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Racing a Maserati Without Wheels
Champion Sailor Giovanni Soldini Has Mastered the Art of Racing a Maserati Without Wheels
His boat, the Maserati Multi 70, doesn't float—it flies.
By Nick Sullivan Published: Aug 7, 2019
If you want an easy life, the mantra might be, "Don't take up offshore sailing." As the skipper of arguably the fastest multi-hull on water, Giovanni Soldini, a master yacht racer with countless epic voyages behind him, knows that better than anyone.
Soldini is a leading light in the fast-moving and fast-developing sport of foiling, which is racing boats that, at their best, fly rather than float, and can reach speeds of 40 knots (about 46 mph) in winds of just 15 knots. Since they were first introduced in competitive sailing in the America's Cup in the early 2000s, foiling multi-hull yachts have transformed yacht racing from top to bottom. At the cutting-edge of material science and engineering, foiling yachts work like hydrofoils. With them, an entire yacht can rocket along as much as five feet out of the water on two narrow, L-shaped blades set into the booms on either side of the main hull. With the boat out of the water and the drag removed, these yachts can reach speeds only dreamed of until a decade ago, often four to five times the speed of the wind—which makes them dangerous close to shore. Soldini and the crew of his 70-foot Maserati Multi 70 do this out over thousands of miles of rolling, open ocean, in voyages that can reach halfway round the world.
While the basic principles of making a boat fly have been established in the relatively flat inshore waters of Americas Cup courses, making it work in open ocean is down to innovators like Soldini and his crew, who over six years have made hundreds of minute adjustments, much of them with the help of Maserati's stellar automotive design team in Modena, Italy, home of the Quattro Porte, the Ghibli and the Gran Turismo.
Giovanni Soldini
A lot of Soldini's tweaks, however, are by gut instinct. And all of the innovation is designed to get the yacht up on her foils and keep her there. Rudders on each boom and "Manta" fins on the main hull have had elevators added that can control the amount of lift. Anything out of the water is given aerodynamic shaping to coax a fraction-of-a-knot advantage. In terms of innovation, the Multi 70 is in a constant battle to keep ahead of the opposition, a handful of other equally futuristic super-boats with equally fanatical crews. It's the space race at sea level.
The ride is anything but the serene feeling of a yacht under sail. It's a soaking, bruising, jolting, adrenaline-rush joyride. And at these speeds, when things go wrong, they go wrong fast. On Soldini's last race, the Transpac 50 between Los Angeles and Hawaii, the Multi 70 struck a large, heavy, submerged object at 4 a.m. while doing 24 knots. The unidentified flotsam (previous collisions have been with a household boiler, a tractor tire, and a suspected tuna) ripped off part of the port prow and half the elevator on the rudder. Submerged objects like this one are an all-too-common hazard in ocean races. The only hope—when you're traveling faster than any sailboat in history—is that you'll miss them.
Soldini is an engaging, beardy 50-something, with a shag of salt- and sun-bleached hair, and a disarming piratical cackle (with matching earring) that erupts often, especially when he's talking about the ups and downs of manhandling a thoroughbred yacht in an environment as unpredictable as the open ocean. Dyslexic as a child, he turned his back to the land at 16 and made his first Atlantic crossing. He has spent more time at sea than on land ever since.
Soldini has been busting records in the new Maserati Multi70
Erik S Simonson
On his second solo race round-the-world-race, in 1999, Soldini spent almost 24 hours looking for a stricken fellow competitor, Isabelle Autissier, whose yacht had capsized in mountainous seas in the southern Pacific ocean, 60 degrees south of the Equator, or two thirds of the way to the South Pole. Scouring a 100 square-kilometer patch of roiling sea, much of it clamped to the top of the mast, Soldini found her, saved her, and with Autissier as a now-passive guest, continued on to win the race in his class. He earned the Legion D'Honneur from a grateful France two years later.
After three years at the helm of Maserati's VOR70, Soldini switched in 2016 to the new Maserati Multi 70, and has been busting records wide open since. Every nautical mile travelled is research. And the boat gets faster with each adjustment Soldini makes to trim and hardware.
"The next race we won by just 10 minutes. Nothing! But we won. Then there's always the next problem."
"Until last year, we never won a race," he says, "except when an opponent made a wrong move. Slowly, slowly, we solved the problems, and this past year, from the first races in October, we won the races even in very changeable conditions. We were like 'Wow!' But we won by 20 minutes—it's nothing over a 600-mile race. Then we did the transatlantic and won by 45 minutes. The next race we won by just 10 minutes. Nothing! But we won. Then there's always the next problem. The next problem is always to make the boat better, more efficient. It's about making an advantage from almost nothing. There is always something we can improve. Then we learn."
On our brief test run out of Long Beach last month, before the Transpac50, the newly tweaked and stiffened rudders coaxed almost 40 knots out of the yacht in just 17 knots of wind. We rocketed under the bows of vast, anchored supertankers, their crew emerging from the bridges high above to take videos on their phones as we disappeared into the engulfing spray. Soldini, beaming (and of course cackling) at the starboard helm, professed himself very happy with the run. What a way to travel.
"These boats are fantastic," he says again with that laugh. "You can go really fast; they're not so expensive compared to a big monohull, but they are so much faster. The speed is everything. But I like all boats. I have a cruising boat that goes only ten knots max, and I love it. Its about getting the best from the yacht. When I go on holiday with my family in Italy, you know, we will probably go sailing."
Nick Sullivan
Nick Sullivan is Creative Director at Equire, where he served as Fashion Director from 2004 until 2019. Prior to that, he relocated from London with his young family to Boerum Hill, Brooklyn. He has styled and art directed countless fashion and cover stories for both Esquire and Big Black Book (which he helped found in 2006) in exotic,uncomfortable, and occasionally unfeasibly cold locations. He also writes extensively about men's style, accessories, and watches. He describes his style as elegantly disheveled.
The Super Bowl Lineup Is Still Getting Better
I Thought Arsenal—and I—Were Cursed
The Australian Open Will Usher in a New Era
Praise the Tennis Gods, 'Break Point' Will Return
Gronk on Tom Brady's Rumored Patriots Return
Ronnie Lott and the Art of NFL Intimidation
The Game That Changed Steph Curry's Life
Aaron Donald Plays Football Like Nobody Else Ever
I Met Pelé in a Drab Midtown Hotel Room
Tom Brady Shares an Update on His Retirement Plans
Why Ed Reed Was a Quarterback's Worst Nightmare
JJ Redick is Putting the NBA Through Therapy


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Welcome to the Connellsville Canteen!
An Initiative of the Fayette County Cultural Trust
Canteen Rental
Event Catering Menu
WWII MuseumChevron
Casualties Fayette County
Connellsville Canteen Ladies
Canteen Volunteers
Research A WWII Veteran
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Connellsville Area KIA
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Piter, Andy Jr.Rename
RESEARCH A VETERAN: How to Locate Someone Who Fought in World War II - Individuals Who Never Made It Home
Request the Individual Deceased Personnel File (IDPF). The IDPF will almost always establish his unit and give information on his burial. In many cases, it will also give valuable information about where and when he died, possibly including reports of the action in which he died. For men whose remains were never recovered or identified, extremely valuable records of the testimonies of his buddies are usually included, giving extraordinary information about the action, what happened to him, and when they last saw him. NOTE: You must send a letter before any information can be sent out to you. The letter should include your signed statement of willingness to pay the Freedom of Information Act fees for the work involved. If you are requesting your relative's IDPF, they may not charge you.
U.S. Army Human Resources Command
ATTN: AHRC-FOIA
1600 Spearhead Division Avenue, Dept. 107
Fort Knox, Kentucky 40122-5504
You can find a listing of dead and missing Army and Air Force personnel by county at The National Archives and Records Administration website.
If the deceased was buried overseas and you want information on a grave-site or possible memorial site, contact the American Battle Monuments Commission.
American Battle Monuments Commission
Courthouse Plaza II
Individuals Who Made It Home After the War
If the individual came home then his discharge papers will provide a lot of valuable information. If you do not have these papers you will want to contact the National Personnel Records Center To get this information you must fill out a Standard Form 180. To get a form, call the following numbers and leave your name and address. The Standard Form 180 will be mailed to you.
National Personnel Records Center
(Military Personnel Records)
1 Archives Drive
The National Personnel Records Center might not have any information about the individual due to a fire in 1973 that destroyed many records. If this is the case, you may try contacting the Department of Veteran Affairs. They have addresses and information on veterans who applied for benefits. To find out if they have any information on your veteran, call them at 800-827-1000.
If the Department of Veteran Affairs does not have any information you can try contacting the Veteran Affairs Insurance Center at 800-669-8477.
If you do not know the individual's Social Security number and they applied for veterans benefits after April of 1973 you can send a $2 check made payable to the Department of Veteran Affairs. In a letter to them, ask for the individual's VA claim number, not his Social Security number. If the claim number is nine digits, then it is also the individual's SS number. Mail this letter to:
Records Management Processing Center
Finding a Military Unit
Once you find the individual's information, or if you already knew it, you can contact members of their military unit. Many can be easily found with Internet research. From there you can contact the person in charge of the group to get further detailed information. This is the best way to get in contact with the soldiers who served with this person.
Other Links That Might Help You
The Seeker: Military Search Forum
WWII U.S. Veterans Website
Department of Veterans Affairs Homepage
VetFriends
You can also contact:
The United States Veteran Support Information Index
Morris, NY 13808
Dad's War: Finding and Telling Your Father's WWII Story
How to Locate Anyone Who Is or Has Been in the Military by Lt. Col. Richard Johnson and Debra Johnson Know, MIE Publishing, Spartanburg, SC, 1999
Finding Your Father's War: A Practical Guide to Researching and Understanding Service in the World War II U.S. Army by Jonathan Gawne, Casemate Publishers, Havertown, PA, 2006
The Connellsville Canteen is a project of the
Fayette County Cultural Trust
The official registration and financial information of the organization may be obtained from the Pennsylvania Department of State by calling toll-free, within Pennsylvania,
1-800-732-0999. Registration does not imply endorsement.
www.fayettetrust.org
Connellsville Canteen copyright 2023

redpajama_set_name: RedPajamaCommonCrawl


The primary purpose of the Stanford University Libraries is to serve the academic and research needs of the faculty, students and staff. Persons not currently members of the Stanford community may use some of the Libraries' collections and facilities. Visitors must agree to voluntarily yield to the needs of our primary clientele when necessary, particularly when the library is very busy.
Access policies described here apply to Green Library.
Members of the public can register for seven free day passes (building access only) each year. Day passes are required for entry into some libraries. You can get them at the visitor kiosks at each Green Library entrance. A valid government-issued picture ID (passport, driver's license, etc.) is required.
For access beyond the free day passes, or for borrowing privileges for non-Stanford-affiliated individuals and corporations, we offer a fee-based library membership. Stanford-affiliated groups may qualify for courtesy access and borrowing privileges.
Visitor wireless Internet access is available, but does not provide access to licensed resources. Public computers are available in Green Library near the Information Center.
Licensed electronic resources are available from computers located in the libraries. However, some databases are restricted to Stanford University faculty, staff, students, and other authorized Stanford-affiliated users.


