A natural parameter family is defined as follows

𝑝(𝑥|𝜂)=ℎ(𝑥)𝑒𝑥𝑝(𝜂𝑇(𝑥)+𝐴(𝜂))p(x|η)=h(x)exp(ηT(x)+A(η))where T: sufficient statistics A: log partition function.

We want to prove that the natural parameter space N given by

N={𝜂:∫(𝑒𝑥𝑝(𝐴(𝜂)))<∞}N={η:∫(exp(A(η)))<∞}is convex.

The proof rests on holder inequality and is given here. I am attaching a picture for a quick reference I have looked at the definition of holder inequality. I am not really sure how the 1/𝜆1/λ and 1/1−𝜆1/1−λ are written in the denominator in eq 8.35 when applying the holder inequality in the proof given.

Also in Eq 8.36 how is the $e^{\lambda n^T T(x)} is discared for the integral.

Please help in explaining these things?

Sharing is caring. Below is a consolidated list of most recent news of new RNG infrastructure, facilities or deals being dealt across the U.S. and Canada. RNG just like Uranium is a booming industry that will double or triple by 2025. Below is the prove. On average I estimate over 4-6 new deals coming out per week.

1. Renewable gas producer Archaea surges in debut after SPAC deal Renewable gas producer Archaea surges in debut after SPAC deal | Reuters
2. U.S. RNG Market Expanding as BP, Chevron Snag More Supply Agreements U.S. RNG Market Expanding as BP, Chevron Snag More Supply Agreements - Natural Gas Intelligence
3. Archaea Energy Inc., formerly known as Rice Acquisition Corp., announced Sept. 15 that it has completed its previously announced business combination with Aria Energy LLC and Archaea Energy LLC, creating the industry leading renewable natural gas (RNG) platform. Archaea Energy, Aria Energy close business combination | Biomassmagazine.com
4. Greenlane Renewables Inc. today announced upgrading system supply agreement for $6.1 million (US$4.8 million) for a renewable natural gas (RNG) project in the State of Colorado. Greenlane Renewables signs contract for Colorado RNG project | Biomassmagazine.com
5. FortisBC to reopen its RNG program on Oct. 15 FortisBC to reopen its RNG program on Oct. 15 | Biomassmagazine.com
6. Aemetis Biogas LLC has signed the standard renewable gas interconnection agreement (SRGIA) with the Pacific Gas & Electric Company and funded the final $1.2 million payment for installation of PG&E’s interconnection equipment to deliver renewable natural gas (RNG) Aemetis Biogas signs utility pipeline interconnect agreement | Biomassmagazine.com
7. The Landfill Group, LS Power announce South Carolina RNG project [The Landfill Group, LS Power announce South Carolina RNG project | Biomassmagazine.com](ht

https://youtu.be/W2UT8NjUqrk

Backpropagation is the workhorse of deep learning, but unfortunately, it only works for continuous functions that are amenable to the chain rule of differentiation. Since discrete algorithms have no continuous derivative, deep networks with such algorithms as part of them cannot be effectively trained using backpropagation. This paper presents a method to incorporate a large class of algorithms, formulated as discrete exponential family distributions, into deep networks and derives gradient estimates that can easily be used in end-to-end backpropagation. This enables things like combinatorial optimizers to be part of a network's forward propagation natively.

OUTLINE:

0:00 - Intro & Overview

4:25 - Sponsor: Weights & Biases

6:15 - Problem Setup & Contributions

8:50 - Recap: Straight-Through Estimator

13:25 - Encoding the discrete problem as an inner product

19:45 - From algorithm to distribution

23:15 - Substituting the gradient

26:50 - Defining a target distribution

38:30 - Approximating marginals via perturb-and-MAP

45:10 - Entire algorithm recap

56:45 - Github Page & Example

Paper: https://arxiv.org/abs/2106.01798

Code (TF): https://github.com/nec-research/tf-imle

Code (Torch): https://github.com/uclnlp/torch-imle

AquaPig was stealth launched just over 1 week ago.

The developer was not committed and left shortly after creation, and cashed out their holdings. Left us on the floor.

50 % of the LP was burned, Liq locked, and the ownership was renounced. 5% transaction fee distributes solely to the growth of the Liquidity pool.

Rather than dropping the project, the community then took over the reigns as we saw a lot of potential in this meme.

A new telegram group was made so that the previous developer had no control over the chat if they came back. A few admins were assigned and now it’s being carried on as a full-blown, unruggable community project. In the truest sense.

