Model: zacbrld/MNLP_M3_document_encoder
Author: zacbrld
Pipeline: sentence-similarity
Library: sentence-transformers
Tags: sentence-transformers, safetensors, bert, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:42185, 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:42185, loss:TripletLoss
base_model: sentence-transformers/all-MiniLM-L6-v2
widget: source_sentence: For example, t ∈ { 0 , 1 , … , N } , N 0 ,  or {\mbox{ or }}[0,+\infty ).} Similarly, a filtered probability space (also known as a stochastic basis) ( Ω , F , { F t } t ≥ 0 , P ) {\displaystyle \left(\Omega ,{\mathcal {F}},\left\{{\mathcal {F}}_{t}\right\}_{t\geq 0},\mathbb {P} \right)} , is a probability space equipped with the filtration { F t } t ≥ 0 {\displaystyle \left\{{\mathcal {F}}_{t}\right\}_{t\geq 0}} of its σ {\displaystyle \sigma } -algebra F {\displaystyle {\mathcal {F}}} . A filtered probability space is said to satisfy the usual conditions if it is complete (i.e., F 0 {\displaystyle {\mathcal {F}}_{0}} contains all P {\displaystyle \mathbb {P} } -null sets) and right-continuous (i.e. F t = F t + := ⋂ s > t F s {\displaystyle {\mathcal {F}}_{t}={\mathcal {F}}_{t+}:=\bigcap _{s>t}{\mathcal {F}}_{s}} for all times t {\displaystyle t} ).It is also useful (in the case of an unbounded index set) to define F ∞ {\displaystyle {\mathcal {F}}_{\infty }} as the σ {\displaystyle \sigma } -algebra generated by the infinite union of the F t {\displaystyle {\mathcal {F}}_{t}} 's, which is contained in F {\displaystyle {\mathcal {F}}}: F ∞ = σ ( ⋃ t ≥ 0 F t ) ⊆ F .
sentences: These individuals can experience these symptoms from failed attempts of depression like symptoms.Narcissistic personality disorder is characterized as feelings of superiority, a sense of grandiosity, exhibitionism, charming but also exploitive behaviors in the interpersonal domain, success, beauty, feelings of entitlement and a lack of empathy. Those with this disorder often engage in assertive self enhancement and antagonistic self protection. All of these factors can lead an individual with narcissistic personality disorder to manipulate others., {\displaystyle {\mathcal {F}}_{\infty }=\sigma \left(\bigcup _{t\geq 0}{\mathcal {F}}_{t}\right)\subseteq {\mathcal {F}}.} A σ-algebra defines the set of events that can be measured, which in a probability context is equivalent to events that can be discriminated, or "questions that can be answered at time t {\displaystyle t} ". Therefore, a filtration is often used to represent the change in the set of events that can be measured, through gain or loss of information. A typical example is in mathematical finance, where a filtration represents the information available up to and including each time t {\displaystyle t} , and is more and more precise (the set of measurable events is staying the same or increasing) as more information from the evolution of the stock price becomes available., Section: Structure and dynamics > Composition. Like microtubules, neurotubules are made up of protein polymers of α-tubulin and β-tubulin, globular proteins that are closely related. They join together to form a dimer, called tubulin. Neurotubules are generally assembled by 13 protofilaments which are polymerized from tubulin dimers. As a tubulin dimer consists of one α-tubulin and one β-tubulin, one end of the neurotubule is exposed with the α-tubulin and the other end with β-tubulin, these two ends contribute to the polarity of the neurotubule – the plus (+) end and the minus (-) end. The β-tubulin subunit is exposed on the plus (+) end. The two ends differ in their growth rate: plus (+) end is the fast-growing end while minus (-) end is the slow-growing end. Both ends have their own rate of polymerization and depolymerization of tubulin dimers, net polymerization causes the assembly of tubulin, hence the length of the neurotubules., source_sentence: We want to find the value of $X$ in the given situation. We are told that James has $X$ apples, and 4 of them are red and 3 of them are green. We want to find the probability that both apples he chooses are green. The total number of apples James has is $X$, and the total number of green apples is 3. To find the probability, we can use the formula: In this case, the number of favorable outcomes is choosing 2 green apples out of the 3 available green apples. The total number of possible outcomes is choosing any 2 apples out of the $X$ total apples. So, the probability is: Probability = (Number of ways to choose 2 green apples) / (Number of ways to choose 2 apples) Since we are given that the probability is $\frac{1}{7}$, we can write: $\frac{1}{7} = \frac{3 \choose 2}{X \choose 2}$ Simplifying, we have: $\frac{1}{7} = \frac{3}{\frac{X(X-1)}{2}}$
