Model: mrm8488/gte-large-ft-webinstruct
Author: mrm8488
Pipeline: sentence-similarity
Library: sentence-transformers
Tags: sentence-transformers, safetensors, new, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:2335220, loss:MultipleNegativesRankingLoss, custom_code, arxiv:1908.10084, arxiv:1705.00652, base_model:Alibaba-NLP/gte-large-en-v1.5, base_model:finetune:Alibaba-NLP/gte-large-en-v1.5, model-index, text-embeddings-inference, endpoints_compatible, region:us
Base models (finetune): id: Alibaba-NLP/gte-large-en-v1.5
Card metadata: base_model: Alibaba-NLP/gte-large-en-v1.5
library_name: sentence-transformers
metrics: pearson_cosine, spearman_cosine, pearson_manhattan, spearman_manhattan, pearson_euclidean, spearman_euclidean, pearson_dot, spearman_dot, pearson_max, spearman_max
pipeline_tag: sentence-similarity
tags: sentence-transformers, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:2335220, loss:MultipleNegativesRankingLoss
widget: source_sentence: How do you solve the equation #-6 = \frac{y}{5} + 4#?
sentences: To solve the equation, follow these steps:

1. Subtract 4 from both sides:
   \[-6 - 4 = \frac{y}{5} + 4 - 4\]
   \[-10 = \frac{y}{5}\]

2. Multiply both sides by 5 to isolate y:
   \[-10 \cdot 5 = \frac{y}{5} \cdot 5\]
   \[-50 = y\]

So the solution is \(y = -50\)., An organism refers to a living entity, typically composed of cells, capable of growth, reproduction, and response to stimuli. The definition primarily includes all forms of life, excluding viruses, which are considered non-living by some scientists due to their inability to replicate independently.

One of the smallest known organisms is Mycoplasma gallicepticum, a parasitic bacterium measuring approximately 200 to 300 nanometers (nm). It infects primates, inhabiting the bladder, waste disposal organs, genital tracts, and respiratory system.

For comparison, the smallest virus known to humans is the Porcine circovirus type 1 (PCV1), a single-stranded DNA virus. Its genome consists of just 1759 nucleotides, and its capsid diameter measures a mere 17 nm. This virus causes wasting disease in weaned pigs.

[Insert images of Mycoplasma gallicepticum and Porcine circovirus type 1 here, with appropriate captions.]

Keep in mind that the boundary of what constitutes the "smallest organism" can change with advances in scientific research and understanding., Slope is given by #"rise"/"run"#, or the change in the #y# coordinate divided by the change in #x#. Mathematically this is written as 
#(deltay)/(deltax)#
You calculate it by taking the second coordinate and subtracting the first, so
#(deltay)/(deltax) = (y_2 - y_1)/(x_2 - x_1)#
# = (8 - (-2))/(10 - 10) = 10/0#
Since division by zero is undefined, this line has an undefined slope. This means that it is a vertical line., source_sentence: Let $f$ be an analytic function defined on the domain $D = \{z \in \mathbb{C} : |z| < 1\}$ with the property that the range of $f$ lies within $\mathbb{C} \setminus (-\infty, 0]$. Show that there exists an analytic function $g$ on $D$ such that $\text{Re}(g(z)) \geq 0$ and $g(z)^2 = f(z)$ for all $z \in D$.
sentences: In mathematics, equality is often treated as a primitive notion, especially in modern first-order logic. It is understood that two objects, such as real numbers, are equal if they are the same object. However, for a more formal approach in different settings:

1. Set Theory: Equality on a set $I$ can be seen as a chosen equivalence relation that defines equality. For example, in Zermelo-Frankel set theory, equality can be defined as:
   $$x = y \equiv \forall z(z \in x \iff z \in y)$$
   While this works well in set theory, it may not align with the intuitive understanding of equality in other branches of mathematics.

2. Category Theory: Equality in a fibration $E\to B$ can be viewed categorically as a left adjoint to the re-indexing functor induced by the diagonal $I\to I\times I$, evaluated at the terminal object in the fiber.

3. Type Theory: Equality can be understood through the concept of evaluation. For instance, in arithmetic, the equation $2 + 2 = 3 + 1$ can be verified by evaluating both sides to the same result, $s(s(2))$.

