Model: Lysandrec/MNLP_M2_document_encoder
Author: Lysandrec
Pipeline: sentence-similarity
Library: sentence-transformers
Tags: sentence-transformers, safetensors, bert, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:100000, loss:TripletLoss, arxiv:1908.10084, arxiv:1703.07737, base_model:sentence-transformers/all-MiniLM-L6-v2, base_model:finetune:sentence-transformers/all-MiniLM-L6-v2, text-embeddings-inference, endpoints_compatible, region:us
Base models (finetune): id: sentence-transformers/all-MiniLM-L6-v2
Card metadata: tags: sentence-transformers, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:100000, loss:TripletLoss
base_model: sentence-transformers/all-MiniLM-L6-v2
widget: source_sentence: Consider the set of points $S = \{(x,y) : x \text{ and } y \text{ are non-negative integers } \leq n\}$. Find the number of squares that can be formed with vertices belonging to $S$ and sides parallel to the axes.
sentences: <page_title> Waller Plan </page_title> <path> Waller_Plan > City plan </path> <section_title> City plan </section_title> <content> The plan also designated spaces for a hospital, an academy and university, churches, a courthouse and jail, an armory, and a penitentiary.With the surveying and grid plan completed, Waller and his associates drew up a plat dividing the city blocks into land lots. The first auction of lots was held on August 1, 1839, under a group of live oak trees in what was to be the city's southwestern public square; these trees have since been known as the "Auction Oaks". The auction raised $182,585 (equivalent to $5,018,000 in 2022), funds used to pay for the construction of government buildings for the new capital city. </content>, <page_title> Heilbronn triangle problem </page_title> <path> Heilbronn_triangle_problem > Specific shapes and numbers </path> <section_title> Specific shapes and numbers </section_title> <content> Goldberg (1972) has investigated the optimal arrangements of n {\displaystyle n} points in a square, for n {\displaystyle n} up to 16. Goldberg's constructions for up to six points lie on the boundary of the square, and are placed to form an affine transformation of the vertices of a regular polygon. For larger values of n {\displaystyle n} , Comellas & Yebra (2002) improved Goldberg's bounds, and for these values the solutions include points interior to the square. These constructions have been proven optimal for up to seven points. </content>, <page_title> 14:9 aspect ratio </page_title> <path> 14:9_aspect_ratio > Mathematics </path> <section_title> Mathematics </section_title> <content> The aspect ratio of 14:9 (1.555...) is the arithmetic mean (average) of 16:9 and 4:3 (12:9), ( ( 16 / 9 ) + ( 12 / 9 ) ) ÷ 2 = 14 / 9 {\displaystyle ((16/9)+(12/9))\div 2=14/9} . More practically, it is approximately the geometric mean (the precise geometric mean is ( 16 / 9 ) × ( 4 / 3 ) ≈ 1.5396 ≈ 13.8: 9 {\displaystyle {\sqrt {(16/9)\times (4/3)}}\approx 1.5396\approx 13.8:9} ), and in this sense is mathematically a compromise between these two aspect ratios: two equal area pictures (at 16:9 and 4:3) will intersect in a box with aspect ratio the geometric mean, as demonstrated in the image at top (14:9 is just slightly wider than the intersection). In this way 14:9 balances the needs of both 16:9 and 4:3, cropping or distorting both about equally. Similar considerations were used in the choice of 16:9 by the SMPTE, which balanced 2.35:1 and 4:3. </content>, source_sentence: Solve the equation \(7k^2 + 9k + 3 = d \cdot 7^a\) for positive integers \(k\), \(d\), and \(a\), where \(d < 7\).
