Bonuses. That's what they all seem to be after. Well, I am talking about the workforce at Nepal's ever-reliable public enterprises like Nepal Electricity Authority, Nepal Telecom and Nepal Oil Corporation. Recently, there was much hype in the media about NOC management's efforts to distribute a small fortune to its staff in bonuses for their 'great performance'. While the NOC side said they deserved it for excellent services, others outside the company said they most certainly should not get it. The outsiders suggested, and rightly in my view, that NOC use the profits to improve its infrastructure.
Isn't this ironic? I mean NOC is a public enterprise that imports petroleum products, keeps its cut, and only then supplies these products to distributors, passing the added cost to the helpless motorists. The more oil it sells, the more profit it garners in a country that is 'rich' in water resources (though taps often run dry in its cities and villages). The country can, theoretically, produce thousands of megawatts of electricity to light up not just Nepal but also many parts of South Asia.
As the recent Indian blockade showed, NOC does not have adequate infrastructure to store petroleum products and deal with emergencies like blockades for, say, six months.
You may ask: What's wrong in taxing motorists as they are all affluent folks? Well, most of the motorists may not be that affluent, after all. Most, I am sure, would opt for public transport if there was an efficient and reliable public transport system in place. Basically, these people have been buying and using private vehicles by paying heavy taxes because of the state's inability to develop a public transport system that caters to their needs. And why would it when our ministers and top bureaucrats are free to import SUVs from taxpayer money?
This means motorists have been paying for the absence of the state as a regulator in a transport system where syndicates have long ruled the proverbial roost.
In a country so 'rich' in water resources, PEs like NOC should, in the long run, invest whatever profit they accumulate in generating hydropower so that Nepal is one day completely free from load-shedding. Electricity is greener and cheaper, at least compared to the dirty fossil fuels. So, why should we not go green and reduce our carbon footprint? Just so those at NEA can continue to collect their fat checks and bonuses?
The aim of lighting up the whole of South Asia by exporting Nepal's hydropower through the satellite, the dream of an exceptionally visionary former prime minister, can wait, at least for now. At this juncture, the idea is to reduce our energy dependence on other countries. We can, of course, dream big if are able to get rid of the scourge of power outage completely.
Now more about NEA and NT. These days, in my neighborhood in Nagarjun municipality, electricity supply tends to go off abruptly now and then. I have talked to a number of people in Kathmandu to see whether this problem is prevalent only in my locality. I find that they are all facing the same problem. Is there some foul play that aims to undo what NEA Chief Kul Man Ghising has done? I know not.
One of these days, telephone line also went dead at my home, taking me offline.
Repeated complaints at 198 and some other helplines did not help. So, one day, I went to the NT exchange at Chhauni from where I got this gem of information from a top official: The official said 150 lines at my locality had gone dead because some NEA staffers had cut off phone cables that passed through the poles belonging to the NEA!
While I had gone there to lodge my complaint, I, a helpless member of the public, ended up receiving NT's complaint! The official lamented to me thus: 'We pay them for using their electric poles, and still they do this to us'. How do you reply to that?
Soon after the telephonic disaster, power supply also went off and I started to wonder if NT staffs were paying back their NEA counterparts with the same coin. Whatever the case, consumers were again at the receiving end.
It's public knowledge that officials at NEA and NT are also not shy when it comes to staking their claim on unearned bonuses and other perks, whenever there is an opportunity, by pointing that they have done this and that. Despite their claims, these days, electricity goes off abruptly and so does the phone line. Is it only because of windy weather conditions? In case of electricity, is inverter mafia again trying to disrupt power supply and aspiring to make way for prolonged power outage? Those at the helm of affairs at NEA probably know better.
While staffers at these PEs seldom fail to claim more pay, bonuses and perks, no one comes to the fore when it comes to claiming responsibility for losses arising from unannounced power cuts and disruption in telephony—like breakdown of machines, loss of business, useless trips to PE offices, so on and so forth.
This tendency of claiming benefits and shrugging off responsibility should stop, once and for all. Carrot is fine for excellent service delivery; but these people should also get sticks if they fail to do their jobs properly. It works both ways.
These state monopolies, long used to claiming bonuses and fat paychecks, should be made to pay for losses to the public arising from disruption in services in which they enjoy monopoly. Only then can one expect to get excellent services from these entities. Or am I too optimistic in hoping that these seasoned public sector employees can change their time-worn ways?


text:
Q: SQL query taking Jan Month as 13 instead of 01 SELECT STR_TO_DATE( CONCAT( YEAR(MAX(my_date)) , '-', MONTH(MAX(my_date))+1 , '-', 01 ) , '%Y-%m-%d')

I am using this to extract date. I get following output:
Output        Data Entry till
2017-07-01    2017 June entry complete
2017-08-01    2017 July entry complete

But as soon as the data entry is done for 2017 December I get 2018-13-01 instead of 2018-01-01. I know it is because of the +1 I am adding in month value. I am unsure how do I loop it back to 01 after 12?
The value in csv file for my_date looks like 2017-01-06. It is in string format.

A: You are doing date arithmetic on a string by adding 1 to the month. Instead, use the DateAdd() function.
SELECT date_add(STR_TO_DATE( CONCAT( YEAR(MAX(my_date)) , '-', MONTH(MAX(my_date)) , '-', 01 ) , '%Y-%m-%d'), INTERVAL 1 MONTH)

redpajama_set_name: RedPajamaStackExchange


When we think of obesity, we tend to blame junk food, but diet isn't the only culprit when it comes to weight gain. Discover the lifestyle factor that increases obesity-linked gut microbes.
We all know that junk food is harmful to our health. I recall some friends many years ago referring to cola as "gut rot" and probably for good reason. We all know that soda as well as other junk foods harm our gut health but new research shows that stress can be just as damaging to our gut health as junk food.
In the study, published in the medical journal Nature, researchers found that stress had a significant effect on changing gut microbes among female animals but not on males. The researchers explored the connections between obesity, stress, mood disorders, and gut microbes. They found that the gut microbes of lean female animals changed when they experienced stress to more closely resemble the varieties and volumes of microbes in obese mice. The male animals did not experience the same effect from stress.
As an aside: While stress did not have the adverse effect on males' gut microbes, the researchers also explored the effects of a high fat diet on both female and male mice and they found that males were more likely to experience anxiety caused by eating a high fat diet. But, I digress.
The study shows us that stress, particularly when it becomes chronic, can cause us to gain weight or become obese, so it is imperative that we find coping methods for reducing stress in our lives. Obviously, there are many and some will be more effective than others depending on your unique personality, but here are a few of my favorites: deep breathing, venting with a trusted friend, changing jobs if it is job-related stress, changing homes if housing costs exceed our budget, meditation, exercise, getting out into nature, or into a hot bath with some stress-alleviating essential oils like lavender or vetiver.
While few studies truly examine the ways that different things affect females versus males, this study demonstrates that this should be a consideration in future studies, because clearly there are major differences.
Additionally, the study gives us insight into how stress may be damaging humans, and that it may severely alter metabolism in women by transforming gut microbes to resemble the gut microbes found in obese women. Obviously, more studies need to be done, and human studies in particular, to determine the effects.
Having said that, there is a growing body of research that clearly demonstrate the link between gut microbes and obesity. Another study showed promising results in preventing and treating obesity and related metabolism disorders simply by changing the balance of intestinal flora in favor of the healthy probiotics found in many fermented foods.
In that study scientists examined the effects of administering probiotics and they found that the beneficial microbes balanced blood sugar levels (which in turn, reduces cravings for sweets and fatty foods but also the levels of fat storage hormones in the body). The probiotics also resulted in lower body weight, lower abdominal fat, lower cholesterol and triglyceride levels, all markers for improving obesity.
In addition to reducing the stress in your life as much as possible, you can also increase the variety of fermented foods in your diet to boost beneficial microbes. There are many excellent choices, including: vegan yogurt, sauerkraut (not the pasteurized varieties sold in most grocery stores), kimchi, and kombucha. By eating a range of fermented foods daily you'll increase the number beneficial microbes in your intestines but also increase the diversity of microbes in favor of ones that promote a healthy weight and healthy body and mind.


text:
La Tour de Maria Josepha ( en allemand) est une tour d'observation en acier d'une hauteur de  construite sur le Totenstein ( d'altitude) à Grüna, quartier de Chemnitz, en Saxe, Allemagne.

Histoire

La tour, commandée par l'association régionale des monts Métallifères, a été construite par la serrurerie Viktor Ludwig de Grüna et inaugurée le . Durant les mois d'été, des banquets avaient lieu sous la tour, de sorte qu'elle est devenue un objectif d'excursion populaire. En raison de son entretien déficient, la tour s'est progressivement détériorée jusqu'à être démolie en 1953. À sa place a été construite plus tard une tour hertzienne massive. En 1998, une nouvelle tour d'observation a été construite sur le Totenstein sur le modèle de l'ancienne ; elle a été inaugurée le .

Liens externes
  : tour d'observation actuelle
  : tour hertzienne

Chemnitz
Maria Josepha

redpajama_set_name: RedPajamaWikipedia


text:
Third Global Knowledge Conference
11 - 13 December 2007, Kuala Lumpur, Malaysia
Global Knowledge Partnership (GKP)
The Third Global Knowledge Conference (GK3) is a gathering of 2000 global visionaries, innovators, practitioners and policy makers, all geared to sharing knowledge and building partnerships. It will take place in Kuala Lumpur, Malaysia, from 11 to 13 December 2007. The GK3 theme Emerging People, Emerging markets, Emerging Technologies is a dynamic focus on the interplay, interface and interweaving of issues related to Knowledge for Development and Information and Communication Technologies for Development within the context of evolving societies, economics and technologies worldwide.
As a member of Global Knowledge Partnership (GKP), ICVolunteers organised a round table and participated in a high level panel jointly organized by the Global Alliance for ICT for Development (GAID) and GKP. ICV also lead the cybervolunteering group exhibition together with other NGOs from different parts in the world.
SS4: Special Cross-Cutting Session on Volunteerism
Volunteerism in the Digital Age
Volunteering is a mass social phenomenon and an expression of solidarity in development action involving hundreds of millions of people worldwide. In an era when the international community and decision makers are grappling with the challenges of spreading opportunities for human development as widely as possible, it is timely to consider the role and contribution of Volunteerism in the Digital Age.
Rapid advancement in the field of ICT has made the world more connected. It has also led to a vast divide between those with ICT access and skills, and those without. Without ICT access and skills, people are unable to connect and reap opportunities presented by a networked world, and are thus in danger of being left behind. ICT Volunteerism has a crucial role to play in furthering the Millennium Development Goals (MDGs) and in bridging this divide.
ICT Volunteerism provides one of the solutions to the problem of building human capacity that helps nations harvest the benefits of the digital age for development purposes. It also helps under-served communities to be part of the Information Society, particularly in developing countries, by enabling a transfer of valuable ICT skills and knowledge.
This session organised by GKP and the UN Global Alliance for ICT and Development (UN-GAID) aims to raise awareness on the impact and importance of ICT volunteerism in spreading digital dividends worldwide with examples drawn across sectors and thematic areas covering health, education, disaster management and more. Challenges in delivering ICT volunteerism effectively will also be highlighted. Discussion with participants will revolve around issues of how to sustain volunteer initiatives with the support of public and private sector players, how to enhance collective advocacy on ICT Volunteerism, and how to continue the knowledge sharing on lessons learned.
Barbara Waugh, Director, University Relations Hewlett-Packard Company [presentation]
Paul Jhin, Director of Special Initiatives, Peace Corps Headquarters [presentation]
Quinn Sutton, Executive Director, Digital Alliance Foundation [presentation]
Sobri Ahmad, Secretary-General of the Committee of ASEAN Youth Cooperation [presentation]
Viola Krebs, Executive Director, ICVolunteers [presentation]
Statement on cybervolunteering presented at GK3
Session outline on cybervolunteering panel
More: www.gkpeventsonthefuture.org
Posted: 2007-12-05 Updated: 2007-12-23

redpajama_set_name: RedPajamaCommonCrawl


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Comparison results for Mega Bloks Skylanders Dark Spyro's Battle Portal and Mega Bloks Skylanders Giants Turret Air Raid With Terrafin (95409). What is best?


