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User talk:Egm6341.s11.team5.shin

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title: User talk:Egm6341.s11.team5.shin


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User talk:Atmoth

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license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:Atmoth


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User talk:Faisalwar

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title: User talk:Faisalwar


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User talk:Egm6341.s11.team2.franklin

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You have uploaded this file without information on its copyright status. It therefore has been speedily deleted. Please provide a relevant copyright license to all files uploaded in the future. Thanks. --S Larctia 07:53, 25 September 2011 (UTC)

title: User talk:Egm6341.s11.team2.franklin


text:
User talk:Piroon.t

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What is the copyright of File:Best pc.jpg and File:Best pc 2.jpg?
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title: User talk:Piroon.t


text:
User talk:Praveen.mk9968

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title: User talk:Praveen.mk9968


text:
User talk:EML5526.S11.Team1.HS

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title: User talk:EML5526.S11.Team1.HS


text:
User talk:EGM6341.S11.team2.lee

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title: User talk:EGM6341.S11.team2.lee


text:
User talk:Egm6341.s11.team2.DT

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title: User talk:Egm6341.s11.team2.DT


text:
User talk:Egm6341.s11.team2.zou

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title: User talk:Egm6341.s11.team2.zou


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User talk:Egm6341.s11.team3.russo

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title: User talk:Egm6341.s11.team3.russo


text:
User talk:Egm6341.s11.team2.cleveland

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title: User talk:Egm6341.s11.team2.cleveland


text:
User talk:Eml5526.s11.team2.sandhu

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title: User talk:Eml5526.s11.team2.sandhu


text:
TESOL/Go and go to

Using go / go to can be a confusing grammatical problem.

Activities
Using "go" as an auxiliary verb with activities usually requires "go", not "go to". For example:
 * go shopping
 * go fishing
 * go scuba diving
 * go hiking
 * go travelling
 * go sightseeing

Nouns
Specific locations usually require "go to." For example:
 * go to Tokyo
 * go to Africa
 * go to the store
 * go to school
 * to to work

Exceptions:
 * go home

Adverbs and Prepositions
Locations relative to the position or the speaker or audience usually require "go" without "to." For example:
 * go left
 * go there
 * go away
 * go down
 * go past

Quiz
{shopping - go shopping + go to shopping
 * type=""}

{school + go to school - go school
 * type=""}

{skiing + go skiing - go to skiing
 * type=""}

{London - go London + go to London
 * type=""}

{home + go home - go to home
 * type=""}

{left - go to left + go left
 * type=""}

title: TESOL/Go and go to


text:
Talk:Genetics/Human Leukocyte Antigen/Linkage Disequilibrium

Page created on 31 Dec 2010. PCano 16:45, 19 January 2011 (UTC)


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Template:VotingHypothesis

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title: Template:VotingHypothesis


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Psycholinguistics/Dyslexia

Introduction
Dyslexia is a group of learning disabilities which affect an individual's ability to read and write. There are key characteristics which cluster these disorders together. For example, one characteristic would be not being explained by intellectual impairment. There are several distinct types of dyslexia that are divided based on how they manifest themselves. Dyslexia does not seem to have a single cause, but a collection of different types of problems which influence one another to produce reading and writing difficulties.Having multiple causes can make the diagnostic and treatment process very long and complicated, but the results are highly specialized to the individuals disorder and needs.The diversity of treatment and assessment is most likely due to how long dyslexia has been a focus of research and treatment. Having a wide variety of treatment is ideal since in allows a majority of cases to be re mediated which is especially important in the modern world of personal computers and information technology (Beaton, 2004; Dehaene, 2009; American Psychiatric Association [DSM-IV-TR], 2000; Johnson, 1986). What is Dyslexia

History
Reading difficulty, the disorder which would eventually be called dyslexia, was first described in 1887 by Rudolf Berlin, an Opthamologist. Reports of dyslexia appear as early as the 1890s: Pringle-Morton described the disorder in 1896 and Kerr in 1897 and reports of it running in families began to appear around 1905 (Pennington & Olson, 2005). The modern concept of dyslexia began to be officially reported in the 1970s through observational studies of children which revealed that dyslexia could be explained by an impairment at the word processing level rather than, as was previously thought, a anomaly in eye movements or inappropriate use of sentence context (Dehaene, 2009).

