties.
RAF Royal Review held at RAF Odiham on 15th July 1953.
A first hand account of flying in the Flypast by the pilot of one of the Avro Lincolns that took part on the Review.
The last but one Seafire produced at Eastliegh by Cunliffe Owen as well as an appeal for information regarding the occasion of the photograph .
A small collection of photos taken at Portsmouth Airport - mostly in the late 40s.The photos were kindly provided by J.B."Tommy" Thompson, via Pete Pitman.
US,British , Australian and Canadian Aircraft Carriers and other aviation equipped vessels at Portsmouth & Southampton 1955-2011.A recently greatly expanded section.
Airwork Fleet Requirements Unit at Hurn 1951-1972.
The crash at Corfe Castle of Swordfish K5985.
402FS USAAF at Andover in 1944,Photos.
405FG USAAF at Christchurch in 1944,Photos..
The U S Navy's VCS-7 Squadron at Lee-on-Solent flying Spitfires for D-Day.
The Army Balloon Factory and early airships at Farnborough in picture postcards.
Seaview and Sopwith: June 1913 photos of Harry Hawker and the Sopwith D1 Three Seater at Seaview on the Isle of Wight..
Hamble & the AW Ensign : 1938 Photos of the AW Ensign Prototype a5 Hamble (via John Turner)..
Spartan VT-AAT , Pictures and information about VT-AAT and it's owner P.M.Kabali;From Captain Herman Vinayak of Mumbai.
Stella at Lytchett Minster, B 17F "Stella"- Forced landing at Lytchett Minster and subsequent recovery.


From an award-winning developer, The Clouds offers large, spacious living areas on large, spacious plots, beautifully landscaped gardens, large shaded terraces and 12 x 5 metre blue sky stone swimming pools.
Other notable features include volcanic rock driveways, 5.6 kw solar panels, solar management glass, low maintenance fee, government water supply, large communal area with children's playground and on site architects to work with clients on the designs of their dream property.
With all these features and more, clients are able to give themselves the lifestyle they deserve in a beautiful, tropical location.
With 2 designs and 63 plots of various sizes.
Full chanote land title deed.


What is better SalesNexus or HubSpot CRM? Today's businesses require the most effective CRM Software product to continue to be competitive. On this page we help you with choosing the best software, by allowing you to evaluate SalesNexus and HubSpot CRM down to the very details of their individual offers.
You may also make use of our general scoring values, which rate the software overall quality and performance. SalesNexus got a 8.1 score, while HubSpot CRM has a score of 9.8. Likewise, you may compare their general user satisfaction rating: 100% (SalesNexus) against 99% (HubSpot CRM). Don't forget to select the solution that best addresses your most crucial issues, not the software with the higher number of features.
In the event you need to quickly identify the top CRM Software according to our experts we advise you take a look at one of these services: Salesforce CRM, HubSpot CRM, Freshsales.
SalesNexus is customized in order to grow the business of users, and offers marketing automation and lead generation solutions.
In case you continue having doubts about which product will work best for your company it may be a sensible idea to analyze each service's social metrics. Such metrics are frequently an indicator of how popular a given service is and how large is its online presence. For instance, in case of Facebook SalesNexus has 5489 likes on their official profile while HubSpot CRM profile is liked by 1294790 users.


text:
Codici
 A91 – codice ECO della difesa olandese, apertura degli scacchi

Strade
 A91 – autostrada italiana Roma – Fiumicino

redpajama_set_name: RedPajamaWikipedia


text:
Mark Lowry's New Music Video Goes Viral
August 17, 2017 Absolutely Gospel Music News & Scoops 0
Hendersonville, TN (August 17th, 2017) – Platinum-selling recording artist, Mark Lowry, has once again made waves across social media with his brand new music video, 'What's Not To Love?' The fun, upbeat video, featuring the GRAMMY-Award winning Gaither Vocal Band, made its Facebook debut on July 24th and reached over a million views just a week later. 'What's Not To Love?' is the title cut on Lowry's new Daywind Records project, available August 18th, as well as his current radio single.
"I had such a blast shooting this video, and the reaction online has been amazing!" shares Mark Lowry. "These songs that I've been writing with my friends, Reba Rambo-McGuire & Dony McGuire, and some they wrote with Chip Davis, are saying the things that I've been saying in my shows for years, but condenses it into a 3 minute nugget."
Anchored by songs co-written by Lowry, Reba Rambo-McGuire and Dony McGuire, What's Not To Love? embodies the messages of grace, compassion and the love of Christ predominately featured at Lowry's live events. Songs such as 'Love Is The Golden Rule' and 'No Room For Hate' carry messages of love and extending grace, 'Feels Like I'm Already There' reaches those going through a valley, while 'Mama Prayed' resonates with those who had a praying mother of their own.
To view the music video for 'What's Not To Love?' visit https://www.youtube.com/watch?v=wp4sla1tU2w.
Amber Nelon Thompson – Sing-a-long
The Nelons – Where Are You Christmas?
REVIEW: Legacy Five – In the Hands of a Carpenter

redpajama_set_name: RedPajamaCommonCrawl


Finally had the chance to head down to Lululemon Athletica at iON Orchard to view the painting created at the event on the 20th of August 2016. This piece was created instantaneously together with the very talented musician, Andy Chia. Born out of the interaction and response between visual arts and sound. Love the energy. Definitely an experience that will be long remembered and cherished. Totally beyond words.


text:
Lessons & Bookings
Where the Passion Begins
Lana Orgovanyi
Head Coach | Owner
Although born and raised in Cape Town, Lana's golfing career began in Europe where she became the No 1 amateur in Belgium and enjoyed a successful period as a professional on the Ladies European Tour. Lana switched full time to a coaching career over 20 years ago allowing her to match her wealth of experience gained in tournament play with her natural flair to teach golf. She has taught with distinction throughout the years as a member of the South African Women's PGA.
Paul McKenzie
Head Professional AAA PGA
Paul learned to play golf as a teenager at Rondebosch Golf Club whilst at Rondebosch Boys High School. Turning professional at the age of 25, he first gained his PGA Diploma and is now an AAA class PGA Professional. Paul has previously taught as an Assistant Coach the Golf Village in Kenilworth within the Jamie Gough Academy, Royal Cape Golf Club and Rondebosch Golf Club. His experience in coaching golf for over 15 years has quickly proved to be very successful at the Pure Motion Golf Academy where his aims are to coach the individual and avoid stereotyping.
Matthew Kilfoil
Teaching Professional
Matthew learned his golf at Durbanville Golf Club aged just seven and although playing several other sports whilst at Fairmont High School, golf remained his passion. He was a key member of Durbanville Golf Club's victorious team in both the Western Province Premier League and the Bradshaw Cup in 2017. Unfortunately an ongoing injury curtailed his hopes of a full time career as a player. Keen to commit himself to golf, Matthew successfully completed his PGA Diploma, which included a six month stint in the Pro Shop at Durbanville Golf Club. He leapt at the chance to coach when offered the opportunity at Pure Motion Golf Academy. He has quickly settled in with his Junior clients, both beginners and those who are already under way, as well as a growing list of golfers of all ages.
©2020 by Pure Motion Golf Academy


text:
//
//  RDVCalendarYearPickerView.h
//  RDVCalendar
//
// Copyright (c) 2014 Douglas Drouillard
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.

#import <UIKit/UIKit.h>
#import "RDVCalendarPickerCell.h"

/**
 * 'RDVCalendarYearPickerView' allows for easily selecting the year to use when displaying a Calendar.
 * It is designed to be a complement to the existing 'RDVCalendarView' by allowing to quickly
 * select the year of the month that is currently being shown.
 *
 * 'RDVCalendarYearPickerView' works by displaying a range of selectable years that are created around
 * an 'anchor' year. Once the range has been created, the user can then 'select' a year, or
 * can page between ranges of years using the prev/next buttons or by swiping left/right.
 *
 * anchor year - The year the range of displayed years is created around. Updated by user through
 * forward/back buttons or swiping.
 *
 * selected year - The year the user wishes to use in the associated calendar's month view. Updated by
 * user tapping on a year cell.
*/

@class RDVCalendarYearPickerView;

#pragma mark - Managing the Delegate

@protocol RDVCalendarYearPickerViewDelegate <NSObject>
@optional

/**
 * Tells the delegate that the specified year is now selected.
 */
- (void)yearPickerView:(RDVCalendarYearPickerView *)yearPickerView didSelectYear:(NSDateComponents *)year;

@end

@interface RDVCalendarYearPickerView : UIView

/**
 * The object that acts as the delegate of the receiving Year Picker View.
 */
@property (nonatomic, weak) id <RDVCalendarYearPickerViewDelegate> delegate;

/**
 * Returns the back (previous month) button. (read-only)
 */
@property (nonatomic, readonly) UIButton *backButton;

/**
 * Returns the forward (next month) button. (read-only)
 */
@property (nonatomic, readonly) UIButton *forwardButton;

/**
 * The Title for range of years displayed
 */
@property UILabel *title;

/**
 * Returs the color of the current year picker cell.
 */
@property (nonatomic) UIColor *currentYearColor;

