on 16-Jan-2017 (Mon)

Th e β sheet is formed through interac- tions between noncontiguous amino acids in the polypeptide chain

β strands are usually from fi ve to 10 residues long

To satisfy their hydrogen-bonding capacity, they (Beta strands) form sheets in which β strands are aligned adjacent to each other

Th e β sheets that are formed from several such β strands are “pleated”, with C α atoms alternately a little above and below the plane of the β sheet. Th e sidechains follow this pattern, pointing alternately above and below the β sheet.

The body begins with a base case, a conditional statement that defines the behavior of the function for the inputs that are simplest to process

Recursive calls always have a certain character: they simplify the original problem

Recursive functions express computation by simplifying problems incrementally.

The first idea is that Bayesian inference is reallocation of credibility across possibilities.

The second foundational idea is that the possibilities, over which we allocate credibility, are parameter values in meaningful mathematical models.

Holmes conceived of a set of possible causes for a crime. Some of the possibilities may have seemed very improbable, apriori. Holmes systematically gathered evidence that ruled out a number of the possible causes. If all possible causes but one were eliminated, then (Bayesian) reasoning forced him to conclude that the remaining possible cause was fully credible, even if it seemed improbable at the start

Because we assume that the candidate causes are mutually exclusive and exhaust all possible causes, the total credibility across causes sums to one.

judicial exoneration. Suppose there are several possible culprits for a crime, and that these suspects are mutually unaffiliated and exhaust all possibilities. If evidence accrues that one suspect is definitely culpable, then the other suspects are exonerated

data have only probabilistic relations to their underlying causes

All scientific data have some degree of “noise” in their values. The techniques of data analysis are designed to infer underlying trends from noisy data.

The beauty of Bayesian analysis is that the mathematics reveal exactly how much to re-allocate credibility in realistic probabilistic situations

The distribution of credibility initially reflects prior knowledge about the possibilities, which can be quite vague. Then new data are observed, and the credibility is re-allocated. Possibilities that are consistent with the data garner more credibility, while possibilities that are not consistent with the data lose credibility.

After the analysis, we can examine whether the data are well described by the most credible possibilities in the considered set. If the data seem not to be well described, then we can consider expanding the set of possibilities. This process is called a posterior predictive check

How big is the difference between the typical blood pressure in one group versus the typical blood pressure in the other group, and how certain can we be of the difference? The magnitude of difference describes the data, and our goal is to assess which possible descriptions aremoreorlesscredible.

In general, data analysis begins with a family of candidate descriptions for the data. The descriptions are mathematical formulas that characterize the trends and spreads in the data. The formulas themselves have numbers, called parameter values, that determine the exact shape of mathematical forms.

You can think of parameters as control knobs on mathematical devices that simulate data generation.

mathematical devices that simulate data generation.

The normal distribution has two parameters, called the mean and standard deviation. The mean is a control knob in the mathematical formula for the normal distribution that controls the location of the distribution’s central tendency. The mean is sometimes called a location parameter. The standard deviation is another control knob in the mathematical formula for the normal distribution that controls the width or dispersion of the distribution. The standard deviation is sometimes called a scale parameter.

The mathematical formula for the normal distribution converts the parameter values to a particular bell-like shape for the probabilities of data values

The role of Bayesian inference is to compute the exact relative credibilities of candidate parameter values, while also taking into account their prior probabilities.

the mathematical form should be comprehensible with meaningful parameters. Just as it would be fruitless to describe the data in a language that we do not know, it would be fruitless to describe the data with a mathematical form that we do not understand, with parameters that we cannot interpret

Bayesian analysis re- allocates credibility among parameter values within a meaningful space of possibilities defined by the chosen model.

The second desideratum for a mathematical description is that it should be descrip- tively adequate, which means, loosely, that the mathematical form should “look like” the data.

Bayesian analysis is very useful for assessing the relative credibility of different candidate descriptions of data

mathematical descriptions of data are not necessarily causal explanations of data

In general, Bayesian analysis of data follows these steps: 1. Identify the data relevant to the research questions. What are the measurement scales of the data? Which data variables are to be predicted, and which data variables are supposed to act as predictors? 2. Define a descriptive model for the relevant data. The mathematical form and its parameters should be meaningful and appropriate to the theoretical purposes of the analysis. 3. Specify a prior distribution on the parameters. The prior must pass muster with the audience of the analysis, such as skeptical scientists. 4. Use Bayesian inference to re-allocate credibility across parameter values. Interpret the posterior distribution with respect to theoretically meaningful issues (assuming that the model is a reasonable description of the data; see next step). 5. Check that the posterior predictions mimic the data with reasonable accuracy (i.e., conduct a “posterior predictive check”). If not, then consider a different descriptive model

In the English language a construct is usually symbolized by a single word which does not make explicit the composite character of the construct. In an agglutinated language like German, a construct is more commonly symbolized by a compound word which does make explicit its composite character, for example, Abwehrflammenwerfer (defensive flame-thrower). Also, the English word t a n k in German is Raupenschlepperpanzerkampfwagen (a caterpillarlike, self-moving, armored war wagon). This has been shortened to panzer, a term familiar through films and books.