• through only organic hearsay the community took it from a 10k MC to an ATH near 2m, now consolidating around 1.3m.
• no whale wallets
• fair launched -liquidity is locked forever -truly unruggable community project.
• only 8000 holders, still early
• easy 50x to 100x potential here
• cg and cmc applied
• TechRate Audit Passed
• Everyone is equal.

CONTRACT: 0xce393c06594a5d91210fd4f157cd8f6d86006d57

Being that this is now a community coin, it really has the power of going wherever the community is capable of taking it.

Our website at Aquapig-io

TG is at officialAquaPigBsc

There is a donation wallet set up and if certain milestones in growth and donations are reached, we will further develop use cases and donations will be made to small-local pig farms who are struggling to stay up from the economic turmoil the pandemic has caused. Pigs look out for one another.

I know this is obvious to most of you, but I haven’t seen this specific point brought up much in discussions on Reddit or elsewhere, and I think it’s a really powerful way to argue about the uselessness of all the insane interventions to “slow the spread”.

When you compare the graphs of infections from two areas (say, a state with mask mandates vs a neighboring state without mandates) if something lowers the rate of spread in one state vs another, it’s not gonna just look like one peak is slightly lower than the other; on the contrary, even slight difference in the rates of spread with produce two wildly different graphs.

Let’s say masks, for example, work at preventing spread by even 10% (let alone that doomers routinely claim they offer 50% protection which would make this example even more obviously insane). Let’s also assume a delta R0 of 5 (so without masks an infected person spreads it to 5 people, with a mask an infected person would spread it 10% less, so to 4.5 people). Now let’s look at this example.

City A, run by authoriarian fascist despots require masks (in this example assume mask mandates truly reduce spread by 10%). City B is run by people of normal and doesn’t require masks.

Day 1: both cities have 100 infected people.

First iteration of the infective course runs. Now city A has 450 infected people, city B has 500.

2nd iteration. City A has 2,025 cases. City B has 2,500.

3rd iteration. City A has 9,112 cases, City B has 12,500.

4th iteration. City A has 41,000 cases. City B has 62,500

5th iteration. City A has 184,000 cases. City B has 312,000

Importantly, both cities will reach a maximal amount within the population based on population size (unless R0 can be driven below 1 then essentially everyone will get infected eventually), but city b will hit a much higher peak and will hit it much earlier. That’s just the nature of exponential growth. Minor differences in spread are magnified to the extreme in the setting of exponential growth and the resulting graphs would not appear remotely similar to eachother when using the same axis.

I really want to emphasize this point, because it’s so powerful and should be trivially easy to see in graphical form if there were true benefits to these measures. If masks are 10 percent protective, then the peaks of the one graph will NOT just be 10 percent taller or shorter. The graphs will be wildly different on both the x and y axis.

So the next time someone says mask mandates work, p

Some people seem to think it's not a big deal because the illness it causes is likely less severe. While that may be true, if this new variant is inherently more infectious than Delta (which it almost certainly is, the only question is by how much), it can still lead to overwhelming of hospitals, for one simple reason: while reduced severity will cut hospitalizations, it is still only a constant and thus doesn't change, while the number of new infections is dictated by exponential growth, meaning that cases and hospitalizations will continue to increase, and under most scenarios this will eventually overcome any benefit conferred by reduced severity.

To illustrate this process, let's assume that Omicron is only 1/4 as severe as delta, and only 2x as transmissible, both of which may be fairly optimistic assumptions, particularly the one about transmissibility, since some estimates suggest it might be 4-5x more transmissible. Let's assume that the average doubling time for Delta is 14 days. If Omicron infects twice as many people, that means that 2 weeks into an outbreak, the number of hospitalizations would be 2/4 or half as many as Delta's. So far, so good. But after two doubling periods, or 4 weeks, the number of cases would be quadrupled, meaning hospitalizations would now be on par with delta. After 6 weeks, hospitalizations would be 2^3 /4=8/4= 2x as high as delta, then 4x as high after 8 weeks, and so on until enough people had immunity that the outbreak came to an end.

So the bottom line is, just because the disease may be less severe, doesn't mean it can't ravage the healthcare system. On an individual level, you and your family might be less likely to fall ill, especially if young, healthy, and vaccinated. But on a societal level, both the death toll and the strain on the healthcare system can still end up being much higher than Delta's, and the main driver of this phenomenon would be exponential growth

Bargain Bin Superheroes

(Arc ?, Interlude ?: Archcommander Varney)

(Note: Bargain Bin Superheroes is episodic; each part is self-contained. This story can be enjoyed without reading the previous sections.)

