text:
What is the Difference Between a Theory and a Hypothesis?
Biological Theory
Psychodynamic Theory
Culture Theory
Identity Theory
R. Kayne
The fossil record is highly consistent with Charles Darwin's theory of evolution.
A hypothesis attempts to answer questions by putting forth a plausible explanation that has yet to be rigorously tested. A theory, on the other hand, has already undergone extensive testing by various scientists and is generally accepted as being an accurate explanation of an observation. This doesn't mean the theory is correct; only that current testing has not yet been able to disprove it, and the evidence as it is understood, appears to support it.
Outside of systems that are very small, Einstein's theory of relativity has withstood over one hundred years of testing.
A theory will often start out as a hypothesis -- an educated guess to explain observable phenomenon. The scientist will attempt to poke holes in his or her hypothesis. If it survives the applied methodologies of science, it begins to take on the significance of a theory to the scientist. The next step is to present the findings to the scientific community for further, independent testing. The more a hypothesis is tested and holds up, the better accepted it becomes as a theory.
Scientists working in a lab may do research to test a hypothesis they have.
The theory of evolution, for example, is supported by a plethora of scientific evidence in the form of cosmological, geophysical and archaeological research data, to name just a few relevant fields. Scientists have not only traced the evolution of species through skeletal records, but the earth itself, our solar system, the stars and galaxies can be "dated" through various scientific methods. This evidence appears to track the universe back about 13.7 billion years to a "Big Bang" event.
While there appears to be no end to the evidence supporting the theory of evolution, it is still only a theory. Theories, no matter how well accepted, are always subject to change as new knowledge comes to light. Einstein's Theory of Relativity, for example, explained the world on a massive scale, but broke down when it came to the world of the infinitesimally small. This famous theory was augmented more recently by superstrings' M-theory, which very nicely united the four known forces in the universe in one elegant mathematical equation. M-theory exotically predicts we live in a world of ten dimensions, plus one for time, for a total of 11 dimensions. While many aspects of M-theory make it difficult to test, the mathematical perfection of this theory has lent it strength in scientific circles.
A current hypothesis of great importance is that of dark energy. Scientists can calculate how much mass is present in the universe, yet physical matter – matter made from atoms – makes up only four percent of the total. Dark matter is believed to make up another twenty percent, leaving about seventy-six percent unaccounted for. Enter the hypothetically summoned dark energy to fill the gap. There are a few competing candidates for dark energy with research underway. However, one of the problems is difficulty in detecting it. So even while its interaction with gravity on a massive scale is sufficient to cause the universe to rapidly expand outwards, in the lab detecting it is a bit like checking for a light breeze using a weathervane full of gigantic holes. Nevertheless, as scientists untangle the mystery of the missing mass, the answer will one day rise from mere hypothesis to generally accepted theory.
What Is the Big Rip?
What Are the Different Types of Archaeological Theory?
What Is the Interaction Hypothesis?
What is Soft Science?
What is a Hypothesis?
What is M-Theory?
What is Biophilia?
anon347404
Hypotheses can never become theories. They are separate things. There is no hierarchy.
To anon65339 and anon91831: You're both obviously logical, scientifically minded, free-thinking people.
However, whoever wrote this article is obviously not.
I would imagine that s/he is probably just another Darwinist member of the 'scientific' community, pushing the official belief-system.
I do not agree with this article.
A theory means a model. Evolution has nothing to do with the big bang or with Abiogenesis.
This is the kind of confusion I would expect from a creationist.
There are two parts to evolution. There is the fact of evolution, namely that there occurs heritable changes in the gene pool of a population over time. This is irrefutable and can be simply demonstrated. To deny this part of evolution would be like asserting that the earth is flat.
The second portion is what most people think of as the theory of evolution. The theory is based on the fact of evolution and attempts to explain the relative importance of different mechanisms of evolution such as mutations, genetic drift, migration and natural selection. Hope this helps.
If a hypothesis and theory are different, then why are they considered synonyms in dictionaries?
Also: This site is the first I came across, where it says Dark Energy is a hypothesis, where the science channel, sometimes discovery channel, and their websites all say it's a theory?
There is no cosmological evidence for the theory of evolution.
The theory of evolution is about the origin of species, not about the formation of the universe.
All theories are based upon other theories. At the core of all science there must always be some assumptions.
For string theory it rests on basic theories of quantum mechanics and theories about the functioning of gravity.
For evolution there's a basis in chemical theories and physical theories.
All theories are constantly open to modification and even outright dismissal. As an example, it wasn't until at least the 1980s that horizontal gene transfer began to be part of the theory of evolution.
string theory is really, a hypothesis. evolutionary theory, however, is not. there is a plethora of molecular evidence for evolution that is not merely fossil record.
fossil record is cute, but protein and mitochondrial DNA sequences don't lie. A good example is the "mitochondrial distance". You can compute this distance between any two eukaryotic species.
between you and say, your cousin, or a monkey or a naked mole-rat. And they show precisely what you would expect.
For example, george burns was related more closely to the naked mole-rat and george bush was more closely related to the monkey than my cousin. etcetera
The problem with the "theory" of evolution is that all the evidences are based on assumptions--it cannot be tested. There is a huge difference between observable science and historical science since the former is repeatable while the latter can not.
"Scientists have not only traced the evolution of species through skeletal records..." is historical science since there is nothing to tie that one set of skeletons is related to another.
"...the stars and galaxies can be 'dated' through various scientific methods." Even this author uses "dated" in quotes, reinforcing that this is not observable science and an assumption.
"This evidence appears to track the universe back about 13.7 billion years to a 'Big Bang' event." Even though the stars and galaxies can be shown to move at a certain rate, it is still an assumption that that rate has been constant. What we observe today tells us only that this is how they are moving today, and nothing about how they did move.
Really, it should be call the "Hypothesis of Evolution".
The others who commented are under the misconception that "testing" only refers to physical experiment. If a theory is expressable mathematically, it is tesatable in the sense of mathematical proofs (consider it a mental test of a hypothesis). If the hypothesis survives numerous, rigorous mathematical "tests", it is a theory where each test is very real, supporting evidence of its accuracy.
I agree. In fact, any version of string "theory", due to the inability to test, perhaps is merely a conjecture.
It seems the stated difference between a hypothesis and a theory is then contradicted by calling string theory (M or otherwise) a "theory." Since at present it is impossible to test, mathematical elegance aside, is it not simply a hypothesis?
By: Bastos
By: FotolEdhar
By: nandyphotos


text:
Excerpt from Zerø Day
Zerø Day will be available in the first half of 2018. Signup for a free ebook when it becomes available.
These binoculars are ridiculous. I find using them annoying, and they magnify so much that any slight movement of the hand makes it hard to keep the frame still. You stand there with your elbows on your belly to keep it steady. I can see the woman we're supposed to kill wandering in and out of the field of vision. She's in a building full of other people. It's just a house where people live. But here's our target.
I hate this. The cost is so high and they hate us even more. I don't know why we do this, but orders are orders. The technicians at the back always say they try to minimise casualties but I think that's lies. They say that they killed some militants but that could be anybody that isn't one of us. They don't care about the kids and nobodies at all. Weapons are meant to be used, they have that about them. They're meant to kill. They have no other purpose. Well, except making threats of killing, but where's the fun in that?
Criminals should be put on trial. This? It's just murder. But orders are orders, and that's the way it is. For some reason the massive power of the country I live in needs rid of this woman, and whoever's nearby. So that's that.
"North East corner."
"Confirm North East corner."
The missile is called a Hell Fire. Some religious fuckwit thought it an appropriate name, obviously. It comes in and obliterates the building. Making the world a safer place for democracy. The drone dudes with the game controls in a shed far away from here raining the fire down get medals and so do I. What a joke. But no-one's laughing anymore. Another $120,000 thermobaric warhead sucking the air out of a building and collapsing it. Kaboom, use before sell by date. Sorry about the kids.
The Toxic Empire
It informs (makes form) everything we do on this flat earth. Each step a burden, each breath laboured under the drag of the Empire's goodness. We carry an us-sized weight when we first draw breath and it follows us all the way to whatever shallow death we end up saddled with. The shallowness is part of it. None of this is real, all is chimeric, fantastic, ungraspable, painful.
Woman now, has heavier weights. The wrong skin as much or more. Just not being the same accidental stamp as the empire's owners brings you more to worry about if it turns its jaundiced eye on you, and maybe picks you out for extra pain or ridicule. This is even if you keep quiet, if you start speaking out the tiny minded will find you. Then, of course, the eager lackeys with the lighter weights queue up to tell you how lucky you are one of their febrile number didn't rape you recently.
They have privilege, entitlement, the Empire taught them so. That makes it real and the swirl of garbage thoughts create a never-ending miasma for everyone else. But they're so clever, even though they can't understand no-one cares about their empty heads full of mephitic grasping. You're grateful for their helping you with the ignorance you never knew you had. All that whining and posturing still never gets the girl, haven't you noticed? No wonder they're all so obsessed with robots and drowning in porn.
The empire, the lightless abyss, stole their human side and weaponised the brains of an endless parade of mummy's boys who won't go out on their own and live vicariously through limp collections of childhood toys. The spinning wheels of commerce have manufactured trophic, inchoate armies of light sabre wielding babies who are always heroes in the story of their own heads. Never working together, never a team achieving. Just individuals who can't see, who have volunteered their empathy to what they see in the mirror. Rock stars made of rock, unable to see the irony.
We used to know we were slaves. No-one forced us to work for them but the false choice of starvation made it pretty clear who was what. Owned or owner, master or slave. But then the empire's systemic weakness, pressure and change morphed the harsh reality into a smiling beneficent paradox. The machine needed massed ranks marching to military beat to spread out and conquer the world and those ranks function better when they believe. The sky cloth was cut for worship, and our beating hearts' beauty perverted for their wars. The butcher's apron raised above the fray, bright colours in the darkest of times. The butcher's bill becomes almost infinite when everything is for sale.
So we are still free to starve, but as we starve our betters can pat us on the head and tell us how grateful we should be. The things we won from them years ago when they were weak from fighting, that we assumed would always be there, are being taken away. Too blinded by the spectacle, the dancing empty masks, we cannot see how everything we love is being consumed and turned toxic. We are freer than we ever were with their laws. We have no recourse to violence, even saying self defence. If they have that monopoly they hold the keys to the cages.
But, of course, their freedom is our slavery. They own, we starve. They control, we are controlled. We are volunteers for the unequal exchange, the grist to their mill, and the volunteering is what makes it ok. Every virtue, original thought, fragile beauty, is taken and made worthless by the touch of their markets. The system has no human face, don't be fooled, don't appeal to something that has never been there for a worthless boon. To make change you have to make change, don't beg, they'll just laugh at you. For humans it is, has been, and always will be broken. It has no human shape, takes no human values, except to sell them back to us as feeble flickering two dimensional writing on water of what we could have had or been. The naked, the sexy rebellion, backwards R revolution with no love or heart that goes nowhere.
The last gasp of the Toxic Empire will come when it chokes on its own waste, when it falls under its own weight. If we didn't cooperate it could not bind us, blind us to its deadly machinations and empty pied piper certainties. But it's so pretty, the flashing lights!
Can you feel it twisting inside you? The subtle inescapable knife of living now, in this hole? The blurring of vision, nothing sharp or clear? Your words babbling, the tears streaming? The black rain gathering in pools nearby. They dug us up, bright lights, because we weren't dead enough.
Signup for a free Zerø Day ebook when it becomes available.

