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Related Concept Videos

Summation Notation01:25

Summation Notation

250
Sigma notation, also known as summation notation, provides a concise method for representing the sum of a sequence of terms that follow a regular pattern. It utilizes the uppercase Greek letter sigma (∑), A typical expression is:In this form, k the index of summation is 1, the starting value, and n the ending value. The term ak​ represents the general term of the sequence.For example, the increasing sequence 5, 7, 9, ..., 23 over 10 terms can be expressed as:This simplifies the...
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meta-Directing Deactivators: –NO2, –CN, –CHO, –⁠CO2R, –COR, –CO2H01:13

meta-Directing Deactivators: –NO2, –CN, –CHO, –⁠CO2R, –COR, –CO2H

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All meta-directing substituents are deactivating groups. These substituents withdraw electrons from the aromatic ring, making the ring less reactive toward electrophilic substitution. For example, the nitration of nitrobenzene is 100,000 times slower than that of benzene because of the deactivating effect of the nitro group. The first step in an electrophilic aromatic substitution is the addition of an electrophile to form a resonance-stabilized carbocation. The energy diagrams for...
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2° Amines to N-Nitrosamines: Reaction with NaNO201:20

2° Amines to N-Nitrosamines: Reaction with NaNO2

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Secondary amines react with nitrous acid to form N-nitrosamines, as depicted in Figure 1. Nitrous acid, a weak and unstable acid, is formed in situ from an aqueous solution of sodium nitrite and strong acids, such as hydrochloric acid or sulfuric acid, in cold conditions. In the presence of an acid, the nitrous acid gets protonated. The subsequent loss of water results in the formation of the electrophile known as nitrosonium ion.
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SN2 Reaction: Kinetics02:14

SN2 Reaction: Kinetics

10.3K
Kinetic Studies and Significance
In a chemical reaction, a relationship exists between the concentration of reactants and the rate at which the reaction proceeds. The study to measure this relationship is known as the kinetics of a chemical reaction. Kinetic studies are used to deduce the rate law of a chemical reaction, which provides information about the species involved during the transition state of the rate-determining step. Thus, kinetic studies help to derive the mechanism of a...
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SN2 Reaction: Mechanism02:27

SN2 Reaction: Mechanism

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The kinetic studies of SN2 reactions suggest an essential feature of its mechanism: it is a single-step process without intermediates. Here, both the nucleophile and the substrate participate in the rate-determining step.
The presence of the more electronegative halogen in the substrate creates a polarized carbon-halide bond. The halide pulls the electron cloud generating an electrophilic center at the carbon atom. Thus, the carbon atom carries a partial positive charge while the halide has a...
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SN2 Reaction: Transition State02:26

SN2 Reaction: Transition State

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An SN2 reaction of an alkyl halide is a single-step process in which bond formation between the nucleophile and the substrate and bond breaking between the substrate and the halide occurs simultaneously through a transition state without forming an intermediate.
When the nucleophile approaches the electrophilic carbon with its lone pairs, the halide acts as a leaving group and moves away with the electron-pair bonded to the carbon. Dotted partial bonds represent the bonds being formed or broken...
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How to Create and Use Binocular Rivalry
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Binocular summation revisited: Beyond √2.

Daniel H Baker1, Freya A Lygo1, Tim S Meese2

  • 1Department of Psychology.

Psychological Bulletin
|August 14, 2018
PubMed
Summary
This summary is machine-generated.

Two eyes improve faint image detection more than previously thought. This meta-analysis reveals binocular summation (enhanced vision with two eyes) is significantly greater than the canonical √2 value, varying with stimulus conditions.

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Area of Science:

  • Vision Science
  • Psychophysics
  • Neuroscience

Background:

  • Human vision benefits from using two eyes (binocular vision) over one (monocular vision).
  • The extent of this binocular advantage, known as binocular summation, has been debated, with a canonical value of √2 often cited.

Purpose of the Study:

  • To definitively quantify psychophysical binocular summation using a large meta-analysis.
  • To investigate methodological factors influencing binocular summation estimates.
  • To develop a model for understanding binocular summation and its variability.

Main Methods:

  • Meta-analysis of 65 studies spanning over 5 decades.
  • Analysis of binocular summation (ratio of binocular to monocular contrast sensitivity).
  • Investigation of stimulus properties (spatial/temporal frequency, speed) and individual differences in monocular sensitivity.

Main Results:

  • Binocular summation is significantly greater than the canonical √2 value.
  • Summation levels are systematically influenced by spatial and temporal stimulus frequencies, with slower speeds yielding stronger summation.
  • Individual differences in monocular sensitivity and visual disorders like amblyopia affect summation estimates.

Conclusions:

  • There is no single value for binocular summation; it depends on methodological factors.
  • A nonlinearity early in the visual pathway influences binocular summation.
  • Proposed best-practice guidelines for accurate neural summation estimation in future research, especially with patient groups.