Early research on modern dyslexia characterized it as a visual pathology which could be described as "congenital word blindness". This theory was based on the reversal errors commonly seen in people suffering from dyslexia (Ex. mistaking "saw" for "was"). In 1925 Orton termed this phenomena "stephosymbolia", meaning "twisted symbols" and hypothesized that it arose due to a problem with hemispheric dominance where the left hemisphere's processing is somehow inhibited and the right hemisphere processes the mirror image of the word being perceived because it is not inhibited (Dehaene, 2009). In 1979 Velluntino showed that these reversal errors are not visual, but linguistic in nature. This was shown by demonstrating that this only occurred with printed text in the language of the dyslexic individual (Dehaene, 2009).

While dyslexia is now thought to have a neurological basis, it was for a long time thought to be completely unrelated to brain pathology. This was because analysis of of brain anatomy (via MRI) showed no difference between the brain of someone with dyslexia and someone without dyslexia. Dyslexia was given a neurological perspective once it was shown that it ran in families (Dehaene, 2009).

Causes
Even though dyslexia has been observed and studied for over 100 years, the exact cause has only recently begun to become clear. This is most likely because dyslexia has many disorders which may seem to be causing it, but might actually just co-occur with dyslexia. For example, deficits in categorical perception, where one has difficulty making the distinction between syllables, often occurs in individuals with dyslexia but has also been shown to extend beyond language. This problem may, in part, cause dyslexia or it might just commonly occur along side it (Dehaene, 2009).

Neurological Components
Since the left temporal lobe is generally where language functions are dominant, it is the most likely place for any issues to occur in dyslexia. Indeed, most brain-imaging studies show a reduction in activity in the left temporal lobe of people with dyslexia compared to that of people without dyslexia. This under activity can be seen early in life and the lack of activity tends to correlate with the severity of the individual's reading impairment (Dehaene, 2009). It's also been shown through neuro-imaging studies that right prefrontal mechanisms are involved in reading difficulties and reading improvement (Hoeft et al., 2010).

Interestingly, the Broca's area of the brain tends to be over activated in people with dyslexia. This is seen as compensatory behavior in that the brain is attempting to use its speech production faculties to make up for its lack of speech decoding faculties. This same type of compensatory activation can be seen when looking at the lateralization of activity when a person with dyslexia tries to read. Ordinary readers show brain activation mostly within the left hemisphere, while those with dyslexia tend to have more activation in the right hemisphere. This reflects their lack of access to phonology (Dehaene, 2009; Beaton, 2004).

Many brain-imaging studies have suggested a link between difficulties in visual processing and the phonological deficits seen in people with dyslexia. People with dyslexia don't seem to be able to simultaneously recognize all the letters that make up a word. This anomaly explains their slow reading speeds (Dehaene, 2009; Beaton, 2004). Studies have also suggested a link between the phonological ability of people with dyslexia and decreased working memory capacity (Jeffries & Everatt, 2004).

Studies have also shown that there tend to be abnormal clusters of neurons around the areas of the brain which are related to language. These clusters have been shown to be caused by anomalous neuronal migration early in life which causes the neurons to group together in these specific areas rather than evenly distributing throughout the brain like they're supposed to. As the brain develops, this causes disorganization and impacts the neuronal connections negatively. It has been theorized that these disruptive neuron bundles may cause a disconnect of the left hemisphere from the rest of the brain, which would explain the lack of access to phonology. Why it is that these neurons decide to cluster around the language areas of the brain is currently unknown (Dehaene, 2009).

Phonological Components
At the core of dyslexia is a problem with phonological decoding, the conversion of written symbols into speech sounds. Specifically, people who suffer from dyslexia seem to have difficulty processing phonemes. This has been seen in studies where people suffering from dyslexia are given a phonemic awareness test. Typically, a person with dyslexia will be impaired in their ability to make rhyme judgments, segment words into component phonemes, and recombine speech sounds to form new spoonerisms (Dehaene, 2009).

Longitudinal studies conducted in Finland followed children with and without dyslexia to assess the association between dyslexia and phonological ability. Results indicate that there is a strong link between early phonological ability and dyslexia. Children with dyslexia seem to suffer from a phonological misrepresentation. Poor functioning at this level of processing leads to poor functioning association between spoken language and the symbols used to represent it (Dehaene, 2009; Beaton, 2004). As well, studies have suggested that there are less integrated cross-modal and intra-modal temporal processing systems in children with dyslexia compared to people without dyslexia (King, Wood, & Faulker, 2007).

While most instances of dyslexia can be characterized by poor performance in phonological processing, recent research suggests that dyslexia has a more fundamental cause. This stems from biological evidence that dyslexia may be linked to motor and sensory difficulties caused by defective genetics. Errors in phonological processing would be a result of these more basic causes (Dehaene, 2009; Beaton, 2004).

