## Tagged: Vector Toggle Comment Threads | Keyboard Shortcuts

• #### Nathan Paglinawan 1:54 pm on May 29, 2017 Permalink | Reply Tags: Vector

Force

If you pull upon an object in an upward and rightward direction, then you are exerting an influence upon the object in two separate directions – an upward direction and a rightward direction. The vector sum of these two components is always equal to the force at the given angle.

References:
Independence of Perpendicular Components of Motion, http://www.physicsclassroom.com/Class/vectors/u3l1g.cfm

## Real Estate

Week 2: Vectors

DIBS: 3D weight matrices in modeling real estate prices

“Vector” can be pretty much just a fancy word for “list”. Specifically, an ordered list of numbers. [1]

For example, let’s say that you were doing some analytics about house prices, and the only features you cared about were square footage and price. You might model each house with a pair of numbers: the first indicating square footage, and the second indicating price. Since the length of this vector or list is two (a pair), this is two dimensional or 2D. [1]

This is a very simplified way of knowing house prices in real estate. There are other factors such as amenities (parking, good view, bedrooms, etc.) or even floor level (level 1, level 2, level 3, etc.). An example would be “3D weight matrices in modeling real estate prices”.[2]

sources:
[1] 3Blue1Brown. Vectors, what even are they? URL: https://youtu.be/fNk_zzaMoSs (visited on May 20, 2017).

[2] (2017). Int-arch-photogramm-remote-sens-spatial-inf-sci.net. Retrieved 20 May 2017, from http://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/XLII-2-W2/123/2016/isprs-archives-XLII-2-W2-123-2016.pdf

• #### Paul Rossener 6:47 am on May 3, 2017 Permalink | Reply

Hi Justin, please elaborate the application of vectors in real estate modeling.

Liked by 1 person

## Vectors

Makakatulong yung vectors sa pagprotekta sayo mula sa init. Pwede ka pang dumamoves kay crush. Syempre itututok mo yung payong sa kung nasaan yung araw para hindi kayo masunog tapos pwede ka na rin gumawa ng rason para akbayan sya hehehe.

## "One Shot, One Kill" – US Marine Scout Sniper School

Vectors are used in physics to express both magnitude and direction, and almost everything runs on basic kinetic motions.

The most basic of kinetic motions would be the projectile, which is affected by gravity. However, to become a sniper, one must understand more than just this. A sniper has understanding of gravity (y axis) as well as other factors that affect their shot like wind (x axis), temperature, humidity, bullet weight, muzzle velocity, and other factors that they need to control in order to guarantee or secure a shot every time.

To sight in a target, the sniper aims their crosshairs at a target, and ideally, the crosshairs are zeroed for a specific rifle, using a specific type of bullet, and at a specific distance. When a rifle is zeroed, it means that a certain distance, given certain weather/external conditions, the rifle will always hit where its crosshairs are sighted on. However, the different external conditions affect the path of the bullet, which can make it hit higher or lower or offset to the right or left. To combat these effects, a sniper can use adjustments (the math of which I will no longer discuss) in order to compensate for the offset, or the sniper can choose to forego making the scope adjustments (to adjust the line of sight) and physically compensate for the shot themselves (raising or lowering the rifle, offset the aim to the left or right). I’d like to think of it in terms of linear combinations in which we can express the zero of a rifle at a certain distance as a zero vector [0 0]. However, external conditions added (vector addition) to the zero vector would offset our shot. So, the adjustments can be represented as coefficients to the vectors going to be added such that when all these vectors are added altogehter (c1v1 + c2v2 + c3v3… cnvn), we eventually achieve our zero vector again, thus giving us a zeroed shot.

Sources:

• years obsessing over sharpshooting
• ROTC Military Science 1, 2, 3 (RSCT), 31, 32, 41, 42
• US Army Field Manual 23-10: Sniper Training

## J2: Vector Gaming

In what other ways can we use vectors? Give one sample application and describe/illustrate how the vector can be used.

We can use vectors to illustrate possible movements in games. See picture of the chessboard below. Hehe.

If anyone wants to play Chess, I’m g! :DD

## The use of visual vectors in film editing

You can employ the use of visual vectors like graphical vectors and motion vectors in editing so as to give your audience visual cues of the tone, direction, and location of connected scenes in a film. Graphic vectors have something to do with non-moving objects like horizons, lines along a silhouette of a building, etc., and are used in such a way that scenes following one another have to maintain the lines and angles (or at least their “nature”), so as when cutting from one shot to another, the audience does not feel lost because of abrupt changes that do not feel continuous.

Besides these are motion vectors, wherein movement even across shot changes have to be maintained so as not to again, break continuity, leading to the audience feeling lost. (ex. you can’t show one shot of a character walking to the left and showing a close-up shot of them where the movement across the shot is oriented in such a way that the character is facing the right edge of the shot)

## Superman Punch

Superman punch is a technique where a fighter moves his rear leg forward (faking a kick), then snapping it back while throwing a cross punch and using his front leg to lunge his body forward. It is one of the signature moves of George Saint Pierre(GSP), and is is also the finisher of Roman Reigns.

For a the superman punch to be effective/powerful, the fighter should be able to use all of the vectors(forces) applied in his movement effectively. When executing a superman punch, the body travels in a parabolic path and for it to be powerful, the fighter should be able to land his punch in the direction of the tangent line because it indicates the direction where his body is heading, thus making his superman punch more effective.

sources:
https://en.wikipedia.org/wiki/Superman_punch
The Mathematics of Martial Arts (Tityik Wong and James Lee)

## Vectors in Cartography

Cartography is the Science of Mapmaking.

In what ways can mapmaking, you say, be related to vectors?

In Math 55, topography has been one of the applications of vector fields. In the real world, maps and computer science are very much related as vertices and weighted edges.

Check this Google Street map of UP Diliman for example:

https://goo.gl/maps/fNFb6gHp71s

There you will see streets with arrows to indicate one-way streets. Some are unlabeled, to indicate that they go both ways.

Street maps aside, a much wider application in Cartography is for seafarers, for them to know the ocean currents. Similar to vector fields in winds in relation to the weather, these maps are used around the 14th to 17th centuries during the exploration of the world.