sentences: <page_title> Rational square </page_title> <path> Square_numbers > Properties </path> <section_title> Properties </section_title> <content> Three squares are not sufficient for numbers of the form 4k(8m + 7). A positive integer can be represented as a sum of two squares precisely if its prime factorization contains no odd powers of primes of the form 4k + 3. This is generalized by Waring's problem. </content>, <page_title> Personally Controlled Electronic Health Record </page_title> <path> Personally_Controlled_Electronic_Health_Record > Registration > Healthcare Identifiers Service (HI Service) </path> <section_title> Healthcare Identifiers Service (HI Service) </section_title> <content> The Healthcare Identifiers Service (HI Service) was established by the federal, state and territory governments to create unique identifiers for healthcare providers and individuals seeking healthcare. It was designed and implemented by Medicare Australia under the control of the NEHTA. The HI Service allocates three types of Healthcare Identifiers: Individual healthcare identifier (i.e., who received the service) The Individual Healthcare Identifier (IHI) is a unique 16 digit reference number that is used to identify individuals within the healthcare system. The healthcare provider can retrieve a registered patients IHI via the Healthcare Identifier Service by entering in the correct name, DOB, and Medicare number which will automatically retrieve the patients unique IHI from the system. </content>, <page_title> Systematic sampling </page_title> <path> Systematic_sampling </path> <section_title> Summary </section_title> <content> We want to give unit A a 20% probability of selection, unit B a 40% probability, and so on up to unit E (100%). Assuming we maintain alphabetical order, we allocate each unit to the following interval: A: 0 to 0.2 B: 0.2 to 0.6 (= 0.2 + 0.4) C: 0.6 to 1.2 (= 0.6 + 0.6) D: 1.2 to 2.0 (= 1.2 + 0.8) E: 2.0 to 3.0 (= 2.0 + 1.0) If our random start was 0.156, we would first select the unit whose interval contains this number (i.e. A). Next, we would select the interval containing 1.156 (element C), then 2.156 (element E). If instead our random start was 0.350, we would select from points 0.350 (B), 1.350 (D), and 2.350 (E). </content>, source_sentence: Given the linear transformation \( T: \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) defined by \( T(x) = A(x) \) where \( A = \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 1 & 2 & 2 \end{pmatrix} \), find the inverse transformation \( T^{-1}(x) \).
sentences: <page_title> Genome sequence </page_title> <path> Genomic_sequence > Eukaryotic genomes </path> <section_title> Eukaryotic genomes </section_title> <content> In addition to the chromosomes in the nucleus, organelles such as the chloroplasts and mitochondria have their own DNA. Mitochondria are sometimes said to have their own genome often referred to as the "mitochondrial genome". The DNA found within the chloroplast may be referred to as the "plastome". </content>, <page_title> Right realism </page_title> <path> Right_realism > Overview > Rational choice theory </path> <section_title> Rational choice theory </section_title> <content> For example, in 1960 the steering columns of all cars in Germany were equipped with locks and the result was a 60 per cent reduction in car thefts. Whereas, in Great Britain only new cars were so equipped with the result being crime was displaced to the older unequipped cars. However, no evidence exists to suggest that an obscene phone caller will begin a career as a burglar. In response, Akers (1990) says that rational choice theorists make so many exceptions to the pure rationality stressed in their own models that nothing sets them apart from other theorists. Further, the rational choice models in literature have various situational or cognitive constraints and deterministic notions of cause and effect that render them, "...indistinguishable from current 'etiological' or 'positivist' theories." </content>, <page_title> Elementary row operations </page_title> <path> Row_operations > Elementary row operations > Row-switching transformations > Properties </path> <section_title> Properties </section_title> <content> The inverse of this matrix is itself: T i , j − 1 = T i , j . {\displaystyle T_{i,j}^{-1}=T_{i,j}.} Since the determinant of the identity matrix is unity, det ( T i , j ) = − 1. {\displaystyle \det(T_{i,j})=-1.} </content>, source_sentence: If |x - 5| = 23 what is the sum of all the values of x.
A. A)46
B. B)10
C. C)56
D. D)-46
E. E)28
sentences: <page_title> BMX racing </page_title> <path> BMX_racing > General rules of advancement in organized BMX racing > Professionals </path> <section_title> Professionals </section_title> <content> For example, if a rider participates in 13 national events, their best 10 will be considered and their worst three disregarded. This qualification must be met on the national level to wear National numbers one through ten on the number plate the following year. </content>, <page_title> Construction of the real numbers </page_title> <path> Constructions_of_real_numbers > Axiomatic definitions > Axioms > On models </path> <section_title> On models </section_title> <content> f(x +ℝ y) = f(x) +S f(y) and f(x ×ℝ y) = f(x) ×S f(y), for all x and y in R . {\displaystyle \mathbb {R} .} x ≤ℝ y if and only if f(x) ≤S f(y), for all x and y in R . {\displaystyle \mathbb {R} .} </content>, <page_title> Rod calculus </page_title> <path> Rod_calculus > Subtraction > Without borrowing </path> <section_title> Without borrowing </section_title> <content> In situation in which no borrowing is needed, one only needs to take the number of rods in the subtrahend from the minuend. The result of the calculation is the difference. The adjacent image shows the steps in subtracting 23 from 54. </content>, source_sentence: For some constant $b$, if the minimum value of \[f(x)=\dfrac{x^2-2x+b}{x^2+2x+b}\] is $\tfrac12$, what is the maximum value of $f(x)$?
