Практические задания.

Задание 1. Определите тип текста, переведите, руководствуясь стилем русского языка. Обратите внимание на поиск точных соответствий терминам.

Monte Carlo method

The name Monte Carlo was applied to a class of mathematical methods first by scientists working on the development of nuclear weapons in Los Alamos in the 1940s. The essence of the method is the invention of games of chance whose behavior and outcome can be used to study some interesting phenomena. While there is no essential link to computers, the effectiveness of numerical or simulated gambling as а serious scientific pursuit is enormously enhanced by the availability of modern digital computers.

It is interesting, and may strike some as remarkable, that carrying out games of chance or random sampling will produce anything worthwhile. Indeed some authors have claimed that Monte Carlo will never be а method of choice for other than rough estimates of numerical quantities. Before asserting the contrary, we shall give а few examples of, what we mean and do not mean by Monte Carlo calculations.

Consider а circle and its circumscribed square. The ratio of the area of the circle to the area of the square is /4. It is plausible that if points were placed at random in the square, а fraction /4 would also lie inside the circle. If that is true (and we shall prove later that in а certain sense it is), then one could measure /4 by putting а round cake pan with diameter L inside а square cake pan with side L and collecting rain in both. It is also possible to program а computer to generate random pairs of Cartesian coordinates to represent random points in the square and count the fraction that lie in the circle. This fraction as determined from many experiments should be close to /4, and the fraction would be called an estimate for /4. In 1,000,000 experiments it is very likely (95% chance) that the number of points inside the circle would range between 784,600 and 786,200, yielding estimates of /4 that are between 0.7846 and 0.7862, compared with the true value of 0.785398....

The example illustrates that random sampling may be used to solve а mathematical problem, in this case, evaluation of а definite integral,

. (1.1)

The answers obtained are statistical in nature and subject to the laws of chance. This aspect of Monte Carlo is а drawback, but not а fatal one since one can determine how accurate the answer is, and obtain а more accurate answer, if needed, by conducting more experiments. Sometimes, in spite of the random character of the answer, it is the most accurate answer that can be obtained for а given investment of computer time. The determination of the value of  can of course be done faster and more accurately by non-Monte Carlo methods. In many dimensions, however, Monte Carlo methods are often the only effective means of eva1uating integrals.

А second and complementary example of а Monte Carlo calculation is one that S. Ulam cited in his autobiography. Suppose one wished to estimate the chances of winning at solitaire, assuming the deck is perfectly shuffled before laying out the cards. Once we have chosen а particular strategy for placing one pile of cards on another, the problem is а straightforward one in elementary probability theory. It is also а very tedious one. It would not be difficult to program а computer to randomize lists representing the 52 cards of а deck, prepare lists representing the different piles, and then simulate the playing of the game to completion. Observation over many repetitions would lead to а Monte Carlo estimate of the chance of success. This method would in fact be the easiest way of making any such estimate. We can regard the computer gambling as а faithful simulation of the real random process, namely, the card shuffling.

Задание 2. Определите тип текста, переведите, руководствуясь стилем русского языка. Обратите внимание на поиск точных соответствий терминам.

Artificial Intelligence and Intelligence

There are two goals to AI, the biggest one is to produce an artificial system that is about as good as or better than а human being at dealing with the real world. The second goal is more modest: simply produce small programs that are more or less as good as human beings at doing small specialized tasks that require intelligence. To many AI researchers simply doing these tasks that in human beings require intelligence counts as Artificial Intelligence even if the program gets its results by some means that does not show any intelligence, thus much of AI can be regarded as "advanced programming techniques".

The characteristics of intelligence given here would be quite reasonable I think to most normal people however AI researchers and AI critics take various unusual positions on things and in the end everything gets quite murky. Some critics believe that intelligence requires thinking while others say it requires consciousness. Some AI researchers take the position that thinking equals computing while others don't.