How literate are Australians? Large-scale studies of grade four children, 15-year-olds, and adults suggest that far too many Australians are struggling with reading and spelling.
This study by the International Association for the Evaluation of Educational Achievement investigates fourth-grade students' reading achievement.
The Australian Council for Educational Research has published highlights of the 2016 PIRLS data from an Australian perspective. Click here to read this document yourself.
Australian kids' average score had improved by 17 points to 544 points since the 2011 study, putting them ahead of kids in 24 countries, but behind 13 countries (see p16 of the report).
However, many kids continue to have serious problems. Only 81% of Australian students met the "proficient" standard (475 points), and 6% of kids fell below the Low standard (400 points). Only 57% of indigenous kids achieved the "proficient" standard and 18% fell below the Low one.
This is an OECD assessment of 15-year-olds' ability to apply learning to real-life situations, which started in 2000. 72 countries were involved in the 2015 study, with 14530 Australian students participating.
Australia was equal 12th in the world on reading, but its students' performance declined by 12 points between 2009 and 2015, a significant change.
Only 61% of Australian students achieved the National Proficient Standard in reading literacy. 11% were high performers and 18% were low performers.
Here's a lay-person's explanation from the Sydney Morning Herald.
The Australian Bureau of Statistics has been involved in surveying adult literacy since 1996, with major reports published then, in 2006 and most recently in early 2013.
Like the earlier surveys, the most recent survey found that a very significant number of Australian adults have very poor literacy skills or are functionally illiterate, and that an astonishing 44% of adults lack the literacy skills required to cope with the complex demands of modern life. No, that is not a typo. Forty-four percent of Australian adults can't read at the level our society expects of them. Why nobody is rioting about this remains a mystery.
For a summary of the most recent data, see the ABS website.


Arizona is a good place to tap into solar power, and this proposal for a solar train that would travel from Tucson to Phoenix does exactly that. The concept is a high speed solar train, that would cover the distance in just 30 minutes, traveling at a maximum speed of 220mph, powered solely by the sun.
To meet logistic purposes, the flexibility of commercial road vehicle is essential. But transportation by road is one of the major reasons of environmental pollution and the planet is paying a high price to increase the economic efficiency. Chiron is a means of transportation designed to minimize the ecological damage which combines the flexibility of road vehicles with the environmental suitability of the railway. This design incorporates the latest 21st century engine that applies an algae-powered fuel cell which will surely increase the business efficiency by minimizing the fuel cost. Moreover, this concept includes satellite tracking system to navigate the supplementary dimension of railroad.
Alstom, a renowned manufacturer of high-speed trains and Citadis trams, collaborating with Stockholm Local traffic department (SL) has come up with an innovative public transportation called the "Autonomous Tram" for the Stockholm city that not only solve the traffic problems, but also give an altogether new face to the Swedish capital. Brainchild of designer Patrik Petersson, the double-decker tram, featuring a Scandinavian design style (both exterior and interior), can carry about 170 passengers comfortably. Being spacious, the tram also presents a clean, open and user-friendly atmosphere to the commuters. Removing a number of seats from the ground floor, the Tram creates an extra space for wheelchairs, prams and luggage; while on the other hand, the top floor promises a thrilling ride, apart from the lovely view of the celebrated city. Moreover, the Autonomous Tram, reducing the number of on road vehicles, helps in improving the environment of the city.


text:
\section{Introduction}

Generative modeling has recently been experiencing a renaissance in modeling efforts driven largely by denoising diffusion probabilistic models (DDPMs). At a high level, DDPMs are trained by learning how to denoise a noisy version of an input example. For example, in the context of computer vision, Gaussian noise may be successively added to an input image, and, with the goals of a DDPM in mind, we would desire for a generative model of images to learn how to successfully distinguish between the original input image's feature signal and the noise signal added to the image thereafter. If a model can achieve such outcomes, we can use the model to generate novel images by first sampling multivariate Gaussian noise and then iteratively removing from the current state of the image the noise predicted by our model. This classic formulation of DDPMs has achieved significant results in the space of image generation (\cite{rombach2022high}), audio synthesis (\cite{kong2020diffwave}), and even meta-learning by learning how to conditionally generate neural network checkpoints (\cite{peebles2022learning}). Furthermore, such an approach to generative modeling has expanded its reach to encompass scientific disciplines such as computational biology (\cite{anand2022protein}), computational chemistry (\cite{xu2022geodiff}), and even computational physics (\cite{mudur2022can}).

Concurrently, the field of geometric deep learning (GDL) (\cite{bronstein2021geometric}) has seen a sizeable increase in research interest lately, driven largely by theoretical advances within the discipline (\cite{joshi2023expressive}) as well as by novel applications of such methodology (\cite{stark2022equibind}). Notably, such applications even include what is considered by many researchers to be a solution to the problem of predicting 3D protein structures from their corresponding amino acid sequences (\cite{jumper2021highly}). Such an outcome arose, in part, from recent advances in sequence-based language modeling efforts (\cite{vaswani2017attention}) as well as from innovations in equivariant neural network modeling (\cite{thomas2018tensor}).

With such diverse, successful use cases of DDPMs and GDL in mind, in this work, we explore the intersection of geometric graph representation learning and DDPMs to answer the following questions.
\begin{itemize}
    \item What is the impact of geometric representation learning on DDPMs designed to generate molecular data?
    \item What are the limitations of current equivariant graph neural networks empowering contemporary molecular DDPMs?
    \item What role do physical inductive biases play within the generative denoising of molecular DDPMs?
\end{itemize}
\section{Related Work}

\textbf{Generative Modeling.} The field of deep generative modeling (\cite{ruthotto2021introduction}) has pioneered a variety of techniques by which to train deep neural networks to create new content similar to that of an existing data repository (e.g., a text dataset of English sentences). Language models such as GPT-3 and ChatGPT (\cite{brown2020language, schulman2022chatgpt}) have become known as hallmark examples of successful generative modeling of text data. In the domains of computer vision and computational biology, techniques such as latent diffusion (\cite{rombach2022high}) and equivariant graph diffusion (\cite{luo2022antigen}) have established some of the latest state-of-the-art results in generative modeling of images and biomolecules such as proteins, respectively.

\textbf{Geometric Deep Learning.} Data residing in a geometric or physical space (e.g., $\mathbb{R}^{3}$) can be processed by machine learning algorithms in a plethora of ways. However, in recent years, the field of geometric deep learning has become known for its proficiency in introducing powerful new deep learning methods designed specifically to process geometric data efficiently (\cite{cao2020comprehensive}). Examples of popular GDL algorithms include convolutional neural networks designed for working with image data (\cite{lecun1995convolutional}), recurrent neural networks for processing sequence-based data (\cite{medsker1999recurrent}), and graph neural networks for handling graph-structured model inputs (\cite{zhou2020graph}).

\textbf{Equivariant Neural Networks.} To process geometric data efficiently, however, recent GDL research (\cite{cohen2016group, bronstein2021geometric, bulusu2021generalization}) has specifically shown that designing one's machine learning algorithm to be equivariant to the symmetry groups the input data points naturally respect (e.g., 3D rotation symmetries) often helps such an algorithm generalize to datasets beyond those used for its cross-validation (e.g., training and testing datasets). As a particularly relevant example of a neural network that is equivariant to several important and common symmetry groups of geometric data, equivariant graph neural networks (\cite{fuchs2020se, satorras2021n, kofinas2021roto, morehead2022geometry}) that are translation and rotation equivariant to inputs residing in $\mathbb{R}^{3}$ have become known as hallmark examples of geometric deep learning algorithms that generalize remarkably well to new inputs and require notably fewer training iterations to converge.

\textbf{Representation Learning of Scientific Data.} Scientific data, in particular, requires careful consideration in the context of representation learning. As much scientific data contains within it a notion of geometry or latent structure, equivariance has become a key algorithmic component for processing such inputs as well (\cite{han2022geometrically}). Moreover, equivariant graph representation learning algorithms have recently become a de facto methodology for processing scientific data of many shapes and origins \cite{musaelian2022learning, batzner20223}.

\textbf{Contributions.} In this work, we connect ideas at the forefront of GDL and generative modeling to advance the state-of-the-art (SOTA) for 3D molecule generation. In detail, we provide the following contributions.
\begin{itemize}
    \item We introduce the Geometry-Complete Diffusion Model (\textsc{GCDM}) which establishes new SOTA results for unconditional 3D molecule generation.
    \item We investigate the impact of geometric message-passing on the behavior and performance of DDPMs trained to generate 3D molecular data.
    \item Our experiments demonstrate the importance of incorporating physical inductive biases within DDPM denoising neural networks when training them on data from physical domains.
\end{itemize}
\section{Preliminaries}
\subsection{Diffusion Models}
Key to understanding our contributions in this work are denoising diffusion probabilistic models. As alluded to previously, once trained, DDPMs can generate new data of arbitrary shapes, sizes, formats, and geometries by learning to reverse a noising process acting on each model input. More precisely, for a given data point $\mathbf{x}$, a diffusion process adds noise to $\mathbf{x}$ for time step $t = 0, 1, ..., T$ to yield $\mathbf{z}_{t}$, a noisy representation of the input $\mathbf{x}$ at time step $t$. Such a process is defined by a multivariate Gaussian distribution:
\begin{equation}
    \label{equation:standard_denoising_distribution}
    q(\mathbf{z}_{t} | x) = \mathcal{N}(\mathbf{z}_{t} | \alpha_{t} \mathbf{x}_{t}, \sigma_{t}^{2} \mathbf{I}),
\end{equation}
where $\alpha_{t} \in \mathbb{R}^{+}$ regulates how much feature signal is retained and $\sigma_{t}^{2}$ modulates how much feature noise is added to input $\mathbf{x}$. Note that we typically model $\alpha$ as a function defined with smooth transitions from $\alpha_{0} = 1$ to $\alpha_{T} = 0$, where a special case of such a noising process, the variance preserving process (\cite{sohl2015deep, ho2020denoising}), is defined by $\alpha_{t} = \sqrt{1 - \sigma_{t}^{2}}$. To simplify notation, in this work, we define the feature signal-to-noise ratio as SNR($t$)$\ = \alpha_{t}^{2} / \sigma_{t}^{2}$. Also interesting to note is that this diffusion process is Markovian in nature, indicating that we have transition distributions as follows:
\begin{equation}
    q(\mathbf{z}_{t} | \mathbf{z}_{s}) = \mathcal{N}(\mathbf{z}_{t} | \alpha_{t | s} \mathbf{z}_{s}, \sigma_{t | s}^{2} \mathbf{I}),
\end{equation}
for all $t > s$ with $\alpha_{t | s} = \alpha_{t} / \alpha_{s}$ and $\sigma_{t | s}^{2} = \sigma_{t}^{2} - \alpha_{t | s}^{2} \sigma_{s}^{2}$.
In total, then, we can write the noising process as:
\begin{equation}
    q(\mathbf{z}_{0}, \mathbf{z}_{1}, ..., \mathbf{z}_{T} | \mathbf{x}) = q(\mathbf{z}_{0} | x) \prod_{t = 1}^{T} q(\mathbf{z}_{t} | \mathbf{z}_{t - 1}).
\end{equation}
If we then define $\bm{\mu}_{t \rightarrow s}(\mathbf{x}, \mathbf{z}_{t})$ and $\sigma_{t \rightarrow s}$ as
\begin{align*}
    \bm{\mu}_{t \rightarrow s}(\mathbf{x}, \mathbf{z}_{t}) = \frac{\alpha_{t | s} \sigma_{s}^{2}}{\sigma_{t}^{2}}\mathbf{z}_{t} + \frac{\alpha_{s} \sigma_{t | s}^{2}}{\sigma_{t}^{2}}\mathbf{x}\ \mbox{ and }\ \sigma_{t \rightarrow s} = \frac{\sigma_{t | s} \sigma_{s}}{\sigma_{t}},
\end{align*}
we have that the inverse of the noising process, the \textit{true denoising process}, is given by the posterior of the transitions conditioned on $\mathbf{x}$, a process that is also Gaussian:
\begin{equation}
    \label{equation:true_denoising_process}
    q(\mathbf{z}_{s} | \mathbf{x}, \mathbf{z}_{t}) = \mathcal{N}(\mathbf{z}_{s} | \bm{\mu}_{t \rightarrow s}(\mathbf{x}, \mathbf{z}_{t}), \sigma_{t \rightarrow s} \mathbf{I}).
\end{equation}

