Some foot problems seem to favour women. More women than men develop bunions, callus, corns, hammertoes, and ingrown toenails. The primary reason is the shoes they wear. They are narrow, pointed, high in the heel, often flimsy, and designed for appearance rather than fit.
Waiting to resolve a foot problem until it`s troublesome enough to merit a visit to the doctor is usually a mistake. Because feet are under the constant foot wear and pressure of bearing the body`s entire weight, even a small problem can grow large quickly, then take longer than necessary to clear up. It`s a lot harder to "rest" the feet than other parts of the anatomy unless you`re willing to stay in bed or a chair all day. Ninety percent of women wear shoes that are too small for their feet, and 80 percent of women say their shoes are painful. As a result, nine times more women than men are likely to develop bunions, hammertoes and other painful foot deformities because of ill-fitting shoes.
Shoe Bites can occur due to wearing new or ill-fitting shoes.
Feet sometimes spread and get larger with age and wear. Yet most people don`t have their feet re-measured periodically, as they should. The width of some people`s feet can increase over the years from a size B to as much as a size E, especially if their shoes are too short, and particularly after age 55.
On average, women buy shoes one size too small. In one study, 90 percent were wearing shoes that were too small for them. It`s no surprise that women over age 55 have particular trouble getting a proper fit.
In constructing their lines of shoes, many manufacturers start with their smallest size, perhaps 5 or 6, and build up in the same proportions to a size 8 or 10. But an individual`s heel may be up to 1/4 of an inch wider than the larger size allows for, and the toe even more.
Applying a little petroleum jelly inside your shoe. Then leave it on overnight. Clean it off with a cloth and then wear your shoes.
Apply coconut oil inside your shoes for three consecutive nights to soften them before wearing. You could apply castor oil too.
Apply some raw potato slices inside the shoe and particularly the heel area. Repeat for two nights before wearing your new shoes.
Take half cup rice. Pound it to a powder and then add enough water to make a thick paste. Apply the paste on the shoe bite. Leave it on till dry. Rinse gently with lukewarm water. Dry the feet thoroughly. You will get immense relief.
Neem and Turmeric Paste: Take a few Neem leaves and add to them a tablespoon of turmeric powder. Add a little water and put it into mixer to form a thick paste. Apply this paste on the painful shoe bite. This gives tremendous relief and also dries up the bite.
If you want to own a pair of lotus feet, you just need to treat them right. A little care goes a long way.
Corns and calluses are both a thickening of the outer layer of skin. This thickening is known medically as hyperkeratosis. Corns and calluses develop as part of the skin`s normal defense against prolonged rubbing, pressure and other forms of local irritation.
A callus can develop anywhere on the body where there is regular or prolonged pressure of friction, providing a protective pad against injury. Calluses are extensive patches of toughened skin that can occur on any part of the body, especially the feet, hands and knees since, that part of the body that absorbs the most friction on a daily basis.
However, manual laborers and athletes (such as tennis players) often develop calluses on their hands, desk workers get them from resting on their elbows and guitarists have them on their fingertips. Even pushing a pen may create a "writer`s" lump where the pen presses into the finger. Calluses are not usually painful, although they do blemish the skin.
A thick callus on a toe is known as a corn, and it has a hard kernel formed in the centre. Because it often presses on the nerves below, a corn can be painful. You can use corn-removing plasters, which are available from pharmacies, to remove a corn. They consist of a foam circle with salicylic acid in the centre, which eats away the plug of dead skin. Or you can visit a chiropodist who will carefully pare away the thickened layers of skin with a scalpel. Remember that for a complete cure you must remove the pressure that caused the corn in the first place. Make sure that your shoes fit properly.
Corns and calluses can be a long-term problem if you consistently wear shoes that do not fit properly. Even with good footwear, you may continue to have painful corns and calluses if there is some underlying abnormality in your gait or foot structure that causes unusual stress on parts of your feet when you walk.
Your health-care provider probably will ask questions about your shoes, because shoes with narrow toes are more likely to cause corns. Some types of foot problems can alter the mechanics of the foot, producing abnormal pressure on certain areas and leading to calluses. Also, any previous surgery or trauma to the feet may affect the structure and alignment of foot bones, increasing the risk of calluses. A detailed review of past medical problems, especially diabetes and circulation problems, are a routine part of the evaluation.
To assess whether your corns and calluses are related to foot abnormalities, your dermatologist will inspect your feet for toe deformities, structural abnormalities of the bones, poor bone alignment and problems related to an abnormal way of walking (gait). If your doctor finds some abnormality during this part of the foot exam, he or she may suggest a specific type of padding or shoe insert that will help to prevent your corns and calluses from returning or causing as much discomfort.
Apart from this, you should wear proper shoes and avoid wearing tight-fitting footwear.
You should not use "corn plasters." These contain acids intended to eat away at the corns. But they also eat into nearby normal flesh.
Avoid cutting corns and calluses. This only makes the situation worse. This especially applies to diabetic people. As soon as a corn develops, apply oil to soften it.
Soak your feet in very diluted chamomile tea. It would soothe and soften the hard skin. Then apply a hand cream, which contains 20% urea. This will help dissolve the hard skin. Do this daily.
Another formula is to soak the area in a mixture of oil of wintergreen, witch hazel, and black walnut tincture, daily. Use a pumice stone and emery board to trim down the corn or callus.
Put a few drops of citric acid on the area. The next morning, use an emery board or a pumice stone and rub off the dead skin.
Yet another formula is to crush 5-6 aspirin tablets and mix into a paste, by adding a half-teaspoon each of water and lemon juice. Apply this to the hard-skin areas. Put the foot in a plastic bag, wrap a warm towel around it, and sit for 10 minutes. Then unwrap the foot and scrub the area with pumice stone. The dead, hardened flesh should come loose and flake off.
A variant method is to soak a piece of cotton in fresh lemon juice or pineapple. Bandage the cotton over the area. It will dissolve it. But you must be persistent.
Any sweet oil rubbed on the area several times a day, plus the use of the emery board or pumice stone, will skim off the dead flesh.
Try putting some lamb`s wool between the toes, to separate them (after buying larger shoes).
Women should avoid wearing high-heel shoes. They ruin the feet, damage the spine, and throw the pelvic organs out of place.
Women should not wear pumps; these are shoes which cause the foot to slide forward, jamming everything into the front. Instead, wear an oxford-style shoe, with laces. This properly cradles the foot.
Always buy shoes which breathe and for this purpose, leather is the best.
An undersized shoe will damage the toes and cause corns, etc. An oversized shoe will produce friction and break the skin. But, of the two, oversized shoes are the less harmful.
Some calluses are useful, never painful, and should not be disturbed.
On the feet, a small corn or callus may not cause any symptoms. However, a large, bulky corn or callus can cause foot pain and difficulty walking. Also, after prolonged irritation, a discolored area (brown, red or black) may develop under a large corn or callus. This discoloration is caused by a small amount of bleeding in the space between thick and normal skin. In severe cases, the thick and normal skin may separate, exposing the area to possible infection, especially in persons with diabetes.
Ingrown toe nails are a common, painful condition that occurs when skin on one or both sides of a nail grows over the edges of the nail, or when the nail itself grows into the skin. There are three stages of ingrown toenails. In the first stage the skin on either side of the nail is red and painful to the touch. This is due to inflammation or irritation only infection. In the second stage the skin is infected and may bulge over the side of the nail. The affected area may ooze clear fluid or pus. In the third stage the skin has been infected for a prolonged time and is trying to heal itself. The skin does this by forming granulation tissue. This is heaped up extra red tissue that bleeds easily and migrates over the nail edge.
There are several factors that can lead to an ingrown toenail.
The first is an abnormality of the soft tissue on the side of the nail.
The nail plate can be forced out of the nail groove by shoes that have a toe box that is too small for the forefoot, by trauma, or by cutting the nail back in a curvilinear fashion.
Cutting your toenails incorrectly can cause them to re-grow into the skin. This occurs because the ingrown nail is often in a warm, moist and bacteria-rich environment. When the nail penetrates the skin, it provides a convenient entry for germs that can cause infection.
Heredity - Inwardly curved nail with distortion of one or both nail margins.
Untreated, the nail can go under the skin, causing a more severe infection. In either case, the infection needs to be cured with sterile instruments and antibiotics.
The sharp end of the nail will be pressing into the flesh on one or both sides of the nail bed.
Skin near the nail may feel tender and look red and swollen as the nail pushes on the skin. Once the nail pokes through the skin, the skin will look redder and more swollen. You may feel a sharp pain that is worse when walking. With time, the skin will grow over the nail. It may also cause yellow drainage come from the nail. This may mean you have an infection.
Ingrown toenails need to be treated immediately.
Soak the feet in warm salt water. Dry them thoroughly with a clean towel. Apply a mild antiseptic solution to the area and bandage the toe. However, If you have diabetes, do not try to treat an ingrown nail by yourself. Always call your caregiver first. Do not treat an ingrown nail without a caregiver`s help if you have certain long-term health problems.
If your nail is infected or your ingrown nail keeps coming back, you may need surgery. Many types of surgeries can be done to treat an ingrown nail. Often, a podiatrist will cut and remove a small section from the side of your nail. The section of nail is cut from the side of the fingernail or toenail that is ingrown.
You may continue to have problems with a recurring (keeps coming back) ingrown nail or bad infection. If this happens, the surgeon may need to remove your entire nail to stop the ingrown nail problem.


