© 2009 Pearson Education, Inc. 1.1 **Number** Theory Slide 5 - 4 Copyright © 2009 Pearson Education, Inc. **Number** Theory The study of **numbers** and their properties. The **numbers** we use to count are called **natural** **numbers**,, or counting **numbers**. Slide 5 - 5 Copyright © 2009 Pearson Education, Inc. Factors The **natural** **numbers** that are multiplied together to equal another **natural** **number** are called factors of the product. **Example**: The factors of 24 are 1/

(1643-1727) Gottfried Wilhelm von Leibniz (1646- 1716) http://www.guptalab.org Laboratory of **Natural** Information Processing SC105 Class 1 Fields & Numeration The set of **Natural** **Numbers**: = { 1, 2, 3, …} **Natural** **numbers** allowed “counting” Allowed development of mathematical equations Some of the equations could not be solved with current set for **example**: 1 + X = 0 hence the set of integers evolved http://www.guptalab.org Laboratory/

express themselves as differences in land value. Using those land value differences, environmental value can be converted into **numbers** – in other words, quantified. Environmental value indicators = Changing land value caused by changing environmental conditions / individual. Existence value Value derived from only the knowledge of the existence of environmental properties/services. (**Example**) Rural **nature** full of organisms … People feel nostalgic about their birthplace. … People feel sadness and longing over /

(UNESCOs Man and the Biosphere Program, See Chapter 9) Copyright 2010 Research Institute for Humanity and **Nature**. All Rights Reserved. (**Example**) Giant honeybee - Primary pollinator in tropical rainforest in Southeast Asia - Migratory honeybee Swidden and secondary/ use 2. Reduced Impact Logging (RIL) RILUsual method Copyright 2010 Research Institute for Humanity and **Nature**. All Rights Reserved. Comparison: **number** of species according to logging methods Diversity of tree species is higher with RIL. (Seino et/

The 7 crystal systems differ in terms of the angles between the faces, and in the **number** of edges of equal length on each face Section 13.3 The **Nature** of Solids The shape of a crystal depends upon the arrangement of the particles within it The/13.4 Changes of State Sublimation- the change of a substance from a solid directly to a vapor, without passing through the liquid state **Examples**: iodine (Fig. 13.14, p. 401); dry ice (-78 oC); mothballs; solid air fresheners Section 13.4 Changes of State Sublimation/

Smoking, Sport, Studying abroad, Taxes, Television, Third world countries, Unemployment, and so on… Press Escape to quit STRUCTURE **number** 1 To present the main reason(s) for a choice (présenter la/les raisons dun choix) "What are the main/galement abandonner le sentiment quils ont depuis longtemps quun employé productif est un employé que lon peut voir. Press Escape to quit **EXAMPLES** (5) **Nature** : (Ecologists) will have to abandon their long- cherished notion that (a safe policy) is (a policy) that (ignores /

-produced elements are too unstable (radioactive) to occur **naturally** in appreciable amounts. 17.1 Elements More than 99% of the material on Earth is formed from only about a dozen of the elements. Living things, for **example**, are composed primarily of five elements: oxygen (O/around the nucleus. 17.8 Electrons in the Atom The periodic table is a chart that lists atoms by their atomic **number** and by their electron arrangements. As you read across from left to right, each element has one more proton and/

knowledge of language and of the domain 7 **Natural** Language Generation Language Technology Meaning **Natural** Language Understanding **Natural** Language Generation Text Text Speech Recognition Speech Synthesis Speech Speech **Example** System #1: FoG Function: Input: User:/WeatherReporter The Message Set: MonthlyTempMsg ("cooler than average") MonthlyRainfallMsg ("drier than average") RainyDaysMsg ("average **number** of rain days") RainSoFarMsg ("well below average") RainSpellMsg ("8 days from 11th to 18th") /

Inflectional Categories (Nouns) The following properties influence the inflection of nouns: only vaguely related to **natural** gender gender: masculine, feminine, neuter, ... **number**: singular, plural, dual, trial, ... case: nominative, accusative, dative, ablative... class: /g., the Porter Stemmer for reduction to the stem) Stochastic Stemming Stochastic Stemming learns how to find the lemma from **examples**. **Examples**: computer, computers COMPUTER hit, hits HIT box, boxes BOX Learned rules: Cut off the “s/

about the set of whole **numbers** and the set of **natural** **numbers**. a. What are some similarities between the set of whole **numbers** and the set of **natural** **numbers**? b. What are some differences between the set of whole **numbers** and the set of **natural** **numbers**? The **numbers** –3 and 3 are **examples** of opposites The **numbers** –3 and 3 are **examples** of opposites. On the **number** line, these two **numbers** are the same distance/

