Figure 2

Field types

Figure 1. Presentation of information in the database

Basic concepts

Database fields

The language of modern DBMS

The language of the modern DBMS includes subsets of commands that previously belonged to the following specialized languages:

Data description language - a high-level non-procedural language of a declarative type, designed to describe the logical structure of data.

Data Manipulation Language is a DBMS command language that provides basic operations for working with data - input, modification and selection of data by request.

Structured query language (Structured Query Language, SQL) - provides data manipulation and determination of the relational database schema, is a standard means of accessing the database server.

Ensuring the integrity of the database is a necessary condition for the successful functioning of the database. Database integrity is a property of a database, which means that the database contains complete and consistent information necessary and sufficient for the correct functioning of applications. Security is achieved in the DBMS by encryption of application programs, data, password protection, support for access levels to a separate table.

Field- the smallest named element of information stored in the database and considered as a whole.

The field can be represented by a number, letters, or a combination of them (text). For example, in a telephone directory, the fields are surname and initials, address, telephone number, i.e. three fields, all text fields (the phone number is also treated as some text).

Recording- a set of fields corresponding to one object. Thus, a subscriber of the telephone network corresponds to a record consisting of three fields.

File- a set of records related by some attribute (i.e. relation, table). Thus, in the simplest case, the database is a file.

All data in the database is divided by type. All field information belonging to the same column (domain) is of the same type. This approach allows the computer to organize the control of the input information.

Main types of database fields:

Symbolic (text). This field can store up to 256 characters by default.

Numerical. Contains numerical data in various formats used for calculations.

Date Time. Contains a date and time value.

Monetary. Includes monetary values ​​and numeric data up to fifteen integer and four fractional digits.

Note field. It can contain up to 2^16 characters (2^16 = 65536).

Counter. A special numeric field in which the DBMS assigns a unique number to each record.

Logical. Can store one of two values: true or false.

OLE (Object Linking and Embedding) object field. This field can contain any spreadsheet object, microsoft word document, picture, sound recording, or other binary data embedded in or associated with the DBMS.

Substitution master. Creates a field that offers a choice of values ​​from a list or containing a set of constant values.

Database fields do not just define the structure of the database - they also define the group properties of the data written to the cells belonging to each of the fields.

The main properties of database table fields are listed below using the Microsoft Access DBMS as an example:

Field name- determines how the data of this field should be accessed during automatic operations with the database (by default, field names are used as table column headings).

Field type- defines the type of data that can be contained in this field.

Field size- defines the maximum length (in characters) of data that can be placed in this field.

Field Format- determines how data is formatted in the cells belonging to the field.

input mask- defines the form in which data is entered in the field (data entry automation tool).

Signature- defines the table column heading for the given field (if the label is not specified, then the Field name property is used as the column heading).

Default value- the value that is entered into the field cells automatically (data entry automation tool).

Value condition- a constraint used to validate data entry (an input automation tool that is typically used for data that has a numeric, currency, or date type).

Error message- a text message that is displayed automatically when you try to enter erroneous data in the field (error checking is performed automatically if the Condition on value property is set).

Obligatory field- a property that determines the mandatory filling of this field when filling the database.

Blank lines- a property that allows the input of empty string data (it differs from the Required field property in that it does not apply to all data types, but only to some, for example, text).

Indexed field- if the field has this property, all operations related to searching or sorting records by the value stored in this field are significantly accelerated. In addition, for indexed fields, you can make it so that the values ​​in the records will be checked against this field for duplicates, which automatically eliminates data duplication.

Since different fields may contain data of different types, the properties of the fields may differ depending on the type of data. So, for example, the list of field properties above applies primarily to fields of the text type. Fields of other types may or may not have these properties, but may add their own to them. For example, for data representing real numbers, the number of decimal places is an important property. On the other hand, for fields used to store pictures, sound recordings, video clips, and other OLE objects, most of the above properties are meaningless.

Field - a set of parts, united by the commonality of those signs by which they (parts) enter into integration.

The three fields of the MEZ correspond to the three possible directions of the human thought process, the categorization of which occurs in the process of understanding ";by a qualitative attribute";. (Bruner J., 1977:30).

Field of thinking with subject representations (MPP) contains MEZ about visual signs of people, objects, various figures, nature.

The field of thought-action with representations in abstract paradigms (MAP) contains MEZ acquired: as a result of sensory experiences or only MEZ about these experiences; from any physical state or MEZ about these states; from being in a situation or MEZ about possible situations; in the process of communicating with people or MEZ about them, about characters.

The field of thought-action with ideas about communication (MC) includes MEZ acquired in the process of listening, speaking, reading, analyzing literary texts.

The proposed concept allows us to indicate that thinking operates with information that is preliminarily organized and ordered in the form of specific MEZs.

It should be noted that in the proposed work, the division into three fields is carried out very conditionally, since it is impossible to divide the thought process of an individual into fields (especially autonomous ones). Such a division in the work is undertaken conditionally and only in order to show that all the information available in the memory of the individual is ordered and organized in a certain way.