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Crucial vote on smacking bill delayed for two weeks
14 Mar, 2007 10:16pm 2 minutes to read
Stadium poll in Dunedin
15 Mar, 2007 6:00am Quick Read
Schools to put sign language on curriculum
14 Mar, 2007 11:53pm
By: Juliet Rowan
New Zealand is set to become one of the first countries in the world to introduce sign language into the school curriculum.
It follows the enactment of the New Zealand Sign Language Act 2006, which made sign language an official language.
The Deaf Association has hailed it as another step forward in giving signing equal status to spoken languages.
Education Minister Steve Maharey and Disability Issues Minister Ruth Dyson will officially announce the move this morning in a ceremony at Parliament.
Mr Maharey's office said he would use sign language in parts of his speech.
The sign language curriculum, which will be optional, will start in intermediate schools, but eventually roll out to include students up to Year 10.
Sign-language teaching materials have already been prepared for students in Years 7 and 8.
Students up to Year 10 will have the option of learning sign language as a second language.
Deaf Association chief executive Rachel Noble said it would improve long-term potential for the deaf community to be able to access education and other services, and other opportunities in their lives.
"The main thing it will do is increase awareness of sign language and therefore widen the group of people with whom sign-language speakers can communicate."
She said the Deaf Association would like more inclusion in the curriculum's development and to see schools treating sign language in the same way as Maori language, which was more broadly taught.
The New Zealand Sign Language Act became law on April 10 last year.
It was developed by the Office for Disability Issues to provide official recognition for New Zealand Sign Language (NZSL) as a unique language, with the same status as spoken languages.
The act aims to ensure access to NZSL interpreters in legal proceedings, and to provide deaf people with equal access to education, health, employment and public broad-casting.
Switzerland and several European Union countries, including Sweden, Denmark and Norway, have signed a resolution to recognise sign languages as official languages.
Deaf NZers
* 240,000 deaf or hearing-impaired people.
* An estimated 18,300 are children.
* 28,000 use sign language.
* 51,000 are able to lip read.


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Varanus flavescens är en ödleart som beskrevs av  Thomas Hardwicke och Gray 1827. Varanus flavescens ingår i släktet Varanus och familjen Varanidae. IUCN kategoriserar arten globalt som livskraftig. Inga underarter finns listade i Catalogue of Life.

Arten förekommer i Bangladesh, Indien, Nepal och Pakistan. Kanske även i Bhutan. Varanus flavescens vistas nära de stora floderna. Honor lägger ägg.

Bildgalleri

Källor

Externa länkar

Fjällbärande kräldjur
flavescens
Kräldjur i orientaliska regionen

redpajama_set_name: RedPajamaWikipedia


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The American Zinc Recycling leadership team consists of industry veterans and seasoned professionals who are helping us create and maintain a sustainable future. Learn more about each of them here.
Joel Hawthorne
President & Chief Executive Officer
Joel joined AZR as President & CEO in 2020. He has over 30 year of experience in the steel, carbon, and graphite industries. He came to AZR from Specialty Steel Works Incorporated where he served as the CEO. Previously, Joel was the CEO of Graftech International, a producer of carbon and material science products. He also served in various leadership and financial roles at ACME Metals Incorporated and LTV Corporation which are both now known as Arcelor Mittal. Mr. Hawthorne is the Chairman and Board Member of the nonprofit organization CE National.
Bachelor of Science, Accounting, The University of Akron
Master of Science, Technical Education, The University of Akron
Stephen Bishop
Executive Vice President and Chief Financial Officer
Stephen Bishop joined the AZR team in 2019. With 25 years of management and financial experience, he most recently served as President and CFO of Arsenal Resources. He was also an investment banker for 11 years with DLJ, Credit Suisse, and Deutsche Bank. He served 7 years as an officer in the US Navy.
Bachelor of Science, US Naval Academy
Master of Business Administration, UCLA Anderson School
Michael J. Griffin
Michael J. Griffin joined AZR in January 2017 and adds 33 years of experience in the metals industry to the leadership team. Before AZR, he was the Aluminum President at Noranda; VP, COO, and CEO of Ormet Aluminum; and held various roles at Alcoa and Reynolds Metals, including Plant Manager and other operations, technical, and maintenance roles in the US and Canada.
Bachelor of Science, Electrical and Power Engineering, Clarkson University
William P. Breedlove
Bill joined AZR as Senior Vice President and CCO in 2020. He has over 35 years of industry experience in metals and minerals. Bill joined AZR after working with several private equity companies completing acquisitions in the metals and mining sector. Other prior experience includes President level roles at Somerset Coal International, Inc. and Quality Magnetite LLC. Bill had a long career in metals industry waste and by-product recycling at National Recovery Systems, Inc., and its successor Harsco Corporation, where he ultimately held the global role of EVP Marketing & Business Development for the metals and minerals division.
Bachelor of Science, Business Administration, The Pennsylvania State University
Senior Vice President – Human Resources and Environmental, Health and Safety
Bruce Morgan joined AZR in May 2010, bringing 20 years of industry experience to the role. He formerly worked as the Director of Human Resources – North America for the steel mill services division of Harsco Corporation. Prior to that, Bruce spent 10 years with Vesuvius USA as the Director of Human Resources for both its steel and foundry divisions. He was part of the start-up team for the construction of the Gallatin Steel Company.
Bachelor of Science, Industrial and Labor Relations, Cornell University
Gary R. Whitaker
Senior Vice President – General Counsel and Secretary
Gary R. Whitaker joined AZR in December 2011. He formerly served as Vice President, General Counsel and Secretary for GrafTech International and Vice President, General Counsel and Secretary for the US operations of SK Group.
Bachelor of Arts, UCLA
Juris Doctor, University of Houston Law School
Frank Vallelunga
Vice President – Controller
Frank Vallelunga joined AZR in 1991. Throughout his tenure, he's held various positions in accounting and finance, and served as the General Manager of Specialty Products. Prior to AZR, he held staff positions at Ernst & Young and Geac Computer Corporation.
Bachelor of Arts, Accounting, Washington and Jefferson College
Master of Business Administration, Robert Morris College
Timothy R. Basilone
Vice President – Environmental Affairs
Tim Basilone joined AZR in 2010, bringing 30 years of experience in environmental programs and regulation to our company. Previously, he held progressively more responsible positions at Koppers, Inc and Westinghouse Electric Corporation, and was an exploration geologist for Marathon Oil Company.
Bachelor of Science, Geology, College of Wooster
Master of Science, Geology and Planetary Science, University of Pittsburgh
Registered Professional Geologist, Pennsylvania
Lee Burkett
Vice President – Engineering
Since Lee Burkett joined AZR in 2006, he's had several operational and engineering roles. He has 40 years of metals industry experience behind him, and he's previously held Plant and General Manager-level roles with Universal Stainless & Alloy Projects, J&L Specialty Steel, TIMET, and Lukens Steel.
Bachelor of Science, Mechanical Engineering, The Pennsylvania State University


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Gartner CIO survey: enterprises are entering third IT era
Digital business is maturing, from tentative experiment to application at a massive scale. CIOs must evolve their thinking to be in tune with this new era of rapid increases in the scale of digital business.
Gartner's annual global survey of CIOs showed that the CIO role will remain critical in transformation workflows.
The 2019 Gartner CIO Agenda survey gathered data from more than 3,000 CIO respondents in 89 countries and all major industries, representing approximately US$15 trillion in revenue/public-sector budgets and US$284 billion in IT spending.
The survey results show that digital business reached a tipping point this year - 49% of CIOs report their enterprises have already changed their business models or are in the process of changing them.
"What we see here is a milestone in the transition to the third era of IT, the digital era," says Gartner vice president and distinguished analyst Andy Rowsell-Jones.
"Initially, CIOs were making a leap from IT-as-a-craft to IT-as-an-industrial-concern. Today, 20 years after we launched the first CIO Agenda survey, digital initiatives, along with growth, are the top priorities for CIOs in 2019. Digital has become mainstream."
Scaling digital business
The survey found that 33% of respondents worldwide evolved their digital endeavours to scale, up from 17% in the previous year. The major driver for scale is the intent to increase consumer engagement via digital channels.
"The ability to support greater scale is being invested in and developed in three key areas: volume, scope and agility. All aim at encouraging consumers to interact with the organisation," Rowsell-Jones says.
"For example, increasing the scope means providing a variety of digital services and actions to the consumer. In general, the greater the variety of interactions that are available via digital channels, the more engaged a consumer becomes and the lower the costs to serve them are."
Steady IT budgets
The transformation toward digital business is supported by steady IT budget growth. Globally, CIOs expect their IT budgets to grow by 2.9% in 2019, only slightly less than the 2018 average growth rate of 3%.
A look at the regional differences shows that the regions are moving closer together: The leader in budget growth is once again Asia/Pacific with an expected growth of 3.5%. However, this is a significant cut from the 5.1% projected budget increase in 2018.
EMEA (3.3%) and North America (2.4%) both project an increase, while Latin America trails behind with projected growth of 2% in 2019, down from 2.8% this year.
"CIOs should use their financial resources to make 2019 a transformative year for their businesses," Rowsell-Jones adds.
"Stay active in the transformation discussions and invest time, money and human resources to remove any barriers to change. Enterprises that fall behind in digital business now will have to deal with a serious competitive disadvantage in the future."
AI and cybersecurity shape the CIO agenda
Disruptive emerging technologies will play a major role in reshaping business models as they change the economics of all organisations.
Gartner asked CIOs and IT leaders which technologies they expect to be most disruptive.
Artificial intelligence (AI) was by far the most mentioned technology and takes the spot as the top game-changer technology away from data and analytics, which is now occupying second place.
Although this year's question was asked slightly differently, the jump to first place is enormous: even the top performers went from only 7% to 40%.
With regards to implementation, when asked about their organisation's plans in terms of following digital technologies and trends, 37% responded that they already deployed AI technology or that deployment was in short-term planning. In fact, AI comes in second, behind cybersecurity (88%).
"On the surface, this looks revolutionary. However, this bump in adoption rate of AI may indicate irrational exuberance instead," says Rowsell-Jones.
"While CIOs can't afford to ignore this class of technologies, they should retain a sense of proportion. This latest batch of AI tools is yet to go through its trough of disillusionment."
The strong focus on cybersecurity shows the necessity of creating a secure base for a digital business that shields their organisation and clients.
The survey indicates that in most enterprises the CIO still owns the responsibility for cybersecurity. However, the IT organisation alone can't provide cybersecurity anymore.
The rise of social engineering attacks, such as phishing, require a broader behavioural change of all employees.
In 24% of the digitally top-performing organisations, it is the boards of directors that are accountable for cybersecurity rather than the CIO alone. Nevertheless, to improve security against cyber threats CIOs are combining measures to harden information-processing assets with efforts to influence the people that use technology.
"Last year, I said that CIOs must start scaling their digital business. They excelled," Rowsell-Jones says.
"This year, they have to take it one step further and put their growing digital business on a stable and secure base. Success in the third era of enterprise IT hinges on a sound strategy that combines new, disruptive technologies with a rebalancing of existing investments."
Security week
IT budget


