by an integer vector

USAGE SUMMARY

The phrase "by an integer vector" is correct and usable in written English.
It can be used in mathematical or programming contexts where you are referring to a vector composed of integer values. Example: "The transformation was achieved by an integer vector that defined the direction and magnitude of the change."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

First we "cut" the parity-check matrix into two γ p×p 2 matrices, H u and H l. The cutting pattern is defined by an integer vector δ=(δ 0,δ 1,δ 2,⋯,δ γ−1), where 0≤δ 0≤δ 1≤⋯≤δ γ−1≤p.

EURASIP Journal on Advances in Signal Processing

We represented each compound by an integer vector of length 53 679 in which the occurrence of a substructure is coded as an integer value.

Bioinformatics

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

We estimate the discrimination power of a set of genes by computing an integer vector of length 812, containing an entry for each of the 29 × 28 ordered pairs of distinct conditions, which itself is a sum computed over all genes in the set.

BMC Infectious Diseases

The market split problem given in [15] is to determine whether the system, (Cx = d), has a 0-1 integer solution, where (C=(c_{ij})) is a (ptimes q) (e.g., (q=10 p-1))) nonnegative integer matrix and (d=(d_{1},ldots,d_{p},d_{p})^{top}) is an integer vector given by (d_{i}=lfloorsum_{j=1}^{n} c_{ij}/2rfloor), (i=1,2,ldots,p).

Fixed Point Theory and Applications

We represent a compound C by a D-dimensional integer vector (an integer vector of length D) as Φ (C ) = (c 1, c 2,..., c D ) T, where c k ∈ ℤ, k = 1,..., D and each element corresponds to the number of times a given chemical substructure from a library of defined substructures occurs in the compound.

Bioinformatics

On the other hand, vector b, defined in (48), is an integer vector.

EURASIP Journal on Wireless Communications and Networking

The NS-descriptor is an integer vector, and the other fingerprints are binary vectors.

Bioinformatics

It is defined by a integer coefficient vector γ ∈ ℤ s (the dimension s is the number of reactions in R I ) satisfying the following three conditions: (24) S I γ = 0 (25) γ i ≥ 0,   if the reaction    i    is irreversible (26)|| S T γ || > 0 Reaction routes are usually defined [ 39] without the condition (26).

BMC Systems Biology

A solution is represented by an m-dimensional integer vector (Y_i= y_{i1},ldots},y_{im}y_{im})), where (y_{ij}in x_j) for (j=1,2,ldots,m) and are randomly selected from (x_j).

Vietnam Journal of Computer Science

The state of the system is represented by a N-length integer vector X t) denoting the number of molecules of each species at time t.

ACS Synthetic Biology

For color images, a pixel typically has a three-dimensional integer vector, for example, (120, 80, 5), where each vector element represents red, or green, or blue values.

Development Growth and Differentiation

Expert writing Tips

Best practice

When using "by an integer vector", ensure the context clearly indicates what is being defined, represented, or affected by the vector. Always define the integer vector's dimensions and purpose for clarity.

Common error

Avoid using "by an integer vector" without specifying the vector's role or the data it represents. Ambiguity can arise if the vector's purpose and dimensions are not clearly defined.

Linguistic Context

The phrase "by an integer vector" functions primarily as a prepositional phrase modifying a verb or noun. It specifies the means or method by which something is defined, represented, or affected. As Ludwig AI shows, this is common in scientific and technical writing.

Expression frequency: Rare

Frequent in

Science

100%

News & Media

0%

Formal & Business

0%

Less common in

Encyclopedias

0%

Wiki

0%

Social Media

0%

Ludwig's WRAP-UP

In summary, the phrase "by an integer vector" is a grammatically sound prepositional phrase predominantly used in scientific and technical contexts. Ludwig AI indicates that the phrase serves to specify a method or means of representation where integer vectors play a crucial role. It's characterized by its formal and scientific register. While examples are somewhat limited, the phrase is correct and usable, particularly when providing clear context and specifying the vector's parameters.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

using an integer vector

Focuses on the tool being used, rather than the method.

via an integer vector

Emphasizes the pathway or means.

through an integer vector

Highlights the channel or medium.

with an integer vector

Indicates accompaniment or instrumentation.

defined by an integer vector

Specifies the vector as a defining element.

represented by an integer vector

Emphasizes the representational aspect.

characterized by an integer vector

Highlights the vector as a characteristic feature.

determined by an integer vector

Indicates the vector as a determinant.

governed by an integer vector

Suggests the vector as a controlling element.

specified via an integer vector

Focuses on precise specification through the vector.

FAQs

How can I use "by an integer vector" in a sentence?

Use "by an integer vector" to describe how something is defined, represented, or affected by a vector of integers. For instance, "The cutting pattern is defined by an integer vector δ=(δ 0,δ 1,δ 2,⋯,δ γ−1)".

What does "by an integer vector" mean?

It means that a certain property or characteristic is determined or represented using a vector, where each element of the vector is an integer. This is common in mathematical models, computer science, and data representation.

Which is correct, "defined by an integer vector" or "defined with an integer vector"?

"Defined by an integer vector" is generally preferred when the vector is the defining characteristic. "Defined with an integer vector" might be used if the vector is just one of several factors.

What are some alternatives to using "by an integer vector"?

Depending on the context, you could use alternatives such as "using an integer vector", "via an integer vector", or "through an integer vector".