all possible topologies

USAGE SUMMARY

The phrase "all possible topologies" is correct and usable in written English.
It can be used in contexts related to mathematics, particularly in topology, to refer to every conceivable arrangement or structure that can be defined within a given set. Example: "In our study, we will explore all possible topologies on the given set to understand their properties and implications."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

18 human-written examples

The primary design problem can be described as follows: Given a set of network nodes, it is required to find a topology Ψ, selected from all possible topologies, so that the cost of Ψ (measured possibly in terms of the maximum diameter, maximum node degree, etc). is less than that of any other network topology and such that Ψ satisfies some given design constraints.

Journal of Network and Computer Applications

We developed a model to approximate the compact parallel and antiparallel arrangement of α-helices and β-strands, enumerated all possible topologies formed by up to five secondary structural elements (SSEs), searched for their occurrence in spatial structures of proteins, and documented their frequencies of occurrence in the PDB.

Journal of Molecular Biology

Routing protocols for ad-hoc networks, e.g., the Collection Tree Protocol (CTP), are designed with simple node-local behaviour, but are deployed on testbeds with uncontrollable physical topology; exhaustively verifying the protocol on all possible topologies at design time is not tractable.

Ad Hoc Networks

Thus, real phylogenies should be expected to range throughout all possible topologies, with no reasonable way of a priori delimiting tree space.

Plosone

Here, using a heuristic optimization-based approach, we dissected the design space containing all possible topologies and parameter values of the FFL circuits.

Plosone

These methods typically consider all possible topologies.

BMC Systems Biology

Human-verified similar examples from authoritative sources

Similar Expressions

42 human-written examples

Moreover, all the possible topologies switch aperiodically.

Advances in Difference Equations

When both LS methods included all the possible topologies in the confidence set, other pieces of evidence supported a low phylogenetic signal in the data: Table 2 lists the percentage of four-taxon subsets for which the star topology was the ML solution calculated using TREE-PUZZLE [ 25].

BMC Evolutionary Biology

It has been for long stressed that the partition function of a quantum gravitational theory has to have a sum over all the possible topology.

Journal of Theoretical and Applied Physics

This result implies that, among all the possible topology candidates for a given skeleton, evolution has selected the native topology as the one that can accommodate the largest structural variations, not the one rigidly trapped in a deep, but narrow, conformational energy well.

Journal of Molecular Biology

In this test, the relationships among the closely related species shown in Table 1 were fixed, and all the remaining possible topologies (maximally 945 topologies among the 7 taxa) were generated and tested.

BMC Genomics

Expert writing Tips

Best practice

When discussing network design or phylogenetics, ensure the context clarifies whether you are considering all mathematically possible topologies or only those feasible under certain constraints. State explicitly which scope you are analyzing.

Common error

Avoid assuming that "all possible topologies" are automatically relevant or realistic in a given scenario. Always specify any limitations or filtering criteria applied to the set of topologies under consideration.

Linguistic Context

The phrase "all possible topologies" acts as a determiner phrase, specifically quantifying the set of network or structural arrangements under consideration. As Ludwig AI confirms, it is correctly used to describe the entire scope of potential configurations.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

The phrase "all possible topologies" is a technical term primarily used in scientific contexts, especially in fields like network design, phylogenetics, and molecular biology. According to Ludwig, the phrase is grammatically correct and used to define the entire set of structural arrangements under consideration. While not frequently encountered in general writing, its use signals a comprehensive and exhaustive approach to analysis. Considering the limited contexts and complexity of the expression, it is important to explicitly clarify the scope and constraints when using this phrase. The expression is mostly frequent in scientific contexts.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

every conceivable configuration

Replaces "topologies" with "configuration", emphasizing arrangement rather than structure type.

all conceivable network architectures

Substitutes "possible" with "conceivable" and "topologies" with "network architectures", adding specificity.

the complete range of structural arrangements

Rephrases the concept using "range of structural arrangements" for broader coverage.

each potential network layout

Focuses on "network layout", simplifying the technical term "topology".

every attainable structural design

Uses "attainable structural design" to emphasize feasibility within design constraints.

the entirety of network structures

Emphasizes completeness using "entirety", while retaining "network structures".

all theoretical network forms

Highlights the theoretical aspect of network structures.

the universe of possible configurations

Uses "universe" to describe the set of possibilities and configuration in place of topologies

every potential structural form

Uses "potential structural form" as a generalized replacement of topology.

the exhaustive set of network layouts

Highlights exhaustiveness using the word exhaustive and configuration in place of topologies

FAQs

In what fields is the phrase "all possible topologies" commonly used?

The phrase "all possible topologies" is frequently used in network design, phylogenetics, and molecular biology to describe the complete set of structural arrangements or connections being considered. These fields often require exploring numerous configurations to find the most optimal or likely solution.

What does it mean to enumerate "all possible topologies"?

To enumerate "all possible topologies" means to systematically list or generate every conceivable structural arrangement within a given set of elements. This is often done to analyze, test, or optimize systems where the arrangement significantly impacts performance or outcomes. However, it quickly becomes computationally intensive as the number of elements increases.

How does considering "all possible topologies" aid in network design?

Considering "all possible topologies" in network design allows engineers to evaluate the full spectrum of potential configurations, identifying the most cost-effective, efficient, or resilient design. While exhaustive analysis might not always be feasible, exploring a broad range of topologies can uncover solutions that might otherwise be overlooked.

What are some alternatives to the phrase "all possible topologies"?

Alternatives to the phrase "all possible topologies" include "every conceivable configuration", "the complete range of structural arrangements", or "each potential network layout", depending on the specific context.