Ex 1.12 - Pattern Recognition and ML by Christopher Bishop

Pre-read

Question

Solution from Book

Solution Using ChatGPT

Are you aware of the result E[xn, xm] = mu^2 + I . sigma ^ 2

I assume you meant $E[X_n \cdot X_m] = \mu^2 + I \cdot \sigma^2$, where $I$ is the Kronecker delta, which is 1 when $n = m$ and 0 otherwise.

In that case, $E[X_n \cdot X_m]$ simplifies to:

$E[X_n \cdot X_m] = \begin{cases} \mu^2 + \sigma^2 & \text{if } n = m \\ \mu^2 & \text{if } n \neq m \end{cases}$

This is because when $n = m$, you have the product of a variable with itself, and the additional $\sigma^2$ term comes from the covariance term. When $n \neq m$, the covariance term is zero, and you are left with the square of the mean.

If you have further questions or if there's anything specific you'd like to clarify, feel free to ask!

Can you derive this expression?

Certainly! Let's derive the expression for $E[X_n \cdot X_m]$ for two continuous random variables $X_n$ and $X_m$ from the same Gaussian distribution $N(\mu, \sigma^2)$ with mean $\mu$ and variance $\sigma^2$.

The expectation of the product is given by:

$E[X_n \cdot X_m] = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} x_n \cdot x_m \cdot f(x_n) \cdot f(x_m) \,dx_n \,dx_m$

Since $X_n$ and $X_m$ are from the same distribution, let's denote $f(x)$ as the probability density function (PDF) of $X$. The expression becomes:

$E[X_n \cdot X_m] = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} x_n \cdot x_m \cdot f(x) \cdot f(x) \,dx_n \,dx_m$

Now, split the integral into two cases: $n = m$ and $n \neq m$.

Case 1: $n = m$

$E[X_n \cdot X_m] = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} x_n^2 \cdot f(x) \cdot f(x) \,dx_n \,dx_m$

$= \left(\int_{-\infty}^{\infty} x_n^2 \cdot f(x) \,dx_n\right) \cdot \left(\int_{-\infty}^{\infty} f(x) \,dx_m\right)$

$= \mu^2 + \sigma^2$

This result comes from the fact that the integral of $x^2$ over the entire range for a Gaussian distribution with mean $\mu$ is $\mu^2 + \sigma^2$.

Case 2: $n \neq m$

$E[X_n \cdot X_m] = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} x_n \cdot x_m \cdot f(x) \cdot f(x) \,dx_n \,dx_m$

$= \left(\int_{-\infty}^{\infty} x_n \cdot f(x) \,dx_n\right) \cdot \left(\int_{-\infty}^{\infty} x_m \cdot f(x) \,dx_m\right)$

$= \mu \cdot \mu$

This result comes from the fact that the integral of $x$ over the entire range for a Gaussian distribution with mean $\mu$ is $\mu$.

Therefore, combining both cases:

$E[X_n \cdot X_m] = \mu^2 + I \cdot \sigma^2$

where $I$ is the Kronecker delta, equal to 1 when $n = m$ and 0 otherwise.

References

• give me math expression for: (1/n) * sum_for_n_equals_1_to_N(E[ (1/n^2) * sum_for_m_equals_1_to_N(sum_for_l_equals_1_to_N(xm*xl)) ])
• what is the mathematical expression for (1/N) * sum_n_equal_1_to_N(E[(2/N) * xn * sum_m_equals_1_to_N(xm)])

Tags: Mathematical Foundations for Data Science,Machine Learning,

Solution 1.11 - On Gaussian Distribution and it's Log Likelihood (Pattern Recognition and ML by Christopher Bishop)

Can you give me the equation for Gaussian distribution?

Can you give me it's log likelihood function?

Note: This is already given as part of the problem statement.

Can you show the detailed steps how you arrived at it?

Some paperwork

In the next slide we will solve for the below expression:

Some Logarithm Properties we would use:

Can you maximize the log likelihood expression w.r.t. mu and show the detailed steps?