a philosophaster dabbles. sometimes serious, other times not.
the internet is a fast place. but not only the internet, the world is hyper-accelerated: travel, communication, food, publishing, fast production generally. at philosophasters we offer ourselves, and whoever is interested, strategies and therapies for slowing down and reclaiming thought.
through our interviews, articles, collections, blasters, dialogues, retreats and public events we seek both free and playful exploration, but also careful peregrinations. our goal is to make philosophical, scientific and artistic ideas part of common discourse. our podcast and articles are about making connections. thus, it is essential to present ideas and people that reach across diverse and often fragmented disciplines; we focus on words, research, and art that builds bridges and resists the push towards specialization, while at the same time not skating around complexity and subtlety of thought.
our projects grow from the inside, they happen by planting seeds. the site's content emerges organically; a result of the shared experience of the philosophaster community. we don't follow production schedules, or fill space to fill space, talk for the sake of talking. all our content (editor commissioned, or writer-submitted) and events are a horticultural undertaking: some of these grow into new projects and events, and some do not. we always take each new seedling seriously. they've all made it here for a reason, however vague, and for this simple truth they deserve our attending to.
we work in a variety of mediums, because well, quite simply, ideas come in many forms, not just academic papers. philosophasters is not committed to any particular subject matter, but simply the praxis of philosophizing, wherever that may take us, and in whatever form.
Thanks, looking forward to chatting!
What is semiotics and what has it got to do with the history of Philosophy? In this feature length interview, Winfried Nöth details the close relationship between the doctrine of signs and Western Philosophy.
Tim Ingold explores the entangled relations between human beings and the environments they inhabit. Over the last 30 years, he has written and taught widely on how embodied processes of enskillment (learning to hunt-fish-forage, weave or sing, making and expressing art and craft alike) fundamentally determine and shape the diverse ways in which we perceive, understand, and 'dwell' in the world.
A longform reflection on the role of improvisation within creative practice, and the essential similarities between inquiry processes; artistic, artisanal and scholarly alike.
This short sound-text was recorded by the philosophaster team for the SSHRC storyteller's contest. It explains some of the central notions of the emerging edusemiotic research program before going on to touch on the relevance of these ideas to arts education.


Nathan is a passionate developer, designer and agile evangelist. In his day time job he is Senior Software Architect at Dot Net Solutions developing software for clients that ranges from simple web applications to full featured cloud solutions. Nathan has successfully boot strapped scrum & agile teams in various companies that he has worked at and has given presentations on Scrum & Kanban at a number of events.


Elizabeth M Jacob: little sailor girl.
she sat in our backyard, her blue eyes gazing from the soaring green trees to the colorful garden. she pointed up towards the open sky and giggled. a bird gently circled over our heads. she stood, with one shoe on, by the fence. waiting for a glimpse of daddy. as we waited we laughed and played on this warm summer day.
Jessica is wearing a vintage sailor dress.
head over to Mama Loves Papa for some more Small Style!
What gorgeous blue eyes! Can I tell you that I'm lusting after a vintage sailor outfit. I'd better get one for next summer - before my girl is too old to wear them. Love the pop of colour the scarf provides.
seriously... can I have her?
My little sister had that dress, Jessica looks just as cute as she did 24 years ago.
Oh gosh, too too cute!!
so precious! that dress beyond adorable. and those big blue eyes. she is just to cute for words.
what a cutie. beautiful blue eyes.
she is such a doll and the dress goes swimmingly well with those eyes!
Such a pretty baby. Love these photos.
Beautiful little girl :) I want one of those dresses in my size!
Oh my goodness, I recognize this dress...I'm certain I wore it when I was little! Your little one is beautiful, by the way.
That dress is adorable- good find.
I love a sweet sailor dress for summertime and this one is super sweet!
sooo cute, love that dress!


NGC 1977 is a complex nebula containing a diffuse reflection cloud and a bright HII region. It comprises the southern portion of S279, a more extended HII region 30 arc minutes north of the Orion Nebula. The stars of NGC 1977 are part of the Orion 1d subgroup, the youngest members of the Orion OB1 stellar association. NGC 1977 is bounded on the south by the extreme northern end of the Orion A Molecular cloud. The lone exciting star of NGC 1977 and the surrounding HII region, S279 is the B1 V star HD 37018 (42 Ori). This star and the other bright stars of NGC 1977 make up the youngest subgroup (subgroup d) of the Orion OB association. The stars in this region are between 2 and 4 million years old. The region of NGC 1977 represents the northern boundary of the OMC-2 and OMC-3 molecular cloud cores which is one of the most active sites of low and intermediate mass star formation known. A large number of energetic outflows, Herbig-Haro objects, and embedded protostars have been found in this region between NGC 1977 and M42-43 mostly at infrared wavelengths. The bright rim along the southwestern edge of NGC 1977 represents the interface of the nebula with its molecular cloud complex.


There's more than one way to support your troops, who are sacrificing life and limb to protect American freedom and liberty. Don't forget about their loyal military canines. Here's how to help. Please share with your friends.


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What is Kashmir Premier League
The Need for The League:
The Kashmir Premier League: The countdown to the inaugural season of the Kashmir Premier League (KPL2021) began on July 3 in Islamabad with a draught ceremony. The entrance of the invitees, which included several well-known figures from various areas, began off the event's red carpet. According to him, Pakistani talent has enthralled the cricketing globe, and now Kashmiri brilliance would do the same.
Establishment of The League:
The Kashmir Premier Competition will begin in 2021 as a professional Twenty20 cricket league. The league includes six clubs, five of which represent cities in Pakistan's Azad Kashmir region. One squad represents Kashmiris living in other countries. The first season of the league will run from August 6th through August 16th, 2021.
Renowned Player's Being a Part of The Historical Event:
The participation of Pakistani international players contributes to the development of community spirit among the people of AJK", according to the organizers.
The KPL will include retired talents like Tillakaratne Dilshan, Matt Prior, and Monty Panesar. Apart from these individuals, the Bagh Stallions will include current Pakistan players like Shadab Khan, Shan Masood, and Iftikhar Ahmed. Shadab, by the way, will be commanding the team.
The Most Awaited Official Anthem of The Kashmir Premier League:
On February 16, 2021, Rahat Fateh Ali Khan sang the official anthem of kashmir premier league.Shan Shahid directed the song. As a charitable organization, KPL has collaborated with the Shahid Afridi Foundation.
Blitz Advertising as its Streaming Partner:
For the inaugural Kashmir Premier League, the Cutting Edge Group has chosen Blitz Advertising as its worldwide media rights agent and live stream partner (KPL).
Tags: kplWhat is Kashmir Premier Leaguewhat is kpl


At the GSMA Mobile 360 event taking place in Kigali, Rwanda, the company released a mobile report based on sub-Saharan Africa. According to their report, an estimated 52% of Africans which translates to 634 million will be connected to a mobile service by 2025. The report released in 2017 shows that at present, 44% are connected to a mobile service, which are an estimated 444 million people on the continent. This will be a significant rise over the next seven years.
The Chief Regulatory officer, John Giusti says that more needs to be done to connect the underserved populations in Africa, as mobile devices act as more than just a communications device. It is also a vital tool used to improve the livelihoods of people. Today, everything can be done on a smart device. Read, edit and save docs. Entertainment via streaming service is also provided through mobile devices. Hence serving people much more than through communication alone.
The CRO says that there needs to be a focus on the long-term industry sustainability that can only be achieved through investment friendly policies and supportive regulatory frameworks, across Africa. Now although Africa has had the highest adoption rate of mobile technology, penetration is still below average. This is in large part because of affordability and the youthful age of the continent's inhabitants. The world average s at 66% while Africa hovers at 44%. The demographic stands at 40% of them being under the age of sixteen which proves it harder for the youngsters to own a smartphone at that age.
However, many companies continue to flock to Africa with new pocket-friendly devices, which has caused ownership to pick up. More than that it has accelerated migration to 3G/LTE broadband connectivity. Which is a pretty good speed. Additionally, about 300 million people are expected to have access to the internet by the turn of a quarter century mark comes.
GSMA continued to praise the growth taking place stating that the mobile industry in Africa is showing strong progress. In thanks to increased connectivity and access to information as well as mobile money which has increased productivity and reduced poverty on the continent.


text:
Pyrrhopoda viossati är en skalbaggsart som beskrevs av Franz Antoine 1992. Pyrrhopoda viossati ingår i släktet Pyrrhopoda och familjen Cetoniidae. Inga underarter finns listade i Catalogue of Life.