(Z) Integers (-6) (W) Whole #’s (0) (N) **Natural** #’s (1) **Example** 1 Name the sets of **numbers** to which each apply. **Example** 1 Name the sets of **numbers** to which each apply. **Example** 1 Name the sets of **numbers** to which each apply. **Example** 1 Name the sets of **numbers** to which each apply. (a) √ 16 **Example** 1 Name the sets of **numbers** to which each apply. (a) √ 16 = 4/

The resolution principle, first introduced by Robinson [1965], provides a way of finding contradictions by trying a minimum **number** of substitutions. The idea is to keep clauses in their general form as long as possible and only introduce specific/to eliminate x. Unification has deep mathematical roots and is a useful operation in many AI programs, for **example**, theorem provers and **natural** language parsers. As a result, efficient data structures and algorithms for unification have been developed. For an /

Work Area Debugging NATRJE ZZTDOC LEN Consulting LLC 05/02/2004 17:52 **Natural** Utilities ZZUtils v2.1 Generate Code Walkthrough Document Profile: ZZUTIL/RALPH Old: Env/INIT 29 NC-SW-02 Uses of the Source Work Area Simple Code **Example** 0010 DEFINE DATA 0020 LOCAL USING ZZL1057 /* Retrieve source 0030 LOCAL USING/ (A01/1:C-SCRLEN) 0620 * 0630 LOCAL 0640 1 C-SESNUM (B2) 0650 1 ERROR-**NUMBER** (N4) 0660 * --------------------------------------------------------------------- 0670 1 #I (I4) 0680 1 #ED-SCRNUM (I4) 0690 /

Ex5.3 – Step 2 – prepare trip ends RUN PGM=MATRIX PRNFILE="C:Modelling Transport_CGAPPLICATIONSCHAPTER5E5MAT03D.PRN“, MSG=**Example** 5.3 - total **number** of trips after (1) FILEO RECO[1] = "C:Modelling Transport_CGAPPLICATIONSCHAPTER5E5MAT03B.DBF", FIELDS=ZONE SUM_J(10./ENDPROCESS ; script continues on NEXT page ________________________________________________________ NEXT … Ch11-DA: Ex11.4 – The Dynamic **Nature** of Traffic ; SCRIPT CONTINUED FROM PREVIOUS PAGE PROCESS PHASE=ILOOP ; This phase performs a zonal /

mount –less weight than mount optimized with best so far method –geometrically better deformation LIACS **Natural** Computing Group Leiden University86 Safety Optimization – **Example** of use Production Run ! Minimization of body mass Finite element mesh –Crash ~ 1.000/for the airfoil High Lift! Low Drag! Start Cruise LIACS **Natural** Computing Group Leiden University94 Traffic Light Control Optimization Objective: Minimization of total delay / **number** of stops Variables: Green times for next switching schedule Dynamic/

year that population B does. C) Population A may undergo instantaneous speculation by the doubling of its chromosome **numbers** (polyploidy). D) Under laboratory conditions, cross-fertilization between members of the two populations may be successful even /the two populations. Label the original population and the population after **natural** selection. **Example** of a given diagram (labels included) : The recessive gene of black fur would be **naturally** favored because these mice better fit their new environment. The /

cycles Biogeochemical cycle: Renewable and Non-Renewable Resources **Natural** resources which can be used but can be regenerated by **natural** processes, provided if there is no intervention in **natural** regeneration cycle. **Example**: Water, Wood Non Renewable Resources Those which will/ trend to develop small hydroelectric generation units. Multiple small dams have less impact on the environment. China has the largest **number** of these - 60,000, generating 13,250 megawatts, i.e. 30% of China’s electricity. Sweden, US/

disruptions to their dynamic homeostasis Disruptions to ecosystems impact the dynamic homeostasis or balance of the ecosystem **Example** – Invasive species, Human impact, **Natural** disasters, Water limitation, Salination L.O. 2.28 Most communities are in a state of nonequilibrium/. Fig. 52.21 Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings Age structure is the relative **number** of individuals of each age. Age structure diagrams can reveal a population’s growth trends, and can point to /