/**
 * Returs the color of normal year picker cell.
 */
@property (nonatomic) UIColor *normalYearColor;

/**
 * Returs the color of the selected year picker cell.
 */
@property (nonatomic) UIColor *selectedYearColor;

/**
 * Returns the currently selected year.
 */
@property (nonatomic) NSDateComponents *selectedYear;

/**
 * Returs the color of the selected year picker cell.
 */
-(void) setSelectedYear:(NSDateComponents *)year;

@end

redpajama_set_name: RedPajamaGithub


Last week while traveling south on I-26 in North Carolina I took notice of a trailering oddity. On the intersecting side road I see a pickup towing a 5th wheel long horse trailer with a 4-wheel dolly and a second long 5th wheel attached to the dolly. It was only a quick view as we passed on the interstate but I've never seen anything like that. I suppose he was pushing a length limit if NC has one.
Total length was probably over 60' ?
I see doubles towing frequently. Some states allow and some don't but I don't think there's heavy enforcement in either case. But I think even where it's allowed there is a max length restriction. But this is the first time I've ever seen a double 5th wheel except in the big rigs.
I believe all states allow tandem trailers as long as the lead trailer is a 5th wheel/gooseneck on "designated highways" which includes all interstates and most secondary roads. Some - I know Minnesota does - allow a bumper hitch lead so you can pull your travel trailer and a boat. Land of 10,000 lakes you know!!! Motor on!!!
I towed a 23' Streamline TT and boat trailer (overall length 63'), for years with my 1/2 ton International Travelal and was never stopped. I had seen others and the only advice was to use sway control between the trailers. I even learded to back up both rigs. Sometime i had to pull forward ans straighten everything out, then back up some more. Patience! Go slow and watch the mirrors!
At least in PA, the rules seem to restrict you to two trailers. Each one must be < 28.5 feet long. They don't seem to dig much into how they are connected. That may be in a part of the rules I did not find.
Getting fuel must be fun.
Once in Colorado I followed a motorhome towing a car towing a boat. Folks out west are more flexible in their restrictions.


text:
Home » For a third consecutive year Therapure Biopharma Inc. ranks in the PROFIT 500 list of the Fastest-Growing Companies in Canada and ranks 10th in the GTA manufacturing sector (2nd largest employer).
By: chandra
Mississauga, Ontario (September 30, 2016) – Therapure Biopharma Inc. is pleased to announce that it placed 121th in the annual PROFIT 500 ranking of Canada's Fastest-Growing Companies by Canadian Business and PROFIT (PROFITguide.com). The ranking is based on Canada's most successful growth companies using their five-year revenue growth. Therapure is especially pleased to announce that it ranked 24th on the list of Canada's Fastest-Growing Manufacturing Companies in 2016.
"Companies become a part of the PROFIT 500 through innovative thinking, smart strategy and sheer grit," says James Cowan, Editor-in-chief of PROFIT and Canadian Business. "These firms demonstrate what Canadian entrepreneurs can achieve, both at home and across the globe."
Closer to home in the GTA, Therapure ranked 10th overall and is the second largest employer within the manufacturing sector. As a contract development manufacturing organization (CDMO) of biologic therapeutics, Therapure is involved with technologically complex and extremely regulated processes attracting highly skilled employees who made this award possible.
"Therapure is honoured to be in the PROFIT 500 ranking for a third consecutive year, says Nick Green, Therapure's President and CEO. "Our talented and dedicated people are passionate about making a difference and having a positive impact on people's lives."
In addition to continued growth in revenue and job creation, Therapure recently celebrated one million hours without a lost-time accident. "This milestone is an excellent achievement which demonstrates our collective efforts and commitment to provide a safe working environment. This accomplishment is particularly impressive considering the growth and activities we've experienced over the last 8 years", says Green. "The health, safety and well-being of our employees and the public is a key foundation of our business."
Therapure Biomanufacturing's capabilities and expertise include cell line development, upstream and downstream process development, cGMP manufacturing for preclinical, clinical and commercial drug supply and aseptic fill/finish of injectable drugs. These integrated services allow Therapure to compete successfully in the global biomanufacturing sector.
About Therapure Biopharma Inc.
Therapure is a biopharmaceutical company focused on manufacturing complex biologics for its clients and on developing, manufacturing and selling its own blood and plasma-related therapeutic products. Its passion for quality and patient safety underpins everything it does in its three divisions: Therapure Biomanufacturing, an award-winning contract development and manufacturing division; Therapure Biologics, a division focused on using its proprietary PlasmaCap EBA™ technology to develop a portfolio of plasma-derived pharmaceutical products; and Therapure Innovations, a proprietary therapeutics and platform technologies research and development division. Therapure operates out of two facilities located in Mississauga: a 136,000 sq. ft. cGMP facility that includes biomanufacturing, research and quality control laboratories and is built to meet FDA (US), HPFB (Canada), EMA (Europe) and MHRA (UK) standards, and a new 44,000 sq. ft. facility housing 30,000 sq. ft. of cGMP warehouse.
Visit www.therapurebio.com for more information about Therapure Biopharma Inc. and its divisions.
About PROFIT
PROFIT is Canada's leading media brand dedicated to entrepreneurial business. For 30 years, Canadian entrepreneurs and senior managers across a vast array of economic sectors have remained loyal to PROFIT because it's a timely and reliable source of actionable information that helps them achieve business success and get the recognition they deserve for generating positive economic and social change.
In 2013, PROFIT joined forces with Canadian Business to create an all-encompassing business magazine for Canada's business leaders. Canadian Business is a monthly magazine (published 12 times per year with two additional bonus issues), available in print, tablet and mobile phone platforms.
PROFITguide.com
PROFITguide.com is Canada's Online Guide to Business Success. Featuring Canada's preeminent stable entrepreneur and expert columnists, PROFIT's full slate of business rankings, podcasts, videos, white papers and Web-exclusive news and analysis, PROFITguide.com helps the entrepreneur in everyone seize opportunity and succeed in a fast-changing business world.
Dina Iezzi
Director, Marketing and Special Projects
diezzi@therapurebio.com
Therapure Biopharma Inc.


2014 Caribbean Colour -The next Caribbean Colour exhibit "Seeing Red" is scheduled for Saturday, May 10, 2014 at Yacht Haven Grande. If you're interested in participating please email:phintz@gmail.com for submission information and application.
Provides financial assistance to at-risk youths who wish to attend visual and performing arts classes.
The Young @ heART project is designed to connect the young at heart with the arts in the Virgin Islands.
This annual juried art exhibition celebrates the diversity, creativity and quality of work being produced in the U.S. Virgin Islands.
Artvi Advocates is a nonprofit organization of energetic and creative advocates who have a keen interest in furthering the cause of arts and cultural advocacy in the U.S. Virgin Islands.


"Occupation" or "Colonization"? | لماذا غزة؟ Why Gaza?
Professor and historian Ilan Pappe is well-respected and condemned at the same time. He's one of the new historians who has brought to light the ugly truth of the Zionists' cleansing and colonization of Palestine. His book, The Ethnic Cleansing of Palestine, is a must read for anyone who truly wants to learn about the history of Israel / Palestine.
Unfortunately, I must disagree with Professor Pappe's current call to jettison the term "occupation" in favor of "colonization". Listen to his explanation here.
He's absolutely correct …. an occupation should be considered a short-term, temporary state of affairs, and Israel's 50-year occupation of Palestine has far-exceeded the limits of a lawful occupation.
But jettisoning the term "occupation" is not the answer. Under international law, the occupier has responsibilities and duties to those subjected to his occupation. Under international law, the victims of occupation have rights and claims against the occupier.
The State of Israel has been waging a stealth lawfare campaign for many years to convince the world that it is not occupying Palestine.
The answer is not to cave and agree with Israel that there is no occupation.
Instead, Professor Michael Lynk has the answer. He's the U.N. special rapporteur for the Palestinian territories. Professor Lynk is urging the United Nations to examine Israel's prolonged occupation to determine if it is an unlawful occupation. This is the right strategy to pursue in my opinion. I hope Professor Pappe and others concerned about Israel's prolonged occupation will read Professor Lynk's report, and join his effort.
why do the so-called armchair Zionist critics always try to legitimise the apartheid and genocide actions of the Israeli carpetbaggers? I am always called an antisemite by one ZIONIST BLOG whenever I mention Israel, then decried with vitriolic language, their sensitivity is getting to the extreme their aim is to have total control, censorship of thought word or deed. Believe me, his posts often contain statements directed against your good self.
Israel's 70 year occupation of Palestine. To write that it's 50 years, is liberal Zionism, in other words, liberal colonialism and racism, an obvious oxymoron.
Nope, I respectfully disagree. The term "Occupation" has a definite legal meaning …. and Israel has legally occupied the Palestinian territories for 50 years. But the Zionists have been colonizing Palestine for 70+ years. A subtle difference but legally significant.


