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Most modern medicines are carefully synthesized organic molecules so potent that each pill contains only a few milligrams of the active ingredient. Pepto-Bismol is a fascinating exception, both because its active ingredient is bismuth, a heavy metal commonly used in shotgun pellets, and because there is a lot of it in each dose. So much, in fact, that I was able to extract a slug of bismuth metal from a pile of pink pills.

One two-pill dose of Pepto-Bismol contains 262 milligrams (more than a quarter of a gram) of bismuth subsalicylate, and about an eighth of that weight is bismuth. It’s not just bits of ground-up bismuth metal, though. The bismuth is combined chemically with salicylate, an organic molecule. To get bismuth metal, you have to reduce it chemically, the way iron ore has to be reduced to make iron metal.

I tried reducing Pepto-Bismol by heating it with charcoal, the same method used to reduce iron ore, but that didn’t work very well. All I got was crumbly slag. Fortunately, I found a better procedure with an assist from science-experiment website chúng tôi which recommends isolating the bismuth by reaction with aluminum in an acid solution. This way requires only muriatic acid (found in the paint department at my local hardware store) and aluminum foil (found in my kitchen).

Start Here

I started with 180 generic Pepto-Bismol pills, which together contain about 24 grams of bismuth.


I ground up the pills with a mortar and pestle.


I dissolved the pills in a solution of six parts water to one part concentrated muriatic acid. (Warning: Concentrated muriatic acid is extremely corrosive and its fumes will burn the lungs.)


After a very slow filtering step, I had a clear pink solution containing dissolved bismuth ions.


I dipped aluminum foil into the solution, turning it black. The acid dissolves the aluminum, which reacts with the bismuth ions. The ions precipitate out as bismuth metal particles.

Filtering Again

After filtering the liquid through a pillowcase, the powder left in the filter is the bismuth metal.


Heating with a plumbing torch is the moment of truth: Will the black powder melt into shiny metal?


A few grams of actual solid metal with the characteristic iridescent sheen of bismuth.

You're reading Gray Matter: Extracting Bismuth From Pepto

Decimal Equivalent Of Gray Code And Its Inverse

Gray code or reflected binary code is a form of a binary representation of numbers in which two consecutive numbers only differ by one bit.

For example, the gray code of 1 is 001, while the gray code of 2 is 011.

Gray code is usually used in error correction because it prevents some data errors that can happen in the usual binary representations while state changes.

Gray code is also helpful in k-maps, communication, etc., because of its unique property.


Study decimal, binary and gray code notations before reading further.

Problem Statement 1

Given a decimal number n, find the gray code of the number in decimal form.

Examples Input: 3 Output: 2

Hence, the decimal equivalent of the gray code of 3 is 2.

Input: 5 Output: 7

Hence, the decimal equivalent of the gray code of 5 is 7.


The compiler understands the numbers in binary format.

Thus, in our program, when we input a number in decimal format, it is interpreted in binary.

Hence, we only need to convert a number from its binary equivalent to its gray code.

Binary to Gray Code Conversion

The leftmost bits of the binary representation and the gray code is equal. The following bits to the right can be found by taking xor of successive binary bits.

For example −

Consider n = 3. The binary code of 3 is 011.

The leftmost bit of binary and gray code is equal. Hence, the first bit from the left in the gray code is 0.

For the second bit from the left, xor the first and second bit from the left in the binary code. 0 XOR 1 = 1.

For the third bit from the left, xor the second and third bit from the left in the binary code. 1 XOR 1 = 0.

Thus the gray code: 010.

Algorithm: Using Bitwise Operators

We can obtain the gray code of a number n by the following steps −

Right shift n by 1.

Xor the right shifted number with original n.


Below is a C++ program for finding gray code from binary code using bitwise operators

using namespace std; int dec_equi_of_gray(int n) { } int main(){ int n = 3; cout<<“The decimal equivalent of the gray code of 3 is: “;

cout << dec_equi_of_gray(n) << endl; return 0; }

Output The decimal equivalent of the gray code of 3 is: 2 Problem Statement 2

Given the decimal value of the gray code, find its decimal code value.

Examples Input: 15 Output: 10

Now, converting gray code to binary code gives 1010 from 1111.

And 1010 is the binary value of 10. Hence, the output.

Input: 10 Output: 12

The binary code of gray code 1010 is 1100. And 1100 is 12 in decimals.

Gray code to Binary Code Conversion

The leftmost bit (MSB) of the binary code is the same as the MSB of the gray code. The following bits can be found by taking xor of the previous index binary bit and the current index gray bit.

For example: Consider the gray code 1111.

The MSB of the binary code will be the same as the MSB of gray code. Hence, the MSB will be 1.