Genetic Components
Twin studies conducted by DeFries, Fulker, and LaBuda (1987) as well as Petryshen et al. (2001) show heritability estimates ranging from as low as 0.5 to as high as 0.93, suggesting that dyslexia has a strong genetic component. It has been shown that this genetic component is especially strong in people who have both a high IQ and dyslexia (Davis, Knopik, Olson, Wadsworth, & DeFries, 2001; Pennington & Olson, 2001). While empirical evidence strongly suggest a genetic component to dyslexia, it is not a "monogenic" (linked to a single gene) disorder. Many genes work together to create the ability to read and dyslexia disrupts enough of them to dramatically hinder this ability (Dehaene, 2009; Beaton, 2004). In fact, recent genetic studies have suggested that there are four genes which may be the cause(s) of dyslexia (Pennington, McGrath, & Smith, 2009).

Diagnoses
Dyslexia is diagnosed based on the symptoms which are presented in the individual, their background information, and behavioral observations made to assess the validity of their symptoms (Pennington, Peterson, and McGrath, 2009). Symptoms and assessments are compared against the DSM-IV diagnostic criteria for reading disorder to determine whether or not an individual has dyslexia (American Psychiatric Association [DSM-IV-TR], 2000).

Presenting symptoms
People suffering from dyslexia have key symptoms which characterize their disorder and determine diagnoses and treatment. The primary symptoms are a difficulty in learning to read and spell that cannot be attributed to an un-enriching childhood, mental retardation, or a sensory deficit. These symptoms can be assessed through secondary symptoms through behavioral observation. Secondary symptoms include: difficulty reading aloud, difficulty learning phonics, slow reading or writing speed, number or word reversals, and unusual reading or spelling errors. Most individuals with dyslexia also exhibit a tendency towards anxiety and depression (Pennington, Peterson, & McGrath, 2009).

Symptoms may change over time and may be confounded by adaptations by the individual. While they find it difficult to read (slower reading times, misreading), they may enjoy reading and do it regularly. This makes it difficult to diagnose dyslexia later in life (Pennington, Peterson, and McGrath, 2009). Studies have shown, however, that the spelling ability of people with dyslexia remains constant over time (Bourassa & Treiman, 2008).

History
Individuals with dyslexia do not tend to have any extreme events in their past which would influence the disorder. As well, they do not tend to be delayed in developmental milestones, though some speech and articulation delay may be exhibited. The three types of histories which tend to characterize dyslexia are family history, reading and language history, and school history (Pennington, Peterson, & McGrath, 2009).

Family history
Since it has been shown that dyslexia has a genetic component which runs in families, the first and second order family members of an individual with dyslexia tend to exhibit dyslexia. When diagnosing someone with dyslexia it is common practice to examine their parents and grandparents language abilities (Pennington, Peterson, & McGrath, 2009; DeFries, Singer, Foch, & Lewitter, 1978).

Reading and language history
When symptoms occurred and how severe they were is collected from accounts by friends and family. Accounts made by parents and teachers are usually examined the most (Pennington, Peterson, & McGrath, 2009).

School history
Accounts of ability on school work and in school activities that involve reading and writing is reported by teachers. Difficulties are usually obvious by first or second grade but can be seen as early as kindergarten. School histories may not be readily available if an individual is not diagnosed until their teenage years (Pennington, Peterson, & McGrath, 2009).

Behavioral observations
Usually, spelling and reading tasks are given to an individual to assess their symptoms. It is important to pay attention to what type of tasks the individual does poorly on. Generally, people with dyslexia will do better on tasks which do not have a time limit. There are four main errors to look for on spelling and reading tasks:

i) Errors on function words. This is when an individual makes a substitution for a preposition or an article. For example, interchanging "a" and "the" in a sentence.

ii) Visual errors, when an individual makes substitutions for content words within a sentence.

iii) Lexicalizations, the realization of the meaning of a word, when they read non-words.

iv) Disfluency, irregular breaks or utterances in speech.

As well, the individual's attitude towards reading should be assessed. It is common that individuals with dyslexia exhibit a negative attitude, such as shame or embarrassment, towards the act of reading and do not enjoy reading (Pennington, Peterson, & McGrath, 2009). Once an individual has been shown through observation and history to potentially be afflicted with dyslexia, appropriate assessments of their level of functioning must be made in order to determine how to treat them (Hoien & Lundberg, 1997).