One of the worst ideas to come up in these debates is the Turing test for thinking. People argue the validity of this test forever and ever. Every few months one of these discussions gets going in the Internet and then goes on for а month or so before it dies out. Notice that the goal of the Turing test is to fool naive questioners for а little while so in effect а major pre-occupation of AI has been to devise programs that fool the public and this is а very bad way go give the subject credibility. In fact one analog to the Turing test is the following test. I give you two test tubes, one has а tiny amount of fools gold at the bottom and the other has а tiny amount of real gold. I give you а few minutes to JUST look at them (no chemical or physical tests!) and then you must tell me which one has the real gold. Odds are that after 1 test а fair number of ordinary people half the people will be right and the other half will be wrong. Then since ordinary people after а short amount of time can’t tell the difference between the two are they the same? Would you buy fools gold from me at the current price for gold (about $300 an ounce)? Yet this is exactly what the Turing test proposes for thinking. Maybe this IS one of Turing's jokes?

А much more meaningful method of determining whether or not а computer is thinking would be to find out exactly what people are doing and then if the artificial system is doing the same thing or so close to the same thing as а human being then it becomes fair to equate the two. One of the positions on intelligence that I mention in this section is that it requires consciousness and consciousness is produced by quantum mechanics. For those of you who have been denied а basic education in science by our schools quantum mechanics goes like this. By the beginning of the 20th Century physicists had discovered electrons, protons and various other very small particles were not obeying the known laws of Physics. After а while it became clear that particles also behave like waves. The most well known formula they found to describe how the particles move around is the Schrodinger wave equation, а second order partial differential equation that uses complex numbers. Since then quantum formulas have been developed for electricity and magnetism as well. Although as far as anyone can tell the formulas get the right answers the interpretation of what’s really going on is in dispute. The formulas and some experiments apparently show that at times information is moved around not just as the very slow speed of light but INSTANTLY. Results like this are very unsettling. One of the developers of QM, Neils Bohr once said: "Anyone who isn't confused by quantum mechanics doesn't really understand it."

Задание 3. Переведите текст на русский язык, найдите точное соответствие терминам.

Ontolingua

Knowledge sharing is an increasingly important problem for AI. Knowledge-based systems do not solve problems right out of the bох; they depend on custom knowledge bases (sometimes called "domain theories" or "background knowledge") to get the job done. То build on existing AI work one must construct the required knowledge base, which is an expensive and under specified task. Our hypothesis is that knowledge sharing — using and extending existing, carefully designed knowledge bases — is more productive than building them from scratch. However, knowledge sharing is currently difficult, because knowledge bases are typically ad hoc designs intended for narrow tasks, implemented in а babel of incompatible representation systems. We need mechanisms for developing and using shared knowledge bases. In particular, we need mechanisms for representing the sharable content of the knowledge used by AI systems.

Neches describe а strategy for developing the technology to support large-scale knowledge sharing. An essential part of that strategy is the use of common ontologies to specify the terminology upon which knowledge-based systems depend. Consider а planning system based on а theory in which plans are composed of "steps" which form "sequences" with specific kinds of "resource dependencies," and that the search for plans is guided by "ordering heuristics" and "optimization criteria." If one wished to use this planning system, one would need to understand what these words mean, and build а knowledge base in which domain-specific knowledge was formulated in terms that the planning program also understands.

An ontology is а vocabulary of such terms (names of relations, functions, individuals), defined in а form that is both human and machine readable.¹ An ontology, together with а kernel syntax and semantics, provides the language by which knowledge-based systems can interoperate at the knowledge-level: exchanging assertions, queries, and answers.

As а software engineering construct, ontologies play the role of а coupling interface among shared knowledge bases and knowledge-based systems, much like the formal argument list of а procedure is а coupling construct for entries in а conventional software library. Ontologies are also like conceptual schemata in database systems, which provide the basis for many application programs and databases to interoperate on the basis of shared definitions. An ontology allows а group of (programmers of) knowledge-based systems to agree on the meaning of а few terms, from which an infinite number of assertions and queries may be formulated. The use of ontologies is not sufficient to guarantee sharability, but it is an enabling mechanism.