For the second leftmost bit, check the xor of the second leftmost bit of gray code and the leftmost bit of binary code. Hence, 1 ^ 1 = 0.

Similarly, for the third leftmost bit, 0 ^ 1 = 1.

For the fourth leftmost bit, 1 ^ 1 = 0.

Hence the binary code: 1010.


Below is a C++ program for finding binary code from gray code using bitwise operators

using namespace std;

//This function returns the decimal value of int gray_to_binary(int n){ int binary = n; binary ^= n; } return binary; } int main(){ int n = 15; cout<<“The decimal value of the binary code converted from the gray code is: “;

cout << gray_to_binary(n) << endl;

return 0; }

Output The decimal value of the binary code converted from the gray code is: 10 Conclusion

This article solved the problem of finding the Decimal Equivalent of Gray Code and its Inverse for a given number n. We solved the problem using bitwise operators. C++ programs are provided for both of the parts of the problem.

Summer Internship: Getting To The Heart Of The Matter

Summer Internship: Getting to the Heart of the Matter Cardio testing lab welcomes SAR senior as part of team

Anubhav Nangia (SAR’15) became a valued team member when he interned this summer at a cardiovascular testing center at Brigham and Women’s Hospital. Photos by Cydney Scott

Internships often play a critical role in job hunting as employers increasingly seek graduates with some real-world experience. A 2012 Marketplace and Chronicle of Higher Education survey found that employers place more weight on experience, particularly internships and employment during school, rather than academic credentials, when evaluating a recent graduate for employment. Name:

Anubhav Nangia (SAR’15)

My internship:

I worked at the noninvasive cardiovascular imaging center at the Carl J. and Ruth Shapiro Cardiovascular Center at Brigham and Women’s Hospital in Boston.

How I landed the internship:

I was recommended for it by a professor, applied, and was promptly accepted. I’d emailed the center’s supervisor, who said to come in for an interview, and I said, sure why not? I was accepted after a couple of days.

A typical day on the job:

I’d arrive at the center by 7:45 a.m. When a physiologist was ready to test a patient, I would get the person from the waiting room and prepare him or her for the test. I performed standard treadmill tests, stress echocardiograms, and cardiopulmonary stress tests. Once I had obtained the patient’s consent, I would ask questions to document the medical history and enter the information into the computer.

I prepared patients for electrocardiograms (ECG), which involves the placement of electrodes on their chest and abdominal region. After briefing the physiologist on the patient’s history, we’d interpret the baseline ECG together. This was by far the most challenging aspect of the internship. Each ECG is unique, and the basic information I had learned about ECGs at school had not prepared me for the extensive analysis I performed at the center.

The test is always performed under the supervision of a physiologist. I had to constantly eye the ECG for any changes, while printing a 12-lead every three minutes, taking blood pressures, monitoring the patient’s progress, and documenting observations on the reports. It gets very hard to take a blood pressure after about nine minutes of exercise due to the surrounding noise and the patient’s movements. I had to communicate with the patient constantly to try and push him or her to maximal effort. The test stopped either at the request of the patient or when a physiological sign or signs that I was looking for has been attained. Those signs would depend on the patient’s history. Patients are monitored for eight minutes following exercise, during which blood pressure and ECG are constantly monitored. It took me time to get adjusted to maintaining a watch on so many aspects of the test.

Once the recovery period had ended, I would unhook the patient from the apparatus and help the physiologist with the final report. This required further interpretations of the ECGs obtained throughout the test. The entire process—from getting the patient to finishing the report—usually took about an hour.

Career skills I acquired:

I strongly believe the following new skills I acquired will benefit my future in the health care industry.

I am now very good at taking relevant, detailed patient histories. I learned that casual conversation with patients puts them at ease and helps them to be thorough in the details they provide. A good history saves time for the physiologists.

Although I learned about electrode placement in theory in class, the practical side is quite different. Each patient has a unique body structure, which means that the electrodes must be adjusted to ensure a good voltage for the ECG. Since the patients’ blood pressure is taken manually and not digitally, it took a few attempts before the physiologists agreed that I was ready to take them on my own. I am now comfortable prepping any patient and have a good instinct for gauging the quality of the placement.

I have become good at taking blood pressures during exercise. Due to the surrounding noise of the machinery and patient’s movement, this was hard to learn. Thanks to the physiologists who hopped onto treadmills during their free time, I am now confident in my ability to measure the blood pressure of a patient at any stage of exercise.

I can efficiently use the software involved in stress tests at the Brigham.

My most remarkable achievement has been the ability to interpret ECGs independently. From knowing just the basic anatomy of an ECG to understanding terms like premature ventricular/atrial contractions, left/right bundle branch blocks, fusion beats, and so forth, I have come a long way. I am sure that this knowledge will benefit me immensely in medical school, should I go down that track.