Assessments
Using tests allows us to assess the strong and weak sides of the individual and to find what factors prevent them from reading effectively. These tests are not used to provide diagnostic categories, but to act as a guide for proper remediation for therapists and teachers. Some assessments are informal and fun for the individual, while others are typical, formal surveys. As a general rule there are no distinct categories as a result of these assessments, each individual has their own, unique case and should be dealt with based on their singular combination strengths and weaknesses (Hoien & Lundberg, 1997). Here we will detail the purpose of each category of assessment.

Word decoding problems
These assessments investigate the strategies that individuals use for decoding single words, how well those strategies work, and the reasons why those strategies are not working as effectively as they could be (Hoien & Lundberg, 1997).

Spelling
The spelling mistakes made by the individual are examined to determine which strategies they use when spelling words and how these strategies function. There are many tasks which can be used to assess spelling skill: dictation of words, writing nonwords, dictation of sentences, and free compositions. Specially designed tasks have also been created to allow for easy examination of strategies that are being used and the level of skill for each. How difficult a task is must be adjusted for by age and skill level of the individual (Hoien & Lundberg, 1997).

Reading text aloud
Individuals are given texts of increasing difficulty to read. This determines whether or not the difficulty of the text affects their reading ability. Other information can also be derived, such as how the individual reads (ex. "do they sound out the words?") (Hoien & Lundberg, 1997).

Reading comprehension
Individuals are instructed to read a short text which is followed by a short quiz on the content of the text. Sometimes individuals are given a text with every fifth or sixth word is removed and they are asked to read along and fill in the blanks; this is called a cloze test. Another assessment consists of the individual reading a text and then being presented with five or six pictures and being asked to choose the picture which best fits the content of the text. Typically the individual is also quizzed on how familiar they are with the background information involved in which ever text they are asked to read (Hoien & Lundberg, 1997).

Metacognition
This assessment is closely tied to the assessment of reading comprehension.( the word assessment twice in a short sentence) It simply involves talking to the individual while they are reading. This allows the person who is assessing the individual to get a sense of how aware the individual is of different reading strategies and goals and how they can manipulate them (Hoien & Lundberg, 1997).

Obstacles
These can include medical problems which make it physically difficult for an individual to read, such as poor sight or deafness, as well as psychological problems, such as poor intellectual ability. The purpose of assessing these problems is to find which ones can be remedied independently of the intervention of dyslexia, which difficulties must be worked around during intervention, and whether or not their reading difficulty is caused by dyslexia or something else (Hoien & Lundberg, 1997).

Interventions
Most of the interventions of dyslexia focus on remediation of particular problems through exercises or therapy. The goal of remediation is to make the individual a more efficient reader by using as many strategies as possible. Specific interventions can be divided between those that are effective for adults and those that are effective for children because adults have lived longer with their disorder than children have. Because of the difference in time, adults may have developed background knowledge and techniques to deal with their disability. Due to this potential difference, interventions that worked with children not be as effective with adults and vice versa (Johnson, 1986). Interventions in this chapter will not be separated into adult and child interventions, however, as that is beyond the scope of this text. What will be presented are general remediation methods which can be applied to individuals with dyslexia of all ages.

General principles of remediation
Individuals who suffer from dyslexia benefit from particular principles in remediation and do not benefit from others. Early identification and help, basic phonological work, direct instruction, multisensory stimulation, overlearning, and a good learning environment all benefit the individual in remedying their disorder. Positive punishment for failure, derogatory remarks, visual and auditory perceptions training, psychotherapy, and non-activity do not support the remediation of their difficulties (Hoien & Lundberg, 1997).

Remediation processes and programmes
At the beginning of remediation the individual is made aware of the many strategies they can use to increase their efficiency as a reader. They discuss the strategies they already use and find which are more effective than others and try out some new ones which may be better. Simply by becoming more conscious about the options they have to remediate their issues they become more proficient. As well, early on focus is placed on structural analysis of language rather than phonics and strategies which allow the individual to identify words through examination of the meaning units. This is done because most people with dyslexia tend to overemphasize the importance of phonics for comprehension (Johnson, 1986).

One of the major goals of intervention is to increase the individuals sight vocabulary. This is increased by teaching them strategies for recognizing particular words. Content words, such as "cat" or "clothing", are emphasized in the form of nouns and verbs because they are easier to retain than non-content words, like "the" or "is", due to the mental imagery attached to them which makes them easier to retain. Non-content words are emphasized in context of words that the individual has already learned (Johnson, 1986).

As words are added to the individuals sight vocabulary, structural analysis is given more focus. Suffixes and prefixes as well as verb endings are added to the words that are being learned to show how they cause variation amongst words. Lists and homework exercises are given to practice the differences between the words on their own and the words with the new additions (Johnson, 1986).