Genetic Programming is Genetic Algorithm wherein the population contains programs rather than bitstrings. Evolution in the **nature** Genetic Algorithms and Genetic Programming A simple **example** for Genetic Algorithms An **example** for Genetic programming A simple **example** Problem: “Find” the binary **number** 11010010. Initialization We start with 5 random binary **numbers** with 8 digits each. 1.01001010 2. 10011011 3.01100001 4.10100110 5.01010011 The fitness/

areas… Outline Overview MAC Routing Wireless TCP Wireless in real world Leverage broadcasting **nature** Wireless security Why Control Medium Access Wireless channel is a shared medium When conflict/ TCP with no errors (1.30 Mbps) TCP Reno (280 Kbps) Sequence **number** (bytes) Time (s) 2 MB wide-area TCP transfer over 2 Mbps /hiding them Outline Opportunistic forwarding (ExOR) Network coding (COPE) Background Famous butterfly **example**: All links can send one message per unit of time Coding increases overall /

from the effects of selection © 2011 Pearson Education, Inc. Balancing Selection Balancing selection occurs when **natural** selection maintains stable frequencies of two or more phenotypic forms in a population Balancing selection includes Heterozygote /common in the population Selection can favor whichever phenotype is less common in a population For **example**, frequency-dependent selection selects for approximately equal **numbers** of “right-mouthed” and “left-mouthed” scale-eating fish © 2011 Pearson Education, /

in the consolidated returns, because the **nature** of their assets is such that their inclusion would not be meaningful (for **example** industrial or insurance companies). This assessment includes, for **example**, consideration of the controls within a group/the BIS Principles for Effective Banking Supervision and EU directives have therefore supplemented quantitative capital regulation with a **number** of flanking policies. These include: Solo supervision “Fitness and properness” criteria for major shareholders in and/

that reaction time is a linear function of **number** of items being processed. As with the code box **example**, what we don’t know is whether this pattern is fortuitous or principled. There are several ways in which we could show that it is principled: If it can be derived from a basic law of **nature** (very rarely happens). Note that this is/

of undetermined structure. The complexity of meaning representations required for the general cases is one of the chief difficulties of **natural** language understanding. 17.11.2005 Levels of language Words, parts of words (lexical level, morphology) Structure of words Phrases/ because she wasnt hungry. "They" and "it" have the same referent in the following **example**, despite the fact that they differ in **number** and hence are syntactically incomplete: Mother picked an apple They are good sources of pectin. She/

with a very limited initial vocabulary. A program program add-**numbers**-in-the-table (input, output); var table: array [1..200] of integer; index: integer; sum: real; begin index := 1 sum:=0 while index <= 100 sum := sum + table[index]; index := index+1; end; end. **Natural** Languages tend to be far less precisely defined. **Examples** include the languages we speak, write and read: English/

this product is called a factorization of 30. © 2008 Pearson Addison-Wesley. All rights reserved 5-1-8 **Example**: Finding Factors Find all the **natural** **number** factors of each **number**. a) 24b) 13 Solution a) To find factors try to divide by 1, 2, 3, 4/ is disregarded). This unique product of primes is called the prime factorization of the **natural** **number**. © 2008 Pearson Addison-Wesley. All rights reserved 5-1-18 **Example**: Unique Prime Factorization Find the prime factorization of 240. Solution Using a tree format/

5.1 **Number** Theory The study of **numbers** and their properties. The **numbers** we use to count are called the **Natural** **Numbers** or Counting **Numbers**. Factors The **natural** **numbers** that are multiplied together to equal another **natural** **number** are called factors of the product. **Example**: The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. Divisors If a and b are **natural** **numbers** and the quotient of b divided by/

is the product of these factors. LCM = 24 32 52 = 16 9 25 = 3600 Hence, the LCM of 144 and 300 is 3600. Thus, the smallest **natural** **number** divisible by 144 and 300 is 3600. **Example** 6: Solving a Problem Using the Least Common Multiple A movie theater runs its films continuously. One movie runs for 80 minutes and a second runs for/

Two-locus two-allele exemplars Even with more loci: All **examples** are single-peaked so HC can solve in time linearly proportional to **number** of mutations required No **example** where recombination allows evolution of something that’s unevolvable with/, and precludes multi-level hierarchical organisation. 2.Although modularity and hierarchical organisation are ubiquitous in the **natural** world/ biological systems, strong interdependencies between modules are also ubiquitous 3.Therefore, their evolution is not/

are similar in age and weight. Ideally, offspring for a given livestock enterprise should be born within a specified **number** of days; for **example**, 40 to 60 days is a common time frame for cattle. Factors to consider: Climatic conditions will affect /. Producers tend to select and keep ewes that consistently deliver healthy twins. Photo by Ron Nichols courtesy of USDA **Natural** Conservation Resource Services. Flushing, a practice of feeding ewes good high-quality green pasture or additional concentrates four to /