\textbf{The Generative Denoising Process.} In diffusion models, we define the generative process according to the \textit{true denoising process}. However, for such a denoising process, we do not know the value of $\mathbf{x}$ \textit{a priori}, so we typically approximate it as $\hat{\mathbf{x}} = \phi(\mathbf{z}_{t}, t)$ using a neural network $\phi$. Doing so then lets us express the generative transition distribution $p(\mathbf{z}_{s} | \mathbf{z}_{t})$ as $q(\mathbf{z}_{s} | \hat{\mathbf{x}}(\mathbf{z}_{t}, t), \mathbf{z}_{t})$. As a practical alternative to Eq. \ref{equation:true_denoising_process}, we can represent this expression using our approximation for $\hat{\mathbf{x}}$:
\begin{equation}
    p(\mathbf{z}_{s} | \mathbf{z}_{t}) = \mathcal{N}(\mathbf{z}_{s} | \bm{\mu}_{t \rightarrow s}(\hat{\mathbf{x}}, \mathbf{z}_{t}), \sigma_{t \rightarrow s}^{2} \mathbf{I}).
\end{equation}
If we choose to define $s$ as $s = t - 1$, then we can derive the variational lower bound on the log-likelihood of $\mathbf{x}$ given our generative model as:
\begin{equation}
    \log p(\mathbf{x}) \ge \mathcal{L}_{0} + \mathcal{L}_{base} + \sum_{t = 1}^{T} \mathcal{L}_{t},
\end{equation}
where we note that $\mathcal{L}_{0} = \log p(\mathbf{x} | \mathbf{z}_{0})$ models the likelihood of the data given its noisy representation $\mathbf{z}_{0}$, $\mathcal{L}_{base} = -\mbox{KL}(q(\mathbf{z}_{T} | \mathbf{x}) | p(\mathbf{z}_{T}))$ models the difference between a standard normal distribution and the final latent variable $q(\mathbf{z}_{T} | \mathbf{x})$, and
\begin{align*}
    \mathcal{L}_{t} = -\mbox{KL}(q(\mathbf{z}_{s} | \mathbf{x}, \mathbf{z}_{t}) | p(\mathbf{z}_{s} | \mathbf{z}_{t})) \ \mbox{ for } t = 1, 2, ..., T.
\end{align*}
Note that, in this formation of diffusion models, our neural network $\phi$ directly predicts $\hat{\mathbf{x}}$. However, \cite{ho2020denoising} and others have found optimization of $\phi$ to be made much easier when instead predicting the Gaussian noise added to $\mathbf{x}$ to create $\hat{\mathbf{x}}$. An intuition for how this changes the neural network's learning dynamics is that, when predicting back the noise added to the model's input, the network is being trained to more directly differentiate which part of $\mathbf{z}_{t}$ corresponds to the input's feature signal (i.e., the underlying data point $\mathbf{x}$) and which part corresponds to added feature noise. In doing so, if we let $\mathbf{z}_{t} = \alpha_{t}\mathbf{x} + \sigma_{t}\bm{\epsilon}$, our neural network can then predict $\hat{\bm{\epsilon}} = \phi(\mathbf{z}_{t}, t)$ such that:
\begin{equation}
    \hat{\mathbf{x}} = (1 / \alpha_{t})\ \mathbf{z}_{t} - (\sigma_{t} / \alpha_{t})\ \hat{\bm{\epsilon}}.
\end{equation}
\cite{kingma2021variational} and others have since shown that, when parametrizing our denoising neural network in this way, the loss term $\mathcal{L}_{t}$ reduces to:
\begin{equation}
    \label{equation:noise_parametrization}
    \mathcal{L}_{t} = \mathbb{E}_{\bm{\epsilon} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})}\left[\frac{1}{2}(1 - \mbox{SNR}(t - 1) / \mbox{SNR}(t)) \norm{\bm{\epsilon} - \hat{\bm{\epsilon}}}^{2} \right]
\end{equation}
Note that, in practice, the loss term $\mathcal{L}_{base}$ should be close to zero when using a noising schedule defined such that $\alpha_{T} \approx 0$. Moreover, if and when $\alpha_{0} \approx 1$ \textit{and} $\mathbf{x}$ is a discrete value, we will find $\mathcal{L}_{0}$ to be close to zero as well.

\subsection{SE(3) Equivariance}
\label{section:se3_equivariance}
In this work, we will consider designing denoising neural networks, here denoted as $f$, that are equivariant to the action of the special Euclidean group (i.e., \textit{SE}(3)). We say that a function $f$ is equivariant to the action of a group $G$ if, for all $g \in G$, we have $T_{g}(f(\mathbf{x})) = f(S_{g}(\mathbf{x}))$, where $T_{g}$ and $S_{g}$ are linear representations associated with the group element $g$ (\cite{serre1977linear}). Given that we are considering the SE(3) group, which is generated by 3D translations and rotations, we can represent $T_{g}$ and $S_{g}$ by a translation $\mathbf{t}$ and an orthogonal matrix $\mathbf{R}$ that rotates coordinates. Then we consider $f$ to be equivariant to a rotation $\mathbf{R}$ if transforming its input $\mathbf{x}$ yields an equivalent transformation of its output, that is, we have $\mathbf{R}f(\mathbf{x}) = f(\mathbf{R}\mathbf{x})$.

\textbf{Diffusion Models and Equivariant Distributions.} In this work, we desire for the marginal distribution $p(\mathbf{x})$ of our denoising neural network to be an invariant distribution. We begin by observing that a conditional distribution $p(y | x)$ is equivariant to the action of 3D rotations by meeting the criterion:
\begin{equation}
    p(y | x) = p(\mathbf{R}y | \mathbf{R}x)\ \mbox{ for all orthogonal } \mathbf{R}.
\end{equation}
Moreover, a distribution is invariant to rotation transformations $\mathbf{R}$ when
\begin{equation}
    p(y) = p(\mathbf{R}y)\ \mbox{ for all orthogonal } \mathbf{R}.
\end{equation}
As \cite{kohler2020equivariant} and \cite{xu2022geodiff} have collectively demonstrated, we know that if $p(\mathbf{z}_{T})$ is invariant and the neural network we use to parametrize $p(\mathbf{z}_{t - 1} | \mathbf{z}_{t})$ is equivariant, we have, as desired, that the marginal distribution $p(\mathbf{x})$ of our denoising model is an invariant distribution.

\textbf{SE(3)-Equivariant Points and Features.} In the context of our work, we represent a point cloud as a fully-connected 3D graph $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ with $\mathbf{X} = (\mathbf{x}_{1}, \mathbf{x}_{2}, ..., \mathbf{x}_{N}) \in \mathbb{R}^{N \times 3}$ as the respective Cartesian coordinates for each node, where $N = |\mathcal{V}|$ and $E = |\mathcal{E}|$. Each node is described by scalar features $\mathbf{H} \in \mathbb{R}^{N \times h}$ and $m$ vector-valued features $\bm{\chi} \in \mathbb{R}^{N \times (m \times 3)}$. Likewise, each edge is described by scalar features $\mathbf{E} \in \mathbb{R}^{E \times e}$ and $x$ vector-valued features $\bm{\xi} \in \mathbb{R}^{E \times (x \times 3)}$. Important to note is that the features $\mathbf{H}$ and $\mathbf{E}$ are invariant to rotations, reflections, and translations, whereas the features $\bm{\chi}$ and $\bm{\xi}$ are equivariant to rotations and reflections. In particular, we describe a function $\bm{\Phi}$ as \textit{SE}(3)-equivariant if it satisfies the following constraint:
\begin{definition}
    \label{definition:equivariance_constraint}
    (SE(3) Equivariance)\textbf{.} \\ \\
    Given $(\mathbf{H}', \mathbf{E}', \mathbf{X}', \bm{\chi}', \bm{\xi}') = \bm{\Phi}(\mathbf{H}, \mathbf{E}, \mathbf{X}, \bm{\chi}, \bm{\xi})$, \\
    we have $(\mathbf{H}^{\prime}, \mathbf{E}^{\prime}, \mathbf{Q}\mathbf{X}^{\prime^{\mathrm{T}}} + \mathbf{g}, \mathbf{Q}\bm{\chi}^{\prime^{\mathrm{T}}}, \mathbf{Q}\bm{\xi}^{\prime^{\mathrm{T}}}) = \bm{\Phi}(\mathbf{H}, \mathbf{E}, \mathbf{Q}\mathbf{X}^{\mathrm{T}} + \mathbf{g}, \mathbf{Q}\bm{\chi}^{\mathrm{T}}, \mathbf{Q}\bm{\xi}^{\mathrm{T}})$, \\ $\quad \forall \mathbf{Q} \in \textit{SO}(3), \forall \mathbf{g} \in \mathbb{R}^{3 \times 1}$.
\end{definition}

\textbf{Geometry-Complete Perceptron Networks.} \textsc{GCPNets} are a type of geometric Graph Neural Network that satisfies our SE(3) equivariance constraint (\ref{definition:equivariance_constraint}). In this setting, with ($h_{i} \in \mathbf{H}$, $\chi_{i} \in \bm{\chi}$, $e_{ij} \in \mathbf{E}, \xi_{ij} \in \bm{\xi}$), \textsc{GCPNet} consists of a composition of Geometry-Complete Graph Convolution ($\mathbf{GCPConv}$) layers $(h_{i}^{l}, \chi_{i}^{l}), x_{i}^{l} = \mathbf{GCPConv}[(h_{i}^{l - 1}, \chi_{i}^{l - 1}), (e_{ij}^{0}, \xi_{ij}^{0}), x_{i}^{l - 1}, \mathcal{F}_{ij}]$ which are defined as:
\begin{equation}
    n_{i}^{l} = \phi^{l}(n_{i}^{l - 1}, \mathcal{A}_{\forall j \in \mathcal{N}(i)} \Omega_{\omega}^{l}(n_{i}^{l - 1}, n_{j}^{l - 1}, e_{ij}, \mathcal{F}_{ij})),
\end{equation}
where $n_{i}^{l} = (h_{i}^{l}, \chi_{i}^{l})$; $e_{ij}=(e_{ij}^{0}, \xi_{ij}^{0})$; $\phi$ is a trainable function; $l$ signifies the representation depth of the network; $\mathcal{A}$ is a permutation-invariant aggregation function; $\Omega_{\omega}$ represents a message-passing function corresponding to the $\omega$-th $\mathbf{GCP}$ message-passing layer; and $\bm{\mathcal{F}}_{ij}^{t} = (a_{ij}^{t}, b_{ij}^{t}, c_{ij}^{t})$, with $a_{ij}^{t} = \frac{x_{i}^{t} - x_{j}^{t}}{ \lVert x_{i}^{t} - x_{j}^{t} \rVert }, b_{ij}^{t} = \frac{x_{i}^{t} \times x_{j}^{t}}{ \lVert x_{i}^{t} \times x_{j}^{t} \rVert },$ and $c_{ij}^{t} = a_{ij}^{t} \times b_{ij}^{t}$, respectively.