Consideration of the process of understanding as an integration of thought activity and thought action is based on the concept of understanding as thought action with representations. In the process of understanding, the activated MEZ group contributes to the perception of ideas about appearance, about an object, or about nature, which is called a scheme of action with a representation of a person, object, or nature.

The basic set of MEZs is enriched and activated in the process of understanding due to the formation of new links between units. (Alekseev N. G., 1991).

If units of knowledge are considered as the result of any experience, activity, then it becomes necessary to distinguish between ordinary experience and scientific experience. The significance of everyday experience is obvious, since the primary form of human cognitive activity, which occurs soon after his birth, is everyday, everyday experience. This experience, which is generally accessible, but far from equally inherent in all human individuals, is an unsystematized variety of impressions, experiences, and observations. The richness of life experience is not fully realized by its owner, because. this experience is formed, multiplied mainly without conscious cognitive efforts, simply because a person lives, uses objects, communicates with other people, sees, hears, experiences, involuntarily remembers perceived, experienced, without even knowing what exactly was deposited in his memory, not thinking about him until circumstances call up imprinted images in his mind. Joys and sorrows, love and hate, birth and death, health and disease, high and low deeds, historical events experienced differently by human individuals - all this, and especially knowledge about other human individuals, constantly enriches everyday experience. But no matter how great the significance of scientific knowledge, their existence, functioning, development is undoubtedly dependent on the mass of everyday experience, the accumulation of which takes place outside the scope of scientific research or the assimilation of ready-made scientific knowledge. "Of course, ordinary experience is not free

from delusions and illusions. And yet, everyday experience is not alien to reflection, self-criticism, especially when its delusions are exposed by practice ";. (Oizerman T.P., 1990: 4).

The second layer of MEZ (transformed from experience) is the result of scientific activity. "Unlike ordinary experience, science constantly invades the sphere of the unknown, the unknown; in the bosom of scientific research, a transition is invariably made from ignorance to knowledge, from one knowledge to another, deeper, more accurate, adequate"; (Oizerman T.P., 1990:5).

Both scientific experience and everyday experience are a set of transformed mnemo-units of knowledge and are stored in the basic set of knowledge units of an individual. The identification and study of these units of knowledge in the process of understanding can be considered as another representation of the understanding mechanism model. Such a model will not have a stable form with obvious stable links between MEZs.

An approach to the process of understanding as an integration of mental activity and

thought action is fundamentally determined by the model structure. On the one hand, the model sets the program task of mental activity, if ";the task is a differential element";. (Deleuze J., 1998:201). On the other hand, the model is determined by stable, multiple relationships between units that reveal subjective criteria for understanding. The structure of knowledge of an individual, presented in the form of a model, has an abstract character, since "specific knowledge systems, although they model reality quite adequately, are characterized by considerable diversity, which is explained by different life experiences, as well as the goals and objectives of the cognitive activity of various people";. (Novikov A.P., 1983:42). If the goal of cognitive activity is the same, then it is legitimate to expect identical results for the models in the studies, although the diversity of knowledge and their model representation is provable.

The results of practical research given in the book by A. N. Luka ";Thinking and Creativity"; confirm the emergence of not only identical connections in the form of a model between individual words in the process of understanding a person, which the author calls associations, but also a logically determined possible chain of grouped associations caused by a number of lexical units. So, A. N. Luk suggests taking two words "sky"; and ";tea";, the connection between which ";is established with the help of four natural associations:

sky - earth

earth - water

water - drink

drink - tea ";. (Luk A.N., 1976: 15).

The scientist comes to the conclusion that "associative links are the basis for the orderly storage of information in a person's thinking, which ensures a quick search for the necessary information, arbitrary access to the necessary material";. (Ibid., p. 16). Thus, in the thinking of an individual, elements of knowledge are encoded in the form of units that reveal stable ties each other in the process of understanding. The stability of connections allows us to speak about the possibility of such a model construction of the process of understanding a person, which is based on ";a general principle of unanimity, deeply hidden to all people, in assessing the forms in which objects are given to them";. (Kant P., 1995:225). This principle is the principle of categorization, characterized by the unity of the logical structure of thinking of all mankind.

The process of understanding as an integration of thought activity and thought action in the construction of meaning is complicated due to the fact that reflection is out of direction (reflection that occurs instinctively, as I. Kant believes (Kant P., 1995) ";affects the totality of past experience (as a unit)" (Ukhtomsky A. A., 1959:40), without contributing to

discretion of a number of representations, categorizing which the recipient forms mnemo-patterns. Comprehension of one's own way of categorization in the process of understanding requires indicating those activated MEZs, thanks to which the recipient comes to the result of understanding in the form of meaning construction.

Understanding Algorithm Model is presented as a process that begins with the activation and integration of the MEZ, which leads to the discretion of representations, with the assignment of an object to a certain category, and "the categories to which perceived objects belong are not isolated from each other"; (Bruner J., 1977:24), because they are due to the relationship between those MEZs that are included in the content of the category. Communication, in turn, is interdependence on a related qualitative attribute. In other words, in accordance with the proposed concept, the three fields of the mental activity scheme (MPP, MAP, MK)interconnected and plastically interdependent.