Fun fact: If anyone has taken Kas 1, one might know that the route back to Mexico from the Philippines was discovered by the Spanish friar Andres de Urdaneta, thus opening the route of the Manila Galleon Trade. Sailors from Mexico travel west to reach the Philippines, and in order for one to go back, one must sail North towards Japan then east back to Mexico.

• #### Lois Velasco 12:52 pm on February 17, 2017 Permalink | Reply Tags: Vector

Vectors are also used in economics. One example of this is the use of vectors in predicting the consumption demand of a system. It uses an input-output matrix to show how goods from one industry are consumed in other industries.

The rows represent the producing sector of the economy and the columns represent the consuming sector of the economy. The total internal demand for the economy is equal to the sum of the entries per row in the input-output matrix and it can be represented as:

The image below shows an example and the result of the computation.

This shows the flow of goods between industries.

Now, if we get relative size of industries with respect to currency, we construct a diagonal matrix where the each entry is the price of the goods that the corresponding industry produces then multiply it to the input-output matrix we obtained before to have the value input-output matrix. We’ll then arrive at the internal demand vector with respect to currency when we get the sum of each rows.

Source:

http://kurser.math.su.se/pluginfile.php/30620/mod_resource/content/0/matrix-ex%20leontif.pdf

• #### Paul Rossener 6:48 am on May 3, 2017 Permalink | Reply

Hi Lois, this topic was already taken by Kyle Rosales (collision detection).

Like

## ’til I found you

You  may have heard from the news about the  discovery of a nearly submerged continental fragment that sank after breaking away from Australia 60-80 million years ago. This vast landmass which is attached to New Zealand has been named Zealandia, and with a total area of approximately 4,920,000 km2 it is currently the world’s largest microcontinent. It was considered because of its distinct geological features which met all the criteria applied to Earth’s seven other continents—elevation above the surrounding area, distinctive geology, a well-defined area and a crust much thicker than that found on the ocean floor.

The team composed of 11 researches discovered Zealandia using upgraded satellite-based elevation and gravity maps. The same technology was used to to get much detailed images of Mars’ hidden interior, just like a doctor uses X-ray to see the inside of a patient. This technique also known as Gravity Gradiometry, is the study and measurement of variations in the acceleration due to gravity. The gravity gradient is the spatial rate of change of gravitational acceleration.

Mars gravity map showing Tharsis volcanoes and surrounding flexure.  https://www.nasa.gov/feature/goddard/2016/mars-gravity-map/

Gravity gradiometry is used by oil and mineral prospectors to measure the density of the subsurface, effectively the rate of change of rock properties. From this information it is possible to build a picture of subsurface anomalies which can then be used to more accurately target oil, gas and mineral deposits. It is also used to image water column density, when locating submerged objects, or determining water depth.

Gravity measurements are a reflection of the earth’s gravitational attraction, its centripetal force, tidal acceleration due to the sun, moon, and planets, and other applied forces. Gravity gradiometers measure the spatial derivatives of the gravity vector. The most frequently used and intuitive component is the vertical gravity gradient, Gzz, which represents the rate of change of vertical gravity (gz) with height (z). It can be deduced by differencing the value of gravity at two points separated by a small vertical distance, l, and dividing by this distance.

The two gravity measurements are provided by accelerometers which are matched and aligned to a high level of accuracy.

Gravity gradiometry has predominately been used to image subsurface geology to aid hydrocarbon and mineral exploration. Over 2.5 million line km has now been surveyed using the technique. The surveys highlight gravity anomalies that can be related to geological features such as  Salt diapirs, Fault systems, Reef structures, Kimberlite pipes, etc. Other applications include tunnel and bunker detection and the recent GOCE mission that aims to improve the knowledge of ocean circulation.

References:

http://www.gmanetwork.com/news/story/600011/scitech/science/scientists-confirm-discovery-of-lost-continent

http://www.express.co.uk/news/world/768426/ZEALANDIA-DISCOVERED-Scientists-find-ENTIRE-NEW-CONTINENT

http://timesofindia.indiatimes.com/home/science/Most-detailed-gravity-map-gives-us-peek-inside-Mars/articleshow/51506068.cms

## The use of vectors in making Interactive Dynamic Videos

An Interactive Dynamic Video (IDV) is an imaging technique where you can “touch” and manipulate objects in a captured video recording [1]. They analyze the vibrations (or find what they call “vibration modes”) in the video in different frequencies to be able to predict how the object in the video would act/move in new situations (such as when poked or pushed). This technique involves acceleration, velocity, and displacement vectors (for modal analysis). [2]

As a result, the videos can now be manipulated and be used to apply special effects.

Sources:

Link to their website: http://interactivedynamicvideo.com/ (they have videos where they explain and apply this technique to create different special effects + possible application in Pokémon GO)

• #### Paul Rossener 6:46 am on May 3, 2017 Permalink | Reply

Hi Michelle, this topic was already taken by Arlan Uy (Pathogens).

Like

• #### Michelle Dela Rosa 5:37 pm on May 3, 2017 Permalink | Reply

oh no 😦

sige po sir, will update!

Like

## "Netflix and Ch– Vectors"

Apparently, Netflix uses vectors to build a specific and unique recommendation list for each user. It’s like Netflix creates a user vector where it stores all of the rating records for all the shows/movies that a user watches there.

here’s a good blog article where you can learn more about Netflix’s usage of vectors for recommendation 😀
https://nikhilwins.wordpress.com/2015/09/18/movie-recommendations-how-does-netflix-do-it-a-9-step-coding-intuitive-guide-into-collaborative-filtering/

:>

• #### Paul Rossener 6:46 am on May 3, 2017 Permalink | Reply

Hi Camille, this topic was already taken by Abby Del Castillo (Path finding).

Like

• #### Camille Razal 3:21 pm on May 21, 2017 Permalink | Reply

Hello sir! Di ko alam kung i-coconsider niyo pa rin ito, pero binago ko na po yung post ko 🙂

Like

## Vectors

• In what other ways can we use vectors? We can use it in making real-world stuff. In fact, 3D models of infrastructures, products, and even equipment are done by companies in terms of design prototyping
• Give one sample application and describe/illustrate how the vector can be used. A sample application of vectors that are very popular right now is 3D printing. 3D printers use vectors in creation of the computer generated image of the product because it makes it possible to scale the printing to a bigger and/or smaller size than the original design.

