#euclidean algorithm

[haggishlyhagging]

It took about two hours for Daina Taimina to find the solution that had eluded mathematicians for over a century. It was 1997, and the Latvian mathematician was participating in a geometry workshop at Cornell University. David Henderson, the professor leading the workshop, was modelling a hyperbolic plane constructed out of thin, circular strips of paper taped together. 'It was disgusting,' laughed Taimina in an interview.

A hyperbolic plane is 'the geometric opposite' of a sphere, explains Henderson in an interview with arts and culture magazine Cabinet. 'On a sphere, the surface curves in on itself and is closed. A hyperbolic plane is a surface in which the space curves away from itself at every point.' It exists in nature in ruffled lettuce leaves, in coral leaf, in sea slugs, in cancer cells. Hyperbolic geometry is used by statisticians when they work with multidimensional data, by Pixar animators when they want to simulate realistic cloth, by auto-industry engineers to design aerodynamic cars, by acoustic engineers to design concert halls. It's the foundation of the theory of relativity, and thus the closest thing we have to an understanding of the shape of the universe. In short, hyperbolic space is a pretty big deal.

But for thousands of years, hyperbolic space didn't exist. At least it didn't according to mathematicians, who believed that there were only two types of space: Euclidean, or flat space, like a table, and spherical space, like a ball. In the nineteenth century, hyperbolic space was discovered - but only in principle. And although mathematicians tried for over a century to find a way to successfully represent this space physically, no one managed it - until Taimina attended that workshop at Cornell. Because as well as being a professor of mathematics, Taimina also liked to crochet.

Taimina learnt to crochet as a schoolgirl. Growing up in Latvia, part of the former Soviet Union, 'you fix your own car, you fix your own faucet - anything', she explains. 'When I was growing up, knitting or any other handiwork meant you could make a dress or a sweater different from everybody else's.' But while she had always seen patterns and algorithms in knitting and crochet, Taimina had never connected this traditional, domestic, feminine skill with her professional work in maths. Until that workshop in 1997. When she saw the battered paper approximation Henderson was using to explain hyperbolic space, she realised: I can make this out of crochet.

And so that's what she did. She spent her summer 'crocheting a classroom set of hyperbolic forms' by the swimming pool. 'People walked by, and they asked me, "What are you doing?" And I answered, "Oh, I'm crocheting the hyperbolic plane."' She has now created hundreds of models and explains that in the process of making them 'you get a very concrete sense of the space expanding exponentially. The first rows take no time but the later rows can take literally hours, they have so many stitches. You get a visceral sense of what "hyperbolic" really means.' Just looking at her models did the same for others: in an interview with the New York Times Taimina recalled a professor who had taught hyperbolic space for years seeing one and saying, 'Oh, so that's how they look.' Now her creations are the standard model for explaining hyperbolic space.

-Caroline Criado Perez, Invisible Women

Photo credit

[escxelle]

i'm convinced sleep token are stem girlies because the amount of physics, maths and chemistry in their lyrics hmmm. lemme list all the references below the cut <3 (just as an fyi: this is a joke and i'm not being serious!! i'm just pointing out all the science references in their songs, dw)

alright, bit of a stretch to start but: "sulfur on your breath, granite in my chest." - granite from take me back to eden (2023). sulfur obviously being an element and granite is a rock (i'm not a chem student, i do astrophysics sorry idk anything else skdjsjd)

i'm being really picky but like "these days i'm a circuit board, integrated hardware you cannot afford." - aqua regia from take me back to eden (2023). vessel is an engineering girlie!! /j also i could point out the latin title is a mixture of nitric acid and hydrochloric acid sooo

still in aqua regia, we have "sugar on the blood cells, carbon on the brain." mhm, speak stem girlie!

aqua regia is full of stem textbooks: "oxytocin running in the ether. silicon ballrooms. subatomic interactions if it's all good. gold rush, acid flux. saturate me, i can't get enough. cold love, hot blood." so the debrief: oxytocin is a hormone. ether are a class of compounds. the rest i think is self-explanatory, as they're elements and cute little stem terms oxox

i love stretching. "your viscera welcome me in." - vore from take me back to eden (2023). viscera are the large organs inside the body, including the heart, stomach, lungs, and intestines. biology girlies!! /j

more stretching <3 "who encrypted your dark gospel in body language? synapses snap back in blissful anguish." - ascensionism from take me back to eden (2023). encryption is the process of encoding information!! a computer science girlie!! then synapses are the places where neurons connect and communicate with each other <3

"half algorithm, half deity. glitches in the code or gaps in a strange dream." who ate a programming textbook?! /j

"digital demons make the night feel heavenly." side note but i think we should start calling trolls digital demons.