sentences: Article: A common type system for clinical natural language processing. One challenge in reusing clinical data stored in electronic medical records is that these data are heterogenous. Clinical Natural Language Processing (NLP) plays an important role in transforming information in clinical text to a standard representation that is comparable and interoperable. Information may be processed and shared when a type system specifies the allowable data structures. Therefore, we aim to define a common type system for clinical NLP that enables interoperability between structured and unstructured data generated in different clinical settings. We describe a common type system for clinical NLP that has an end target of deep semantics based on Clinical Element Models (CEMs), thus interoperating with structured data and accommodating diverse NLP approaches. The type system has been implemented in UIMA (Unstructured Information Management Architecture) and is fully functional in a popular open-source clinical NLP system, cTAKES (clinical Text Analysis and Knowledge Extraction System) versions 2.0 and later. We have created a type system that targets deep semantics, thereby allowing for NLP systems to encapsulate knowledge from text and share it alongside heterogenous clinical data sources. Rather than surface semantics that are typically the end product of NLP algorithms, CEM-based semantics explicitly build in deep clinical semantics as the point of interoperability with more structured data types., Furthermore, the majority of all the male skeletons from the European Neolithic period have so far yielded Y-DNA belonging to this haplogroup. The oldest skeletons confirmed by ancient DNA testing as carrying haplogroup G2a were five found in the Avellaner cave burial site in Catalonia, Spain and were dated by radiocarbon dating to about 5000 BCE. Haplogroup I-M253 (I1) at 4,3% of which L22, Z58 and Z63. According to a study published in 2010, I-M253 originated between 3,170 and 5,000 years ago, in Chalcolithic Europe. A 2014 study in Hungary uncovered remains of two individuals from the Linear Pottery culture, one of whom was found to have carried the M253 SNP which defines Haplogroup I1. This culture is thought to have been present between 7,500 and 6,500 years ago. Finally, there are also some other Y-DNA Haplogroups presented at a lower levels among Bulgarians ~ 10% all together, as J-M267 (J1) at ~3.5%, E-M34 (E1b1b1b2a1) at ~2%, T-M70 (T1a) at ~1.5%, at less than 1% Haplogroup C-M217 (C2), H-M82 (H1a1), N-M231 (N), Q-M242 (Q), L-M61 (L), I-M170 (I*), E-M96 (E*) excl., So, the probability is: Probability = (Number of ways to Multiplying both sides of the equation by $\frac{X(X-1)}{2}$, we get: $\frac{X(X-1)}{2} = 3 \times 7$ $X(X-1) = 6 \times 7$ $X(X-1) = 42$ Expanding the equation, we have: $X^2 - X = 42$ Rearranging the equation, we get: $X^2 - X - 42 = 0$ This is a quadratic equation that can be factored as: $(X - 7)(X + 6) = 0$ Setting each factor equal to zero, we have two possible solutions: $X - 7 = 0$ or $X + 6 = 0$ Solving for $X$, we find: $X = 7$ or $X = -6$ Since the number of apples cannot be negative, the value of $X$ is 7., source_sentence: Section: Model. The Oppenheimer–Snyder model of continued gravitational collapse is described by the line element d s 2 = − d τ 2 + A 2 ( η ) ( d R 2 1 − 2 M R − 2 R b 2 1 R + + R 2 d Ω 2 ) {\displaystyle ds^{2}=-d\tau ^{2}+A^{2}(\eta )\left({\frac {dR^{2}}{1-2M{\frac {R_{-}^{2}}{R_{b}^{2}}}{\frac {1}{R_{+}}}}}+R^{2}d\Omega ^{2}\right)} The quantities appearing in this expression are as follows: The coordinates are ( τ , R , θ , ϕ ) {\displaystyle (\tau ,R,\theta ,\phi )} where θ , ϕ {\displaystyle \theta ,\phi } are coordinates for the 2-sphere. R b {\displaystyle R_{b}} is a positive quantity, the "boundary radius", representing the boundary of the matter region. M {\displaystyle M} is a positive quantity, the mass.