redpajama_set_name: RedPajamaCommonCrawl


text:
package org.lilyproject.repository.impl.test;

import org.junit.After;
import org.junit.AfterClass;
import org.junit.Before;
import org.junit.BeforeClass;
import org.lilyproject.repository.impl.HBaseTypeManager;
import org.lilyproject.repository.impl.IdGeneratorImpl;
import org.lilyproject.testfw.HBaseProxy;
import org.lilyproject.testfw.TestHelper;
import org.lilyproject.util.hbase.HBaseTableFactory;
import org.lilyproject.util.hbase.HBaseTableFactoryImpl;
import org.lilyproject.util.io.Closer;
import org.lilyproject.util.zookeeper.ZkUtil;
import org.lilyproject.util.zookeeper.ZooKeeperItf;

/**
 *
 */
public class TypeManagerRecordTypeTest extends AbstractTypeManagerRecordTypeTest {

    private final static HBaseProxy HBASE_PROXY = new HBaseProxy();
    private static ZooKeeperItf zooKeeper;
    private static HBaseTableFactory hbaseTableFactory;

    @BeforeClass
    public static void setUpBeforeClass() throws Exception {
        TestHelper.setupLogging();
        HBASE_PROXY.start();
        zooKeeper = ZkUtil.connect(HBASE_PROXY.getZkConnectString(), 10000);
        hbaseTableFactory = new HBaseTableFactoryImpl(HBASE_PROXY.getConf(), null, null);
        typeManager = new HBaseTypeManager(new IdGeneratorImpl(), HBASE_PROXY.getConf(), zooKeeper, hbaseTableFactory);
        setupFieldTypes();
    }

    @AfterClass
    public static void tearDownAfterClass() throws Exception {
        Closer.close(typeManager);
        Closer.close(zooKeeper);
        HBASE_PROXY.stop();
    }

    @Before
    public void setUp() throws Exception {
    }

    @After
    public void tearDown() throws Exception {
    }
}

redpajama_set_name: RedPajamaGithub


text:
Young learners in Malaysia using Microsoft Teams. Source: Microsoft Malaysia
Microsoft Malaysia – every student has a chance with the right tech
By Joe Devanesan | 29 October, 2020
Microsoft Malaysia joins hands with Google, Apple to bring a nationwide education platform during a time of crisis in the country
An estimated 40% of the world's poorest countries failed to support learners at risk during the COVID-19 crisis. UNESCO forecasts that 23.8 million additional children and youth (from pre-primary to tertiary) may drop out, or not have access, to school next year due to the pandemic's economic impact alone.
Ensuring learning continuity during the time of school closures and academic course suspensions thus became a priority for governments the world over, many of which turned to technology for a solution. 2020 marked the largest ever shift towards new learning tools and outcomes outside of the classroom.
Around Southeast Asian countries, levels of education development can vary greatly, but connectivity is always a challenge for most of these countries. Fortunately in several of these territories, technology partners have stepped in to lend technological support to beleaguered education systems, often at the national level, which provides the greatest chance to reach as many students as possible.
In Malaysia, the biggest technology companies in the world – Google, Apple, and Microsoft Malaysia –all banded together to provide educational technology (edtech) tools to the digital learning platform known as "DELIMa" (Digital Education Learning Initiative Malaysia) that was relaunched earlier this year by the Malaysian Ministry of Education (MOE), as the pandemic caused nationwide school closures.
One of DELIMa's grounding tenets is platform democratization, harnessing a multi-technology ecosystem to make digital learning accessible to all. Which is why edtech resources from Google Classroom, Microsoft 365, and Apple Teacher Learning Centre are all featured on DELIMa.
Virtual launch of the DELIMa national education platform. Source: Microsoft Malaysia
"Every student has the opportunity, regardless of economic status – by having the right device, the right connectivity, and the right platform – every student should be given and must be given the opportunity to have access to this technology," insists Microsoft Malaysia's managing director, K. Raman.
In the name of democratizing edtech for as many as possible, Microsoft Malaysia allowed its Microsoft 365 suite to be available on a Google-hosted platform. "The work we are doing with the MOE is to democratize technology, regardless of what technology and give the students the choice. Whether it is our platform, whether it's our competitor's platform – in this case, Google Classroom – our students must have access to all different technology."
DELIMa was averaging about 1.7 million monthly active users, making it one of the largest nationwide deployments of an e-learning platform in the world. "DELIMa is a great initiative by the Malaysian government in that it offers a platform that is free for students," said Raman. "We are working with MOE by ensuring every student and every educator can have access to our Microsoft Teams, which is our collaboration platform, our Word, our PowerPoint, and our Excel for free and without restriction."
HAS 2020 USHERED IN A NEW ERA OF 'INTELLIGENT EDUCATION'?
Joe Devanesan | 29 September, 2020
Students are limited from learning in physical classrooms right now, but in some ways, learning platforms like DELIMa have freed up students to learn at their own pace. "In terms of the digital classrooms, I would say, it gives an opportunity that learning never stops. So now with a digital platform, students can learn anytime, anywhere."
Microsoft has been empowering other learning platforms as well, both in Malaysia and elsewhere, such as aiding universities with their research-intensive work remotely. "With remote learning you need the right platform that can scale when students are accessing the information. And that's the area that we're working with University Malaya," Raman pointed out.
"With high performance computing, they have moved from their traditional on-premise hardware platform into the Microsoft Azure [cloud]. And this is the ability to help them with a faster turnaround time, for all the huge data that they have in their research work."
By Joe Devanesan
@thecrystalcrown
Joe Devanesan | @thecrystalcrown
Joe's interest in tech began when, as a child, he first saw footage of the Apollo space missions. He still holds out hope to either see the first man on Mars, or Jetson's-style flying cars in his lifetime.


A new grocery store has opened its doors in Pleasanton at Pacific Pearl shopping center. Located at 2701 Stoneridge Drive, the new arrival is called 99 Ranch Market.
This chain offers fresh produce, non-perishable items, meat, frozen goods, fresh seafood, bread, and prepared hot meals like Hong Kong-style barbecue and pork buns. The establishment features buffet items plus fresh pastries and desserts from its bakery.
With a 3.5-star rating out of nine reviews on Yelp so far, the fresh addition has made a promising start.
"Brand new Ranch 99 market in the Pacific Pearl shopping center," Yelper Wolfgang T. wrote. "Parking on a Saturday around noon was not a problem. The store is clean and well organized, and seems larger than the one on Rosewood."
Yelper Raymond L. added, "I think I like this store more than the location in Dublin. The vegetables are fresh and the fish tanks are very clean. The people buy food here with confidence and consume with satisfaction."
99 Ranch Market is open from 9 a.m.-9 p.m. daily.


text:
Ealing to 2022: Our Manifesto
Ealing to receive a share of Mini-Holland cycling fund
Ealing was named as one of eight boroughs to receive funding from TfL as part of the Mayor of London's Mini-Holland initiative, it was announced yesterday.
Ealing's cycling plans were described as 'exceptional', with TfL pledging a share of the £100million funding for the council to implement the plans. The exact amount of funding Ealing will receive is still to be confirmed.
Councillor Julian Bell, leader of the council, said;
"This is great news for cyclists in Ealing. After speaking with cycling commissioner, Andrew Gilligan, I am confident that we will get the TfL funding needed to deliver a sizeable proportion of our Mini-Holland bid. This will enable us to carry out the improvements in Ealing town centre and along the Uxbridge Road. But, our plan is to deliver the whole scheme, so we will also be looking to identify other funding that could be used to make Ealing's full Mini-Holland bid a reality."
Cycling is at the forefront of transport plans for the borough, and it is the council's priority to transform Ealing into a friendlier and safer place for people to travel by bike. This funding announcement is fantastic news for the borough, and the council will continue to bid for additional money to carry out a full cycling-overhaul.
Councillor Bassam Mahfouz, cabinet member for environment and transport, added:
"Our Mini-Holland bid focused on creating transformational cycling highways in key locations throughout the borough, which would make it easier and safer for people to travel on two wheels."
Ealing was named along with Kingston, Enfield, Waltham Forest, Bexley, Merton, Richmond and Newham as the recipients of the £100million funding pot. Kingston, Enfield and Waltham Forest are to receive up to £30million each to implement their full cycling plans.
Ealing was short-listed for the mini-Holland fund in September last year.
Ruskin Hall, 16 Church Road, London, W3 8PP
Email: info@ealinglabour.com
Promoted by and on behalf of Ealing Labour Party at Ruskin Hall, 16 Church Road, W3 8PP. By filling in your personal details and providing us with information about your views, you are opting in to allowing the Labour Party and its representatives to use these, as well as other information to which we are entitled, to contact you by email, text, phone, websites and apps. You may opt out of being contacted at any time. For the Labour Party's full privacy policy and how we use your data please see: www.labour.org.uk/pages/privacy.
©2022 Copyright Labour All rights reserved.