Källor

Skalbaggar
viossati


I don't know.. should I text him back and see what he could possibly need from me, or ignore ?
I mean.. I do miss him.. but anyone that does that to someone they claim to love is complete garbage.
He spent month after month just trying to get me to notice him. Well I'm stubborn af and refused to acknowledge his flirting until I finally gave in, and I fell for him haaaard.
Then when he has me, he throws me in the trash...??
I swear, when it comes to guys I'm just a trainwreck.
I mean I was engaged to a guy that abused me and tortured me for almost 10 years.... that's really stupid.
When you take a shower, do you get out and put the same dirty underwear back on?
So why would you do the same with an ex?
Some people are horrible. You know the saying about misery and company? Same rule applies. Bringing you down will bring them joy. So my vote is "to hell with him".
Support The Miracle League of Michigan -- because EVERY child deserves the chance to play baseball!
But I'm gonna keep wondering non-stop about what he wanted etc.
He wanted to make you wonder what he wanted. Don't.
I'm pretty sure he's genuinely worried about me though as I've dropped off the face of earth a couple months ago.
I have people texting me or calling me several times a week asking how I'm doing or seeing if I'm dead.
Yeah you make a good point.
I actually already once tried to get back with him, but my friend had to stop me.
I just texted him "hello?"
Lol I'm pathetic, I know.
Don't look back, you've been there and know how that part of the story goes.
It's hard to fight that urge to talk to someone or have contact with someone who once was that deeply involved in your life.
You'd be the one at fault..... and he/she is just looking to mess with your head.
Don't do it again.... too many good people out there to have your heart tossed around and thrown against the wall.
Block the number, be done with him/her.
Some rotten things will always remain that way no matter how much your head may "pretty it up" and make it appealing again.
Time to stop allowing him to have that power.
When it comes to exes I always think of Pet Cemetery and that scene where Fred Gwynn is talking about why it is best to let the dead sleep. Good memories are just memories.


text:
Launch of the New UNFSS Website
The United Nations Forum on Sustainability Standards (UNFSS) recently unveiled its newly designed website. The newly revamped website, which was launched last month, has been optimized for easier access to information, improved functionality, and enriched content areas. The website aims to become a hub that provides information on the potential value of voluntary standards for a more equitable, fair and sustainable development.
As a public online platform, the UNFSS website intends to increase understanding stimulate the dialogue among partners, and support national multi-stakeholders initiatives on Voluntary Sustainability Standards (VSS). VSS are guidelines or principles that producers, traders, manufacturers, retailers or service providers follow which relate to a wide range of sustainability metrics such as occupational health, safety, environmental protection.
The website also offers tactile news content on how VSS can open markets, strengthen the quality of goods, promote sustainability along value chains, and drive towards sustainable practices. VSS has the potential to positively contribute to countries' national target goals for sustainability and ultimately help reach the Sustainable Development Goals (SDGs).
Furthermore, the website provides a brand-new space for UNFSS Members and partners to showcase their work. New features such as Projects of UN Partner Agencies, National Platforms or Spotlight on our Partners will help disseminate the information in a timely and efficient manner.
UNFSS is a platform which helps producers, traders, consumers, standard-setters, certification-bodies, trade diplomats, non-governmental organizations and researchers to discuss amongst each other on, to learn and understand more about VSS, and influence decision makers at the intergovernmental level. UNFSS also aims to provide impartial information, analysis, and discussions on VSS.
The new website will be regularly updated with news events, announcements, and special spotlight features. Visitors are encouraged to explore the website and sign up for the mailing list to receive direct emails.
Suppressing Post-Pandemic with Sustainable Development
Photo Credit: A general view of Long Street, usually one
UNFSS took part at the China High Level Sustainability Standards and Certification Development Forum
Last week, representatives from United Nations agencies, Chinese and foreign
The Political Economy of Sustainable Palm Oil in China and India
Andean Community Sustainable Trade Workshop in Lima, Peru on 5-6 June 2018


text:
8 Organizations That Are Helping Black Women Cope And Recharge
As protests continue to sweep the nation in response to the killing of Minneapolis resident George Floyd, self-preservation is key. The pressure to power through racial trauma, the expectation to guide non-blacks through allyship, and the endless scroll of troubling stories on social media can become mentally and emotionally exhausting, as many black women have recently expressed. So taking the time and necessary steps to protect your mental health is crucial, perhaps now more than ever.
As Octavia Raheem, co-owner of Sacred Chill West, wrote on Instagram: "Take deep unapologetic care of yourself today and all days. Your heart. Your mind. Your body...Rest. Then rise." Here, we've highlighted six organizations that are committed to helping black women cope and recharge so that they can continue in the fight for justice that is long overdue. Whether you're looking for access to counseling, safe group discussions for POC or practical self-care advice, we encourage you to look at the different resources these wonderful organizations are providing.
For all non-black allies, we have also listed links to donate throughout.
The Loveland Foundation has long been committed to black mental health and works to break the barriers that prevent communities of color from getting access to treatment. Through the Loveland Therapy Fund, black women and girls are provided financial assistance when seeking therapy. And on the organization's Instagram page, you will free mental health advice, healing meditations, and grief discussions.
Ethel's Club
Through digital memberships, Ethel's Club has created a community for people of color with a focus on wellness, healing, and creation. In response to the recent tragedies, the company is hosting two one-hour virtual group healing and grieving sessions. "Both events will be led by licensed Black therapists to help hold space and process the weight of the many complex emotions that we are feeling and carrying right now," they explain on Instagram. The events will be held on June 9 and June 23 at 6 p.m. EST and are free to black people worldwide. Learn more here. Additionally, on June 5, Ethel's Club is partnering with Rachel Ricketts to offer a free breath-work webinar.
Click here to sponsor a member.
Black Girls Breathing
Black Girls Breathing offers meditational breathwork sessions designed specifically for black women and led by Jasmine Marie, a trained breathworker and mindfulness practitioner. "Breathwork is a powerful active meditation technique used to usher stagnant energy out of the body, help acknowledge and release difficult emotions and traumas, and decrease anxiety and stress by reframing the nervous system's response to triggers," the site reads. This week, you can join the virtual breathwork circles at no cost.
Click here to donate a session.
Therapy For Black Girls
Therapy for Black Girls is described as an online space dedicated to encouraging the mental wellness of Black women and girls, and the organization has become known for its popular podcast by the same name. On Thursday, June 4 at 7 p.m. EST, they are hosting a group discussion with Dr. Key Hallmon, Dr. Joy Harden Bradford, Dr. Ayanna Abrams, and Dr. Joy Beckwith. Attendance is free; register here. Therapy for Black Girls also offers group support sessions at 7 p.m. EST every Thursday night via Facebook, where you can submit suggested topics of discussion. "This is designed to be a safe space for Black women to come and discuss any issues that are standing in the way of really living your life with a sense of purpose and joy," they explain.
HealHaus
HealHaus is a wellness space and cafe located in Brooklyn, NY. While they usually offer in-house workshops and events, like many others, they have recently turned to social media to reach the community. The company is hosting several events this week, including a donation-based moving meditation on Instagram Live on Wednesday, June 3 at 7 p.m. that will be led by Intuitive Wellness Practitioner Tiffani Moore. All proceeds will go to the NAACP Legal Defense Fund, Reclaim the Block, and George Floyd's Family. On Friday, June 5 at 8:00 p.m. EST, HealHaus is hosting a Circle of Care for Black Womxn via Zoom, which will be guided by Thérèse Cator, a leadership coach and Founder of Black Girls Breathe. The event is described as a "safe, life-giving support community for black womxn during tumultuous times to witness and bear witness to one another."
BLH Foundation
The Boris Lawrence Henson Foundation, founded by Taraji P. Henson, in a non-profit that works to "ensure cultural competency in caring for African Americans who struggle with mental illness." The organization is currently offering free therapy for communities of color. Text NOSTIGMA to 707070 to learn more.
The Nap Ministry
The Nap Ministry is an organization that examines the liberating power of rest. "We believe rest is a form of resistance and name sleep deprivation as a racial and social justice issue," the website explains. If you are feeling guilty for resting right now, you will undoubtedly feel better once visiting their Instagram page. "There is deep power in taking a break, honoring your body, and actively participating in your deprogramming from grind culture. We've been brainwashed to be violent towards our own bodies by pushing it to exhaustion," one post reads. The Nap Ministry has also curated playlists that promote rest and mindfulness.
Gurls Talk
Gurls Talk has partnered with Brooklyn-based therapist Wale Okerayi, LMHC, to share tips on how to disengage when necessary, ways to set boundaries with non-POC, and the importance of self-care. The 5-minute video, titled "Taking the Time to Disconnect & Recharge While Fighting for Racial Justice," can be found on the Gurls Talk IGTV. On Friday, June 5 at 1 p.m. EST, the organization's founder Adwoa Aboah will be speaking with the Future, international activist & founder of BLM Canada, on Instagram Live. You can submit questions by direct messaging @gurlstalk.
If you would like to suggest another organization that is dedicated to black mental health for this list, please tag us on Instagram or email us at media@glam.com.
You might also like:Why You Shouldn't Feel Guilty For Taking A Mental Health Day From Work
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Christian Theological Seminary is a non-profit, private higher education institution in Indianapolis, Indiana. It has a religeous affiliation with Disciples of Christ Christian Church.
Programs offered at Christian Theological Seminary include master's and doctoral degrees in over 6 areas of study and 10 concentrations. The school is accredited by the Commission on Accrediting of the Association of Theological Schools and has specialized accreditation from the American Association for Marriage and Family Therapy - Commission on Accreditation for Marriage and Family Therapy Education.
This institution has a study abroad program.


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text:
\section{Introduction}

The study  and  the interpretation of multi-component non-stationary signals require a powerful  analysis tool.   Time-frequency (TF) analysis methods   are used to measure how a signal's frequency components vary with time and  provide an effective tool  in  non-stationary signals analysis [1-7].  The most frequently used TF representation  is the linear TF analysis method, mainly including the short-time Fourier transform (STFT) [8], the continuous wavelet transform (CWT) [9], the Stockwell transform [10], and the chirplet transform (CT) [11].  This kind of method  characterizes the signal  via inner products with a  pre-assigned basis and  has invertibility and  low computation cost. However, restricted by the Heisenberg uncertainty principle [12],  the linear TF analysis  can not simultaneously obtain optimal time and frequency resolution, easily leading to a blurred TF representation.

To solve the above limitation,  the post-processing methods of the linear TF representations have been widely studied in the past decades.  The reassignment method (RM),  proposed by Kodera et al. to the spectrogram [13]  and  generalized by F. Auger and P. Flandrin to the  time-scale distribution and others  [14],  reassigns the TF energy  from the original position to the gravity center of the signal's energy distribution such that a sharped TF representation is yielded.  F. Auger et al. also  extended  the standard  RM  to the Levenberg-Marquardt reassignment [15],  making   the concentration  of the  signal energy  adjustable.  J. Xiao  and  P. Flandrin   [16] presented  the multitaper TF reassignment with the two-fold objective of a sharp localization for the chirp components and a reduced level of statistical fluctuations for the noise.  In [17], Bruni et al. proposed  a  modified  RM  for analyzing multi-component crossing signals with  cross-over instantaneous frequencies (IFs). This method  corrects  the TF result of  the standard  RM  in the non-separable region partly.   Although  RM  and its variants improve the energy concentration of the linear TF representation,  they  lack  an explicit formula for signal reconstruction, which limits  its application [18,19].