The process of understanding is always based on an activated group of such MEZs that enter into integration and contribute to the discretion of one or another representation.

In the process of understanding and interpreting the MEZ is the smallest cognitive unit, the identification of which makes it possible to substantiate the individuality of each interpretation.

2.4 Mnemo pattern as a cognitive structure

If in the thinking of an individual the elements of knowledge are encoded in the form of units that reveal stable ties between themselves in the process of understanding, then it becomes possible to identify the cognitive structures that are formed from these units.

Considering the process of understanding as an integration of thought activity and thought action, it is necessary to point out that the concept of "action with ideas"; corresponds to the Kantian concept of schematism of the process of understanding (Kant P., 1964). Hence, in the present work, thought-action is defined as action with representations. In the active process of understanding, the recipient operates with ideas about appearance, about nature, about objects.

In this paper, representation is the combinatorics of activated MEZs, which is formed in the process of understanding a literary text.

A mnemonic pattern is a mental image formed as a result of categorization of representations of something or about something.

MEZ are always mobile, interdependent and able to enter into integration with other mnemo-units of knowledge. This shows their dialectic. It can be argued that non-dialectical MEZ do not contribute to the discretion of representations, and consequently, the formation of mnemonic patterns, since The dialectical nature of MEZs is due to the possibility of forming links between existing MEZs and newly formed ones. The absence of the MEZ or the lack of the ability to enter into integration leads to misunderstanding. For example, an individual has a unit of knowledge ";round";, can explain what the word ";round";; has a unit of knowledge ";space";, but to form the representation ";round space"; will not be able to, since these two units are ";round"; and ";space"; do not integrate.

The process of MEZ activation, their integration into representation, categorization of representation or representations and formation of mnemonic patterns during the reception of a literary text can be designated as a process in which the extraction of "the socially adequate from the poorly realized physiological" takes place. (Bogin G.P., 1994:15).

If the necessary MEZs for the understanding process are not found, a situation arises that can lead to misunderstanding.

Analyzing and describing the process of understanding, one can identify the MEZ, due to which one or another mnemonic pattern is formed. Such a description is understanding mechanism model.

As an example, we can cite a segment from the novel by I. Turgenev "; Fathers and Sons" ;.

";... but at that moment a man of medium height, dressed in a dark English suit, a fashionable low tie and patent leather ankle boots, Pavel Petrovich Kirsanov, entered the living room. He looked about forty-five years old; his short-cut gray hair shone with a dark sheen, like new silver; his face, bilious, but without wrinkles, unusually regular and clean, as if drawn with a thin and light chisel, showed traces of remarkable beauty; light, black, oblong eyes were especially good. youthful harmony and that aspiration upward, away from the earth, which for the most part disappears after the twenties ";.

In general, during the reception of the given segment of the text, such MEZs are activated that contribute to the discretion of the idea of ​​a man of the described appearance, which is probably predictable due to the fact that the recipient could see a man of the described appearance in the films or have contact with a person corresponding to the description in the text. Categorizing the idea of ​​a man's appearance, we can nominate the following mnemonic pattern ";a fashionably and elegantly dressed man who pays enough attention to his appearance";.

If the recipient has MEZs in the base set acquired as a result of communication with a man of the described appearance (for example, the recipient can activate units of knowledge about the manner of behavior, about the manner of communication), then in the process of understanding, the activation of these MEZs can provoke the perception of such a representation, which is reformed during categorization into the mnemo-pattern ";secular lion";. The basis for the formation of such a mnemonic pattern was the author's mention of the fashionable tie and ankle boots, the grace and harmony of the figure of Pavel Kirsanov, along with the mention of his age (forty-five). This mention helped activate those MEZs that led to the discretion of ideas about age and the ability to look quite elegant, since the recipient may know that the older the person, the more difficult it is for him to look elegant. Comparing and categorizing these two ideas (about age and the ability to look elegant), one can form mnemo-patterns ";striving for beauty";, ";habit to please others";, ";desire to look elegant";.

Activation of MEZ, acquired from reading and analyzing fiction, can contribute to the perception of the idea of ​​the author's intentional use of rustling-hissing notes in the lexical unit "half boots"; and in the refinement ";elegant and thoroughbred";. By categorizing this representation, the recipient forms the mnemo-pattern ";coquettishness";. At the reception of lexical units "; dressed in a dark English suite";, "; short-cropped gray hair"; MEZs acquired from reading and analyzing such fiction are activated, in which the author deliberately shows the character as an old-type person (judging by the severity of clothing and short-cropped hair). When categorizing the perceived representation, a mnemo-pattern "strictness under the circumstances" is formed.

Often in the process of understanding, the activation of mnemonic units of extralinguistic knowledge contributes to the formation of such mnemonic patterns that cannot be formed without the presence of these units of knowledge. As an example, a piece of text from M. Bulgakov's novel "The Master and Margarita" can be taken.

"Where do you live permanently?

I have no permanent home, the prisoner replied shyly, I travel from city to city.