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text:
First Listen: Son of Pearl funks it up on "Your Love Is Overdue"
(November 16, 2021) Tedi "Son of Pearl" Robinson is an artist who can speak nearly every dialect of funk that is out there. And on his new track, "Your Love is Overdue," he proves to be fluent in the kind sleek, pounding and synthesized funk language that we were speaking in the 1980s.
Those who were around during that time understand that we were down for having a good time for a very long time, so the music had to not only draw the ladies and gentlemen to the dance floor, it had to set the stage to keep the party going after last call. And with "Your Love is Overdue," Son of Pearl has created a good time tune.
The cut has that percolating bass line that will have you dancing in your seat and serves as the foundation for funky guitar riffs while Robinson engages in a call and response with keyboard. That's when he's not engaging in a conversation with the lady he pulled on the dance floor. The funky track finds Robinson alternating between letting her know what he can do for her while also telling her where the man she came with falls short.
"Your Love is Overdue" is good, fun music that captures a zeitgeist of a world that is overdue for a good, fun time. Check out "Your Love is Overdue" here.
Son of Pearl – "Your Love Is Overdue"
Son Of Pearl · Your Love Is Overdue
Follow Son of Pearl on Facebook
Son of Pearl on Soundcloud


What is the Resident Quality & Safety Council?
Formed in July 2014, the DMC Resident Quality and Safety Council consists of twenty Resident/ Fellow Directors of Quality responsible for daily monitoring of quality metrics across the DMC.
Working as a team across the system, the Resident Engagement Program led by our Resident/Fellow Directors for Quality brings together training programs from across the spectrum such as critical care, anesthesia, psychiatry, internal medicine, and neurology with one unified vision and goal. This is the only Quality Improvement project in the nation of such magnitude—involving 800 residents and fellows system wide in partnership with DMC top leaders such as CEO Mr. Joe Mullany, our CMO Dr. Suzanne White and Vice President for Academic Affairs Dr. Wilhelmine Wiese- Rometsch.
What are the Core Measures?
What are the SCIP Guidelines?
Dr. Pritha Chitagi (Int Med/SGH) is an Associate Author for First Aid for the USMLE Step 1!


What are the things you need to observe while buying commercial or residential property?
Who will help in the completion of the sale?
The agent will help in the entire completion of the sale. They will charge you a fee for this service. It can be in the form of a commission. The charged commission can either be a percentage of the sale price, a fixed fee or a combination of both.
What points should be taken care of while buying property?
The cost of advertising and other outgoings.
What is the method of sale?
Everybody dreams of owning a property but possessing a house is not easy. There are two main ways of selling a property: by auction or private sale. You should hire an agent as he will recommend what is the best method of sale for your requirement.
What are the Australian Consumer Law and contracts?
The Australian Consumer Law and Contract includes The agent's authority to sell is a legally binding consumer contract. The Australian Consumer Law makes unfair terms in consumer contracts void. Estate agents must make sure their authorities comply with the law.
An unfair term in a consumer contract is one that causes a significant imbalance in the rights and obligations of both parties to the detriment of the consumer and was inserted in the contract intentionally.
What are the actions could be taken on unfair contract terms?
If you believe there is an unfair term in the authority, you can contact consumer affairs Victoria.
What are the things required if you want to sell without a real estate agent?
If you are opting to sell your property without using the services of an agent, you will need to thoroughly research the selling process. Using this service will help you in saving money by not having to pay commission.
What are the methods of a private sale?
If you are choosing the private sale method, then the property is advertised and offers are invited from prospective buyers only. The sale is negotiated between the buyer and seller.
What is the authority period with the agent?
It is completely negotiable and you should consider the length of time carefully. Once you are in contract with the agent, you will not be able to cancel it.
If no period is defined, then the default period is 30 days from the auction date. In private sale, the default period is 60 days from the signing of the authority to sell.
What are the other terms and conditions?
While signing contract makes sure you understand and agree to all terms and conditions. These conditions are negotiable. Any changes further (deletions, amendments or additions) must be made on the authority and initialed by both parties.


Newly designed for 2016, the APT training netball from Gilbert is specifically designed to improve performance during training sessions. The hard wearing rubber surface enhances both grip and accuracy whilst ensuring the longevity. Designed for outdoor use on any surface. Nylon wound construction and a butyl bladder.


text:
Terrorism is a tactic — not a color or ideology
By Adam Maruyama, Opinion Contributor — 01/08/21 08:00 AM EST
© Julia Nikhinson
In 2018, I co-led a team of longtime counterterrorism professionals in drafting the National Strategy for Counterterrorism of the United States of America. Since then, the Department of Homeland Security and the National Counterterrorism Center have unveiled frameworks to counter the rising threats of domestic terrorism. The insurrection at the U.S. Capitol on January 6 is proof that these efforts, while commendable, are not enough. To truly combat the threat of domestic terrorism, we must understand that, fundamentally, terrorism is a tactic, not a color or ideology.
Since the attacks of September 11, 2001, the media narrative and – more regrettably – the national security narrative has framed terrorism as the effort of a small minority of Muslims abroad to coopt a peaceful religion to challenge and reshape American democracy. Our single-minded focus on self-declared "jihadists" attacking from the outside has blinded us to terrorism coming from within.
In 2005, the FBI's counterterrorism retrospective reminded us that "terrorism is defined in the Code of Federal Regulations as 'the unlawful use of force and violence against persons or property to intimidate or coerce a government, the civilian population, or any segment thereof, in furtherance of political or social objectives.'" This definition transcends the violent and corrupt jihadism of al Qaeda and the self-declared Islamic State. In fact, the destruction of property and violent trespass by a large group of President Trump Donald TrumpLil Wayne gets 11th hour Trump pardon Trump grants clemency to more than 100 people, including Bannon Trump expected to pardon Bannon: reports MORE's supporters clearly matches this definition.
But this threat did not emerge on January 6, or even with the president's assertions of fraud following the November elections. As my colleague Bruce Hoffman noted presciently in the wake of the release of the 2018 strategy, that strategy failed in its conflation of true domestic terrorist threats like neo-Nazism and white nationalism with other violent agitators like animal rights activists resorting to vandalism to liberate animals.
Though some of my colleagues, writing in a one-year retrospective on the strategy, highlighted that "the structure of the 2018 NSCT makes almost every strategic line of effort and priority action applicable to domestic terrorism," it is clear that this administration has failed to live up to that aspiration. The actions and rhetoric coming from the White House in the aftermath of the assault on the Capitol are as far from the strategy's lines of "enhancing preparedness" and "countering terrorist radicalization and recruitment" as could be imagined.
Despite that D.C. Mayor Muriel Bowser Muriel BowserInauguration parties lose the glitz and glamour in 2021 Biden's inauguration unprecedented in US history Sunday shows - Capital locked down ahead of Biden's inauguration MORE mobilized part of the National Guard two days before the January 6 protests, which eventually became a violent occupation, the presence of armed security forces at the Capitol on January 6 was laughably smaller than they were during the Black Lives Matter protests — a far cry from "enhanced preparedness." Despite the violent threats made by Trump's supporters in advance of those same protests-turned-violent-occupation, the same president who signed the 2018 strategy posted tweets and a video that failed to denounce the violence and vandalism carried out in his name at the Capitol — a far cry from "countering terrorist radicalization and recruitment."
Over the next few days, many will praise Vice President Pence, House Speaker Nancy Pelosi Nancy PelosiThe Memo: Trump leaves changed nation in his wake New York court worker arrested, accused of threats related to inauguration GOP Rep Marjorie Taylor Greene referred to Parkland school shooting as 'false flag' event on Facebook MORE (D-Calif.) and Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump has talked to associates about forming new political party: report McConnell, Schumer fail to cut power-sharing deal amid filibuster snag McConnell keeps GOP guessing on Trump impeachment MORE (R-Ky.) for their commitment to preserving the Constitution and emphasizing, as McConnell did, that "criminal behavior will never dominate the United States Congress." These actions are a down payment on the domestic terrorism effort that lies before us in the truest sense of the term "down payment": They are not exceptional or heroic actions; they are the bare minimum that we should expect from our leaders.
That we are in an environment in which the leader of our democratic republic – the same leader who endorsed a strategy to enhance preparedness for domestic terrorism and counter terrorist radicalization – cannot do the same is a dereliction of duty. That the administration focused, on the eve of the attack on the Capitol, on an executive order targeting antifa threats from abroad while the real threat was literally knocking at their door is a disgrace.
This dereliction means that the Biden administration will have an unprecedented challenge in counterterrorism at home. It must rise to this challenge and acknowledge that the use of violence and fear to affect political and social ends – no matter the ideology or skin color of the perpetrators – is a threat to our democracy that we can only conquer as a united nation.
In confronting this challenge, the Biden administration should be sure not to throw out the baby with the bathwater. As recommended in the 2018 strategy, it should aggressively integrate domestic terrorism-related threat information across federal, state and local law enforcement to enable a better-orchestrated response to those threats. But it should also accelerate efforts and increase resourcing to understand the magnitude of domestic terrorist threats and the targets of their plans.
Congress should also hold itself liable to continue the work of defending the republic from these dangerous threats. In consultation with experts in both terrorism and civil liberties, it should enact laws that make the domestic terrorism definition in U.S. code a chargeable offense — not only to provide penalties that might deter future threats, but also to provide law enforcement with the tools needed to conduct strategic analysis and organized investigations of such threats and the crimes that result from them.
Adam Maruyama is a national security professional with more than 15 years of experience in cyber operations, cybersecurity and counterterrorism. He served in numerous war zones and co-led the drafting of the 2018 National Strategy to Counterterrorism. Adam currently manages cybersecurity software deployments for a number of federal customers.
Tags terrorism al Qaeda Department of Homeland Security National Counterterrorism Center Donald Trump Mitch McConnell Muriel Bowser Nancy Pelosi Counter-terrorism Definition of terrorism domestic terrorism State terrorism