Lastly, if one desires to update the positions of each node in $\mathcal{G}$, as we do in the context of 3D molecule generation, $\mathbf{GCPConv}$ provides a simple, SE(3)-equivariant method to do so using a dedicated $\mathbf{GCP}$ module as follows:
\begin{align}
    (h_{p_{i}}^{l}, \chi_{p_{i}}^{l}) &= \mathbf{GCP}_{p}^{l}(n_{i}^{l}, \mathcal{F}_{ij}) \\
    x_{i}^{l} &= x_{i}^{l - 1} + \chi_{p_{i}}^{l}, \mbox{where } \chi_{p_{i}}^{l} \in \mathbb{R}^{1 \times 3},
\end{align}
where $\mathbf{GCP}_{\cdot}^{l}(\cdot, \mathcal{F}_{ij})$ is defined as in (\cite{morehead2022geometry}) to provide rotation and translation invariant updates to $h_{i}$ and rotation equivariant updates to $\chi_{i}$ following centralization of the input point cloud's coordinates $\mathbf{X}$ (\cite{du2022se}). The effect of using feature updates to $\chi_{i}$ to update $x_{i}$ is, after decentralizing $\mathbf{X}$ following the final $\mathbf{GCPConv}$ layer, that updates to $x_{i}$ then become SE(3)-equivariant. As such, all the transformations described above collectively satisfy the required equivariance constraint in Def. \ref{definition:equivariance_constraint}. Important to note is that, (1) \textsc{GCPNet} performs message passing directly using vector-valued features corresponding to nodes and edges instead of performing insufficient approximations of such geometric quantities using only scalar features, and (2) \textsc{GCPNet} incorporates a biophysical inductive bias concerning reflection symmetries (e.g., molecular chirality) into the network architecture by encoding into the network's updates to scalar and vector-valued features geometric frames that are not reflection equivariant. For a more detailed description of the subcomponents within \textsc{GCPNet}, we refer interested readers to \cite{morehead2022geometry}.

\section{\textsc{GCDM}: A Geometry-Complete Diffusion Model}

\begin{figure*}[t]
\centering
\includegraphics[width=\textwidth]{images/gcdm}
\caption{A framework overview for our proposed \textit{Geometry-Complete Diffusion Model} (\textsc{GCDM}). Our framework consists of (\textbf{i.}) a graph (topology) definition process, (\textbf{ii.}) a \textsc{GCPNet}-based graph neural network for 3D graph representation learning, (\textbf{iii.}) denoising of 3D input graphs using \textsc{GCPNet}, and (\textbf{iv.}) application of a trained \textsc{GCPNet} denoising network for 3D molecule generation. Zoom in for the best viewing experience.}
\label{figure:gcdm}
\end{figure*}

In this section, we describe \textsc{GCDM}, a new Geometry-Complete SE(3)-Equivariant Diffusion Model, which is illustrated in Figure \ref{figure:gcdm}. In particular, we describe how \textsc{GCDM} defines a noising process jointly on equivariant node positions $\mathbf{X}$ and invariant node features $\mathbf{H}$ and learns a generative \textit{denoising} process using \textsc{GCPNet}.

\subsection{The Diffusion Process}
\label{section:gcdm_diffusion_process}
In this work, we define an equivariant diffusion process for equivariant node coordinates $\mathbf{x}_{i}$ and invariant node features $\mathbf{h}_{i}$, one that adds random noise to such input data. Recall that the graph inputs to our model, $\mathcal{G}$, associate with each node a coordinate representation $\mathbf{x}_{i} \in \mathbb{R}^{3}$ and a feature vector $\mathbf{h} \in \mathbb{R}^{h}$. Subsequently, let $[\cdot, \cdot]$ denote the concatenation of two variables. We then define our equivariant noising process on latent variables $\mathbf{z}_{t} = [\mathbf{z}_{t}^{(x)}, \mathbf{z}_{t}^{(h)}]$ as:
\begin{equation}
    \label{equation:latent_variables_concat}
    q(\mathbf{z}_{t} | \mathbf{x}, \mathbf{h}) = \mathcal{N}_{xh}(\mathbf{z}_{t} | \alpha_{t}[\mathbf{x}, \mathbf{h}], \sigma_{t}^{2} \mathbf{I})\ \mbox{ for }\ t = 1, 2, ..., T,
\end{equation}
where we use $\mathcal{N}_{xh}$ as concise notation to denote the product of two distributions. In this context, the former distribution represents the noised node coordinates $\mathcal{N}_{x}$, and the latter distribution represents the noised node features $\mathcal{N}_{h}$. Being as such, $\mathcal{N}_{xh}$ is given by:
\begin{equation}
    \label{equation:latent_variables_separate}
    \mathcal{N}_{x}(\mathbf{z}_{t}^{(x)} | \alpha_{t} \mathbf{x}, \sigma_{t}^{2} \mathbf{I}) \cdot \mathcal{N}_{h}(\mathbf{z}_{t}^{(h)} | \alpha_{t} \mathbf{h}, \sigma_{t}^{2} \mathbf{I}).
\end{equation}
Note that, with the context of a standard diffusion model in mind, these two equations, Eqs. \ref{equation:latent_variables_concat} and \ref{equation:latent_variables_separate}, correspond to Eq. \ref{equation:standard_denoising_distribution}. To address the translation invariance issue raised by \cite{satorras2021f} in the context of handling a distribution over 3D coordinates, we adopt the zero center of gravity trick proposed by \cite{xu2022geodiff} to define $\mathcal{N}_{x}$ as a normal distribution on the subspace defined by $\sum_{i}\mathbf{x}_{i} = \mathbf{0}$. However, to handle node features $\mathbf{h}_{i}$ that are rotation, reflection, and translation-invariant, we can instead use a conventional normal distribution $\mathcal{N}$.

\textbf{\textsc{GCDM} Generative Denoising Process.} Recall that we need to address the noise posteriors to define a generative process for \textsc{GCDM}. In a similar manner as in Eq. \ref{equation:true_denoising_process}, we can directly use the noise posteriors $q(\mathbf{z}_{s} | \mathbf{x}, \mathbf{h}, \mathbf{z}_{t})$ of Eq. \ref{equation:latent_variables_concat}. To do so, we must replace the input variables $\mathbf{x}$ and $\mathbf{h}$ with the approximations $\hat{\mathbf{x}}$ and $\hat{\mathbf{h}}$ predicted by our denoising neural network:
\begin{equation}
    \label{equation:gcdm_denoising_equation}
    p(\mathbf{z}_{s} | \mathbf{z}_{t}) = \mathcal{N}_{xh}(\mathbf{z}_{s} | \bm{\mu}_{t \rightarrow s}([\hat{\mathbf{x}}, \hat{\mathbf{h}}], \mathbf{z}_{t}), \sigma_{t \rightarrow s}^{2} \mathbf{I}),
\end{equation}
where our values for $\hat{\mathbf{x}}$ and $\hat{\mathbf{h}}$ depend on $\mathbf{z}_{t}$, $t$, and our denoising neural network $\phi$. As mentioned previously, it is often easier to optimize a diffusion model using a noise parametrization to predict the noise $\hat{\mathbf{\epsilon}}$. In this work, we use such a parametrization to predict $\hat{\mathbf{\epsilon}} = [\hat{\mathbf{\epsilon}}^{(x)}, \hat{\mathbf{\epsilon}}^{(h)}]$, which represents the noise individually added to $\hat{\mathbf{x}}$ and $\hat{\mathbf{h}}$. We can then use the predicted $\hat{\mathbf{\epsilon}}$ to derive:
\begin{equation}
    \label{equation:noise_parametrization_outputs}
    [\hat{\mathbf{x}}, \hat{\mathbf{h}}] = \mathbf{z}_{t} / \alpha_{t} - \hat{\bm{\epsilon}}_{t} \cdot \sigma_{t} / \alpha_{t}.
\end{equation}
Observe that rotating $\mathbf{z}_{t}$ with $\mathbf{R}$ yields $\mathbf{R}\hat{\bm{\epsilon}} = (\phi(\mathbf{R} \mathbf{z}_{t}, t))$. Moreover, since the mean of the denoising distribution (\ref{equation:gcdm_denoising_equation}), one that uses isotropic noise, rotates as $\mathbf{R}\hat{\mathbf{x}} = \mathbf{R}\mathbf{z}_{t}^{(x)} / \alpha_{t} - \mathbf{R}\hat{\bm{\epsilon}}_{t}^{(x)} \sigma_{t} / \alpha_{t}$, the distribution is equivariant.

Sampling from the model involves sampling $\mathbf{z}_{T} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$ and then iteratively sampling $\mathbf{z}_{t} \sim p(\mathbf{z}_{t - 1} | \mathbf{z}_{t})$ for $t = T, T - 1, ..., 1$. Lastly, we can sample $\mathbf{x}, \mathbf{h} \sim p(\mathbf{x}, \mathbf{h} | \mathbf{z}_{0})$. For a high-level overview of the sampling algorithm for diffusion models such as \textsc{GCDM}, we refer interested readers to \cite{hoogeboom2022equivariant}.

\textbf{\textsc{GCDM} Optimization Objective.} When we use the noise parametrization referred to in Eq. \ref{equation:noise_parametrization}, the likelihood term of our model, $\mathcal{L}_{t} = -\mbox{KL}(q(\mathbf{z}_{s} | \mathbf{x}, \mathbf{z}_{t}) | p(\mathbf{z}_{s}, \mathbf{z}_{t}))$, notably simplifies. Similar to \cite{hoogeboom2022equivariant}, with this parametrization, we observe that $\mathcal{L}_{t}$ reduces to
\begin{equation}
    \mathcal{L}_{t} = \mathbb{E}_{\bm{\epsilon}_{t} \sim \mathcal{N}_{xh}(\mathbf{0}, \mathbf{I})}\left[\frac{1}{2} w(t) \lVert \bm{\epsilon}_{t} - \hat{\bm{\epsilon}}_{t} \rVert^{2}\right],
\end{equation}
where $\hat{\bm{\epsilon}}_{t} = \phi(\mathbf{z}_{t}, t)$ and $w(t) = (1 - \mbox{SNR}(t - 1) / \mbox{SNR}(t))$. Following \cite{ho2020denoising}, \cite{hoogeboom2022equivariant}, and others, practically speaking, we set $w(t) = 1$ to stabilize training and improve sample quality. For a high-level overview of the optimization algorithm for diffusion models such as \textsc{GCDM}, we refer interested readers once again to \cite{hoogeboom2022equivariant}.

To summarize, we have defined a diffusion process, a denoising model, and an optimization objective function between them. We now need to define the neural network model $\phi$ that we will reside within the denoising model.

\subsection{Equivariant Dynamics}
We use our previous definition of \textsc{GCPNet} in Section \ref{section:se3_equivariance} to learn an SE(3)-equivariant dynamics function $[\hat{\bm{\epsilon}}^{(x)}, \hat{\bm{\epsilon}}^{(h)}] = \phi(\mathbf{z}_{t}^{(x)}, \mathbf{z}_{t}^{(h)}, t)$ as:
\begin{equation}
    \hat{\bm{\epsilon}}_{t}^{(x)}, \hat{\bm{\epsilon}}_{t}^{(h)} = \textsc{GCPNet}(\mathbf{z}_{t}^{(x)}, [\mathbf{z}_{t}^{(h)}, t / T]) - [\mathbf{z}_{t}^{(x)}, \mathbf{0}],
\end{equation}
where we inform our denoising model of the current time step by concatenating $t / T$ as an additional node feature and where we subtract the coordinate representation outputs of \textsc{GCPNet} from its coordinate representation inputs after subtracting from the coordinate representation outputs their collective center of gravity. With the parametrization in Eq. \ref{equation:noise_parametrization_outputs}, we have subsequently achieved rotation equivariance on $\hat{\mathbf{x}}_{i}$.