This can be expressed in short, in one word - a vagabond, - said the procurator and asked: - Do you have any relatives?

There is no one. I am alone in the world."

M. Bulgakov’s novel speaks of the prisoner Yeshua, nicknamed Ga-Notsri from the city of Gamala, but when reading the second chapter, the reader understands that this is not about some other Pontius Pilate, the procurator of Judea, who tried and sent Yeshua to a painful death, namely, the one who sent Jesus to be crucified. Yeshua himself is none other than Jesus. By activating the mnemonic units of extralinguistic knowledge, the recipient can form such a mnemonic pattern, which is carried out in the novel by M.

Bulgakov's leitmotif is the opposition of the House to the Antidome. Yu. M.

Lotman, examining the work of M. Bulgakov, in this regard indicates: "; This tradition is exceptionally significant for Bulgakov, for whom the symbolism of the House - Anti-House becomes one of the organizing ones throughout the entire course of creativity";. (Lotman Yu. M., 1997:748). Forming such a mnemonic pattern, the reader understands that the house or apartment No. 50 in the novel is not a place to live, not a place of life, but a place where the sinister can be associated with the tragic, mystical (the apartment used by Woland for the ball) or the place for life and love (the apartment of the Master and Margarita, in which they were happy).

There are no direct lexical means in the novel that contribute to the discretion of such a representation, which, during categorization, would allow the formation of a mnemo-pattern ";symbolic sounding in the descriptions of the House and Antidome"; with compassion and desire to help the prisoner. All mnemonic patterns are formed from the condition of finding mnemonic units of extralinguistic knowledge. In case of non-detection of mnemonic units of extralinguistic knowledge, the formation of a mnemonic pattern ";symbolic sounding of the House-Antidom"; will not happen.

Since in this paper we operate with the concept of ";mnemo-pattern";, it is necessary to point out the differences that made it possible to use this particular concept, and not the concept of ";concept";. If we compare the mnemonic pattern and the concept, it becomes obvious that the mnemonic pattern covers a wider lexical composition, implying contextual and semantic connections, and is not tied to specific lexical units. The proposed hypotheses about the frame and the concept in some way correspond to the developed hypotheses of psychologists in the field of research of such an identification process, which is interpreted as the moment of comparison ";large perceptual units fixed in the memory, used as integral indicators of the corresponding stimulus classes";. (Shekhter M.S., 1982:304). The result of such a comparison are concepts or frames that each time in the process of cognition enter into interaction and mutual influence. This study does not aim to present the process of recognizing perceived realities from the standpoint of psychologists or neurophysiologists, but rather to show what cognitive units and cognitive structures the recipient operates in the process of understanding and interpreting a literary text, from which the process of constructing the meanings of a literary text is formed.

From the above examples, it becomes clear difference between concept and mnemonic pattern, which consists in the fact that the mnemonic pattern is formed as a result of the categorization of perceived representations, while the concept in the process of understanding will be rather what is taken as a representation in this work.

Another difference can be recognized that the conceptual theory does not show, as a result of which mental categorizations the concept is formed. The mnemonic pattern is formed based on the results of the categorization of such perceived representations, which were formed due to the activation and integration of certain MEZs, and these MEZs can be nominated and analyzed.

The next difference between the concept and the mnemonic pattern can be recognized as the fact that the conceptual theory does not reveal the mechanism for understanding and interpreting a literary text and implies the simultaneous calculation of lexemes that define the original core concept. Consideration of a mnemonic pattern as a cognitive structure makes it possible to reveal both the individuality of the knowledge structure and the individuality of the mechanism of understanding and interpretation, without giving priority to the token composition.

The idea of ​​a mnemonic pattern is interpreted as the formation of such a mnemonic pattern that contributes, on the one hand, to the activation of the process of understanding itself, and on the other hand, to the construction of meaning.

Chapter 3

FORMATION OF MEANINGS IN THE PROCESS OF UNDERSTANDING A ARTISTIC TEXT

3.1 Meaning-building as a process of categorization during reception

artistic text

Features of the perception of the world by a person with all his senses are consistent with the need for his adaptation to different forms of matter and different forms of movement. In order to correctly reflect the world, it is necessary to distinguish between different objects, different forms of their interaction, different relationships between objects and phenomena, etc., and create for the perceived adequate structures of their representation, their representation in the human brain. It is not so much real things, objects, faces, etc. that are subject to naming as their mental representations. But the links themselves established in the chain between a certain impact of a certain objectively existing fragment of the world on a person and the processing of information about this fragment through the formation of its mental representation, and then the nomination of this latter, begin to form in the structures of human activity with the specified fragment of the world, and therefore are determined the joint action of several different factors: among them, an important role is played by the pragmatic goals of the activity being carried out, and therefore not only its ontological prerequisites. "; In the nomination of fragments of the world around us, a person includes, albeit in an indirect form, ideas about such fundamental categories of being as time, space, personality, quality, quantity, etc."; (Kubryakova E.S., 1992:11).