text:
Home»Archives»Florida (Page 3)
Court Backs School District in Transgender Bathroom Fight
By The News Service of Florida on December 31, 2022 Exclusive, Florida
By Jim Saunders, The News Service of Florida TALLAHASSEE — After a five-year legal battle, a sharply divided federal appeals court Friday upheld a St. Johns County School Board policy that prevented a transgender male student from using boys' bathrooms at a high school. The 11th U.S. Circuit Court of Appeals, in a 7-4 decision, […]
DeSantis Takes Aim at Teacher Union Dues
By Jim Saunders, The News Service of Tallahassee TALLAHASSEE — Gov. Ron DeSantis has signaled that he will make a priority of passing a long-debated proposal that would prevent teachers from having union dues deducted from their paychecks. DeSantis supported the proposal Monday during a speech in Orlando, describing it as "paycheck protection legislation." The […]
State Sets Stage for More Marijuana Licenses
By Dara Kam, The News Service of Florida TALLAHASSEE — State health regulators on Monday set in motion a process to issue up to 22 more medical-marijuana licenses, in a highly anticipated move that could double the size of Florida's medical-cannabis industry. The state Department of Health also published an emergency rule that would make […]
Ten Big Issues in Insurance Overhaul
By Staff on December 16, 2022 Exclusive, Florida
By Jim Saunders, The News Service of Florida TALLAHASSEE — Florida lawmakers this week held a special session and passed a 105-page bill aimed at stabilizing the state's troubled property-insurance system. The bill (SB 2-A) deals with numerous issues, including lawsuits, the state-backed Citizens Property Insurance Corp. and critical reinsurance coverage. Here are 10 key […]
Florida Unemployment Claims Down
Unemployment claims in Florida dipped slightly last week, while the number of first-time claims nationally fell to the lowest mark since September. The U.S. Department of Labor on Thursday released a report that estimated 5,685 new claims were filed in Florida during the week that ended Dec. 10, down from a revised count of 6,393 […]
School LGBTQ Support Guides Face Scrutiny
By Ryan Dailey, The News Service of Tallahassee TALLAHASSEE — The State Board of Education is slated this week to scrutinize LGBTQ support guides and bathroom policies for transgender students in 10 school districts, as state officials question whether they are violating a law known as the "Parents' Bill of Rights" and other measures. The […]
Red States, Blue States Choose Sides on Education Law
By Jim Saunders, The News Service of Florida TALLAHASSEE — The legal battle over a Florida law that restricts classroom instruction on gender identity and sexual orientation is pitting red states against blue states. Republican attorneys general of 14 states last week sought approval to file a brief supporting Florida in a fight about the […]
Insurance Proposals Could Bring Big Changes
By Jim Saunders, The News Service of Florida TALLAHASSEE — With a special legislative session poised to start, the Florida House and Senate late Friday released proposals that would make far-reaching changes in the state's troubled property-insurance system. The bills (HB 1A and SB 2A) would take steps to reduce litigation costs, move policies out […]
Lawmaker Resigns After Indictment
By The News Service of Florida on December 9, 2022 Exclusive, Florida
By Ryan Dailey, The News Service of Florida TALLAHASSEE — State Rep. Joe Harding resigned his House seat Thursday after being charged with fraudulently obtaining coronavirus-related business loans. Harding, R-Ocala, submitted his resignation a day after the U.S. Attorney's Office for the Northern District of Florida announced a grand-jury indictment on charges of wire fraud, […]
Major Insurance Issues Teed Up for Special Session
By Staff on December 8, 2022 Exclusive, Florida
By Jim Saunders, The News Service of Florida TALLAHASSEE — With Florida's property-insurance system in turmoil, state lawmakers could be poised to take major steps to try to stabilize the market during a special legislative session next week. Senate President Kathleen Passidomo, R-Naples, and House Speaker Paul Renner, R-Palm Coast, released a formal session proclamation […]


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William Moses And Denise Crosby Have Joined General Hospital
Published on October 19, 2022.
©Arlene Richie/jpistudios.com
At long last, Elizabeth Webber's parents are coming back to Port Charles! General Hospital (GH) has cast actors William Moses and Denise Crosby in the respective roles of Jeff and Carolyn Webber.
After months and months of Liz's absentee parents being name-dropped on the ABC soap, Moses and Crosby will bring these characters to the canvas, according to Soap Opera Digest.
"Thrilled to be part of this epic show and reunite with old friends!" Crosby wrote on Twitter, tagging Finola Hughes, Genie Francis and Moses.
Moses has previously appeared in How To Get Away With Murder and Mystic Pizza, while Crosby has portrayed characters on Ray Donovan, Suits and Star Trek: The Next Generation. She even had a bit role on Days Of Our Lives back in 1980.
The role of Jeff Webber was previously portrayed by Richard Dean Anderson from 1976 until 1981, whereas Carolyn has never appeared on-screen.
Needless to say, Elizabeth's world will be turned upside down by the long-awaited return of her dad, but it'll be very interesting to see how GH approaches Webber's relationship with her mother.
Perhaps this casting news will finally bring some momentum to Elizabeth's backstory, which has been the victim of slow and uneven pacing. Viewers have even suggested that the soap is intentionally dragging out the storyline due to alleged tensions behind the scenes with star Rebecca Herbst.
General Hospital News Round-Up For The Week (October 3, 2022)


If someone had told us 2 years ago that we'd be starting our own business in the world of healthy eating we'd have said they were having a laugh!
Sorry we've been so quiet we've had a slight detour in Clean Supper Clubs direction as we were given an opportunity and decided to run with it. It has meant a lot of dedicated hard work but it appears to be paying off!
Will give you a brief up date and add more soon.
We have started to make and sell some of our delicious recipes. It's very exciting. We've been shocked by the interest in our creations and the response from people tasting them has been completely rewarding. The look on peoples faces when they realise they can still enjoy the occasional cake if they are diabetic or avoid sugar, wheat, dairy or suffer with IBS and related health issues is a picture.
Every Tuesday at Altrincham Market, this is a very special market full of incredible foodies and we feel immensely proud to be invited to play a small part. Here we are in the covered out side market.
Our range is expanding every week with a great selection of super smoothies, our healthy range of cakes, bakes and bliss balls, delicious hot cacaoOlate and warming golden mylk.
We've our Clean Supper Club range of gorgeous granola and a selection of some of our favourite natural super boosters from Indigo Herbs.
So come and see us!
We were there all this weekend too so we'll let you know when are going to be there over the weekends again.
Also we have started to supply a few cafes too, but more on that soon!
We will be updating our website and recipes soon, so stick with us as we've a great range of meals for you to enjoy.
Take care everyone and come and see us if you are in the area.


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Ranveer's Musical 'Gully Boys' Releasing Shortly & All Set to Rock the World
Ranveer Singh is ready to set the stage ablaze yet again after entertaining his fans and followers with mind-blowing hit Simba. Alia Bhatt and Ranveer Singh will soon be seen together as the lead pair for the first time on screen in their much-talked-about upcoming film called 'Gully Boys.' We know that the songs, posters, and the trailers of the film have been successful in creating a tremendous amount of interest and buzz surrounding the film. Ranveer fans are waiting for the release of the musical movie. As per India Times at https://mumbaimirror.indiatimes.com, "the film's makers unveiled the first look on Wednesday, with the on-screen couple looking pensive. In this film, Ranveer will be sharing screen space with Alia Bhatt for the first time."
Music Release of Gully Boys
Ranveer Singh is all set to win millions of hearts by taking his devoted fans on a truly fascinating musical journey in Zoya Akhtar's another unique creation 'Gully Boys''. There have been reports of Ranveer Singh rapping in a music concert for launching the music album of 'Gully Boys'. Ranveer performed along with hot hip-hoppers Naezy and Divine. Ranveer Singh has won a tremendous amount of acclaim and accolades for his brilliant rapping skills. It is, therefore, no secret that the netizens are all praise for Ranveer.
The music album was launched on 24th January in a grand manner amidst a pulsating ambiance. Both Alia Bhatt and Ranveer Singh performed live last Thursday evening at the 'Richardson & Cruddas' located in Byculla. Ranveer performed to the stimulating beat of "Apna Time Aayega", and was definitely at his very best.
As per the latest Bollywood news, the entire team including producer Farhan Akhtar and director Zoya Akhtar were present. Shweta Bachchan Nanda also attended the music launch concert. Alia Bhatt looked dashing in a vibrant top and a green skirt and Ranveer came looking like a star in a neon green sweatshirt, silver jacket, and tracks. Ranveer introduced Divine and Naezy by saying "It is a big day for Indian hip hop. The hip hop scene here is going to change from today. We are going to have a blast. Let me invite the 'asli hip hop' crew on stage," The film is inspired and based on the true-life story of rappers Naved Shaikh or Naezy and Vivian Fernandes aka David. The hip-hoppers performed with their very own gully gang.
Gully Boys Posters: Building up the Hype & Frenzy
One of the movie's posters shows Ranveer and Alia sitting together side by side sharing an earphone for listening to music. The film's tagline says 'Aapna Time Ayega'. Ranveer shared one more poster from the movie with a caption "The voice of the streets." The poster focuses on Ranveer's eyes that seem to be full of hope and at the same time, they convey the fact that he is quite aware of the massive struggle he would be encountering in his musical journey. The poster's backdrop is the location of the hero's residence somewhere close to a slum area. The movie is all about how the hero struggles hard to face the adversities of life yet does not lose his dedication and enthusiasm to fulfill his musical dreams.
Ranveer's Valentine Day's Gift to His Ardent Fans: Hot & Steamy Scenes Galore
The film is all set for release on the Valentine's Day 2019. There are reports that in keeping with the romantic mood of the season, the film has multiple kissing scenes. Ranveer would be involved in three kisses with leading lady Alia and two lock lips with Kalki Koechlin.
The film would be having its world premiere during the period 7th February to 17th February 2019 at the Berlin Film Festival. Even before the film has hit the screens, it is getting a lot of appreciation and acclaim and so, everyone seems to be looking forward to watching it!
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text:
\section{Introduction and tools}

This note is intended to illustrate the claim that (often)
a $q$-deformation of a~non-smooth classical variety or an orbifold produces an algebra which
has properties of the coordinate algebra of a~non-commutative smooth variety or manifold.
More precisely, we say that an algebra $B$ (over an algebraically closed f\/ield ${\mathbb K}$) is {\em
homologically smooth} or simply {\em smooth} provided that as a~$B$-bimodule it has a~f\/initely generated
projective resolution of f\/inite length; see~\cite[Erratum]{Van:rel}.
We prove that several classes of examples of coordinate algebras of $q$-deformed orbifolds are
homologically smooth.
To achieve this aim we use techniques developed in~\cite{Kra:Hoc}, which are applicable to principal
comodule algebras~\cite{BrzHaj:Che}, and those of~\cite{Liu:hom}, which are applicable to generalized Weyl
algebras~\cite{Bav:gweyl}.
We summarize these presently.