Olympic Ice Stadium, Munich – A penalty ridden second period gave the Straubing Tigers the advantage needed against EHC Red Bull München, scoring two goals en route to a 3-0 win.
Grant Lewis scored a power play goal at 6:48 after Munich's Klaus Kathan's second penalty of the period and Daniel Sparre another power play – EHC had too many players on the ice – with gave all the Tigers needed for the win.
The first period started with both teams very equally matched. Both teams had good looks at the goal and were strong on defense. Once the buzzer sounded at the end of the first period neither team had managed to score.
"In the first period we played with self-confidence and were organized, we created some scoring chances," said Munich head coach Pat Cortina.
Editor's Note: EHC Red Bull coach Pat Cortina is the new head coach of the German national ice hockey team. He debuts at the helm at the Deutschland Cup November 9-11. Here's a preview.
Munich was hoping that they would be able to strike first in the second period but it was not meant to be. Instead they shot themselves many times. EHC played their worst 20 minutes of the night in the second period and nine of their ten penalties came in the second period.
"I think that our energy factor was a little low and we are coming off a pretty tough schedule, four games in eight days and I think we lost a little focus," said Cortina.
Down 2-0, Munich tried to make a comeback; unfortunately they had no luck. The Tiger's' René Röthke would score in the 19:02 minute after EHC pulled the goalie. Röthke's goal sealed the victory for the Tigers and handed EHC Munich a shut out at home.
All was not lost for Munich, as General Manager Christian Winkler announced that they had found a solution to cover for the injured Jason Ulmer. Blake Wheeler from the Winnipeg Jets has signed to play for Munich during the next six weeks and potentially longer depending on how long the NHL lockout lasts.
Wheeler will join the club on November 1st, and will play his first game the next day in Dusseldorf.
Munich's next game is Wednesday October 31st against the Hamburg Freezers, who currently sit 6th in the DEL standings. Face-off at 19:30.


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FSNE: DeSantis' action blocking Miami Herald reporter from press conference is alarming
Dear Gov. DeSantis:
These are extraordinary times for our state and country, and Florida's news organizations are striving to keep the public informed of every aspect of the deadly novel coronavirus. It has been challenging because of the rapid-fire pace of breaking news, the lack of understanding of the virus itself, and the challenges posed by social distancing.
Governor, your regular press conferences are one of the most important vehicles for reporters to ask questions about the state's response to the virus and clarify what it means for our cities and towns. (Saturday's) purposeful exclusion of the Miami Herald's bureau chief, Mary Ellen Klas, to your press conference was an alarming development. That city is facing a grave crisis, which you well know, and it deserves representation at all of your press conferences.
The Florida Society of News Editors (FSNE) represents 49 organizations reaching millions of citizens in every corner of this state. We respectfully expect your press office to work with FSNE to achieve a better set-up that allows participation for any news organization that seeks access to your press conferences, either in person or remotely. We recognize this is outside current practice, but we firmly believe the times demand a more transparent and inclusive response.
We look forward to working through the details with your press office, and other media trade organizations that may want to participate, but this is what FSNE proposes:
– Press conferences be held in a large room, such as the Senate Chambers, that could accommodate any member of the Capitol press corps and allow for 6 feet of space between members for recommended social distancing, and
– A livestream video conferencing setup such as Zoom, Microsoft Teams, or any other popular video conferencing platform that allows users to call in, use a microphone or ask questions via text, and record the meeting. This addition would allow press to listen and ask questions from other parts of the state.
– Finally, we expect that the press be given ample prior notice to attend the in-person or remote meetings, preferably at least an hour's notice.
We thank you for considering our proposal and look forward to working with you, on behalf of the public we both serve.
Lisa Nellessen Savage, President
Executive Editor, Pensacola News Journal
Dana Banker, Secretary/Treasurer
Managing Editor, South Florida Sun Sentinel
Cindy McCurry Ross, Immediate Past President
Executive Editor, News-Press
Editor-in-chief, Sun Sentinel Media Group/Orlando Sentinel Media Group
John Hackworth
Commentary Editor, Sun Newspapers
William Hatfield
Executive Editor, Tallahassee Democrat
Mira Lowe
UFCJC INC Director, University of Florida
Ian Mader
Florida News Editor, The Associated Press
Mindy Marques
President, Publisher & Executive Editor, Miami Herald
Nick Moschella
Executive Editor, The Palm Beach Post
Mary Kelli Palka
Editor, The Florida Times-Union
Editor, Daytona Beach News-Journal
Katie Sanders
Managing Editor, PolitiFact

redpajama_set_name: RedPajamaCommonCrawl


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Mintel is a privately owned company which commissions independent reports and reviews of domestic consumer products and services, plus marketing news and reports from UK trade press. Reports include Market Intelligence, Retail Intelligence and Finance Intelligence. Its industrial range complements the retail and includes aerospace, defence and construction. Market sizes, major players, key trends and forecasts are included in every report.