Both philosophers and scientists working in the field of cognitive sciences have been and are engaged in the study of categories, since "a category is one of the cognitive forms of human thinking that allows one to generalize one's experience";. (Babushkin A.P., 1999:68).

The categorical apparatus of an individual is a complex network that has its beginning in the name and selection of an object from a class of objects. Thus, the functions of the category reflect the functions of language, since one of the most important functions of human language is the function of categorization of external reality, which ensures the process of cognition. Naming this or that thing, the thinking subject carries out the operation of superimposing its features or properties on the features and properties of fragments of reality already known and fixed in the language. ";Comparison and association of objects, processes and their

signs occurs on the basis of establishing relationships of similarity or contiguity ";. (Mikhalev A. B., 1995: 13).

Categorization in the process of understanding can be considered as such a thought process in which the assessment and assignment to a certain class of the perceived representation and the formed mnemo-pattern takes place. In such a process of evaluation and attribution, only some features or properties of the material being comprehended are superimposed on individual features or properties of already acquired MEZ.

Improving the means of his abstract, mental activity in the process of understanding the increasingly complex laws of the objective world, a person changes and improves the categorical apparatus of his thought process. As for the order, the sequence of presentation of the categories, it usually depends on the target setting, on what it is done for. "; All categories have equal rights to existence. It would be a rash step to achieve unification in this matter, since categories should be understood as a set of concepts that express the most general laws of the development of being and their reflection in human thinking" ;. (Tulenov Zh. T., 1986:26).

A category, on the one hand, is a reflection in human thinking of the most general properties of being, on the other hand, a category is a certain form of thought that focuses on revealing oneself in the subject under study. This orientation is determined by the unity of the structure of logical thinking of all individuals.

Similar to the fact that categories are a reflection in our thinking of the most general, basic properties of being, Aristotle was the first to give a classification of categories, which we took as a basis in this work, modifying it in accordance with the specifics of the material being studied. Aristotle singled out "essence, quantity, quality, relation, place, time, position, possession, action, suffering";. (Aristotle, 1976:178).

True, Aristotle did not formulate a clear definition of his understanding of categories, which serves as the basis for the existence of different points of view regarding what, in fact, he understood by categories. Many tend to think that Aristotle's categories are the main types of being and, accordingly, the main types of concepts about being, its properties and relationships.

Like all mental operations, categories have their own functions. The main functions of the category are division and synthesis. Dividing and synthesizing are such functions of categories, "; which belong to their very entity, so that the category as such without them does not exist at all; if these functions are separated from the category, then it becomes concept";(Bulatov M.A., 1983:21).

The earliest stages in the development of categorization include primary categorization of things. Under such categorization is understood the selection of objects, objects from the background surrounding them with the help of words. In this case, the presence of lexical designations is already assumed, therefore, in this study, the principle of categorization is put as the basis for the perception of representations and the formation of mnemo-patterns. and interpretation(to the grounds interpretations text as an analytical activity) // Sat. scientific papers, vol. 459 " Problem... modern style", M.: 2001, p. 3-13. For reference: Kashirina, N.A. Understanding and interpretation in...

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Random fields are random functions of many variables. In the future, four variables will be considered: coordinates, which determine the position of a point in space, and time. The random field will be denoted as . Random fields can be scalar (one-dimensional) and vector (-dimensional).

In the general case, a scalar field is given by the set of its -dimensional distributions

and the vector field - a set of its own - dimensional distributions

If the statistical characteristics of the field do not change when the time reference changes, i.e., they depend only on the difference, then such a field is called stationary. If the transfer of the origin does not affect the statistical characteristics of the field, i.e., they depend only on the difference, then such a field is called spatially homogeneous. A homogeneous field is isotropic if its statistical characteristics do not change when the direction of the vector changes, i.e., they depend only on the length of this vector.

Examples of random fields are the electromagnetic field during the propagation of an electromagnetic wave in a statistically inhomogeneous medium, in particular, the electromagnetic field of a signal reflected from a fluctuating target (generally speaking, this is a vector random field); volumetric radiation patterns of antennas and patterns of secondary radiation of targets, the formation of which is influenced by random parameters; statistically uneven surfaces, in particular the earth's surface and the sea surface during waves, and a number of other examples.

In this section, some issues of modeling random fields on a computer are considered. As before, the modeling task is understood as the development of algorithms for the formation of discrete field realizations on a digital computer, i.e., sets of sample values ​​of the field

,

where - discrete spatial coordinate; - discrete time.

In this case, it is assumed that independent random numbers are the initial ones when modeling a random field. The set of such numbers will be considered as a random -correlated field, hereinafter called -field. A random -field is an elementary generalization of discrete, white noise to the case of several variables. Modeling of the -field on a digital computer is carried out very simply: the space-time coordinate is assigned a sample value of a number from a generator of normal random numbers with parameters (0, 1).

The problem of digital simulation of random fields is new in the general problem of developing a system of efficient algorithms for simulating various kinds of random functions, focused on solving statistical problems of radio engineering, radiophysics, acoustics, etc. by computer simulation.

