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About 63 light years from our Sun, you’ll find a relatively young star called Beta Pictoris. A mere 20 million years old, Beta Pictoris is surrounded by a very active and eclectic mix of objects – including clouds of gas and dust, as well as a plethora of orbiting comets.

Now researchers are learning a little bit more about the cometary hoard that circulates around this baby star. Utilizing very precise instruments at the La Silla Observatory in Chile, French astronomers analyzed hundreds of exocomets orbiting Beta Pictoris. They discovered two distinct types of comets: an older class that have passed by the sun many times, and younger, rougher comets that are perhaps the products of a planetary breakup or collision.

Astronomers have been studying Beta Pictoris for nearly 30 years, documenting subtle variations in its light over time. It is thought that these light changes denote a comet passing in front of the star. “When the comet passes in front, there is a cometary tail which absorbs some of the starlight,” Flavien Kiefer, lead author of the study, tells Popular Science. “And when that light is absorbed, it has an impact on the light spectrum.”

Kiefer and his team of researchers reviewed more than 1,000 observations of light changes around Beta Pictoris, which were captured by the HARPS instrument on the European Southern Observatory’s 3.6-meter telescope in Chile. They selected a sample of 493 separate exocomets, sometimes analyzing them on multiple passes by the star.

Beta Pictoris In Infrared

This composite image reveals the close environment of Beta Pictoris in near infrared light. The outer part shows the reflected light on the dust disc, and the inner part is the innermost part of the system.

They noticed some distinct differences in how the comet tails warped the star’s light, which revealed a lot about the physical properties and the origins of the comets. They also observed differences in the comets’ orbits.

“The two families had different behaviors,” Kiefer explains. “One family of comet had a wide variety of orbits. The orbits have an orientation, and we saw a wide variety of orientation of this family. While in the other family, we saw one particular formation of orbit.”

Taking all these observations into account, the research team concluded that two very different types of comets surround Beta Pictoris. The first type of comets are much older and smoother, having passed by the star many times. Their wide variety of orbits indicates that a planet is controlling them. This object could very well be the giant planet Beta Pictoris b.

The second exocomet family consists of more active comets that evaporate a lot of gas and dust, much more so than the first family. Many comets are rich in ices, but as they get closer to a star, these ices evaporate. Since the second comet class is still giving off a lot of gaseous material, it means they are much younger than their older comet counterparts.

The uniform orbits of the young comets also reveal something very cool about their origin. It’s likely that these exocomets are the result of a breakdown of a larger object, possibly a planet. And now, that object’s fragments are in an orbit that grazes Beta Pictoris.

All of these discoveries provide clues as to how this planetary system formed millions of years ago, as well as how our own solar system formed. Just like around Beta Pictoris, there are many different classes of comets in our own system, some of which are similar to those in the study. “We see objects that are very analogous to what we know. Comets in our solar system are trapped inside by Jupiter,” Kiefer says, comparing them to the older family of exocomets. “This is just one of many similar behaviors we see.”

The researchers published their work in the journal Nature.

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Merge Contents Of Two Files Into A Third File Using C

This is a c program to merge the contents of two files into the third file.

For Example.