## Vectors in Virtual Video Capture Software

3D rendering software that simulate cameras often use vectors to represent physical camera parameters. Settings like focal length, depth of field, and field of view can be controlled by adjusting input vectors for their respective calculations.

Screenshot of a virtual camera setup in Source Filmmaker. Notice the vectors extending from the origin of the camera denoting the field of view of the left screen.

If you guys want a more in-depth (pun intended) look on how the camera vectors work within Source Filmmaker (and if you’re interested in 3D animation), you can download SFM for free here.

## Vectors in Markov Chains

A Markov Chain is a stochastic model describing a sequence of possible events. Markov Chains have many different applications, such as predictive text, search engines (Google’s PageRank algorithm makes use of Markov Chains), cruise control in vehicles, and even currency exchange rates.

Markov Chains may be visualized as finite state automata, or as stochastic matrices with transition vectors. These vectors determine the odds of each event occuring, and will change after every transition. However this method of representing a Markov Chain will only work if the state space finite.

Although vectors are only a small part of Markov Chains as a whole, they still play a key role in helping us visualize them in a manageable way.

http://www.sosmath.com/matrix/markov/markov.html

## 02: Dancing bees~~~ young and sweet, only seventeen. . .

One fine afternoon during my Lingg 1 class, we were talking about animal communication system and our prof mentioned how bees communicate to other bees the location of a flower/food source they saw. Bees actually dance in front of the group and use vectors to describe the location of the food source! They walk in a straight line while shaking their body nang super intense with matching flap ng wings.

Basically, may meaning yung steps na ginagawa nila. They align their body in the direction of the food source in accordance with the sun. So if they do the dance step nang pa-straight north, it means that exactly nasa direction ng sun yung food source. Kapag pa-straight south naman, it means that nasa south yung food source. They also do a 45 degree-inclination to the left or right of the sun para mas accurate yung direction na ibibigay nila. The distance is conveyed by the number of repetitions they do the dance. Amazing bees!!! 🙂

References:

## Vectors in Speech Recognition

Feature vectors are used in speech recognition to identify phonetic sounds between each other. Usually, each sound clip is divided into several short snippets. Features are then extracted from each of these snippets, which are then used to identify between different sounds between the audio snippets.

Reference: https://www.quora.com/What-are-frame-based-feature-vectors-as-used-in-speech-recognition

## Dancing bees~~~ young and sweet, only seventeen. . .

NOTE EDIT: Sir, can’t delete this post po.

DIBS

sumasayaw yung mga bees to communicate to other bees yung food source na nakita nila using vectors

• #### Edrich Chua 7:29 am on February 5, 2017 Permalink | Reply Tags: Vector

A geographical state vector is a set of data describing exactly where an object is located in space, and how it is moving. From a state vector, and sufficient mathematical conditions (e.g. the Picard-Lindelöf theorem), the object’s past and future position can be determined A geographical state vector typically will contain seven elements: three position coordinates, three velocity terms, and the time at which these values were valid. Mathematically, if we are to describe positions in a N-dimensional space R^n, then a state vector x belongs to R^(2n): x(t) = r(t) taken v(t) where r is the position vector and v is the velocity vector. Due to the freedom one has in choosing coordinate systems for position, a state vector may also be expressed in a variety of coordinate systems

https://en.wikipedia.org/wiki/State_vector_(geographical)

• #### Paul Rossener 6:43 am on May 3, 2017 Permalink | Reply

Hi Edrich, this topic was already taken by Ryan Rivera (GPS) and Jem Apolinario (Airplane navigation).

Liked by 1 person

• #### Edrich Chua 3:36 pm on May 4, 2017 Permalink | Reply

Hi sir! Na-edit ko na 🙂 I can’t seem to write it in an HTML format though so ang panget tuloy ng formatting. Sorry!

Like

## Molecular Polarity

The polarity from each bond between atoms of different electronegativity and the shape of the molecule can be used to determine the overall polarity of molecules with more than one bond. Each bond’s dipole moment can be treated as a vector quantity with a magnitude and direction. Therefore, the molecular polarity results from the vector sum of the individual bond dipoles.

Molecular Polarity of CHCl3 (Chloroform)

## Vectors in Music

Internal vector is a set of numbers that expresses the intervals in a set of pitches. It is used to manipulate the sound of a set of pitch class (set of pitches octaves apart) by inversion and octave displacement of pitches to emphasize certain intervals over others.

How to compute an interval vector:

## Sea Breeze Analysis using Vector Integration

In fluid dynamics, circulation is the line integral around a closed curve of the velocity field. It can be obtained by taking the line integral of Newton’s second law for a closed chain of fluid partial. It is know as the Bjerknes Circulation Theorem.

This theorem uses vector integration. It is used in analyzing the bartropic fluids. Bartropic fluids are a useful model for fluid behavior in many fields of science. Most liquids have a density which varies weakly with pressure or temperature, which is the density of a liquid, is nearly constant, so to first approximation liquids are bartropic.

The sea breeze analysis can be explained using the bartropic flow.

The sea breeze will develop in which lighter fluid the warm land air is made to rise and heavier fluid sea is made to sink. So the air from sea will come to land to fill the free place this occurs seas breeze.

## Simulating Spiking Neural P Systems with Vectors, a Matrix, and the GPU.

WARNING: LONG POST

tl;dr Turing started it, Computational model based on neurons, Math magic, GPU magic

The Turing Machine is perhaps the most well known computational model out there. It is the theoretical basis of a modern computer which is one of if not the most important inventions of man. The Turing Machine however, is not perfect. There are some problem that are hard to solve using the Turing Machine, that is the problems that are in $NP$ but not in $P$assuming of course that $P \neq NP$.

Because of this problem, people started to look for ways around this problem. Alan Turing himself wrote papers, both published and unpublished, to move this effort forward. In one of his unpublished papers, he proposed two types of randomly connected neural networks with one key feature being the possibility of learning and training it to solve problems [1]; sound familiar? The same year he wrote about the former, he also wrote a paper proposing genetical or evolutionary search [1]. But perhaps the most important  proposal Turing had in this effort is his idea of a machine beyond the Turing machine, this machine he dubbed the O-Machine which is basically a Turing Machine with an oracle that can solve any decision problem within a class of problems, such as $NP$, for free [1].