Ontolingua is а system for maintaining ontologies portably, in а form that is compatible with multiple representation languages. It is implemented in а program that translates definitions written in а simple syntax into the forms that are input to а variety of implemented representation systems. Ontologies written in Ontolingua can thereby be shared by multiple users and research groups using their own favorite representation systems, and can be easily ported from system to system. The single-source / multiple-translation approach allows one to use the same source for development (е.g., using а terminological reasoning system for classification and а constraint checking system for integrity) and runtime application (е.g., using а special purpose reasoner that ignores the definitions of terms).

The development of Ontolingua was motivated by the needs of the Summer Ontology Project, а pilot study in which researchers from several groups and institutions met weekly to design an ontology of terms used in modeling electromechanical devices. The participants used а wide variety of representation systems, yet their models shared many of the same underlying concepts. The project needed а medium for collaboratively developing the ontology and а delivery vehicle for sharing the results.

Ontolingua is now available as а public domain tool, in Common Lisp, as а mechanism for defining common ontologies. It reads definitions, specified in а simple syntax, and translates them into appropriate forms given to implemented knowledge representation systems. It recognizes when definitions contain sentences that cannot be translated into а given implementation, and informs the user.

The syntax of Ontolingua definitions is based on а standard notation and semantics for predicate calculus called Knowledge Interchange Format (KIF) [9, 10, 11]. KIF is intended as а language for communication (i.е., for "literary publication" of knowledge). It is designed to make the epistemological level [19] content of а knowledge base clear to the reader, but not to support automated reasoning in that form. It is very expressive, so much so that it is impossible to implement а tractable theorem prover, which can answer arbitrary queries in the language.

Задание 4. Переведите текст на русский язык, руководствуясь стилем переводящего языка.

Spatial Database Engine

Overview

The demand for organizationwide access to geographic data has driven the requirement to create database management system (DBMS) based repositories for geographic data. This in turn has driven the requirement for solutions that provide the capability to store and manage complex spatial structures, open, standard interfaces, close integration with core organizational data, support for large geographic data sets, support for large numbers of users, and a wide range of client applications.

This paper examines the Environmental Systems Research Institute, Inc. (ESRI), Spatial Database Engine (SDE) software, which is a comprehensive solution that provides a distributed, standards-based, open interface between the user and all of the geographic data in an organization, whether they are stored in a DBMS or as a collection of files.

Introduction

Over the past twenty-five years, enormous volumes of digital spatial data have been created using geographic information system (GIS) software, computer-aided design (CAD), and image processing systems. Billions of dollars have now been invested in creating digital geographic information. The need to leverage this spatial information is becoming widely recognized in application areas such as municipal government, utilities, land management, telecommunication, insurance, resource management, transportation, and health care.

Today three major emerging trends are increasing the demand for a new open approach to spatial data management. First, there is a growing desire to expand the access to geographic data within organizations. Second, organizations are beginning to use spatial location to integrate their core business data and are adding spatial analysis to their business processes (i.e., spatially enabling the enterprise). Third, the growing popularity and access to the Internet is increasing pressure on all levels of government to provide increased public Internet access to existing geographic data.

Open access to geographic data has been constrained by the fact that much of the available data exist in a variety of vendor-proprietary, file-based formats. While file-based geographic data may easily be shared among a small project group, the distribution of data across an organization has been more problematic. This has often resulted in multiple copies of geographic data being distributed among various groups within an organization. Without highly structured procedures to manage this replication of data, the consistency and integrity of the data are at risk, ultimately putting decisions based on the data at risk.

In addition, until very recently, open access to geographic data was constrained because it could not be easily incorporated with other core organizational data stored in a relational database management system (DBMS). This was because the relational DBMS model was designed to support a very limited set of data types (i.e., numeric, character, and date). In addition, CAD and image processing systems have developed their own data formats, requiring anyone that wanted to integrate GIS, CAD, and raster image data to use multiple data translators.

Задание 4a. Переведите текст на русский язык, руководствуясь стилем переводящего языка.