The idea of proving two things are equal often involves demonstrating that they satisfy the same properties or relations. For example, to show $\pi \neq 2\pi$, one would compare their algebraic or geometric properties rather than their "membership" in sets.

For further exploration, consider the work of Ansten Klev on identity elimination in Martin-Löf’s Type Theory, and the philosophical discussion in Benecereaf's paper "What numbers could not be." Category theory and type theory also offer rich perspectives on equality., Given that $f$ is analytic in the unit disc and has no zeros, we can define an analytic logarithm of $f(z)$, denoted by $Log f(z)$. We consider the principal branch of the logarithm, which has a branch cut along the negative real axis.

We define $g(z)$ as follows:
\[ g(z) = \sqrt{f(z)} = e^{\frac{1}{2} Log f(z)} \]

Now, the real part of $g(z)$ is given by:
\[ \text{Re}(g(z)) = e^{\frac{1}{2} \log|f(z)|} \cos\left(\frac{\arg{f(z)}}{2}\right) \]

Since $f(z)$ lies outside the negative real axis, we have $|f(z)| > 0$ and $-\pi < \arg{f(z)} < \pi$. Thus, $\cos\left(\frac{\arg{f(z)}}{2}\right)$ is non-negative, which implies that $\text{Re}(g(z)) \geq 0$.

As a result, $g(z)$ is an analytic function on $D$ with a non-negative real part, and it satisfies the property $g(z)^2 = f(z)$ for all $z \in D$., Let $\epsilon > 0$ be given. We need to find a natural number $N_\varepsilon$ such that
$$ \left|\frac{1}{1+n+2^n}\right| < \epsilon $$
for all $n > N_\varepsilon$. Since $1/n \to 0$ as $n \to \infty$, there exists an $N_\varepsilon$ such that $1/n < \epsilon$ for all $n > N_\varepsilon$. Since $2^n \ge n$ for all $n$, we have
$$ \frac{1}{1+n+2^n} < \frac{1}{n+2^n} < \frac{1}{n} < \epsilon $$
for all $n > N_\varepsilon$. Therefore,
$$ \lim_{n\to\infty} \frac{1}{1+n+2^n} = 0.$$, source_sentence: I know that by definition of basis, the vectors v1 and v2 should span the entire subspace. Therefore, if the first constant is not equal to the second constant, and if both of the constants give a linear transformation, then they must be linearly independent and therefore must form a basis. Is that the correct proof, or am I missing something? Also, I don't know what the matrix of the linear transformation is.
sentences: To prove that v1 and v2 form a basis, we need to show that they are linearly independent and that they span the entire subspace.

To show linear independence, suppose that c1v1 + c2v2 = 0 for some scalars c1 and c2. Multiplying both sides by A, we get c1λ1v1 + c2λ2v2 = 0. Multiplying the first equation by λ1 and subtracting it from the second, we get (λ2 - λ1)c2v2 = 0. Since λ2 - λ1 is nonzero (because the eigenvalues are distinct), we must have c2 = 0. Substituting this back into the first equation, we get c1v1 = 0, so c1 = 0. Therefore, v1 and v2 are linearly independent.

To show that v1 and v2 span the entire subspace, we need to show that every vector in the subspace can be written as a linear combination of v1 and v2. Let w be an arbitrary vector in the subspace. Then w can be written as a linear combination of the eigenvectors of A, so w = c1v1 + c2v2 for some scalars c1 and c2. Therefore, v1 and v2 span the entire subspace.

Since v1 and v2 are linearly independent and span the entire subspace, they form a basis for the subspace.

The matrix of the linear transformation T_A is the matrix whose columns are the coordinate vectors of the images of the basis vectors of the domain under T_A. In this case, the basis vectors of the domain are v1 and v2, and their images under T_A are λ1v1 and λ2v2, respectively. Therefore, the matrix of T_A is

$$\begin{bmatrix} \lambda_1 & 0\\ 0 & \lambda_2\end{bmatrix}.$$, To find $E[\tilde{\beta_1}]$, we first need to derive the formula for $\tilde{\beta_1}$. Under the assumption that the intercept is 0, the slope estimator $\tilde{\beta_1}$ is given by:

$$\tilde{\beta_1} = \frac{\sum_{i=1}^n (x_i - \bar{x})y_i}{\sum_{i=1}^n (x_i - \bar{x})^2}$$

where $\bar{x}$ is the sample mean of the $x_i$.