FUN FACT!

The paper where Turing proposed neural networks wasn’t published because his boss at the time dismissed it as a “schoolboy essay”. Do you know who his boss was? Sir Charles Darwin, not the Charles Darwin writer of The Origin of Species, but rather his grandson [1].

## Vectors in Golf

“When you hit a golf ball, the direction of motion of the club head determines the direction of the force vector, which can be broken into two perpendicular components that determine the direction of motion of the ball and its spin.

Golfers can use golf clubs with different club head angles to vary the vertical direction as well as the spin. They can also adjust the way they hit the ball to change angles and spin” (kaya pala nagpapalit sila ng golf club :O)

http://www.school-for-champions.com/science/forces_golf.htm#.WI8uvFN97Dc

## Vectors in Baking and Cooking

Vectors can be used as a way to represent ratio and proportion. This is a list of possible ways you can use the ratios are:

• Converting temperature from Celsius to Fahrenheit and vice versa
• Converting sizes and amounts (eg cups to mL)
• Cooking/baking in batches
• Cooking time with respect to its size and/or weight
• Estimated cost of a dish
• Amount of serving

For example, we the ingredients of a recipe that can yield 30 cookies:

(C)1/2 cup (1 stick) unsalted butter
(D)3/4 cup packed dark brown sugar
(E)3/4 cup sugar
(F)2 large eggs
(G)1 teaspoon pure vanilla extract
(H)1 (12-ounce) bag semisweet chocolate chips, or chunks
(I)2 1/4 cups all-purpose flour
(J)3/4 teaspoon baking soda
(K)1 teaspoon fine salt

Let’s say that these amount of cookies can feed 3 people. You can represent the ratio of number of people fed(A), amount of cookies(B), and the ingredients(C-K) in the set of R^11 where:

A:B:C:D:E:F:G:H:I:J:K

with the values:

3:30:0.5:0.75:2:1:1:2.25:0.75:1

If you want enough cookies to feed 30 people, you’d have to multiply this ratio by 10.

Not following the correct ratio might end up: (1) not being edible, (2) not having enough cookies, and (3) not being able to feed everyone and causing World War 10.

References:

http://mathcentral.uregina.ca/beyond/articles/Cooking/Cooking1.html

https://www.reference.com/food/math-used-cooking-b7b5f8ef8bc81e81

http://www.learner.org/interactives/dailymath/cooking.html

## Vectors in Pathfinding

Goal based vector field pathfinding is used as an alternative solution aside from Dijkstra’s and other pathfinding algorithms. The vector field is used to see the direction of the goal from the current position. This is just one component of the algorithm since it also uses heatmaps and particles which looks for the shortest path. Without the use of vector fields, this alternative solution wouldn’t be possible.

## Vectors in Magnetic Flux

Flux, defined generally, is the amount of “something” that passes through a surface. In electromagnetism, magnetic flux is the number of magnetic field lines passing through an area. While flux in this context is a scalar quantity, measuring it requires the presence of a magnetic field (which in itself is a vector field, i.e. a collection of arrows with a given magnitude and direction). Getting the magnetic flux through a surface is done by calculating the surface integral of the normal component of the magnetic field passing through that same surface.

## “King – Man + Woman = ?”

A word vector is a continuous word representation wherein the vector’s weight is distributed across various elements. So, instead of having a one-to-one mapping between a vector element and a word, the representation of a word is spread across all of the elements in the vector, and each element in the vector contributes to the definition of many words. These vectors somehow represent the “meaning” of a word.

These vectors are good in answering analogies like man:woman as uncle:____ (aunt) by using a simple vector offset method based on cosine distance. With this, we can answer “King – Man + Woman = ?” question and arrive at the result “Queen”.  This shows that using a word offset technique where simple algebraic operations are performed on the word vectors results in a vector that is closest to the vector representation of the word “Queen”.

Vectors for King, Man, Queen, & Woman:

The result of the vector composition King – Man + Woman = ?

Word vectors with such semantic relationships could be used to improve many existing Natural Language Processing applications, such as machine translation, information retrieval and question answering systems, and may enable other future applications yet to be invented.

Reference:

The amazing power of word vectors

## Vectors: Life Mapping

I guess I’m not really sure if this can actually be implemented but this one’s just an idea I thought of.
Maybe in an ideal world where I’m successful and I’m more motivated to pursue my goals and dreams this might be a reality. I think vectors can be used to represent and map people and not just map geographically or via location, I mean map like decision maps. Like we can delve into the possibilities of where each person might end up in in their own lives. In a 3D space we’re allowed to think that there’re no boundaries, infinitesimal possibilities and we can make a vector for each person in the world maybe linked to our brains and let it begin on the 0 vector and as we make our own choices we make our own vectors scale larger or smaller or even add new vectors to the end of each vector but each vector is specific only to us although maybe sometimes we might find someone in our lives and we might coincide on the same line and maybe even arrive at a point where both our vectors split into three vectors, creating a new relative 0 vector to this newly born vector. Each point in this never ending 3D space could be acquainted with a specific point in time or place where everyone’s vectors are just intermingled with each other in a vast vast 3D space. Who knows, maybe this kind of thinking might arrive at a new dimension and open new possibilities for science. [more ideas but I think this is long now so yeah…]

If we’re talking about vector application that’s real though we might acquaint it with gaming but more on positioning like if you attempt to program using Scratch you might be able to make a side-scrolling game wherein you use vectors to determine your sprite’s movement and change it if it need be.

## Get’cha Head In The Game!

Physics uses a lot of vectors. For example, you can use vectors to compute where a ball will go using velocity and acceleration vectors. Studying motion requires a knowledge of many vectors, like force, displacement, and torque.

This picture illustrates Gabriella Montez and Taylor McKessie using vectors in high school to support their boyfriends in their upcoming basketball game:

Source: High School Musical 1 and Physics 71

## Spam Filtering

Many machine learning models use vectors to classify data. Support Vector Machines (SVMs) for example have made large contributions to spam email filtering. SVM kernels use feature vectors generated through preprocessing data, a vital part of text classification.