In the English language a construct is usually symbolized by a single word which does not make explicit the composite character of the construct.

In an agglutinated language like German, a construct is more commonly symbolized by a compound word which does make explicit its composite character, for example, Abwehrflammenwerfer (defensive flame-thrower).

Language has logical and psychological meanings which may be illustrated through a closer look at the words house and home. If house is represented as a b, then home may be represented as a b x. Objectively, the definition (the logical dimension) of house and home are similar and may be represented by the lines ab; but subjectively, home is a much richer word, for to its logical content is added an emotional content (the psychological dimension) associated with the word and represented by the line bx. The fact that house has practically no psychological dimension while home has much accounts for the different effects produced by the following lines, which are equivalent in the logical dimensions.

ILLUSTRATION: Psychological dimension of language
House, house, loved, loved house!
There’s no place like my house! There’s no place like my house!
“Home, Home, sweet, sweet Home!
There’s no place like Home! There’s no place like Home!”
—John Howard Payne, “Clari, the Maid of Milan”

Language has logical and psychological meanings which may be illustrated through a closer look at the words house and home.

If house is represented as a b, then home may be represented as a b x.

Objectively, the definition (the logical dimension) of house and home are similar and may be represented by the lines ab; but subjectively, home is a much richer word, for to its logical content is added an emotional content (the psychological dimension) associated with the word and represented by the line bx.

The fact that house has practically no psychological dimension while home has much accounts for the different effects produced by the following lines, which are equivalent in the logical dimensions.

ILLUSTRATION: Psychological dimension of language
House, house, loved, loved house!
There’s no place like my house! There’s no place like my house!
“Home, Home, sweet, sweet Home!
There’s no place like Home! There’s no place like Home!”
—John Howard Payne, “Clari, the Maid of Milan”

The logical or intellectual dimension of a word is its thought content, which may be expressed in its definition, given in the dictionary. In rhetoric this is called the denotation of the word.

C’era una volta una scrofa con tre porcellini. Li amava moltissimo, ma non c’era abbastanza cibo per tutti, quindi lì mandò per il mondo a cercar fortuna.


Once upon a time there was a mama pig who had three little pigs. She loved them very much, but there was not enough food for all of them, so she sent them out into the world to seek their fortune.

The logical dimension of language may be compared to the incandescent electrified wire in a transparent bulb; the wire is obvious and its limits are clearly defined. The psychological dimension may be compared to a frosted bulb, in which all the light, it is true, comes from the incandescent wire within, but the light is softened and diffused by the bulb, which gives it a more beautiful and psychologically warmer glow.

Language with a purely logical dimension is desirable in legal document s and in scientific and philosophical treatises, where clarit y, precision, and singleness of meaning are requisite. Consequently, synonyms, which usually vary in shades of meaning, ought to be avoided, and the same word should be employed throughout to convey the same meaning; or if it is used with a different meaning, that fact should be made clear. Abstract words are usually clearer and more precise than concrete words, for abstract knowledge is clearer, although less vivid, than sense knowledge. Yet to communicate abstract knowledge, one should employ concrete illustrations from which the reader or listener can make the abstraction for himself since by so doing he grasps the abstract ideas much better than if the writer or speaker gave them to him ready-made.

Language with a purely logical dimension is desirable in legal document s and in scientific and philosophical treatises, where clarit y, precision, and singleness of meaning are requisite.

In legal texts and scientific treatises synonyms, which usually vary in shades of meaning, ought to be avoided, and the same word should be employed throughout to convey the same meaning; or if it is used with a different meaning, that fact should be made clear.

Abstract words are usually clearer and more precise than concrete words, for abstract knowledge is clearer, although less vivid, than sense knowledge.

To communicate abstract knowledge, one should employ concrete illustrations from which the reader or listener can make the abstraction for himself since by so doing he grasps the abstract ideas much better than if the writer or speaker gave them to him ready-made.

The psychological dimension of language is in its emotional content—the related images, nuances, and emotion spontaneously associated with words. In rhetoric this is called the connotation of the word. Propagandists often abuse the connotative value of words. Language with a rich psychological dimension is desirable in poetry and other literature, where humor, pathos, grandeur, and sublimity are communicated. In literary composition, one should employ words that are concrete rather than abstract, that are rich in imagery and idiomatic. Synonyms should be used in order to avoid monotony of sound and to convey subtle shades of meaning that vary in both the logical and the psychological dimension. A sensitive awareness of the subtleties of language, particularly in its psychological dimension, enables one to recognize good style in the speech and writing of others and to cultivate good style in one’s own composition, both oral and written. The substance of a given composition may be translated almost perfectly from one language to another in the logical dimension. Translation is seldom satisfactory, however, in the psychological dimension. That is why poet ry in translation is usually less pleasing than in the original.