text:
1 Mom's New Podcast Blows the Roof Off All Those "Unpleasant" Infertility Topics That Are So Hard to Talk About
Mom Starts Podcast About Infertility
March 27, 2019 by Murphy Moroney
Alison Prato — a mom of two from Brooklyn, NY, and professional writer with bylines in a slew of publications ranging from Maxim to Rolling Stone — was on top of the world when she gave birth to her daughter, Ever, in 2009 at 35 years old. But after taking a few years to soak up those sweet baby years, Alison was ready to bring a second child into the world. Her issue? She was struggling to get pregnant again.
"I didn't think it would be hard to have another baby, but long story short, over the next four years, I tried to have another baby and ended up having four miscarriages," explained Alison. "My husband and I went through the wringer emotionally. Our marriage was in turmoil. We were kind of on different wavelengths about how far we wanted to push this. When you're clocking your ovulation, and having sex on-demand, it's just the least sexy thing in the world."
While it's no secret that struggling to conceive often does a number on couples' marriages — just look at Netflix's Friends From College, for example — Alison admitted that we don't talk about it enough.
Here's How Stress Affects Fertility — and Here's What to Do About It
FertilityFamily Self-CareIVFMotherhood
Julia Fox Is a Mom of a 2-Year-Old, and Her Apartment Proves It
by Melanie Whyte 5 hours ago
Chrissy Teigen Keeps It Real About the "Soggy" Postpartum Period
by Sara Youngblood Gregory 2 days ago
10 Shows to Watch When Your Baby Is Keeping You Up at Night
by Devan McGuinness 6 days ago
Emma Roberts Officially Understands Why Parents Are "Always So Tired"
by Maggie Ryan 1 week ago
How to Find the Right Parenting Group For You, According to Experts
by Tiffany Ayuda 2 weeks ago
Yes, Pregnancy Nose Is Real — Here's What Experts Want You to Know
by Devan McGuinness 2 weeks ago
Latest Family


text:
\section{Introduction}
\label{sec:intro}

The MIMO detection problem is a fundamental problem in modern digital communications, which has been extensively studied for several decades \cite{Yang}.
Recently, it has received renewed interest, due to its potential applications in massive MIMO technology in 5G \cite{Yang,Huikang}. The MIMO detection problem is generally modeled as a complex quadratic optimization problem. Various algorithms have been proposed to solve the problem.
One of the most celebrated algorithms is the sphere decoder algorithm \cite{Damen,Murugan}.
The sphere decoder algorithm is a special branch-and-bound based enumeration algorithm, which is guaranteed to find the globally optimal solution of the problem. However, the worst-case and expected complexity of the sphere decoder algorithm are exponential \cite{Verdu1989,complexitysphere}. Motivated by some real-time applications, some efficient sub-optimal algorithms have also been proposed. For instance, the zero-forcing detector algorithm \cite{Schneider}, the minimum mean-squared error detector algorithm \cite{Honig}, and the decision feedback detector algorithm \cite{Varanasi}, are all low-complexity sub-optimal algorithms.
The performance of these algorithms are generally not good in the sense that their detection error rates are very high.

In the past two decades, the semidefinite relaxation (SDR) detector algorithms have received great attention \cite{Tan}--\cite{So2010}. The SDR detector has been proposed first for the BPSK constellation \cite{Tan,Ma} and then extended to the QPSK constellation \cite{Ma2004,Steingrimsson}.
It has been shown that the SDR detector achieves a considerably lower detection error rate than all previously mentioned sub-optimal algorithms.
Moreover, the SDR detector has a guaranteed polynomial-time worst-case complexity.
To understand why the SDR detector performs remarkably well in practice, the approximation ratios of some SDR based algorithms have been
studied in \cite{So2007,Zhang,Kisialiou}. In particular, for the BPSK case, it has been shown in \cite{Jalden2008} that the SDR based algorithm can achieve the maximum possible diversity order. In addition to the above analysis results, some sufficient conditions, under which the SDRs are tight, have been also identified in \cite{Jalden,So2010}.

Besides the BPSK and QPSK cases, the SDR based algorithms have also been extended to other general constellation cases, especially the high-order QAM and $M$-PSK constellations \cite{Ma2004b,Sidiropoulos2006}. Various SDR models have been proposed. For example,
in \cite{Mobasher}, the detection problem is first reformulated as a quadratic integer optimization problem, and then some SDRs are designed by exploiting the special structure of the quadratic integer optimization problem. In \cite{Fan}, the number of design variables in the above quadratic integer optimization reformulation is further reduced, and a more compact SDR is proposed. Very recently, an SDR for the general $M$-PSK constellation is proposed in \cite{Lu}, which is an enhanced SDR over the classical complex SDR and is obtained by
adding valid linear cuts into an equivalent real reformulation of the classical complex SDR. Numerical results in \cite{Lu} show that the enhanced SDR is much tighter than the classical complex SDR.

While various SDRs have been proposed for the MIMO detection problem due to different motivations and/or by using
different techniques, there are very few works studying the relationship between these SDRs. To the best of our knowledge,
the only work along this line is \cite{Ma2009}, where some SDRs for the QAM constellation have been compared.
The goal of this work is to provide a comprehensive comparison of existing SDRs for the MIMO detection problem with a general constellation.
Due to the space limitation, we only present one of our main results here (and more results will be presented in the journal extension).
In particular, we show that an enhanced SDR proposed in \cite{Lu} and a famous SDR proposed in \cite{Mobasher} are equivalent; see (E$\mathbb{R}$SDR1) and (E$\mathbb{R}$SDR2) further ahead.
As a byproduct of the above equivalence result, we can show the tightness of (E$\mathbb{R}$SDR2) proposed in \cite{Mobasher} under a sufficient condition. This tightness result remains unknown until this paper.

We adopt the following standard notations in this paper. We use $\mathbb{C}^{m\times n}$ ($\mathbb{R}^{m\times n}$) and $\mathbb{C}^{m}$ ($\mathbb{R}^{m}$) to denote the set of $(m\times n)$-dimensional complex (real) matrices and $m$-dimensional complex (real) vectors, respectively. We use $(\cdot)^{\T}$ and $(\cdot)^{\dagger}$ to denote the transpose and Hermitian transpose of a matrix/vector, respectively. We use $\mathrm{Re}(\cdot)$ and $\mathrm{Im}(\cdot)$ to denote the element-wise real and imaginary parts of a complex matrix/vector/number, respectively. We use $\|\cdot\|_2$ and $\|\cdot\|_{\infty}$ to denote the $2$-norm and $\infty$-norm of a matrix/vector. The notations $\be,~\bm{0},$ and $\bI$
represent the all-one vector, the all-zero matrix/vector, and the identity matrix of appropriate sizes, respectively. For a given complex number $x,$  $\arg{(x)}$ denotes its argument. For a given vector $\bt,$ $\text{Diag}(\bt)$ denotes the diagonal matrix formed by it. Finally, for two given matrices $\bA$ and $\bB$ (of appropriate sizes), $\bA\succeq \bm{0}$ means that $\bA$ is a Hermitian positive semidefinite (PSD) matrix; $\bA\bullet \bB$ denotes the trace of their product $\bA\bB$, i.e., $\sum_{i}\sum_{j}A_{i,j}B_{j,i}$; and $\bA\otimes\bB$ denotes their Kronecker product.

\section{MIMO Detection Problem Formulation}

Consider a complex-valued MIMO channel model \begin{equation}\label{rHv}\br=\bH\bx^{\ast}+\bm{\nu},\end{equation} where $\br \in\mathbb{C}^{m}$ is
the vector of received signals, $\bH\in\mathbb{C}^{m\times n}$ is an
$m\times n$ complex channel matrix (for $n$ inputs and $m$ outputs with $m\geq n$), $\bx^{\ast}\in\mathbb{C}^{n}$ is the vector of transmitted
symbols, and $\bm{\nu}\in\mathbb{C}^{m}$ is an additive {white circularly symmetric Gaussian noise} with zero mean.
Throughout the paper, we assume that the $M$-PSK modulation scheme with $M\geq 2$ is adopted\footnote{The main results in this paper can also be extended to the QAM case.}. Then, each entry $x_i^{\ast}$ of $\bx^{\ast}$ belongs to a finite set of symbol
$$\left\{\exp(\textbf{i}\theta)\mid\theta=\frac{2(j-1)\pi}{M},~j=1,2,\ldots,M\right\},~i=1,2,\ldots,n,$$ where $\textbf{i}$ is the imaginary unit (which satisfies $\textbf{i}^2=-1$).
The MIMO detection problem is to recover the vector of transmitted symbols $\bx^{\ast}$ from the vector of received signals $\br$ based on the knowledge of the channel matrix $\bH$.
The mathematical formulation of the problem is
\begin{equation*}\begin{array}{cl}
\displaystyle \min_{\bx \in \mathbb{C}^{n}} & \left\|\bH\bx-\br\right\|_2^2 \\[3pt] \tag{P}
\mbox{s.t.} & |x_i|^2=1,~\arg{(x_i)}\in \mathcal{A},~i=1,2,\ldots,n,
\end{array}\end{equation*}
where $\mathcal{A}=\left\{0, 2\pi/M,\ldots,2(M-1)\pi/M\right\}.