Phonetic analysis is remediated through the learning of words with consistent phoneme-grapheme correspondence and which vary in length. For example, "an, and, sand, stand, strand" would be a block of these words. This is supplemented with the presentation of the learned words and the instructions to find the similarities and differences between all the words as well as word identification exercises (ex. "Does this say 'sand'? Why not?"). This training seems to enhance phonetic segmentation, temporal organization, visual scanning, and crossmodal integration (Johnson, 1968).

To decode multisyllabic words individuals are presented with words as their wholes as well as broken down into their syllabic components with spacing between each syllable. They are asked to say the word as a whole and as separate syllables. Syllables are then presented separately so that the individual can learn how to combine them and create new words. These exercises are designed to improve understanding of the abstract rules which allow people to recognize words based on their syllables and how to recombine syllables into whole words (Johnson, 1986).

There are many programmes which use these general techniques as well as variations and expansions on them. Some focus specifically on decoding difficulties, such as the VAKT method, the Orton method, the Lindamood Auditory Discrimination in Depth programme, the Reading Recovery programme, and the Early Steps programme. Others focus on improving reading comprehensions, like the CRISS programme (Hoien & Lundberg, 1997).

Remediation and technical aids
It has been shown that printed text which is accompanied by audio recordings of the text being read aloud (Ex. audio books or podcasts) can help increase reading skill. This is ideal when the text is simple and the individual listens to the recording and follows along in the text, reading aloud, at the same time. This provides an auditory (listening to the recording), motor (reading/repeating aloud), and visual (reading the printed text) experience which increases the strength of the connections between different sensory inputs. Working with aids like these also tends to increase an individuals attitude towards reading as well as their ability to concentrate and listen (Hoien & Lundberg, 1997).

Learning exercise
This is a learning exercise designed to help you review some of the key concepts from the chapter and think more critically about the content.

 * 1) Imagine that you are a doctor in 1903. A young man comes to your office complaining that he is no longer able to read. He tells you that words get "flipped around" and that he wasn't like this before. How would you, given the thinking of the time, explain what is wrong with the young man?
 * 2) If you were using a brain imaging technique (MRI, for example) to look at someone with dyslexia, what areas of activation would you see? How does this activation pattern differ from that of someone who doesn't have dyslexia? Would seeing this pattern of activation be enough for an official diagnosis and treatment? Why or why not?
 * 3) If you were a doctor in 1974 (the year after the MRI is invented) and you are looking at an MRI scan of an individual who has been diagnosed with dyslexia, to you, would the MRI show anything significant? What would you conclude about the nature of dyslexia?
 * 4) There are three different types of causes for dyslexia: genetic, phonological, and neurological causes. If someone has developmental dyslexia (dyslexia from birth), which of these three causes would be the most fundamental? Why is this? Please use an example to help explain your answer.
 * 5) Jimmy is 23. He enjoys reading and displays some of the basic symptoms of dyslexia: word reversals, slow reading speed, and trouble reading aloud. If you were in the process of diagnosing Jimmy, how would you start your investigation of his difficulties? What would be some further assessments you would use to specify his treatment and why would you use them?
 * 6) When looking at an individual's family history, reading history, and school history what would be examples of things which would stand out and suggest that the individual has dyslexia? Don't use examples from this chapter.
 * 7) You are observing a child reading and attempting to figure out if she has dyslexia. There are five characteristic errors that you should look for. Give at least two examples for each of the characteristic errors and explain why you chose those them and what it tells you about the child's reading difficulties.
 * 8) Once you have diagnosed an individual with dyslexia, why would you bother with assessments? Why not just send them into intervention sessions? Use an example.
 * 9) There are principles of remediation which do no benefit the individual. What are they and why don't they help? Use detailed examples for each principle.
 * 10) If you were treating someone who has dyslexia, what would be two examples of results you would plan to see in your patient and how would you try to achieve them through remediation? Why would you choose these methods?

title: Psycholinguistics/Dyslexia


text:
User:EGM6341.s11.TEAM1.Sujin.HW1

=Problem 4: Infinity Norms=

Given
for $$ x\epsilon\ [0,1] $$ and

for $$x \epsilon\ [0,1] $$

Find
1) Plot $$ f(x) \ $$ and $$ g(x) \ $$ 2) Solve for:

Solution
{| style="width:100%" border="0"
 * style="width:95%" |
 * style="width:95%" |

1) Plot $$ f(x) $$ and $$ g(x) $$
(i)Plot $$f(x)=3x+5x^3\ $$  Matlab code:

(ii)Plot $$g(x)=\sinh\ x$$  Matlab code:

(iii)Plot $$f(x)-g(x)=(3x-2x^3)-(\sinh x)\ $$  Matlab code:

2)Find infinity norms
$$ ||f(x)||_{\infin}=1.4142 $$

$$ ||g(x)||_{\infin}=1.1752 $$

$$ ||f(x)||_{\infin} - ||g(x)||_{\infin}=0.2390$$

$$ ||f(x) - g(x)||_{\infin}=0.7392$$ As a result, we can verify the property of 'Infinity norm' as presented in lecture note, (1) p.5.3. Ref: Lecture Notes [[media:nm1.s11.mtg5.djvu|Mtg 5 (d)]]
 * }

Author --Sujin 00:26, 19 January 2011 (UTC)EGM6341.s11.TEAM1.JANG

title: User:EGM6341.s11.TEAM1.Sujin.HW1


text:
God/The iam conjecture

A Scientific Proof that God Exists

(The proof below is done by contradiction [which is an acceptable method in mathematics]. However, I recognize some math purists will not accept it based on that fact.)

It's not a tautology if we accept Q.E.D. as a fact. If we accept Q.E.D. as a fact, we accept that there is no other way to deterministically explain the explosion of a singularity in 5D (other than the Prime Cause), and we are not in a cyclic universe.

We do not have to develop Iam space to prove the conjecture. All we have to do is simply develop a realistic version of Feynman's virtual particle scheme -- something like charged anti-photons in 5D.

To state the conjecture formally: *For example, take a ruler -- it's one dimensional. However, if one were to bend it, it would require two dimensions *For another example, take a piece of paper -- it's two dimensional. However if one were to bend it, it would require three dimensions
 * 0.a. We live in a 5D universe which is somewhat trivial to prove:

*There's two options here: total overhaul or incorrect.. only time will tell but.. *One would assume "incorrect" (based on the incorrect primary assumption that   *Elementary particles are probability waves interacting via virtual bosons) *We assume this but don't acknowledge it   *I've developed temporal relativity theory which is equivalent to    *General relativity minus Lense-Thirring (twisting of space)
 * 0.b. The Standard Model will soon be proved incorrect due to non-detection of Higgs Particles
 * 0.c. Time is elastic just like space

1. Feynman's QED is accepted fact, based on his virtual particle scheme 2. A singularity cannot explode in any deterministic way in 5D (x,y,z,t,C)[Where C represents spacetime curvature at x,y,z,t as described in other documents] 3. Our universe is not cyclic (successive explosions/implosions) 4. We can develop a realistic particle scheme in 5D that mimics Feynman's virtual particles [Such as the proposed charged anti-particle scheme recently described elsewhere]

Conclusion: If all 4 statements above are correct, then God must exist as the Prime Cause.

1 is true, 2 needs proving, 3 appears true, and 4 is trivial.

I'm most certainly not a genius but it doesn't take one to accomplish 4. It just takes a certain perspective or amount of insight. If any physicist worth his/her salts pursued a similar path as i have, they most certainly would have developed this theory in much less time (3 years vs. 30 years). So again, i'm not criticizing physicists or blaming them for anything.. The above realization was the simple result of holding to a way of looking at things for long enough (and did not include the conjecture itself!) .. Put another way, I have always believed in God, but i never believed we could prove God exists!

I promised to 'shoot myself in the foot' if i ever wrote Stephen Hawking again (because I wrote to him too many times about these ideas). (I asked him to allow me to use a toy gun in case I was right.) ;) So please don't make me use a real gun on my own foot! Write to Hawking for me! It should be trivial for him to prove 2 .. Can you imagine that? A guy who continually avoids God proves He exists! How ironic! (In all defense of Stephen, he probably believes in God; he just does not want to develop science based on Him.)

sam iam / salvatore gerard micheal, 2011/JAN/20, Maeaeb, Thailand Micheals 18:48, 19 January 2011 (UTC)

title: God/The iam conjecture


text:
Psychology of online social networking

Psychological aspects of online social networking are a relatively new area of research - or at least research is some way behind popularity and ubiquity of online social networking behaviours and their associated impacts on people's lives.