Some paperwork for derivative of:

We will prove it next:

Some ‘Differentiation’ identities we would see next

And now maximize log likelihood w.r.t. sigma-squared and show the detailed steps

Identity:

References

https://chat.openai.com/share/4278db33-9b76-4d8b-9586-4e1e78844433

Tags: Mathematical Foundations for Data Science,Machine Learning,

Question 1.11 - On Gaussian Distribution and it's Log Likelihood (Pattern Recognition and ML by Christopher Bishop)

Pre-read:

(1)


(2)


(3)

From (1.46) and (1.53), the log likelihood function can be written in the form:



Question:

By setting the derivatives of the log likelihood function (1.54) with respect to µ and σ^2 equal to zero, verify the results (1.55) and (1.56).

Link to Solution

Valprol - CR 500 Tablet

Valprol - CR 500 Tablet

Prescription Required

Marketer: Intas Pharmaceuticals Ltd
SALT COMPOSITION: Sodium Valproate (333mg) + Valproic Acid (145mg)

Product introduction

Valprol -CR 500 Tablet is a combination of two medicines used to treat epilepsy, a neurological disorder in which there are recurrent episodes of seizures or fits. It controls the abnormal activity of the brain, relaxes the nerves and hence, prevents seizures or fits.

Valprol -CR 500 Tablet should be taken with food. Your doctor will decide the correct dose for you. This may increase gradually until your condition is stable. This medicine may take several weeks to work but it is important to take it regularly to get the benefit. Do not stop taking it, even if you feel fine unless your doctor advises you to. You may have more seizures, or your bipolar disorder may get worse.

The most common side effects of this medicine include nausea, vomiting, loss of appetite, swelling of gums, headache, sleepiness, tremor, hair loss and liver injury. Most side effects wear off, but if they bother you or do not go away, tell your doctor. There may be ways of preventing or reducing these effects.

Before taking this medicine, tell your doctor if you have kidney or liver problems, meningitis or depression or suicidal thoughts. Also let your doctor know about all other medications you are using as some may affect, or be affected by, this medicine, including contraceptive pills. If you are pregnant or breastfeeding, Valprol -CR 500 Tablet can be taken if it is clearly needed but the dose may be adjusted. You should avoid driving or riding a bicycle if this medicine makes you drowsy or dizzy. You may need frequent blood tests to check how you are responding to this medicine.

You should avoid alcohol while taking Valprol -CR 500 Tablet, as it may worsen certain side effects. This medicine can also lead to weight gain, eat a healthy balanced diet, avoid snacking with high-calorie food, and exercise regularly. Inform your doctor if you develop any unusual changes in mood or behavior, new or worsening depression, or suicidal thoughts or behavior.
Uses of Valprol Tablet CR

    Epilepsy

Benefits of Valprol Tablet CR

In Epilepsy

Valprol -CR 500 Tablet slows down electrical signals in the brain which cause seizures (fits). It can also help reduce symptoms such as confusion, uncontrollable jerking movements, loss of awareness, and fear or anxiety. The medicine can allow you to do some activities that you would otherwise be forbidden or scared to do (such as swimming and driving). It can take a few weeks for this medicine to work (because the dose has to be increased slowly) and during this time you may still have seizures. Do not stop using this medicine even if you feel well, until your doctor advises you to. Missing doses may trigger a seizure.

Side effects of Valprol Tablet CR

Most side effects do not require any medical attention and disappear as your body adjusts to the medicine. Consult your doctor if they persist or if you’re worried about them
Common side effects of Valprol

    Nausea
    Vomiting
    Weight gain
    Loss of appetite
    Gum swelling
    Headache
    Sleepiness
    Tremors
    Hair loss
    Liver injury
    Increased liver enzymes
    Bleeding gums
    Epigastralgia
    Diarrhea
    Memory impairment
    Decreased sodium level in blood
    Anemia (low number of red blood cells)
    Thrombocythemia
    Pain during periods

How to use Valprol Tablet CR

Take this medicine in the dose and duration as advised by your doctor. Swallow it as a whole. Do not chew, crush or break it. Valprol -CR 500 Tablet is to be taken with food.

How Valprol Tablet CR works

Valprol-CR 500 Tablet is a combination of two antiepileptic medicines: Sodium Valproate and Valproic Acid.

Safety advice

Alcohol
UNSAFE
It is unsafe to consume alcohol with Valprol -CR 500 Tablet.

Pregnancy
CONSULT YOUR DOCTOR
Valprol -CR 500 Tablet is unsafe to use during pregnancy as there is definite evidence of risk to the developing baby. However, the doctor may rarely prescribe it in some life-threatening situations if the benefits are more than the potential risks. Please consult your doctor.