Input java.txt is having initial content “Java is a programing language.” kotlin.txt is having initial content “ kotlin is a programing language.” ttpoint.txt is having initial content as blank Output files are merged ttpoint.txt will have final content as “Java is a programing language. kotlin is a programing language.” Algorithm Begin    Declare a[] array to the character datatype.       Initialize a[] = "Java is a programing language.".    Declare i of the integer datatype.       Initialize i =0.    Declare f1 as a pointer to the FILE type.    Open a file “java.txt” to perform write operation using f1 pointer.    while (a[i] != '')       call fputc(a[i], f1) to put all data of a[] into f1 file object i++    Close the f1 file pointer.    Declare a[] array to the character datatype.       Initialize b[] = " kotlin is a programing language.".    Declare i of the integer datatype.       Initialize j =0.    Declare f2 as a pointer to the FILE type.    Open a file “kotlin.txt” to perform write operation using f2 pointer.    while (b[j] != '')       call fputc(b[j], f1) to put all data of b[] into f2 file object j++    Close the f2 file pointer.    Open a file “java.txt” to perform read operation using f1 pointer.    Open a file “ttpoint.txt” to perform write operation using f2 pointer.    Declare f3 as a pointer to the FILE datatype.    Open a file “ttpoint.txt” to perform write operation using f3 pointer.    Declare a variable “c” to the character datatype.       print “couldn’t open the file.”       Exit.    While ((c = fgetc(f1)) != EOF) do       Put all data of “c” variable into f3 file pointer using fputc() function.    while ((c = fgetc(f2)) != EOF) do       Put all data of “c” variable into f3 file pointer using fputc() function.    Call fclose(f3) function to close the file pointer.    Open the file chúng tôi using f3 file pointer.    Print “Merged chúng tôi and chúng tôi into ttpoint.txt”    while (!feof(f3))       Call putchar(fgetc(f3)) function to print the content of f3 file pointer.    Close the f1 file pointer.    Close the f2 file pointer.    Close the f3 file pointer. int main() {    char a[] = "Java is a programing language.";    int i=0;    FILE *f1;    f1 = fopen("java.txt", "w");    while (a[i] != '') {       fputc(a[i], f1);       i++;    }    fclose(f1);    char b[] = "kotlin is a programing language.";    int j =0;    FILE *f2;    f2 = fopen("kotlin.txt", "w");    while (b[j] != '') {       fputc(b[j], f2);       j++;    }    fclose(f2);    f1 = fopen("java.txt", "r");    f2 = fopen("kotlin.txt", "r");    FILE *f3 = fopen("ttpoint.txt", "w");    char c;       puts("Could not open files");       exit(0);    }    while ((c = fgetc(f1)) != EOF)    fputc(c, f3);    while ((c = fgetc(f2)) != EOF)    fputc(c, f3);    fclose(f3);    f3 = fopen("ttpoint.txt", "r");    printf("Merged chúng tôi and chúng tôi into ttpoint.txtn");    while (!feof(f3))    putchar(fgetc(f3));    fclose(f1);    fclose(f2);    fclose(f3);    return 0; } Output Merged chúng tôi and chúng tôi into ttpoint.txt Java is a programing language.kotlin is a programing language.

Element Wise Concatenation Of Two Numpy Arrays Of String

Python’s element-wise union of two NumPy string arrays is a potent method with a wide range of uses. This blog article will go over NumPy’s setup and implementation procedures, the syntax for joining two NumPy string arrays together element-wise in Python, and the underlying method. Element-wise concatenation, for instance, is commonly used in data manipulation tasks to combine two data sets.

Installation and Setup

Simply use pip or conda. NumPy is a powerful library that provides support for mathematical operations and arrays. Once installed, you can import it into your Python script using the following command −

import numpy as np Syntax

Element-wise concatenation of two NumPy arrays of string in Python is done using the numpy.core.defchararray.add() function.

numpy.core.defchararray.add(arr1, arr2)

The two NumPy arrays that you want to combine in this case are arr1 and arr2. The add() method will join the components of arr1 and arr2 element by element, so the first element of arr1 will be combined with the first element of arr2, the second element of arr1 with the second element of arr2, and so forth.

Example import numpy as np arr1 = np.array(['hello', 'world']) arr2 = np.array(['!', '?']) result = np.core.defchararray.add(arr1, arr2) print(result) Output ['hello!' 'world?']

Here, NumPy arrays of string, arr1 and arr2 are created. Use the add() function to concatenate the elements of these arrays element-wise. The resulting array, result, contains the concatenated strings.

Example import numpy as np arr1 = np.array(['apple', 'banana', 'cherry']) arr2 = np.array([' pie', ' split', ' tart']) result = np.core.defchararray.add(arr1, arr2) print(result) Output ['apple pie' 'banana split' 'cherry tart']

We have two NumPy arrays of string, arr1 and arr2. We then use the add() function to concatenate the elements of these arrays element-wise. The resulting array, result, contains the concatenated strings.