Another popular TF post-processing method is the synchrosqueezing transform (SST), initialized in  [20]  and further analyzed in  [21].  This method was  developed in understanding the principle of  the empirical mode decomposition [22]. By squeezing the TF coefficients into the instantaneous frequency (IF) trajectory  in  the frequency direction, SST  not only enhances  the TF distribution  but also allows for mode retrieval. Because of  advantages to mode representation and reconstruction,   many new developments of SST have been carried out in various directions.  First,  an extension to the STFT case  was proposed in [23],  while a generalization of the wavelet approach by means of wavelet packets decomposition for both one-dimensional and two-dimensional cases was available in [24,25].  Extensions to  other  transform frameworks included,  but not  limited  to,  the synchrosqueezing S-transform [26],  the  synchrosqueezing three-parameter wavelet transform [27], and the fractional synchrosqueezing transformation [28].  Second, the robust  analysis of SST  has been studied in [29-31]  and a new IF estimator within the framework of the signal's phase derivative and the linear canonical transform was introduced in [32]. Moreover,  a study of SST  applied to multivariate data  was done in [33].    An adaptive SST with a time-varying parameter was recently introduced in [34,35], which obtains  the well-separated condition for multi-component signals using the linear frequency modulation to approximate a non-stationary signal at every  time instant.  The theoretical analysis of adaptive SST was studied  in [36,37].   Finally,  combining  the SST  with the ideal TF representation  theory,  the synchroextracting transform (SET) [38] was proposed to  improve the TF concentration by extracting the ridges of the STFT.

SST works well for sinusoidal signals but suffers from  low TF resolution when dealing with strong modulation  signals  that consist of a fast-varying  feature. To address this drawback,  many improvements have been presented, mainly including   the demodulated SST [39,40], the high-order SST  [41,42], the multi-synchrosqueezing transform [43,44], and the time-reassigned SST [45,46].  The demodulated SSTs [39,40]  aim to  change  broad-band signals to narrow-band signals and  the standard  SST  is followed then.  The high-order SSTs  [41,42] aim to calculate an IF estimation in the TF or time-scale  domain  for more general signal  types.  The multi-synchrosqueezing transformations [43,44] apply an iterative reassignment technique to sharpen  the blurred TF energy step-by-step. The time-reassigned SSTs [45,46], in fact, introduce  a dual operator by considering time reassignment instead of frequency reassignment and such methods have a good performance in addressing pulse-like signals. A  comprehensive review of the subject of reassigned TF representations  is provided in Ref. [5,19].

The mechanism of the SST  and its variants  introduced  above  is  to derive  an  IF or group delay (GD) estimator for different transform frameworks and different-type signals,  and further to reassign TF coefficients  from the original position  to  the estimated instantaneous trajectory. Indeed, the IF (or GD) estimator  is critical  because it determines the  accuracy of high-concentration TF representations.  Differing from the mechanism of the SST-based methods,  another high-concentration  TF representation is based on the  IF equation [47-49], i.e.,  a non-linear function in the TF domain  with the IFs as its  solution. This kind of method enhances  the TF concentration by solving the IF equation  using the fixed point iterative algorithm [47] or the extractor [48,49]. Such methods have  been used in the sound  signal analysis [47,48], machine signal processing [48,50], and medical data analysis [51].  However, several issues should be considered.  First,  its strengths and weaknesses over the SST-based methods are not clear. The common goal of both methods is to improve the TF readability, but we have to know  which one is  preferable in various applications. Second,  how to use the IF equation to concentrate the TF distribution should be explained more comprehensively, involving  the uniqueness of the IF equation, and the  convergence of its solution algorithm. Last but not least, we should consider  if there is  a  theoretical model  to cover the prevailing TF analysis methods, including   the SET [38], the multi-synchrosqueezing transformation [43,44],  and the time  synchroextracting transform [52]. The relationship between these methods and the IF equation-based methods  should also  be  studied.

In this paper, we  focus on the  IF equation-based  TF post-processing methods and  attempt to build a theoretical framework for them.  We first review the SST-based TF analysis methods and then define IF equation followed by two concrete expressions under the STFT framework. We  study  the ways, that is, by the extractor to detect signal information   and  by iterative algorithms for TF  reassignment,     to concentrate the TF localization   using  the IF equation.  The uniqueness of the IF equation  and the  convergence of its solution algorithm are also studied. The difference between the SST-based methods and the  IF equation-based methods is discussed. By comparison, we find that one of the merits of the IF equation-based methods over the former is that IF equation  contains not only  the IF information but also the GD information, which unifies the IF   and  GD  estimator  of  the SST-based methods.  Finally,  numerical examples of the theoretical derivations  are  presented.

The remainder of the paper is organized as follows. In Section 2, we review the SST-based TF analysis methods.    In Section 3, we provide the unified mathematical model  for  IF equation-based  TF post-processing methods, and  some properties of IF equation are given. Comparative studies with the SST-based methods are  presented in Section 4. Finally, the conclusions are drawn  in Section 5.

\section{SST-based TF post-processing methods}

The following section presents the multi-component non-stationary  signal model and reviews  the SST-based TF analysis methods.

\subsection{Signal model}
Multi-component non-stationary signals are comprised of several mono-components and form the general case. In this paper we use the  popular amplitude-modulation and frequency-modulation  (AM-FM) model  to  describe   the time-varying  features of multi-component non-stationary signals, which is defined as
\begin{equation}
f(t)=\sum_{k=1}^{K}f_k(t)=\sum_{k=1}^{K}A_k(t)\mathrm{e}^{j\phi_k(t)},
\end{equation}
where $K$ is a positive integer representing the number of AM-FM components, $\sqrt{-1}=j$ denotes the imaginary unit,  $A_k(t)>0$  and $\phi_k(t)$   are  the instantaneous amplitude and  instantaneous phase of the $k$-th component (or mode), respectively. The first and the second  derivatives of the  phase,  i.e.,   $\phi'_k(t)$, $\phi''_k(t)$, are referred to as  the instantaneous  frequency (IF) and chirp rate (CR) of the $k$-th component.

\subsection{SST-based TF post-processing method}
We give  the introduction of SST class under the STFT framework.  Given signal  $f(t)\in L^2(\mathbb{R})$, its Fourier transform is defined as
\begin{equation}
	\hat{f}(\omega)=\int_{-\infty}^{+\infty}f(t)\mathrm{e}^{-j\omega t} \mathrm{d}t.
\end{equation}
The  STFT  of $f(t)$,  which is obtained through the use of a sliding window $g(t)\in L^2(\mathbb{R})$,  is given by
\begin{equation}
\begin{split}
S_{f}^{g}(t, \omega)=\int_{-\infty}^{+\infty}f(\mu)g^*(\mu-t) \mathrm{e}^{-j\omega(\mu- t)}\mathrm{d}\mu,
\end{split}
\end{equation}
where the superscript $*$ denotes the complex conjugate.
It is well known that the STFT can not simultaneously localize  a signal in both time and frequency precisely due to the limitation of the  Heisenberg uncertainty principle [12], i.e.,  long windows provide good frequency resolution but poor
temporal resolution, whereas short windows increase temporal resolution at the expense of frequency resolution.

To address this drawback, the  SST-based TF post-processing methods [21,23,24,26,41,42] are developed. Here the "post-processing" means that the SST methods make a further operation on the original TF representation, such as STFT and CWT,  to relocate the TF coefficients. With this regard, a key problem is to know where are the blurred  TF  points rearranged.  The ideal one  is to relocate  the  TF points  to  the true  IF curves of the signal analyzed, which leads to the development of   IF  estimations based on  STFT.

Thanks to  G. Thakur and  H.T. Wu, they develop  I. Daubechies's work [21] and give a two-dimensional  IF estimator in the TF domain  as follows [23]:
\begin{equation}
	\hat{\omega}_{1}(t,\omega)=\Re\left\lbrace \frac{\frac{\partial}{\partial t}S^g_f(t,\omega)}{jS^g_f(t,\omega)}\right\rbrace,
\end{equation}
here $|S^g_f(t,\omega)|>0$,  and  $\Re\{\cdot\}$ is the real  part of complex number. With $\hat{\omega}_{1}(t,\omega)$ defined by (4), the STFT-based SST (FSST) [23] is to reassign the TF coefficients from the original location  to the estimated IF trajectory  along  the frequency direction:
\begin{equation}
	T_f^1(t,\omega)=\int_{|S^g_f(t,\eta)|>\lambda}S^g_f(t,\eta)\delta (\omega-\hat{\omega}_{1}(t,\eta))\mathrm{d}\eta,
\end{equation}
where $\lambda>0$, and  $\delta(\cdot)$  is  the  Dirac delta function, a generalized  function  formulated as  $\delta (t)=0$ when $ t\neq0$, and $\int_{-\infty}^{+\infty}\delta(t)\mathrm{d}t=1$.

The IF estimator  (4)  is accurate for the cosine-like  signals with slow-varying instantaneous information,  i.e., the multi-component non-stationary signal $f(t)$ satisfies $|A'_k(t)|<\epsilon$, $|\phi''_k(t)|<\epsilon$ for $k=1,2,\cdots,K$ (here $\epsilon$ is a small positive constant).  For the fast-varying signals, such as chirp-like signals,   FSST suffers from  a low TF resolution at the modulated part.  To  address  this  shortcoming, paper [41] introduced  another IF estimation as follows:
\begin{equation}
	\begin{split}
		\hat{\omega}_{2}(t,\omega)=
		\begin{cases}
			\Re\left\lbrace \frac{\frac{\partial}{\partial t}S^g_f(t,\omega)}{jS^g_f(t,\omega)}\right\rbrace+\Re\left\lbrace \tilde{q}(t, \omega) \frac{\frac{\partial}{\partial \omega}S^g_f(t,\omega)}{S^g_f(t,\omega)}\right\rbrace,   & ~\text{if}~ \frac{\partial}{\partial t} \left( \frac{\frac{\partial }{\partial \omega} S^g_f(t,\omega)}{S^g_f(t,\omega)} \right) \neq j,   \text{and}~ S^g_f(t,\omega)\neq 0, \\
				\hat{\omega}_{1}(t,\omega),  & ~\text{if}~ \frac{\partial}{\partial t} \left( \frac{\frac{\partial }{\partial \omega} S^g_f(t,\omega)}{S^g_f(t,\omega)} \right) = j,   \text{and}~ S^g_f(t,\omega)\neq 0,
		\end{cases}
	\end{split}
\end{equation}
where
\begin{equation}
	\tilde{q}(t, \omega)=\frac{\frac{\partial}{\partial t} \left( \frac{\frac{\partial }{\partial t} S^g_f(t,\omega)}{S^g_f(t,\omega)} \right)}{j-\frac{\partial}{\partial t} \left( \frac{\frac{\partial }{\partial \omega} S^g_f(t,\omega)}{S^g_f(t,\omega)} \right)}.
\end{equation}
The quantity $\hat{\omega}_{2}(t,\omega)$ corresponds to the true IFs  of the Gaussian modulated  linear chirp [41]. The second-order FSST then consists in replacing $\hat{\omega}_{1}(t,\omega)$ by $\hat{\omega}_{2}(t,\omega)$ in the standard FSST:
 \begin{equation}
 	T_f^2(t,\omega)=\int_{|S^g_f(t,\eta)|>\lambda}S^g_f(t,\eta)\delta (\omega-\hat{\omega}_{2}(t,\eta))\mathrm{d}\eta.
 \end{equation}

Form (5) and (8),  the  SST-based TF post-processing methods  can thus be unified  as
 \begin{equation}
	T_f(t,\omega)=\int_{|S^g_f(t,\eta)|>\lambda}S^g_f(t,\eta)\delta (\omega-\hat{\omega}(t,\eta))\mathrm{d}\eta,
\end{equation}
where $\hat{\omega}(t,\eta)$ is an  IF estimator calculated  in a transform domain.
Similarly, based on the GD estimator $\hat{t}(t,\omega)$ of various TF transformations, the time-reassignment  SST  [45,46]  can be formulated  as
\begin{equation}
\tilde{	T}_f(t,\omega)=\int_{|S^g_f(\mu,\omega)|>\lambda}S^g_f(\mu,\omega)\delta (t-\hat{t}(\mu,\omega))\mathrm{d}\mu.
\end{equation}

Differing from the squeezing manner of the SST that is based on an IF estimation, in the following we will introduce the IF equation-based TF post-processing methods and  build  an  unified mathematical model for them.