\section{Review of Some Existing SDRs for (P)}

The MIMO detection problem (P) is NP-hard \cite{Verdu1989}. Therefore, there is no polynomial-time algorithms which can solve it to global optimality in general (unless P=NP). In the last two decades, the SDR based algorithms have
been widely studied in the signal processing and wireless communication community \cite{Luo2010,Pu2018} and particularly have been designed for solving problem (P).
The SDR based algorithms for solving problem (P) not only enjoy a polynomial-time worst-case complexity but also generally achieve a very good detection error rate performance. In this section, we
briefly review some existing SDRs for problem (P).

For notational simplicity,
let $\bQ=\bH^{\dag} \bH$ and $\bc=-\bH^{\dag} \br;$ let $\bs=[s_1, s_2, \ldots, s_M]^T\in \mathbb{C}^{M}$ be the vector of all constellation symbols, where $$s_j = \cos\left(\frac{2(j-1)\pi}{M}\right) + \textbf{i} \sin\left(\frac{2(j-1)\pi}{M}\right),~j=1,2,\ldots,M;$$ and finally let $\bs_R=\mathrm{Re}(\bs)$ and $\bs_I=\mathrm{Im}(\bs).$

By introducing an $n\times n$ complex matrix $\bX=\bx\bx^\dagger$, problem (P) can be equivalently reformulated as
\begin{align*}
\min_{\bx,\bX} ~&~ \bQ\bullet \bX+2\mathrm{Re}\left(\bc^{\dagger}\bx\right) \\
\mbox{s.t.~} ~&~ X_{i,i} = 1,~i=1,\ldots,n,\\
&~\arg\left(x_i\right)\in \mathcal{A},~i=1,\ldots,n,\\
&~ \bX=\bx\bx^\dagger,
\end{align*}where the variables $\bx \in \mathbb{C}^{n}$ and $\bX \in \mathbb{C}^{n\times n}$ and $X_{i,i}$ is the $i$-th diagonal entry of $\bX.$ A straightforward (but loose) SDR of problem (P) is \begin{align*}
\min_{\bx,\bX} ~&~ \bQ\bullet \bX+2\mathrm{Re}\left(\bc^{\dagger}\bx\right) \\ \tag{$\mathbb{C}$SDR}
\mbox{s.t.~} ~&~  X_{i,i} = 1,~i=1,\ldots,n,\\
&~ \bX\succeq \bx\bx^\dagger,
\end{align*} which drops the argument constraints
$\arg\left(x_i\right)\in \mathcal{A}$ for all $i=1,2,\ldots,n$ and relaxes the nonconvex constraint
$\bX=\bx\bx^\dagger$ to $$\bX\succeq \bx\bx^\dagger\Longleftrightarrow \begin{bmatrix}
1 &\bx^{\T}\\
\bx &\bX\\
\end{bmatrix}
\succeq \bm{0}.$$  It has been shown in \cite{Lu} that ($\mathbb{C}$SDR) is equivalent to the following real SDR
\begin{equation}\begin{array}{cl}
\displaystyle \min_{\by,\bY} & \hat{\bQ} \bullet \bY +2\hat{\bc}^{\T}\by\\[3pt]
\mbox{s.t.} & Y_{i,i}+Y_{n+i,n+i}=1,~i=1,2,\ldots,n, \\[5pt]
& \bY\succeq\by\by^{\T},\tag{$\mathbb{R}$SDR}
\end{array}\end{equation}
where the variables $\by\in \mathbb{R}^{2n}$ and $\bY\in \mathbb{R}^{2n\times 2n}$ and
\begin{align}\label{Qcy}
\hat{\bQ}=\begin{bmatrix}
\textrm{Re}(\bQ) ~&-\textrm{Im}(\bQ)\\[3pt]
\textrm{Im}(\bQ) ~&\textrm{Re}(\bQ)\\
\end{bmatrix},~ \hat{\bc}=\begin{bmatrix}
\textrm{Re}(\bc)\\[3pt]
\textrm{Im}(\bc) \\
\end{bmatrix},~\by=\begin{bmatrix}
\textrm{Re}(\bx) \\[3pt]
\textrm{Im}(\bx)\\
\end{bmatrix}.
\end{align}

Based on ($\mathbb{R}$SDR), an enhanced SDR for (P) has recently been proposed in \cite{Lu}. Define the following $3\times 3$ matrices
\begin{equation}\label{Yi}{\bY}_i=\begin{bmatrix}
1 ~&y_{i} ~&y_{n+i}\\[3pt]
y_{i} ~&Y_{i,i} ~&Y_{i,n+i}\\[3pt]
y_{n+i} ~&Y_{n+i,i} ~&Y_{n+i,n+i}\\
\end{bmatrix},~i=1,2,\ldots,n\end{equation}
and \begin{equation}\label{Pk}\bP_j=  \begin{bmatrix}
1 \\[3pt]
\textrm{Re}(s_j)\\[5pt]
\textrm{Im}(s_j)
\end{bmatrix}
\begin{bmatrix}
1 & \textrm{Re}(s_j) & \textrm{Im}(s_j)
\end{bmatrix},~j=1,2,\ldots,M.\end{equation} By the definition of $\by$ in \eqref{Qcy}, ideally each ${\bY}_i$ in \eqref{Yi} must be one of matrices
$\bP_j$ with $j=1,2,\ldots,M,$ i.e., $${\bY}_i\in\left\{\bP_1,~\bP_2,\ldots,\bP_{M}\right\},~i=1,2,\ldots,n.$$
By relaxing the above combinatorial constraints and dropping some redundant constraints, reference \cite{Lu} proposes the following enhanced SDR for (P):
{\xiaowuhao{\begin{equation}
\begin{array}{cl}
\displaystyle \min_{\by,\bY,\bt} &  \hat{\bQ} \bullet \bY + 2\hat{\bc}^{\T}\by\\[3pt]
\mbox{s.t.} & \displaystyle {\bY}_i=\sum_{j=1}^{M} t_{i,j} \bP_j,~i=1,2,\ldots,n,\\[3pt] \tag{E$\mathbb{R}$SDR1}
& \bA\bt = \be_n,~\bt\geq\bm{0},\\[3pt]
& \bY\succeq\by\by^{\T},
\end{array}
\end{equation}}}where the variables $\by\in \mathbb{R}^{2n},$ $\bY\in \mathbb{R}^{2n\times 2n},$ $\bt\in \mathbb{R}^{Mn},$ $\hat \bQ$ and $\hat \bc$ are defined in \eqref{Qcy}, ${\bY}_i$ is defined in \eqref{Yi}, $\bP_j$ is defined in \eqref{Pk}, and
$$\bS = \bI_n \otimes \bs^{\T},~\bA = \bI_n \otimes \be_M^{\T}.$$ In (E$\mathbb{R}$SDR1), $\bt=[\bt_1^{\T}, \bt_2^{\T}, \ldots, \bt_n^{\T}]^T$ and $\bt_i=[t_{i,1},t_{i,2},\ldots, t_{i,M}]^{\T}\in \mathbb{R}^{M}.$ Due to the symmetry of ${\bY}_i,$ the constraint ${\bY}_i=\sum_{j=1}^{M} t_{i,j} \bP_j$ can be explicitly expressed as the following $5$ linear constraints:
\begin{equation}\label{linearcons}
\begin{array}{rl}
\displaystyle y_i=\displaystyle\bt_i^{\T}\bs_R,~y_{n+i}=\bt_i^{\T}\bs_I,~Y_{i,i}=\displaystyle\bs_R^{\T}\text{Diag}(\bt_i)\bs_R, \\[12pt]
\displaystyle Y_{n+i,n+i}=\bs_I^{\T}\text{Diag}(\bt_i)\bs_I,~Y_{i,n+i}=\displaystyle\bs_R^{\T}\text{Diag}(\bt_i)\bs_I.
\end{array}
\end{equation}

Another interesting SDR for problem (P) is proposed in \cite{Mobasher} based on the following observation: for each $x_i^{\ast}$ of $\bx^{\ast},$ there holds $x_i^{\ast} = \bt_i^{\T} \bs,$
where only one entry of $\bt_i\in \mathbb{R}^{M}$ is one and all the others are zero. Then, problem (P) is reformulated in \cite{Mobasher} as follows:
\begin{align*}
\min_{\bt} ~&~ \bt^T \bar \bQ \bt+2 \bar \bc^{\T}\bt \\
\mbox{s.t.~} ~&~ \bA\bt = \be_n,~\bt\geq\bm{0},\\
&~\bt \in \left\{0, 1\right\}^{Mn},
\end{align*} where \begin{equation}\label{hatS}\bar \bQ =   \hat \bS^{\T}\hat \bQ \hat \bS,~\bar \bc = \hat \bS^{\T} \hat \bc,~\text{and}~\hat \bS = \left[
                                \begin{array}{c}
                                  \textrm{Re}(\bS) \\
                                  \textrm{Im}(\bS) \\
                                \end{array}
                              \right].\end{equation}
Based on the above reformulation and by exploiting the special structure of vector $\bt,$ reference \cite{Mobasher} proposes the following SDR\footnote{A slight difference between (E$\mathbb{R}$SDR2) presented here and (Model III) in \cite{Mobasher} lies in the elimination of one variable in each $\bt_i$ by using the property that the summation of $\bt_i$ is equal to one for $i=1,2,\ldots,n.$}
\begin{align*}
\min_{\bt,\bT} ~&~ \bar \bQ \bullet \bT +2 \bar \bc^{\T}\bt \\ \tag{E$\mathbb{R}$SDR2}
\mbox{s.t.~} ~&~ \bA\bt = \be_n,~\bt\geq\bm{0},\\
             ~&~ \bT\succeq \bt\bt^{\T},\\
             ~&~ \bT_{i,i} = \text{Diag}(\bt_i),~i=1,2,\ldots, n,
\end{align*} where the variables $\bt\in \mathbb{R}^{Mn}$ and $\bT\in \mathbb{R}^{Mn\times Mn}$ and $\bT_{i,i}\in \mathbb{R}^{M\times M}$ denotes the $i$-th diagonal block of matrix $\bT.$
The last constraint $\bT_{i,i} = \text{Diag}(\bt_i)$ requires that $\bT_{i,i}$ is a diagonal matrix and all its diagonal entries are equal to $\bt_i.$

