can be defined over

USAGE SUMMARY

The phrase "can be defined over" is correct and usable in written English.
It is typically used in mathematical or technical contexts to indicate that a certain concept or function can be established or described within a specific framework or domain. Example: "The function can be defined over the set of real numbers, allowing for a broader application in calculus."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

8 human-written examples

Last, combinative preferences can be defined over properties of objects.

SEP

While linear autoencoders can be defined over any field, only real-valued linear autoencoders have been studied so far.

Neural Networks

The potential function ( Vleft( {vec{x}} right) ) can be defined over the same ( n )-dimensional feature space and defined as the function for which ( varphi left( {vec{x}} right) ) satisfies the time-independent Schrodinger equation.

Data Science and Engineering

The ElGamal encryption scheme can be defined over any cyclic group G. Its security depends upon the difficulty of a certain problem in G related to computing discrete logarithms.

Data Science and Engineering

Then, the following discrimination measure (DM) can be defined over a set of synthesized FVs, S = {s}, DM S = FP S + δ mean l n / δ min l n, l m, where δ mean l n = 1 L ∑ n = 0 L − 1 ∑ ∀ s ∈ l n μ n − s l n, δ min l n, l m = min n ≠ m μ n − μ m. (14).

EURASIP Journal on Audio, Speech, and Music Processing

For example, once the joint rotation axes and range of motion can be defined over a wide range of behaviors, these can be used to further constrain the 3D search for more distal leg points.

Plosone

Human-verified similar examples from authoritative sources

Similar Expressions

51 human-written examples

Cellular aging can be defined as over-activation of signaling pathways (such as mTOR) with secondary signal resistance [ 14].

Aging

Based on CyTOF® data, immune cell populations can be quantified at single-cell resolution according to their phenotype and can be defined using over 30 parameters.

Arthritis Research and Therapy

No object can be defined by quantifying over a totality which contains the object itself as element; hence the order of every propositional function must be greater than the order of propositional functions over which it quantifies.

SEP

The basic iterative, synchronous consensus protocol can be defined as follows over iterations k: begin{aligned} {tilde{h}}_i^{ k+1)} = {tilde{h}}_i^{ k)} + xi sum limits _{jin N_i} left( {tilde{h}}_j^{ k)} - {tilde{h}}_i^{ k)}right) end{aligned} (15 where (xi) is the step size.

Journal of Modern Power Systems and Clean Energy

This frequent phenomenon, known as hemoglobin cycling, can be defined as fluctuations over time in measured Hb levels, increasing above or decreasing below the target and reversing direction [ 7].

BMC Nephrology

Expert writing Tips

Best practice

When using "can be defined over", ensure that the domain or framework you are defining it over is clearly specified. This adds precision and avoids ambiguity.

Common error

Avoid using "can be defined over" without clearly stating the specific set, space, or conditions that the definition applies to. For instance, instead of saying "The function can be defined over", specify "The function can be defined over the interval [0, 1]".

Linguistic Context

The phrase "can be defined over" functions as a declarative statement indicating the possibility or ability to establish a definition within a specified domain or set. As Ludwig AI points out, this usage is grammatically correct and common in technical contexts.

Expression frequency: Uncommon

Frequent in

Science

71%

News & Media

14%

Encyclopedias

14%

Less common in

Formal & Business

0%

Social Media

0%

Reference

0%

Ludwig's WRAP-UP

In summary, the phrase "can be defined over" is a grammatically correct and technically precise expression used to indicate that a concept or function can be defined within a specific domain or framework. As Ludwig AI points out, this phrase is most commonly encountered in scientific and academic contexts, serving to clarify the scope and applicability of definitions. Related phrases include "is definable within" and "can be characterized across". A key writing tip is to clearly specify the domain or framework to which the definition applies to avoid ambiguity. Ludwig has identified that the phrase appears in authoritative sources such as PlosOne, BMC Systems Biology and The New York Times. It is important to avoid vagueness in specifying the domain.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

is definable within

Emphasizes the ability to establish a definition within a specific context or system.

can be characterized across

Focuses on describing the attributes or qualities across a certain range or spectrum.

is applicable to

Highlights the relevance or suitability of a concept to a particular area or subject.

can be expressed in terms of

Indicates the possibility of formulating a concept using specific language or notation.

can be formulated within

Suggests that a concept can be structured or created inside a certain framework.

is understood through

Focuses on gaining insight or comprehension via a specific lens or methodology.

can be conceptualized as

Emphasizes a particular way of thinking about or understanding a concept.

is determined by

Highlights that a concept's value or properties are set according to certain values.

can be mapped onto

Suggests a correspondence or relationship between two different domains or systems.

is circumscribed by

Focuses on defining the boundaries or limits within which something exists or operates.

FAQs

How do I use "can be defined over" in a sentence?

Use "can be defined over" to indicate that a concept or function can be established or described within a specific domain or framework. For example, "The ElGamal encryption scheme "can be defined over" any cyclic group G."

What are some alternatives to "can be defined over"?

Alternatives include "is definable within", "can be characterized across", or "is applicable to" depending on the specific context and nuance you want to convey.

What does it mean when something "can be defined over" a set?

It means that the properties, behavior, or values of that thing are specified and valid within the boundaries of that particular set. It establishes the scope of its definition.

Is "can be defined over" formal or informal language?

"Can be defined over" is generally considered formal, technical language and is more appropriate for academic, scientific, or professional writing. More informal contexts would require different phrasing.