\section{IF equation-based TF post-processing method}

The central idea of the IF equation-based TF post-processing methods is to find an IF equation in the TF domain to characterize  the instantaneous features of the signal. By solving  the  IF  equation,  we want to  output a concentrated and accurate TF representation.

\subsection{Definition  of IF equation}
\begin{definition}
For signal $f(t)=\sum_{k=1}^{K}A_k(t)\mathrm{e}^{j\phi_k(t)}$,  a  binary  equation $h_f(t,\omega)=0$ is called the  IF equation of  $f(t)$,  if $h_f(t,\omega)$ is not identically zero  and  the set of points $\omega=\phi'_k(t)$ ($k=1,2,\cdots,K$)  satisfies
\begin{align}
 h_f(t,\phi'_k(t))=0, ~   k=1,2,\cdots,K.
\end{align}
\end{definition}
From Definition 1, we can  know that the IF curves $\omega=\phi'_k(t)$ of each model of $f(t)$ are the  solutions of its IF equation. Since the IF equation includes the IF information of the studied  signal,  it can be considered as a feature extractor.

In order to show the IF equation more clearly, we now  consider a specific  example  of constant amplitude and linear frequency modulation signal (also known as chirp), i.e., $f(t)=Ae^{j\phi (t)}$,  where $A$ is a positive  constant,  $\phi(t)=a+bt+\frac{c}{2}t^2$,  $a, b, c$ are real numbers. In this case, the STFT under the Gaussian window  $g(t)=\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{t^2}{2\sigma^2}}$  is calculated as
\begin{equation}
	S_{f}^{g}(t, \omega)=f(t) \frac{1}{\sqrt {1-j\sigma^2c}}\exp\left( -\frac{\sigma^2}{2}\frac{(\omega-\phi'(t))^2}{1-j\sigma^2 c} \right) ,
\end{equation}
where $\phi'(t)=b+ct$. From (12),  we can obtain that
\begin{equation}
	\begin{split}
		\frac{\partial}{\partial \omega}S_{f}^g(t, \omega)=S_{f}^g(t, \omega)\left( -\frac{\sigma^2(\omega-\phi'(t))}{1-j\sigma^2c} \right).
	\end{split}
\end{equation}
The set of points $\omega=\phi'(t)$ satisfies $ \left| \frac{\frac{\partial}{\partial \omega}S_{f}^g(t, \omega)}{S_{f}^g(t, \omega)} \right| =0 \text{~~for} ~| S_{f}^g(t, \omega)|>\lambda$.
Therefore, we can define an  IF equation of  signal  $f(t)=Ae^{j\phi (t)}$  as
\begin{equation}
	\begin{split}
		\left| \frac{\frac{\partial}{\partial \omega}S_{f}^g(t, \omega)}{S_{f}^g(t, \omega)} \right| =0, \text{~~for} ~| S_{f}^g(t, \omega)|>\lambda.
	\end{split}
\end{equation}
This equation can be more efficiently computed by
\begin{equation}
	\begin{split}
		\left| \frac{S_{f}^{tg}(t, \omega)}{S_{f}^g(t, \omega)} \right| =0, \text{~~for} ~| S_{f}^g(t, \omega)|>\lambda,
	\end{split}
\end{equation}
where $S_{f}^{tg}(t, \omega)$ denotes the STFT of $f(t)$ using $tg(t)$  as its window.

It is easy to see that   another   IF equation of the chirp signal $f(t)$ is formulated as
\begin{equation}
\Re\left\lbrace  \frac{\frac{\partial}{\partial \omega}S_{f}^g(t, \omega)}{S_{f}^g(t, \omega)}\right\rbrace  =0, \text{~~for} ~| S_{f}^g(t, \omega)|>\lambda.
\end{equation}
Therefore, the IF equation is not unique  for signals of the same type.  Finding a powerful  IF equation that covers as many signal types as possible and has some good properties for its solutions is an important work that needs exploration.

  It is also noted that  other window functions can  be used to define the IF equation. If an even  one is employed, the IF equation of chirp signal can also be defined as  (14) (or (16)).  In the following section,  we discuss some properties of IF equation (14).
\subsection{Properties of IF equation (14)}
1) \textit{Uniqueness of the  solution:} For each time $t$, $\omega=\phi'(t)$ is the unique solution of  IF equation (14). This property denotes that the IF equation (14) of chirps  can  characterize its IF information and excludes  some unwanted information,  which is important for detecting the  signal feature.

2) \textit{Impulse signals detection:} The instantaneous information $t=t_0$ of impulse signal $f(t)=A\delta(t-t_0)$ is the  unique  solution of IF equation (14).

The STFT of the transient signal $f(t)=A\delta(t-t_0)$  with the Gaussian window  is  computed as
\begin{align}
	S_{f}^{g} (t,\omega) =A{(\sqrt{2\pi}\sigma)}^{-1}\mathrm{e}^{-\frac{(t_0-t)^2}{2\sigma^2}}\mathrm{e}^{-j\omega(t_0-t)}.
\end{align}
From (17), we can obtain that
\begin{equation}
	\begin{split}
      \left| \frac{\frac{\partial}{\partial \omega}S_{f}^g(t, \omega)}{S_{f}^g(t, \omega)}\right| =|t-t_0|.
	\end{split}
\end{equation}
Therefore, $t=t_0$  is the unique solution of  IF equation (14).

Whereas IF equation (16) does not include the transient feature for the  impulse  signal.  Therefore,  equation (14) is more  preferred than (16) when dealing with impulse signals.

3) \textit{Linear group delay detection:} The GD of linear group delay  signal $\hat{f}(\omega)=Ae^{-j(a+b\omega+\frac{c}{2}\omega^2)}$ is the   unique  solution of  IF equation (14) .

Since the STFT of $f(t)$ can be rewritten as
\begin{equation}
	\begin{split}
		S_{f}^{g}(t, \omega)&=\int_{-\infty}^{+\infty}f(\mu)g^*(\mu-t) \mathrm{e}^{-j\omega(\mu- t)}\mathrm{d}\mu
		=\frac{1}{2\pi}\int_{-\infty}^{+\infty}\hat{f}(\nu)\hat{g}^*(\nu-\omega) \mathrm{e}^{jt\nu}\mathrm{d}\nu,
	\end{split}
\end{equation}
then the STFT of linear group delay  model  can be expressed as
\begin{equation}
	\begin{split}
		S_{f}^{g}(t,\omega)=\frac{1}{2\pi}\hat{f}(\omega)\mathrm{e}^{jt\omega}\int_{-\infty}^{+\infty}\mathrm{e}^{-j\frac{c}{2}\nu^2}\hat{g}^*(\nu) \mathrm{e}^{j(t-b-c\omega)\nu}\mathrm{d}\nu.
	\end{split}
\end{equation}
From (20), we have
\begin{equation}
	\begin{split}
		\frac{\partial}{\partial \omega}S_{f}^g(t, \omega)=j(t-b-c\omega)S_{f}^g(t, \omega)-\frac{jc}{2\pi}\hat{f}(\omega)\mathrm{e}^{jt\omega}\int_{-\infty}^{+\infty}\mathrm{e}^{-j\frac{c}{2}\nu^2}\nu \hat{g}^*(\nu) \mathrm{e}^{j(t-b-c\omega)\nu}\mathrm{d}\nu.
	\end{split}
\end{equation}
Due to the  Fourier transform of Gaussian window $g(t)=\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{t^2}{2\sigma^2}}$ is calculated as
\begin{equation}
\hat{g}(\nu)=\mathrm{e}^{-\frac{\sigma^2}{2}\nu^2},
\end{equation}
which yields that
$$
\int_{-\infty}^{+\infty}\mathrm{e}^{-j\frac{c}{2}\nu^2}\nu \hat{g}^*(\nu) \mathrm{d}\nu=0.$$
Consequently,  $t=b+c\omega$ satisfies
\begin{equation}\label{key}
\left|  \frac{\frac{\partial}{\partial \omega}S_{f}^g(t, \omega)}{S_{f}^g(t, \omega)}\right| =0, \text{~~for} ~| S_{f}^g(t, \omega)|>\lambda.	\nonumber
\end{equation}

This result shows that  IF equation (14) not only  covers the  instantaneous characteristic of chirp signals  but also covers the instantaneous information of the linear group delay model,  which  can  unify  the well-known  IF and GD  estimators  proposed  in  the SST [21,23] and the time-reassigned SST [45,46].

4) \textit{Characterizing a mixture of harmonic-like and pulse-like signals:}    Suppose $f(t)=\sum_{k=1}^{K}A_k(t)\mathrm{e}^{j\phi_k(t)} $ be a multi-component signal consisting of a harmonic  and pulse  signals, due to the analysis above, we have $\left|  \frac{\frac{\partial}{\partial \omega}S_{f_k}^g(t, \omega)}{S_{f_k}^g(t, \omega)}\right| =0 ~ (| S_{f_k}^g(t, \omega)|>\lambda$) for each component   $f_k(t)$.  Since  $\left| \frac{\frac{\partial}{\partial \omega} S_{f}^g(t, \omega)}{S_{f}^g(t, \omega)}\right|\leq \sum_{k=1}^{K}\left|  \frac{\frac{\partial}{\partial \omega}S_{f_k}^g(t, \omega)}{S_{f}^g(t, \omega)}\right|=\sum_{k=1}^{K}\left|  \frac{\frac{\partial}{\partial \omega}S_{f_k}^g(t, \omega)}{S_{f_k}^g(t, \omega)} \frac{S_{f_k}^g(t, \omega)}{S_{f}^g(t, \omega)}\right|$, then $\left| \frac{\frac{\partial}{\partial \omega} S_{f}^g(t, \omega)}{S_{f}^g(t, \omega)}\right|=0$.  Furthermore,  if  $f_k(t)$  $(k=1,2,\cdots, K)$ are  separable, leading to that $|S_{f}^g(t, \omega)|=|S_{f_k}^g(t, \omega)|$  when $(t, \omega)$ located in the energy spread band  of $f_k(t)$,  we  can obtain that $\left| \frac{\frac{\partial}{\partial \omega} S_{f}^g(t, \omega)}{S_{f}^g(t, \omega)}\right|= \sum_{k=1}^{K}\left|  \frac{\frac{\partial}{\partial \omega}S_{f_k}^g(t, \omega)}{S_{f_k}^g(t, \omega)}\right|=0$.  This means that IF equation (14) extracts the instantaneous information of signals consisting of a mixture of harmonic-like and pulse-like components.