This might be a choice if two data sets can be merged based on a field that is comparable to another field, like a product Number. Use element-wise concatenation to merge the numbers from the product ID and another column to create a new column in each data gathering.

Data Manipulation − Element-wise concatenation, for instance, is commonly used in data manipulation tasks to combine two data sets. Consider combining two data sets based on a field that is comparable to another field, such as a product ID. Element-wise concatenation can be used to merge the values of the product ID and another column to create a new column in each data gathering.

Natural Language Processing (NLP) − Element-wise concatenation is commonly used in NLP tasks like attitude analysis and text classification. The text data in these tasks is frequently presented as a matrix, with each row designating a passage of text or a sentence and each column designating a word or a symbol. Each sentence or text’s word embeddings or word vector representations can be merged using element-wise concatenation.

Data Cleaning − Likewise, missing values can be replaced or unwanted symbols can be eliminated from data by using element-wise concatenation. For instance, in a data gathering that contains phone numbers, element-wise concatenation can be used to merge the area code and the phone number. Then, using regular expressions, unwanted symbols can be eliminated, including brackets and hyphens.


An excellent technique that can be used for many tasks, such as data administration, natural language processing, and data cleaning, is the element-wise concatenation of two NumPy text arrays in Python. Two NumPy strings can be combined into one array using the numpy.core.defchararray.add() method. When working with big datasets that call for quick and effective procedures, this tool is especially helpful. It also offers freedom when managing text data that may be in a variety of lengths or styles.

Number Of Triangles In A Plane If No More Than Two Points Are Collinear

Let us see how to calculate the number of triangles in a plane with n number of points given, with the constraint that not more than two points are collinear.

Computing the number of triangles in a plane with no more than two collinear points is a typical problem in computational geometry, and it is used in computer graphics, image processing, and other areas of computer science.

While creating a 2D image from a 3D scene in 3D graphics, for instance, the issue of counting triangles in a plane with no more than two points collinear can come up. The triangle counting procedure can be used to determine how many triangles are present in the final 2D image after projecting the 3D scene onto a plane in this situation. The complexity of the scene can be ascertained with this, and rendering speed can be improved.

In image processing, where we might want to count the number of unique objects or shapes in an image, this problem comes helpful. In this instance, we can represent the image as a collection of points on a plane, and then we can count the number of triangles that can be created between these points by applying the triangle counting technique. We may determine the approximate number of distinct items or shapes in the image by counting how many triangles are formed.


Let’s understand the problem with a few examples and try to solve it.

The aim is to determine how many triangles are formed in a plane with n points such that no more than two points are collinear.

Example −

Suppose N is the number of points in a plane.

N = 3

We can draw only one triangle using these points.

So, the total number of triangles made using 3 points is 1.

Let’s N = 4

Let’s draw triangles using these four points.

The total number of triangles formed using 4 points is 4.

Let’s see some mathematics involved in calculating the number of triangles. This can be obtained using Permutations and Combinations. To construct a triangle 3 points are needed at a time from the total number of points.

So, if a plane contains n points and no more than two of them are collinear, then the number of triangles in the plane is given by the formula.



Program to find the number of triangles in a plane if no more than two points are collinear uses the following Algorithm.

Take the number of points in a plane as input with constraints not more than two of them are collinear.

Calculate the total number of triangles using the above-mentioned formula.

Print the total number of triangles as output.


C++ program to find the number of triangles in a plane if no more than two points are collinear.

using namespace std;

int main() { int number_of_points = 4; int number_of_triangle;

number_of_triangle = number_of_points * (number_of_points – 1) * (number_of_points – 2) / 6; cout << “Total number of triangles formed using ” << number_of_points<< ” points = ” << number_of_triangle << endl;

return 0; }

Output Total number of triangles formed using 4 points = 4 Complexities

Time complexity: O(1), As this code performs a fixed number of calculations, regardless of the size of the input.

Space complexity: O(1), As the code uses a fixed number of variables to store input values and results, regardless of the size of the input.


In this article, we have tried to explain the approach to find the total number of possible triangles with n given points, with the constraint that no two points are collinear. I hope this article helps you to learn the concept in a better way.