Breast feeding
SAFE IF PRESCRIBED
Valprol -CR 500 Tablet is safe to use during breastfeeding. Human studies suggest that the drug does not pass into the breastmilk in a significant amount and is not harmful to the baby.

Driving
UNSAFE
Valprol -CR 500 Tablet may decrease alertness, affect your vision or make you feel sleepy and dizzy. Do not drive if these symptoms occur.

Kidney
SAFE IF PRESCRIBED
Valprol -CR 500 Tablet is probably safe to use in patients with kidney disease. Limited data available suggests that dose adjustment of Valprol -CR 500 Tablet may not be needed in these patients. Please consult your doctor.
However, talk to your doctor if you have any underlying kidney disease.

Liver
CAUTION
Valprol -CR 500 Tablet should be used with caution in patients with liver disease. Dose adjustment of Valprol -CR 500 Tablet may be needed. Please consult your doctor.
Use of Valprol -CR 500 Tablet is not recommended in patients with severe liver disease and active liver disease.

What if you forget to take Valprol Tablet CR?
If you miss a dose of Valprol -CR 500 Tablet, take it as soon as possible. However, if it is almost time for your next dose, skip the missed dose and go back to your regular schedule. Do not double the dose.

All substitutes

For informational purposes only. Consult a doctor before taking any medicines.
Valprol -CR 500 Tablet
₹9.67/Tablet CR
Valprolex Chrono 500 CR Tablet
Zeelab Pharmacy Pvt Ltd
₹3.42/tablet cr
65% cheaper
Valtec CR 500 Tablet
Cipla Ltd
₹9.07/tablet cr
6% cheaper
Encorate Chrono 500 Tablet CR
Sun Pharmaceutical Industries Ltd
₹9.66/tablet cr
same price

Valparin Chrono 500 Tablet CR
Sanofi India Ltd
₹9.67/tablet cr
same price

Torvate Chrono 500 Tablet CR
Torrent Pharmaceuticals Ltd
₹7.6/tablet cr
21% cheaper

Quick tips

    You have been prescribed Valprol - CR 500 Tablet for treatment and prevention of seizures.
    Take it at the same time every day to maintain consistent levels in your body.
    Do not drive or do anything that requires mental focus until you know how Valprol -CR 500 Tablet affects you.
    Avoid consuming alcohol when taking Valprol -CR 500 Tablet, as it may cause excessive sleepiness or drowsiness.
    Monitor your weight during the treatment as Valprol -CR 500 Tablet can cause weight gain.
    Your doctor may monitor Valprol -CR 500 Tablet level, blood counts and liver function regularly throughout your treatment.  Inform your doctor if you develop fever, stomach pain, nausea or yellowing of your eyes or skin.
    Do not take Valprol -CR 500 Tablet if you are pregnant or planning to conceive or breastfeeding.
    Do not stop taking the medication suddenly without talking to your doctor as it may increase the seizure frequency.

Fact Box

Habit Forming: No
Therapeutic Class: NEURO CNS

Lithosun 300 Tablet

Lithosun 300 Tablet

Prescription Required

Marketer: Sun Pharmaceutical Industries Ltd
SALT COMPOSITION: Lithium carbonate (300mg)

Product introduction

Lithosun 300 Tablet is used in the treatment of bipolar disorder and mania in adults. It is sometimes used to treat other behavioral disorders as well. It reduces the frequency of manic episodes and decreases the intensity of those episodes that might occur.

Lithosun 300 Tablet should be taken with food. However, it is advised to take it at the same time each day as this helps to maintain a consistent level of medicine in the body. Do not skip any doses and finish the full course of treatment even if you feel better. If you have missed a dose, take it as soon as you remember it. You should continue to take this medicine for as long as the doctor advises and do not stop taking it suddenly as it may result in harmful effects.

Side effects associated with the use of this medicine include tremors, slurred speech, uncoordinated body movements, nausea, acne, increased white blood cell count, and memory impairment. It may also cause hair loss, enlarged thyroid gland, skin rash, and increased thirst. This medicine may also cause weight gain and to control it, you should have a balanced diet and exercise regularly. If you have been taking this medicine for a long time then regular monitoring of thyroid and kidney function may be required.