5) \textit{Multi-resolution IF equation:}  It is known that a single-window is difficult to balance time resolution and frequency resolution, the combination of  multiple spectrograms or wavelet transforms  with short and long windows or a set of wavelets  has  been shown to result in good joint TF resolution for signals consisting of mixtures of tones and pulses [53,54]. Inspired by this idea, we  can  also define  a multi-resolution IF equation of chirp (impulse or linear group delay) signal:
\begin{equation}
	\begin{split}
		MrIF(t, \omega):=\left|\left( \prod_{i=1}^m \frac{S_f^{g_{i}}(t, \omega)}{S_{f}^{g_{i}}(t, \omega)}\right)  ^{\frac{1}{m}}\right| =0, \text{~~for} ~| S_{f}^{g_{i}}(t, \omega)|>\lambda,
	\end{split}
\end{equation}
where $S_f^{g_{i}}(t, \omega)$ denotes the STFT of $f(t)$ using  the Gaussian window with parameter $\sigma_i$.  This  equation  corresponds to the geometric  mean   of   multiple IF equations and it is  built on high-resolution TF  representation, with this regard,  it can be used to characterize closely-spaced instantaneous  information.

\subsection{TF post-processing method using  IF equation}

This section will introduce how to use the given IF equation $h_f(t,\omega)$ to concentrate the TF distribution.
Generally, there are two classical ways to achieve such goal: extraction  and reassignment.  In the following we will discuss these two ways  in detail.

\subsubsection{Extracting  transform }

The main idea of extracting transform is to extract   the solutions of the IF equation because which characterize  the instantaneous  features of  the signal.  Define an extractor  as
\begin{equation}
	\begin{split}
	\delta(\omega)=
		\begin{cases}
			1,   & ~\text{if}~ \omega= 0, \\
				0,  & ~\text{if}~ \omega\neq 0,
		\end{cases}
	\end{split}
\end{equation}
then  a concentrated TF representation is obtained  by  keeping only the TF points on the  IF trajectories,   which is  given by
\begin{equation}
	\begin{split}
	T_e(t, \omega)=S_{f}^g(t, \omega)	\delta(h_f(t,\omega)).
	\end{split}
\end{equation}
We  refer to (25)  as the extracting transform. This transform   retains the TF coefficients  consistent with  the solutions of the IF equation,  making the TF location match the IF or GD estimates. Therefore, the extracting transform greatly sharpens the energy distribution of multi-component non-stationary signals, even with  slowing-varying and fast-varying components.

It should be  pointed out that the popular synchroextracting transform (SET) [38] can be classified in the IF equation-based extracting  transform. Indeed, from expression (12), it is easy to get:
 \begin{equation}
 \hat{\omega}(t,\omega)=\Re \left\lbrace \frac{\frac{\partial}{\partial t}S^g_f(t,\omega)}{jS^g_f(t,\omega)}\right\rbrace =\phi'(t)+\frac{\sigma^4{c}^2(\omega-\phi'(t))}{1+\sigma^4{c}^2}.
 \end{equation}
Expression  (26) indicates  that the set of points  $\omega=\phi'(t)$ satisfies
\begin{equation}
\omega-\hat{\omega}(t,\omega)=0.
\end{equation}
Thus, equation  (27) is a special  IF equation of constant amplitude and linear frequency modulation signal.  Based on equation  (27), it is easy to define the extracting transform  as
\begin{equation}
	\begin{split}
	T_e(t, \omega)=S_{f}^g(t, \omega)	\delta(\omega-\hat{\omega}(t,\omega)),
	\end{split}
\end{equation}
which  corresponds  to the SET given in  [38].

It is  known that the extracting transforms are not the type being energy conservation because they only remain the signal energy on the TF curves satisfying the IF equation. Differing from the extracting operation,  we will introduce  an  approach  that  maintains the signal energy.

\subsubsection{TF reassignment based on   iterative  algorithm}

Another way to sharpen  the spread TF distribution is  to  move the TF values towards the IF or GD curves. Due to the fact that  the IFs  or  GDs of the studied signal $f(t)$ are the solutions of a given IF equation $h_f(t,\omega)=0$, i.e., the  roots of $h_f(t,\omega)$, then for any TF point  ($t, \omega$) with TF energy larger than zero,     we can consider it as  an  initial point of a numerical algorithm  to  solve  a root of $h_f(t,\omega)$.   When  the numerical algorithm   converges to  the  solutions of the IF equation  with the increasing of iteration times, the spreading TF energy  can be relocated to the instantaneous curves of the studied signal.

There are many algorithms, such as the fixed point algorithm, the Newton algorithm, and the Levenberg-Marquardt (LM) algorithm [55] can be used to obtain a solution of that
\begin{align}
	h_f(t, \omega)=0.
\end{align}
Specifically, starting  with an arbitrary initial point ($t_0, \omega_0$),  the fixed point algorithm yields the  iteration that
\begin{align}
	\omega_{k+1}=	\omega_{k}+ \tau h_f(t_0, \omega_{k}),
\end{align}
where $\tau\neq 0$ is hoped to converge to a root of $ h_f$.  Assume  iteration (30) is convergent, i.e., $\lim_{k\rightarrow\infty} 	\omega_{k}=	\omega^{*} $ (here $\omega^{*}$ is a function of $t_0$ and $\omega_0$,  and it can   rewritten  as  $\omega^{*}(t_0, \omega_{0})$),  we can  obtain that
\begin{align}
	h_f(t_0, \omega^{*})=0.
\end{align}

To  show the instantaneous information of the signal more accurately and with better readability for the TF plot,   we  reassign  the TF value of ($t_0, \omega_0$) to  the location  ($t_0, \omega^{*}$) as follows:
\begin{equation}
S_f(t_0,\omega_{0})	+ S_f(t_0,\omega^*)\rightarrow S_f(t_0,\omega^*),
\end{equation}
where $S_f(t,\omega)$ is one of the TF representations, such as the STFT,  CWT, chirplet transform, and their modules. In fact,  similar to the expression (9) in the SST, this reassigment operation can be formulated as
\begin{equation}
	 {S}^*_f(t,\omega)=\int_{|S_f(t,\eta)|>\lambda}S_f(t,\eta)\delta (\omega-{\omega^*}(t,\eta))\mathrm{d}\eta.
\end{equation}

In the following, we  utilize  a concrete  IF equation, i.e., the IF equation (16) of  chirp signals,  to discuss the  convergence of  the fixed point algorithm (30).  In this case,  the iteration  can be expressed as
\begin{align}
	\omega_{k+1}=	\omega_{k}+ \tau \Re\left\lbrace  \frac{\frac{\partial}{\partial \omega}S_{f}^g(t, \omega)|_{\omega=\omega_k}}{S_{f}^g(t, \omega_k)} \right\rbrace
	= 	\omega_{k}- \tau\frac{\sigma^2(\omega_k-\phi'(t))}{\sqrt{1+\sigma^4c^2}}.
\end{align}
From (34), we have
\begin{align}
	|\omega_{k+1}-\omega_{k}|&=	|\omega_{k}-\omega_{k-1}-\frac{\tau\sigma^2}{\sqrt{1+\sigma^4c^2}}(\omega_k-\phi'(t)-(\omega_{k-1}-\phi'(t)))|\\
	&\leq  |1-\frac{\tau\sigma^2}{\sqrt{1+\sigma^4c^2}}||\omega_{k}-\omega_{k-1}|.
\end{align}
Therefore,  iteration (34) is convergent if $\tau$ is taken as  a value such that  $|1-\frac{\tau\sigma^2}{\sqrt{1+\sigma^4c^2}}|<1$.

It should be pointed out that the multi-synchrosqueezing transform [43] is a special case of the  IF equation-based reassignment method. Indeed, when we consider the  IF equation (27), and take the value of $\tau$ as -1, then the form of iteration (30) becomes
\begin{align}
	\omega_{k+1}=	\hat{\omega}(t,\omega_k),
\end{align}
which corresponds to the multiple SST operation in [43].

Moreover, we also can use the  Newton algorithm or the LM algorithm to get a root of $h_f(t,\omega)$, which are  expressed  respectively as
\begin{align}
	\omega_{k+1}&=\omega_k-\frac{h_f(t,\omega_k)}{\frac{\partial}{\partial \omega}h_{f}(t, \omega)|_{\omega=\omega_k}}, ~\text{(Newton algorithm)}\\
	\omega_{k+1}&=\omega_k-\frac{h_f(t,\omega_k)}{\frac{\partial}{\partial \omega}h_{f}(t, \omega)|_{\omega=\omega_k}+ \rho},  ~\text{(Levenberg-Marquardt  algorithm)}
\end{align}
where $ \rho>0$. The LM algorithm is generally considered to be more robust than the Newton algorithm because it converges
even if the starting point is far from the final value [15,55].

\section{Comparison}

The setion above  introduces  the  IF equation-based TF post-processing method to obtain  a concentrated and accurate TF output. In the following, we compare its performance  with the SST-based TF post-processing method.