\subsection{Zeroth Likelihood Terms}
For the zeroth likelihood terms corresponding to each type of input feature, we adopt the respective terms previously derived by \cite{hoogeboom2022equivariant}. In particular, for integer node features, we adopt the zeroth likelihood term:
\begin{equation}
    \label{equation:node_integer_feature_likelihood}
    p(\mathbf{h} | \mathbf{z}_{0}^{(h)}) = \int_{\mathbf{h} - \frac{1}{2}}^{\mathbf{h} + \frac{1}{2}} \mathcal{N}(\mathbf{u} | \mathbf{z}_{0}^{(h)}, \sigma_{0}) \mbox{d}\mathbf{u},
\end{equation}
where we use the CDF of a standard normal distribution, $\Phi$, to compute Eq. \ref{equation:node_integer_feature_likelihood} as $\Phi((\mathbf{h} + \frac{1}{2} - \mathbf{z}_{0}^{(h)}) / \sigma_{0}) - \Phi((\mathbf{h} - \frac{1}{2} - \mathbf{z}_{0}^{(h)}) / \sigma_{0}) \approx 1$ for reasonable noise parameters $\alpha_{0}$ and $\sigma_{0}$. For categorical node features, we instead use the zeroth likelihood term:
\begin{equation}
    p(\mathbf{h} | \mathbf{z}_{0}^{(h)}) = C(\mathbf{h} | \mathbf{p}), \mathbf{p} \propto \int_{1 - \frac{1}{2}}^{1 + \frac{1}{2}} \mathcal{N}(\mathbf{u} | \mathbf{z}_{0}^{(h)}, \sigma_{0}) \mbox{d}\mathbf{u},
\end{equation}
where we normalize $\mathbf{p}$ to sum to one and where $C$ is a categorical distribution. Lastly, for continuous node positions, we adopt the zeroth likelihood term:
\begin{equation}
    p(\mathbf{x} | \mathbf{z}_{0}^{(x)}) = \mathcal{N}\left(\mathbf{x} | \mathbf{z}_{0}^{(x)} / \alpha_{0} - \sigma_{0} / \alpha_{0} \hat{\bm{\epsilon}}_{0}, \sigma_{0}^{2} / \alpha_{0}^{2}\mathbf{I}\right)
\end{equation}
which gives rise to the log-likelihood component $\mathcal{L}_{0}^{(x)}$ as:
\begin{equation}
    \mathcal{L}_{0}^{(x)} = \mathbb{E}_{\bm{\epsilon}^{(x)} \sim \mathcal{N}_{x}(\mathbf{0}, \mathbf{I})}\left[\log Z^{-1} - \frac{1}{2} \lVert \bm{\epsilon}^{x} - \phi^{(x)}(\mathbf{z}_{0}, 0) \rVert^{2} \right],
\end{equation}
where $d = 3$ and the normalization constant $Z = (\sqrt{2\pi} \cdot \sigma_{0} / \alpha_{0})^{(N - 1) \cdot d}$ - in particular, its $(N - 1) \cdot d$ term - arises from the zero center of gravity trick mentioned in Section \ref{section:gcdm_diffusion_process}.

\textbf{Scaling Node Features.}
In line with \cite{hoogeboom2022equivariant}, to improve the log-likelihood of our model's generated samples, we find it useful to train and perform sampling with our model using scaled node feature inputs as $[\mathbf{x}, \frac{1}{4} \mathbf{h}^{(categorical)}, \frac{1}{10} \mathbf{h}^{(integer)}]$.

\textbf{Deriving The Number of Atoms.}
Finally, to determine the number of atoms with which our model will generate a 3D molecule, we first sample $N \sim p(N)$, where $p(N)$ denotes the categorical distribution of molecule sizes over the model's training dataset. Then, we conclude by sampling $\mathbf{x}, \mathbf{h} \sim p(\mathbf{x}, \mathbf{h} | N)$.

\begin{table}[ht]
    \caption{Comparison of \textsc{GCPNet} with baseline methods for 3D molecule generation. The results are reported in terms of each method's negative log-likelihood (NLL) - $\log p(\mathbf{x}, \mathbf{h}, N)$, atom stability, and molecule stability with standard deviations across three runs on QM9, each drawing 10,000 samples from the model. The top-1 (best) results for this task are in \textbf{bold}, and the second-best results are \underline{underlined}.}
    \label{table:3dmg_stability_results}
    \centering
    \footnotesize
    \begin{tabular}{lllll}
        & & & & \\ \midrule
        Type & Method & NLL \ $\downarrow$ & Atoms Stable (\%)\ $\uparrow$ & Mol Stable (\%)\ $\uparrow$ \\ \midrule
        Normalizing Flow & E-NF & -59.7 & 85.0 & 4.9 \\ \midrule
        Graph Autoregression & G-Schnet & N/A & 95.7 & 68.1 \\ \midrule
        DDPM & GDM & -94.7 & 97.0 & 63.2 \\
        & GDM-aug & -92.5 & 97.6 & 71.6 \\
        & EDM & -110.7 $\pm$ 1.5 & 98.7 $\pm$ 0.1 & 82.0 $\pm$ 0.4 \\
        & Bridge & & 98.7 $\pm$ 0.1 & 81.8 $\pm$ 0.2 \\
        & Bridge + Force & & \textbf{98.8} $\pm$ 0.1 & \underline{84.6} $\pm$ 0.3 \\ \midrule
        DDPM - Ours & \textsc{GCDM} w/o Frames & \underline{-162.3} $\pm$ 0.3 & 98.4 $\pm$ 0.0 & 81.7 $\pm$ 0.5 \\
        & \textsc{GCDM} w/o SMA & -131.3 $\pm$ 0.8 & 95.7 $\pm$ 0.1 & 51.7 $\pm$ 1.4 \\
        & \textsc{GCDM} & \textbf{-171.0} $\pm$ 0.2 & \underline{98.7} $\pm$ 0.0 & \textbf{85.7} $\pm$ 0.4 \\ \midrule
        Data & & & 99.0 & 95.2 \\ \midrule
    \end{tabular}
\end{table}

\begin{table}[ht]
    \caption{Comparison of \textsc{GCPNet} with baseline methods for 3D molecule generation. The results are reported in terms of the validity and uniqueness of 10,000 samples generated by each method, with standard deviations across three runs on QM9. The best results for this task are in \textbf{bold}, and the second-best results are \underline{underlined}.}
    \label{table:3dmg_validity_results}
    \centering
    \footnotesize
    \begin{tabular}{lllll}
        & & & & \\ \midrule
        Type & Method & Valid (\%)\ $\uparrow$ & Valid and Unique (\%)\ $\uparrow$ \\ \midrule
        Normalizing Flow & E-NF & 40.2 & 39.4 \\ \midrule
        Graph Autoregression & G-Schnet & 85.5 & 80.3 \\ \midrule
        DDPM & GDM-aug & 90.4 & 89.5 \\
        & EDM & 91.9 $\pm$ 0.5 & 90.7 $\pm$ 0.6 \\
        & Bridge & & 90.2 \\
        & Bridge + Force & & 90.7 \\ \midrule
        DDPM - Ours & \textsc{GCDM} w/o Frames & \underline{93.9} $\pm$ 0.1 & \underline{92.7} $\pm$ 0.1 \\
        & \textsc{GCDM} w/o SMA & 83.1 $\pm$ 1.7 & 82.8 $\pm$ 1.7 \\
        & \textsc{GCDM} & \textbf{94.8} $\pm$ 0.2 & \textbf{93.3} $\pm$ 0.0 \\ \midrule
        Data & & 97.7 & 97.7 \\ \midrule
    \end{tabular}
\end{table}

\begin{table}[ht]
    \caption{Comparison of \textsc{GCPNet} with baseline methods for property-conditional 3D molecule generation. The results are reported in terms of the mean absolute error for molecular property prediction by an EGNN classifier $\phi_{c}$ on a QM9 subset, \textsc{GCDM}-generated samples, and two different baselines "Naive (Upper-bound)" and "\# Atoms". The top-1 (best) results for this task are in \textbf{bold}, and the second-best results are \underline{underlined}.}
    \label{table:3dmg_conditional_qm9_results}
    \centering
    \footnotesize
    \begin{tabular}{llllll}
        & & & & & \\ \midrule
        Task & $\alpha$ & $\Delta \epsilon$ & $\epsilon_{HOMO}$ & $\epsilon_{LUMO}$ & $\mu$ \\
        Units & $Bohr^{3}$ & $meV$ & $meV$ & $meV$ & $D$ \\ \midrule
        Naive (Upper-bound) & 9.01 & 1470 & 645 & 1457 & 1.616 \\
        \# Atoms & 3.86 & 866 & 426 & 813 & 1.053 \\
        EDM & \underline{2.76} & \underline{655} & \underline{356} & \underline{584} & \underline{1.111} \\
        \textsc{GCDM} & \textbf{1.97} & \textbf{602} & \textbf{344} & \textbf{479} & \textbf{0.844} \\
        QM9 (Lower-bound) & 0.10 & 64 & 39 & 36 & 0.043 \\ \midrule
    \end{tabular}
\end{table}

\section{Experiments}

\subsection{Unconditional 3D Molecule Generation - QM9}
The QM9 dataset (\cite{ramakrishnan2014quantum}) contains molecular property descriptions and 3D atom coordinates for 130k small molecules. Each molecule in QM9 can contain up to 9 heavy atoms, that is, 29 atoms when including hydrogens. For the task of 3D molecule generation, we train \textsc{GCDM} to unconditionally generate molecules by producing atom types (H, C, N, O, and F), integer-valued atom charges, and 3D coordinates for each of the molecules' atoms. Following \cite{anderson2019cormorant}, we split QM9 into training, validation, and test partitions consisting of 100k, 18k, and 13k molecule examples, respectively.

\textbf{Metrics.} We adopt the scoring conventions of \cite{satorras2021f} by using the distance between atom pairs and their respective atom types to predict bond types (single, double, triple, or none). Subsequently, we measure the proportion of generated atoms that have the right valency (atom stability) and the proportion of generated molecules for which all atoms are stable (molecule stability).

\textbf{Baselines.} We compare \textsc{GCDM} to three existing E(3)-equivariant models: G-Schnet (\cite{gebauer2019symmetry}), Equivariant Normalizing Flows (E-NF) (\cite{satorras2021f}), and Equivariant Diffusion Models (EDM) (\cite{hoogeboom2022equivariant}). For each of these three models, we report their results as reported in \cite{hoogeboom2022equivariant}. For comparison with models for this task that are not equivariant, we also report results from \cite{hoogeboom2022equivariant} for Graph Diffusion Models (GDM) trained with random data rotations (GDM-aug) and without them (GDM). To the best of our knowledge, the force-guided molecule generation methods of \cite{wu2022diffusion} are the most recent and performant state-of-the-art methods for 3D molecule generation, so we include their results for this experiment as well.

We further include two \textsc{GCDM} ablation models to more closely analyze the impact of certain key model components within \textsc{GCDM}. These two ablation models include \textsc{GCDM} without local geometric frames $\mathcal{F}_{ij}$ (i.e., \textsc{GCDM} w/o Frames) and \textsc{GCDM} without scalar message attention (SMA) applied to each edge message (i.e., \textsc{GCDM} w/o SMA) as $\mathbf{m}_{ij} = e_{ij} \mathbf{m}_{ij}$, where $\mathbf{m}_{ij}$ represents the scalar messages learned by \textsc{GCPNet} during geometric graph message passing and $e_{ij}$ represents a 1 if an edge exists between nodes $i$ and $j$ (and 0 otherwise) via $e_{ij} \approx \phi_{inf}(\mathbf{m}_{ij})$. Here, $\phi_{inf} : \mathbb{R}^{e} \rightarrow [0, 1]^{1}$ resembles a linear layer followed by a sigmoid function \cite{satorras2021n}. All \textsc{GCDM} models use 9 $\mathbf{GCPConv}$ layers; SiLU activations (\cite{elfwing2018sigmoid}); 256 and 64 scalar node and edge hidden features, respectively; and 32 and 16 vector-valued node and edge features, respectively. All \textsc{GCDM} models are also trained using the AdamW optimizer (\cite{loshchilov2017decoupled}) with a batch size of 64, a learning rate of $10^{-4}$, and a weight decay rate of $10^{-12}$.