Possible research questions

 * 1) What are users' main motivations for using online social networking services? To what extent are these motivations satisfied? Does the match between motivations and satisfactions predict usage and retention? (Based on Clary and Snyder's functional approach to volunteerism motivation)
 * 2) What are "effective" and "ineffective" uses of online social networking? (i.e., how does use of online social networking services help or hinder people's lives?)
 * 3) How can effective uses be fostered and latter uses minimised?
 * 4) How stressful or beneficial do people find use of online social networking services to be?
 * 5) What coping functions does online social networking provide?
 * 6) How effective is online social networking as a coping method for dealing with different types of hassles and stress?
 * 7) How do people envisage their "ideal" online social networking environment and usage?
 * 8) What is the role of personality in prosocial and antisocial behaviour in online social networking?
 * 9) What are users' most and least favourable aspects of their online social network usage?
 * 10) What is the effect of online social networking on high school student relationships?
 * 11) To what extent does online social networking use increase or decrease social anxiety (and why)?
 * 12) To what extent does online social networking affect shyness?
 * 13) What is the effect of individuals' use of online social networking public and private self-awareness?

title: Psychology of online social networking


text:
User:Egm6341.s11.team5

=  Homework page = Homework #1

Homework #2

Homework #3

Homework #4

Homework #5

Homework #6

Homework #7

=  Members  = Junsu Shin

Sangmin Oh

Cavalcanti,Eunice H

Davis, James

Aditya Raghunathan

Reiss, Phillip J

=  Class page  = EGM 6341 Class wiki

Spring 2011 Report table

Spring 2011 Lecture plan

title: User:Egm6341.s11.team5


text:
User:Egm6341.s11.team5/HW1

= Problem 1 - L'Hôpital's rule = From (meeting 3 page 1)

If $$\displaystyle f(x)= \frac{e^x-1}{x}$$,

Find

 * $$\displaystyle \lim_{x \to 0}f(x)$$ and plot $$\displaystyle f(x)$$ for $$\displaystyle x \in [0,1] $$.

Solution
Using L'Hospital's Rule, the limit can be evaluated. L'Hospital's Rule:
 * {| style="width:100%" border="0" align="left"

\lim_{x \to 0}\frac{g(x)}{h(x)}=\lim_{x \to 0}\frac{g^{'}(x)}{h^{'}(x)} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (1)
 * }
 * }

Applying the Rule:

As a result, the limit is computed as follows.
 * $$\displaystyle g(x)=e^x-1$$,|| $$\displaystyle g^{'}(x)=e^x$$
 * $$\displaystyle h(x)=x$$, || $$\displaystyle h^{'}(x)=1$$
 * }
 * $$\displaystyle h(x)=x$$, || $$\displaystyle h^{'}(x)=1$$
 * }
 * $$\lim_{x \to 0}\frac{e^x-1}{x}=\lim_{x \to 0}\frac{e^x}{1}$$
 * $$\lim_{x \to 0}\frac{e^x}{1}=\frac{1}{1}=1$$

Hence,
 * {| style="width:100%" border="0" align="left"

$$\displaystyle \ \lim_{x\rightarrow 0} \frac{e^{x}-1}{x} \ = \ 1 $$
 * style="width:30%; padding:10px; border:2px solid #8888aa" align="center" |
 * style="width:30%; padding:10px; border:2px solid #8888aa" align="center" |
 * }
 * }
 * }

Plot: Matlab code:
 * {| style="width:100%" border="0" align="left"

Plot: Matlab code:
 * style="width:30%; padding:10px; border:1px solid #888888" align="center" |
 * style="width:30%; padding:10px; border:1px solid #888888" align="center" |
 * }
 * }
 * }
 * {| style="width:100%" border="0" align="left"

 * style="width:30%; padding:10px; border:1px solid #888888" align="center" |
 * style="width:30%; padding:10px; border:1px solid #888888" align="center" |
 * }
 * }
 * }

Author and proof-reader
[Author] Oh

[Proof-reader] cavalcanti, Shin, Raghunathan, Reiss

= Problem 2 - Taylor series expansion = From (meeting 3 page 4)

If $$\displaystyle f(x)= \frac{e^x-1}{x}$$,

Find

 * $$\displaystyle P_n(x)$$ and $$\displaystyle R_{n+1}(x)$$ of $$\displaystyle e^x$$ and $$\displaystyle \frac{e^x-1}{x}$$.

Solution
Through Taylor series, a function $$\displaystyle f(x) $$ can be decomposed into $$\displaystyle P_n(x)$$ and $$\displaystyle R_{n+1}(x)$$. From the lecture notes p.3-3, $$\displaystyle P_n(x)$$ and $$\displaystyle R_{n+1}(x)$$ is defined as

 * {| style="width:100%" border="0" align="left"

P_{n}(x)=f(x_{0})+\frac{(x-x_{0})}{1!}f^{(1)}(x_{0})+\cdots+\frac{(x-x_{0})^{n}}{n!}f^{(n)}(x_{0}) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (2)
 * }
 * }

 * {| style="width:100%" border="0" align="left"