In~\cite[Corollary~6]{Kra:Hoc} Kr\"ahmer gives a~criterion for smoothness of quantum homogeneous spaces,
which through an immediate extension to a~more general class of Hopf--Galois extensions and then
specif\/ication to strongly group-graded algebras, provides us with a~tool for showing the smoothness of
the noncommutative pillow algebra studied in~\cite{BraEll:sph}, the quantum lens space algebras ${\mathcal
O}(L_q(l;1,l))$
introduced in~\cite{HonSzy:len}, the quantum teardrop algebras~\cite{BrzFai:tea},
the coordinate algebras of quantum real weighted
projective planes ${\mathcal O}({\mathbb R}{\mathbb P}_q(l;-))$ def\/ined in~\cite{Brz:Sei}, the quantum
Seifert manifold ${\mathcal O}(\Sigma_q^3)$~\cite{BrzZie:pri} and the quantum Seifert lens spaces
${\mathcal O}(\Sigma_q^3(l;-))$~\cite{BrzFai:rps}.
More specif\/ically, let $G$ be a~group (with the neutral element~$e$).
A $G$-graded algebra $A=\oplus_{g\in G} A_g$ is said to be {\em strongly graded} if, for all $g,h\in G$,
$A_gA_h = A_{gh}$.
For such algebras, Kr\"ahmer's criterion for smoothness takes the following form.
\begin{criterion}
\label{cri.smooth}
Let $A$ be a~strongly $G$-graded algebra and set $B= A_e$.
If the enveloping algebra ${\mathcal E} A:= A\otimes A^{\rm op}$ of $A$ is left Noetherian of finite global
dimension, then the enveloping algebra of~$B$ is also left Noetherian of finite global dimension.
Consequently, $B$ is a~homologically smooth algebra.
\end{criterion}

Although~\cite[Corollary~6]{Kra:Hoc} is formulated for quantum homogeneous spaces obtained via surjective
homomorphism of Hopf algebras with a~cosemisimple codomain, the proof extends immediately to all faithfully
f\/lat Hopf--Galois extensions $B\subseteq A$ or principal comodule algebras such that $B$ is a~direct
summand of $A$ as a~$B$-bimodule.
In the case of $G$-graded algebras, $B=A_e$ is a~direct summand of $A$ as a~$B$-bimodule,
and~\cite[Proposition~AI.3.6]{NasVan:gra} ensures that a~strongly $G$-graded algebra is a~principal
${\mathbb K} G$-comodule algebra.
In particular $A$ is projective and faithfully f\/lat as a~left and right $B$-module.
The way Criterion~\ref{cri.smooth} is stated indicates its iterative nature which is implicit in the proof
of~\cite[Corollary~6]{Kra:Hoc}.
Note in passing that the assumption about the dimension of ${\mathcal E} A$ is not necessary to conclude
that ${\mathcal E} B$ is left Noetherian.

An ef\/fective way of checking whether a~graded $G$-algebra $A$ is strongly graded is described
in~\cite[Section~AI.3.2]{NasVan:gra}:
\begin{lemma}\label{lem.strong}
$A= \oplus_{g\in G} A_g$ is strongly graded if and only if there exists a~function $\omega: G \to A\otimes A$ such that

$(a)$ for all $g\in G$, $\omega(g) \in A_{g^{-1}}\otimes A_g$,

$(b)$ for all $g\in G$, $\mu\circ\omega(g) = 1$, where $\mu$ is the multiplication map of $A$.
\end{lemma}

Furthermore, if $G$ is a~cyclic group, then conditions $(a)$ and $(b)$ need only be checked for a~generator $g$ of~$G$.
If $\omega(g)=\sum\limits_i\omega'_i\otimes \omega''_i$, satisf\/ies $(a)$ and $(b)$, then $\omega$ is def\/ined by
setting $\omega(e) =1\otimes 1$~and
\begin{gather*}
\omega\big(g^{n+1}\big)=\sum_i\omega'_i\omega(g^n)\omega''_i,
\qquad
\text{for~all}
\quad
n>0.
\end{gather*}
A function $\omega$ satisfying conditions $(a)$ and $(b)$ in Lemma~\ref{lem.strong} is a~predecessor of a~{\em
strong connection form} on a~principal comodule algebra;
see~\cite{BrzHaj:Che, DabGro:str,Haj:str}.

Let $R$ be an algebra, let $p$ be an element of the centre of $R$ and let $\pi$ be an automorphism of~$R$.
The {\em $($degree-one$)$ generalized Weyl algebra} $R(\pi,p)$ is the extension of $R$ by genera\-tors~$x_+$,~$x_-$
subject to the relations, for all $r\in R$,
\begin{gather*
x_-x_+=p,
\qquad
x_+x_-=\pi(p),
\qquad
x_{\pm}r=\pi^{\pm1}(r)x_\pm;
\end{gather*}
see~\cite{Bav:gweyl}.
In~\cite[Theorem~4.5]{Liu:hom} Liu gives the following criterion of smoothness of a~generalized Weyl
algebra over the polynomial algebra.
\begin{criterion}
\label{cri.Weyl}
Let $R={\mathbb K}[a]$ be a~polynomial algebra and an automorphism $\pi: {\mathbb K}[a]\to {\mathbb K}[a]$
be determined by $\pi(a) = \kappa a+\chi$.
Then the generalized Weyl algebra $R(\pi,p)$ is homologically smooth with homological dimension~$2$ if and
only if the polynomial $p\in {\mathbb K}[a]$ has no multiple roots.
\end{criterion}

Furthermore, Liu proves that if the smoothness Criterion~\ref{cri.Weyl} is satisf\/ied, then $A=R(\pi,p)$
is a~{\em twisted Calabi--Yau algebra} of dimension $2$ with the Nakayama (twisting) automorphism $\nu: A\to
A$ given by $\nu(x_\pm) = \kappa^{\pm 1} x_\pm$ and $\nu(a) = a$.
This means that the Hochschild cohomology of $A$ with values in its enveloping algebra is trivial in all
degrees except degree~2, where it is equal to $A$ with the $A$-bimodule structure $a\cdot b \cdot a' = ab\nu(a')$.

The reader should observe that, except for some special cases, the algebras described herein\-after are not
smooth whenever the deformation parameters $\lambda$ or $q$ are equal to 1.
By noting this they will fully grasp the main message of this note, namely that deformation may (and quite
often does) result in smoothing classically singular objects.

\section{Results}

Throughout we work with associative complex $*$-algebras with identity.
We write ${\mathcal E} A$ for the enveloping algebra $A\otimes A^{\rm op}$ of $A$.
We often use the {\em $q$-Pochhammer symbol} which, for an indeterminate $x$ and a~complex number $q$, is
def\/ined as
\begin{gather*}
\Poch xqn:=\prod_{m=0}^{n-1}\big(1-q^{m}x\big).
\end{gather*}

\subsection{The noncommutative pillow}

Let $\lambda = e^{2\pi i\theta}$, where $\theta$ is an irrational number.
Recall that the coordinate $*$-algebra ${\mathcal O}(\mathbb{T}^2_\theta)$ of the {\em noncommutative
torus} is generated by unitaries $U,V$, such that $UV=\lambda VU$; see~\cite{Rie:alg}.
The involutive algebra automorphism given by
\begin{gather*}
\sigma: \ {\mathcal O}\big(\mathbb{T}^2_\theta\big)\to{\mathcal O}\big(\mathbb{T}^2_\theta\big),
\qquad
U\mapsto U^{*},
\qquad
V\mapsto V^{*},
\end{gather*}
makes ${\mathcal O}(\mathbb{T}^2_\theta)$ into a~${\mathbb Z}_2$-graded algebra.
The f\/ixed point (or degree-zero) subalgebra ${\mathcal O}(P_\theta)$ is generated by $U+U^*$ and $V+V^*$.
It has been introduced and studied from a~topological point of view in~\cite{BraEll:sph} (see
also~\cite[Section~3.7]{EvaKaw:sym}) as a~deformation of the coordinate algebra of the {\em pillow
orbifold}~\cite[Chapter~13]{Thu:geo} (an orbifold rather than manifold since, classically, the ${\mathbb
Z}_2$-action determined by the automorphism $\sigma$ is not free).
\begin{theorem}
\label{thm.main.pil}
{}${\mathcal O}(\mathbb{T}^2_\theta)$ is a~strongly ${\mathbb Z}_2$-graded algebra and the noncommutative
pillow algebra ${\mathcal O}(P_\theta)$ is homologically smooth.
\end{theorem}
\begin{proof}
Set
\begin{gather*}
\hat{x}=U-U^*,
\qquad
\hat{y}=V-V^*,
\qquad
\hat{z}=UV^*-U^*V.
\end{gather*}
Note that $\sigma(\hat{x}) = - \hat{x}$, $\sigma(\hat{y}) = - \hat{y}$ and $\sigma(\hat{z}) = - \hat{z}$,
i.e.\ all these are homogeneous elements of~${\mathcal O}(\mathbb{T}^2_\theta)$ with the ${\mathbb
Z}_2$-degree $1$.
A straightforward calculation af\/f\/irms that these elements satisfy the following relation
\begin{gather*}
\hat{x}^2+\hat{y}^2-\bar{\lambda}\hat{z}^2-\hat{x}z\hat{y}=2\big(\bar{\lambda}^2-1\big),
\end{gather*}
where $z= UV^* +U^*V\in {\mathcal O}(P_\theta)$.
Therefore, the mapping $\omega: {\mathbb Z}_2 \to {\mathcal O}(\mathbb{T}^2_\theta)\otimes {\mathcal
O}(\mathbb{T}^2_\theta)$, def\/ined as $\omega(0) =1\otimes 1$ and
\begin{gather*}
\omega(1)=\frac{1}{2\big(\bar{\lambda}^2-1\big)}\left(\hat{x}\otimes\hat{x}+\hat{y}\otimes\hat{y}
-\bar{\lambda}\hat{z}\otimes\hat{z}-\hat{x}z\otimes\hat{y}\right),
\end{gather*}
satisf\/ies conditions $(a)$ and $(b)$ in Lemma~\ref{lem.strong}, and ${\mathcal O}(\mathbb{T}^2_\theta)$ is
a~strongly ${\mathbb Z}_2$-graded algebra.

Both ${\mathcal O}(\mathbb{T}^2_\theta)$ and ${\mathcal E}{\mathcal O}(\mathbb{T}^2_\theta)$ can be
understood as iterated skew Laurent polynomial rings and hence they are left Noetherian
by~\cite[Theorem~1.4.5]{McCRob:Noe}.
Furthermore, the global dimension of the latter is less than or equal to 4
by~\cite[Theorem~7.5.3]{McCRob:Noe}.
Therefore, the noncommutative pillow algebra ${\mathcal O}(P_\theta)$ is homologically smooth by
Criterion~\ref{cri.smooth}.
\end{proof}

In short, Theorem~\ref{thm.main.pil} means that for the irrational $\theta$ (or, more generally, for any
real $\theta\in (0,1)\setminus\{\frac12\}$) the action of ${\mathbb Z}_2$ on the noncommutative torus is
free despite the fact that the corresponding action on the classical level is not free.
The set of f\/ixed points corresponds to a~manifold rather than an orbifold.