In the most general form, if the or -dimensional distribution law is known, a random field can be modeled on a computer as a random or -dimensional vector using the algorithms given in the first chapter. However, it is clear that this path, even with a relatively small number of discrete points along each coordinate, is very complicated. For example, the simulation of a flat (independent of ) scalar random field at 10 discrete points along the coordinates and and for 10 times is reduced to the formation on a computer of realizations of a -dimensional random vector.

Simplification of the algorithm and reduction in the volume of calculations can be achieved if, similarly to what was done with respect to random processes, algorithms are developed for modeling special classes of random fields.

Consider possible algorithms for modeling stationary homogeneous scalar normal random fields. Random fields of this class, just like stationary normal random processes, play a very important role in applications. Such fields are completely specified by their spatiotemporal correlation functions

(Here and in what follows, it is assumed that the mean value of the field is zero.)

An equally complete characteristic of the considered class of random fields is the function of the spectral density of the field, which is a four-dimensional Fourier transform of the correlation function (a generalization of the Wiener-Khinchin theorem):

,

where is the scalar product of the vectors and . Wherein

.

The spectral density function of a random field and the energy spectrum of a stationary random process have a similar meaning, namely: if a random field is represented as a superposition of space-time harmonics with a continuous frequency spectrum, then their intensity (total amplitude dispersion) in the frequency band and spatial frequency band is equal to .

A random field with intensity can be obtained from a random field with spectral density , if the field is passed through a space-time filter with a transfer coefficient equal to unity in the band , and equal to zero outside this band.

Spatio-temporal filters (SPFs) are a generalization of conventional (temporal) filters. Linear PVFs, like ordinary filters, are described using the impulse response

and transfer function

.

The process of linear space-time field filtering can be written as a four-dimensional convolution:

(2.140)

where is the field at the output of the PVF with an impulse transient response. Wherein

where are the spectral density functions and the correlation functions of the fields at the input and output of the PVF, respectively.

The proof of relations (2.141), (2.142) completely coincides with the proofs of similar relations for stationary random processes.

The analogy of harmonic expansion and filtering of random fields with harmonic expansion and filtering of random processes allows us to propose similar algorithms for their modeling.

Let it be required to construct algorithms for computer simulation of a stationary, space-homogeneous scalar normal field with a given correlation function or spectral density function .

If the field is given in a finite space, bounded by the limits , and is considered on a finite time interval , then to form discrete realizations of this field on a computer, one can use an algorithm based on the canonical expansion of the field in the space-time Fourier series and which is a generalization of algorithm (1.31):

Here, and are random mutually independent normally distributed numbers with parameters each, and the variances are determined from the relations:

where is a vector representing the limit of integration over space; - discrete frequencies of harmonics, according to which the canonical expansion of the correlation function is performed in the space-time Fourier series.

If the field expansion area is many times larger than its spatiotemporal correlation interval, then the dispersions are easily expressed in terms of the field spectral function (see § 1.6, item 3)

The formation of discrete realizations when modeling random fields using this method is carried out by directly calculating their values ​​according to (formula (2.143), in which sample values ​​of normal random numbers with parameters are taken as and , while the infinite series (2.143) is approximately replaced by a truncated series. Variances are calculated previously by formulas (2.144) or (2.146).

Although the algorithm considered does not allow one to form realizations of a random field that are unlimited in space and time, the preparatory work for obtaining it is quite simple, especially when using formulas (2.145), and this algorithm allows one to form discrete field values ​​at arbitrary points in space and time selected area. When forming discrete realizations of a field with a constant step in one or several coordinates, it is expedient to use a recursive algorithm of the form (1.3) for the reduced calculation of trigonometric functions.

Unlimited discrete implementations of a homogeneous stationary random field can be formed using space-time sliding summation algorithms -fields, similar to sliding summation algorithms for modeling random processes. If is the impulse transient response of the PVF, which forms a field with a given spectral density function from the -field (the function can be obtained by four-dimensional Fourier transform of the function , see § 2.2, item 2), then, subjecting the process of spatiotemporal filtering of the -field to discretization, we get

where - a constant determined by the choice of the sampling step over all variables - discrete -field.

The summation in formula (2.146) is carried out over all values ​​for which the terms are not negligible or equal to zero.

The preparatory work for this modeling method is to find the appropriate weight function of the space-time shaping filter.

The preparatory work and the summation process in the algorithm (2.146) are simplified if the function can be represented as a product

In this case, as follows from (2.144), the correlation function of the field is a product of the form

If the factorization of the correlation function into factors of the form (2.148) is impossible in the strict sense, it can be done with a certain degree of approximation, in particular, by setting

When decomposing into a product (2.149) of spatial, correlation functions of isotropic random fields, for which , partial correlation functions and will obviously be the same. In this case, in view of the approximation of formula (2.149), the spatial correlation function will correspond, generally speaking, to some non-isotropic random field. So, for example, if is an exponential function of the form

then according to (2.149) . In this case, the given correlation function is approximated by the correlation function

. (2.151)

The random field with the correlation function (2.151) is not isotropic. Indeed, if a field with correlation function (2.150) has a constant correlation surface (the locus of space points where field values ​​have the same correlation with the field value at some arbitrary fixed point in space) is a sphere, then in case (2.151) the constant correlation surface is the surface of a cube inscribed in a given sphere. (The maximum distance between these surfaces can serve as a measure of the approximation error).