What it internship taught me about the real world:

I have developed an understanding of what it feels like to work in health care. Every patient who visits a hospital is unique. Health care professionals must do their best to ensure that patients feel relaxed and safe under their supervision. Their reaction to, observation of, and communication with, patients is crucial to the success of a clinical encounter.

Health care workers must not bring the stress of their personal lives into the workplace; it can negatively impact a patient’s experience. A couple of times during my internship, I was stressed out due to family issues. Luckily for me, I noticed right away that my personal troubles had wiped the smile off my face entirely. I made a conscious effort never to let such things bother me again.

I learned what it is like to work in a professional setting. Colleagues have certain expectations of each other with regard to workload, work ethics, and more, and it is important for everyone to align with them. Mutual respect in the workplace is imperative.

Contrary to popular belief, it is okay to make mistakes. The colleagues I worked with became my friends and mentors. I never hesitated to ask questions.

It is important to make the most out of every opportunity provided to you. Although I was required to work only 10 to 14 hours a week, I ended up working 21 a week to gain additional experience.

Biggest mistake I made:

Sometimes, it is hard to take a blood pressure when the so-called Korotkoff sounds cannot be heard clearly. For one such patient, when I was taking a blood pressure during the recovery period, I underestimated the systolic pressure. This mistake caused the physiologist to be confused for several minutes, and we assumed that the patient was having a hypotensive response postexercise. But when the physiologist took additional blood pressures, she realized that my measurement was probably inaccurate.

Most frustrating thing about the internship:

Nothing about the experience frustrated me per se; I enjoyed my time at the center thoroughly.

My proudest accomplishment:

The ability to interpret ECGs independently. It takes a lot of training, and I am proud to have learned the necessary techniques and definitions so quickly.

Most important lesson I learned:

Never hesitate to ask questions.

My most surprising or unexpected experience:

The first time I was asked to take blood pressures of patients during exercise, I did not find it hard. All the physiologists were surprised and excited that I was able to learn to take them so quickly.

What I learned about the real world that inspired or frustrated me:

When you work in a health care setting, everyone helps each other. You are never alone. You become part of a team trying to deliver the best possible service to patients.

Overall grade and whether the internship lived up to my expectations:

Grade: A.

The internship lived up to, and in fact exceeded, my expectations. My initial ambition of working in the health care industry was strengthened. I got incredible amounts of hands-on experience with patients and cherished the opportunity to participate in their treatment regimens, even if it was in a relatively small way. I was treated like any other employee at the center and was expected to perform to similar standards. Supported by an incredibly welcoming staff that was eager to teach, I now feel like a competent exercise physiologist.

If I had it to do over, I’d…

Probably work longer hours to get the opportunity to learn even more.

Apply to internships that you are truly interested in. Do not work at a place simply because you want to boost your résumé. It will seem like a burden for you more than anything else. Be cordial and respectful at your job site. Try to meet as many people as possible. You never know when someone will turn out to be a great resource for you personally or professionally.

And don’t be afraid to ask questions. It is expected that interns are only getting their feet wet. You are not meant to be an expert in any way.

Tomorrow, part four of our summer internship series: Live from Lincoln Center.

Explore Related Topics:

What To Look For In A Gaming Monitor: Specs That Matter

Running a gaming PC is a lot like being a car enthusiast. You want to get the best parts available, tune them to your liking, and then get out onto the open road, so to speak. The funny thing is, even with the best graphics card and CPU, a gaming PC can’t demonstrate its full glory without a solid gaming monitor to bear witness.

With so many options, where do you begin and how do know what matters most? Choosing the ideal gaming monitor gets easier once you decide on the resolution you want, and understand how different features will affect your experience. Price matters too, of course, but with sale periods like Black Friday, Prime Day, and general deals throughout the year, pricing can be more flexible for the patient shopper.

Here’s a look at the key features you want in a monitor, as well as some recommendations on what to buy. 


Brad Chacos/IDG

Choosing the right resolution for gaming is all about the capabilities of your graphics card.

The first thing to think about is the monitor’s resolution, and this depends entirely on what your graphics card is capable of. There’s no point getting a 4K monitor, for example, if your graphics card can only handle the lower resolution of 1080p. The only caveat to that would be if you plan on upgrading soon and want to “future proof” by getting a higher-resolution monitor before you get the new GPU.

If you’re shopping for a new graphics card to go with your new monitor, read our roundup of the best graphics cards for PC gaming at every resolution (it has budget recommendations too!).

1080P: Standard 1080p monitors have a resolution of 1920×1080 pixels. This is still the most popular resolution for gaming, according to the Steam hardware survey. Graphics cards in this range include the Nvidia GeForce GTX 1650 Super, GeForce GTX 1660 Super (our favorite 1080p GPU), and the AMD Radeon RX 5500 XT.