"lipstick, chemtrails, red flags, pink nails." has someone maybe studied chemtrails in their chemistry classes hmmm? /j

as i'm an astrophysics student i have to mention this: "the shifting states you follow me through." - the apparition from take me back to eden (2023). states, huh? liquid turning into a solid time is it? /j

"i feel my shadown dissolving." - rain from take me back to eden (2023). a metaphor or a chemistry textbook? /j

"it's that chemical cut that i can get down with." have many chemical cuts, huh?? /j

i'm an astrophysics girlie (gn) so i have to include this one: "a dangerous disposition somehow refracted in light, reflected in sound."

"i dream in phosphorescence." - take me back to eden from take me back to eden (2023). phosphorescence is a type of photoluminescence related to fluorescence. i mean, come on! the rest lyric? really?

"sink porcelain stained, choking up brain matter and make-up. just two days since the mainframe went down and i'm still messed up." biology and software engineering much? /j

"if my fate is a bad collision." - euclid from take me back to eden (2023). collision? huh are you a particle, hm? also euclid was a greek mathematician ! currently in my special relativity notes i have written "flat euclidean space"! riddle me that, sleep token. /j

"just orbiting the vacuum i am." - atlantic from this place will become your tomb (2021). yes, orbiting like the sun and moon and planets, right?? /j

"push down into membranes and layers, creating a slow dissection." - like that from this place will become your tomb (2021). yeah we get it, you're a biology student /j

"you lie an inch apart on your own continuum." - the love you want from this place will become your tomb (2021). continuum, huh?

"and though echoing futures are the buckling sutures." - fall for me from this place will become your tomb (2021). i bet you've seen many sutures huh dr. vessel! /j

right prepare for a lot of references here folks. "she's not acid nor alkaline." - alkaline from this place will become your tomb (2021). do i really have to explain the actions of this chem girlie? /j

"ooh, let's talk about chemistry 'cause i'm dying to melt through to the heart of her molecules 'til the particles part like holy water. if anything, she's an undiscovered element." i'm sure you'd love to infodump about your favourite subject! /j

"'cause i am broken into fractions." - distraction from this place will become your tomb (2021). i bet you deal with fractions all the time, you maths nerd!! /j

"and we go beyond the farthest reaches where the light bends and wraps beneath us and i know as you collapse into me." - telomeres from this place will become your tomb (2021). light bending? how very relativity of you. also telomeres are structures made from DNA sequences and proteins found at the ends of chromosomes.

"and i choke myself on sacred vapour." - high water from this place will become your tomb (2021). vapour because it's changed state, right? /j

"keep up on the charm offensive anymore." - missing limbs from this place will become your tomb (2021). i'm doing particle physics right now so i know exactly what a charm quark is! also limbs??? hello again dr. vessel /j

"'cause i look for scarlet and you look for ultraviolet." - higher from sundowning (2019). using ultraviolet filters for your astrophotography are you?? /j

"let the impulse to love and the instinct to kill entangle to one." - say that you will from sundowning (2019). entangle? entanglement? quantum entanglement? i'm connecting the dots.

"i want to roll the numbers. i want to feel my stars align again even if the earth breaks like burnt skin." - blood sport from sundowning (2019). an astrophysics fr /j

"and somewhere, somewhere the atoms stopped fusing." more stem!

"and out there, stuck in a quantum pattern, tangled with what i never said." this is something a theoretical physicist would say is all i'm saying. /j

now you have to listen to sleep token to hear these bangers >:)

[klavierpanda]

🌻 :3

I will tell you& about a cool topology fact that uses one of my favourite theorems!

First, a primer of finitely presented groups:

Given a finite set with n elements S={a₁,...,aₙ}, we define a word to be a finite concatenation of elements in S. For example, a₁a₇aₙ is a word. We define the empty word e to be the word containing no elements of S. We also define the formal inverse of the element aᵢ in S, written aᵢ⁻¹, to be the word such that aᵢaᵢ⁻¹=e=aᵢ⁻¹aᵢ, for all 1≤i≤n.

We define the set ⟨S⟩ to be the collection of all words generated by elements of S and their formal inverses. If we consider concatenation to be a binary operation on ⟨S⟩, then we have made a group. This is the free group generated by S, and is called the free group generated by n elements.

