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Granularity

Granularity is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Granularity rather than just read about it. In short: Granularity (also called graininess) is the degree to which a material or system is composed of distinguishable pieces, "granules" or "grains" (metaphorically). It can either refer to the extent to which a larger entity is subdivided, or the extent to which groups of smaller indistinguishable entities have joined together to become larger distinguishable entities.

Key takeaways

  • Granularity belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Granularity to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Granularity from memory before moving on to harder problems.

Reference excerpt

Granularity (also called graininess) is the degree to which a material or system is composed of distinguishable pieces, "granules" or "grains" (metaphorically). It can either refer to the extent to which a larger entity is subdivided, or the extent to which groups of smaller indistinguishable entities have joined together to become larger distinguishable entities.

Precision and ambiguity Coarse-grained materials or systems have fewer, larger discrete components than fine-grained materials or systems.

A coarse-grained description of a system regards large subcomponents. A fine-grained description regards smaller components of which the larger ones are composed. The concepts granularity, coarseness, and fineness are relative; and are used when comparing systems or descriptions of systems. An example of increasingly fine granularity: a list of nations in the United Nations, a list of all states/provinces in those nations, a list of all the cities in those states, etc.

Physics A fine-grained description of a system is a detailed, exhaustive, low-level model of it. A coarse-grained description is a model where some of this fine detail has been smoothed over or averaged out. The replacement of a fine-grained description with a lower-resolution coarse-grained model is called coarse-graining. (See for example the second law of thermodynamics)

Molecular dynamics In molecular dynamics, coarse graining consists of replacing an atomistic description of a biological molecule with a lower-resolution coarse-grained model that averages or smooths away fine details. Coarse-grained models have been developed for investigating the longer time- and length-scale dynamics that are critical to many biological processes, such as lipid membranes and proteins. These concepts not only apply to biological molecules but also inorganic molecules. Coarse graining may remove certain degrees of freedom, such as the vibrational modes between two atoms, or represent the two atoms as a single particle. The ends to which systems may be coarse-grained is simply bound by the accuracy in the dynamics and structural properties one wishes to replicate. This modern area of research is in its infancy, and although it is commonly used in biological modeling, the analytic theory behind it is poorly understood.

Computing

Parallel computing

In parallel computing, granularity means the amount of computation in relation to communication, i.e., the ratio of computation to the amount of communication. Fine-grained parallelism means individual tasks are relatively small in terms of code size and execution time. The data is transferred among processors frequently in amounts of one or a few memory words. Coarse-grained is the opposite: data is communicated infrequently, after larger amounts of computation. The finer the granularity, the greater the potential for parallelism and hence speed-up, but the greater the overheads of synchronization and communication. Granularity disintegrators exist as well and are important to understand in order to determine the accurate level of granularity. In order to attain the best parallel performance, the best balance between load and communication overhead needs to be found. If the granularity is too fine, the performance can suffer from the increased communication overhead. On the other side, if the granularity is too coarse, the performance can suffer from load imbalance.

Reconfigurable computing and supercomputing

In reconfigurable computing and supercomputing, these terms refer to the data path width. The use of about one-bit wide processing elements like the configurable logic blocks (CLBs) in an FPGA is called fine-grained computing or fine-grained reconfigurability, whereas using wide data paths, such as, for instance, 32 bits wide resources, like microprocessor CPUs or data-stream-driven data path units (DPU]) like in a reconfigurable datapath array (rDPA) is called coarse-grained computing or coarse-grained reconfigurability.

Data and information

The granularity of data refers to the size in which data fields are sub-divided. For example, a postal address can be recorded, with coarse granularity, as a single field:

address = 200 2nd Ave S #358, St. Petersburg, FL 33701-4313 USA or, with fine granularity, as multiple fields:

street address = 200 2nd Ave S #358 city = St. Petersburg state = FL postal code = 33701-4313 country = USA or even finer granularity:

street = 2nd Ave S address number = 200 suite/apartment = #358 city = St. Petersburg state = FL postal-code = 33701 postal-code-add-on = 4313 country = USA Finer granularity has overheads for data input and storage. This manifests itself in a higher number of objects and methods in the object-oriented programming paradigm or more subroutine calls for procedural programming and parallel computing environments. It does however offer benefits in flexibility of data processing in treating each data field in isolation if required. A performance problem caused by excessive granularity may not reveal itself until scalability becomes an issue. Within database design and data warehouse design, data grain can also refer to the smallest combination of columns in a table which makes the rows (also called records) unique.

See also

Notes

References de Pablo, J. J. (2011). "Coarse-grained simulations of macromolecules: From DNA to nanocomposites". Annual Review of Physical Chemistry. 62: 555–74. Bibcode:2011ARPC...62..555D. doi:10.1146/annurev-physchem-032210-103458. PMID 21219152. Spacey, S.; Luk, W.; Kelly, P. H. J.; Kuhn, D. (2012). "Improving Communication Latency with the Write-Only Architecture". Journal of Parallel and Distributed Computing. 72 (12): 1617–1627. doi:10.1016/j.jpdc.2012.08.007.

Worked examples

Example 1 — a first encounter with Granularity

Start with the simplest possible case. Write down what Granularity claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Granularity before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Granularity ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Granularity

In research
Granularity appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Granularity in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Granularity is common in secondary-school and first-year university syllabi. It links to neighbouring topics Business terms, Statistical mechanics, so understanding it makes those chapters shorter.
In everyday life
Look for Granularity outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Granularity in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Granularity means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Granularity out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Granularity in simple terms?

Granularity (also called graininess) is the degree to which a material or system is composed of distinguishable pieces, "granules" or "grains" (metaphorically). It can either refer to the extent to which a larger entity is subdivided, or the extent to which groups of smaller indistinguishable entit…

Why does Granularity matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Granularity?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Granularity.

Tags

  • Business terms
  • Statistical mechanics

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