sentences: A standard demonstration in general relativity is to show how, in the "Newtonian limit" (i.e. the particles are moving slowly, the gravitational field is weak, and the field is static), curvature of time alone is sufficient to derive Newton's law of gravity. : 101–106 Newtonian gravitation is a theory of curved time. General relativity is a theory of curved time and curved space. Given G as the gravitational constant, M as the mass of a Newtonian star, and orbiting bodies of insignificant mass at distance r from the star, the spacetime interval for Newtonian gravitation is one for which only the time coefficient is variable:: 229–232 Δ s 2 = ( 1 − 2 G M c 2 r ) ( c Δ t ) 2 − ( Δ x ) 2 − ( Δ y ) 2 − ( Δ z ) 2 {\displaystyle \Delta s^{2}=\left(1-{\frac {2GM}{c^{2}r}}\right)(c\Delta t)^{2}-\,(\Delta x)^{2}-(\Delta y)^{2}-(\Delta z)^{2}}, Section: Examples > Example 1. s ( t ) = A cos ⁡ ( ω t + θ ) , {\displaystyle s(t)=A\cos(\omega t+\theta ),} where ω > 0. s a ( t ) = A e j ( ω t + θ ) , φ ( t ) = ω t + θ . {\displaystyle {\begin{aligned}s_{\mathrm {a} }(t)&=Ae^{j(\omega t+\theta )},\\\varphi (t)&=\omega t+\theta .\end{aligned}}} In this simple sinusoidal example, the constant θ is also commonly referred to as phase or phase offset. φ(t) is a function of time; θ is not. In the next example, we also see that the phase offset of a real-valued sinusoid is ambiguous unless a reference (sin or cos) is specified. φ(t) is unambiguously defined., M {\displaystyle M} is a positive quantity, the mass. R − = m i n ( R , R b ) {\displaystyle R_{-}=\mathrm {min} (R,R_{b})} and R + = m a x ( R , R b ) {\displaystyle R_{+}=\mathrm {max} (R,R_{b})} . η {\displaystyle \eta } is defined implicitly by the equation τ ( η , R ) = 1 2 R + 3 2 M ( η + sin ⁡ η ) . {\displaystyle \tau (\eta ,R)={\frac {1}{2}}{\sqrt {\frac {R_{+}^{3}}{2M}}}(\eta +\sin \eta ).} A ( η ) = 1 + cos ⁡ η 2 {\displaystyle A(\eta )={\frac {1+\cos \eta }{2}}} . This expression is valid both in the matter region R < R b {\displaystyle R<R_{b}} , and the vacuum region R > R b {\displaystyle R>R_{b}} , and continuously transitions between the two., source_sentence: Section: Properties and parameters > Plasma potential. Since plasmas are very good electrical conductors, electric potentials play an important role. The average potential in the space between charged particles, independent of how it can be measured, is called the "plasma potential", or the "space potential". If an electrode is inserted into a plasma, its potential will generally lie considerably below the plasma potential due to what is termed a Debye sheath. The good electrical conductivity of plasmas makes their electric fields very small. This results in the important concept of "quasineutrality", which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma ( n e = ⟨ Z ⟩ n i {\displaystyle n_{e}=\langle Z\rangle n_{i}} ), but on the scale of the Debye length, there can be charge imbalance. In the special case that double layers are formed, the charge separation can extend some tens of Debye lengths. The magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density. A common example is to assume that the electrons satisfy the Boltzmann relation: n e ∝ exp ⁡ ( e Φ / k B T e ) . {\displaystyle n_{e}\propto \exp(e\Phi /k_{\text{B}}T_{e}).} Differentiating this relation provides a means to calculate the electric field from the density: E → = k B T e e ∇ n e n e .