\textbf{Results.} In Table \ref{table:3dmg_stability_results}, we see that \textsc{GCDM} outperforms previous methods (E-NF, G-Schnet, EDM, Bridge, and Bridge + Force) as well as their non-equivariant counterparts (GDM and GDM-aug) for all metrics, except concerning \textsc{Atom stable (\%)} compared to Bridge + Force. We note that the variance of this metric for Bridge + Force is notably larger than that of \textsc{GCDM}. Importantly, when evaluating this metric in conjunction with $\textsc{Mol stable (\%)}$, we see that \textsc{GCDM} generates a significantly larger proportion of realistic and stable molecules (negative log-likelihood \& $\textsc{Mol stable (\%)}$) compared to all other methods. It is specifically interesting to note how much lower the negative log-likelihood (NLL) of \textsc{GCDM} is compared to that of EDM, the previous NLL-based SOTA method for 3D molecule generation, indicating the generative distribution that \textsc{GCDM} learns from QM9 likely contains much sharper peaks compared to EDM.

To offer additional insights into the behavior of each method for 3D molecule generation, we report as additional metrics the validity of a generated molecule as determined by RDKit (\cite{landrum2013rdkit}) and the uniqueness of the generated molecules overall. Note that for G-Schnet, EDM, Bridge, and Bridge + Force, we directly derive the bonds from the distance between atom pairs. We see in Table \ref{table:3dmg_validity_results} that \textsc{GCDM} generates the highest percentage of valid and unique molecules compared to all other methods, improving upon previous SOTA results in such measures by a notable margin. A possible explanation for why \textsc{GCDM} can achieve such results over equivariant methods such as EDM is that \textsc{GCDM} performs geometric (and geometry-complete) message-passing over each 3D input graph to remove the noise present therein, whereas other methods operate solely on scalar features. In future work, it would be interesting to investigate the impact of performing different kinds of geometric message-passing (e.g., type-2 tensor message-passing) on the performance of diffusion models for tasks such as 3D molecule generation.

\subsection{Conditional 3D Molecule Generation - QM9}

\textbf{Baselines.} Towards conditional generation of 3D molecules, we compare \textsc{GCDM} to an existing E(3)-equivariant model, EDM (\cite{hoogeboom2022equivariant}), as well as to two naive baselines: "Naive (Upper-bound)" where a property classifier $\phi_{c}$ predicts molecular properties given a method's generated 3D molecules and shuffled (i.e., random) property labels; and "\# Atoms" where one uses the numbers of atoms in a method's generated 3D molecules to predict their molecular properties. For each baseline method, we report its mean absolute error in terms of molecular property prediction by an EGNN classifier $\phi_{c}$ \cite{satorras2021n} as reported in \cite{hoogeboom2022equivariant}. For \textsc{GCDM}, we train each conditional model by conditioning it on one of five distinct molecular properties - $\alpha$, gap, homo, lumo, and $\mu$ - using the QM9 validation split of \cite{hoogeboom2022equivariant} as the model's training dataset and the QM9 training split of \cite{hoogeboom2022equivariant} as the corresponding EGNN classifier's training dataset. Consequently, one can expect the gap between a method's performance and that of "QM9 (Lower-bound)" to decrease as the method generates molecules that more accurately model a given molecular property.

\textbf{Results.} We see in Table \ref{table:3dmg_conditional_qm9_results} that \textsc{GCDM} outperforms all other methods in conditioning on a given molecular property. In particular, \textsc{GCDM} improves upon the mean absolute error of the SOTA EDM method for the properties $\alpha$, gap, homo, lumo, and $\mu$ by 28\%, 8\%, 3\%, 18\%, and 24\%, respectively, demonstrating that, using geometry-complete message passing, \textsc{GCDM} can more accurately model important molecular properties for 3D molecule generation.

\section{Conclusion}
In this work, we introduced \textsc{GCDM}, an SE(3)-equivariant geometry-complete denoising diffusion probabilistic model for 3D molecule generation. While previous equivariant methods for this task have had difficulty establishing sizeable performance gains over non-equivariant methods for this task, \textsc{GCDM} establishes a clear performance advantage over all other methods, generating more realistic, stable, valid, unique, and property-specific 3D molecules compared to existing approaches.

\subsubsection*{Acknowledgments}
This work is partially supported by two NSF grants (DBI1759934 and IIS1763246), two NIH grants (R01GM093123 and R01GM146340), three DOE grants (DE-AR0001213, DE-SC0020400, and DE-SC0021303), and the computing allocation on the Summit compute cluster provided by the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05- 00OR22725, granted in part by the Advanced Scientific Computing Research (ASCR) Leadership Computing Challenge (ALCC) program.

redpajama_set_name: RedPajamaArXiv


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Mumbai: E-commerce firms are the new kids on the block for marquee properties at key locations in major cities. This segment till recently used to be the preserve of global multinationals.
Realty industry watchers say that demand for office space is picking up thanks to the rising demand from large e-commerce players and start-ups. Corporates in expansion mode are also coming back.
Most of the action is in Bengaluru, Gurgaon and Mumbai though the trend is seen in other Tier 1 and even in Tier 2 cities.
E-commerce companies Amazon and Flipkart have already built up a bank of office space as they scale up.
Amazon is understood to have inked a deal to lease 1.3 million sq ft of prime office space in Bengaluru, while Flipkart last year cut a deal with the Embassy Group. Jabong has leased 1.2 lakh sq ft in Gurgaon and Snapdeal 1.1 sq ft in Delhi. Taxi aggregator Ola Cabs has signed up for 20,000 sq ft of prime office space at Embassy Golf and Housing.com for 1.5 lakh sq feet in Mumbai's Powai area.
"Overall business sentiment has improved with the office market seeing significant activity in the second half of 2014. Companies have begun implementing their plans with greater confidence, leading to improvement in demand for office space. We believe that demand for office space will remain robust for the next two years," said Sanjay Dutt, Executive MD, Cushman & Wakefield.
E-commerce companies are scrambling to pick up space to accommodate their burgeoning workforce and the backend operations.
According to another real estate consultant CBRE, more than 8 million sq ft of office space was completed across key cities during the first quarter of 2015. More than 50 per cent of the new office space supply was in the Delhi National Capital Region.
According to CBRE's India Office Market View, the total office space taken up in Q1 of 2015 stood at more than 5 million sq ft.
Anshuman Magazine, Chairman and Managing Director, CBRE, said, "The demand for prime office space is expected to pick up in the coming months as companies implement their business plans across cities.
CBRE said that in line with trends observed during the second half of 2014, the first three months of 2015 saw the completion of a number of large office projects in the Delhi NCR, Mumbai, Bangalore, Hyderabad and Pune.
According to industry observers, PEs are also eyeing Grade A office properties to invest in as sentiment improves. "The investment size has gone up and more funds are coming into commercial and office space as corporates expand. We are optimistic about the office space category," said Ashish Singh, MD (Real Estate Investments), Standard Chartered Private Equity Advisory.