h = 6.6310-34 J s Topic 13: Quantum and nuclear physics 13.1 Quantum physics The Quantum **Nature** of Radiation Describe the photoelectric effect. **EXAMPLE**: Using Planck’s hypothesis show that the energy E of a single quanta with frequency f is given by / argued that since electrons must exhibit wavelike properties, in order to exist in a bound orbit in a hydrogen atom a whole **number** of the electrons wavelength must fit precisely in the circumference of that orbit to form a standing wave. Thus: Note that n/

transformation according to an algorithm, no more and no less. Some **examples**: SEL2211: Contexts Lecture 5: Computer Science 1. The **nature** of computation 1.2 Fundamental ideas 1.2.4 Computation -- Arithmetic: The computation is to multiply two **numbers** together, divide the result by a third **number**, and output the result. The **numbers** are represented by symbols taken from the symbol system {0..9}, the/

time to learn their names. **Natural** **numbers** are also called counting **numbers** because they’re the **numbers** used to count with — 1, 2, 3, and so on. Whole **numbers** are like the **natural** **numbers** except that they include the **number** zero. Integers include all the **natural** **numbers**, the negative versions of them, and zero. Lesson 1.1.1 Comparing Integers **Example** 4 Describe the following **numbers** as **natural**, whole, or integer. There may/

designation involves a slightly different way of managing the area. The table omits a huge **number** of small **nature** or wildlife reserves. Some of these are owned and run by county councils and local /6] ………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………….. Examiner’s Reports/Model Answers 1.Explain the consequences (impacts) of suburbanisation Use an **example** or **examples** in your answer [6] Many responses, whilst having good explanations did not include enough specifi cs /

on the grid. Developed originally in philosophy of mind in an attempt to link mind and brain. 12 Supervenience **example** H: {An odd **number** of bits is on:. True, False. The bits that are on are the start of the Fibonacci sequence:/ owner/operators? –How will decisions be made about enhancements? 93 Principles of Complex Systems: How to think like **nature** Organizations: how **nature** builds systems; the wisdom of crowds Innovation required individual autonomy. What do groups add? Russ Abbott 94 “Self-organizing/

or as short as a ms or less. Radiocarbon Dating 14C is an **example** of an isotope that is continuously produced in our environment. 99.9% of the **naturally** abundant 14C is produced in the upper atmosphere by neutrons reacting with 14N, / 14C present in a sample, or by measuring the activity due to b emission. (Recall that activity is proportional to the **number** of decaying nuclei: ) http://www.c14dating.com/ Radiocarbon Dating Measuring Activity - scintillation counter. Scintillation is the emission of light /

). –Standard Generalized Markup Language or SGML (related: HTML, TEI, XML) Fall 2001EE669: **Natural** Language Processing27 SGML **Examples** This book does not delve very deeply into SGML. … In XML, such empty elements/2001EE669: **Natural** Language Processing31 Tag Sets for other Languages Differences: –Larger **number** of tags –categories covered (POS, **Number**, Case, Negation,...) –level of detail –presentation (short names vs. structured (“positional”)) **Example**: –Czech: AGFS3----1A---- POS SUBPOS GENDER **NUMBER** CASE /

AND DIALOGUE SYSTEMS LABUC SANTA CRUZ WordNet **Example** **NATURAL** LANGUAGE AND DIALOGUE SYSTEMS LABUC SANTA CRUZ WordNet Resources “greenhouse” as noun (X) Synonyms, “nursery” Hypernyms (designating whole class, X IS_A), e.g., “building” Hyponyms (designating subclass, Y IS_KIND_OF), e.g., “orangery”, “conservatory” Meronyms (constituent parts or substance, X HAS_PART), e.g., “door”, “wall” Polysemy count (**number** of senses of word in a syntactic/

their logical form. NL MR Training Exs Semantic-Parser Learner **Natural** Language Meaning Rep Semantic Parser 12 Engineering Motivation Most computational language-/) = PLAYER SCISSOR 30 Overview of S CISSOR Integrated Semantic Parser SAPT Training **Examples** TRAINING SAPT ComposeMR MR NL Sentence TESTING learner 31 Extending Collins’ (1997)/ (half our) 117 Based on maximum-entropy model: Features f i (d) are **number** of times each transformation rule is used in a derivation d Output translation is the yield of/