\section{Main Results}
In this section, we present the main result of this paper. We show, somewhat surprisingly, that (E$\mathbb{R}$SDR1) and (E$\mathbb{R}$SDR2) are equivalent,
although they are derived by using different techniques and due to different motivations and they take quite different forms. The equivalence here means
that, for any given feasible point $(\bT, \bt)$ of (E$\mathbb{R}$SDR2), there exists a feasible point $(\by, \bY, \bt)$ of (E$\mathbb{R}$SDR1) such that the two problems have the same objective value at the corresponding points; and for any given feasible point $(\by, \bY, \bt)$ of (E$\mathbb{R}$SDR1), there exists a feasible point $(\bT, \bt)$ of (E$\mathbb{R}$SDR2) such that the two problems also have the same objective value.

\begin{dingli}\label{thmequivalence}
  (E$\mathbb{R}$SDR1) and (E$\mathbb{R}$SDR2) are equivalent.
\end{dingli}
\textbf{Proof:} Due to the space reason, we only give a proof outline here. To show the theorem, it suffices to show that a pair of the feasible points of (E$\mathbb{R}$SDR1) and (E$\mathbb{R}$SDR2) satisfies the following relationship
\begin{equation}\label{connection}
  \hat \bS \bT  \hat \bS^{\T} = \bY~\text{and}~\hat \bS \bt = \by,
\end{equation} where $\hat\bS$ is given in \eqref{hatS}. The conditions in \eqref{connection} guarantee that the two SDRs have the same objective value.

Now, given any feasible point $(\bT, \bt)$ of (E$\mathbb{R}$SDR2), one can easily check that the same $\bt$ jointly with $\by$ and $\bY$ given in \eqref{connection} is a feasible point of (E$\mathbb{R}$SDR1) and they achieve the same objective value as that of (E$\mathbb{R}$SDR2) at $(\bT, \bt)$. Next, given any feasible point $(\by, \bY, \bt)$ of (E$\mathbb{R}$SDR1), we shall construct a matrix $\bT$ such that it, jointly with the given $\bt,$ is a feasible point of (E$\mathbb{R}$SDR2) and the two problems have the same objective value at these two points.

Without loss of generality, suppose that the PSD matrix $\bY-\by\by^{\T}$ is not zero.
Let $r\geq 1$ denote the rank of $\bY-\by\by^{\T}.$ Furthermore, suppose $\bY-\by\by^{\T}$ has the following eigenvalue decomposition $\bY-\by\by^{\T} = \bU \bm{\Lambda} \bU^{\T},$
where $\bU\in \mathbb{R}^{2n\times r}$ and $\bm{\Lambda} \succ \bm{0}.$
Similarly, for each $i=1,2,\ldots,n,$ one can easily show that $\text{Diag}(\bt_i) -\bt_i\bt_i^{\T}$ is PSD due to the fact that $\be_M^{\T}\bt_i =1$ and $\bt_i\geq \bm{0}.$
Suppose that $\text{Diag}(\bt_i) -\bt_i\bt_i^{\T} = \bU_i \bm{\Lambda}_i \bU_i^{\T},$
where $\bU_i\in \mathbb{R}^{M\times M}$ and $\bm{\Lambda}_i \succeq \bm{0}.$
Construct the vectors
\begin{equation*}\label{eta}\bm{\eta}_{i}=\left\{\begin{array}{@{}ll}
\bm{\Lambda}_i^{1/2}\bU_i^T \bs_R,~~\textrm{for}~ i=1,2,\ldots,n;\\[3pt]
\bm{\Lambda}_i^{1/2}\bU_i^T \bs_I,~~\textrm{for}~ i=n+1,n+2,\ldots,2n.
\end{array}\right.\end{equation*}
By using \eqref{linearcons}, one can check that the above $\left\{\bm{\eta}_i\in\mathbb{R}^{M\times 1}\right\}$ satisfy
\begin{equation}\label{etanorm}
\begin{array}{rl}
  \left\|\bm{\eta}_{i}\right\|^2=Y_{i,i}-y_i^2,~i=1,2,\ldots,2n,\\[5pt]
  \bm{\eta}_{i}^T\bm{\eta}_{n+i}=Y_{i,n+i}-y_iy_{n+i},~i=1,2,\ldots,n.
\end{array}
\end{equation}

Suppose
$\bY-\by\by^T= \left[
              \begin{array}{ccc}
                \bm{\xi}_1  & \ldots & \bm{\xi}_{2n} \\
              \end{array}
            \right]^T\left[
              \begin{array}{cccc}
                \bm{\xi}_1 & \ldots & \bm{\xi}_{2n} \\
              \end{array}
            \right],
$ where $\bm{\xi}_i\in\mathbb{R}^{r\times 1}$ for all $i.$ Obviously,
\begin{equation}\label{xiproduct}\bm{\xi}_i^T \bm{\xi}_j = Y_{i,j}-y_iy_j,~i,j=1,2,\ldots,2n.\end{equation}
One can show from \eqref{etanorm} and \eqref{xiproduct} that there exist $\left\{\bZ_i\in \mathbb{R}^{r\times M}\right\}$ such that
  \begin{equation}\label{Zi}
    \bZ_i^T \bZ_i \preceq \bI_{M},~\bZ_i\bm{\eta}_i = \bm{\xi}_i,~\bZ_i\bm{\eta}_{n+i} = \bm{\xi}_{n+i},~i=1,2,\ldots,n.
  \end{equation}

Now, we can construct the desired matrix $\bT\in \mathbb{R}^{nM \times nM}.$ Let the $(i,j)$-th block of $\bT$ be
\begin{equation*}\bT_{i,j}=\left\{\begin{array}{@{}ll}
\bt_i\bt_j^T + \bX_i^{\T}(\bY-\by\by^T)\bX_j,~~\textrm{if}~ i\neq j;\\[3pt]
 \text{Diag}(\bt_i) ,~~\textrm{if}~ i=j,
\end{array}\right.\end{equation*} where $\bX_i=\bU\bm{\Lambda}^{-1/2}\bZ_i \bm{\Lambda}_i^{1/2}\bU_i^{\T}\in \mathbb{R}^{2n \times M},~i=1,2,\ldots, n$
and $\left\{\bZ_i\right\}_{i=1}^n$ are given in \eqref{Zi}. One can check that the above constructed $\bT$ and the given $\bt$ jointly satisfy all constraints in (E$\mathbb{R}$SDR2) and equations in \eqref{connection} (and thus they achieve the same objective value as that of (E$\mathbb{R}$SDR1) at $(\by, \bY, \bt)$).  This completes the proof. \hfill {\bf Q.E.D.}

Two remarks on Theorem \ref{thmequivalence} are in order.~First, combining Theorem \ref{thmequivalence} and \cite[Theorem 4.4]{Lu}, we can immediately obtain the following tightness result of (E$\mathbb{R}$SDR2).
\begin{dingli}\label{thmtightness}
  Suppose that $M\geq 2.$ If the inputs $\bH$ and $\bm{\nu}$ in \eqref{rHv} satisfy
  \begin{equation}\label{condition}
  \lambda_{\min}\left(\bH^{\dag}\bH\right)\sin\left(\frac{\pi}{M}\right)>\left\|\bH^{\dag}\bm{\nu}\right\|_{\infty},
\end{equation} where $\lambda_{\min}\left(\bH^{\dag}\bH\right)$ denotes the smallest eigenvalue of $\bH^{\dag}\bH,$
   then (E$\mathbb{R}$SDR2) is tight for (P).
\end{dingli}
The sufficient condition in \eqref{condition} is intuitive, which roughly says that problem (P) is an ``easy'' problem (polynomial-time solvable) if {the channel matrix} is well conditioned and {the number of constellation points} and {the noise level} are below a certain threshold.
Second, Theorem \ref{thmequivalence} reveals that there is some ``redundancy'' in (E$\mathbb{R}$SDR2).
In particular, we can see from \eqref{connection} that there is a correspondence between the feasible sets of (E$\mathbb{R}$SDR2) and (E$\mathbb{R}$SDR1) and
all information contained in the high-dimensional space $\left(\bT,\bt\right)$ in (E$\mathbb{R}$SDR2) is kept in the low-dimensional space $\left(\by,\bY,\bt\right)$ in (E$\mathbb{R}$SDR1) under the mapping in \eqref{connection}. To be more specific, the matrix variable in (E$\mathbb{R}$SDR1)
is of dimension $2n\times 2n$ but the matrix variable in (E$\mathbb{R}$SDR2) is of dimension $Mn\times Mn.$ Hence, (E$\mathbb{R}$SDR1) should be more efficiently solvable
than (E$\mathbb{R}$SDR2) especially when $M$ is much larger than $2.$ The equivalence shown in Theorem \ref{thmequivalence} provides useful insight into
possibly reducing the ``redundancy'' in existing SDRs for more general combinatorial optimization problems and designing new computationally more efficient SDRs.