Uses of Lithosun Tablet

    Mania
    Bipolar disorder

Benefits of Lithosun Tablet

In Mania

Mania means extremely excited or elevated mood. Lithosun 300 Tablet helps calm the mood and relax the nerves. This stabilises the mood and prevents the symptoms of mania from recurring again. Taking Lithosun 300 Tablet will ensure that you have a better social life and are able to do daily activities more comfortably.

In Bipolar disorder

Lithosun 300 Tablet works to restore the normal balance of nerve activity in your brain. It can help prevent extreme changes in mood and help you feel less agitated. You may experience fewer episodes of low mood. It can take several weeks for this medicine to work and you may still feel low during this time. It is likely that you will take this medicine for at least six months but possibly much longer. It needs to be taken regularly to work effectively. Do not stop taking it unless your doctor advises you to. You should continue to eat well and keep fit to reduce symptoms of bipolar disorder.

Side effects of Lithosun Tablet

Most side effects do not require any medical attention and disappear as your body adjusts to the medicine. Consult your doctor if they persist or if you’re worried about them

Common side effects of Lithosun

    Tremors
    Slurred speech
    Uncoordinated body movements
    Nausea
    Acne
    Increased white blood cell count
    Memory impairment
    Hair loss
    Goiter (enlarged thyroid gland)
    Skin rash
    Increased thirst
    Weight gain
    Polyuria
    Diarrhea

How to use Lithosun Tablet

Take this medicine in the dose and duration as advised by your doctor. Swallow it as a whole. Do not chew, crush or break it. Lithosun 300 Tablet is to be taken with food.
How Lithosun Tablet works
Lithosun 300 Tablet works by suppressing the abnormal and excessive activity of the nerve cells in the brain.

Safety advice

Alcohol
UNSAFE
It is unsafe to consume alcohol with Lithosun 300 Tablet.


Pregnancy
CONSULT YOUR DOCTOR
Lithosun 300 Tablet is unsafe to use during pregnancy as there is definite evidence of risk to the developing baby. However, the doctor may rarely prescribe it in some life-threatening situations if the benefits are more than the potential risks. Please consult your doctor.

Breast feeding
SAFE IF PRESCRIBED
Lithosun 300 Tablet is probably safe to use during breastfeeding. Limited human data suggests that the drug does not represent any significant risk to the baby.

Driving
UNSAFE
Lithosun 300 Tablet may cause side effects which could affect your ability to drive.
Lithosun 300 Tablet may make you feel sleepy, tired or dizzy. Lithosun 300 Tablet may also cause other effects that can make it dangerous to drive such as numbness, paralysis, weakness or fits (seizures).

Kidney
CAUTION
Lithosun 300 Tablet should be used with caution in patients with kidney disease. Dose adjustment of Lithosun 300 Tablet may be needed. Please consult your doctor.
Use of Lithosun 300 Tablet is not recommended in patients with severe kidney disease.

Liver
SAFE IF PRESCRIBED
Lithosun 300 Tablet is probably safe to use in patients with liver disease. Limited data available suggests that dose adjustment of Lithosun 300 Tablet may not be needed in these patients. Please consult your doctor.

All substitutes

For informational purposes only. Consult a doctor before taking any medicines.
No substitutes found for this medicine

Quick tips

    Lithosun 300 Tablet is one of the most effective long-term treatment for bipolar disorder.
    It may also be used for the treatment of mania.
    Your lithium blood levels, thyroid function, and kidney function may be monitored as long as you take this medicine.
    It may cause diarrhea and dehydration. Drink plenty of water and and use normal amounts of salt. Inform your doctor if you start or stop a low-salt diet.
    Monitor your weight during treatment as Lithosun 300 Tablet can cause weight gain.
    Do not drive or do anything that requires mental focus until you know how it affects you.
    Inform your doctor if you have persistent stomach upset, problems with your speech, or extreme drowsiness. Your dose may need to be adjusted.
    Do not take Lithosun 300 Tablet if you are pregnant or breastfeeding.
    Do not stop taking the medication suddenly without talking to your doctor.

Fact Box

Chemical Class: Organic Carbonic Acids
Habit Forming: No
Therapeutic Class: NEURO CNS
Action Class: Mood stabilizers

Clonotril 0.5 Tablet

Clonotril 0.5 Tablet

Prescription: Required
Marketer: Torrent Pharmaceuticals Ltd
SALT COMPOSITION: Clonazepam (0.5mg)

Product introduction

Clonotril 0.5 Tablet is a prescription medicine used to treat epilepsy (seizures) and anxiety disorder. It helps to decrease the abnormal and excessive activity of the nerve cells and calms the brain.