The psychological dimension of language is in its emotional content—the related images, nuances, and emotion spontaneously associated with words.

In rhetoric the psychological dimension of language is called the connotation of the word.

Language with a rich psychological dimension is desirable in poetry and other literature, where humor, pathos, grandeur, and sublimity are communicated.

In literary composition, one should employ words that are concrete rather than abstract, that are rich in imagery and idiomatic.

In literary composition synonyms should be used in order to avoid monotony of sound and to convey subtle shades of meaning that vary in both the logical and the psychological dimension.

A sensitive awareness of the subtleties of language, particularly in its psychological dimension, enables one to recognize good style in the speech and writing of others and to cultivate good style in one’s own composition, both oral and written.

The substance of a given composition may be translated almost perfectly from one language to another in the logical dimension.

Translation is seldom satisfactory, however, in the psychological dimension. That is why poetry in translation is usually less pleasing than in the original.

Various characteristics of words affect the psychological dimension of language. The mere sound of a word may produce a pleasing effect which another word of the same meaning lacks. In “Silver” by Walter de la Mare, the poet’s substitution of words like shoon for shoes and casements for windows are examples of the poet’s use of sound to create a psychological effect.

A pedantic or pompous style is psychologically displeasing. Compare these sentence pairs, identical in logical meaning.

Behold! The inhabitants have all ret ired to their domiciles.
Look! The people have all gone home.


The vaulted dome of heaven is cerulean.
The sky is blue.

The emotional effect of a word, often a by-product of its historical development, belongs to the idiom of language and would often be lost in translation. The following examples show that sentences alike in logical dimension can be quite different in psychological dimension.

ILLUSTRATION: Idiom

A young man tells a young woman, “Time stands still when I look into your eyes.”

Another tells her, “You have a face that would stop a clock.”

A young man tells a woman, “You are a vision.” Another, “You are a sight.

Every value in Python has a class that determines what type of value it is.

Values that share a class also share behavior.

The built-in type function allows us to inspect the class of any value

The values we have used so far are instances of a small number of native data types that are built into the Python language. Native data types have the following properties:

1. There are expressions that evaluate to values of native types, called literals.
2. There are built-in functions and operators to manipulate values of native types.

The int class is the native data type used to represent integers. Integer literals (sequences of adjacent numerals) evaluate to int values, and mathematical operators manipulate these values.

Python includes three native numeric types: integers ( int ), real numbers ( float ), and complex numbers ( complex ).

int objects represent integers exactly, without any approximation or limits on their size. On the other hand, float objects can represent a wide range of fractional numbers, but not all numbers can be represented exactly, and there are minimum and maximum values. Therefore, float values should be treated as approximations to real values.

Although int values are combined above, dividing one int by another yields a float value: a truncated finite approximation to the actual ratio of the two integers divided.

 >>> type ( 1 / 3 ) <class 'float'> >>> 1 / 3 0.3333333333333333 

Problems with this approximation appear when we conduct equality tests.

 >>> 1 / 3 == 0.333333333333333312345 # Beware of float approximation True 

The general technique of isolating the parts of a program that deal with how data are represented from the parts that deal with how data are manipulated is a powerful design methodology called data abstraction. Data abstraction makes programs much easier to design, maintain, and modify.

data abstraction isolates how a compound data value is used from the details of how it is constructed.

The basic idea of data abstraction is to structure programs so that they operate on abstract data. That is, our programs should use data in such a way as to make as few assumptions about the data as possible. At the same time, a concrete data representation is defined as an independent part of the program.

We are using here a powerful strategy for designing programs: wishful thinking. We haven't yet said how a rational number is represented, or how the functions numer , denom , and rational should be implemented. Even so, if we did define these three functions, we could then add, multiply, print, and test equality of rational numbers:

a list , which can be constructed by placing expressions within square brackets separated by commas. Such an expression is called a list literal.

The elements of a list can be accessed in two ways. The first way is via our familiar method of multiple assignment, which unpacks a list into its elements and binds each element to a different name.

One intuition that supports this indexing convention is that the index represents how far an element is offset from the beginning of the list.

The equivalent function for the element selection operator is called getitem , and it also uses 0-indexed positions to select elements from a list.

The floor division operator, // , expresses integer division, which rounds down the fractional part of the result of division.

In general, the underlying idea of data abstraction is to identify a basic set of operations in terms of which all manipulations of values of some kind will be expressed, and then to use only those operations in manipulating the data. By restricting the use of operations in this way, it is much easier to change the representation of abstract data without changing the behavior of a program.

An abstraction barrier violation occurs whenever a part of the program that can use a higher level function instead uses a function in a lower level.

Abstraction barriers make programs easier to maintain and to modify. The fewer functions that depend on a particular representation, the fewer changes are required when one wants to change that representation.