\section{Simulation Results}
In this section, we present some preliminary simulation results to verify the equivalence between (E$\mathbb{R}$SDR1) and (E$\mathbb{R}$SDR2).
In our simulations, all entries of the channel matrix $\bH\in\mathbb{C}^{m\times n}$ are generated independently and identically according to the standard complex Gaussian distribution, and all entries of the transmitted symbol vector $\bx^{\ast}\in\mathbb{C}^{n}$ are drawn independently and uniformly from the $8$-PSK constellation. In our simulation, we focus on the 8-PSK constellation with $(m, n) = (10, 10)$. We define the SNR as follows:
\begin{equation*}
\mbox{SNR}=\frac{\mathbb{E}[\|\bH \bx^{\ast}\|_2^2]}{\mathbb{E}[\|\bm{\nu}\|_2^2]}= \frac{m\sigma_{\bx}^2}{\sigma_{\bm{\nu}}^2}
\end{equation*}
where $\sigma_{\bx}^2 = \mathbb{E}[\|\bx^{\ast}\|_2^2],$ $\sigma_{\bm{\nu}}^2 = \mathbb{E}[\|\bm{\nu}\|_2^2],$ and $\mathbb{E}[\cdot]$ is the expectation operator.
For each SNR value, we randomly generate $100$ problem instances $(\bH,\bx^{\ast}, \bm{\nu})$ and the results presented below are obtained by averaging over all generated instances. We use the solver SeDuMi in CVX \cite{cvx} to solve the two SDRs, i.e., (E$\mathbb{R}$SDR1) and (E$\mathbb{R}$SDR2).

Fig. \ref{error} shows the average difference of the optimal objective values of (E$\mathbb{R}$SDR1) and (E$\mathbb{R}$SDR2) and the average difference of the first and second equations in \eqref{connection} at the optimal solutions, i.e.,  $\|\hat \bS \bT  \hat \bS^{\T} - \bY\|_2$ and $\|\hat \bS \bt - \by\|_2$, versus different SNRs. As can be observed from Fig. \ref{error}, the difference under all these three measures is very small (in the order of $1$e$-4$) over the whole range of tested SNRs, and this shows that (E$\mathbb{R}$SDR1) and (E$\mathbb{R}$SDR2) are indeed equivalent. Fig. \ref{fig_time} shows the average CPU time taken to solve  (E$\mathbb{R}$SDR1) and (E$\mathbb{R}$SDR2) versus different SNRs. We can see clearly from Fig. \ref{fig_time} that solving (E$\mathbb{R}$SDR1) is much more efficient than solving (E$\mathbb{R}$SDR2). It is expected that the time difference of solving the two SDRs will become larger as the dimension of the problem (especially the number of constellation points) increases. All the above simulation results are consistent with our analysis.

\begin{figure}[t]
	\includegraphics[width=0.42\textwidth]{difference.eps}
	\caption{Average difference of solutions of (E$\mathbb{R}$SDR1) and (E$\mathbb{R}$SDR2) under different measures.}
	\label{error}
\end{figure}

\begin{figure}[t]
	\includegraphics[width=0.42\textwidth]{time.eps}
		\caption{Average CPU time of solving (E$\mathbb{R}$SDR1) and (E$\mathbb{R}$SDR2).}
	\label{fig_time}
\end{figure}

\newpage

{

redpajama_set_name: RedPajamaArXiv


Dr. Gregory W. Anderson is a board-certified pediatrician with over 20 years military service split between the Army and Air Force. He has special interests in well child care, emergency medicine and Star Wars. He is a fellow of the American Academy of Pediatrics. Dr. Anderson attended medical school at the Kirksville College of Osteopathic Medicine in Kirksville, Missouri and residency at Wright-Patterson Medical Center in Dayton, Ohio. He was an Air Force pediatrician at Altus AFB in Oklahoma and at Ellsworth AFB here in Rapid City. Dr. Anderson is the Chairman of the Pediatric Department at Rapid City Regional Hospital and is the current Managing Partner of Black Hills Pediatrics, L.L.P. He is married with three children.


This is a double page spread illustration I did for Seattle Met magazine. The article is about the struggles the key players had in raising the city's minimum wage to $15 per hour. Many thanks to AD Sara D'Eugenio for a great assignment.


text:
Burn Notice is an American television series that originally aired on the cable television channel USA Network from June 28, 2007 to September 12, 2013. The show follows the life of protagonist Michael Westen (Jeffrey Donovan), a covert operative who has been "burned" (identified as an unreliable or dangerous agent) and tries to find out why. With his assets frozen, he is unable to leave Miami and forced to live off any small investigative jobs he can find, with the help of his girlfriend Fiona Glenanne (Gabrielle Anwar) and his old military friend Sam Axe (Bruce Campbell), who briefly informed on him to the FBI. His return to Miami also reunites him with his mother Madeline Westen (Sharon Gless), who becomes an increasingly important part of Michael's life even as he tries to hide his activities from her. Underpinning the episodic stories of Michael's investigative jobs is the running subplot exploring Michael's efforts to find out who burned him, and to get his job and reputation back.

As creator of the show, Matt Nix serves as executive producer and often writes episodes for the show.  He made his directorial debut with the season two episode "Do No Harm", which he had also written. Seven seasons have completed airing in the United States, with 12 episodes in the first season, 16 episodes in the second and third seasons, and 18 episodes in the fourth season. The fourth season introduced new regular character Jesse Porter (Coby Bell), a counterintelligence agent whom Michael unintentionally burns but later makes part of his team. In October 2009, USA Networks announced the renewal of the series for seasons 5 and 6. The show's fifth season, comprising 18 episodes, began airing June 23, 2011, and entered a mid-season break after twelve episodes on September 8, 2011. The remaining episodes aired in November and December 2011, for a finale on December 15, 2011.  The program concluded its 18-episode sixth season, which premiered on June 14, 2012, and ended on December 20, 2012, with a two-hour finale. On November 7, 2012, USA Networks renewed Burn Notice for a seventh season, and, on May 10, 2013, announced that it would be the series' final season. The seventh season premiered on June 6, 2013, and the series reached its 100th episode with "Forget Me Not", the second episode of that season. The series finale aired on September 12, 2013. A total of 111 episodes of Burn Notice were broadcast over seven seasons.

Series overview

Episodes

Season 1 (2007)

Season 2 (2008–09)

Season 3 (2009–10)

The third season of Burn Notice premiered on June 4, 2009. Both Nix and Donovan have revealed that the season will focus on the past of Michael, Fiona and Sam. Ben Shenkman ("Tom Strickler"), Moon Bloodgood ("Detective Paxson"), and Otto Sanchez ("Agent Diego Garza") appeared in recurring roles during the summer season. The winter season premiered on January 21, 2010, opening with the reunion of actors Tyne Daly and Sharon Gless nearly 14 years after they last teamed up as Cagney and Lacey. Recurring characters in the winter season include Chris Vance as Mason Gilroy, a spy handler known as a "puppetmaster" with whom Michael must work.

Season 4 (2010)

Burn Notice was renewed for a fourth season that began airing on June 3, 2010.  The season also featured the directorial debut of Jeffrey Donovan who directed the third aired episode of the season "Made Man". Coby Bell joined the cast as Jesse Porter, a counterintelligence expert who can easily assume cover identities and has a burning desire to catch criminals.  Robert Wisdom portrayed Vaughn, a spy working for those who burned Michael, in a minimum of six episodes.  Burt Reynolds guest-starred as a legend in the spy business whose story serves as a look forward to what Michael's life could become.  Additionally, Tim Matheson reprised his role as "Dead" Larry Sizemore and Jay Karnes reprised his role as Tyler Brennen. The fourth season was extended by two episodes to 18. The season was broadcast in two parts, with the first part ending on August 26, and the final six episodes beginning on November 11 and concluding on December 16, 2010.

Season 5 (2011)

Burn Notice was renewed for a fifth season, consisting of 18 episodes, on April 16, 2010.  The first half of the fifth season concluded airing after 12 episodes on September 8, 2011, with the remaining six episodes beginning on November 3, 2011. The season concluded in December, 2011.