## Vector as a malware

In computing, the word ‘Vector’ could either mean matrices or in the case of malicious code, it is the process on how viruses, malwares and worms infect a system to another. This term is derived from the biological meaning of a ‘vector’ like how malaria uses mosquitoes as vectors to spread diseases.

As the dawn of malicious code came about known as ‘virus’ or ‘worm’ or ‘malware’ (malicious ware), different methods of spread also came about over the years. At first malicious code can only affect machines that are directly connected to one another. Then came the use of removable disks such as floppy disks (side note: i miss these) which made it easier to transfer data from one machine to another. As the technology boomed, malware (or worm) used floppy disks as a ‘carrier’ or vector in order to affect more machines. Soon different media/devices have been used as vectors from electronic mails, html, flash drives, CD’s, etc.

So as we can see here, I used the term vector more as a carrier, like in biology, than its mathematical or computing definition. But if you think about it, as you trace these vectors in their evolution, we will be able to trace the path onto which technology has progressed as well. And we can learn a thing or two about them.

## 2d line-to-line collision detection using vectors (Week 2: Vectors)

• As we’ve seen in class, vectors can be used to represent several objects such as physical quantities like velocity or force; 2-dimensional images; and even the bag-of-words model.
• In what other ways can we use vectors?
• Give one sample application and describe/illustrate how the vector can be used.

While computers are good at calculating lots and lots of numbers that would be impossible for a human to do, amusingly some trivial things for humans are much more complex when it is done by a computer. One of these things is checking whether two lines intersect or not.

At one glance it is easy for a human to check if two lines intersect or not, but how would you make a computer do it? This problem seems simple and doesn’t seem to be useful for anything, however it has its use in some areas like collision detection in video game development.

One way to do line-to-line collision is through the use of vectors. We can represent each line as a vector with one end as the the tail and the other head as a tail.

From here we can get the “projection” of each vector on a certain axis, like the x-axis. This can be easily done by getting the dot product of the vector and a unit vector in the same direction as the axis you want to project on. In this case since we will be projecting each vector to the x-axis, we will get the dot product of each vector with the (1,0) unit vector.

Once the vectors are projected into an axis, it’s easier to compare whether the projection lines intersect or not (the details on how exactly would depend on what you are using). If the projections do not intersect, then we are sure that the original lines do not intersect.

This method does not handle all cases of collisions though, for example in case A below if we use the x-axis as a projection it would say that they intersect even though they aren’t. If we projected case A along the y-axis we would detect that indeed they aren’t intersecting. Case B passes both x and y axis tests even though they do not intersect. It seems testing for x and y axis isn’t sufficient.

The correct axis to use is the two normal axis perpendicular to any of the two vectors. This check works for any case and is sufficient on its own (no need to check other axis). The image below shows a projection onto the axis perpendicular to the blue line. Note that if we project using the axis perpendicular to the red line it would seem that they are intersecting, that’s why it’s important to use the two normal axis for checking.

The use of vectors for collision detection can even be used on other things that aren’t two lines. For example, a 2d rectangle can be represented by a vector from the lower left corner to the upper right corner of the box. A 3d cube can also be represented by a vector in a similar manner. Vectors are useful in collision detection and game development in general.

## Vectors in First Person Shooter Games

So there was a time when I delved a bit into game development. One thing I learned was how the game would know you hit someone with a bullet you fired, or if you were hit by an enemies bullet.

It seemed impractical for the game to literally create every bullet fired and track its velocity, speed, how gravity would affect it, etc. Especially in bigger games where you would have 30+ people all firing a lot of bullets in a short amount of time.

What actually happens is when the player fires his gun, the game draws an imaginary vector starting from the tip of the gun and extending outwards. The first object to touch this vector is what the bullet hits, whether it be a wall, or a player.

Please refer to my well rendered diagram as an example. Here you fire a bullet. The game then draws the vector and sees that the first thing it hits is the enemy player followed by the wall. The game then registers the enemy player as being “hit”.

• #### Carlo Lopez 4:08 pm on January 29, 2017 Permalink | Reply

Please note this applies only for what we call “hitscan” weapons in video games. There’s a lot of shooters (especially in older shooters like Quake etc) that really would create every bullet fired and track its velocity, etc.

Liked by 2 people

## Protein Folding

Protein Folding – Protein folding is the process by which a protein structure assumes its functional shape or conformation.

So basically, from your DNA string (ATGC), to amino acid (TQAE…) folds a 3D structure based on the charges of your AAs. Then this 3D structure dictates (generally) the function of your protein. Vectors are used to simulate the direction of aa parts for the 3d struct.

References:

https://www.sciencedaily.com/terms/protein_folding.htm

## Vectors in Data Mining and Pattern Recognition

Data Mining (sometimes called data or knowledge discovery) is the process of analyzing data from different perspectives and summarizing it into useful information. [1]

Pattern recognition is often considered to be a technique separate from data
mining, but its definition is related: “the act of taking in raw data and making
an action based on the ‘category’ of the pattern. [2]

There are numerous application areas for data mining, ranging from e-business
to bioinformatics, from scientific applications such as the classification of volcanos on Venus to information retrieval and Internet search engines.

Linear algebra and data analysis are basic ingredients in many data mining techniques and to treat data by mathematical methods, it needs structures such as matrix and vectors to analyze and predict patterns.

References:
[1] Data Mining: What is Data Mining? (n.d.). Retrieved January 29, 2017, from http://www.anderson.ucla.edu/faculty/jason.frand/teacher/technologies/palace/datamining.htm

[2] Vectors and Matrices in Data Mining and Pattern Recognition, from https://www.siam.org/books/fa04/FA04chapter1.pdf

## Week 2: Vectors

Table tennis

Vectors can be observed when playing table tennis. Kapag nilalagyan ng spin ng players yung ping pong ball kailangan tama yung force at direction ng paghampas para umayon yung trajectory ng bola sa gusto ng player.

In what other ways can we use vectors? Give one sample application and describe/illustrate how the vector can be used.
Flood prediction softwares – Vectors can be used to predict where flood will eventually flow in the event of strong rains and/or typhoons.

## Free Body Diagrams

We can use vectors to visualize all the forces acting on a rigid body, showing the relationships between forces. Which in turn makes calculating forces(or other values) easier. This also helps physics students get a better understanding of the concept of mechanical forces.