1440P: The step up from 1080p is 2560×1440 pixels, a nice middle ground between 1080p and 4K. These 1440p monitors are widely considered PC gaming’s sweet spot, providing a noticeable fidelity boost over 1080p monitors without forcing you to break your budget. Solid choices for graphics card in this range include our favorite 1440p graphics card the GeForce RTX 3070, as well as the Radeon RX 6800.

8K: We’re also in the very early days of 8K, which offers four times the pixel count of 4K. But gaming at 8K is expensive, and the gaming industry isn’t there yet. Enthusiasts can, of course, adopt early with the GeForce RTX 3090, but it’s not cheap and you’re likely to get better value from 4K at the moment.

Refresh rate and response time

In general, with higher frame rates, game motion appears smoother, responds faster, and just generally looks better. That’s why higher refresh rate monitors are popular choices. A 144Hz monitor, for example, can display more than double the frames of a 60Hz monitor with the appropriate graphics card.

Once you’ve tried a 120Hz or 144Hz, it’s hard to go back to 60Hz, even for productivity tasks. If you’re an e-sports enthusiast, blistering 240Hz and even 360Hz panels are available, but they’re very expensive and limited to 1080p resolution.

In addition to refresh rate, response times are also an important factor. It dictates how fast it takes a monitor at the pixel level to shift from one color to the next. A lower number is better here, as a poor response time can cause ghosting and other visual artifacts to appear. Many monitors have a 5ms or 4ms response time, which is acceptable, although 1ms (or sometimes even lower) is best for gaming.

Asus ROG Swift PG279Q ($849). This 1440p monitor has a refresh rate of 165 Hz, it’s rocking G-Sync and it supports the full sRGB color gamut, with 4ms response time. 

Acer Predator XB271HU ($510). Another 1440p monitor with a 144Hz refresh rate and Nvidia G-Sync, with 4ms response time.

Adaptive sync


The Dell S2417DG.

Next up we have adaptive sync. This feature syncs the refresh rate between your graphics card and your display. The idea is that when both the graphics card and your monitor are synced up there is less chance of screen tearing and stutter for what we love to call “buttery-smooth gaming.” 

Adaptive sync comes in two flavors: Nvidia G-Sync and AMD’s royalty-free FreeSync. The latter is by far the most common and the cheapest for manufacturers to add, which is perhaps why Nvidia’s GeForce graphics cards now work with FreeSync. Using FreeSync with a GeForce card is fine, but for the truly best performance it’s still better to use G-Sync with Nvidia cards.

Here are two good monitors to consider, one rocking FreeSync and one with G-Sync:

Dell S2417DG ($470). This is a 24-inch 1440p monitor with a 165Hz refresh rate and a 1ms response time. It also supports G-Sync.

AOC G2590FX ($214). This 25-inch 1080p monitor features FreeSync, a 144Hz refresh rate, and a 1ms response time.

Display size


The AOC C32V1Q.

If you have a 24-inch 1080p display, for example, then your count is going to be a little less than 92 ppi, which is respectable for 1080p. At 32-inches, however, the ppi drops below 70. Upgrade to 1440p, and a 32-inch monitor gets about the same ppi as that 1080p 24-inch monitor, and a 4K monitor at 32 inches is nearly 138 ppi.

In general, any modern monitor that’s between 24 and 32 inches will be just fine for gaming. Obviously, the higher the resolution, the higher the pixel count, which does improve image quality. But if you love the notion of a large display, and can only afford a 1080p display at that size, just go for it.

Dell S2421HGF ($171). A 24-inch 1080p monitor with a 144Hz refresh rate, FreeSync, and a 1ms response time.

Asus VG278QR ($249). Going up in size, we have this 27-inch 1080p display with FreeSync, a 165Hz refresh rate, and a 0.5ms refresh rate.

AOC C32V1Q ($200). Go big or go home with this budget 31.5-inch 1080p monitor with an above-average refresh rate, and a 4ms response time.

High dynamic range


The Acer Predator CG437LK.

Anyone in the market for a 4K monitor should seriously consider the addition of high dynamic range if they can afford it—HDR monitors come at a steep premium. HDR allows for a drastically wider range of color variation, which means a better picture overall. The difference between HDR and non-HDR is simply stunning.

Here are some good choices for monitors with 4K resolution and HDR:

Acer Predator CG437LK ($1,300). This is one heck of a display at 43-inches, with G-Sync, a 120Hz refresh rate, a 1ms response time, and DisplayHDR 1000.

Philips 436M6VBPAB Refurbished ($655). This monitor is hard to come by, but this refurbished version at Newegg offers a lot of value.