Next, we can substitute the true regression model $y_i = \beta_0 + \beta_1 x_i + u_i$ into the formula for $\tilde{\beta_1}$:

$$\tilde{\beta_1} = \frac{\sum_{i=1}^n (x_i - \bar{x})(\beta_0 + \beta_1 x_i + u_i)}{\sum_{i=1}^n (x_i - \bar{x})^2}$$

Simplifying this expression, we get:

$$\tilde{\beta_1} = \beta_1 + \frac{\sum_{i=1}^n (x_i - \bar{x})u_i}{\sum_{i=1}^n (x_i - \bar{x})^2}$$

Now, we can take the expected value of both sides of this equation:

$$E[\tilde{\beta_1}] = E[\beta_1] + E\left[\frac{\sum_{i=1}^n (x_i - \bar{x})u_i}{\sum_{i=1}^n (x_i - \bar{x})^2}\right]$$

Since $\beta_1$ is a constant, $E[\beta_1] = \beta_1$. For the second term, we can use the fact that $E(u_i) = 0$ (by assumption SLR.3) and the linearity of expectation to get:

$$E\left[\frac{\sum_{i=1}^n (x_i - \bar{x})u_i}{\sum_{i=1}^n (x_i - \bar{x})^2}\right] = \frac{\sum_{i=1}^n (x_i - \bar{x})E(u_i)}{\sum_{i=1}^n (x_i - \bar{x})^2} = 0$$

Therefore, we have:

$$E[\tilde{\beta_1}] = \beta_1 + 0 = \beta_1$$

This shows that $\tilde{\beta_1}$ is an unbiased estimator of $\beta_1$ when the intercept is assumed to be 0.

In addition to the case where $\beta_0 = 0$, $\tilde{\beta_1}$ is also an unbiased estimator of $\beta_1$ when $\sum_{i=1}^n x_i = 0$. This can be seen by noting that in this case, $\bar{x} = 0$ and the formula for $\tilde{\beta_1}$ simplifies to:

$$\tilde{\beta_1} = \frac{\sum_{i=1}^n x_iy_i}{\sum_{i=1}^n x_i^2}$$

which is the same as the formula for the ordinary least squares (OLS) estimator of $\beta_1$ when the intercept is included in the model., Sure. Here is an example of a continuous map that is not proper:

$$
f: \mathbb{R} \to [0, 1]
$$

$$
x \mapsto \frac{1}{1 + |x|}
$$

This map is continuous because it is the composition of continuous functions. However, it is not proper because the preimage of the compact set [0, 1] is not compact. Specifically, the preimage of [0, 1] is the set of all real numbers, which is not compact.

This example shows that the converse of the statement "if a map is proper then it is continuous" is not true., source_sentence: Consider the scenario from the original question, but now suppose that you draw two balls from the same random box. If both balls are gold, what is the probability that the box contains exactly two gold balls?
sentences: The term $\frac{\partial{F}}{\partial{u}}$ appears because $F$ is a function of not only $x$, $y$, and $z$, but also of $u$ and $v$. When we differentiate $F$ with respect to $x$, we must consider how $F$ changes with respect to $u$ as well, since $u$ is a function of $x$., To prove that U ∪ V is an open set, we must show that for every point x in U ∪ V, there exists a ball B(x, r) with radius r > 0, entirely contained within U ∪ V.

Let x be an arbitrary point in U ∪ V. We consider two cases:

Case 1: If x ∈ U, since U is open, there exists a ball B(x, r_1) with r_1 > 0 such that B(x, r_1) ⊆ U.

Case 2: If x ∈ V, as V is also open, there exists a ball B(x, r_2) with r_2 > 0 such that B(x, r_2) ⊆ V.

Now, consider the ball B(x, r), where r = min(r_1, r_2). In both cases (x ∈ U and x ∈ V), this ball has a radius that is less than or equal to the radii of the balls in the respective sets. Therefore, B(x, r) will be entirely contained within either U or V, and as x is in U ∪ V, B(x, r) must be contained within the union of U and V.