sentences: <page_title> Lagrangian multiplier </page_title> <path> Lagrange_multiplier > Examples > Example 1 </path> <section_title> Example 1 </section_title> <content> Evaluating the objective function f at these points yields f ( 2 2 , 2 2 ) = 2 , f ( − 2 2 , − 2 2 ) = − 2 . {\displaystyle f\left({\tfrac {\sqrt {2\ }}{2}},{\tfrac {\sqrt {2\ }}{2}}\right)={\sqrt {2\ }}\ ,\qquad f\left(-{\tfrac {\sqrt {2\ }}{2}},-{\tfrac {\sqrt {2\ }}{2}}\right)=-{\sqrt {2\ }}~.} Thus the constrained maximum is 2 {\displaystyle \ {\sqrt {2\ }}\ } and the constrained minimum is − 2 {\displaystyle -{\sqrt {2}}} . </content>, <page_title> Second degree polynomial </page_title> <path> Quadratic_function > Graph of the univariate function > Vertex > Maximum and minimum points </path> <section_title> Maximum and minimum points </section_title> <content> Using calculus, the vertex point, being a maximum or minimum of the function, can be obtained by finding the roots of the derivative: f ( x ) = a x 2 + b x + c ⇒ f ′ ( x ) = 2 a x + b {\displaystyle f(x)=ax^{2}+bx+c\quad \Rightarrow \quad f'(x)=2ax+b} x is a root of f '(x) if f '(x) = 0 resulting in x = − b 2 a {\displaystyle x=-{\frac {b}{2a}}} with the corresponding function value f ( x ) = a ( − b 2 a ) 2 + b ( − b 2 a ) + c = c − b 2 4 a , {\displaystyle f(x)=a\left(-{\frac {b}{2a}}\right)^{2}+b\left(-{\frac {b}{2a}}\right)+c=c-{\frac {b^{2}}{4a}},} so again the vertex point coordinates, (h, k), can be expressed as ( − b 2 a , c − b 2 4 a ) . {\displaystyle \left(-{\frac {b}{2a}},c-{\frac {b^{2}}{4a}}\right).} </content>, <page_title> Dimer model </page_title> <path> Domino_tiling > Counting tilings of regions </path> <section_title> Counting tilings of regions </section_title> <content> The number of ways to cover an m × n {\displaystyle m\times n} rectangle with m n 2 {\displaystyle {\frac {mn}{2}}} dominoes, calculated independently by Temperley & Fisher (1961) and Kasteleyn (1961), is given by (sequence A099390 in the OEIS) When both m and n are odd, the formula correctly reduces to zero possible domino tilings. A special case occurs when tiling the 2 × n {\displaystyle 2\times n} rectangle with n dominoes: the sequence reduces to the Fibonacci sequence.Another special case happens for squares with m = n = 0, 2, 4, 6, 8, 10, 12, ... is These numbers can be found by writing them as the Pfaffian of an m n × m n {\displaystyle mn\times mn} skew-symmetric matrix whose eigenvalues can be found explicitly. This technique may be applied in many mathematics-related subjects, for example, in the classical, 2-dimensional computation of the dimer-dimer correlator function in statistical mechanics. The number of tilings of a region is very sensitive to boundary conditions, and can change dramatically with apparently insignificant changes in the shape of the region. This is illustrated by the number of tilings of an Aztec diamond of order n, where the number of tilings is 2(n + 1)n/2. If this is replaced by the "augmented Aztec diamond" of order n with 3 long rows in the middle rather than 2, the number of tilings drops to the much smaller number D(n,n), a Delannoy number, which has only exponential rather than super-exponential growth in n. For the "reduced Aztec diamond" of order n with only one long middle row, there is only one tiling. </content>
pipeline_tag: sentence-similarity
library_name: sentence-transformers
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Created: 2025-05-22 09:04:12