An example in which expansion (2.149) is exact is a correlation function of the form

Decomposition (2.149) allows us to reduce the rather complicated process of quadruple summation in algorithm (2.146) to the repeated application of a single sliding summation.

These are the basic principles of modeling normal homogeneous stationary random fields. Modeling of non-normal homogeneous stationary fields with a given one-dimensional distribution law can be done by an appropriate non-linear transformation of normal homogeneous stationary fields using the methods discussed in § 2.7.

Example 1 Let the impulse response of the spatial filter for the formation of a flat scalar time-constant field have the form

where and are discretization steps in variables and with a weight function form discrete realizations of the field. The process of such double smoothing - the field is illustrated in Fig. 2.11.

In the example under consideration, the process of moving summation can easily be reduced to a calculation in accordance with the recursive formulas (§ 2.3)

This example allows for generalizations. First, in a similar way, it is obviously possible to form realizations of more complex fields than a flat, time-constant field. Secondly, the example suggests the possibility of using recurrent algorithms for modeling random fields. Indeed, if the impulse transient response of the PVF, which forms a field with a given correlation function from the -field, is represented as a product of the form (2.151), then, as was shown, the formation of field realizations is reduced to the repeated application of algorithms for modeling stationary random processes with correlation functions . These algorithms can be made recurrent if the correlation functions , have the form (2.50) (stochastic processes with rational spectrum).

In conclusion, it should be noted that in this section only the basic principles of digital modeling of random fields have been considered and some possible modeling algorithms have been given. A number of issues remained untouched, for example: modeling of vector (in particular, complex), non-stationary, non-homogeneous, non-normal random fields; questions of finding the weight function of the space-time shaping filter according to the given correlation-spectral characteristics of the field (in particular, the possibility of using the factorization method for multidimensional spectral functions); examples of the use of digital models of random fields in solving specific problems, etc.

The presentation of these questions is beyond the scope of this book. Many of them are the subject of future research.

FIELD - a set of linguistic (ch. arr. lexical) units united by a common content (sometimes also by a common formal indicators) and reflecting the conceptual, subject or functional similarity of the designated phenomena. On the possibility of the existence of different types of lexic. associations, scientists drew attention back in the 19th century. (M. M. Pokrovsky), certain features of the field structure of vocabulary were noted in the construction of thesauri (P. Roger, F. Dorn-seif, R. Hallig and W. von Wartburg). First theoretical comprehension of the concept of P. in the language was contained in the works of J. Tri-ra, G. Ipsen, where oio received the name “semantic. field". For the semantic P. postulates the presence of a common (integral) semantic. a sign that unites all units of P. and is usually expressed by a lexeme with a generalized meaning (archilexeme), for example. sign "moving in space" in the semantic. P. verbs of motion: “go”, “run”, “ride”, “swim”, “fly”, etc., and the presence of private (differential) features (from one or more), according to Crimea units P . differ from each other, eg. "speed", "method", "environment" of movement. Integral semantic. signs in the definition conditions can act as differential. For example, the sign "kinship relationship", which combines the terms of kinship "father", "mother", "son", "daughter", etc., becomes differential when moving to semantic. P., which includes designations and other relations between people such as “colleague”, “fellow traveler”, “classmate”, “boss”, etc. This is one of the types of semantic connection. Items in vocabulary (hierarchical). On the relationship of semantic. fields within the entire dictionary also indicates the belonging of a polysemantic word to dec. semantic P. Thus, semantic. P. are characterized by the connection of words or their otd. values, the systemic nature of these connections, interdependence and veimodeterminability of lexical. units, relates, the autonomy of P., the continuity of the semantic space, visibility and psychological. reality for the average native speaker. Semantic structure. fields are usually studied by methods of component analysis, oppositions, graphs, combinatorial methods, etc. In addition to the actual semantic. P. stand out: morphosemantic P., for elements to-rykh (words) in addition to semantic. proximity is characterized by the presence of a common affix iln stems (P. Gyro); associative P. (Sh. Bally), studied within the framework of psycholinguistics and psychology, for which the association around the word-stimulus is defined by the characteristic. groups of associated words; the latter, in spite of their varying composition among the Raev informants, reveal, therefore, a degree of generality (homogeneity). The words of one associative P. are often characterized by semantic. proximity; grammatical phrases, for example. voice field (M. M. Gukhman, A. V. Bondarko), represented in the language by both grammatical (morphologized; units) and units that are on the verge of paradigmatics and syntagmatics (free and semi-free phrases); and other syntactic units as manifestations of the semantic compatibility of their components, for example - "legs", "barking" - "dog > (V. Porcig); sets of structural models of sentences united by a common semantic task; for example, in syntactic The field of imperativeness includes all models, with the help of which an order is expressed. ., snntaksich. paradigm), etc. Ufimtseva A. A., Theories of the "semantic field" and the possibility of their application in the study of the vocabulary of the language, in the collection: Questions of the theory of language in modern foreign linguistics. M .. 1961; Shchur G S, Field Theories in Linguistics, M .-L.. 1974; Karaulov Yu. N., General and Russian. ideography, M.. 1976; Kuznetsov A. M. Structural-semantic. parameters in the lexicon. Based on the English language. M.. 1980; I p s e n G., Der alte Orient und die Indogermanen, in: Stand und Aufgaben der Sprachwissenschaft, Hdlb., 1924; Trier J.. Der deutsche Wortschatz im Sinnbezirk des Verstandes. HDlb., 1931; his own, Altes und Neues vom sprachlichen Feld. Mannheim - Z., ; P o r z i g W., Wesenhafte Bedeutungsbeziehungen, "Beitrage zur Geschichte der deutschen Sprache und Literatur". 1934, Bd 58. A. M. Kuznetsov.