Trim Healthy Mama CAN be this easy! I am a planner. I know that if I don't have a plan, nothing is going to get done! As much as I try to plan menus and have all my food prep finished, some weeks it just doesn't happen! There isn't always time to make our own bread or stay in the kitchen for hours. Sometimes we literally need a snack or meal that can be thrown together quick!
My Top 10 Store Bought THM items!
I have been an avid follower of THM for YEARS and have just found the best bread EVER! Finding breads that are on plan can be tough! "Sprouted" is your key word here! Sprouted grains break down much slower in your body and doesn't cause the spike in blood sugar like non Sprouted breads do. I use this toast for bread with sugar free jam and for sandwiches with LEAN meat. This yummy bread is even hubby improved!
These handy things make lunches really easy. The carbs are low and it's tasty. I usually take a pita and cut it in half then fill both sides with salami, light miracle whip and onions! This is personal choice item that has been approved by the creators of THM, but it's best not to eat EVERY day! It's delicious and now I want one!
Nuts are such a great source of protein! These are such an easy and filling snack to take on the go or fit into your day. The best part? Even gas stations have nuts!
Yum, yum and yum. You will feel like you are completely cheating eating these. Be sure you're grabbing the bag that says "baked." Do not exceed 45 carbs in one sitting (more info on carb limits and fuels in the Trim Healthy Plan book) Find or make "no sugar added" salsa to go with it. All salsa has natural sugar in it, so just look for sugar to NOT be in the ingredient list.
This Greek yogurt comes in many different flavors. My favorite is vanilla and then I add blackberries! You can eat 1 full container as a Fuel Pull and use the whole container as the protein source in an E and S setting!
The fat the cheese makes this an S snack or meal! I love having ham and cheese roll ups for lunch! I personally add a little bit of light miracle whip and enjoy!
You can actually use any low carb tortilla, but I'm partial to Mission. I love the taste and texture. These are great for for taco night and take 5 minutes to throw together!
These amazing things are pretty new to me! I really like these with some unsweetened almond milk, sweetner and fruit! These are made from beans (they do NOT taste like it) are a healthy E meal or snack.
** I found these on Vitacost.com but some Walmart's and Kroger's carry them too.
You can purchase Trim Healthy Mama Products here!
Did you know THM makes their own healthy chocolate bars? Did you know chocolate is actually good for you? It's the junk we add to chocolate that makes it unhealthy. These are great things to keep around and will keep you for cheating!
Popcorn is okay every now and then! I adore this brand and flavor so much that I "subscribe and save" to them on Amazon!
What to learn more about Trim Healthy Mama? Click here!
THM Challenge Week 1: Goodbye Sugar!
As some of you know, I am a Trim Healthy Mama certified coach! I have started a THM challenge to promote good healthy habits for 2019!
Join the group HERE! Please be sure to read the pinned post to know how to join in the fun! This week will probably be the hardest challenge we will have!
When we want to see real change, we can't overload our lives with new things. This is the only thing you need to focus on this week!
We aren't focusing on things that turn into sugar in our blood stream…. yet. That's a different week!
The Bible tells us that once we accept Jesus as our Savior, we are a new creature. As we grow to become more like Christ, we put off the old man and put on the new man.
Don't focus on the whole plan. Don't worry about S meals or E meals yet. Focus on getting the blatant sugar out of your life!
You will be detoxing from sugar this week. It may not be fun! Some experience headaches and just feel icky! Brace yourself! It wouldn't be a THM Challenge if it wasn't a little hard, right!?
Click Here to find a list of treats that I personally keep in my home that are store bought to help me "put on" the new mindset!
To learn more about Trim Healthy Mama click HERE!
Trim Healthy Mama has a pretty good learning curve to it! It's a lifestyle change and sometimes you need "crutches" to help you get through! In this post you will find a list of Trim Healthy Mama store bought treats, to save your sanity.
When I first started THM, I had 2 very young children and I just COULDN'T make everything. The time or energy wasn't there! I hope this list will be a blessing to you and please know it is not meant to be exhaustive!
THM has their own chocolate bars and chips now, but sometimes they are sold out. You can find Lilly's at some healthy food stores and even Kroger.
Sometimes in THM you will have "personal choice" items. Such as, a small amount of corn is acceptable under the plan, but some folks just choose not to eat it. Either way is totally ok! I am not a purist and I have lost weight eating these "personal choice" items, so I'm gonna keep eating them! I actually Subscribe and Save through Amazon to save a couple of dollars!
This is meant to be an occasional snack! Sometimes when I'm craving chips, I will pop a bag of popcorn and enjoy that! You do not one with butter them or you will be having a crossover snack. Below is my FAVE brand and flavor!
Nuts are a wonderful snack that is filled with protein! Peanuts are my fave, so I linked them below!
Again, These are not meant to be eaten everyday! The baked chips below are on plan and really yummy paired with salsa!
This list will EVER BE growing!
Where to find Modest Tops!
I think we can all agree how HARD shopping can be! When you are looking for modest clothing, it's even harder! I've collected my favorite 5 modest tops to help make your life easier!
I recently found a boutique called "Mountain Aire Boutique" on Instagram and I have fallen in LOVE with everything I see!
I have a 10% off coupon JUST for you, my readers! If you find some awesome clothes that you can't live without, be sure to use my code DARLING10 at checkout! You can view the the full catalog HERE.
I'm obsessed with this top! The sleeves, the buttons, the colors! This top could be worn in 3 of the 4 seasons!
Hi, my name is Lacey and I love pattern mixing on my shirts! Seriously, I love EVERYTHING about it! I adore how the sleeves match the pocket! I can see myself wearing this top while wrangling my children!
I was with one of my younger brothers a few days ago and he said, "Why aren't you wearing polka dots? You love polka dots!" That statement right there explains why I love this sweater and need it ASAP! Modest, cute AND keeps me warm? Yes, please!
I can't get over how stinking cute this Cardigan is! Stylish and modest? What more can a girl ask for? I love the neutral color of this piece, it will fit in nicely with my current wardrobe! I need this!
Look at that texture! I am envisioning this top being dressed up and dressed down! It's SO cute!
I hope you love these modest tops as much as I do! If you have any questions about this boutique, please feel free to reach out to me! Let me know if you grab any of these treasures!
For more modest clothing options click HERE!
Trim Healthy Mama Darling Dare 60 Day Challenge!
There's no fear of the new year around here! I am starting a Trim Healthy Mama Darling Dare 60 Day Challenge for the new year. We will be communicating through a Facebook group which is located here! We'd love to have you, so feel free to join! The challenge starts January 1, 2019!
Before we get started there's a few things I need from you!
4. I recommend getting a planner ( like the one below!) If we write our goals down, we are more likely to achieve them! Certainly, you can use this planner for meal planning and keeping track of your goals and progress!
5. Please be prepared to share your #1 goal for 2019 and a Bible verse you'd like to claim for 2019! We will share these and encourage each other with them in the facebook group!
I have lots of Tried and True Trim Healthy Mama recipes that I use on a regular basis! They can be found HERE, HERE and HERE!
You can find a sample menu to get started HERE!
I am so excited to start 2019 WELL and THRIVE right along side you!
A couple of weeks ago, I asked my community if they would like me to actually make some of the 20 MILLION Trim Healthy Mama recipes I have pinned on Pinterest. They said yes and I agreed to report back!
Trim Healthy Mama has a learning curve and sometimes it's nice to just know that a recipe is easy and tastes great. I really like EASY recipes. In fact, if it has too many ingriendents, I don't even bother!
To learn more about the eating plan, Trim Healthy Mama, click here!
To order Trim Healthy Mama supplies, click here!
For more tried and true Trim Healthy Mama Recipes, click here and click here!
1. Cream Cheese Pancakes – These are gluten free and a THM S! These will not be fluffy, but they taste marvelous! We use sugar free syrup and fat free Reid whip! You can also top with a small amount of fruit!
2. Raspberry Cheesecake Roll- Ups – These are delish and are such a treat!
3. Instant Pot Boneless Pork Chops – This is the first recipe I was brave enough to make in my Instant pot! I threw in some potatoes in with the chops for my family too! This was a hit with the man and kids!
4. Green Chili – This is my Grandma's recipe! It takes about 10 minutes to throw together and tastes amazing!
5. Crustless Quiche – Whenever I tell anyone in my family that I'm making this recipe they all say, "YES!" To say it's a favorite is an understatement!
I hope this is helpful to you! Don't be shy about jumping in and trying out some of these great Trim Healthy Mama recipes! Let me know if you love any of these as much as I do!
Would you like a community where you can ask questions and hear about the latest Trim Healthy Mama news and deals? Please join here!
One of the hardest things for me when I started eating this way, was how complex the recipes can be. I NEEDED something easy! Homeschooling 3 small children takes most of my time and I do not have hours to spend on meals. I live for "throw together" recipes that taste amazing! In fact, that's mainly what you will find here on this blog!
If you click the tab "Trim Healthy Mama" at the top of this blog, you can scroll through all the recipes available here at the Farmhouse!
Trim Healthy Mama is an eating plan that is low glycemic and teaches you what food is doing to your body. Our bodies need different fuels and they need to be separated for weight loss to occur. THM was created by 2 sisters, Serene and Pearl, who care deeply about eating healthy. Thankfully, they have since came out with a much smaller book called "The Plan" that is very helpful along the way. THM is a plan that can be done by all budgets, lifestlyles and people.
I am a certified Trim Healthy Mama Coach and I am passionate about this eating plan!
2. Cut Sausage into small cubes and set aside.
3. Place eggs, cream, mustard, salt and pepper into a large bowl and whisk until smooth.
4. Stir in Sausage, 1 cup of cheese and the bell pepper.
5. Pour egg mixture into a greased 9x13.
6. Bake 40-45 minutes or until eggs are set.
8. Let stand 5 minutes before serving.
I hope you love this recipe as much as my family does!
Would you like a community where you can ask questions and hear about the latest Trim Healthy Mama new and deals? Please join here!
Trim Healthy Mama is an eating plan that is low glycemic and teaches you what food is doing to your body. There are different fuels our bodies need and they need to be separated for weight loss to occur. THM was created by 2 sisters, Serene and Pearl, who care deeply about eating healthy. Thankfully, they have since came out with a much smaller book called "The Plan" that is very helpful along the way. THM is a plan that can be done by all budgets, lifestlyles and people.
Brown the hamburger and drain if there is any grease. Add all the other ingredients to the hamburger. Simmer for 10-15 minutes and serve!
I told you it was easy! This is a recipe you can literally throw together! I hope you love this recipe as much as I do!
It's important that we have Trim Healthy Mama pancakes that are gluten free for our family! Our son Ryland has been gluten free for about a year. This recipe is one that I founnd probably 4 years ago and I'm really glad it suits our needs now! I went to source it at the original website, Lauren Conrad's blog, and it's no longer there.
This pancake batter is pretty runny so it works better if you let the batter sit overnight in the fridge. Truthfully, I don't always plan that far ahead and I make it work if I need to do it same day. You just have to attend to them more as they cook! However, these are SO sweet and taste like something that you shouldn't be eating, so it's worth a little runny batter to me!
We typically top it with fat free Redi Whip and sugar free syrup! You can enjoy a small amount of fruit as well! I'm getting hungry for these as I type this!
Pour 1/4 cup of batter into a hot pan or griddle that is greased. Cook until golden, flip and cook the other side.
Please note that you can use any sweetener you prefer for this recipe! I just like truvia! Here's a conversion chart for you!
Be sure to come back and let me know how you like these yummy pancakes! How awesome that these are healthy AND gluten free?
Don't miss goodies and fun!


text:
ePreskripce, elektronické předepisování nebo e-předepisování je elektronické psaní, generování, přenos lékařského předpisu (receptu) na počítači, způsob který nahrazuje papírové a faxové recepty. ePreskripce umožní lékaři, lékárníkovi, nebo zdravotní sestře použít software pro digitální předepisování k elektronickému přenosu nového nebo obnovení staršího povolení vydat z místní nebo zásilkové lékárny lék na předpis. Umožní elektronicky odesílat bezchybné, přesné a srozumitelné recepty od poskytovatele zdravotní péče do lékárny. Účelem elektronického předepisování je snížit rizika spojená s tradičním způsobem psaní předpisů. Je to také jeden z hlavních důvodů tlaku na elektronické lékařské záznamy. Sdílením informací o lékařském předpisu se ePreskripce snaží propojit osoby poskytující pacientovi zdravotní péči s cílem usnadnit jim informované rozhodování.

Funkce ePreskripce
Systém elektronického předepisování musí být schopen plnit všechny tyto funkce:

 identifikace pacienta,
 vytvoření úplného seznamu aktuálně užívaných léků, případně včetně dat získaných od zdravotní pojišťovny,
 přístup k historickým údajům o pacientovi,
 možnost předepsat lék nebo přidat další a vybrat lékárnu, kde bude předpis realizován.
Při práci s existujícím lékem to v praxi může zahrnovat prohlížení podrobností o léku, odebrání léku ze seznamu aktivních léků, změnu dávkování atd.
 vytištění předpisu,
 elektronické odeslání předpisu do transakčního centra,
 provádění všech bezpečnostních kontrol pomocí integrovaného systému podpory rozhodování, známého jako utilizace neboli přehled o využití léků.
Bezpečnostní kontroly zahrnují: automatické nabídky informující o předepsaném léku, potenciální nevhodné dávce nebo cestě podání, vzájemných interakcích mezi léčivy, alergické obavy nebo výzvy k opatrnosti.
 označení možnosti úspor, terapeuticky vhodných alternativ (pokud existují),
 informace o účinných látkách, bezpečnosti a účinnosti, o vhodnosti pro pacienta a požadavcích na autorizaci obdržených elektronicky od pojišťovny pacienta,
 systémová integrace, například propojení s různými databázemi, propojení s lékárnami a slevové systémy na léky,
 funkce pro vzdělávání pacientů, zpětná vazba od poskytovatele.

Česká republika

Systém eRecept byl v ČR vytvořen k předepisování léků elektronickou formou už od roku 2011 a od ledna 2018 je tento způsob povinný. Ministerstvo zdravotnictví v případech, kdy není možný přístup k elektronickému systému, umožňuje předepsat léky klasickou formou - papírový lékařský předpis. eRecepty vytváří a eviduje centrální úložiště, které provozuje Státní ústav pro kontrolu léčiv. Historie jeho budování a historie zavádění eReceptů je uvedena v článku Systém eRecept.

Vkládání dat
Elektronický recept vytváří a zasílá centrálnímu úložišti receptů lékař po dohodě s pacientem. Odesílá se číslo pojištěnce, které je zároveň jeho rodným číslem, jméno a množství léku, cena léku, úhrada od pojišťovny, šarže lékárny a identifikační číslo předepisujícího lékaře.

Vystavení a použití eReceptu
Kód eReceptu může lékař pacientovi zaslat na mobilní telefon jako SMS, na e-mail, nebo předat prostřednictvím aplikace v mobilním telefonu. Pacient může od svého lékaře získat i papírovou průvodku (vytištěný eRecept). Vystavení lékařského předpisu v původní listinné podobě je přípustné jen ve vyjmenovaných případech a lékař je musí zdůvodnit.

eRecept na běžné léky má platnost čtrnáct dní. Výjimku tvoří antibiotika a chemoterapeutika, na jejich vyzvednutí má pacient pouze pět dní. Platnost začíná běžet dnem vystavení eReceptu, počítají se i víkendy a svátky. Opakovací eRecept platí půl roku, může platit až rok. Recept vystavený pohotovostní službou platí nejdéle 1 den následující po jeho vystavení.