\subsection{Quantum teardrops and lens spaces}
\label{sec.lens}
Here we deal with three (classes of) complex $*$-algebras given in terms of generators and relations.

The coordinate algebra of the quantum three-sphere, ${\mathcal O}(S^{3}_q)$, is generated by $\alpha$ and
$\beta$ such that
\begin{gather}
\alpha\beta=q\beta\alpha,
\qquad
\alpha\beta^*=q\beta^*\alpha,
\qquad
\beta\beta^*=\beta^*\beta,
\nonumber
\\
\alpha\alpha^*=\alpha^*\alpha+\big(q^{-2}-1\big)\beta\beta^*,
\qquad
\alpha\alpha^*+\beta\beta^*=1,
\label{su}
\end{gather}
where $q\in(0,1)$; see~\cite{Wor:com}.
For any positive integer $l$, the coordinate algebra of the quantum lens space ${\mathcal O}(L_q(l;1,l))$
is a~$*$-algebra generated by $c$ and $d$ subject to the following relations:
\begin{gather*
cd=q^{l}dc,
\qquad\!
cd^*=q^{l}d^*c,
\qquad\!
dd^*=d^*d,
\qquad\!
cc^*=\Poch{dd^*}{q^2}l,
\qquad\!
c^*c=\Poch{q^{-2}dd^*}{q^{-2}}l,
\end{gather*}
see~\cite{HonSzy:len}.
Finally, for a~positive integer $l$, the coordinate algebra of the quantum teardrop ${\mathcal
O}(\mathbb{WP}_q(1,l))$ is the $*$-algebra generated by $a$ and $b$ subject to the following relations
\begin{gather*
a^*=a,
\qquad
ab=q^{-2l}ba,
\qquad
bb^*=q^{2l}a\Poch a{q^2}l,
\qquad
b^*b=a\Poch{q^{-2}a}{q^{-2}}l;
\end{gather*}
see~\cite{BrzFai:tea}.
These algebras form a~tower ${\mathcal O}(\mathbb{WP}_q(1,l))\hookrightarrow {\mathcal
O}(L_q(l;1,l))\hookrightarrow {\mathcal O}(S^{3}_q)$ with embeddings $a\mapsto dd^*$, $b\mapsto cd$ and
$c\mapsto \alpha^l$, $d\mapsto \beta$, respectively.
We thus can and will think of ${\mathcal O}(\mathbb{WP}_q(1,l))$ and ${\mathcal O}(L_q(l;1,l))$ as
subalgebras of ${\mathcal O}(S^{3}_q)$.
{}${\mathcal O}(S^{3}_q)$ is a~${\mathbb Z}_l$-graded algebra with grading given by $\deg(\alpha) =1$,
$\deg(\alpha^*) = l-1$, $\deg(\beta)=\deg(\beta^*) =0$, and the above embedding identif\/ies the
degree-zero part of ${\mathcal O}(S^{3}_q)$ with ${\mathcal O}(L_q(l;1,l))$.
By~\cite[Theorem~3.3]{BrzFai:tea}, the latter is a~strongly ${\mathbb Z}$-graded algebra with grading
provided by $\deg(c) = \deg(d^*) = 1$, $\deg(c^*) = \deg(d) =-1$ and with the degree-zero part isomorphic
to ${\mathcal O}(\mathbb{WP}_q(1,l))$.

That ${\mathcal O}(\mathbb{WP}_q(1,l))$ is homologically smooth can be argued as follows.
{}${\mathcal O}(S^{3}_q)$ is a~coordinate algebra of the quantum group ${\rm SU}(2)$ and thus ${\mathcal
E}{\mathcal O}(S^{3}_q)$ is left Noetherian and has a~f\/inite global dimension; see~\cite{GooZha:hom}.
Hence, if it were a~strongly ${\mathbb Z}_l$-graded algebra, then ${\mathcal E}{\mathcal O}(L_q(l;1,l))$
would be left Noetherian and would have a~f\/inite global dimension (so, in particular ${\mathcal
O}(L_q(l;1,l))$ would be homologically smooth) by Criterion~\ref{cri.smooth}.
Since, in turn ${\mathcal O}(L_q(l;1,l))$ is a~strongly graded algebra, Criterion~\ref{cri.smooth} would
imply smoothness of the teardrop algebra ${\mathcal O}(\mathbb{WP}_q(1,l))$.
This arguing leads~to:
\begin{theorem
${\mathcal O}(S^{3}_q)$ is a~strongly ${\mathbb Z}_l$-graded algebra with the degree-zero subalgebra
isomorphic to ${\mathcal O}(L_q(l;1,l))$.
Consequently, both ${\mathcal O}(L_q(l;1,l))$ and ${\mathcal O}(\mathbb{WP}_q(1,l))$ are homologically
smooth algebras.
\end{theorem}
\begin{proof}
The case $l=1$ is dealt with in~\cite{Kra:Hoc}, the remaining cases follow from
\begin{lemma}
\label{lemma.l.1}
For all integers $l>1$, there exist elements $\omega(1) \in {\mathcal O}(S^{3}_q)_{l-1}\otimes {\mathcal
O}(S^{3}_q)_{1}$ such that $\mu(\omega(1)) = 1$.
\end{lemma}
\begin{proof}
Set:
\begin{gather*}
\omega(1)=x_1\alpha^{l-1}\otimes\alpha^{*l-1}+\sum_{p=1}^{l-1}y_p a^{p-1}\alpha^*\otimes\alpha,
\end{gather*}
where $x_1, y_1, \ldots, y_{l-1} \in {\mathbb C}$ are to be determined and $a=\beta\beta^* = dd^*$.
Then $\omega(1) \in {\mathcal O}(S^{3}_q)_{l-1}\otimes {\mathcal O}(S^{3}_q)_{1}$.
Using~\eqref{su} one f\/inds that
\begin{gather}
\label{aa*}
\alpha^m\alpha^{*m}=\Poch{a}{q^{2}}m=:\sum_{p=0}^m c^m_p a^p,
\end{gather}
where $c^m_p$ are the appropriate $q$-binomial coef\/f\/icients (def\/ined by the second equality
in~\eqref{aa*}).
In view of~\eqref{su}, the condition $\mu(\omega(1)) =1$ leads to
\begin{gather*}
x_1\sum_{p=0}^{l-1}c^{l-1}_p a^p+\sum_{p=0}^{l-2}y_{p+1}a^{p}-q^{-2}\sum_{p=1}^{l-1}y_p a^{p}=1.
\end{gather*}
By comparing the powers of $a$, this is converted into an inhomogeneous system of $l$ equations with
unknown $x_1, y_1, \ldots, y_{l-1}$, whose determinant is
\begin{gather*}
\Delta_{l:1}=\left|
\begin{array}{c c c c c c c}
c^{l-1}_0& 1& 0& 0& \cdots& 0& 0
\\[6pt]
c^{l-1}_1& -q^{-2}& 1& 0& \cdots& 0& 0
\\[6pt]
c^{l-1}_2& 0& -q^{-2}& 1& \cdots& 0& 0
\\[2pt]
\vdots& & & \vdots
\\[2pt]
c^{l-1}_{l-2}& 0& 0& 0& \cdots& -q^{-2}& 1
\\[6pt]
c^{l-1}_2& 0& 0& 0& \cdots& 0& -q^{-2}
\end{array}
\right|.
\end{gather*}
{}$\Delta_{l:1}$ can be evaluated by expanding by the f\/irst column to give
\begin{gather*}
\Delta_{l:1}=(-1)^{l-1}\big(q^{-2(l-1)}c^{l-1}_0+q^{-2(l-2)}c^{l-1}_1+\cdots+c^{l-1}_{l-1}\big)
=\big({-}q^2\big)^{l-1}\prod_{p=1}^{l-1}\big(1-q^{2p}\big)\neq0.
\end{gather*}
The f\/inal equality follows from the def\/inition of the $q$-binomial coef\/f\/icients~\eqref{aa*}.
This proves the existence of $\omega(1)$ as stated.
\end{proof}

Since 1 is a~generator of ${\mathbb Z}_l$, Lemma~\ref{lemma.l.1} ensures the existence of mappings $\omega:
{\mathbb Z}_l\to {\mathcal O}(S^{3}_q)\otimes {\mathcal O}(S^{3}_q)$ that satisfy conditions $(a)$ and $(b)$ in
Lemma~\ref{lem.strong}.
Hence ${\mathcal O}(S^{3}_q)$ is a~strongly ${\mathbb Z}_l$-graded algebra, and the second assertion of the
theorem follows by Criterion~\ref{cri.smooth}.
\end{proof}

Therefore, for any $q\in (0,1)$ the action of ${\mathbb Z}_l$ on the quantum three-sphere described above
is free despite the fact that the corresponding action on the classical level is not free (unless,
obviously, $l=1$).
The f\/ixed points correspond to a~manifold rather than an orbifold.

\subsection[Odd weighted real projective planes ${\mathbb R} {\mathbb P}_q^2(l;-)$ and quantum Seifert lens
spaces]{Odd weighted real projective planes $\boldsymbol{{\mathbb R} {\mathbb P}_q^2(l;-)}$\\ and quantum Seifert lens spaces}

For a~positive integer $l$, the coordinate $*$-algebra ${\mathcal O}({\mathbb R}
{\mathbb P}_q^2(l;-))$ of the odd quantum weighted real projective plane is generated by $a$, $b$, $c_-$
which satisfy the relations:
\begin{gather*}
a=a^*,
\qquad
ab=q^{-2l}ba,
\qquad
ac_{-}=q^{-4l}c_-a,
\qquad
b^2=q^{3l}ac_-,
\qquad
bc_-=q^{-2l}c_-b,
\\
bb^*=q^{2l}a\Poch{a}{q^{2}}l,
\qquad
b^*b=a\Poch{q^{-2}a}{q^{-2}}l,
\qquad
b^*c_-=q^{-l}\Poch{q^{-2}a}{q^{-2}}l b,
\\
c_-b^*=q^{l}b\Poch{a}{q^{2}}l,
\qquad
c_-c_-^*=\Poch{a}{q^{2}}{2l},
\qquad
c_-^*c_-=\Poch{q^{-2}a}{q^{-2}}{2l},
\end{gather*}
see~\cite{Brz:Sei}.
To prove homological smoothness of ${\mathcal O}({\mathbb R} {\mathbb P}_q^2(l;-))$ we make use of
Criterion~\ref{cri.smooth} and build a~tower of strongly graded algebras with ${\mathcal O}({\mathbb R}
{\mathbb P}_q^2(l;-))$ as the foundation.