Panel types and color gamut


The LG 27GL850-B is a new breed of IPS display with faster response times.

There are two major types of panels used for gaming displays: TN and IPS (short for twisted nematic and in-plane switching, respectively, which describes their different underlying pixel-rendering technology.) Both can be suitable for gaming, so it really comes down to what you prefer. (There’s a third panel type called VA—vertical alignment—which largely splits the difference between TN speeds and IPS color reproduction, with excellent contrast ratios.)

TN panels tend to have lower response times, which means less chance for “ghosting” issues, where visual artifacts briefly remain on the screen. But TN panels have a narrower viewing angle, so if you are viewing from outside the sweet spot—say, your monitor is angled slightly—it might be harder to see details, especially in darkly lit scenes.

IPS, meanwhile, is a visual treat, but you don’t get those 1 millisecond response times as with TN. At least, not typically. For about a year now, there have been IPS displays with 1ms response times, but they tend to be more expensive.

Color space, meanwhile, is how faithful a monitor is to a defined set of colors such as sRGB or AdobeRGB. Accurate colors are always better, but it’s most important for content creation work.

Here are some good TN panels for gaming:

BenQ Zowie XL2411P ($200). A 24-inch 1080p monitor with a 144Hz refresh rate, and a 1ms response time. It lacks FreeSync or G-Sync, but it does come with a height- and tilt-adjustable stand.

Acer KG271 ($260). This 27-inch 1080p monitor features a 144Hz refresh rate, FreeSync, and the TN panel’s tell-tale 1ms response time.

LG 27GL850-B ($447). This is one of the early IPS displays featuring a 1ms response time. It also has a 1440p resolution, a 144Hz refresh rate, and FreeSync.

HP VH240a ($125). A classic example of a budget monitor. It’s 24 inches, 1080p, a 60Hz refresh rate, and a 5ms response time. It’s not powerful, but for a little over $100, it’ll do a respectable job.

Curved displays, ultrawide monitors, and aspect ratios


The Samsung Odyssey G5.

For the most part, when you look at a standard display, you are looking at a screen with a 16:9 aspect ratio. But when you start looking at curved displays, you’ll come across ultrawide monitors with aspect ratios like 21:9. These types of displays are generally more immersive, but they do look different than what you’re used to, and have a “learning curve” of a few days before they feel natural.

Curved monitors are intriguing since they add depth simply by changing the shape of the screen. The curve of a monitor is displayed as “R,” which stands for radius, or how big the monitor would be if it formed a complete circle. A 1000R monitor would form a circle with a radius of 1,000mm, or 1 meter, for example.

Some people love these types of monitors, especially with games that feature large vistas, such as driving games or flight simulators.

Samsung Odyssey G5 ($290). This 32-inch monitor has an immersive 1000R curvature, a 144Hz refresh rate, 1440p resolution, a 1ms response time, and FreeSync. This monitor is still within the usual range of viewing ratio at 16:9.

Acer Nitro XZ342CK ($500). A 34-inch display with a 1500R curvature, 1440p resolution, FreeSync, a 144Hz refresh rate, a 1ms response time, and a 21:9 aspect ratio.

Learn Attention Models From Scratch


Attention models, also known as attention mechanisms, are input processing techniques used in neural networks. They allow the network to focus on different aspects of complex input individually until the entire data set is categorized. The goal is to break down complex tasks into smaller areas of attention that are processed sequentially. This approach is similar to how the human mind solves new problems by breaking them down into simpler tasks and solving them step by step. Attention models can better adapt to specific tasks, optimize their performance, and improve their ability to attend to relevant information.

The attention mechanism in NLP is one of the most valuable developments in deep learning in the last decade. The Transformer architecture and natural language processing (NLP) such as Google’s BERT have led to a recent surge of progress.

Learning Objectives

Understand the need for attention mechanisms in deep learning, how they work, and how they can improve model performance.

Get to know the types of attention mechanisms and examples of their use.

Explore your application and the pros and cons of using the attention mechanism.

Get hands-on experience by following an example of attention implementation.

This article was published as a part of the Data Science Blogathon.

When to Use the Attention Framework?

The attention framework was initially used in encoder-decoder-based neural machine translation systems and computer vision to enhance their performance. Traditional machine translation systems relied on large datasets and complex functions to handle translations, whereas attention mechanisms simplified the process. Instead of translating word by word, attention mechanisms assign fixed-length vectors to capture the overall meaning and sentiment of the input, resulting in more accurate translations. The attention framework is particularly useful when dealing with the limitations of the encoder-decoder translation model. It enables precise alignment and translation of input phrases and sentences.