sentences: When the integers a and b are coprime, the standard way of expressing this fact in mathematical notation is to indicate that their greatest common divisor is one, by the formula gcd(a, b) = 1 or (a, b) = 1. In their 1989 textbook Concrete Mathematics, Ronald Graham, Donald Knuth, and Oren Patashnik proposed an alternative notation a ⊥ b {\displaystyle a\perp b} to indicate that a and b are relatively prime and that the term "prime" be used instead of coprime (as in a is prime to b). A fast way to determine whether two numbers are coprime is given by the Euclidean algorithm and its faster variants such as binary GCD algorithm or Lehmer's GCD algorithm. The number of integers coprime with a positive integer n, between 1 and n, is given by Euler's totient function, also known as Euler's phi function, φ(n). A set of integers can also be called coprime if its elements share no common positive factor except 1. A stronger condition on a set of integers is pairwise coprime, which means that a and b are coprime for every pair (a, b) of different integers in the set. The set {2, 3, 4} is coprime, but it is not pairwise coprime since 2 and 4 are not relatively prime., Let's assume the number of cans of corn Beth bought is C. Twice the number of cans of corn she bought would be 2C. So, 15 more than twice the number of cans of corn she bought would be 2C + 15. We know that Beth purchased 35 cans of peas, so we can set up the equation: 2C + 15 = 35. To isolate C, we can subtract 15 from both sides of the equation: 2C = 35 - 15 = 20. Dividing both sides of the equation by 2, we get C = 20/2 = 10. Therefore, Beth bought 10 cans of corn., {\displaystyle n_{e}\propto \exp(e\Phi /k_{\text{B}}T_{e}).} Differentiating this relation provides a means to calculate the electric field from the density: E → = k B T e e ∇ n e n e . {\displaystyle {\vec {E}}={\frac {k_{\text{B}}T_{e}}{e}}{\frac {\nabla n_{e}}{n_{e}}}.} It is possible to produce a plasma that is not quasineutral. An electron beam, for example, has only negative charges. The density of a non-neutral plasma must generally be very low, or it must be very small, otherwise, it will be dissipated by the repulsive electrostatic force., source_sentence: If X {\displaystyle X} is a linear space and g {\displaystyle g} are constants, the system is said to be subject to additive noise, otherwise it is said to be subject to multiplicative noise. This term is somewhat misleading as it has come to mean the general case even though it appears to imply the limited case in which g ( x ) ∝ x {\displaystyle g(x)\propto x} . For a fixed configuration of noise, SDE has a unique solution differentiable with respect to the initial condition.
sentences: Nontriviality of stochastic case shows up when one tries to average various objects of interest over noise configurations. In this sense, an SDE is not a uniquely defined entity when noise is multiplicative and when the SDE is understood as a continuous time limit of a stochastic difference equation. In this case, SDE must be complemented by what is known as "interpretations of SDE" such as Itô or a Stratonovich interpretations of SDEs., Article: RNA-Seq technology and its application in fish transcriptomics.. High-throughput sequencing technologies, also known as next-generation sequencing (NGS) technologies, have revolutionized the way that genomic research is advancing. In addition to the static genome, these state-of-art technologies have been recently exploited to analyze the dynamic transcriptome, and the resulting technology is termed RNA sequencing (RNA-seq). RNA-seq is free from many limitations of other transcriptomic approaches, such as microarray and tag-based sequencing method. Although RNA-seq has only been available for a short time, studies using this method have completely changed our perspective of the breadth and depth of eukaryotic transcriptomes. In terms of the transcriptomics of teleost fishes, both model and non-model species have benefited from the RNA-seq approach and have undergone tremendous advances in the past several years. RNA-seq has helped not only in mapping and annotating fish transcriptome but also in our understanding of many biological processes in fish, such as development, adaptive evolution, host immune response, and stress response. In this review, we first provide an overview of each step of RNA-seq from library construction to the bioinformatic analysis of the data. We then summarize and discuss the recent biological insights obtained from the RNA-seq studies in a variety of fish species., This is the σ-algebra generated by the singletons of X . {\displaystyle X.} Note: "countable" includes finite or empty. The collection of all unions of sets in a countable partition of X {\displaystyle X} is a σ-algebra.
pipeline_tag: sentence-similarity
library_name: sentence-transformers
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Created: 2025-06-09 00:02:51