Some notation: if a word contains multiple of the same element consecutively, then we use exponents as short hand. For example, the word babbcb⁻¹ is shortened to bab²cb⁻¹.

Note: concatenation is not commutative. So ab and ba are different words!

We now define a relation on the set ⟨S⟩ to be a particular equality that we want to be true. For example, if we wanted to make the elements a and b commute, we include the relation ab=ba. This is equivalent to aba⁻¹b⁻¹=e. In fact, any relation can be written as some word equal to the empty word. In this way, we can view a relation as a word in ⟨S⟩. So we collect any relations on ⟨S⟩ in the set R.

Finally, we define the group ⟨S|R⟩ to be the group of words generated by S subject to the relations in R. This is called a group presentation. An example is ⟨z,z²⟩, which is isomorphic to the integers modulo 2 with addition ℤ/2.

If both S and R are finite, we say that ⟨S|R⟩ is a finite group presentation. If a group G is isomorphic to a finite group presentation we say G is a finitely presented group. It is worth noting that group presentation is by no means unique so as long as there is one finite group presentation of G, we are good.

In general, determining whether two group presentations is really really hard. There is no general algorithm for doing so.

Lots of very familiar groups of finitely presented. Every finite group is finitely presented. The addative group of integers is finitely presented (this is actually just the free group generated by one element).

Now for the cool topology fact:

Given a finitely presented group G, there exists a topological space X such that the fundamental group of X is isomorphic to G, i.e. π₁(X)≅G. This result is proved using van Kampen's Theorem which tells you what happens to the fundamental group when you glue two spaces together.

The proof involves first constructing a space whose fundamental group is the free group of n elements, which is done inductively by gluing n loops together at a single shared basepoint. Each loop represents one of the generators. Then words are represented by (homotopy classes of) loops in the space. Then we use van Kampen's Theorem to add a relation to the fundamental group by gluing a disc to the space identifying the boundary of the disc to the loop in the space that represents the word for the relation we want. We do this until we have added all of the relations we want to get G.

We can do a somewhat similar process to show that any finitely presented group is the fundamental group of some 4-manifold (a space that locally looks like 4-dimensional Euclidean space, the same way a sphere locally looks like a plane). This means that determining whether two 4-manifolds are homeomorphic or not using their fundamental groups is really hard in general because distinguishing finitely generated groups is hard in general.

P.s. I also want to tell you that you're really wonderful :3 <2

[janmisali]

Number Tournament: THE SQUARE ROOT OF TWO vs THE FAST INVERSE SQUARE ROOT "WHAT THE FUCK?" CONSTANT

[link to all polls]

the square root of two

seed: 35 (15 nominations)

previous opponent: three

class: irrational number

definition: the Euclidean distance from the origin to the point (1,1)

hex 5F3759DF (// what the fuck?)

seed: 47 (9 nominations)

previous opponent: twelve

class: hex constant

definition: a number that allows a certain algorithm to get a decent approximation of the inverse square root after only one iteration of Newton's method

[synths-and-sensibility]

Microtonal quantizer, is that anything?

So, I was staring at the keyboard on our piano and realized that the diatonic scale is analogous to a Euclidean rhythm with 12 steps and 7 beats. It wouldn't be too much effort to adapt an algorithm for a quantizer to divide up an octave into an arbitrary scale given numbers of generic and specific intervals. Add in an offset and you can cycle through different modes. And why stop there? Why not give it the ability to divide up an interval other than an octave?

(I fell down a music theory hole today that started getting into set theory and such. No idea what the resulting scales would actually sound like, but it might be a fun project)

[number1euclideanalgorithmfan]

Whenever I see your name I see it as number1euclidiangothfan

Instead of number1euclidianalgorithmfan.

I just thought that would be a funny bit of info to share with you!

Euclidean goths sound badass tbh, I appreciate you sharing. The backstory to my name, in case you're curious, is that I was bitching about the Euclidean Algorithm in my math classes and then I just kept having to do it over and over in back to back to back courses and started slowly going insane. I think the goths could have kept me sane

[humangirlshelley]

my sister needed help w polynomial long division for her algebra 1 hw and i was like oops I never learned how to do that and I took a few minutes to figure it out and realized it's literally just the euclidean division algorithm!! I love math sm

[enderearcheck]

A new reader has entered the ring! Thank you @thefirewolfblogger for making part 7 possible! 

Twitter knew, as soon as He’d entered tumblrs domain, that He’d made a mistake. Back home the algorithms always took him exactly where he wanted to go, but here? Where were the algorithms?! left to wander, unsure where to go. Twitter was utterly lost. 