Unlike encoding the entire input sequence into a single fixed-content vector, the attention mechanism generates a context vector for each output, which allows for more efficient translations. It’s important to note that while attention mechanisms improve the accuracy of translations, they may not always achieve linguistic perfection. However, they effectively capture the intention and general sentiment of the original input. In summary, attention frameworks are a valuable tool for overcoming the limitations of traditional machine translation models and achieving more accurate and context-aware translations.

How do Attention Models Operate?

In broad terms, attention models make use of a function that maps a query and a set of key-value pairs to generate an output. These elements, including the query, keys, values, and final output, are all represented as vectors. The output is calculated by taking a weighted sum of the values, with the weights determined by a compatibility function that evaluates the similarity between the query and the corresponding key.

In practical terms, attention models enable neural networks to approximate the visual attention mechanism employed by humans. Similar to how humans process a new scene, the model focuses intensely on a specific point in an image, providing a “high-resolution” understanding, while perceiving the surrounding areas with less detail, akin to “low-resolution.” As the network gains a better understanding of the scene, it adjusts the focal point accordingly.

Implementing the General Attention Mechanism with NumPy and SciPy

In this section, we will examine the implementation of the general attention mechanism utilizing the Python libraries NumPy and SciPy.

To begin, we define the word embeddings for a sequence of four words. For the sake of simplicity, we will manually define the word embeddings, although in practice, they would be generated by an encoder.

import numpy as np # encoder representations of four different words word_1 = np.array([1, 0, 0]) word_2 = np.array([0, 1, 0]) word_3 = np.array([1, 1, 0]) word_4 = np.array([0, 0, 1])

Next, we generate the weight matrices that will be multiplied with the word embeddings to obtain the queries, keys, and values. For this example, we randomly generate these weight matrices, but in real scenarios, they would be learned during training.

np.random.seed(42) W_Q = np.random.randint(3, size=(3, 3)) W_K = np.random.randint(3, size=(3, 3)) W_V = np.random.randint(3, size=(3, 3))

We then calculate the query, key, and value vectors for each word by performing matrix multiplications between the word embeddings and the corresponding weight matrices.

query_1 =, W_Q) key_1 =, W_K) value_1 =, W_V) query_2 =, W_Q) key_2 =, W_K) value_2 =, W_V) query_3 =, W_Q) key_3 =, W_K) value_3 =, W_V) query_4 =, W_Q) key_4 =, W_K) value_4 =, W_V)

Moving on, we score the query vector of the first word against all the key vectors using a dot product operation.

scores = np.array([,key_1),,key_2),,key_3),,key_4)])

To generate the weights, we apply the softmax operation to the scores.

weights = np.softmax(scores / np.sqrt(key_1.shape[0]))

Finally, we compute the attention output by taking the weighted sum of all the value vectors.

attention=(weights[0]*value_1)+(weights[1]*value_2)+(weights[2]*value_3)+(weights[3]*value_4) print(attention)

For a faster computation, these calculations can be performed in matrix form to obtain the attention output for all four words simultaneously. Here’s an example:

import numpy as np from scipy.special import softmax # Representing the encoder representations of four different words word_1 = np.array([1, 0, 0]) word_2 = np.array([0, 1, 0]) word_3 = np.array([1, 1, 0]) word_4 = np.array([0, 0, 1]) # word embeddings. words = np.array([word_1, word_2, word_3, word_4]) # Generating the weight matrices. np. random.seed(42) W_Q = np. random.randint(3, size=(3, 3)) W_K = np. random.randint(3, size=(3, 3)) W_V = np. random.randint(3, size=(3, 3)) # Generating the queries, keys, and values. Q =, W_Q) K =, W_K) V =, W_V) # Scoring vector query. scores =, K.T) # Computing the weights by applying a softmax operation. weights = softmax(scores / np.sqrt(K.shape[1]), axis=1) # Computing the attention by calculating the weighted sum of the value vectors. attention =, V) print(attention) Types of Attention Models

Global and Local Attention (local-m, local-p)

Hard and Soft Attention


Global Attention Model

The global attention model considers input from every source state (encoder) and decoder state prior to the current state to compute the output. It takes into account the relationship between the source and target sequences. Below is a diagram illustrating the global attention model.

Local Attention Model Hard and Soft Attention

Soft attention and the Global attention model share similarities in their functionality. However, there are distinct differences between hard attention and local attention models. The primary distinction lies in the differentiability property. The local attention model is differentiable at every point, whereas hard attention lacks differentiability. This implies that the local attention model enables gradient-based optimization throughout the model, while hard attention poses challenges for optimization due to non-differentiable operations.

Self-Attention Model

The self-attention model involves establishing relationships between different locations in the same input sequence. In principle, self-attention can use any of the previously mentioned score functions, but the target sequence is replaced with the same input sequence.