The coordinate $*$-algebra of the quantum Seifert manifold ${\mathcal O}(\Sigma_q^3)$ is generated by
a~central unitary $\xi$ and elements $\zeta_0$, $\zeta_1$ such that
\begin{gather}
\label{sigma.rel}
\zeta_0\zeta_1=q\zeta_1\zeta_0,
\qquad
\zeta_0\zeta_0^*=\zeta_0^*\zeta_0+\big(q^{-2}-1\big)\zeta^2_1\xi,
\qquad
\zeta_0\zeta_0^*+\zeta_1^2\xi=1,
\qquad
\zeta_1^*=\zeta_1\xi.
\end{gather}
It has been shown in~\cite[proof of Proposition~5.2]{BrzZie:pri} that ${\mathcal O}(\Sigma_q^3)$ can be
understood as the degree-zero part of a~${\mathbb Z}_2$-grading of ${\mathcal O}(S_q^2)[u,u^{-1}]$, where
$u^{-1}=u^*$ and ${\mathcal O}(S_q^2)$ is the coordinate $*$-algebra of the equatorial Podle\'s
sphere~\cite{Pod:sph}, generated by $z_0$ and self-adjoint $z_1$ such that
\begin{gather}
\label{sphere}
z_0z_1=q z_1z_0,
\qquad
z_0z_0^*=z_0^*z_0+\big(q^{-2}-1\big)z_1^2,
\qquad
z_0z_0^*+z_1^2=1.
\end{gather}
The ${\mathbb Z}_2$-grading of ${\mathcal O}(S_q^2)[u,u^{-1}]$ is determined by setting, for all monomials
$w$ of degree $k$ in the basis $\{z_0^rz_1^s, z_0^{*r}z_1^s \; | \: r,s\in {\mathbb N}\}$ of ${\mathcal
O}(S_q^2)$, $\deg(wu^m) = (k+m)\mod 2$.
{}${\mathcal O}(\Sigma_q^3)$ can be identif\/ied with the degree-zero part of ${\mathcal
O}(S_q^2)[u,u^{-1}]$ by $*$-embedding $\zeta_i\mapsto z_iu$, $\xi\mapsto u^{-2}$.
Thanks to the last of equations~\eqref{sphere}, the function
\begin{gather*}
\omega:{\mathbb Z}_2\to{\mathcal O}\big(S_q^2\big)\big[u,u^{-1}\big]\otimes{\mathcal O}\big(S_q^2\big)\big[u,u^{-1}\big],
\qquad
0\mapsto1\otimes1,
\qquad
1\mapsto z_0\otimes z_0^*+z_1\otimes z_1,
\end{gather*}
satisf\/ies conditions (a) and (b) in Lemma~\ref{lem.strong}, hence ${\mathcal O}(S_q^2)[u,u^{-1}]$ is
a~strongly ${\mathbb Z}_2$-graded algebra.
Since ${\mathcal E}{\mathcal O}(S_q^3)$ is Noetherian, and there is a~surjective $*$-algebra homomorphism
${\mathcal O}(S_q^3)\to {\mathcal O}(S_q^2)$, $\alpha\mapsto z_0$, $\beta\mapsto z_1^*$, both ${\mathcal
E}{\mathcal O}(S_q^2)$ and ${\mathcal E}{\mathcal O}(S_q^2)[u,u^{-1}]$ and hence also ${\mathcal
E}{\mathcal O}(\Sigma_q^3)$ are Noetherian.

As explained in~\cite{BrzFai:rps}, ${\mathcal O}(\Sigma_q^3)$ is a~${\mathbb Z}_{l}$-graded algebra with
grading given by
\begin{gather*}
\deg(\zeta_0)=1,
\qquad
\deg(\zeta_0^*)=l-1,
\qquad
\deg(\zeta_1)=\deg(\xi)=0.
\end{gather*}
The degree-zero part of ${\mathcal O}(\Sigma^3_q)$ is isomorphic to the $*$-algebra ${\mathcal
O}(\Sigma^3_q(l;-))$ generated by $x$, $y$ and central unitary $z$ subject to the following relations
\begin{gather*}
y^*=yz,
\qquad
xy=q^l yx,
\qquad
xx^*=\Poch{y^2z}{q^{2}}l,
\qquad
x^*x=\Poch{q^{-2}y^2z}{q^{-2}}l.
\end{gather*}
The embedding of ${\mathcal O}(\Sigma^3_q(l;-))$ into ${\mathcal O}(\Sigma_q^3)$ is given by $x\mapsto
\zeta_0^l$, $y\mapsto \zeta_1$ and $z\mapsto \xi$.
The similarity of relations~\eqref{sigma.rel} and~\eqref{su} leads immediately to equations~\eqref{aa*}
with $\alpha$ replaced by $\zeta_0$ and $a= \zeta_1^2\xi$.
This allows one to use the same arguments as in Lemma~\ref{lemma.l.1} to prove that there exist $x_1, y_1,
\ldots, y_{l-1}\in {\mathbb C}$ such that
\begin{gather*}
\omega(1)=x_1\zeta_0^{l-1}\otimes\zeta_0^{*l-1}+\sum_{i=1}^{l-1}y_ia^{i-1}\zeta_0^{*}\otimes\zeta_0^{}
\in{\mathcal O}\big(\Sigma_q^3\big)_{l-1}\otimes{\mathcal O}\big(\Sigma_q^3\big)_l,
\end{gather*}
has the required property $\mu(\omega(1)) =1$.
Therefore, ${\mathcal O}(\Sigma^3_q)$ is a~strongly graded ${\mathbb Z}_l$-algebra.

Finally, it is proven in~\cite{BrzFai:rps} that ${\mathcal O}(\Sigma^3_q(l;-))$ is a~strongly ${\mathbb
Z}$-graded algebra with grading given by $\deg(x)=\deg(y)=1$, $\deg(x^*) =-1$ and $\deg(z) = -2$.
The degree-zero subalgebra of ${\mathcal O}(\Sigma^3_q(l;-))$ can be identif\/ied with the coordinate
algebra of weighted real projective plane ${\mathcal O}({\mathbb R}{\mathbb P}^2_q(l;-))$ via the map
$a\mapsto y^2z$, $b\mapsto xyz$ and $c_-\mapsto x^2z$.

Summarizing, we have presented in this section a~tower of $*$-algebras
\begin{gather}
\label{seq}
{\mathcal O}\big({\mathbb R}{\mathbb P}^2_q(l;-)\big)\hookrightarrow{\mathcal O}
\big(\Sigma^3_q(l;-)\big)\hookrightarrow{\mathcal O}\big(\Sigma^3_q\big)\hookrightarrow{\mathcal O}\big(S_q^2\big)\big[u,u^{-1}\big].
\end{gather}
The second, third and fourth terms are strongly group graded algebras.
Each antecedent term is the degree-zero part of the subsequent one.
Since the enveloping algebra of ${\mathcal O}(S_q^2)[u,u^{-1}]$ is Noetherian, so are the enveloping
algebras of all its predecessors.
By~\cite[Corollary~4.6]{Liu:hom} the global dimension of ${\mathcal E}{\mathcal O}(S_q^2)$ is f\/inite,
hence so is the global dimension of ${\mathcal E}{\mathcal O}(S_q^2)[u,u^{-1}]$, and, by
Criterion~\ref{cri.smooth}, the global dimensions of enveloping algebras of all its predecessors
in~\eqref{seq}.
This proves the following
\begin{theorem
The algebras ${\mathcal O}(\Sigma^3_q)$, ${\mathcal O}({\mathbb R}{\mathbb P}^2_q(l;-))$
and ${\mathcal O}(\Sigma^3_q(l;-)) $ are homologically smooth.
\end{theorem}

\subsection[Quantum real weighted projective planes ${\mathbb R}{\mathbb P}_q^2(l;+)$ and teardrops
(revisited)]{Quantum real weighted projective planes $\boldsymbol{{\mathbb R}{\mathbb P}_q^2(l;+)}$\\ and teardrops (revisited)}

Let $k$ be a~natural number and $l$ be a~positive integer.
Write ${\mathcal A}(k,l)$ for the $*$-algebra generated by $a$ and $b$ subject to the following relations
\begin{gather*
a^*=a,
\qquad
ab=q^{-2kl}ba,
\qquad
bb^*=q^{2kl}a^k\Poch{a}{q^{2}}l,
\qquad
b^*b=a^k\Poch{q^{-2}a}{q^{-2}}l.
\end{gather*}
If $k$ and $l$ are coprime then ${\mathcal A}(k,l)$ is the coordinate algebra of the quantum weighted
projective line or the {\em quantum spindle} ${\mathcal O}(\mathbb{WP}_q(k,l))$ introduced
in~\cite{BrzFai:tea}.
The special case $k=1$ is simply the {\em quantum teardrop}; see Section~\ref{sec.lens}.
For $l$ odd, ${\mathcal A}(0,l)$ is the coordinate algebra of the quantum weighted even real projective
plane ${\mathcal O}({\mathbb R}{\mathbb P}_q^2(l;+))$ introduced in~\cite{Brz:Sei}.
The following theorem is a~consequence of Criterion~\ref{cri.Weyl}.
\begin{theorem
The algebras ${\mathcal A}(k,l)$ are homologically smooth $($of dimension $2)$ if and only if $k=0,1$.
\end{theorem}
\begin{proof}
We only need to observe that each ${\mathcal A}(k,l)$ is a~generalized Weyl algebra over the polynomial
algebra ${\mathbb C}[a]$ given by the automorphism $\pi(a) = q^{2l} a$, element $p=a^k
\prod\limits_{m=1}^l(1-q^{-2m}a)$ and generators $x_-=b$, $x_+ =b^*$.
Since $p$ has no multiple roots if and only if $k=0,1$, the assertion follows by Criterion~\ref{cri.Weyl}.
\end{proof}

Furthermore, for $k=0,1$, ${\mathcal A}(k,l)$ are twisted Calabi--Yau algebras with the twisting
automorphism $\nu(b) = q^{-2l}b$, $\nu(b^*)= q^{2l}b^*$ and $\nu(a)=a$.
Hence they enjoy the Poincar\'e duality in the sense of Van den Bergh~\cite{Van:rel}.