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\section{Introduction}
From early alchemists looking for the elixir of life, to modern day researchers, humans have always wanted to understand aging.  As people age, their cells go through replication cycles.  Each replication reduces the length of the telomeres in the cells.  If a cell's telomeres are too short, it may not be able to replicate\cite{herbig}.  Cells that can no longer replicate are termed senescent.  Cellular senescence is thought to play a major role in age-related diseases, which cause nearly 67\% of all human deaths worldwide\cite{degrey}.  Recent research in mice showed that exercising mice had higher levels of telomerase, an enzyme that helps maintain telomere length, than non-exercising mice\cite{werner}.  In humans, runners had longer telomeres than non-runners\cite{werner}.  Since shortened telomeres are thought to be related to death, this research would seems to indicate that people who exercise live longer lives.  Population studies do indeed show this, however, most studies show that only the
mean lifespan increases in exercising populations, not maximum lifespan\cite{holloszy,sarna}.
\par
A commonly used model for biological aging was proposed by Penna in 1995\cite{penna, stauffer}.  The model looks at death from a mutation  accumulation standpoint.  In the last 10 years, papers have been published describing methods for finding the age distributions created by the Penna model without actually simulating the model\cite{coe1,coe2,coe3}.  However, the research on senescence indicates that age-related death is not caused by mutation accumulation, but rather by an inability to reproduce after a number of cycle
.  I propose two modifications of the Penna model that use this mechanism instead of a mutation accumulation, and show that a mean lifespan can increase without affecting the maximum lifespan, which cannot be done by changing parameters in the original Penna model.
\section{Calculations}
The Penna model assigns a bit-string to each individual in the population.  Each bit corresponds to a timestep of the simulation.  A 1 in the string represents a mutation, and a 0 means no mutation.  If an individual has gone through $T$ 1s, then it dies. Each individual can have offspring, with probability $b$.  The child's bit-string is derived from the the bit-string of the parent, where each 0 has probability \it m \rm of becoming a 1.  The Penna model ignores positive mutations, because they are rare.  The length of the bit-string provides a hard limit for lifespan.  In this paper, I will work with only the $T=1$ case.
\par
\begin{figure}
 \includegraphics[scale=0.35]{treediagram.png}
 \caption{\label{treediagram} The possible paths until death, after reaching $l$, in the SP.}
\end{figure}
In the first proposed modification, which we will call the senescent Penna (SP) model, each individual can only get one disease, which is essentially the beginning of aging.  After the individual starts to age, it has probability $p$ of staying alive to reproduce at each time step.  The maximum number of replication cycles is $M$.  This is the Penna model, except instead of definitely dying, the individual has only a probability of dying.  People who exercise generally have longer telomeres, so once senescence starts, they have a smaller probability of dying.  Higher values of $p$ represent exercising populations.
\par
The first 1 in an individual's bit string is the age, $l,$ at which senescence begins.  The number of people alive at time  $j$, with age $x$, is $n_j(x,l,m)=pn_{j-1}(x-1,l,m-1)$ if $x>l$, where $p$ is the probability of living after senescence, and $m$ is the time since the inception of senescence.  If $x\leq l$, then $n_j(x,l)=n_{j-1}(x-1,l)$.  If $b$ is the probability of birth, and $e^{-\beta}$ is the probability of an individual going unmutated, then the number of children born in the next time step with disease acquisition time $l$, $n_{j+1}(0,l,0)$ is given by
\begin{equation}
\begin{aligned}n_{j+1}(0,l,0)&=be^{-\beta l}\sum_x\sum_m n_j(x,l,m)\\&+(1-e^{-\beta})be^{-\beta l}\sum_{l'>l}\sum_x\sum_m n_j(x,l',m)\end{aligned}\end{equation}
Since $m$ is just the maximum of 0 and $x-l$, \begin{equation}\sum_x\sum_m n_j(x,l,m)=\sum_{x=0}^{l-1}n(x,l) + \sum_{x=l}^{M+l-1}n(x,l)\end{equation} where M is the maximum number of replication cycles allowed after disease.  Assuming a steady state, $n_{j+1}(x,l)=n_j(x,l)$.  Therefore, \begin{equation}\sum_{x=0}^{l-1}n(x,l,0)=l\cdot n(0,l,0),\end{equation} since each $x$ has the same number of people.  Since $n_j(x,l)=pn_{j-1}(x-1,l)$ for $x>l$, and since $n_{j+1}(x,l)=n_j(x,l)$ in a steady state \begin{equation}\sum_{x=l}^{M+l-1}n(x,l)=n(0,l)\sum_{x=1}^M p^x=p\frac{1-p^M}{1-p}n(0,l)\end{equation}  Defining $q_l$ as  \begin{equation}q_l=l+p\frac{1-p^M}{1-p},\end{equation}  and $n(l)=n(0,l)$, eq. 1 can be simplified to \begin{equation}0=be^{-\beta l} n(l)-\frac{n(l)}{q_l}+(1-e^{-\beta})be^{-\beta l}\sum_{l'>l+1}n(l')\end{equation}  Writing the same equation for $l+1$, some algebra leads to
\begin{equation}n(l+1)=n(l)
\frac{be^{-\beta l}-1/q_l}
{be^{-\beta (l+1)}-e^{\beta}/q_{l+1}}
\end{equation}
\par
This equation leads to some limiting cases, in order to maintain a steady state. Neither the numerator, nor the denominator should vanish in eq. 7.\begin{equation}q_{max}<\frac{1}{1-e^{-\beta}},\end{equation} (and $l_{max}=q_{max}-p\frac{1-p^M}{1-p}$) and \begin{equation}b=\frac{1}{q_{max}e^{-\beta l}}\end{equation}
However, eq. 7 only gives the time of senescence, not the lifespan.  In the original Penna model, at  $l$ the individual dies, but here the individual has only a $(1-p)$ probability of dying.  The number of individuals who die at age $t$ is just \begin{equation}D(t)=p^Mn(t-M)+\sum_{x=t-M+1}^{t} (1-p)p^{t-x}n(x),
\end{equation} assuming $t\geq M$. The first term ensures that when $t=l+M$, all the remaining people alive with $n(l)$ die, not just a proportion of $1-p$.
\par
It is also possible to combine the original Penna model with the modification described previously, making a combination Penna (CP)  model.  Some people have a genetic tendency for heart disease, or stroke\cite{hassan}. These diseases are not directly affected by senescence.  In a combination of the two models, there would be two classes of death, one instantaneous, as in the original model, and one probability based, as in the proposed modification.  Then each individual is defined in terms of $l$ and $l_P$, where $l$ is the time of a probabilistic mutation and $l_P$ is the time to a Penna mutation, or instant death. $n_{j+1}(0,l,l_P)$ can come from $n_j(x,l',l_P')$ where $l'\geq l$ and $l_P'\geq l_P$.  Note that $l$ cannot be greater than $l_P$.  Therefore, \begin{equation}\begin{aligned}n_{j+1}(0,l,l_P)&=be^{-\alpha l}e^{-\beta l_P}[\sum_x n_j(x,l,l_P)\\
&+(1-e^{-\alpha})(1-e^{-\beta})\sum_{l'>l}\sum_{l_P'>l_P}\sum_x n_j(x,l',l_P')\\
&+(1-e^{-\beta})\sum_{l'>l}\sum_x n_j(x,l',l_P)\\
&+(1-e^{-\alpha})\sum_{l_P'>l_P}\sum_x n_j(x,l,l_P')],\end{aligned}\end{equation}
where $e^{-\alpha}$ and $e^{-\beta}$ are the probabilities of not getting a senescence or death mutation, respectively.  The death distribution is given by probabilistic and instantaneous deaths, \begin{equation}\begin{aligned}
D(t)=&\sum_{x=t-M}^tp^{t-x}n(x,t)\\&+\sum_{l_P>t}\sum_{l<t}\sum_{x=t-M+1}^{t}p^{t-x}(1-p)n(x,l_P)\\&+p^Mn(t-M,l_P)
\end{aligned}\end{equation}\par
As time passes in the Penna model, the mutations slowly move downwards.  However, there is no evolutionary pressure preventing an individual with $l=0$ from reproducing.  Since there are no positive mutations, my ansatz is that in a steady state, $l=0$ for all individuals.  If $l_P=0$, the individual does not reproduce, so there is an evolutionary pressure for $l_P>0$.  If this happens, then any terms summing over different values of $l$ vanish, so
\begin{equation}\begin{aligned}
n_{j+1}(0,l,l_P)=&be^{-\alpha l}e^{-\beta l_P}[\sum_{l_P'=l_P}\sum_x n_j(x,l,l_P)\\
&+(1-e^{-\alpha})\sum_{l_P'>l_P}\sum_x n_j(x,l,l_P')].\end{aligned}\end{equation}
Simplifying in the same manner as in the previous model, the steady state form is the same as eq. 7, except \begin{equation}q_l=p\frac{1-p^{l_P}}{1-p}.\end{equation}  However, since $l=0$, the time until senescence is always 0, eq. 12 is not needed.  The recursive form just gives the age of death.
\section{Results}
\begin{figure}
 \includegraphics[scale=0.35]{1.png}
 \caption{\label{fig1} Higher values of $p$ result in earlier times of senescence in the SP.  In this picture, $M=5$.}
\end{figure}
\begin{figure}
 \includegraphics[scale=0.35]{5.png}
 \caption{\label{fig2} The death curve in the SP is a shift of the senescence curve, with the amount shifted varying on $p$.  Here $M=5$ and $p=.8$.}
\end{figure}
\begin{figure}
 \includegraphics[scale=0.35]{2.png}
 \caption{\label{fig3} Higher values of $p$ have a higher proportion of their population reach larger ages, but that proportion difference is countered in the middle of the death distribution. $M=5$}
\end{figure}
Interestingly, in the SP model higher values of $p$ show a ``younger population'' (fig. 2).  With lower $p$ values, an individual with low $l$ will not have as many opportunities to reproduce, since chances are it will die out soon.  This provides an evolutionary pressure for higher values of $l$.  However, if $p$ is high, then individuals with low $l$ can still reproduce.\par
While senescence begins later for populations with lower $p$, death comes earlier once senescence is reached.  The average death time for $n(l)$ is $l+(1-p)+2p(1-p)+3p^2(1-p)+\ldots+(M+1)p^M$, where the last term has no $1-p$ factor, since everybody left alive has to die.  Higher values of $p$ result in later deaths, as would be expected.  The later deaths are more apparent after $l_{max}$, when any living members of the population are undergoing senescence.  Figures 4 and 5 show the differences in percentages, which have to add up to 0.  The increased proportion of older individuals for higher values of $p$ has to be balanced by a reduced proportion of the population at lower ages.  The jump in the differences of death proportions early in figs. 4 and 5 is caused by $M$.  For larger values of $p$, the $1-p$ term in eq. 10 is small enough to make the $p^{t-x}$ term negligible.  However, once $M$ is reached, the final term has no $(1-p)$ factor, causing the jump.\par
The SP model does not show an increase in the mean for higher values of $p$, but it does show that the probability of living to a higher age is greater.  Even though the probability of living to a high age is greater, the maximum age for both populations with higher and lower $p$ is still $l_{max}+M$.  Higher values of $M$ push the time of senescence further forward, since there is less evolutionary incentive for an individual to have a higher $l$.  \begin{figure}
 \includegraphics[scale=0.35]{3.png}
 \caption{\label{fig4} This shows the same break as fig. 4, but at age 10, since $M=10$ in the SP here.}
\end{figure}
 \begin{figure}
 \includegraphics[scale=0.35]{diffM.png}
 \caption{\label{fig5} The differences in the death distribution curves of the SP of $M=5$ and $M=10$, for different values of $p$.}
\end{figure}
\begin{figure}
 \includegraphics[scale=0.35]{4.png}
 \caption{\label{fig6} The death distributions for different values of $p$ look approximately the same, but there is a slightly higher proportion of people alive at later times for higher values of $p$. }
\end{figure}
However, just like $p$, higher values of $M$ also afford a longer time until death, balancing out the earlier senescence times.  Since higher values of $M$ allow for a longer life, the proportion of people alive at a higher age is greater for higher values of $M$.  The breaks in fig. 5 are caused by the same mechanism as the breaks in figs. 3 and 4, except instead of the deaths coming at one specific $M$, they come at the two values of $M$, 5 and 10.\par
\begin{figure}
 \includegraphics[scale=0.35]{combodiffp.png}
 \caption{\label{combodiffp}This is the death distribution in the CP, for different values of $p$. Notice that even a slight change in $p$ has a large change on the death distribution. }
\end{figure}
The CP model shows a different structure than the SP model.  It shows a quicker increase in age expectancy, and a slower decrease.  The combination requires a high $p$, because otherwise $q$ degenerates rapidly to $\frac{p}{1-p}$.  If $p$ is too low, then the CP model will not be stable without a Verhulst factor, \begin{equation}V=1-\frac{N(t)}{N_{max}},\end{equation} where $N(t)$ is the number of people alive at time $t$, $N_{max}$ is the maximum allowed number of people, and $V$ is the probability that an individual survives a timestep. This also explains why even small differences in the value of $p$ show large differences in the age distribution curve.
\section{Conclusion}
In this paper, I showed that simple modifications to the Penna model allow for shifts in the lifespan distribution  without changing the maximum lifespan.  Higher values of $p$ in the SP result in younger populations, but they die later.\par
Thinking about the original context for this modification, higher values of $p$ can represent exercising populations.  The maximum age of two populations with different $p$ and the same $M$ is the same, but the exercising population has a higher chance of reaching later ages.  What is interesting, is that this model shows that the exercising population will also be younger.  The times of senescence for high $p$ are lower than low $p$, yet the probability of reaching a high age is greater.  \par
The Penna model is a tool used to help us understand population dynamics.  My modifications of the Penna model take into account senescence of a population, which is a critical part of the aging process, and help to explain the changes in lifespan observed in exercising and non-exercising populations. By adjusting $e^{-\beta}, p,$ and $M$, these should be able to fit actual data.  Further improvements to the models could take into account recent research in autism which suggests that $e^{-\beta}$ is actually a function of time\cite{kong}, and also looking at positive mutations.

redpajama_set_name: RedPajamaArXiv


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

The discovery of the Higgs boson in LHC experiments \cite{Aad:2012tfa,Chatrchyan:2012ufa} completed the particle listing of the standard model (SM), but it is known that still several cosmologically important phenomena cannot be explained.
One of them is the matter abundance of the Universe, which, under the criteria of Sakharov \cite{Sakharov:1967dj}, revealed us that the CP violation is crucially lacking \cite{Farrar:1993hn,Huet:1994jb}.
This is why the search of new sources of CP violation beyond the SM is currently so actively pursued.