## Vectors in Prosthetic Research

Vectors are actually used in the research in making prosthetics. Being a very useful way of modeling certain movements in the muscles and the actual forces a real body can make, vectors are used to model the “proper” movement of a body part. This constitutes the different forces a body part makes when it hits the ground, when it is idle, and it is used to fulfill its main function. It’s way more interesting today as robotics are slowly being integrated in prosthetics research. Using vectors as raw data, a robotic arm can simulate a “natural grip”, being able to hold an object with limited force not enough to break it. Each step in the function of a prosthetic leg was made possible by stress vectors extracted from a test using an actual human leg.

## Sound maps

I remember stumbling upon an article on my news feed wherein it said that a computer algorithm designed a concert hall with a really long and weird name. The architects consulted an “acoustician” that provided them an optimal sound map for the auditorium. They used vectors for this so that they could illustrate how the sounds would bounce off the walls and which parts of the room would produce echoes. Using the values produced by the sound map as parameters, the architects created the algorithm that would design the intricate acoustic panels they used to construct the room.

PS. The concert hall is called Elbphilharmonie. 😁
Source: https://www.wired.com/2017/01/happens-algorithms-design-concert-hall-stunning-elbphilharmonie/

## QUANTUM MECHANICS

According to Jenann Ismael, Quantum Mechanics is a mathematical machine for predicting the behaviors of microscopic particles. In relation to vectors, Quantum Mechanics deals with Hilbert space, a vector space with an inner product defined. An example of this finite hilbert spaces are real numbers and complex numbers. Quantum mechanics may sound seem too complex, and it is, but it’s practical uses are for building precise clocks, creating super computers, imporivng microscopes, and formulating uncrackable codes.

References:
Ismael, Jenann. “Quantum Mechanics.” From Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/entries/qm/#QuaMec

Weisstein, Eric W. “Hilbert Space.” From MathWorld–A Wolfram Web Resource.
http://mathworld.wolfram.com/HilbertSpace.html

Jenner, Nicola. “Five Practical Uses for ‘Spooky’ Quantum Mechanics.” From
Smithsonian.com http://www.smithsonianmag.com/science-nature/five-practical-uses-spooky-quantum-mechanics-180953494/

## (2) Vectors

Give one sample application and describe/illustrate how the vector can be used.

Archery: There are a lot of things to consider when it comes to archery and wind is one of them since it has an effect on a projectile’s trajectory. In order to hit the target, the wind + other factors must be considered to direct it to the target. When we draw back the bowstring, force is exerted on the string to bend it in order to fire a shot. The right amount of force (must not exceed the limit of draw length) and pointing it at the right direction (consider factors that will affect its trajectory) will increase the chances of hitting the target.

## Vectors

Machine Learning

A Support Vector Machine (SVM) is a discriminative classifier formally defined by a separating hyperplane. In other words, given labeled training data (supervised learning), the algorithm outputs an optimal hyperplane which categorizes new examples.

Here is a video to show how it works: https://www.youtube.com/watch?v=1NxnPkZM9bc

## Vector gaming is real

In sports, baseball for example, vectors are used as strategic method by the player to anticipate what direction the ball will be coming from and how far it from the player before it drops and move to the best location to catch the ball.

The technique is to move to a certain direction for a specific distance to reach a highly fly ball before it touches the ground.

## Wavelengths [Lasers]

One of the applications (one of the best in my perspective as of now) that lives on concept of vectors are lasers. As we all know, lasers are waves of light or signal that are being beamed from one location to another, which is possible because of the mathematics of vectors. Typical usage of this technology is fiber optics (firing a laser through a medium where it bounces light travelling in its superb speed!), which greatly helped our entire race in communicating effectively despite great distances. 🙂

## R2 Vectors

Week 2: Vectors

In what other ways can we use vectors? Give one sample application and describe/illustrate how the vector can be used.
Vectors can be used when playing volleyball. When a player is receiving/tossing/spiking the ball, the person uses a specific amount of force (magnitude) to send it to a specific position/person (direction). The team with members who can control both the magnitude and direction of the ball has a higher chance of winning a game.

## Down! Set! HUT-HUT!

American Football~

“Sports instructions are based on using vectors. Wide receivers playing American football, for example, might run a route where they run seven yards down the field before turning left 45 degrees and running in that direction. Sports commentary also depends on vectors. Only a few sports have fields with grids [like football], so discussions revolve around the direction and speed of the player. Illustrations of plays in a variety of sports rely on simple vector images as well [1].”

Vectors are also used to compute the speed and direction a player needs to complete a pass [2].

## Rocket Science

To fly a rocket, there are many factors to consider and one of them is force. As we or some of us know, force is a vector quantity as it has both a magnitude and a direction and there are four types of forces to which rocket flight is subjected to such as weight, thrust as well as lift and drag which are aerodynamic forces. Weight is a gravitational forces while thrust and aerodynamics forces are mechanical force. The main difference between these two types of forces acting on the rocket is the latter requires physical contact with the medium that generates the force.

The magnitude of the gravitational force or the weight depends on the mass of the parts of the rocket, the amount of fuel and payloads such as satellites or space crafts. Have you seen a full scale rocket launch already, may it be on videos or in real life? Sometimes we see a rocket gets broken down into smaller rockets or staged where a smaller rocket rides a bigger rocket. I’ve researched that its actually engineers way to increase the rocket’s performance as the weight of the rocket changes when it exhausts fuel therefore having a constantly changing mass.

The thrust is the force responsible for moving the rocket through air and space. An application of Newton’s Law of Motion, particular the third law which is “For every action, there is an equal and opposite reaction”, which manifests through a propulsion system. This propulsion system accelerates a “working fluid” which is either a liquid or gas and expels this in one direction. The reaction to this expulsion is that it produces a thrust force which is then applied to the opposite direction to which the working fluid is expelled. The simplest rocket engine uses air as working fluid. There are many more factors to consider in thrust force but we’re not going to delve into that.

Lastly, the aerodynamics force which is broken down into two components: lift and drag, acts and is generated as rocket flies through the air. Drag is considered as aerodynamic friction and as we know friction opposes the direction of motion, therefore a source of drag is when solid surface of moving rockets comes in contact with the molecules of the air. Lift, on the other hand, is another application of Newton’s third law wherein the flow of gas is steered or turned by a solid object such as the nose cone or fins of a rocket in one direction, and the lift is generated in the opposite direction which is inclined to the flight direction. Aerodynamics force, however, is pretty negligible when it comes to full scale rockets but are very important in model rockets.