Could A Black Hole Be Blocking The Light From That ‘Alien Megastructure’ Star?

About 1480 light-years away from Earth, a star is doing something astronomers have never seen before. Every now and then, at random intervals, its light dips by as much as 22 percent. That’s way too much to be a planet. And the star (officially named KIC 8462852, but informally called “Tabby’s Star” or “Boyajian’s Star”) seems to have gotten dramatically darker over the past century.

This odd behavior defies all known explanations, and astronomer Jason Wright has pointed out that these light patterns are similar to what we might expect if aliens built a complex of machines around the star to harvest its energy. But even Wright admits it’s much more likely there’s a natural explanation. In September, he and coauthor Steinn Sigurd̵sson rounded up and analyzed some of the most common explanations.

Wright has been been fleshing out those analyses in a series of posts on his blog.

We’ve rounded up our favorite explanations here, in rough order from least likely to most plausible.

Did Kepler mess up? Nope.

The data checks out. When the Kepler telescope detected the huge light dips from KIC 8462852, nothing was wonky in the telescope, and there’s nothing particularly odd about any of the other data it collected at the same time.

Between 2009 and 2013, the Kepler space telescope stared at a single patch of the sky, searching for exoplanets. Around the star KIC 8462852, it appears to have spotted something much stranger. Artist illustration, NASA / Wendy Stenzel

It’s not possible that the telescope pixels that imaged Boyajian’s Star were faulty, because the star’s image wasn’t always on the same pixels. As the star moved throughout the month, and as the telescope shifted positions, different detectors monitored Boyajian’s Star, and they all showed that the star was acting bizarre. “The dips are real,” writes Wright.

For a few months, scientists argued about whether the star has been getting dimmer over the past century. Those observations were based on old and imprecise astronomy data. But a new analysis indicates the star dimmed significantly over the four years that the Kepler telescope watched it, and therefore probably over the past century as well.

Could a black hole eat up the light? Nope.

Despite the popular image of a black hole gobbling up everything in its path, including light, black holes could not be responsible for darkening Boyajian’s Star.

Wright explained to Popular Science that if a black hole were sitting close to Boyajian’s Star, its massive gravity would make the star wobble, which scientists would be able to observe from Earth. It doesn’t wobble. Plus, if it were sucking material off of the star, the stuff falling into the black hole would actually give off bright light and extra xrays, which scientists don’t see.

But what if a black hole were sitting farther away from Boyajian’s Star, between the star and Earth? Still no. Counter intuitively, the black hole would act like a lens, actually brightening the light we would see from Earth.

Could it be a sunspot? Unlikely.

Spots on our sun do cause tiny drops in brightness, but we’re talking about a few tenths of a percent. To cause a huge dip in KIC 8462852’s light levels, on the order of 20 percent, the starspots would need to be “10–100 times larger than the strongest effects known in other stars,” Wright noted in his blog post. Plus Boyajian’s Star is spinning rapidly, so the dips caused by those starspots would appear and disappear every day, instead of lasting for days.

But what if the spots were on the poles of the spinning star, and the pole is constantly pointed at us? That still seems pretty unlikely, says Wright, given the fact that Boyajian’s Star is a type of star that doesn’t usually have big spots.

Comets? Maybe, but probably not.

Comets are actually the explanation favored by Tabetha Boyajian, the star’s discoverer. The idea is that a family of extra-large comets may be jumbled up in the star’s orbit, blocking its light in irregular ways.

If the comets are there, they must be pretty far away from the star, otherwise astronomers would be able to see extra heat coming off of them. The lack of extra heat rules out pretty much every potential explanation that relies on something big being in orbit around the star.

Illustration of the star KIC 8462852

Although scientists have suggested the weird light dips from this star might come from a family of mega-sized comets, there isn’t yet a scientific explanation that fits.

But while the comet hypothesis could explain the short-term dips in light that occurred in 2011 and 2013, it doesn’t explain the star’s long-term dimming, says Wright. And in his opinion, the best hypothesis should explain both phenomena.