The electric dipole moment (EDM) \cite{He:1990qa,Bernreuther:1990jx,khriplovichbook,Pospelov:2005pr,Fukuyama:2012np,Engel:2013lsa,Yamanaka:2014mda,Hewett:2012ns} is a very sensitive experimental probe of CP violation, and it may be measured in many systems.
Recently, the experimental result of the EDM of neutron was updated ($|d_n | < 1.8 \times 10^{-26}e$ cm) \cite{Abel:2020gbr}, and the constraint on the hadronic CP violation became tighter.
The measurements of the EDM of diamagnetic atoms \cite{Graner:2016ses,Bishof:2016uqx,Allmendinger:2019jrk} also constrain the neutron EDM at a similar level \cite{Ginges:2003qt,Yamanaka:2017mef,Chupp:2017rkp,Yanase:2020agg}.
Regarding the EDM of the proton, experimental measurements using storage rings are currently in development, with impressive prospective sensitivity of $O(10^{-29})e$ cm \cite{Farley:2003wt,Anastassopoulos:2015ura,bnl}.
There are also attempt to measure the EDM of flavored baryons in high energy accelerator experiments \cite{Aiola:2020yam}.
It is known that the nucleon EDM receives contribution from many CP violating quark-gluon level processes.
The most well-known one is the quark EDM, for which the systematics is now quite well controlled thanks to extensive lattice analyses \cite{Yamanaka:2018uud,Gupta:2018lvp,Alexandrou:2019brg,Cirigliano:2019jig,Horkel:2020hpi}, although there are still discussion regarding the disagreement with perturbative QCD extractions \cite{Bacchetta:2012ty,Kang:2015msa,Benel:2019mcq,DAlesio:2020vtw,Anselmino:2020nrk}.
Contributions from purely QCD operators such as the chromo-EDM or the $\theta$-term are also well studied in chiral effective field theory \cite{Crewther:1979pi,Pich:1991fq,Borasoy:2000pq,Mereghetti:2010tp,deVries:2010ah,Mereghetti:2010kp,deVries:2012ab,Fuyuto:2012yf,Mereghetti:2015rra,deVries:2015gea}, and there are also available lattice QCD results for the latter one \cite{Abramczyk:2017oxr,Dragos:2019oxn}, while the ab initio calculation of the former one is more challenging \cite{Rizik:2020naq}.

As a more obscure CP-odd strong interaction, we have the Weinberg operator \cite{Weinberg:1989dx,Dine:1990pf,Braaten:1990zt,Chemtob:1991vv}.
This is a dimension-6 CP-odd interaction defined by
\begin{eqnarray}
{\cal L}_w
&=&
\frac{1}{3!} w
f^{abc} \epsilon^{\alpha \beta \gamma \delta} G^a_{\mu \alpha } G_{\beta \gamma}^b G_{\delta}^{\ \ \mu,c}
,
\label{eq:weinberg_operator}
\end{eqnarray}
where $f^{abc}$ is the structure constant of the $SU$(3) Lie algebra.
It was first introduced by Weinberg as a potentially large contribution of the CP violation of the Higgs sector to the neutron EDM \cite{Weinberg:1989dx}.
The Weinberg operator is relevant in many candidates of new physics beyond standard model such as the Higgs-doublet models \cite{Weinberg:1989dx,Dicus:1989va,Boyd:1990bx,Cheng:1990gg,Bigi:1991rh,Bigi:1990kz,Hayashi:1994xf,Hayashi:1994ha,Wu:1994vx,Jung:2013hka,Brod:2013cka,Dekens:2014jka,Cirigliano:2016nyn,Cirigliano:2016njn,Panico:2017vlk,Cirigliano:2019vfc,Haisch:2019xyi,Cheung:2020ugr}, supersymmetric models \cite{Dai:1990xh,Arnowitt:1990je,Abel:2001vy,Demir:2002gg,Demir:2003js,Degrassi:2005zd,Abel:2005er,Ellis:2008zy,Li:2010ax,Zhao:2013gqa,Hisano:2015rna}, and other models \cite{Chang:1990sfa,Rothstein:1990vd,Xu:2009nt,Choi:2016hro,Abe:2017sam,Dekens:2018bci,DiLuzio:2020oah}.
The SM contribution generated by the CP phase of the CKM matrix \cite{Kobayashi:1973fv} is negligibly small due to suppression by the GIM mechanism \cite{Booth:1992tv,Pospelov:1994uf,Yamaguchi:2020dsy}.
An example of the process generating the Weinberg operator in the Higgs-doublet model is shown in Fig. \ref{fig:weinberg_higgs}.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=4cm]{weinberg_higgs.eps}
\caption{\label{fig:weinberg_higgs}
Typical Feynman diagram contributing to the Weinberg operator in Higgs-doublet models.
}
\end{center}
\end{figure}

The analysis of the nucleon EDM generated by the Weinberg operator involves sizable theoretical uncertainty.
The most important obstruction in the quantification of its contribution to the nucleon level CP violation is the absence of quark field in Eq. (\ref{eq:weinberg_operator}) which implies that chiral techniques are not very powerful. Nevertheless, there were several attempts to quantify this effect.
The contribution of the Weinberg operator to the neutron EDM was treated in the original work of Weinberg \cite{Weinberg:1989dx} using the {\it na\"{i}ve dimensional analysis}, giving
\begin{equation}
d_N (w)
\approx
e\frac{\Lambda}{4\pi}w
\approx
w \times 90 \, e \, {\rm MeV}
,
\label{eq:NDA}
\end{equation}
where $\Lambda = 4\pi f_\pi$, being not more accurate than the order estimation.
Bigi and Uraltsev then inspected it in more detail at the hadron level, and came out that the neutron EDM is generated by the one-particle reducible and irreducible parts (see Fig. \ref{fig:nucleon_EDM_Weinberg_operator}) \cite{Bigi:1991rh,Bigi:1990kz}.
The reducible contribution is obtained by ``$\gamma_5$-rotating'' the anomalous magnetic moment with the CP-odd baryon mass.
The CP-odd mass was then evaluated using QCD sum rules, and the resulting nucleon EDMs were given as \cite{Demir:2002gg,Haisch:2019bml}
\begin{eqnarray}
d_N^{\rm (red)} (w)
&\approx&
\left\{
\begin{array}{rl}
 w \times 25 \, e \, {\rm MeV} & (N = n ) \cr
-w \times 23 \, e \, {\rm MeV} & (N = p ) \cr
\end{array}
\right.
.
\label{eq:weinbergop_gpinn}
\end{eqnarray}
with 50\% of theoretical uncertainty \cite{Haisch:2019bml} (we note that the result of Ref. \cite{Haisch:2019bml} used the magnetic moment, instead of the anomalous magnetic moment, of the proton so we corrected the proton EDM result).
The ideal method to obtain the coefficient relating $w$ and $d_N$ is lattice QCD, for which quantitative results are not yet available \cite{Cirigliano:2020msr,Rizik:2020naq}.
Another potentially interesting approach is to analyze higher twist contribution to the parton distribution functions \cite{Hatta:2020ltd}.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=12cm]{nucleon_EDM_Weinberg_operator.eps}
\caption{\label{fig:nucleon_EDM_Weinberg_operator}
Diagrammatic representation of the nucleon EDM in the hadron level effective field theory.
Diagrams (a) and (b) are the contribution from the ``$\gamma_5$-rotated'' anomalous magnetic moment (black blob) by the CP-odd baryon mass (grey blob).
Diagram (c) is the short-distance irreducible contribution, evaluated in this work.
}
\end{center}
\end{figure}

The irreducible part, however, has never been evaluated and has been neglected in previous studies, but there is no reason to omit it.
The reducible ``$\gamma_5$-rotated'' contribution may in some sense be considered as the relativistic effect, since the CP-odd baryon mass and the anomalous magnetic moment are higher order terms in the velocity expansion.
On the other hand, the irreducible one has no reason to be generated from relativistic physics, and we may thus expect it to be derived from the evaluation of the internal structure in a nonrelativistic framework.
In this work we propose to calculate the Weinberg operator contribution to the nucleon EDM in the quark model.