As they say, the only thing that is constant is change and this applies to rockets too. Magnitude of the four forces constantly changes as it flies through the air and sometimes the direction too. Adding up these forces, we gain a net external force and the resulting motion which is also a vector quantity in terms of displacement, velocity and acceleration, is explained by Newton’s laws of motion

https://spaceflightsystems.grc.nasa.gov/education/rocket/rktfor.html

## Fluid Mechanics

Vector algebra and calculus are useful to demonstration the applications of the laws of forces and motion on different kinds of fluids.

## Time as a vector

…but hey time is scalar!

I was browsing topics related to real-life applications of vectors when I stumbled upon the free-space diagram of a simple pendulum. And when you think of a pendulum, the next thing that comes in to your mind is…what? Yes, that’s right! A clock!

So before I even realized what I was searching on Google, I have already typed “vector quantity application in clocks .” It makes no sense but that is how I saw this interesting Quora question- “Why are we looking at time as scalar and not a vector, do you know of a method to display time as a vector?” And surprisingly, someone answered that it is indeed possible to measure time as a vector. Specifically, it is possible through the Minkowski diagram which is used for Einstein’s theory of special relativity. So what is this all about?

Time is absolute. Space is absolute. One hour for you is the same as an hour for me. One meter for you is a meter for me. But what if…

You are walking by the sidewalk when you see a car pass by. Assume that the car is moving equal to the speed of light, and you are walking half as fast. You say that the car is moving twice faster than you, but for the person inside that car you are seemingly walking half as fast. This is a contradiction since we know from our Physics class that the speed of light is ALWAYS equal to 3×10^8m/s wherever we are. But how is it that the speed of light could be twice as fast or half as fast? Well…

They say that when you are enjoying what you are doing, time flies by fast. And when you are bored, it goes oh so slow. Taking this into account, we can think that time is relative depending on our reference.
Now, Physicists thought of combining time and space into “one continuum of spacetime” where in time and space are not absolute. Now we say that a time for you is not the same time for me. And a meter for you is not a meter for me.

There are a lot of technicalities happening here so if you want to know the details, you can watch the source video below.

So where does time as a vector come in to play?
By graphical representation we can see that there a lot of time and space axes plotted over each other depending on the frame of reference. But still, we measure time in seconds, and space in meters. But since they are now contained in spacetime, we can measure both as one unit. Time can now be represented in meters since 1s*3×10^8m/s = 3×10^8m, and space can be measured as seconds!

And that’s it! I don’t want to go blabbing about the really technical stuff since I am not well versed in this theory. And I am not even sure if i understood it correctly (so do tell me if there are any mistakes.)

• #### Michelle Dela Rosa 3:03 pm on February 2, 2017 Permalink | Reply

Really interesting!

Like

## Surface Currents

Vectors are used to describe the behavior of ocean currents

## Data representation

Vector spaces are relevant in most Data Science problems where a dataset arranged in rows and columns (rows are data, columns are attributes). From this, we can picture that a dataset is an mxn matrix. To be short you can approximate any point in your data as a linear combination of some vectors, a base of a vector space. The choice of base depends on the problem you are trying to solve, different algorithms create different bases for example algorithms such as SVD/PCA, ICA, NMF and K-Means will create different bases.

So from the point of view of Data Science a vector space creates a representation of data from the point of view of a given base and thus it’s a very powerful and important concept.

## Roller Coasters!

No engines are mounted on the cars of roller coasters! The movement of the cars are due to the Earth’s gravitational pull. Here the calculation of the vectors of forces, velocity, acceleration, and friction ensure the safety of the riders.

## Wayfinding 101

Vectors are used in sailing. They are represented by sideways and forward components, as explained below. Looks like Moana needs that science after all.

The physics behind sailing is very interesting in that sailboats do not need the wind to push from behind in order to move. The wind can be blowing from the side and the sailboat can still move forward. How is this possible?

The answer lies in the well-known principle of aerodynamic lift. Imagine you are a passenger in a car as it’s moving along, and you place your right hand out the window. If you tilt your hand in the clockwise sense your hand will be pushed backwards and up. This is due to the force of the air which has a sideways component and upwards component (therefore your hand is pushed backwards and up).

In a similar fashion, when the wind blows against the sails from the side, this creates a force which has a sideways component and a forward component.

However, we do not want the sailboat to move sideways. We only want it to move forward (as much as possible). This is accomplished with a keel, located underneath the sailboat. The keel provides the counter-force necessary to resist sideways motion of the sailboat, as much as possible.

So in general, there are two main components of a sailboat which enable it to move forward effectively. They are the sail and the keel, as shown below.

Thus, the physics of sailing involves the interaction of the wind and sails, and the interaction of the water and keel.

## Liquids

Vectors are used to measure the forces involved in flowing liquids. This information can be used in the manufacture of pipes and containers which the liquids will flow through. Plumbing infrastructure need to be able to withstand the pressure of water in order to work properly.

## Vector Analysis on Pathogens

A pathogen or infectious agent is a biological agent that causes disease or illness to its host. Vector analysis can track a possible bioterrorism by knowing where it started, a probable point of release. It can also be used to track the links between victims and to predict the spread of the illness. Tracking such can be complicated for it is a multi-variable problem. It takes complex statistical analysis and graph theory.
Not everyone that gets exposed gets sick.

The data of such  can be discovered with the use of a Geographic Information System  which allows mathematicians to map victims and potential disease clusters with real-time data. Working hand-in-hand  with G.I.S is the Susceptible Infectious Recovered (SIR) model is a differential equation model  which identifies the independent and dependent variables. Namely, the independent variable is time t, measured in days while the two related sets of dependent variables are 1.) the number of people in each of the groups of susceptible, infected and recovered individuals and 2.) the fraction of the total population in the same mentioned 3 categories . These G.I.S and S. I.R model are the two things that allows us to know what is the source or is it a person or a place.