Clonotril 0.5 Tablet may be taken with or without food. However, take it at the same time each day as this helps to maintain a consistent level of medicine in the body. Take this medicine in the dose and duration as advised by your doctor as it has a high potential of habit-forming. If you have missed a dose, take it as soon as you remember it and finish the full course of treatment even if you feel better. You should not stop this medicine suddenly without talking to your doctor as it may increase the seizure frequency and can cause nausea, anxiety, flu-like symptoms, and muscle pain.

Some common side effects of this medicine include fatigue, depression and impaired coordination. It may also cause dizziness and sleepiness, so do not drive or do anything that requires mental focus until you know how this medicine affects you. It is important to inform your doctor if you develop any unusual changes in mood or depression as this medicine may cause suicidal thoughts.

Uses of Clonotril Tablet

Treatment of Anxiety disorder

Treatment of Epilepsy/Seizures

Benefits of Clonotril Tablet

In Treatment of Anxiety disorder

Clonotril 0.5 Tablet stops your brain from releasing the chemicals that make you feel anxious so it can reduce the symptoms of excessive anxiety and worry. It can also reduce feelings of restlessness, tiredness, difficulty concentrating, feeling irritable and sleep problems that often come with Anxiety Disorder. It will therefore help you go about your daily activities more easily and be more productive. Keep taking this medicine even if you feel well. Stopping suddenly can cause serious problems.

In Treatment of Epilepsy/Seizures

Clonotril 0.5 Tablet slows down electrical signals in the brain which cause seizures (fits). It can also help reduce symptoms such as confusion, uncontrollable jerking movements, loss of awareness, and fear or anxiety. The medicine can allow you to do some activities that you would otherwise be forbidden or scared to do (such as swimming and driving). It can take a few weeks for this medicine to work (because the dose has to be increased slowly) and during this time you may still have seizures. Do not stop using this medicine even if you feel well, until your doctor advises you to. Missing doses may trigger a seizure.

Side effects of Clonotril Tablet

Most side effects do not require any medical attention and disappear as your body adjusts to the medicine. Consult your doctor if they persist or if you’re worried about them

Common side effects of Clonotril

    Depression
    Dizziness
    Drowsiness
    Fatigue
    Impaired coordination
    Memory impairment

How to use Clonotril Tablet

Take this medicine in the dose and duration as advised by your doctor. Swallow it as a whole. Do not chew, crush or break it. Clonotril 0.5 Tablet may be taken with or without food, but it is better to take it at a fixed time.

How Clonotril Tablet works

Clonotril 0.5 Tablet is a benzodiazepine. It works by increasing the action of a chemical messenger (GABA) which suppresses the abnormal and excessive activity of the nerve cells in the brain.

Safety advice

Alcohol
UNSAFE
It is unsafe to consume alcohol with Clonotril 0.5 Tablet.
warnings
Pregnancy
CONSULT YOUR DOCTOR
Clonotril 0.5 Tablet is unsafe to use during pregnancy as there is definite evidence of risk to the developing baby. However, the doctor may rarely prescribe it in some life-threatening situations if the benefits are more than the potential risks. Please consult your doctor.
warnings
Breast feeding
SAFE IF PRESCRIBED
Clonotril 0.5 Tablet is safe to use during breastfeeding. Human studies suggest that the drug does not pass into the breastmilk in a significant amount and is not harmful to the baby.
warnings
Driving
UNSAFE
Clonotril 0.5 Tablet may cause side effects which could affect your ability to drive.
warnings
Kidney
CAUTION
Clonotril 0.5 Tablet should be used with caution in patients with kidney disease. Dose adjustment of Clonotril 0.5 Tablet may be needed. Please consult your doctor.
Use of Clonotril 0.5 Tablet can cause excessive sleepiness in patients with end stage kidney disease.

Liver
CAUTION
Clonotril 0.5 Tablet should be used with caution in patients with liver disease. Dose adjustment of Clonotril 0.5 Tablet may be needed. Please consult your doctor.

What if you forget to take Clonotril Tablet?