How long had He been wandering?! What day was it? Why were shoelaces important?! 

Adds screamed at him to ‘shave his balls!’ And the creepy Pikachu hybrid man was definitely following him, 🦀

🦀Crabs 🦀 fell f🦀rom 🦀the sky, seemingly 🦀at random.  And the 🦀sky 🦀was a miasma of ever 🦀changing colors.        🦀

       🦀.                  🦀.          🦀

He was trapped in a cite of cringe 🦀🦀and debauchery. Just like he remembered…A war torn blog space of non-🦀Euclidean P*rnless mosterf*ckers. Strange posts that made no sense. Every word was a tw waiting to happen. Bloggers were Cat calling him… literally Hissing ferociously. The bird app cringed away. Accidentally bumping into a girl blogger. “Ew a Fucking bot!” They said disgusted. 

“Oh no no miss um…I’m not a—-

Twitter wasn’t able to finish that sentence because a giant crab screamed “SILENCE BOT!” and began shooting lasers at him. Twitter ducked into an alleyway desperately trying to escape only to run into another group of blogs. 

Hey a newbie! Looks like we found ourselves a fuck boi. How hasn’t He been devoured by bees yet? He’s so pathetic…I could take Him. Man anyone could take a piece of that Twink! I Bet this idiot has weak bones! Yeah! Get Gonched idiot! 

W-What?!

Oh my gon, he hasn’t seen Goncharov!

The crowd was closing in! Twitter was afraid.

LIKE/COMENT for PART 8!  @gondremark @ladyver0nica @r3nvy

[its-a-hil]

so why does the math tutoring program i work for teach kids to calculate gcf's by looking for common factors when the euclidean algorithm is right there and so much easier to use

(edit: ctrl-enter my beloved, enter my beloathed)

[systemtek]

Yubico YubiKey 5 Series ECDSA secret-key extraction attack vulnerability [CVE-2024-45678]

CVE number = CVE-2024-45678 Yubico YubiKey 5 Series devices with firmware before 5.7.0 and YubiHSM 2 devices with firmware before 2.4.0 allow an ECDSA secret-key extraction attack (that requires physical access and expensive equipment) in which an electromagnetic side channel is present because of a non-constant-time modular inversion for the Extended Euclidean Algorithm, aka the EUCLEAK issue. Other uses of an Infineon cryptographic library may also be affected. Not Affected Products YubiKey 5 Series version 5.7.0 and newer YubiKey 5 FIPS Series 5.7 and newer (FIPS submission in process) YubiKey Bio Series versions 5.7.2 and newer Security Key Series versions 5.7.0 and newer YubiHSM 2 versions 2.4.0 and newer YubiHSM 2 FIPS versions 2.4.0 and newer Affected YubiKey 5 Series versions prior to 5.7 YubiKey 5 FIPS Series prior to 5.7 YubiKey 5 CSPN Series prior to 5.7 YubiKey Bio Series versions prior to 5.7.2 Security Key Series all versions prior to 5.7 YubiHSM 2 versions prior to 2.4.0 YubiHSM 2 FIPS versions prior to 2.4.0 How To Tell If You Are Affected Identify YubiKey Version To identify the YubiKey, use Yubico Authenticator to identify the model and version of the YubiKey. The series and model of the key will be listed in the upper left corner of the Home screen. In the following example, the YubiKey is a YubiKey 5C NFC version 5.7.0. Further information - https://www.yubico.com/support/security-advisories/ysa-2024-03/ Read the full article

[particle196]

Mind Blowing Physics Tessellation Algorithm 

A "Mind Blowing Physics Tessellation Algorithm" sounds intriguing! While there's no widely recognized algorithm by that name, I can imagine it might involve using tessellation principles to model complex physical systems. Tessellation refers to covering a surface with geometric shapes without gaps or overlaps, and it has applications in various fields, including physics.

Here’s a speculative outline of what such an algorithm might entail:

1. Objective

To develop an algorithm that uses tessellation to model and analyze complex physical systems, such as crystal structures, particle arrangements, or space-time geometries.

2. Conceptual Framework

Tessellation Principles: Understanding how basic geometric shapes (tiles) can fill a space without gaps or overlaps.

Physical Systems: Identifying the physical systems or phenomena where tessellation can provide insights, such as the arrangement of particles in a lattice, or the distribution of energy in a field.

3. Algorithm Design

Shape Selection: Choose appropriate geometric shapes for tessellation based on the physical system being modeled (e.g., hexagons for honeycomb structures, or tetrahedra for certain crystal lattices).