2.1 Types of mathematical discourse

Part of mathematical discourse is written in a special variety of English or some other natural language that we call the mathematical register. A piece of text in a natural language, possibly containing embedded symbolic expressions, is in the mathematical register if it communicates mathematical reasoning and facts directly. The presumption is that discourse in the mathematical register could be translated into a sequence of statements in a formal logical system such as first order logic. The mathematical register is the register in which definitions, theorems and proof steps are written.

Other kinds of mathematical writing describe the history of a concept, how to think about the concept, physical examples, and so on. They are in some kind of general scientific or academic register that could be analyzed further, but they are not in the mathematical register even though they are concerned with mathematics. These are discussed in Section 2.3 below.

The distinction between the mathematical register and other kinds of writing that occur in mathematics texts is certainly not precise. We are after all discussing an aspect of natural language and so cannot expect to give the mathematical register a mathematical definition. Nevertheless, we believe that most mathematical writing can be easily seen to contain segments that are clearly intended to communicate mathematical facts and reasoning, and are thus in the mathematical register, and other segments that are clearly not in that register.

Lanham [22, Chapter 6] compares college students taking courses in more than one department to anthropologists who must come to understand three or four cultures simultaneously while having only occasional fifty-minute contacts with each of them. One aspect of mathematical culture is that mathematicians in speaking and writing pass in and out of the mathematical register freely and without comment. Like many aspects of any culture, this practice is commonly quite unconscious. It is a serious challenge to many students to determine whether a statement is or is not in the mathematical register, a challenge made more difficult by the fact that neither teacher nor student normally makes the distinction explicit. A clear articulation of the concept of the mathematical register (whatever name one uses) should help.

2.1.1 On terminology A “register" of a natural language is a special form of the language used for certain purposes. A good brief introduction to the idea is that of Halliday in [13, pag 86]. A register may use special words, special grammatical constructions (such as “thou” in a religious register), and words and grammatical constructions with meanings different from those in other registers, such as “definition" and “if … then" in the mathematical register (see 2.2.1 below). Many of these special uses are surveyed in [2], with references to the literature.

2.1.2 References Steenrod [33, page 1] called the mathematical register the \formal structure". That is the earliest reference to it that we know of. Note that word “formal" also refers to a non-colloquial style of writing. Writing in the mathematical register can be either formal or informal in style.

Other writers who have discussed the mathematical register include DeBruijn [6] (the “mathematical vernacular" (his work contains a partial taxonomy) and F. Schweiger [31, 32]. Laborde [20] discusses mathematics and language in connection with younger students, and some of her comments amount to a partial taxonomy. Halliday and Martin [13] study the more general (scientific register" in depth, but make little mention specifically of mathematics.

2.2 Kinds of discourse in the mathematical register

We describe briefly the main kinds of discourse in the mathematical register. As in any taxonomy, this inevitably involves occasionally stating the obvious (for example in discussing what a definition or a theorem is). However, it is important in a taxonomy to state as exactly as possible what each descriptive term means: we must define “definition", “theorem" and so on. The definitions we give are necessarily of the sort a dictionary would give; they do not constitute mathematical definitions. (As the reader may check, the definitions of these words actually given by dictionaries are quite unsatisfactory as descriptions of their use in mathematics.) Giving a precise description of something “everyone knows" is a valuable exercise which often uncovers ambiguities and misunderstandings and provides new insights.

2.2.1 Definitions A definition prescribes the meaning of a word or phrase in terms of other words or phrases that have previously been defined or whose meanings are assumed known. Note that definitions are distinct in subtle ways from other kinds of discourse in the mathematical register. For example, “if" in a definition can mean “if and only if". This sort of thing is discussed in [2] and in [19, p. 71].

2.2.2 Specifications A textbook, particularly at the elementary level, sometimes must describe a type of object for which the author might consider it pedagogically unwise to provide an explicit definition. An explicit definition might be pedagogically unwise because of its technical difficulty (for example defining sets as elements of a model of Zermelo-Frankel set theory) or because it is unrelated to the way in which we usually think of the object (for example defining an ordered pair <a, b> as {a, b,{a}}.)