The quark model was first conceived in the 60's by Gell-Mann to classify hadrons \cite{GellMann:1964nj}.
It is possible to describe with Lie algebra arguments the hadron mass splitting and the magnetic moment by assuming that hadrons are $SU(3)_c$ singlet states composed of nonrelativistic (anti)quarks in the {\bf 3} ({\bf 3}$^*$) representation.
It is now considered to be one of the most successful model to describe low energy QCD, and the discovery of $\Omega$ in the early era \cite{Barnes:1964pd}, as well as that of double charmed baryons quite recently \cite{Aaij:2017ueg}, are demonstrating this.
The phenomenological interaction used is confining, i.e. the interquark potential becomes infinitely high at long distance and resembles the one-gluon exchange at short range.
Although the first principle derivation of the quark model from QCD is not available, lattice QCD calculations are strongly suggesting this picture \cite{Bali:1992ab,Takahashi:2000te}.
In the quark model, the nucleons are thus considered as a nonrelativistic three-quark system with this confining potential.
The calculation of the wave function of such systems is possible using the Gaussian expansion method \cite{Hiyama:2003cu} which is a powerful tool to solve few-body Schr\"{o}dinger equations.
This method has been applied in the calculations of the EDM of light nuclei \cite{Yamanaka:2015qfa,Yamanaka:2015ncb,Yamanaka:2016itb,Yamanaka:2016fjj,Yamanaka:2016umw,Lee:2018flm,Yamanaka:2019vec}, and we expect it to also work well for the present case of the nucleon EDM.

We organize this paper as follows.
In the next section, we derive the one-loop level CP-odd gluon exchange potential between quarks generated by the Weinberg operator.
In Section \ref{sec:edm}, we present the setup of the calculation of the EDM of nucleons.
In Section \ref{sec:analysis}, we analyze our result by comparing it with the former result obtained using the QCD sum rules.
The final section is devoted to the conclusion.

\section{Quark level processes generated by the Weinberg operator\label{sec:quarklevel}}

In this section we calculate the CP-odd interquark force induced by the Weinberg operator.
It is generated by the one-loop level diagram of Fig. \ref{fig:2qint} (the Feynman rule for the three-gluon vertex is given in Appendix \ref{appendix:Feynman_rules}).
This diagram is diverging if we calculate it directly, so it is required to evaluate it with a scheme with cutoff.
Here we use the heavy quark effective theory which removes the relativistic degrees of freedom, corresponding to integrating out field configurations with energy-momentum component higher than the constituent quark mass $m_Q$.
This scheme is adequate for deriving interquark potentials which will be used in quark models.
The final form of the two-body scattering amplitude is
\begin{eqnarray}
i{\cal M}
&\approx &
w
\frac{N_c g_s \alpha_s m_g }{2 }
\frac{1}{|\vec{q}|^2 + m_g^2}
\bar H_2 t_a H_2
\cdot
\bar H_1
t_a \vec{\sigma}\cdot \vec{q}
H_1
+(1 \leftrightarrow 2)
.
\label{eq:amplitude3}
\end{eqnarray}
where $q$ is the exchanged momentum, $H_i$ is the ``large'' component of the spinor of the $i$th quark, and $\alpha_s = 0.3$ is the QCD coupling chosen at the energy scale close to the nucleon mass.
We denote by $t_a$ the generator of the $SU(3)_c$ group.
The derivation is given in Appendix \ref{appendix:2-body}.
Here the mass of the gluon is given by $m_g \approx 350$ MeV, which we took from the gluon propagator calculation in Landau gauge lattice QCD \cite{Falcao:2020vyr}.
The Compton wave length of this gluon is $1/m_g \approx 0.6 $ fm which is quite compatible with the picture where gluons are confined in a proton with the radius $r_N \sim 0.8$ fm.
The velocity counting of this CP-odd two-body force is $O(v)$, due to $\sigma^{0 \gamma} q_\gamma \gamma_5$.
After Fourier transforming Eq. (\ref{eq:amplitude3}), we obtain the following nonrelativistic CP-odd 2-body force in the coordinate space
\begin{equation}
{\cal H}_{CPV}
=
-
\frac{N_c g_s \alpha_s m_g }{2 }
w
(\vec{\sigma}_1- \vec{\sigma}_2)
\cdot
\vec{\nabla} \frac{e^{- m_g |\vec{r}_1 -\vec{r}_2| }}{4 \pi |\vec{r}_1 -\vec{r}_2|}
(t_a)_1 \otimes (t_a)_2
.
\label{eq:cpvhamiltonian}
\end{equation}
This interaction has exactly the same Lorentz structure as the phenomenological CP-odd nuclear force with $\omega$ meson-exchange \cite{Towner:1994qe,Liu:2004tq,Yamanaka:2015qfa,Yamanaka:2016umw,deVries:2020iea}.
The EDM of a nucleon, composed of three quarks, can therefore be calculated like the EDMs of $^3$He and $^3$H with the CP-odd one-pion exchange force.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=4cm]{2qint.eps}
\caption{\label{fig:2qint}
The one-loop level quark-quark amplitude generated by the Weinberg operator.
The thick lines denote the constituent quarks.
The double line is the dressed quark propagator which will be considered to be heavy.
}
\end{center}
\end{figure}

The Weinberg operator also generates the CP-odd three-quark potential, through the three-quark amplitude depicted in Fig. \ref{fig:3qint} \cite{Blundell:2012ei}.
However, the momentum dependence of the Weinberg operator (see Fig. \ref{fig:wein_feyn} of Appendix \ref{appendix:Feynman_rules}) brings a velocity suppression of $O(v^3)$, so the CP-odd three-quark interaction should therefore be subleading.
In the calculation of the nucleon EDM, we therefore only consider the 2-body force (\ref{eq:cpvhamiltonian}) as the source of CP violation.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=5cm]{3qint.eps}
\caption{\label{fig:3qint}
The three-quark amplitude generated by the Weinberg operator.
The thick lines denote the constituent quarks.
}
\end{center}
\end{figure}

\section{Calculation of the nucleon EDM\label{sec:edm}}

\subsection{Definition of the nucleon EDM}

Now that we have the CP-odd interquark force, we can evaluate the nucleon EDM.
The nucleon EDM is defined as
\begin{eqnarray}
d_{N}
&=&
\sum_{i=1}^{A} \frac{e}{2}
\langle \, \Psi_N \, |\, (1/3 +\tau_i^z ) \, {\cal R}_{iz} \, | \, \Psi_N \, \rangle
\nonumber\\
&=&
\sum_{i=1}^{A} \frac{e}{2}
\langle \, \Psi_N \, |\, \tau_i^z \, {\cal R}_{iz} \, | \, \Psi_N \, \rangle
,
\label{eq:nucleonedmpolarization}
\end{eqnarray}
where $|\, \Psi_N \, \rangle$ is the state of nucleon polarized along the $z$-axis, and $\tau^z_i$ is the isospin Pauli matrix.
The $z$-component of the coordinate of the $i$-th constituent quark ${\cal R}_{iz}$ is defined in the center of mass frame of the nucleon (that is why the isosinglet term with $1/3$ of the first equality does not contribute).
The nucleon state must be a mixing of opposite parity states to yield a nonzero nucleon EDM, which is possible if the CP-odd interquark force of Eq. (\ref{eq:cpvhamiltonian}) is present in the Hamiltonian.

\subsection{Quark model\label{sec:quarkmodel}}

In this work, we use the quark model to describe the CP-even strong interaction.
The nucleon is considered as a 3-body system of nonrelativistic constituent quarks.
We use the parameters of Refs. \cite{Bhaduri:1981pn,Semay:1994ht} which considered the interquark 2-body interaction.
The 3-body wave function is calculated with the Gaussian expansion method \cite{Hiyama:2003cu} in the coordinate space.

In this work we use three types of interactions.
The first one is the potential proposed by Bhaduri \cite{Bhaduri:1981pn}, given as
\begin{equation}
V_{qq , ab} (r)
=
-\frac{3}{16}
\lambda_a \lambda_b
\Biggl[
-\frac{\kappa}{r}
+\lambda r
+\Lambda
+\frac{\kappa}{m_Q^2} \frac{e^{- r /r_0}}{r r_0^2} \vc{\sigma}_a \vc{\sigma}_b
\Biggr]
,
\label{eq:bhaduri}
\end{equation}
where $m_Q = 0.337$ GeV, $\kappa = 0.52$, $\Lambda = - 0.9135$ GeV, $\lambda = 0.186 $ GeV$^2$, and $r_0 = 2.305$ GeV$^{-1}$ \cite{Bhaduri:1981pn}.
The other two proposed in Ref. \cite{Semay:1994ht}, named AL1 and AP1, are given by
\begin{equation}
V_{qq , ab} (r)
=
-\frac{3}{16}
\lambda_a \lambda_b
\Biggl[
-\frac{\kappa (1-e^{-r/r_c})}{r}
+\lambda r^p
+\Lambda
+\frac{2 \pi \kappa'}{3 m_Q^2} (1-e^{-r/r_c}) \frac{e^{- r^2 /r_0^2}}{\pi^{3/2} r_0^3} \vc{\sigma}_a \vc{\sigma}_b
\Biggr]
,
\label{eq:semay}
\end{equation}
where $r_0 \equiv A / m_Q^B $.
The parameters are given in Table \ref{table:semay}.

\begin{table}[htb]
\caption{
Input parameters of the interquark potentials AL1 and AP1 \cite{Semay:1994ht}.
}
\begin{center}
\begin{tabular}{l|ccccccccc|}
Potential & $p$ & $r_c$ & $m_Q$ [GeV] & $\kappa$ & $\kappa'$ & $\lambda$ [GeV$^{1+p}$] & $\Lambda$ [GeV] & $B$ & $A$ [GeV$^{B-1}$] \\
\hline
AL1 & 1   & 0 & 0.315 & 0.5069 & 1.8609 & 0.1653 & -0.8321 & 0.2204 & 1.6553 \\
\hline
AP1 & 2/3 & 0 & 0.277 & 0.4242 & 1.8025 & 0.3898 & -1.1313 & 0.3263 & 1.5296 \\
\hline
\end{tabular}
\end{center}
\label{table:semay}
\end{table}

\subsection{Gaussian expansion method}

The object of the Gaussian expansion method is to solve the nonrelativistic Schr\"{o}dinger equation
\begin{eqnarray}
( H - E ) \, \Psi_{JM,TT_z}  = 0 ,
\label{eq:schr7}
\end{eqnarray}
with the variational principle.
The Hamiltonian to diagonalize is
\begin{equation}
H
=
\sum_a T_a+ \sum_{a,b} V_{qq , ab}
+{\cal H}_{CPV , ab}
,
\label{eq:hamil7}
\end{equation}
with the kinetic energy operator $T$, the CP-even interquark potential $V_{qq , ab}$ seen in Sec. \ref{sec:quarkmodel}, and the CP-odd one ${\cal H}_{CPV , ab}$ (\ref{eq:cpvhamiltonian}).
Explicit indices indicating the labels of the constituent quarks $a$ and $b$ were written.