Tessellation Process:

Analysis:

Initialization: Define the initial conditions or constraints of the physical system.

Tiling: Apply the tessellation algorithm to cover the space or surface in question.

Optimization: Adjust the tessellation to fit specific physical constraints, such as minimizing energy or maximizing symmetry.

Use the tessellation pattern to analyze physical properties like stress distribution, energy levels, or spatial organization.

Incorporate physical laws and equations to refine the tessellation model.

4. Applications

Material Science: Modeling crystal structures or composite materials.

Particle Physics: Analyzing particle interactions and distributions.

Cosmology: Exploring the tessellation of space-time in various cosmological models.

Engineering: Optimizing structural designs or material layouts.

5. Implementation

Software Tools: Develop or use existing computational tools and libraries for tessellation and physical modeling (e.g., MATLAB, Python with libraries like NumPy and SciPy).

Visualization: Create visual representations of the tessellation to help interpret the results.

6. Challenges

Complexity: Managing the complexity of tessellation in higher dimensions or with non-standard shapes.

Accuracy: Ensuring that the tessellation accurately represents the physical system and adheres to physical laws.

7. Future Directions

Advanced Tessellation: Explore non-Euclidean or fractal tessellations for more complex systems.

Integration: Combine tessellation with other computational techniques like machine learning to enhance the model’s predictive power.

More Info: physicistparticle.com 

contact us : contact@physicistparticle.com

[crimsonpublishers-oabb]

Adapting Hartigan & Wong K-Means for the Efficient Clustering of Sets1

This paper proposes an algorithm, named HWK-Sets, based on K-Means, suited for clustering data which are variable-sized sets of elementary items. An example of such data occurs in the analysis of medical diagnosis, where the goal is to detect human subjects who share common diseases so as to predict future illnesses from previous medical history possibly. Clustering sets is difficult because data objects do not have numerical attributes and therefore it is not possible to use the classical Euclidean distance upon which K-Means is normally based. An adaptation of the Jaccard distance between sets is used, which exploits application-sensitive information. More in particular, the Hartigan and Wong variation of K-Means is adopted, which can favor the fast attainment of a careful solution. The HWK-Sets algorithm can flexibly use various stochastic seeding techniques. Since the difficulty of calculating a mean among the sets of a cluster, the concept of a medoid is employed as a cluster representative (centroid), which always remains a data object of the application. The paper describes the HWK-Sets clustering algorithm and outlines its current implementation in Java based on parallel streams. After that, the efficiency and accuracy of the proposed algorithm are demonstrated by applying it to 15 benchmark datasets.

Read More About This Article: https://crimsonpublishers.com/oabb/fulltext/OABB.000564.php

Read More About Crimson Publishers: https://crimsonpublishers.com/oabb/index.php

[govindhtech]

Using Vector Index And Multilingual Embeddings in BigQuery

The Tower of Babel reborn? Using vector search and multilingual embeddings in BigQuery Finding and comprehending reviews in a customer’s favourite language across many languages can be difficult in today’s globalised marketplace. Large datasets, including reviews, may be managed and analysed with BigQuery.

In order to enable customers to search for products or company reviews in their preferred language and obtain results in that language, google cloud describe a solution in this blog post that makes use of BigQuery multilingual embeddings, vector index, and vector search. These technologies translate textual data into numerical vectors, enabling more sophisticated search functions than just matching keywords. This improves the relevancy and accuracy of search results.

Vector Index

A data structure called a Vector Index is intended to enable the vector index function to carry out a more effective vector search of embeddings. In order to enhance search performance when vector index is possible to employ a vector index, the function approximates nearest neighbour search method, which has the trade-off of decreasing recall and yielding more approximate results.

Authorizations and roles

You must have the bigquery tables createIndex IAM permission on the table where the vector index is to be created in order to create one. The bigquery tables deleteIndex permission is required in order to drop a vector index. The rights required to operate with vector indexes are included in each of the preset IAM roles listed below:

Establish a vector index

The build VECTOR INDEX data definition language (DDL) statement can be used to build a vector index.

Access the BigQuery webpage.

Run the subsequent SQL statement in the query editor

Swap out the following:

The vector index you’re creating’s name is vector index. The index and base table are always created in the same project and dataset, therefore these don’t need to be included in the name.

Dataset Name: The dataset name including the table.

Table Name: The column containing the embeddings data’s name in the table.