\subsection*{Acknowledgements}

I would like to thank Ulrich Kr\"ahmer for discussions, Li-Yu Liu for
bringing reference~\cite{Liu:hom} to my attention, and Piotr~M.~Hajac and the referees for helpful comments.
I am grateful to Fields Institute for Research in Mathematical Sciences in Toronto, where these results were f\/irst presented, for creating excellent research environment and for support.

\pdfbookmark[1]{References}{ref}

redpajama_set_name: RedPajamaArXiv


text: vf activate seoMonitorApi


Oh. With the trials come like upon line. I think trials actually offer you an insight into love you couldn't see before. The fear I have is calmed as I pray. Cry literally to my Heavenly Father. I know I can't do it alone. I see my flaws. Not in ways I'd like to. But then I remember Samoa. How I prayed to make my weakness strong. To fill my heart with faith. Let go of pride. Fill me with faith I'm afraid to have. Help me to see others as He does. And when it's a bad day and I have just messed it all up. I can see the beauty of the Atonement. How he has paid. And my job is to get up and try to make it better. And it isn't always better right away. But maybe my trials gave me a way to always stay close to God. To seek the Spirit.


text:
Q: PyTorch: in which cases register_hook can return None gradient? Here is an example of using register_hook with nn.Module, also I double check gradient shape using .grad on weights after loss.backward():
class MyModule(nn.Module):
    def __init__(self):
        super().__init__()

        self.layers = nn.Sequential(
            nn.Linear(5, 6)
        )

    def forward(self, x):
        out = self.layers(x)

        h = self.layers[0].weight.register_hook(lambda grad: print(f'DEBUG: grad hook {grad.size()}'))

        return out

a = torch.ones(5)
a.requires_grad = True
print('a.size()', a.size())
m = MyModule()
b = m(a)
print('b.size()', b.size())
loss = b.mean() # Fake loss
loss.backward()
print('grad.size():', m.layers[0].weight.grad.size())

Output:
a.size() torch.Size([5])
b.size() torch.Size([6])
DEBUG: grad hook torch.Size([6, 5])
grad.size(): torch.Size([6, 5])

Here is more complex example with torch.no_grad() (so hook doesn't called):
class MyModule(nn.Module):
    def __init__(self):
        super().__init__()

        self.layers = nn.Sequential(
            nn.Linear(5, 5)
        )

    def break_grad_flow(self, x):
        with torch.no_grad():
            x = x + 1
        return x

    def forward(self, x):
        out = self.layers(x)
        out = self.break_grad_flow(out)
        out = out + x*0 # To overcome RuntimeError: element 0 of tensors does not require grad and does not have a grad_fn

        h = self.layers[0].weight.register_hook(lambda grad: print(f'DEBUG: grad hook {grad.size()}'))

        return out

def get_grad_size(grad):
    if grad is None:
        return None
    else:
        return grad.size()

a = torch.ones(5)
a.requires_grad = True
print('a.size()', a.size())
m = MyModule()
b = m(a)
print('b.size()', b.size())
loss = b.mean() # Fake loss
loss.backward()
print('grad.size():', get_grad_size(m.layers[0].weight.grad))

Output:
a.size() torch.Size([5])
b.size() torch.Size([5])
grad.size(): None

These outputs are valid and in second example hook is not called when gradient is None (https://discuss.pytorch.org/t/register-hook-not-always-working-saving-gradients/56381/6)
But in real big project where I also have torch.no_grad() somewhere in the middle of the architecture (which I can't reproduce in simple example) I get None shape from hook and valid shape from .grad after loss.backward() which looks weird (I expect hook don't called and None shape from .grad after loss.backward()), so is there any reason why hook can return None shape?
Also if I just want to check if gradient is not None what are pros and cons of using register_hook instead of .grad on weights after loss.backward()?

redpajama_set_name: RedPajamaStackExchange


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text:
Clater Jewelers – Towne Post Network
By Albert E. Darnell Last updated Mar 19, 2022
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Megatron is usually depicted as having risen up from the lowly worker to become a champion in gladiatorial combat. As a gladiator, he took the legendary name "Megatronus" as his own and would similarly inspire a later villainous character. He called for an end to his planet Cybertron's corrupted governing body and told the downtrodden that freedom of self-determination was the right of all sentient beings, becoming a mentor to the young Optimus Prime. Prime would later use his teachings against him when he became corrupt. He has the ability to transform between his robot shape and various weapons or vehicles, but these "alternate-modes", his origins and even personality, can vary depending on which "universe" he's seen in. This origin is considered the most consistent between the various incarnations. Further differences are listed in the respective sections below.
The BMW M12/13 turbo 1500 cc 4-cylinder turbocharged Formula One engine, based on the standard BMW M10 engine introduced in 1961, powered the F1 cars of Brabham, Arrows, Benetton and won the world championship in 1983. It also powered the BMW GTP and in the 2.0 liter naturally aspirated form, the successful March Engineering Formula Two cars.
As BMW M12, the engine design since the 1960s became one of the most successful engines in racing. Starting with the European Touring Car Championship, it was also used in Formula 2, expanded to two litre and fitted with four-valve heads, producing over 300 hp (224 kW). In the Deutsche Rennsport Meisterschaft, a 1400 cc variant (with a 1.4 handicap factor equal to 2000cc) was turbocharged by Paul Rosche according to FIA Group 5 rules. At well over 350 hp (261 kW) from the beginning, it rendered the normally aspirated engines in the two liter category useless. After some development, power, driveability and reliability improved, especially in the IMSA car, and BMW began to think about entering F1, where a handicap factor of 2.0 required 1500 cc engines.
Calvin Johnson Jr. (born September 29, 1985) is an American football wide receiver for the Detroit Lions of the National Football League (NFL). He was drafted by the Lions second overall in the 2007 NFL Draft. He played college football at Georgia Tech, where he was recognized as an All-American twice.
On March 14, 2012, Johnson signed an eight-year, US$132 million contract extension with the Lions, one of the largest sports contracts ever. Johnson has a rare combination of size (6 ft 5 in and 239 lb), hands, speed (40-yard dash in 4.35 seconds), strength, leaping ability, body control and hand-eye coordination. His nickname "Megatron," a Transformers character, was given to him by former Lions wide receiver Roy Williams, and the name caught on with fans.
On December 22, 2012, Johnson broke Jerry Rice's single-season record for receiving yards, which had previously been 1,848, and Johnson finished the 2012 season with 1,964 yards, an average of almost 123 yards per game. In that same Saturday night game versus the Atlanta Falcons, Johnson also set the NFL records for consecutive 100-yard games (8) and consecutive games with 10 or more receptions (4). He also tied Hall of Famer Michael Irvin's record for most 100-yard games in a season with 11. In January 2016 Johnson stated that he was considering retiring from the NFL after nine seasons.
Overide: [after the race between herself and Megatron is finished] Let's see who won. [the camera over the finish line reveals that Override has won by a nose] I won! As for that cyber planet key thing I don't know what you're talking about. I just wanted someone to race.::Megatron: I can tell you all about it.
Red Alert, Clocker: I don't know, Hotshot. Ever since we got here you've been disobeying orders. You knew Megatron wasn't fast enough to defeat Override. You jumped into that race and put your life in danger needlessly. Well, are you going to explain yourself?::Hotshot: It wasn't Megatron that I was thinking about. If we're going to get that cup we're going to have to beat Override sooner sooner or later.::Red Alert, Clocker: I don't know. I think you just jumped into that race just so you could prove that you're faster than Override.::Hotshot: No way! Look, Red Alert I'm going to go and talk to Override my own way. Okay?::Red Alert, Clocker: Hotshot! Oh, great.::Red Alert, Clocker: Hotshot! Is he going to be okay?::Red Alert, Clocker: I sure hope so.
Plot: Taking place after the Second Season of Transformers, Scramble City is a story in which the Cybertrons have built a secret lab hidden inside a mountain to build a new super robot, Metroplex to be a mobile base for them. As Ultra Magnus prepares it the Destrons find out its location and attack it. The Cybertron and Destron teams duke it out over the mountain then Metroplex comes out and beats all the Destrons but then out of the water comes Typticon! Can Metroplex defeat Trypticon???
Quem E a Vitima Afinal de Contas?


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Trekking Hellas (http://www.trekking.gr) is one of Greece's leading providers of hiking and other outdoor adventure holidays at a variety of destinations in the country. Trekking is offering self-guided hiking holidays on Kythnos.
Chryssie's Greece (http://www.chryssiesgreece.com) became our first partner. Chryssie offers guided walking and other activities on Lemnos, western Crete and Kythnos. She also offers city walking in Athens and Thessaloniki.
Travel Me To Milos ( http://www.travelmetomilos.com) is based on the island at the south west of the Cycladic group. The operator offers hiking over the geology of Milos as well as kayaking and yachting as part of its packages.
Arachovitika Kalyvia (http://www.arachovitika-kalyvia.gr) is a hotel, farm, nature and hiking centre 900 metres up in the hills between Tripoli and Sparta in the Peloponnese mainland region of Greece, south west of Athens.
Ecotourism-Greece (http://www.ecotourism-greece.com) is an organisation promoting awareness of ecology, heritage and culture. It recommends a series of holidays respecting these values. Hotel Galatas has become a member.
Hellas Reisen (www.hellas-reisen.de) is a German tour operator which specialises in holidays to Greece and Cyprus, including with walking and culture content. We will handle their holidays on Kythnos from the 2017 season.
Responsible Travel (http://www.responsibletravel.com) promotes environmentally sustainable holidays around the globe with a stringent vetting procedure to ensure members, such as Kythnos Hiking, meet its high standards.
For a full statement of our Responsible Travel policy please click here.
Natural Greece (www.natural-greece.gr) operates nature tours across Greece to see bears, dolphins, flowers, birds and other wildlife. It strongly supports conservation issues. We provide help for their Kythnos nature tours.
Sunvil (https://www.sunvil.co.uk) is a UK tour operator specialising in Greek holidays. We have designed a special package for Sunvil. We also provide assistance on Kythnos to non-walkers sent to the island by Sunvil.
ASI (http://www.asi-reisen.de) is an Austrian hiking tour operator which offers hiking around the world. On Kythnos, it is offering a self-guided programme with the option of upgrading to guided with our guide Katerina Filippa.
Tripin Adventures (https://www.tripin.gr) is a Greek hiking holiday provider offering various trips around Greece, guided and self-guided. Our product for Tripin includes a portion of walking in neighbouring island Serifos.