Transformer Network

The transformer network is built entirely based on self-attention mechanisms, without the use of recurrent network architecture. The transformer utilizes multi-head self-attention models.

Enhanced Accuracy: Attention mechanisms contribute to improving the accuracy of predictions by enabling the model to concentrate on the most pertinent information.

Increased Efficiency: By processing only the most important data, attention mechanisms enhance the efficiency of the model. This reduces the computational resources required and enhances the scalability of the model.

Improved Interpretability: The attention weights learned by the model provide valuable insights into the most critical aspects of the data. This helps improve the interpretability of the model and aids in understanding its decision-making process.

However, the attention mechanism also has drawbacks that must be considered. The major drawbacks are:

Training Difficulty: Training attention mechanisms can be challenging, particularly for large and complex tasks. Learning the attention weights from data often necessitates a substantial amount of data and computational resources.

Overfitting: Attentional mechanisms can be susceptible to overfitting. While the model may perform well on the training data, it may struggle to generalize effectively to new data. Utilizing regularization techniques can mitigate this problem, but it remains challenging for large and complex tasks.

Exposure Bias: Attention mechanisms can suffer from exposure bias issues during training. This occurs when the model is trained to generate the output sequence one step at a time but is evaluated by producing the entire sequence at once. This discrepancy can result in poor performance on test data, as the model may struggle to accurately reproduce the complete output sequence.

Tips for Using Attention Frameworks

When implementing an attention framework, consider the following tips to enhance its effectiveness:

Provide Consistent Training: Consistent training of the neural network is crucial. Utilize techniques such as back-propagation and reinforcement learning to improve the effectiveness and accuracy of the attention framework. This enables the identification of potential errors in the model and helps refine and enhance its performance.

Apply Attention Mechanisms to Translation Projects: They are particularly well-suited for language translations. By incorporating attention mechanisms into translation tasks, you can enhance the accuracy of the translations. The attention mechanism assigns appropriate weights to different words, capturing their relevance and improving the overall translation quality.

Application of Attention Mechanisms

Some of the main uses of the attention mechanism are:

Employ attention mechanisms in natural language processing (NLP) tasks, including machine translation, text summarization, and question answering. These mechanisms play a crucial role in helping models comprehend the meaning of words within a given text and emphasize the most pertinent information.

Computer vision tasks such as image classification and object recognition also benefit from attention mechanisms. By employing attention, models can identify portions of an image and focus their analysis on specific objects.

Speech recognition tasks involve transcribing recorded sounds and recognizing voice commands. Attention mechanisms prove valuable in tasks by enabling models to concentrate on segments of the audio signal and accurately recognize spoken words.

Attentional mechanisms are also useful in music production tasks, such as melody generation and chord progressions. By utilizing attention, models can emphasize essential musical elements and generate coherent and expressive compositions.


Attention mechanisms have gained widespread usage across various domains, including computer vision. However, the majority of research and development in attentional mechanisms has centered around Neural Machine Translation (NMT). Conventional automated translation systems heavily rely on extensive labeled datasets with complex features that map the statistical properties of each word.

In contrast, attentional mechanisms offer a simpler approach for NMT. In this approach, we encode the meaning of a sentence into a fixed-length vector and utilize it to generate a translation. Rather than translating word by word, the attention mechanism focuses on capturing the overall sentiment or high-level information of a sentence. By adopting this learning-driven approach, NMT systems not only achieve significant accuracy improvements but also benefit from easier construction and faster training processes.

Key Takeaways

The attention mechanism is a neural network layer that integrates into deep learning models.

It enables the model to focus on specific parts of the input by assigning weights based on their relevance to the task.

Attention mechanisms have proven to be highly effective in various tasks, including machine translation, image captioning, and speech recognition.

Attention mechanisms can enhance model interpretability by visually representing the parts of the input the model is attending to.

Frequently Asked Questions

Q1. What is the mechanism of attention in deep learning?

A. The attention mechanism is a layer added to deep learning models that assigns weights to different parts of the data, enabling the model to focus attention on specific parts.

Q2. Differentiate between local attention and global attention.

A. Global attention considers all available data, while local attention focuses on a specific subset of the overall data.

Q3. What is the attention mechanism in machine translation?

A. In machine translation, the attention mechanism selectively adjusts and focuses on relevant parts of the source sentence during the translation process, assigning more weight to important words and phrases.

Q4. What is the transformer mechanism and attention?

A. The transformer is a neural network architecture that heavily relies on attention mechanisms. It uses self-attention to capture dependencies between words in input sequences and can model long-range dependencies more effectively than traditional recurrent neural networks.

Q5. What are examples of prominent models?