“It is pretty outrageous,” Boyajian admitted in a recent webcast, “but all of the things that have been put forth have been pretty outrageous so far.”

An interstellar black hole disk? Maybe!

Although a black hole is definitely not eating up the light from Boyajian’s Star, there’s another way a black hole could be blocking the light. Maybe there’s something big and dark in the interstellar medium between Boyajian’s Star and Earth.

A disk of material orbiting a black hole is one possible explanation. (Debris disks also orbit stars and planets, but since astronomers don’t see anything like that, this object would have to be dark … such as a black hole.)

For this hypothesis to work, the disk of material clotting around the black hole would have to be huge–something on the order of 600 times the distance between the Earth and the Sun–in order to block the star’s light for such long periods of time, despite the star’s monthly movements.

A disk of debris circling an interstellar black hole is one possible explanation for the weird behavior of Boyajian’s Star. NASA

Wright says that although we’ve never seen a black hole disk that big, it’s not ruled out by physics. If there is a large disk there, scientists might confirm this hypothesis if the debris passes in front of neighboring stars.

Other interstellar stuff? Also maybe!

The space between stars is filled with gas, dust, as well as filaments and sheets of material clumped together by gravity. It’s possible that a particularly dense part of this interstellar medium got caught between us and Boyajian’s Star, absorbing some of its light.

To create the huge light dips, these filaments or sheets would need to be about 1000 times smaller and denser than we think they are, but it’s not impossible, says Wright. Maybe structures like that are just so small and rare that we’ve never spotted anything like it before now.

Like interstellar phantoms, dark nebula called Bok globules have been known to blot out stars. Hubble Heritage Team (STScI/AURA), NASA

Dark nebulae known as Bok globules could also be to blame. These black, star-forming clouds of dust and gas have been known to blot out stars before. Perhaps as turbulent gas and dust swirls around inside the globule, dense patches form and dim the light we see from Boyajian’s Star.

“It would be kind of unusual to see one of these clouds in this part of the sky,” says Wright, but it’s not impossible.

Both phenomena–the interstellar sheets and dark nebulae–would be expected to darken our view of the stars that neighbor Boyajian’s Star. Trouble is, the nearby stars are faint, which makes it difficult to measure their brightness precisely, so astronomers aren’t sure whether or not that’s happening.

Aliens? Who knows.

The hypothesis that aliens are building a megastructure around the star to harvest its energy runs into the same problem the comets did: any object in orbit around the star should absorb light and re-emit it as excess heat, but astronomers aren’t detecting excess heat.

Artist illustration of a crumbling Dyson sphere

Illustration of a Dyson sphere around a star

But who knows, maybe an alien civilization capable of building star-sized structures has also figured out how to utilize all of the sun’s energy, including heat. That’s the problem with alien-related hypotheses–there’s no good way to disprove them, since we don’t know what such a civilization would be like or what they’d be capable of. It’s also impossible to calculate the odds of intelligent alien life out there in the cosmos, so it’s kind of tough to say how this hypothesis stacks up to the rest. However, we know interstellar material exists, and we don’t know whether aliens exist, so our money would be on the natural (non-alien) hypotheses.

Wright has been careful to point out that aliens should always be a last resort hypothesis, after everything else has been ruled out. Nevertheless, he and Boyajian and other scientists are investigating Boyajian’s Star using the most thorough alien-hunting equipment available.

Meanwhile, all manner of telescopes have turned their attention to Boyajian’s Star, from the Swift Observatory to the Spitzer space telescope to the backyard spyglasses of amateur astronomers. They are monitoring the star in optical, infrared, UV, and x ray spectrums. The next time something weird happens around Boyajian’s Star, scientists around the world will be ready to collect as much data as possible, to help settle the question of what the heck is going on around this star.

Should Airtags Get Lost Over Safety Concerns? A Better Solution Can Be Found

We thought AirTag would be the Apple product you think about once, then forget about until you lose something. It turns out that hasn’t quite been the case. Local news headlines across the country tell the story of AirTags being used to track people unknowingly. At the same time, Apple has adjusted how AirTag works and provided additional resources to prevent these events from happening. Is there more Apple can do, or is addressing this a lost cause?