We need two coordinates to express the wave function of three-quark systems.
The wave function of the 3-quark systems is given as the sum over three kinds of Jacobian coordinates shown in Fig. \ref{fig:jacobi}, as
\begin{eqnarray}
\Psi_{JM, I, I_z}(n, p)
&=&
 \sum_{c=1}^{3} \:
\sum_{nl, NL}
\sum_{T} \sum_{\Sigma} \sum_{s}
C^{(c)}_{nl,NL, \Sigma s, T}\: {\cal A} \Biggl[
\Bigl[  \eta^{(c)} ( T_c ) \otimes \eta'^{(c)} ({\scriptstyle \frac{1}{2}} ) \Bigr]_{I={\scriptstyle \frac{1}{2}} ,I_z}
\times
\nonumber  \\
&&
\Bigl[
[ \phi^{(c)}_{nl}({\bf r}_c) \otimes \psi^{(c)}_{NL}({\bf R}_c)]_\Lambda \otimes \, \bigl[ \chi^{(c)} ( s_c ) \otimes \chi'^{(c)} ({\scriptstyle \frac{1}{2}} ) \bigr]_\Sigma \Bigr]_{J={\scriptstyle \frac{1}{2}}, M}
\times
| {\rm color\, singlet} \rangle
\Biggr]
,
\nonumber\\
\label{eq:he7lwf}
\end{eqnarray}
where ($\eta$,$\eta'$), ($\phi$,$\psi$), and ($\chi$,$\chi'$) are two isospin, radial, and spin components of the nucleon state according to the Jacobi coordinate, respectively.
Here $\cal{A}$ antisymmetrizes the whole system, i.e. the arguments inside the large bracket are entangled so as to be odd under the interchange of each quark.
Since the color part is completely antisymmetric, $l+s+T$ must be even.
The spin and isospin matrix elements can be calculated exactly in the same way as those of $^3$He and $^3$H nuclei, except that the antisymmetry requires $l+s+T$ to be even.
The radial components $\phi$ and $\psi$ are expanded with the following basis
\begin{eqnarray}
\phi_{nlm}({\bf r})
&=&
r^l \, e^{-(r/r_n)^2}
Y_{lm}({\widehat {\bf r}})  \;  ,
\nonumber \\
\psi_{NLM}({\bf R})
&=&
R^L \, e^{-(R/R_N)^2}
Y_{LM}({\widehat {\bf R}})  \;  ,
\end{eqnarray}
where the following geometric progression for the Gaussian range parameters is used:
\begin{eqnarray}
      r_n
      &=&
      r_{\rm min} a^{n-1} \quad
      (n=1 - n_{\rm max}) \; ,
\nonumber\\
      R_N
      &=&
      R_{\rm min} A^{N-1} \quad
     (N \! =1 - N_{\rm max}).
\end{eqnarray}
In this work we use all angular momentum channels with $l, L, \Lambda \leq 2$, for which good convergence of the result is obtained.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=14cm]{jacobi.eps}
\caption{\label{fig:jacobi}
The Jacobi coordinate for the 3-quark systems.
}
\end{center}
\end{figure}

To see the validity of the three-quark calculation, we display the up- and down-quark spin matrix elements of the nucleon obtained in the quark model.
The numerical values of the spin of the proton (neutron) are
\begin{equation}
\sigma_{p(n)}
=
(1.32-1.33) \sigma_{u(d)} - (0.32-0.33) \sigma_{d(u)}
,
\label{eq:Nedmquarkmodel}
\end{equation}
where the range is showing the variation due to the change of the interquark potential (Bhaduri, AL1, AP1, see Sec. \ref{sec:quarkmodel}).
This is in very good agreement with the analytic formula of the heavy quark limit $\sigma_{p(n)} = \frac{4}{3} \sigma_{u(d)} - \frac{1}{3} \sigma_{d(u)}$.
The small difference between them is due to the mixing of orbital angular momentum states.
We note that the contribution of the EDM of ``constituent quarks'' to the nucleon EDM is also given by the same coefficients, but the EDM of current quarks does not coincide with that of the constituent quarks due to additional effects such as the gluon dressing \cite{Yamanaka:2013zoa,Yamanaka:2014lva}.
Recent lattice studies \cite{Yamanaka:2018uud,Gupta:2018lvp,Alexandrou:2019brg,Cirigliano:2019jig,Horkel:2020hpi} are giving $d_{p(n)} \approx 0.8 d_{u(d)} - 0.2 d_{d(u)}$ which is smaller than Eq. (\ref{eq:Nedmquarkmodel}).

\section{Result\label{sec:analysis}}

From our quark model calculation, we obtain the following result:
\begin{eqnarray}
d_N^{\rm (irr)} (w)
&\approx&
\left\{
\begin{array}{rl}
-w \times (4-5) \, e \, {\rm MeV} & (N = n ) \cr
 w \times (4-5) \, e \, {\rm MeV} & (N = p ) \cr
\end{array}
\right.
,
\label{eq:weinbergop_result}
\end{eqnarray}
where the range of the values indicates the uncertainty related to the choice of the interactions of the quark model (see Sec. \ref{sec:quarkmodel}).
The values are significantly smaller than the QCD sum rules outputs (\ref{eq:weinbergop_gpinn}) \cite{Demir:2002gg,Haisch:2019bml}.
As mentioned in the introduction, our result corresponds to the irreducible contribution of Fig. \ref{fig:nucleon_EDM_Weinberg_operator} (c), and it is consistent with the dominance of the long-distance effect [Fig. \ref{fig:nucleon_EDM_Weinberg_operator} (a) and (b)] at the hadron level.
We note that the heavy quark approximation that we used in deriving Eq. (\ref{eq:amplitude3}) is not very accurate because the gluon mass is not too far from the constituent quark mass.
However, even with uncertainties of a hundred percent, the correction we calculated will not significantly affect the dominant contribution from the long-distance effect, in particular in light of the sizable uncertainty on the latter.
Keeping the uncertainty in mind, the total contribution to the nucleon EDM is
\begin{eqnarray}
d_N (w)
=
d_N^{\rm (red)} (w)
+
d_N^{\rm (irr)} (w)
&\approx&
\left\{
\begin{array}{rl}
w \times 20 \, e \, {\rm MeV} & (N = n ) \cr
-w \times 18 \, e \, {\rm MeV} & (N = p ) \cr
\end{array}
\right.
.
\label{eq:weinbergop_total}
\end{eqnarray}
The theoretical uncertainty can be estimated by adding in quadrature the absolute values of our result (\ref{eq:weinbergop_result}) and the error bar 50\% for the $\gamma_5$-rotated contribution obtained in Ref. \cite{Haisch:2019bml}.
This amounts to about 60\% for both the neutron and the proton.

Let us derive the constraint on the Weinberg operator imposed by the recent experimental data of the neutron EDM.
The upper limit to $w$ at the scale $\mu = 1$ TeV is
\begin{eqnarray}
|w (\mu =1 \, {\rm TeV})| < 2.3 \times 10^{-10} {\rm GeV}^{-2}
,
\end{eqnarray}
where the renormalization was calculated in the leading logarithm approximation \cite{Braaten:1990gq,Chang:1990jv,Degrassi:2005zd,Kamenik:2011dk,Dekens:2013zca,Yamanaka:2017mef,deVries:2019nsu}.
Naively, we might see that the above equation is constraining the scale of new physics at the level of $O(100)$ TeV, but we have to note that the Weinberg operator only appears from the two-loop level in many known candidates of new physics \cite{Weinberg:1989dx,Abe:2017sam}, so that the constraint on the energy scale can be attenuated.

Let us try to interpret our result.
The reducible part calculated in Refs. \cite{Demir:2002gg,Haisch:2019bml} is obtained after the $\gamma_5$-rotation, so it is inheriting the large size of the anomalous magnetic moment \cite{Seng:2014pba}, which is an $O(1)$ quantity for nucleons.
Our calculation, in contrast, is encompassing the electromagnetic external field and the CP-odd interaction in a same quark level package,
so it cannot be enhanced beyond the extent of the baryon.
Another argument is that the irreducible part must involve opposite parity excited states in the intermediate states, which require $O(100)$ MeV of energy transition.
Our result might also have overlap with the long distance one, but we estimate this effect to be small, since the we calculated in a nonrelativistic framework, while the long distance effect is a relativistic one.