Význam a kritika
V období bezprostředně předcházejícím povinnému používání eReceptů, tzn. v závěru roku 2017, se projekt eReceptu stal terčem silné kritiky lékařů. Na základě systematické analýzy témat v té době diskutovaných na stránkách časopisu Tempus Medicorum (časopis České lékařské komory) lze jako klíčové body této kritiky uvést
 zhoršení zdravotní péče v důsledku možného úbytku lékařů, zejm. lékařů v seniorském věku,
 chybějící výhody eReceptu z pohledu lékařů,
 přesvědčení lékařů, že by medicína neměla být v takové míře závislá na informačních technologiích.
Z pohledu sociálně orientovaného studia informačních technologií lze averzi českých lékařů k eReceptu interpretovat jako příklad rezistence proti nasazování informačních technologií v medicíně. Podle citované studie však nelze chybu hledat jen u lékařů, ale je nutno zohlednit i nevhodně zvolený postup implementace eReceptu, za kterou odpovídá Státní ústav pro kontrolu léčiv.

Podle Zdravotnických novin "z přehledu léků lze zjistit choroby i to, kolik pacient za léky zaplatil. Data o pacientech by rády využily v konkurenčním boji zdravotní pojišťovny, mohly by podle těchto informací provádět výběrový nábor nových pojištěnců." Tento způsob užití eReceptů však jednoznačně není v zájmu pacientů resp. pojištěnců.

Praktický přínos pro pacienty mají zejména opakované eRecepty, pokud je lze získat emailem. Veřejnost oceňuje možnost lékaře (po souhlasu pacienta) nahlédnout do seznamu léků, které pacient užívá. Dále se kladně hodnotí možnost zjistit, zda předpis od lékaře není falešný.

ePreskripce v zahraničí
Elektronické předepisování léků bylo zavedeno kromě ČR také v těchto státech:

 Austrálie
 Bangladéš
 Kanada
 Estonsko
 Indie
 Rusko
 Spojené království
 Spojené státy americké

Bližší informace o těchto systémech jsou na stránce anglické Wikipedie (odkaz níže).

Odkazy

Reference

Externí odkazy
 Státní ústav pro kontrolu léčiv: epreskripce.cz
 Vzor průvodky elektronického receptu

Informační systémy veřejné správy
Farmakologie


In the digitisation age, data increasingly is becoming 'the business' and hence the pressure to protect data and users from more sophisticated attacks calls for new more effective ways of cyber protection. Statistics show that the battle to protect data is not heading in the right direction, unfortunately, according to Gartner the number of breaches are increasing as are the average number of records affected. At the same time, businesses are spending more money on security. So how can the security effectiveness gap be reduced?
One approach that is gaining currency and is slated to become predominant security architecture in the next few years is Zero Trust.
Zero Trust Architecture for networks was devised by Forrester Research analyst John Kindervag in 2010. The essence of Zero Trust is that perimeter security is inadequate for today's security threats. The approach should be that no one inside or outside of the organisation should be trusted and users should only be granted access to resources after the user and their device are identified.
This reminds me of one of my favourite lines from the X Files, "trust no one, be afraid, be very afraid". OK probably not totally relevant but I just thought I would work it in.
Both enterprise Information Security Officers and IT suppliers are embracing Zero Trust as the most effective approach.
Zero Trust addresses the tendency to leave default settings on systems and the fact that many businesses take a very egalitarian approach to internal users – everyone is equal. Also, many organisations do not implement a 2-factor authentication system and can rely on usernames and passwords stored on text files or worst still post-it notes. Generally protecting the perimeter is seen as the main security priority. This approach has been in recent years shown to be fatally flawed. When you consider attacks such as Nyeta, WannaCry etc, the hackers experienced very little resistance once they breached the perimeter and gained access to the network. The network perimeter is increasingly becoming a very blurry concept. As the way we work evolves, cloud services are becoming predominant, users are working remotely, branches are connecting directly to the Internet. So, the Zero Trust approach can easily adapt to the changing landscape because it ensures that security is pervasive.
Zero Trust is gaining currency and it is likely that you are already subject to such an architecture where you access other cloud systems. It will likely be a valuable and effective option for you to deploy in your environment if you haven't done this already. In a future blog, we will look at some best practices for deploying a Zero Trust architecture.


The average Bridgewater household's plumbing system represents approximately 15% of your home's value. It is as important as the roof over your head or the four walls around you. Nothing in the house gets used as much because, although some of us can take it for granted from time to time, it facilitates clean and convenient living. Given its importance, you need to protect your investment.
Of course, this means making sure you are doing what you can on a daily basis to make sure you are not compromising the integrity of your home's plumbing system. This means doing your best to make sure food residue and cooking oils aren't getting washed down the sink or that no one is flushing material that can degrade down the toilet. However, even the most prudent homeowners can encounter problems with their plumbing through no fault of their own.
This can be extremely frustrating, but luckily, an affordable and efficient solution provided by licensed and insured professionals isn't far away. You only need to get in touch with Mason's Plumbing & Heating Inc to see why our residential plumbing services are among the best and most respected in the Bridgewater area.
No matter what your home is faced with, you have our guarantee that one of our highly qualified and courteous plumbers near you will be on site as soon as possible to diagnose the problem and find the best, longest lasting solution so that you can resume enjoying your home.
Whenever something's not right about your home's plumbing, calling in Mason's Plumbing & Heating Inc's professional plumbers is always a good idea. If left unattended or improperly fixed, the consequences could be costly in the future. Even small jobs like leaking faucets and clogged drains are best left to the members of our team because we have fully-stocked vans. With all the necessary tools and equipment on hand, we and the problem with your home's plumbing will be out of your hair in no time.
For more serious problems, like corroded pipes, tree roots or burst pipes, you still have our guarantee to complete the task in a timely manner because we know that your home depends on clean water.
Your reason for contacting Mason's Plumbing & Heating Inc doesn't always have to be so doom and gloom. We can do so much more than put plumbing emergencies to rest. For example, whenever you are upgrading your bathtub, shower or sink, we can help install any kind of water fixture.
Getting a professional to complete your fixture installation is the best way to assure yourself that the job has been done properly. We can also spot things going on behind the scenes and nip them in the bud before they spoil the excitement of your upgraded bathroom or kitchen.
We are familiar with practically all major brands, so if you have a question about our fixture installation services, please do not hesitate to contact us today. We look forward to working with you, no matter what residential plumbing service you require.


text:
Q: What is the probability of successfully leveling a character's attack stat to a given value over $x$ rolls in the dice RPG Too Many Bones? Too Many Bones is a "dice-builder" RPG that has the following rule for leveling up a character's attack stat:
The player must roll a number of D6 equal to the character's current attack value. If no 1's are rolled, the level-up is successful.
It follows that for a character with 1 attack, the probability of success is $\frac{5}{6}$. For a character with 2 attack, the probability of success is $\left(\frac{5}{6}\right)^2$, and so on. Given this rule, what is the most likely number of attempts it would take to get a character from 1 attack to 6 attack?
I wrote a script to simulate the process and found that for this particular scenario the distribution peaks at 7 rolls (a frequency of $\approx 16\%$). How would one arrive at this result analytically?
More abstractly, given the rules of the game, what is the most likely number of rolls $x \in \mathbb{N}$ it would take to level a character from an attack value of $a$ to an attack value of $b$?


The new Colombian president, Iván Duque, has promised that it may cut taxes for crypto and blockchain companies. The information has been released by the local news outlet El Tiempo on August 29.
This is very positive for virtual currency companies in the region that are searching to locate their headquarters.
Mr. Duque delivered a message during the international congress known as ANDICOM. The information is held annually in Cartagena de Indias, Colombia.
Apparently, the president is a strong supporter of the technology. He said that he is 'obsessed' with robotics and artificial intelligence (AI). In the future, the country would be creating a council that would transform the country into a digital society.
The other promise he made was related to cryptocurrencies. He said that the country would not impose taxes on crypto related companies for five years in case they generate new jobs.
Duque is the president of Colombia since August 2018. He won the elections in May and has an important financial background. In the past, he held positions in the Ministry of Finance and the Inter-American Development Bank.
Colombia is an important player in the cryptocurrency market in Latin America. The Colombian Central Bank is working with the R3 Consortium to test a blockchain system with 39 different companies.
Several companies are settling their headquarters in the country. Cities such as Bogotá are competing with Sao Paulo in Brazil, Buenos Aires in Argentina, or Santiago in Chile.
Bitcoin's Intrinsic Value: How To Determine The Real BTC Exchange Rate Value If It Even Exists?


text:
TINTYPES—MAKE THE AMERICAN MUSICAL GREAT AGAIN
IF EVER THERE was a Broadway musical revue that's ripe for revival these days, it's Tintypes.
Tintypes, the Original Broadway Cast, conceived by Mary Kyte, with Mel Marvin and Gary Pearle, DRG Records, 1981.
The Tintypes revue was originally produced by the Arena Stage in Washington, D.C. It opened off-Broadway on April 17, 1980, and ran for 137 performances. The Broadway production, opening on October 23, 1980, ran for 93 more. Having a cast of only five and modest orchestral requirements, the revue has been popular with regional and little theater groups since then.
In its CD notes, Steve Lawson writes, "The world of Tintypes is the curious half-century between the Civil War and the Roaring Twenties, one of the most tumultuous eras in American history.… It was a time of explosive growth: America's population doubled in thirty years, and one-third of the leap came from abroad. A million Irish after the potato famine; three million Germans fleeing Bismarck's 'blood and iron,' nine million Jews, Slavs, and Italians between 1900 and World War I."
Mary Kyte, who conceived Tintypes with Mel Marvin and pianist Gary Pearle, has included familiar songs from the era (the traditional "Sometimes I Feel Like a Motherless Child," "I'll Take You Home Again, Kathleen," 1876, and "America, the Beautiful," 1910). Others are less known (the traditional "Wait for the Wagon," "When It's All Goin' Out and Nothin' Comin' In," 1902, and "She's Gettin' More Like the White Folks Every Day," 1901).
Yes, there's biting satire in Tintypes, with its cast playing various roles encountering challenges not unfamiliar to many today.
For example, "Wait for the Wagon" has counterpoint between two cast members, one portraying radical Emma Goldman; the other, a Wall Street tycoon: Goldman argues, "You put your trust in your political leaders. Fifth Avenue is laid in gold, every mansion a citadel of money and power. And there you stand, a giant starved and fettered."
The tycoon responds, "It is not true that the poor have grown poorer but that some of the rich have grown so much richer that the contrast strikes the onlooker as more violent than before."
This stirring encounter begins at about 30:33 in the following video.
Tintypes, a youtube of the original Broadway production. Uploaded by Adam Camp.
Lawson cites in the CD notes, "On the average workday, Andrew Carnegie's pension was $44,000—and two million children earned 25 cents. ('The most beautiful sight we see anywhere,' rhapsodized the founder of Coca-Cola, 'is the child at labor.' "
Another Lawson citation comes from a Slav immigrant: "My people do not live in America. They live beneath it."
However, don't think that Tintype is in any sense a downer. Its 15 scenes in two acts also celebrate ingenuity and inventions in song ("Electricity," 1905; "Come Take a Trip in My Airship," 1904; and "In My Merry Oldsmobile," 1905); and Ragtime (Scott Joplin's "Elite Syncopations" and "Ragtime Dance," both from 1902, and "Solace: a Mexican Serenade," 1909). Teddy Roosevelt is a recurring character in the musical, sharing his aspirations for a Panama Canal.
Our 26th president is celebrated in a rousing "Teddy Da Roose," 1910. And "I Want What I Want When I Want It," 1905, has repartee by Roosevelt and his newly created Panamanian Republic pal: "Canal?" "Canal." "And You?" "I Can!" It begins around 58:30 in the video.
The Finale is wistfully upbeat with Victor Herbert's "Toyland," 1903, and Callahan and Roberts' "Smiles," 1918.
It's good to smile again. I hope you enjoy Tintype as much as I do. ds
This entry was posted on November 3, 2018 by simanaitissays in And Furthermore... and tagged "Tintypes" CD notes Steve Lawson, "Tintypes" Emma Goldman vs Wall Street tycoon, "Tintypes" Mary Kyte Mel Marvin Gary Pearle, "Tintypes" Teddy Roosevelt Panama Canal.
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