First, the two methods are based on different feature extractors: the former is based on IF equation, while the latter is based on IF estimation.  For a signal $f(t)$,  its IF equation  is not unique, and finding one that covers  as many different types of  signals as possible is  a challenging task. Nevertheless,  we  can find  an IF equation, such as equation (14), to characterize  the information of various signals, including  the harmonic signals, the chirps, and the impulse signals. By comparison,  the IF estimators presented in the SST and its extensions  have limited generalization ability to deal with a mixture of harmonic  and impulsive signals.
\begin{figure}[!tbh]
	\centering
	\begin{minipage}{0.72\linewidth}
		\centerline{\includegraphics[width=1\textwidth]{fig11}}
		\centerline{(a)}
	\end{minipage}
	\begin{minipage}{0.32\linewidth}
		\centerline{\includegraphics[width=1\textwidth]{fig12}}
		\centerline{(b)}
	\end{minipage}
	\begin{minipage}{0.32\linewidth}
		\centerline{\includegraphics[width=1\textwidth]{fig13}}
		\centerline{(c)}
	\end{minipage}
	\begin{minipage}{0.32\linewidth}
		\centerline{\includegraphics[width=1\textwidth]{fig14}}
		\centerline{(d)}
	\end{minipage}
	\begin{minipage}{0.32\linewidth}
		\centerline{\includegraphics[width=1\textwidth]{fig15}}
		\centerline{(e)}
	\end{minipage}
	\begin{minipage}{0.32\linewidth}
		\centerline{\includegraphics[width=1\textwidth]{fig16}}
		\centerline{(f)}
	\end{minipage}
	\begin{minipage}{0.32\linewidth}
		\centerline{\includegraphics[width=1\textwidth]{fig17}}
		\centerline{(g)}
	\end{minipage}
	\caption{ \small Evaluation of TF results on a known signal structure. (a) Waveform of the test signal, (b) TF plot by STFT, (c) TF plot by FSST,  (d)  TF plot by Second FSST, (e)  TF plot by TSST,   (f)  TF plot by ET\_IF, (g) TF plot by RM\_IF.}
\end{figure}

Let us consider an example to illustrate  their performance. The waveform of the test signal is illustrated in  Figure 1(a), which contains two impulsive  signals, a chirp, and a cosine modulation component. We compute the TF representations of the test  signal using STFT, FSST, second-order FSST (Second FSST for short), time-reassigned SST (TSST for short) [45],  the extracting transform based on IF equation (14) (ET\_IF for short), and the reassignment method based on IF equation (16) (RM\_IF for short). From the results, we can see that the TF result of STFT is blurred.  The FSST and second FSST improve the energy concentration of STFT for chirps and  cosine modulated signals but fail to characterize impulsive signals effectively.  The TSST  provides  a better TF localization for the transient signals while  degrading  the TF sharpness  of  the stationary mode. For our proposed RM\_IF approach, it provides a high-concentration TF representation for the chirp and the cosine modulated signal, but  the operation of relocating the TF values along the frequency direction  limits  its ability to  handle the impulsive signals, which results in an  imprecise characterization, as shown in Figure 1(g).   The ET\_IF is clearly superior to others  and provides excellent performance in dealing with a  mixture of impulse-like signals, chirps, and  cosine modulation signals.

\begin{table}[!h]
	\small
	\caption{ \small \label{tab4} The cost times  of different  analysis  methods.} \centering
	\begin{tabular}{ccccccccccc}
		\Xhline{.6pt}  Methods &{STFT} &{FSST}&{Second FSST}& {TSST}&{ET\_IF}&{RM\_IF}\\
		\hline
		Time (s)&0.005 &0.017 & 0.253 &0.107&0.016&0.0672\\
		\Xhline{.6pt}
	\end{tabular}
\end{table}
The computational complexity of the  two kinds of post-processing  methods mainly comes from the STFT calculations with different windows.  We assume that a signal of  $N$ samples is utilized, then the STFT can be implemented by FFT and it requires $O(N^2\log_2N)$  operations.  Therefore, the total computing complexity of the TF  post-processing  methods  is $O(N^2\log_2N)$.  Table 1 list
the cost times of the above-mentioned TF analysis methods in addressing the test signal (see Figure 1(a)). The tested computer configuration is as follows: Intel Core  i9-11900KF 3.50  GHz, 32.0 GB of RAM, and MATLAB version R2021a.  It can be seen from the results that these  methods can finish the analysis within one second. It takes  less time to represent the signal by ET\_IF and  RM\_IF than by Second FSST and TSST.

 \begin{figure}[!tbh]
 	\centering
 	\begin{minipage}{0.72\linewidth}
 		\centerline{\includegraphics[width=1\textwidth]{fig21}}
 		\centerline{(a)}
 	\end{minipage}
 	\begin{minipage}{0.32\linewidth}
 		\centerline{\includegraphics[width=1\textwidth]{fig22}}
 		\centerline{(b)}
 	\end{minipage}
 	\begin{minipage}{0.32\linewidth}
 		\centerline{\includegraphics[width=1\textwidth]{fig23}}
 		\centerline{(c)}
 	\end{minipage}
 	\begin{minipage}{0.32\linewidth}
 		\centerline{\includegraphics[width=1\textwidth]{fig24}}
 		\centerline{(d)}
 	\end{minipage}
 	\begin{minipage}{0.32\linewidth}
 		\centerline{\includegraphics[width=1\textwidth]{fig25}}
 		\centerline{(e)}
 	\end{minipage}
 	\begin{minipage}{0.32\linewidth}
 		\centerline{\includegraphics[width=1\textwidth]{fig26}}
 		\centerline{(f)}
 	\end{minipage}
 	\begin{minipage}{0.32\linewidth}
 		\centerline{\includegraphics[width=1\textwidth]{fig27}}
 		\centerline{(g)}
 	\end{minipage}
 	\caption{ \small Evaluation of TF results on the test signal with SNR=2 dB. (a) Waveform of the test signal, (b) TF plot by STFT, (b) TF plot by FSST,  (c)  TF plot by Second FSST, (d)  TF plot by TSST,   (e)  TF plot by ET\_IF, (f) TF plot by RM\_IF.}
 \end{figure}

Moreover,  Figure 2 provides TF representations of the test signal with strong noise (see Figure 2(a)) using  the six TF methods.  From the results, we can see that these post-processing methods are susceptible to  noise, and  ET\_IF produces   discontinuous  TF curves due to that  the noise  affects the precision of the IF equation. Therefore,  how to improve their noise robustness to obtain an accurate TF plot is required.

\section{Conclusion}
In this paper,  we discussed the IF equation-based TF analysis method to generate a concentrated TF representation for multi-component non-stationary signals.   The IF equation we defined  does serve as a feature  extractor to characterize the slow-varying and fast-varying modes. Several properties of the IF equation were studied and proved theoretically. Based on the IF equation, we introduced  two classical ways, i.e.,  extraction  and reassignment, to obtain a highly-concentrated TF output. The IF equation-based TF post-processing methods provide another way to improve the TF resolution  and cover  many popular TF analysis methods, such as the synchroextracting transform, the multi-synchrosqueezing transform, and the time extracting transform, etc. Compared with the SST-based TF post-processing methods, our proposed method  showed  better  performance in dealing with a  mixture of impulse-like signals, chirps, and  cosine modulation signals.

\section*{Acknowledgements}
This work was supported by the National Natural Science Foundation of China under Grant no. U20B2075, the Fundamental Research Funds for the Central Universities  under Grant no.  G2021KY05103.

redpajama_set_name: RedPajamaArXiv


text:
Galili Itzik,choreographer and director
Itzik Galili was born in Israel. He began his career as a dancer in Batsheva 2 and Bat Dor. In 1990 he began working also as a choreographer. In 1991 he moved to Amsterdam where he founded his own company. A year later his work The Butterfly Effect won the audience award in an international choreographer competition in Groningen, the Netherlands and resulted in numerous invitations to choreograph all over the world. In 1997 the Minister of Culture in the Netherlands appointed Galili as the artistic director of Galili Dance, a new dance company in Groningen. He created a system to work with dance in educating regular children and children who have learning disabilities and his system is still used today by several Dutch dance companies. In 2008 he crated the Dance Group Amsterdam, the city's leading contemporary dance company. He created choreography for opera productions such as Prince Igor (Borodin) at the Metropolitan Opera in New York and also for productions at the Royal Opera House Covent Garden and the Netherlands National Opera as well as for various television shows. Galili has created over 130 dance works for leading international dance companies including the English National Ballet, Ballet Sao Paolo, Ballet Monte Carlo, NDT, Ballet Gulbekian, Les Grand Ballets Canadiens, Ballet Zurich, Ballet Basel, Finnish National Ballet, Royal Winnipeg Ballet, Scapino Ballet, Stuttgart Ballet, Ballet Jazz de Montreal, Batsheva, Bat Dor and many others. He received knighthood from Queen Beatrice of the Netherlands for his continuous work for Dutch dance. He created Man of the Hour, a coproduction of the Israeli Opera and the Suzanne Dellal Centre.
His works at the Israeli Opera include:
Orfeo ed Euridice (2018) - Akko, director and choreographer
Man of the Hour (2016) choreographer


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– Any alterations made to a new custom made saddle once purchased from Heritage after 28 days from purchase are not included within the original sale price and will be charged at our standard rates. This includes flocking, head plate changes and callout/fuel fees. Alterations within this 28 days are subject to a £30 handling fee and fuel costs.
– Special order and Custom saddles are non-returnable and non-refundable.
* Disclaimer, There will be no refund or return accepted on any bespoke saddles or tack made to a customers own instructions and supplied to Heriatge by you the customer. It is the customers responsibility to ensure the instructions are correct and we will accept no responsibility for any errors made by you the customer. The customers own supplied instructions to us, will be followed closely and accurately by Heritage, and any problems with the fit of the saddle will not be the fault of Heritage.
– A deposit of 50% of total cost (half cash/half cheque, or all cash or bank transfer prior to the callout) will be taken at time of order and this is non-refundable.
– Faulty items will be returned to us, at customers cost, for inspection/assessed by Heritage. Please allow up to 28 days for replacement goods.
– Heritage Bespoke Saddles Ltd must be informed of any dissatisfaction or damage to orders as soon as possible after discovery of any issue.
– Your saddle will need to be checked regularly for fit and balanced as explained by our fitter at the time of purchase. It is your responsibility to contact us to arrange this.
– Trees are guaranteed for 5 years, from the date of purchase. This guarantee does not cover damage caused by misuse.
– Tree Materials and workmanship are guaranteed for 12 months subject to fair wear and tear.
– Repairs and alterations on any part of a saddle or tack should only be carried out by Heritage saddlery or any guarantees will be made void.
All deposits taken/given for saddles, saddle fittings, tack orders or any other work taken out by/booked/ordered from the company are non refundable for any reason whatsoever.
This includes any deposits given in person by the customer, either in cash or cheque, on the day of a saddle fitting consultation. In this case the customer will be made aware verbally that the deposit given in non refundable at this time.By giving a deposit on the day of the fitting, by post, bank transfer, Paypal payment or any other means, the customer agrees to these terms and conditions.


Bringing together the latest insights from genetics and cyberculture, this book contends that all life can be conceived of as information. It explores future developments in genetics, both as a consequence of Darwinian natural selection and under the influence of genetic engineering. The ideas are illustrated by writing that draws on a range of surreal examples including hypermarkets containing every toy in the universe, pufferfish that think like flies, Peter Pan-like trips through human genes and creatures that evolve in months and not millennia. It argues that the future will be dominated by biological machines evolved artificially by a process of accelerated evolution which is called evolution compression .


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