Since the choice of x was arbitrary, this shows that for all points in U ∪ V, there exists a corresponding open ball contained within U ∪ V. Hence, U ∪ V is an open set in $\mathbb{C}$., There are a total of 12 balls in the boxes, and 6 of them are gold. If we draw two gold balls, we can eliminate box 4. Out of the remaining 3 boxes, only one box has exactly two gold balls. Therefore, the probability that the box contains exactly two gold balls is $\frac{1}{3}$., source_sentence: What should I do if I'm not satisfied with the answers to a question for which I've offered a bounty?

In my case, I've put a bounty on a question, but the two responses I received don't address the issue effectively. I requested the original poster (OP) to provide an answer so I could reward them for the interesting question, but they haven't done so. 

Are there any acceptable actions in this scenario? For instance, can I post my own non-answer, award myself the bounty, and then start a new bounty on a different question? Or are there alternative suggestions?
sentences: To improve RF signal strength under the given conditions, consider the following suggestions:

1. Bit Rate: Keep the transmitted bit rate low, around 500 bits per second (bps).
2. Balanced Energy Protocol: Implement a biphase or Manchester encoding to ensure a 50% duty cycle, which helps reduce DC offset at the receiver.
3. Preamble: Include a long preamble in your protocol for the receiver to lock onto the signal and set its Automatic Gain Control (AGC) before decoding data.
4. Receiver Tolerance: Design the decoding protocol to tolerate a wide range of pulse widths, as variations due to multi-path, noise, and other factors can affect signal integrity.

While the current setup might be suitable for short distances, increasing the transmitter power voltage could potentially improve range. However, since you cannot change the 3.7V for the receiver, focus on optimizing the mentioned parameters.

For more detailed information and implementation examples, refer to a previous post or access the resources at: http://www.carousel-design.com/ManchesterDesignDocs.zip, The issue you're experiencing with your 40kHz crystal oscillator might be due to insufficient drive strength and an incorrect load capacitance. Here are two potential causes and solutions:

1. High Series Resistance: The 150 kΩ series resistance in your circuit might be too high, which results in a low drive strength for the crystal. This can lead to a reduced overall loop gain and prevents the oscillator from properly starting. To resolve this, try using a lower resistance value as recommended in the crystal's datasheet.

2. Incorrect Load Capacitance: Ensure that the 33 pF load capacitors you're using are compatible with your crystal. Some low-power "watch" crystals require only 5-10 pF load capacitors. Always refer to the crystal's datasheet to verify the appropriate load capacitance value.

In summary, carefully review the crystal's datasheet to determine the correct series resistance and load capacitance values, and make the necessary adjustments to your circuit. By doing so, you should be able to resolve the issue and get your oscillator functioning properly., If all the provided answers do not adequately address your question, it's advisable to let the bounty expire. The system will handle the distribution of the bounty in such situations according to predefined rules.

Bounties carry a risk, as there is no guarantee that you will receive a satisfactory answer, even with the incentive. It's important to understand that you cannot reclaim your bounty once it's been offered. 

Instead of posting a non-answer, you might consider editing and clarifying your original question to attract better responses, or seeking assistance from the community through comments or chat. If needed, you can also start a new bounty on a different question, but ensure that it's clear and well-defined to increase the likelihood of receiving quality answers.
model-index: name: SentenceTransformer based on Alibaba-NLP/gte-large-en-v1.5
results: task: type: semantic-similarity
name: Semantic Similarity
dataset: name: sts dev
type: sts-dev
metrics: type: pearson_cosine
value: 0.8518161048650575
name: Pearson Cosine
verified: no, type: spearman_cosine
value: 0.8590227432558454
name: Spearman Cosine
verified: no, type: pearson_manhattan
value: 0.862661459741618
name: Pearson Manhattan
verified: no, type: spearman_manhattan
value: 0.8594154103524606
name: Spearman Manhattan
verified: no, type: pearson_euclidean
value: 0.8616077663094867
name: Pearson Euclidean
verified: no, type: spearman_euclidean
value: 0.8584194889289465
name: Spearman Euclidean
verified: no, type: pearson_dot
value: 0.8522915008062538
name: Pearson Dot
verified: no, type: spearman_dot
value: 0.8596472575530646
name: Spearman Dot
verified: no, type: pearson_max
value: 0.862661459741618
name: Pearson Max
verified: no, type: spearman_max
value: 0.8596472575530646
name: Spearman Max
verified: no
Likes: 10 | All-time downloads: 242
Created: 2024-09-04 19:06:42