Receptive fields size: d=10 µm or 0.01 mm - outside the central fossa.

Rice. 25. Synaptic connections in the retina ( scheme according to E. Boycott, J. Dowling): 1 - pigment layer;

2 - sticks; 3 - cones; 4 - zone of location of the outer boundary membrane; 5 - horizontal cells; 6 - bipolar cells; 7 - amacrine cells; 8 - glia

(Mullerian fiber); 9 - ganglionic cells; 10 - zone of location of the inner boundary membrane; 11 - synapses between photoreceptors, bipolar and horizontal neurons in the outer reticular layer; 12 - synapses between bipolar, amacrine and ganglion cells in the inner reticular layer.

In the very hole d=2.5 µm (due to this, we are able to distinguish between two points with an apparent distance between them of only 0.5 arc minutes-2.5 microns - if we compare, this is a 5 kopeck coin at a distance of about 150 meters).

Starting from the level of bipolar cells, the neurons of the visual system differentiate into two groups (Fig. 26), which react in opposite ways to illumination and darkening:

1 - cells that are excited when illuminated and inhibited when darkened - "on"-neurons and

2 - cells, Excited by darkness and inhibited by illumination - "off"-neurons.

An on-center cell discharges at a markedly increased frequency. If you listen to the discharges of such a cell through a loudspeaker, then at first you will hear spontaneous impulses, separate random clicks, and then after turning on the light, a volley of impulses occurs, reminiscent of a machine-gun burst.

On the contrary, in cells with an off-reaction (when the light is turned off - a volley of impulses). This division is maintained at all levels of the visual system, up to and including the cortex.

Rice. 26. Concentric receptive fields (RP) of two ganglion cells.

Inhibitory zones of receptive fields are shaded. Reactions to turning on (1 and 4) and turning off (2 and 3) light are shown during stimulation of the RP center (1 and 3) and its periphery (2 and 4) with a light spot.

BUT - "on"-neurons

B - "off"-neurons

Within the retina itself, information is transmitted impulseless way (distribution and transsynaptic transmission of gradual potentials).

In horizontal, bipolar, and amacrine cells, signal processing occurs through slow changes in membrane potentials (tonic response). PD is not generated.

Rod, cone, and horizontal cell responses are hyperpolarizing, while bipolar cell responses can be either hyperpolarizing or depolarizing. Amacrine cells create depolarizing potentials.

To understand why this is so, one must imagine the influence of a small bright spot. The receptors are active in the dark, and light, causing hyperpolarization, reduces their activity. If a the synapse is excitatory, the bipolar will be activated in the dark, a become inactivated in the light; if the synapse is inhibitory, the bipolar is inhibited in the dark, and in the light, turning off the receptor, removes this inhibition, i.e. bipolar cell is activated. Thus, whether the receptor-bipolar synapse is excitatory or inhibitory depends on the mediator secreted by the receptor.

Horizontal cells are involved in the transmission of signals from bipolar cells to ganglion cells, which transmit information from photoreceptors to bipolar cells and then to ganglion cells.

Horizontal cells respond to light with hyperpolarization with pronounced spatial summation. Horizontal cells do not generate nerve impulses, but the membrane has non-linear properties that ensure impulse-free signal transmission without attenuation.

Cells are divided into two types: B and C. B-type cells, or luminosity, always respond with hyperpolarization, regardless of the wavelength of light. C-type cells, or chromatic cells, are divided into two- and three-phase. Chromatic cells respond with either hyper- or depolarization depending on the length of the stimulating light.

Biphasic cells are either red-green (depolarized with red light, hyperpolarized with green) or green-blue (depolarized with green light, hyperpolarized with blue). Triphasic cells are depolarized by green light, while blue and red light cause membrane hyperpolarization.

amacrine cells, regulate synaptic transmission in the next step from bipolars to ganglion cells. The dendrites of amacrine cells branch out in the inner layer, where they are in contact with the bipolar processes and ganglion cell dendrites. Centrifugal fibers coming from the brain terminate on amacrine cells.

Amacrine cells generate gradual and pulse potentials (phasic nature of the response). These cells respond with rapid depolarization to light on and off, and show little spatial antagonism between center and periphery.