The National High Energy and Temperature Lab was abuzz. Professor Hale bustled into the main containment center, where the primordial plasma they'd been studying for the past ten years was evolving. He gave the Archcommander by his side a friendly nod as he passed.

"It's the most incredible thing," Professor Hale said. "The mass-energy equivalent just keeps going up exponentially! We're lucky the late—or should I say early—Alexandre Hubert wasn't a particularly heavy man; it's all we can do to contain the Hubert particles, given how much energy they're emitting right now."

Archcommander Varney grunted. "Hubert particles, eh? Is that what you eggheads are calling them?"

Professor Hale nodded ruefully. "We scientists, er... we're not great at names. They're often descriptors more than anything."

Archcommander Varney eyed the HEaT Lab name tag on Professor Hale's lapel. "Well, I appreciate your honesty. You said they're emitting energy—could we use them as power sources?"

Professor Hale hesitated. "Not... not yet. We... could try, but there are these discontinuous... jumps. It's impossible to track down everyone who has the Hubert gene—it's a good third of the population, by what we can tell—so we can't really control the rate at which the particles go back in time. We're expecting the Hubert particles to stabilize soon. But!" Professor Hale pointed to a large metal cylinder with several ominously-groaning pipes leading out from it. "In the meantime! We're getting the most fascinating data about high-energy particles; we actually think we've figured out how materializer-type superhumans work. At these energies, we can actually observe higher-dimensional motion—"

Archcommander Varney held up a hand to cut him off. "I read as much in your report. You don't need to butter me up, Hale. Your department's grant has already been approved."

Professor Hale wilted slightly. "I—well, I wasn't after more money, Archcommander. It's simply fascinating how—"

"Professor! Professor!" A flushed, out-of-breath assistant ran up to the two of them. Archcommander Varney gave him a disapproving look, which he ignored. "The Hubert particles—they're—the cosmological dating results came back. We've figured out what time period they're from."

"Oh?" Professor Ha

It includes things like rithym method, Billings Ovulatory Method and such. Now, without all the propaganda and BS the church pushes, what's the real failure rate of these methods in preventing pregnancy ?

Natural Family Planning involves ways of monitoring the body and abstaining from sex during fertile times. It is the only form of family planning condoned by the Catholic church. Does anyone here use it? Do you have a problem with it?

I still can't get over this and I am wondering if anyone feels the same way. Before my husband and I got married, we had to sit through the Archdiocese's mandated "Natural Family Planning" workshop.

We already felt awkward enough being there because we knew we never wanted to have children. (So much so that he's snipped and I am on birth control.) We had a speaker or two on the subject and then we had to watch a video. The video was peak Catholic propaganda but the last part of the video was absolutely horrifying. It was a woman who almost died due to childbirth. She got sick while pregnant and was told the child would most likely kill her and she should have an abortion to save her life. With a smile, she said she decided to bring the child to term because it was a gift from god. And guess what; she almost died. She had 5 other children and a husband and she almost died.

Ok, fine. That's faith. Whatever. The doctors have said that another pregnancy will kill her. But, she said that her and her husband are not using condoms or birth control going forward. (Or abstinence.) They are using Natural Family Planning to make sure she doesn't get pregnant again! I was floored and I literally said "what the f*ck!?" to my husband. This husband and wife would rather use this glorified pull-out method rather than taking the wife's health and children's future with their mother into consideration. She went as far to say if she got pregnant again it was a gift from god and she will continue with the pregnancy.

I'm not going to lie; I had been drifting away from the church slowly at this point. I knew the implications of not having children and the legitimacy of my marriage in the eyes of the church. But to hear this smiling woman saying she didn't care if a pregnancy killed her because it was a gift...

This still bothers me even though I left the church and found a religion that is much better for me. I can't get her face out of my head. I can't stop thinking about her kids and if she died or not. And I can't believe that a church could be so greedy that it would rather choose breeding over the health of their members.

Has anyone else felt this way? I've pretty much made my piece with my time as a Catholic but this is one of the things that still shakes me to the core. I regret not standing up then and there during the video and screaming "are you kidding me!?" Maybe I could have saved some of the people who were at this thing with us.

They are very time consuming to calculate.

For me, since I'm greek I wanna say yin-yin leaning and soft types! I think many SN's, SC's, R's and SD's.