A. One example is the “show, attend, and tell” model used in image description tasks. It utilizes an attention mechanism to dynamically focus on different regions of the image while generating relevant descriptive captions.

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Cash Flow From Investing Activities

What is Cash Flow From Investing Activities?

The term “cash flow from investing activities” represents the section of the cash flow statement that records the amount of money invested, the purposes of the investments, and the returns generated from them during a specified period. Some common examples of investing activities include purchasing long-term assets (also known as CapEx), mergers & acquisitions, and investment in marketable securities.

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Investing activities are an essential indicator of a company’s growth strategy. Investors and analysts usually check the sources and uses of funds from the investing section of a company’s cash flow statement to evaluate its growth (CapEx and M&A) strategy and investment in other marketable instruments. Investment in CapEx indicates that the company intends to grow in the future. This section provides an overview of the investment made in long-term assets that have the potential to generate value in the future.


The c.f. from investing activities derives as the summation of three broad activities – sale/ (purchase) of long-term assets, sale/ (purchase) of marketable securities, and sale/ (purchase) of other businesses. Here, sale results in cash inflow, and purchase result in cash outflow. Mathematically, the formula can represent as,

Cash Flow from Investing Activities = Sale/ (purchase) of Long-Term Assets + Sale/ (Purchase) of Marketable Securities + Sale/ (Purchase) of Other Businesses

Examples of Cash Flow from Investing Activities

Different examples are mentioned below:

Example #1

Let us take the example of ADS Inc. to explain the computation. The following information is available about investing activities during the year 2023:

Purchase of marketable securities worth $25.0 million

Proceeds from maturity of marketable securities worth $42.5 million

Payment of $12.5 million made for the acquisition of new PP&E (plant, property, and equipment)

Determine the company’s investing activities for the year 2023.


C.F from Investing Activities for 2023 calculates as,

Cash Flow from Investing Activities = – Purchase of Marketable Securities + Proceeds from Maturity of Marketable Securities – Payment for Acquisition of New PP&E

Cash Flow from Investing Activities = -$25.0 million + $42.5 million – $12.5 million

Cash Flow from Investing Activities = $5.0 million

Example #2

Let us take the example of Apple Inc., wherein the following information is available regarding investing activities for the year 2023:

Purchase of marketable securities worth $39.63 billion

Proceeds from maturity of marketable securities worth $40.10 billion

Proceeds from the sale of marketable securities worth $56.99 billion

A payment of $10.50 billion was made for the acquisition of PP&E

Payment of $0.62 billion made for the acquisition of new business

Purchase of non-marketable securities worth $1.00 billion

Proceeds from non-marketable securities worth $1.63 billion

Another investing cash outflow of $1.08 billion

Determine Apple Inc.’s C.F. from investing activities for the year 2023.


C.F from Investing Activities for 2023 calculates as,

C.F from Investing Activities = – Purchase of Marketable Securities + Proceeds from Maturity of Marketable Securities + Proceeds from Sale of Marketable Securities – Payment for Acquisition of New PP&E – Payment for Acquisition of New Business – Purchase of Non-Marketable Securities + Proceeds from Non-Marketable Securities – Other Cash Outflow

Cash Flow from Investing Activities  = -$39.63 billion + $40.10 billion + $56.99 billion – $10.50 billion – $0.62 billion – $1.00 billion + $1.63 billion – $1.08 billion

Cash Flow from Investing Activities  = $45.89 billion

What’s Included in Cash Flow from Investing Activities?

The items included in this section may vary from company to company. However, some of the common items included under C.F from investing activities are as follows:

Payments for purchase of PP&E/ CapEx (cash outflow)

Proceeds from the sale of PP&E (cash inflow)

Payments for acquisition of other businesses (cash outflow)

Proceeds from the sale of other companies (cash inflow)

Payments for the purchase of marketable securities (cash outflow)

Proceeds from the sale of marketable securities (cash inflow)


The C.F. from investing activities is an important section in the cash flow statement of a company as it shows how much of the money generated from operations is used for investment and under which head. The section is more critical in evaluating companies operating in capital-intensive industries that predominantly require enormous investments in fixed assets. Typically, suppose a business reports regular cash outflows to purchase fixed assets. In that case, it is a strong indication that the company is currently in the growth phase and firmly believes that it will be able to generate a positive return on its investments.


It helps assess the company’s investment strategy’s cash negative/ positive position. It indicates any need for additional funding or if excess cash can be used in other activities, such as debt repayment.

Any discrepancy in sources and uses of funds for any significant investment can be decrypted.


It is one of the three sections of the cash flow statement that captures the cash movement in and out of the company due to various investing activities during a given period. Investors and analysts prefer to look into this section of the cash flow statement as it provides an overview of the overall investment strategy of the business.

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