Sources: http://www.springfieldspringfield.co.uk/view_episode_scripts.php?tv-show=numb3rs&episode=s01e03

• #### Ryan Rivera 8:38 am on January 27, 2017 Permalink | Reply Tags: Vector

Week 2: Vectors

In what other ways can we use vectors? Give one sample application and describe/illustrate how the vector can be used.

Many people use GPS (Global Positioning System) navigators, but not everyone knows that these devices constantly calculate vectors for you.

The Global Positioning System (GPS) is a satellite-based navigation system made up of at least 24 satellites. At most times and places, at least three satellites are visible. GPS satellites circle the Earth twice a day in a precise orbit. Each satellite transmits a unique signal and orbital parameters that allow GPS devices to decode and compute the precise location of the satellite. GPS receivers use this information and trilateration to calculate the user’s exact location. A calculation from three satellites will give the longitude and latitude of the receiver. A calculation from four satellites will also give altitude. Essentially, the GPS receiver measures the distance to each satellite by the amount of time it takes to receive a transmitted signal.

Now, how are vectors used in GPS? The receiver does not just triangulate its position once it constantly listens for the satellites and calculates changes in the receiver position from changes in the triangulation results, it also calculates any changes in distance and direction from the last known position. Within a very short time it has taken several readings, enough to calculate the velocity of your travel. The result? A speed in a particular direction – a velocity vector – which is always part of the receiver’s calculations.

Sources:
Paul A. Tipler, Gene Mosca, Physics for Scientist and Engineers, p. 82

## SNAPCHAAAT!!!

Snapchat uses vectors to track the location of the face’s features which enables the app to apply filters in real time.

nooooo

Like

• #### Jem Apolinario 8:10 am on January 27, 2017 Permalink | Reply Tags: Vector

dibs

Planes are given a vector to travel. They also use their speed to determine how far they need to go before turning or landing.

## VECTOR GRAPHICS

Uses polygons to represent images in computer graphics.

Reference: Vector Graphics (https://en.wikipedia.org/wiki/Vector_graphics)

## Astronomy

Vectors can be used to trace the location/position of the stars surrounding/comprising a constellation.

Reference/example: https://www.ncsu.edu/per/Articles/BigDipperPaper.pdf

## Electromagnetic Field

Vectors are used for simulating EM Fields. This is useful for estimating properties of a signal emitting from one transmitter.

Source: http://inspirehep.net/record/946729/plots

## Vectors in Electric Fields

An electric field is produced by a positively or negatively charged object or particle. It is the area around the said charged object or particle in which other charged objects and particles experience either an attractive force or a repulsive force, depending on the charges of the particles or objects (opposite charges attract, same charges repel). The electric field can be represented as a field of vectors with the charged object or particle in the center being the source of the field. The amount of force exerted on a particle by a certain particle decreases the further away they are from each other, in this way the magnitude of the vectors decrease as their distance from the reference particle.

## Game Development

Angry birds, for example. Yung game po. Vectors are usually used in game development to describe change in positions.

## Sportsz (Billiards)!!

dibsdibsdibsz

Vectors can represent physical objects or phenomena. In the field of sports, specifically in Billiards, vector quantities like velocity and momentum is involved. From our knowledge in Physics, total momentum is conserved when a collision happens in an isolated system. So total momentum before and after the collision is equal.

With the knowledge of vectors like velocity and momentum, Billiard players can predict where balls would go if they collide, therefore, they can think of the strategies that can get them the most goals without sinking the cue ball.

• #### Samantha Lopez 6:58 am on January 27, 2017 Permalink | Reply Tags: Vector

DIBS! Vectors can be used to determine the optimal position to install solar panels.

In the installation of solar panels, one must carefully consider the tilt of the roof and and the direction of the sun to produce the largest possible electrical power in the solar panels. The application of vector dot and cross products will allow us to predict the amount of electrical power the panels can produce.

SOURCE: spacemath.gsfc.nasa.gov

## Wind vectors

Wind maps are generated by computer programs as spaces of wind field vectors. The maps are updated in real-time, can analyse wind vectors for up to a height of 140m and have been used for many applications. They are the ones we usually see on TV when the weather forecaster tells us if we can take a walk in the park or stay at home and have our pandesal and coffee instead since the weather doesn’t permit us to.
As another application, energy researchers use these to find optimal land spaces for energy resource gathering. They use wind maps to know where the most frequent and fast speed winds occur to increase energy production and at the same time lessen wind turbine production costs (taking into account how high a tower for the mechanism needs to be built and how many should be built as well).

To know more about wind energy (and other forms of energy) harnessing: https://www.energy.gov/eere/energybasics/energy-basics

Here is a simple example..

The arrows tell us wind’s direction and each one’s elongation tell us how fast they move with respect to the ground

http://ww2010.atmos.uiuc.edu/%28Gl%29/guides/maps/upa/wndvct.rxml

As a side note, the thought of making these wind maps more refined and more fluid as in the work of Fernanda Viégas and Martin Wattenberg made them worthy to be exhibited in MoMA in New York.

Wind map simulation created by the two googlers: https://thescene.com/watch/wired/wind-maps-by-martin-wattenburg-and-fernando-viegas?save_video=true

• #### AF Formaran 6:30 am on January 27, 2017 Permalink | Reply Tags: Vector

Very useful for setting initialization vectors for primary data encryption.

It can also be expanded to visual crypto wherein you use 3d objects instead, and if ever, on elliptic curve to modify it into saddle. (just my thoughts on potential of vectors)

References:

http://crypto.stackexchange.com/questions/732/why-use-an-initialization-vector-iv

https://www.techopedia.com/definition/26858/initialization-vector

## Thought Vectors

The way I understood it, thought vectors map a word to numerous sentences that contain it. In effect, the meaning of a word can be constructed. And so it can be expected that as more sentences are linked to a word, the closer we get from the true meaning of that word [Krumins].

Thought vectors can be applied to image recognition, specifically for describing the contents of an image [Goh]:

References:
Thought vectors could revolutionize artificial intelligence, A. Krumins, https://www.extremetech.com/extreme/206521-thought-vectors-could-revolutionize-artificial-intelligence
Decoding the thought vector, G. Goh, http://gabgoh.github.io/ThoughtVectors/

c
Compose new post
j
Next post/Next comment
k
Previous post/Previous comment
r