How AirTag is different

Apple is hardly the first tech company to make affordable item trackers that rely on smartphones to function. The difference is AirTag uses Apple’s Find My network of iPhones for remote tracking. This is great for actually finding misplaced items in public places.

Competing products rely on other customers who use the same brand of tracker to populate their network. There are a lot more iPhones in the world compared to Tile trackers. That’s what makes AirTags more effective at turning up lost or stolen items.

Works as intended

Valerie McNulty, a veteran of four military moves herself, had heard enough horror stories. While preparing for a recent move from Fort Carson, Colorado to Fort Drum, New York, she slipped an Apple AirTag, a Bluetooth-powered tracking device, into one of the boxes filled with her family’s household goods.

“You hear so many horror stories when it comes to PCSing,” she told Military Times, using an acronym for permanent change of station. “With those stories in mind, and having read about people putting AirTags with some of their [household goods], I decided it would be worth testing the theory.”

In that story, the AirTag helped her locate most of her family’s items after a dishonest delivery driver pretended to be days away in another state. Unfortunately, some of her family’s possessions are still missing after the move.

“We are hoping to hear something about those by this weekend,” she explained. “Unfortunately, I only hid one AirTag so these items I am not able to track.”

AirTag concern

As we know, however, not all AirTag stories are so positive. Tales of stalking involving AirTag are as common as “Apple Watch saves life” headlines. By the turn of the season, the same Facebook groups where parents recommended AirTag as this year’s must-have product were cautioning parents to beware of Apple’s item tracker.

And who can blame them with stories like these across the country and beyond? Each of these articles involves an AirTag tracking someone unknowingly:

Even in my home state of rural Mississippi, local stories of AirTag stalking are making the news:

It was just another afternoon at the park with her kids for Rankin County resident Amber Norsworthy when she got a notification saying someone was watching her.

“I didn’t even know what it was on,” she said. “It just told me it was in my presence. We checked our shoes, we checked their jackets, we checked our pockets, we checked everywhere. Then I was like, it has to be on the vehicle.”

Campaign to inform

What’s reassuring about this story, though, is that Apple’s safety measures kicked in and alerted the person about the AirTag. That’s how so many of these stories are discovered. If an AirTag registered to someone else’s iPhone follows you, you’ll receive an alert on your iPhone. (Apple has released an Android app for this purpose too, but it should work with Google to integrate the feature into Android.)

This is something Apple includes on its marketing page for the item tracker:

AirTag is designed to discourage unwanted tracking. If someone else’s AirTag finds its way into your stuff, your iPhone will notice it’s traveling with you and send you an alert. After a while, if you still haven’t found it, the AirTag will start playing a sound to let you know it’s there.

Of course, if you happen to be with a friend who has an AirTag, or on a train with a whole bunch of people with AirTag, don’t worry. These alerts are triggered only when an AirTag is separated from its owner.

The good news is that the incident in Mississippi taught everyone involved about these safety measures:

“With any kind of technology, it may be created for the best purposes,” said Paul Holley with the Rankin County Sheriff’s Department, “but certain people are going to create a nefarious purpose for anything.”

“After talking to Apple Support, they actually showed me how to go on my phone and what setting to go look at to see,” said Norsworthy. “It will tell you if you have an Airpod, or an AirTag, or anything that’s Apple related if it is following you or within your presence.”

In addition to checking settings, folks also need to listen for a specific sound to help find an AirTag that you may not know is on or near you.

“One of the things that we have learned about them, that after a certain amount of time away from their host, they’ll start making a beeping noise in your clothing, your purse, your car…” explained Holley.

Again, an important detail in this and many other stories is that the AirTag alerted the person being tracked. GPS trackers intended for precision tracking are designed specifically for stealth and would never reveal their status or location.

Apple shouldn’t shut down the Find My network and issue a recall on AirTag. Instead, Apple should address the reality of how AirTags are being interpreted and launch an honest information campaign to teach the public about their safety measures – Streisand effect be damned.

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