If you miss a dose of Clonotril 0.5 Tablet, take it as soon as possible. However, if it is almost time for your next dose, skip the missed dose and go back to your regular schedule. Do not double the dose.

All substitutes

For informational purposes only. Consult a doctor before taking any medicines.
No substitutes found for this medicine

Quick tips

    The addiction / habit-forming potential of this medicine is very high. Take it only as per the dose and duration advised by your doctor
    It may cause dizziness. Do not drive or do anything that requires mental focus until you know how this medicine affects you.
    Avoid consuming alcohol as it may increase dizziness and drowsiness.
    Inform your doctor if you are pregnant, planning to conceive or breastfeeding.
    Inform your doctor if you experience worsen anxiety, depression angry, or violent behavior and mania while taking this medicine.
    Do not stop taking medication suddenly without talking to your doctor as that may lead to nausea, anxiety, agitation, flu-like symptoms, sweating, tremor, and confusion.

Fact Box

Chemical Class: Benzodiazepines Derivative
Habit Forming: Yes
Therapeutic Class: NEURO CNS
Action Class: Benzodiazepines

Betacap TR 20 Capsule

Betacap TR 20 Capsule

Prescription: Required
Marketer: Sun Pharmaceutical Industries Ltd
SALT COMPOSITION: Propranolol (20mg)
Storage: Store below 30°C

Product introduction

Betacap TR 20 Capsule helps decrease anxiety and relieve tremors. It is also used to help prevent migraine, heart-related chest pain (angina), and bleeding in the stomach caused by high blood pressure in the liver (portal hypertension).

Betacap TR 20 Capsule may also be used to treat high blood pressure and some types of abnormal heartbeat (arrhythmia). The dose will depend on what you are being treated for and how you respond to the medicine. You should always take it as prescribed by the doctor. It should be taken on an empty stomach and at about the same time each day. You should keep taking it even if you feel well, as you are still getting the benefits. If you stop taking it suddenly, your condition may worsen.

The most common side effects are tiredness, weakness cold fingers and toes (Raynaud phenomenon), irregular or slow heartbeat, numbness in your fingers, and breathlessness. You may also experience nausea, vomiting, and diarrhea. Talk to your doctor if the side effects bother you or do not go away. Most side effects are short-lived and improve as your body gets used to the medicine.

You should not use this medicine if you have asthma, very slow or uneven heartbeats, or a serious heart condition, including heart failure. Talk to your doctor before taking it if you have kidney or liver problems or chronic obstructive pulmonary disease (COPD). In terms of lifestyle, alcohol may affect the way this medicine works and should be avoided. You should not drive if this medicine makes you feel dizzy. Ask your doctor whether it is safe to take this medicine if you are pregnant or breastfeeding.

Uses of Betacap Capsule PR

    Treatment of Pheochromocytoma
    Treatment of Hypertension (high blood pressure)
    Prevention of migraine
    Treatment of Anxiety
    Treatment of Arrhythmia
    Prevention of Heart attack
    Prevention of Angina (heart-related chest pain)
    Treatment of Tremors

Benefits of Betacap Capsule PR

In Treatment of Pheochromocytoma

While carrying out surgery for the removal of pheochromocytoma, there is a risk of abnormally high blood pressure. Betacap TR 20 Capsule blocks the effect of some chemicals on your heart and blood vessels. This slows down the heart rate and helps the heartbeat with less force thereby lowering your blood pressure. It is used for the immediate reduction of very high blood pressure (hypertensive emergency). Controlled blood pressure reduces the risk of having a heart attack, stroke, or kidney problems.

In Treatment of Hypertension (high blood pressure)

Betacap TR 20 Capsule relaxes the blood vessels so that blood can flow more easily around your body. This lowers your blood pressure and reduces your risk of having a stroke, a heart attack, or kidney problems in the future. You do not usually feel any direct benefit from taking this medicine, but it works in the long term to keep you well. You should take it regularly as prescribed for this medicine to be most effective, even if you feel better.

In Prevention of migraine

Betacap TR 20 Capsule helps improve the flow of blood in your brain and prevents abnormal activity of muscles that triggers migraines. It is a very effective medicine for preventing migraine attacks, however, it does not treat an attack that has already started. By preventing and reducing the frequency of migraine attacks, the medicine can help you carry out your daily activities and improve your quality of life.