Season 6 (2012)

A sixth season, consisting of 18 episodes, was ordered by USA Network on April 16, 2010. This announcement came just over a month after the third season had completed airing. The season began in summer 2012.

Season 7 (2013)

USA renewed Burn Notice for a 13-episode seventh season on November 7, 2012. Production began Monday, March 18, 2013 and episodes began airing on June 6, 2013. USA Network announced May 10, 2013 that the seventh season of Burn Notice would be its last.

Television film (2011)
The prequel film "The Fall of Sam Axe" both explores Sam's downfall shortly prior to the opening of the series and sets up elements of season five.

Ratings

Home video releases

References

External links

Lists of American crime drama television series episodes
Lists of American espionage television series episodes


text:
Hidden cloud migration gotchas — and how to avoid them
5 secrets of highly effective IoT strategies
6 cloud cost management tips
Infor's Future in the Enterprise Looks Cloudy and Bright
AirTrunk opens Sydney hyperscale data centre
AirTrunk today opened the first of two new hyperscale data centres in Australia aimed squarely at large scale cloud providers.
The Sydney centre, in Huntingwood near Blacktown, will run its first loads within the next two months, with an initial 20 megawatts of capacity.
The next phase of construction has already begun – which will add a further 10MW – and as demand grows, the centre will eventually reach total capacity of 80MW. When finished, the Sydney centre – which covers 64,000 square metre plot – will be home to 30 discrete data halls, each supporting up to 3MW of IT load.
BrandPost Sponsored by HPE
The CIO's Guide to 'IT as a service'
Step 1: Understand how and why your applications are being utilized.
A second data centre in Melbourne will open "within weeks", with 50MW capacity when complete.
The company has secured dedicated electricity infrastructure to both sites – 132KV dual feed power supply in Sydney and 66KV dual feed in Melbourne – that will provide significant resiliency, scalability and lower electricity costs for its customers, it said.
AirTrunk was founded by Robin Khuda, formerly chief commercial officer and deputy CEO of NEXTDC before he left the company in 2013.
Chief technology officer Damien Spillane joined late last year from Digital Realty. This year AirTrunk appointed Paul Slaven from Amazon as its chief development officer and Leo Chen from Alibaba group as technical director.
The company raised a reported $400 million in funding for the two Australia projects from global investment bank Goldman Sachs and private equity group TPG's TSSP.
"I saw the way the market was moving. I took a long term view. I genuinely believed in public cloud in particular how big they were going to grow," Khuda told CIO Australia.
Major cloud providers are seeking high reliability and cost efficiency, as well as quick deployment and the ability to scale up, Khuda added.
"They don't want to wait for 15, 18 months for a data centre operator to deliver capacity. You look at Microsoft or Amazon, they're basically doubling their infrastructure. They do their capacity planning every fortnight. They need it fast," he said.
The ability to scale will mean big cloud providers will make Airtrunk data centres their "long-term home", typically signing contracts of seven to 15 years, Khuda said.
"We're building at a massive scale. That gives us efficiency of scale. 'I have my wish list, these are the four things I would like, I don't care about all that fancy lighting and everything'. I care about what the customer wants and that's how the whole project started. And that's how we differentiate."
The company look set to expand rapidly into the Asia Pacific region, eyeing new builds in Singapore, Hong Kong and Japan. A builder has already been appointed for another data centre in the region.
"We want to continuously drive efficiency. How we can build even cheaper? Faster? Reliability wise we're probably already there. It's continuously getting the cost efficiency and a much, much faster build. That's really the approach," Khuda added.


With your host Joseph Monte, Apocalyptic Weather delves into the latest catastrophic Weather reporting from around the globe. Below you will find a list of all the episodes released under this series. Stay tuned for the latest updates!


Nunes served on Trump's transition group, and Gowdy chaired the particular committee House Republicans created to analyze the 2012 assault on the U.S. compound in Benghazi. The choose stated Weinstein could possibly be deposed, regardless that his legal professional said a deposition could be "tricky" and "fraught with issues," given the ongoing prison investigations.
Paul Manafort , Trump's former marketing campaign chairman, and his associate, Richard Gates , were required to turn themselves into federal authorities Monday as they had been indicted on 12 counts – starting from conspiracy in opposition to the U.S., to conspiracy to launder cash. Mr Kislyak, the previous longtime Russian ambassador to the US, is at the centre of the web mentioned to connect President Donald Trump's marketing campaign with Russia.
And he's alleging not mere technical infractions of law however astonishing criminality on the part of Trump's marketing campaign manager, a man who additionally attended the Trump Tower assembly. Several investigations would lead again to that district, too, together with these into Mr Trump's marketing campaign ties to Russia, and Mr Trump's assertion that Trump Tower was wiretapped on orders from his predecessor.


Can be distinguished from similar species by having spots rather than lines under the eye.
Distribution Indo-Pacific: Red Sea south to East London, South Africa (Ref. 5469) and east to the Marquesan Islands, north to the Mariana Islands, south to New Caledonia. Eastern Pacific: Gulf of California to Colombia and the Galapagos Islands (Ref. 9289).


The Grasp in Management (MiM), Enterprise Administration track, often known as "Grande École," is a two-yr educational programme, taught entirely in English. Managing the advertising operate is a very powerful job the modern pizzeria supervisor has to deal with You possibly can have the perfect pizza obtainable, and without proper advertising you will struggle over the years to maintain ample gross sales development with the proper quantity of gross revenue.
Then you must critically think about a level in business administration. Focused executive training helps strengthen the abilities vital for a business growth supervisor. Administration can be a board of administrators, CEO's, flooring managers, basic managers, and manufacturing managers among others.
College students can count on to achieve information of the completely different areas of a enterprise and the way they perform together as well as technique and management expertise. Recruit and Rent Administration: Means to centrally handle and enhance the method for a brand new or substitute employee in a company.
Enterprise improvement coaching is important for companies who wish to maximize their revenue margins and grow as a whole. Be sure to level your sales and marketing staff in the right path for profitable enterprise. Whatever the reason, this has created a number of confusion around the term Business Development". Critically evaluate the present gross sales pipeline process and recommend the optimum approach for market penetration, which is able to contain the constructing of relationship management expertise.
That eliminates the money and time wasted in sending literature or seeing individuals who won't ever use your companies, and it stops the fruitless observe-up calls that lead nowhere however to frustration. We welcome all discussions concerning co-growth of products that may be positioned inside our strategic enterprise focus, especially in those areas that goal to make the most of our expertise platforms.
These are ten tips that I've used myself to begin a variety of online businesses over the past decade. They can do so once they start their very own engineering businesses. Most people who begin their very own business without doing something to type a separate entity are known as sole proprietors. If you've been fascinated with starting a house based enterprise and you may type at the very least 30 wpm, here is some great information that can allow you to get started.
In case you're trying to grow, you've got to deal with the total "business." As a business proprietor, the cupcake making, painting, music or widget making might be just one component, but it's definitely not the "enterprise." The business is the promotion of your product, the worth level, finances, prospects, money register, accounts receivables and payables, and payroll, and so on.
If you're launching your startup with plans for significant progress, strategic planning will likely be your new greatest buddy. I am not crazy about their marketing approach but I tolerate it as a result of, I like the products they manufacture. On the subject of promoting your walks or hikes, you will use different advertising methods depending upon whether your prospects are local or from out-of-town.
Not enough money to get your corporation concept off the ground. Sure, it's numerous work, but if in case you have a great area of interest, involve girls, do market research, plan, plan, and plan some more, you'll be in enterprise for the lengthy haul. First, ask yourself: Do I really want a business accomplice to construct a successful firm?
For this sort of business you would really need to be sure to had all of your bases lined, as far as passenger insurance coverage, and native permits, and so forth. This may be completed by native gross sales, partnering with local businesses (e.g. hairdressers or florists), maybe taking a table within the restaurant of a giant native employer for a lunchtime once a month.


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Bhrahmapuram landfill is located on 110 acres of land owned by Kochi Corporation at Bhrahmapuram in Vadavukot-Puthankurish Panchayat, 17 km away from Kochi city. A major fire broke out at Bhrahmapuram waste storage center on 2 March 2023 at around three in the afternoon. Smoke rising from Bhrahmapuram made life difficult for the people of Ernakulam. Due to the high level of air pollution after the fire in Ernakulam district, many people experienced cough, difficulty in breathing, headache, dizziness, eye discomfort and itching. It took 12-13 days for the fire to be brought under control.

Origin of fire
The fire brigade received information about the fire at 3.30 pm on 2 March 2023. In the district collector's report, the time reported was 4.15 pm. By the time, the locals arrived at the place within half an hour. The fire originated at the sector one. There were pocklines and excavators but no manpower to operate them. Garbages on the road made it impossible for fire rescue vehicles to pass to the spot. This was the fifth time that the garbage dump caught fire at Bhrahmapuram, but this time the condition of this fire was serious. Areas miles away from Bhrahmapuram were engulfed in smoke. Many people suffered from suffocation and dizziness and had to seek medical help. Many people and medias alleged that the situation was made worse by the failure of the authorities who did not take care to clear the garbage or prepare fire fighting systems despite giving accurate warnings.