Column Name:The column name containing the embeddings data is called Column name. ARRAY is the required type for the column. No child fields may exist in the column. The array’s items must all be non null, and each column’s values must have the same array dimensions. Stored Column Name: the vector index’s storage of a top-level table column name. A column cannot have a range type. If a policy tag is present in a column or if the table has a row-level access policy, then stored columns are not used. See Store columns and pre-filter for instructions on turning on saved columns.

Index Type:The vector index building algorithm is denoted by Index type. There is only one supported value: IVF. By specifying IVF, the vector index is constructed as an inverted file index (IVF). An IVF splits the vector data according to the clusters it created using the k-means method. These partitions allow the vector search function to search the vector data more efficiently by limiting the amount of data it must read to provide a result.

Distance Type: When utilizing this index in a vector search, distance type designates the default distance type to be applied. COSINE and EUCLIDEAN are the supported values. The standard is EUCLIDEAN.

While the distance utilised in the vector search function may vary, the index building process always employs EUCLIDEAN distance for training.

The Diatance type value is not used if you supply a value for the distance type argument in the vector search function. Num Lists: an INT64 value that is equal to or less than 5,000 that controls the number of lists the IVF algorithm generates. The IVF method places data points that are closer to one another on the same list, dividing the entire data space into a number of lists equal to num lists. A smaller number for num lists results in fewer lists with more data points, whereas a bigger value produces more lists with fewer data points.

To generate an effective vector search, utilise num list in conjunction with the fraction lists to search argument in the vector list function. Provide a low fraction lists to search value to scan fewer lists in vector search and a high num lists value to generate an index with more lists if your data is dispersed among numerous small groups in the embedding space. When your data is dispersed in bigger, more manageable groups, use a fraction lists to search value that is higher than num lists. Building the vector index may take longer if you use a high num lists value.

In addition to adding another layer of refinement and streamlining the retrieval results for users, google cloud’s solution translates reviews from many languages into the user’s preferred language by utilising the Translation API, which is easily integrated into BigQuery. Users can read and comprehend evaluations in their preferred language, and organisations can readily evaluate and learn from reviews submitted in multiple languages. An illustration of this solution can be seen in the architecture diagram below.

Google cloud took business metadata (such address, category, and so on) and review data (like text, ratings, and other attributes) from Google Local for businesses in Texas up until September 2021. There are reviews in this dataset that are written in multiple languages. Google cloud’s approach allows consumers who would rather read reviews in their native tongue to ask inquiries in that language and obtain the evaluations that are most relevant to their query in that language even if the reviews were originally authored in a different language.

For example, in order to investigate bakeries in Texas, google cloud asked, “Where can I find Cantonese-style buns and authentic Egg Tarts in Houston?” It is difficult to find relevant reviews among thousands of business profiles for these two unique and frequently available bakery delicacies in Asia, but less popular in Houston.

Google cloud system allows users to ask questions in Chinese and get the most appropriate answers in Chinese, even if the reviews were written in other languages at first, such Japanese, English, and so on. This solution greatly improves the user’s ability to extract valuable insights from reviews authored by people speaking different languages by gathering the most pertinent information regardless of the language used in the reviews and translating them into the language requested by the user.

Consumers may browse and search for reviews in the language of their choice without encountering any language hurdles; you can then utilise Gemini to expand the solution by condensing or categorising the reviews that were sought for. By simply adding a search function, you may expand the application of this solution to any product, business reviews, or multilingual datasets, enabling customers to find the answers to their inquiries in the language of their choice. Try it out and think of additional useful data and AI tools you can create using BigQuery!

Read more on govindhtech.com

[programmingsolver]

CS559-B HW3

Problem 1 (25pt): [K-means] Implement the K-means algorithm. Note that you cannot directly call the built-in kmeans functions. Figure 1: Scatter plot of datasets and the initialized centers of 3 clusters Given the matrix X whose rows represent different data points, you are asked to perform a k-means clustering on this dataset using the Euclidean distance as the distance function. Here k is…

[synths-and-sensibility]

Algorithm for distributional evenness, for use in generating Euclidean rhythms and maximally even microtonal scales.

(I left out the initialization: r = 0; hit[0] = 1)

[myprogrammingsolver]

CS559-B HW3

Problem 1 (25pt): [K-means] Implement the K-means algorithm. Note that you cannot directly call the built-in kmeans functions. Figure 1: Scatter plot of datasets and the initialized centers of 3 clusters Given the matrix X whose rows represent different data points, you are asked to perform a k-means clustering on this dataset using the Euclidean distance as the distance function. Here k is…