In Treatment of Anxiety

Betacap TR 20 Capsule stops your brain from releasing the chemicals that make you feel anxious so it can reduce the symptoms of excessive anxiety and worry. It can also reduce feelings of restlessness, tiredness, difficulty concentrating, feeling irritable and sleep problems that often come with Anxiety Disorder. Betacap TR 20 Capsule will therefore help you go about your daily activities more easily and be more productive. Keep taking this medicine even if you feel well. Stopping suddenly can cause serious problems.

In Treatment of Arrhythmia

Betacap TR 20 Capsule is used to stabilize heart rate. It helps in normalizing an abnormal heart rhythm, preventing it occurring in the first place or slowing down the heart rate during an episode.
In Prevention of Heart attack
Betacap TR 20 Capsule helps lower your blood pressure and make it easier for your heart to pump blood around your body. This reduces the chances of you having a heart attack. It can also reduce the risk of dying if it is given immediately after a heart attack. This medicine needs to be taken regularly to be effective, so keep taking it even if you feel well. Do not stop without talking to your doctor.

In Prevention of Angina (heart-related chest pain)

Betacap TR 20 Capsule relaxes the blood vessels so that blood can flow more easily around your body and makes sure that your heart is getting a good supply of oxygen. This makes it less likely that you will suffer chest pain caused by angina. This medicine can help increase your ability to exercise and go about your daily life more easily by reducing the frequency of angina attacks. You should take it regularly and as long as it is prescribed for it to work effectively.
In Treatment of Tremors
Betacap TR 20 Capsule helps improve the flow of blood and prevents abnormal activity of muscles that trigger tremors. This medicine can therefore enhance the quality of life by improving the ability to carry out daily functions in a better manner.

Side effects of Betacap Capsule PR

Most side effects do not require any medical attention and disappear as your body adjusts to the medicine. Consult your doctor if they persist or if you’re worried about them
Common side effects of Betacap

    Tiredness
    Weakness
    Raynaud's phenomenon
    Arrhythmia (irregular heartbeats)
    Nausea
    Vomiting
    Diarrhea

How to use Betacap Capsule PR

Use it as advised by your doctor or check the label for directions before use. Betacap TR 20 Capsule is to be taken empty stomach.
Avoid Betacap TR 20 Capsule with high-fat meals such as olive oil, nuts & seeds (Brazil nuts), dark chocolate, butter and meat.

How Betacap Capsule PR works

Betacap TR 20 Capsule contains Propranolol, a beta blocker. It works by affecting the body’s response to nerve impulses, especially in the heart. It slows down your heart rate and makes it easier for the heart to pump blood around the body. This prevents arrhythmias. It also widens the blood vessels in the body for better blood flow, thereby preventing angina as well as migraine. The exact mechanism by which it prevents tremors is not known, but experts believe that Betacap TR 20 Capsule helps block the nerve impulses to the muscles responsible for tremors. Propranolol helps block the effects of the chemical messengers namely, adrenaline and noradrenaline, that are produced by the brain and are responsible for increasing your heart rate which makes you feel anxious. This way it helps with anxiety. While treating pheochromocytoma, Betacap TR 20 Capsule may be given to block the action of high-adrenaline hormones, to lower the risk of developing dangerously high blood pressure during surgery for removing the tumor.

Safety advice

warnings
Alcohol
UNSAFE
It is unsafe to consume alcohol with Betacap TR 20 Capsule.
warnings
Pregnancy
CONSULT YOUR DOCTOR
Betacap TR 20 Capsule may be unsafe to use during pregnancy. Although there are limited studies in humans, animal studies have shown harmful effects on the developing baby. Your doctor will weigh the benefits and any potential risks before prescribing it to you. Please consult your doctor.
warnings
Breast feeding
SAFE IF PRESCRIBED
Betacap TR 20 Capsule is probably safe to use during breastfeeding. Limited human data suggests that the drug does not represent any significant risk to the baby.
warnings
Driving
UNSAFE
Betacap TR 20 Capsule may cause side effects which could affect your ability to drive.
Betacap TR 20 Capsule may cause visual disturbances, hallucinations, fatigue, mental confusion, dizziness or tiredness. This may affect your driving ability.
warnings
Kidney
SAFE IF PRESCRIBED
Betacap TR 20 Capsule is safe to use in patients with kidney disease. No dose adjustment of Betacap TR 20 Capsule is recommended.
However, inform your doctor if you have any kidney disease. Betacap TR 20 Capsule may be started with a low dose and then increased further. Regular monitoring of blood pressure is advisable for dose adjustment.
warnings
Liver
CAUTION
Betacap TR 20 Capsule should be used with caution in patients with liver disease. Dose adjustment of Betacap TR 20 Capsule may be needed. Please consult your doctor.
Regular monitoring of blood pressure is advisable for dose adjustment.
What if you forget to take Betacap Capsule PR?
If you miss a dose of Betacap TR 20 Capsule, take it as soon as possible. However, if it is almost time for your next dose, skip the missed dose and go back to your regular schedule. Do not double the dose.