Efforts to extinguish fire
The 75 acre area where the fire broke out was divided into six zones and the fire fighting progressed. Fire units from Kochi Port Trust were also brought and tried to douse the fire along with Kerala Fire Force. They tried to put out the fire by pumping more water from Kadambarayar using pumps brought from Alappuzha. changing wind direction adversely affected firefighting efforts. Due to such strong winds, smoke was rising from the garbage heap. In the early days, efforts were made to stir up the waste by using earthmoving machines and dousing the fire with water. Water was also poured from the helicopter. During the night, 26 excavators and 8 JCBs were involved in digging the garbage. Water was pumped continuously. In the first days, 200 people of fire rescue service, 50 volunteers of civil defense, 35 corporation employees and police were engaged in smoke-extinguishing activities. Three ambulances were also camped. The district collector instructed that all excavators should be kept operational throughout the night. Night activities were coordinated by the sub collector and Deputy Collector camped at Bhrahmapuram.

Allegations on corruption
Allegations of corruption of were raised regarding waste bio-mining contract at Bhrahmapuram waste plant. Demands were also raised for an independent probe into the scandal involving politicians, bureaucrats and the Sontra Infotech company. In 2019, the Chief Minister of Karnataka had ordered a vigilance investigation against Sontra Infotech. In 2020, the same company was given the Bhrahmapuram contract. Opposition parties alleged that the Sontra Infratech got the contract after a special intervention from KSIDC. They also asked the Government of Kerala that where did the proposal to extend the contract to the company that did not complete even half of the work within the contract period come from. Allegations were raised that a huge corruption took place in the Kochi Corporation under the guise of a garbage disposal contract, and that the contract was awarded to the children and sons-in-law of the leaders of political parties and the people of Kochi were the ultimate sufferers.

References

2023 health disasters
2023 in India
Fires in India
Health in Kerala
Industrial fires


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Iribarren is een gemeente in de Venezolaanse staat Lara. De gemeente telt 1.120.000 inwoners. De hoofdplaats is Barquisimeto; de drie overige plaatsen in de gemeente zijn Bobare, Buena Vista en Río Claro.

Gemeente in Venezuela


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Winning for you at work
Keep up the pressure to save our sources
Dominic Ponsford, Editor of Press Gazette
I thought that sweeping police surveillance powers were a price worth paying if it meant that myself, or more importantly my children, were less likely to be vaporised by a terrorist carrying a rucksack full of fertiliser.
And up until around a month ago I rather naively assumed that powers to intercept phone calls and emails would only be used by law enforcement agencies against suspected terrorists and serious criminals (or at the very least to stop terrorism and serious crime).
But when I read the Operation Alice Met Police closing report into the Plebgate affair the scales fell from my eyes. On page 31 of the 56-page report the following sentence revealed the casual and routine way the Met accessed the mobile phone records of Sun political editor Tom Newton Dunn.
"The telecommunications data in respect of Tom Newton Dunn was applied for and evidenced."
The Met asked Newton Dunn who his sources were for the Plebgate front page, which revealed that then chief whip Andrew Mitchell had sworn at police officers and allegedly called them "fucking plebs".
Newton Dunn politely but firmly refused.
So the Met secretly pulled his phone records and worked it out themselves.
They did the same with the phone records of the Sun newsdesk.
They used powers allowed under the Regulation of Investigatory Powers Act (RIPA) and the requests were signed off internally by a superintendent.
Three police officers accused of directly, and indirectly, leaking information about the Plebgate incident to Newton Dunn and The Sun were tracked down via the telecoms data and sacked (notwithstanding the fact that the Crown Prosecution Service said they acted in the public interest and could not be charged with breaking the law).
Pretty much immediately I realised that this was one of those rare issues which the whole journalistic community could get behind.
If law enforcement are able to secretly grab the phone records of journalists and news organisations then no confidential source is safe and pretty much all investigative journalism is in peril.
The Save Our Sources petition, aimed at the Interception of Communications Commissioner, has so far been signed by 1,200 journalists and other concerned citizens.
And it has already woken him from his hundred years' sleep, as one wag on Twitter put it.
He has told every police force in the country to reveal their use of RIPA against journalists and promised a public report.
In the mean time we have discovered that RIPA has also been used to grab the phone records of journalists working for the Mail on Sunday and the Ipswich Star. Again, none of the journalists involved were accused of breaking the law.
It would not surprise me to find out that every police molehunt in recent years prompted by news coverage (and there have been dozens if not hundreds) will have been accompanied by RIPA requests for the phone records of the journalist concerned.
Over the weekend the Home Office confirmed that a revised RIPA code of conduct will be published before Christmas requiring police forces to give more consideration to the special confidentiality which exists between journalists and their sources.
The hope is that this guidance will explicitly state that law enforcement officers must get the approval of a judge before they can view any journalistic material (including telecoms and email records).
But this is by no means a done deal, so we must keep the pressure on once the official consultation starts and the more people who can sign the Save Our Sources petition the better - sign the petition today.
The National Union of Journalists has given its full support to the Save Our Sources campaign and it is an issue which underlines the importance of having a strong and effective journalistic union.
Speaking personally, going up against big institutions like the Met police and the security services I have been glad to have a union which fights for press freedom behind me.
I have no doubt the surveillance offered by modern technology is a wonderful crime fighting tool. And there will be occasions when journalists, like other citizens, will fall under state surveillance.
But such surveillance has to be reserved for fighting serious crime, rather than being used to ensure the secrecy of the police and other public institutions, and must be properly regulated.
Dominic Ponsford is the editor of Press Gazette and member of the NUJ.
An international conference has been organised by the National Union of Journalists and the International Federation of Journalists to discuss concerns about mass surveillance of the media and to explore practical steps for safeguarding journalists and their sources on Thursday 16 October in London. Read more about the event and view the conference resources online.
Read more about the Save our Sources campaign on the Press Gazette website.
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BROOKLYN, NY – The New York State's Empire State Development's Division of Science, Technology and Innovation (NYSTAR) has renewed funding for one of its longest-running research centers, the Center for Advanced Technology in Telecommunications and Distributed Information Systems (CATT).
Part of the NYU Tandon School of Engineering, CATT promotes collaborative R&D between industry and researchers at New York University and Columbia University, with the goal of creating entrepreneurial and economically viable new technology. Shivendra Panwar, professor and department chair in the Electrical and Computer Engineering Department at NYU Tandon, directs the center. The five-year funding renewal will help CATT secure matching funds.
The $4.45 million will be used to focus on three main areas: wireless technology, cybersecurity, and data science. Through the affiliated NYU WIRELESS research center, CATT will continue its efforts centered on the emerging fifth generation (5G) cellular technology. In light of major hacking scandals, cybersecurity remains at the forefront of industry needs, and research will center on resilient networks, particularly for the financial industry. Data science has grown tremendously in importance as companies look for ways to get an advantage over competitors. In addition, CATT will continue to work in media applications.
Founded in 1983, CATT was one of the first Centers for Advanced Technology in the NYSTAR program. Over the years it has played a part in making Brooklyn's MetroTech Center an important technology hub. More recently, CATT researchers played key roles in the growth of the Internet industry. It provided the foundation for the research center that evolved into NYU WIRELESS, recently ranked the world's top university hub for 5G, and for the NYU Center for Interdisciplinary Studies in Security and Privacy, which expands the study of information security beyond technology to human, business, and societal issues.
"The CATT has played an important role in shaping the research culture of the NYU Tandon School of Engineering and furthering the transfer of technology from university laboratories to practical applications," says NYU Tandon Dean and President Katepalli R. Sreenivasan. "Winning this funding amidst rigorous competition indicates the value placed by our sponsors on the work being done in our School. We congratulate Professor Shivendra Panwar and all the researchers of the CATT, and thank NYSTAR and the State of New York for their longtime support of this important economic engine."
In addition to its three core research areas, CATT also helped provide a foundation for the NYC Media Lab, a consortium that includes the New York City Economic Development Corporation, New York University, Columbia University, The New School, CUNY, Pratt Institute, and industry partners. CATT's experience partnering industry and academic research for economic development in the tech sector was particularly useful getting the funding proposal for the NYC Media Lab accepted. Panwar is its faculty director.
Current industry partners for CATT include InterDigital Inc., Consolidated Edison Company, Verizon, L3 Communications, IBM, American International Group (AIG), AT&T, MLB Advanced Media, Google, Intel Corporation, Samsung, McGraw Hill Global Education and Boeing Company.
The NYU Tandon School of Engineering dates to 1854, when the NYU School of Civil Engineering and Architecture as well as the Brooklyn Collegiate and Polytechnic Institute (widely known as Brooklyn Poly) were founded. Their successor institutions merged in January 2014 to create a comprehensive school of education and research in engineering and applied sciences, rooted in a tradition of invention, innovation and entrepreneurship. In addition to programs at its main campus in downtown Brooklyn, it is closely connected to engineering programs in NYU Abu Dhabi and NYU Shanghai, and it operates business incubators in downtown Manhattan and Brooklyn. For more information, visit engineering.nyu.edu.


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