A specification is a description of a type of mathematical object that gives salient features of such objects, but which may fall short of giving a list of properties that completely determine the type of object. The word “specification" is not usually used in this context (it was introduced in [42]), but authors of texts for undergraduate courses often give specifications without calling them specifications.

Задание 5. Определите особенности стиля текста, переведите его, применяя необходимые трансформации, обратите внимания на особенности британского английского.

Light seems to defy its own speed limit

IT'S a speed record that is supposed to be impossible to break. Yet two physicists are now claiming they have propelled photons faster than the speed of light. This would be in direct violation of a key tenet of Einstein's special theory of relativity that states that nothing, under any circumstance, can exceed the speed of light.

Gunter Nimtz and Alfons Stahlhofen of the University of Koblenz, Germany, have been exploring a phenomenon in quantum optics called photon tunnelling, which occurs when a particle slips across an apparently uncrossable barrier. The pair say they have now tunnelled photons "instantaneously" across a barrier of various sizes, from a few millimetres up to a metre. Their conclusion is that the photons traverse the barrier much faster than the speed of light.

To see how far they could make photons tunnel, Nimtz and Stahlhofen sandwiched two glass prisms together to make a cube 40 centimetres on its sides. Since photons tunnel most readily over distances comparable with their wavelength, the physicists used microwaves with a wavelength of 33 cm - long enough for large tunnelling distances yet still short enough that the photons' paths can be bent by the prism.

As expected, the microwaves shone straight through the cube, and when the prisms were separated, the first prism reflected the microwaves (see Diagram). However, in accordance with theory, a few microwave photons also tunnelled across the gap separating the two prisms, continuing as if the prisms were still sandwiched together.

Nimtz and Stahlhofen found that the reflected microwaves and the few microwaves that tunnelled through to the second prism both arrived at their respective photodetectors at the same time. This suggests an ultra-fast transit between the two prisms - so much faster than the speed of light that the experimenters couldn't measure it. Moreover, the pair found that the tunnelling time, if any, did not change as they pulled the prisms further apart. Because tunnelling efficiency also drops off with distance, however, Nimtz says that they could not observe the effect across distances greater than 1 metre

"For the time being," he says, "this is the only violation [of special relativity] that I know of. "How can this be explained" The Heisenberg uncertainty principle dictates that a particle's energy and the time it spends in any one place cannot both be known with absolute precision. This means particles can sometimes sneak over a barrier if the time they spend traversing that barrier is short enough. Bizarre as it may seem, quantum tunnelling is not only a commonplace phenomenon in the quantum world, it also lies at the core of many processes we take for granted.

"In my opinion, tunnelling is the most important physical process, because we have it in radioactivity and we have it in nuclear fusion," Nimtz says. "The temperature of the sun is not high enough to organise regular fusion of protons into helium [without tunnelling]. Some people are saying that the big bang happened because of tunnelling. Recently, many people have argued that processes in biology and in our brain are based on tunnelling."

Aephraim Steinberg, a quantum optics expert at the University of Toronto, Canada, doesn't dispute Nimtz and Stahlhofen's results. However, Einstein can rest easy, he says. The photons don't violate relativity: it's just a question of interpretation.

Steinberg explains Nimtz and Stahlhofen's observations by way of analogy with a 20-car bullet train departing Chicago for New York. The stopwatch starts when the centre of the train leaves the station, but the train leaves cars behind at each stop. So when the train arrives in New York, now comprising only two cars, its centre has moved ahead, although the train itself hasn't exceeded its reported speed.

"If you're standing at the two stations, looking at your watch, it seems to you these people have broken the speed limit," Steinberg says. "They've got there faster than they should have, but it just happens that the only ones you see arrive are in the front car. So they had that head start, but they were never travelling especially fast."

Задание 6. Текст из задания 2 послужил основой для следующей статьи. Переведите ее на английский язык, обращая внимание на различия в стиле.