**number** of solvents used to extract caffeine from coffee and tea. De-caffeinated products produced with ethyl ethanoate are often described on the packaging as "**naturally** decaffeinated" because ethyl ethanoate is a chemical found **naturally** in many fruits. Caffeine (C8H10N4O2) is an **example**/ with free radicals to form stable molecules and prevent chain reactions. Melatonin and Vitamin E are **examples** of **natural** free radical scavengers. Melatonin As UV light can cause wrinkling of skin, some skin-care products/

not contribute to survival and reproduction are not favoured by **natural** selection and hence are not seen in populations in the wild. **Examples** of features maintained only by artificial selection can be seen/**numbers** of plants are produced through **natural** or artificial cloning, the members of the resulting population are genetically identical. As a result, these populations have very limited genetic variation compared with a population that has been produced by sexual reproduction. Bananas are a **natural** **example**/

in the Flip-Flop algorithm, so it is reasonable to stop when there is only an insignificant improvement. Fall 2001 EE669: **Natural** Language Processing 17 **Example** Suppose we want to translate prendre based on its object and have {t 1, …, t m }={take, make, rise,/ The score of a sense is the **number** of times that one of its translations occurs with the translation of v in the second language corpus. Fall 2001 EE669: **Natural** Language Processing 33 Dagan & Itai’s Algorithm For **example**, the relation R could be ‘is/

RNAP Where’s the platform? The DNA → protein processing system. Like the Aerospace- delivers-mail **example**. 49 Introduction to Complex Systems: How to think like **nature** 1998-2007. The Aerospace Corporation. All Rights Reserved. Organizations: when groups are better than / will generally beat an individual of approximately the same skill level. –This is not so much emergence as power in **numbers**. Why groups? Two steps. 54 David Sloan Wilson on groups What holds for chickens holds for other groups as well/

Rodham ClintonSen. John McCain Summary: Senator Barack Obama was declared the presumptive Democratic presidential nominee. **Example** NLP Task: Question Answering Directly answer **natural** language questions based on information presented in a corpora of textual documents (e.g. the web/genes and other entities independently – cad represents over 11 different biomolecular entities in Drosophila and the mouse Large **number** of biomolecular entites – 70,000+ genes, 100,000+ proteins, 1 million species – Requires a /

RNAP Where’s the platform? The DNA → protein processing system. Like the Aerospace- delivers-mail **example**. 50 Introduction to Complex Systems: How to think like **nature** 1998-2007. The Aerospace Corporation. All Rights Reserved. Organizations: when groups are better than / will generally beat an individual of approximately the same skill level. –This is not so much emergence as power in **numbers**. Why groups? Two steps. 55 David Sloan Wilson on groups What holds for chickens holds for other groups as well/

24 Smoothing: an **Example** Fall 2001 EE669: **Natural** Language Processing 25 Laplace’s Law: Smoothing by Adding 1 Laplace’s Law: –P LAP (w 1,..,w n )= (C(w 1,..,w n )+1) / (N+B) C(w 1,..,w n ) is the frequency of n-gram w 1,..,w n, N is the **number** of training instances, B is the **number** of bins training/

RNAP Where’s the platform? The DNA → protein processing system. Like the Aerospace- delivers-mail **example**. 49 Introduction to Complex Systems: How to think like **nature** 1998-2007. The Aerospace Corporation. All Rights Reserved. Organizations: when groups are better than / will generally beat an individual of approximately the same skill level. –This is not so much emergence as power in **numbers**. Why groups? Two steps. 54 David Sloan Wilson on groups What holds for chickens holds for other groups as well/

I/O’s for R is:1000 the **number** of I/O’s for S is10,000*500/100=50,000 162 Joins Using a Sorted Index **Natural** join R(X, Y) S (Y, Z) with index on Y for either R or S Extreme case: Zig-zag join **Example**: relation R(X,Y) and R(Y,Z) with index /placing results in 50 remaining buffers to form 50 buckets for the join of R S with U. 3.Finally, join R S with U bucket by bucket. 303 **Example** (cont.) The **number** of disk I/O’s is: – 20,000 to read U and write its tuples into buckets – 45,000 for two-pass hash-join R S – /

of very short narrow-domain texts Clustering indexes MajorClust method: **number** of clusters is defined automatically Clustering abstracts NN method (hierarchy-based) K-means method (**example**-based) MajorClust method (density-based) Abstracts (preliminary results) / Lexical pattern extraction: mining the web with semantic info Bootstrapping technique for corpora construction: Categorization task (**natural** disaster corpus) Named Entity Recognition Word Sense Disambiguation (Guzmán, Montes, Rosso, 05) The WordNet/

it easier to deal with large **numbers**, especially concentrations Written as A ×10 b, where A is a decimal **number** and b is a whole **number** **Example**: Avogadro’s **number** 602 213 670 000 000 000 /**numbers** more convenient, especially pH Two types: common logarithms and **natural** logarithms Two types: common logarithms and **natural** logarithms Common Logarithms Common log of x is denoted log x gives the power to which 10 must be raised to equal x 10 n = x written as: log 10 x = n (base 10 is not always specified) **Example**/

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