All substitutes

For informational purposes only. Consult a doctor before taking any medicines.
Betacap TR 20 Capsule
₹2.5/Capsule PR
Prohype SR Capsule
Samarth Life Sciences Pvt Ltd
₹2.42/capsule pr
3% cheaper

Quick tips

    It is not the first-choice treatment for high blood pressure according to the latest guidelines.
    It may hide the symptoms of low blood sugar if you have diabetes. Monitor blood sugar levels regularly.
    To lower the chance of feeling dizzy or passing out, rise slowly if you have been sitting or lying down.
    Use caution while driving or doing anything that requires concentration as Betacap TR 20 Capsule can cause dizziness and sleepiness.
    Inform your doctor if you notice increased swelling around your legs or ankles, sudden weight gain or sudden shortness of breath as these may be symptoms of heart failure.
    Do not stop taking the medication suddenly without talking to your doctor.

Fact Box

Chemical Class: Naphthalenes derivatives
Habit Forming: No
Therapeutic Class: CARDIAC
Action Class: Beta blocker - Non selective

Toothpastes for Pyorrhoea

1. Senquel Foaming Medicaled Oral Gel

# Effectively reduces tooth sensitivity

# Reduces the sensation of pain

# Offers a gentle cleansing experience

# Maintains overall oral health

Key Benefits

    Senquel oral gel, with potassium nitrate, effectively reduces tooth sensitivity, allowing you to enjoy hot and cold foods without discomfort

    The foaming gel offers a refreshing and gentle cleansing experience for your teeth and gums

    Potassium nitrate desensitises nerve endings in the teeth, reducing the sensation of pain or discomfort

    This oral gel promotes overall oral comfort, making daily oral care routines more pleasant

2. Stolin-R Foaming Dental Gel 

Key Ingredients:

    Zinc Sulphate I.P, Sodium Monofluorophosphate U.S.P, Alum B.P


Key Benefits:

    Stolin-R Foaming Gel contains minerals that help restore lost minerals in the teeth, which can lead to stronger teeth overall

    The gel is enriched with sodium monofluorophosphate and zinc sulphate, which provide fluoride protection against tooth decay and cavities

    Stolin-R Foaming Gel contains alum and zinc sulphate, which help fight against bacteria and prevent pulp infections

    Stolin-R Foaming Gel provides a complete solution for oral hygiene, helping to keep teeth and gums healthy and clean

3. Stolin Oral Gel

Key Ingredients:

    Strontium Chloride


Key Benefits:

    Stolin oral gel, with strontium chloride, helps alleviate tooth sensitivity, allowing you to enjoy hot or cold foods and drinks without discomfort

    This gel provides thorough cleaning and plaque removal, promoting overall oral health

    Experience a refreshing and cool sensation with each use, leaving your mouth feeling revitalised

    The gel-based formula is gentle on gums, making it suitable for sensitive oral care

4. Pyx-G Toothpaste for Plaque & Tartar Control | Fights Bad Breath, Bleeding Gums & Pyorrhoea

Key Ingredients:

    Potassium Nitrate BP 5% w/w
    Sodium Monofluorophusphote USP 0.7% w/w 3 (Fluoride contents not more than 917 ppm)
    Baking soda


Key Benefits:

    Pyx-G Toothpaste helps in preventing tartar build-up on teeth and keeps them healthy

    The presence of fluoride in the toothpaste helps in fighting tooth decay and reduces the chances of developing cavities

    The baking soda in Pyx-G Toothpaste acts as a natural whitening agent that clears out stains and plaque from the teeth' surface

    Pyx-G Toothpaste can potentially help in avoiding bleeding gums