\section{Summary}

We calculated the CP-odd two-body force generated by the Weinberg operator and the nucleon EDM induced from it in the nonrelativistic quark model.
In the language of the velocity expansion, the CP-odd two-body force gives the leading contribution to the nucleon EDM.
We solved the 3-body problem in the coordinate space formalism using the Gaussian expansion method.
It was possible to calculate the nucleon EDM with the same calculational procedure as that of the EDM of $^3$He/$^3$H.
We obtained a smaller nucleon EDM than the one calculated in the QCD sum rules \cite{Demir:2002gg,Haisch:2019bml}.
We interpret this result as the dominance of the long distance effect over the short distance one.

Our analysis and results make us expect that the leading contribution to the isoscalar contact CP-odd nuclear force is also due to the $\gamma_5$-rotated CP-even contact $NN$ interaction determined in chiral effective field theory by the CP-odd nucleon mass.
This contact CP-odd nuclear force is one of the important subprocesses generating the nuclear and atomic EDMs.
For that we have to show again that the direct contribution to the isoscalar contact CP-odd nuclear force is small.
This analysis is also possible using the quark model, but it will be left for a future work.

\acknowledgments

We thank Jordy de Vries for useful discussions.
This work was supported by the Grant-in-Aid for Scientific Research (Grant No. 18H05407) from the Japan Society For the Promotion of Science.


As military leaders, we both have developed command philosophies to provide vision and purpose to the units we were leading. In communicating our priorities to the troops upon taking command, we received great advice from our senior enlisted advisors to respectfully stick to the military tenet of "keep it simple, stupid" – that is, to concentrate on a few select priorities when communicating what is most important for the unit to accomplish.
the war on terror / homeland security.
We know that this approach may offend many in government or industry, who hang on to the hope of hearing mention of their issue or program in the speech so they can turn around and use the presidential emphasis to seek greater federal investment, congressional support or public attention for their policies or programs. But don't be swayed by those pressures, Mr. President – don't get off message. Your priorities, and the direction in which you want to lead the country, will be crystal clear to all if you keep it simple.
Now we know that other issues are still important to you – they are important to us as well. Let America know that issues such as affordable health care, comprehensive ocean policy, reduction of greenhouse gases, and gays in the military are still on the radar screen. However, you could stress that the complexity or divisiveness of those issues demands deeper bi-partisan consideration and cooperation, which you plan to facilitate. Stress that you will still move these balls, and many others, down the field, but you don't want to dilute your three main priorities on the one night you have America's undivided attention. You might even parlay this into a second media opportunity later in the week, where you communicate these other agenda items to Congress and to the American public in advance of delivering your 2011 budget on February 1.
There is usually so much included in the State of the Union that we can't figure out what's most important. The State of the Union should be used to demonstrate your resolve and sharpen your administration's focus on the most pressing needs of the nation. Such a speech would be a radical departure from the norm and a memorable call for action. Mr. President, on this night, we implore you to talk about CHANGE that we can ALL get behind.


Today, we clunk away at a keyboard and end up with half a gigabyte of meeting minutes on our hard drive that we'll never read again to go with the two dozen scribbled receipts we keep shoved in the glove box. That chaos can be tamed. With the right tools and attitude, we can capitalise on this familiar tool to boost productivity and innovation. Modern note taking takes the familiar scrawl of handwritten notes and pairs it with the sharing and storage capabilities of the Digital Age.
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More to come! Ideally taken outdoors so I don't have to do crazy long exposures.
This entry was posted in misc and tagged experiment, photography, pinhole on April 11, 2013 by me.
I was left with a batch of croissant dough and a lot of cookie dough in my fridge. My eyes are bigger than my friends' stomachs.
This entry was posted in food and tagged baking, experiment on March 13, 2013 by me.
After being defeated last weekend by the Chocolate Egg Cupcakes, Shamiq and I tried again. This time, we started with two sets of frozen eggs — softboiled for four minutes, and raw.
For the softboiled then frozen eggs, I dunked them in hot water for a little bit to warm up the outside. My thinking was that an icy egg may release too much water and interfere with the corn muffin's baking. The texture of a frozen egg white is pretty weird. It's almost spongy.
Lo and behold! A runny yolk. Victory was delicious.
Another shot of the runny yolk, because… why not?
Egg 1: Yolk was more set than I'd like, but not quite hardboiled. It was at that… pudding like stage. 17 minutes.
Egg 2: Runny yolk! Hurray. Muffins baked for about 17 minutes to reach this state.
Egg 3: After about 20 minutes, the yolk was starting to set, but there was still some raw batter under the crackly surface of the top of the muffin. I scooped it out and the remaining muffin was pretty good. But raw batter is meh.
Egg 4: Yolk gets pretty set, and the egg white disappears into the corn muffin, for the most part.
3. whack one particular part with rounded part of spoon until shell is removed, then "push" upwards.
* There was a second round with an egg that had been in the freezer for a few days, the muffin baked and the yolk came out still-frozen. I think freezing for a few hours is probably the sweet spot. Clearly more science is needed.
This entry was posted in food and tagged baking, experiment on March 4, 2013 by me.
After my round of eggs-in-cupcakes, I had some chocolate cake batter left. I thought I'd make them into smore-cupcakes.
From the left, graham crackers + mini marshmallows, just mini marshmallows, half a large marshmallow & a whole large marshmallow.
Topped off the batter, you can still see the shapes of the fillings.
But darn, the cupcakes looked misleadingly gooey.
Upside, the melted marshmallows made the chocolate cupcakes incredibly gooey and moist.
This entry was posted in misc and tagged baking, experiment on February 26, 2013 by me.
While reading 7×7's The Big Eat 2013, I stumbled upon this particularly interesting listing — Rebel Within, from Craftsman & Wolves. I love putting edible things inside other edible things, and the idea of an egg, yolk still running inside a savory biscuit or muffin is just… awesome.
Shamiq and I tried boiling eggs for 2, 3 and 4 minutes, and then putting them in chocolate cupcake batter (just out of laziness, I wanted to figure out the eggs before tackling a savory biscuit/muffin). This is what we found.
2 minute boiled eggs are too raw. Also, torching egg shells can cause exploding egg shells.
3 minutes seemed about right, if you're willing to lose some of the white.
We baked two cupcakes with 4 minute eggs (easy to peel) and six with three minute eggs (harder to peel, but much less done).
Dangit, the yolk was cooked through. But not overcooked.
The yolks in the four minute eggs were definitely overcooked.
Oh well. And, in case it's at all questionable, hard boiled eggs don't go well with chocolate.
This entry was posted in food and tagged baking, eggs, experiment on February 24, 2013 by me.
I tried to make cheesecake brownies following the idea of black bottom cupcakes. I went for Smitten Kitchen's "Favorite Brownies" and doubled the cheesecake section of her Black Bottom Cupcakes.
Results: Cheesecake takes longer to cook than brownies. By the time the center of the cheesecake was set, the edges were cracking and the bottom of the brownies had overcooked to a crust.
Next up: Try this in a cupcake pan, where the heat is more distributed.
This entry was posted in food and tagged baking, experiment on February 20, 2013 by me.
Before the Thanksgiving break, I took home all the bananas the snack staff at work had on hand since they were going to throw them away in anticipation of the holiday. What better to do with over a dozen bananas than some banana bread science?
I took half of each loaf to work and had people take small samples of each and cast anonymous votes. The results were overwhelmingly in favor of banana bread 1. Banana bread 1, however, also has the most sugar, so that very likely affects peoples preferences.
Other notes, banana bread 6 had more banana flavor than 3, but probably needed more sugar. 3 was the clear loser.
I'll try this again with even amounts of sugar.
Science is a good reason to stuff yourself with banana bread.
This entry was posted in food and tagged baking, experiment on December 3, 2012 by me.
Shamiq and I wanted to try to make our own rolls.
Turns out it's pretty hard to make them look pretty. Instead they look more like modern art.
But it was a tasty endeavor.
This entry was posted in food and tagged cooking, experiment on November 26, 2012 by me.


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Avneet Kaur explores her inner dancer in THIS latest video
Choti Sarrdaarni fame Mansi Sharma is now mom to a baby boy
Have a look at Ankita Lokhande's audition for Pavitra Rishta
Published by user1 at May 23, 2020
Aladdin – Naam Toh Suna Hoga stars Siddharth Nigam and Avneet Kaur in the lead roles. Sid plays Aladdin while Avneet is seen as Princess Yasmine. The duo's pairing has become an instant hit among the viewers and fans are loving their chemistry in the show.
Avneet has become a hot favourite among the viewers. The actress enjoys a massive fan following on Instagram, all thanks to her wonderful posts. We have always seen Avneet sharing all the latest updates from her personal and professional life.
While being at home, Avneet has explored lots of things. From cooking to revamping her room, she has done a lot of things. Avneet shared several videos of the same on her social media handles.
We had earlier shared a video where Avneet was seen turning a choreographer for herself. The actress was seen grooving on Senorita and it was such a delight to see her.
And now, Avneet has done it yet again. The actress is showing off her swag in the latest video where she is grooving on ÉCHAME LA CULPA featuring Luis Fonsi and Demi Lovato.
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dc.description.abstract Background and aims: The impact of tobacco use and cessation on atherogenesis remains unclear. We aimed to study the association of tobacco use and prior cessation with the presence, extent and severity of atherosclerosis on coronary computed tomographic angiography (CTA). Methods: We examined 1798 consecutive symptomatic patients without known coronary artery disease (CAD) referred for CTA, stratified by smoking status (never, current [within 30 days], or former [>30 days before CTA]). Plaque severity (none, <50%, >= 50% stenosis), composition (non-calcified [NCP], partially calcified [PCP], or calcified plaque [CP]), and segment involvement score (SIS) were visually graded. Multivariate analysis was performed, adjusting for CAD risk factors and cholesterol lowering medication use. Results: The median age of patients was 50 years [IQR: 42-58] (61% male), with 74% never smokers, 12% current smokers, and 14% former smokers (median quit duration = 12 years [IQR: 3-26]). Smoking exposure in former versus current smokers was 11 [IQR: 5-25] and 10 [IQR: 2-20] pack-years, respectively (p = 0.01). Compared to never smokers, current smokers demonstrated an increased odds ratio of all plaque types (adjusted OR: any NCP = 1.55 [95% CI 1.04-2.32], p = 0.03; any PCP = 1.61 [1.10-2.37], p = 0.02; any CP = 1.93 [1.32-2.81], p = 0.001), non-obstructive CAD (aOR = 1.47 [1.04, 2.07], p = 0.03), obstructive CAD (aOR = 1.81 [1.01-3.24], p = 0.047), and SIS > 4 (aOR = 1.60 [1.04e2.46], p = 0.03). Compared to current smoking, prior smoking cessation (>= 12 years) was associated with a decreased odds ratio of any NCP (aOR = 0.42 [0.19-0.90], p = 0.03), CP (aOR = 0.43 [0.22-0.84], p = 0.02), and obstructive CAD (aOR = 0.40, [0.15-0.98], p = 0.048). Conclusions: Current smoking is independently associated with the presence and extent of coronary plaque, and a higher risk of non-obstructive and obstructive CAD compared to never smoking. Prior smoking cessation correlated with improvements in CTA-identified plaque measures.


Dad's summer turned out to be a very productive one. He wrote two bestsellers, including The Pink Full Moon, which became so popular he was constantly getting phone calls for books tours and appearances on talk shows.
There was some chatter about turning it into a movie, but dad was really trying to discourage it. The story was loosely based on our family life and he didn't want that to be exploited for the screen. Since I had never been to a movie theatre myself, I didn't really understand it all, but regardless it all sounded very exciting!
Mom and dad tried to explain to me what is was like to be a celebrity in the public eye all the time. They wanted me to fully understand that the paparazzi were never a friend and to avoid them as much as possible. They said I had been born into a family of a certain celebrity status and it was part of the reason why we were living on the island. It was mostly to protect me, they said.
When the phone calls and the stress from his new books became too much, we could always find dad fishing behind the barn.
It was his own quiet spot, as he called it and when he was out there, we tried not to disturb him. He tried to get me to fish with him, but I had much better things I wanted to do, then stand there in silence staring at the ocean.
Shortly after Boots left the island dad picked up a great new toy. It wasn't the best telescope out there you could buy, but he said he didn't need much, just something to keep an "eye on things".
I asked him once 'what things', but he told me not to worry, and that I could use the telescope anytime I wanted. As long as it was only during the day. I had a lot of fun with that telescope until the day I found something odd in the ocean. I called my dad up to take a look himself. He said he thought it was a statue of a woman, not the dead body I thought it was.
Dead bodies float or sink depending on how long they have been dead he corrected. When they sink, they don't sink standing up without any movement. That did make me feel a bit better. Dad said that when I got older, we could go scuba diving way out there and take a look. In my head I was thinking no thanks!
Shortly before my birthday, mom started to feel really unwell and it reminded me of how ill she was way back in the winter time. She tried to keep it hidden, but with the amount of times she was throwing up, and as closely as I was watching her, it was hard to miss. I began to worry again.
Before long, my big day had arrived. Party time! Well at least whatever kind of party can be had with three people, a dog and an uninterested cat.
Mom woke me up in the morning with a birthday hug.
Then she spent the morning baking me the best chocolate cake I had ever seen, that kept my mouth watering all day long just at the thought of it. No amount of chatting my mom up could get her to move up the party time, which was to be four o'clock. Just in time to ruin our dinner, so my dad said, but not even he could change her mind.
Mom said she wanted just one more day with her son as a little boy. She reluctantly brought out the cake at four, where I made a wish, blew out the candles and then, felt funny all over. Tingles began to radiate all over my body, while brightly coloured sparkles illuminated all around me.
Then with a spin and a jump, a teenager I was!
A few days later it was dad's birthday as well. The night before, mom and dad decided to have a bit of alone time to celebrate more privately. As a teen I now understood what that meant, so I feigned exhaustion and headed up to bed. If I was about to become an old man, I would want to make the most of it as well. Not that they hadn't spend their entire days making the most of it! I popped on my music, while they headed out to the hot tub down on the beach. Not something I wanted to hear, if I didn't have to, as the all day lip locking was bad enough!
The following night, out came the cake for my dad.
So, in approximately two weeks time, all our lives aged and the dynamic of the household changed. My mother, no longer the face of young youth, yet still very beautiful. My father now into his later years and me, well, no longer a child. Free to do what I wanted to do and start making plans for my future, whatever that may be.
Jin Charles Bell, now teen!!


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The 1965 Texas A&M Aggies football team represented Texas A&M University in the 1965 NCAA University Division football season as a member of the Southwest Conference (SWC). The Aggies were led by head coach Gene Stallings in his first season and finished with a record of three wins and seven losses (3–7 overall, 1–6 in the SWC).

Schedule

References

Texas AandM
Texas A&M Aggies football seasons
Texas AandM Aggies football

redpajama_set_name: RedPajamaWikipedia


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Q: How did Count Otto von Doom's assassin kill Queen Elizabeth I? In Marvel 1602 #3, Count Otto von Doom sends three assassins after key people in England. The implication is that the third and final one arrived in the court of Queen Elizabeth I as an envoy from Latveria, who presents a musical contraption designed by von Doom himself. In the last scene where we see him, he kisses the Queen's hand.

Then a few panels later, we see Queen apparently having had a violent death with the musical contraption standing ominously.

I don't understand this panel; how did Queen Elizabeth I die? My first though is that, since it appears she died violently, the contraption shot her. But I don't see an arrow or even a wound and the angle of the dead Queen compared to the contraption's trumpet seems all wrong. My next thought was poison of some sort from the envoy kissing her finger, but that doesn't seem to match with the final scene.
How did Count Otto von Doom's third assassin kill Queen Elizabeth I?

A: In issue #04 we learn that the "contraption" Doom sent emitted a poison gas which killed the Queen. Doom mentions dropping a "pill" into Aqua Regia (a mixture of nitric acid and hydrochloric acid). If this pill contained potassium cyanide, for example, it would have created deadly hydrogen cyanide gas.

redpajama_set_name: RedPajamaStackExchange


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Player Corner
London Lions: Tushar: Time to re-establish his sta (7/3/2012)
--K. Arumugam
Tushar Khandker: Time to re-establish his status of a star
Never do in the long career of Tushar, he will be so critically watched, as it would happen in London in four week's time. For, it is testing time for the long standing star, what with goals not coming as much as expected of him, and which is a big flaw in the current team.
As a senior player in the team, therefore, his role will come under scrutiny, and he is aware of this. He has everything, a bit of Arjun Halappa in making penalty corners, a bit of Jude Felix in pepping up attack, and a dash of Jagbir Singh what with quick jump for deflection and of course his unique patent of whacking waist-height ball into either corner of the net.
Another one from the junior team of 2001 who made his mark on the senior side as well. Inside the opposition half, Tushar Khandker is a multi-purpose man. He makes the moves, creates goals for others and scores them himself as well. The speedy winger is the current Indian team's livewire and part of the core group of senior players.
A spectators' delight and trainers' asset, Tushar has never shied away from hard work. A product of Delhi-based Air India Academy (now shut down), Tushar belongs to a hockey family – his father Vinod Khandkar was a state-level player and his uncle, Subodh Khandkar, has represented India on the international stage and his grandfather VB Khandkar was also a national level player.
Born on May 4 1985, Tushar established himself as a player in his very first India outing with a good display of talent – victorious 2001 Sub Junior Asia Cup, where he was named Man of the Match in the final. Tushar was also part of gold-winning Indian teams at the Youth Asia Cup (2001), Akhbar Al-Youm Cup (2002 & 2003) and many others in the age groups categories. However, despite his proven skills, Khandker had to wait a long time before breaking into the senior national side. The break finally came in 20003, when he was included for the Hockey Australia Challenge Cup, scoring in his debut match. However, that did not prevent him from continuing with the junior teams, since age was on his side and he managed to successfully straddle both.
At the 2004 Junior Asia Cup final in Karachi, Tushar scored a hat-trick to hog the limelight and prove his selection to the senior side a year before was not a fluke. The next year, he suffered personal tragedy while training in Frankfurt for the 2005 junior World Cup in Rotterdam when his father passes away. Tushar rushed to hometown Indore, only to return within three days and join his team. Despite the tragedy, he excelled at the event.
In 2007, Tushar was part of the gold-winning team at the Asia Cup in Chennai, earning the rare honour of becoming Asia Cup champion in every age group, the only Indian to do so! He led the team on the double-leg four-nation tour to Australia in 20008 after the Olympic qualifiers disaster. Employed with Bharat Petroleum, he led Bangalore Lions to the title in the now-defunct PHL in 2007-8. He married Nidhi last year, getting her name tattooed on his wrist and forearms – one after engagement and the other after marriage.