R_{n+1}(x)=\frac{1}{n!}\int_{x_{0}}^{x}(x-t)^{n}f^{(n+1)}(t)dt=\frac{(x-x_{0})^{n+1}}{(n+1)!}f^{(n+1)}(\xi), \quad \xi\in[x_{0},x] $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (3)
 * }
 * }
 * }

 * $$\displaystyle f(x)=e^x $$
 * We know that n-th derivative of function $$\displaystyle e^x$$.
 * {| style="width:100%" border="0" align="left"

\frac{d^{(n)}}{dx^{(n)}}(e^x) = e^x $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (4)
 * }
 * Substitute Eq.(4) into Eq.(2) to obtain $$\displaystyle P_n(x)$$.
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

P_n(x)=e^{x_0}+\frac{(x-x_0)}{1!}e^{x_0}+\cdots+\frac{(x-x_0)^n}{n!}e^{x_0} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (5)
 * }
 * Simplify Eq.(5).
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

\begin{align} P_n(x)&=\bigl(1+\frac{(x-x_0)}{1!}+\cdots+\frac{(x-x_0)^n}{n!}\bigr)e^{x_0}\\ &=\sum_{i=0}^{n}\bigl(\frac{(x-x_0)^i}{i!}\bigr)e^{x_0} \end{align} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (6)
 * }
 * }

 * Substitute Eq.(4) into Eq.(3) to obtain $$\displaystyle R_{n+1}(x)$$.
 * {| style="width:100%" border="0" align="left"

R_{n+1}(x)=\frac{(x-x_{0})^{n+1}}{(n+1)!}e^{\xi}, \quad \xi\in[x_{0},x] $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (7)
 * }
 * The result of Taylor series expansion on $$\displaystyle f(x)=e^x $$ is shown below.
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

$$\displaystyle \begin{align} P_n(x)&=\sum_{i=0}^{n}\bigl(\frac{(x-x_0)^i}{i!}\bigr)e^{x_0} \\ R_{n+1}(x)&=\frac{(x-x_{0})^{n+1}}{(n+1)!}e^{\xi}, \quad \xi\in[x_{0},x] \end{align} $$
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * }
 * Also, the expansion becomes as below if $$\displaystyle x_0=0 $$.
 * }
 * Also, the expansion becomes as below if $$\displaystyle x_0=0 $$.

 * {| style="width:100%" border="0" align="left"

$$\displaystyle \begin{align} P_n(x)&=\sum_{i=0}^{n}\bigl(\frac{x^i}{i!}\bigr) \\ R_{n+1}(x)&=\frac{x^{n+1}}{(n+1)!}e^{\xi}, \quad \xi\in[0,x] \end{align} $$
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * $$\displaystyle (8)$$
 * }
 * }

 * $$\displaystyle f(x)=\frac{e^x-1}{x} $$
 * To perform Taylor series expansion on $$\displaystyle f(x)=\frac{e^x-1}{x} $$, we need to exploit Eq.(8). Assume the result of the expansion is $$\displaystyle P^{'}_n(x) $$ and the remainder is $$\displaystyle R^{'}_n(x) $$.
 * Then, $$\displaystyle P^{'}_n(x) $$ can be obtained as follows.
 * {| style="width:100%" border="0" align="left"

\begin{align} P_n(x)-1&=\sum_{i=0}^{n}\frac{x^i}{i!}-1 \\ &=\bigl(1+\sum_{i=1}^{n}\frac{x^i}{i!}\bigr)-1 \\ &=\sum_{i=1}^{n}\frac{x^i}{i!} \end{align} $$ \begin{align} P^'_n(x)&=\frac{P_n(x)-1}{x} \\ &=\sum_{i=1}^{n}\frac{x^{i-1}}{i!} \end{align} $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (9) $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (10) $$
 * }
 * Similarly, $$\displaystyle R^'_{n+1}(x)$$ can be computed. Note here that the term $$\displaystyle -1$$ in the function $$\displaystyle f(x)$$ is already taken into account in $$\displaystyle P^'_n(x)$$. Therefore, $$\displaystyle R^'_{n+1}(x)$$ can be computed by dividing $$\displaystyle R_{n+1}(x)$$ by $$\displaystyle x $$.
 * {| style="width:100%" border="0" align="left"

\begin{align} R^'_{n+1}(x)&=\frac{R_{n+1}(x)}{x} \\ &=\frac{x^n}{(n+1)!}e^{\xi}, \quad \xi\in[0,x] \end{align} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (11)
 * }
 * Hence, the expansion result of $$\displaystyle f(x)=\frac{e^x-1}{x} $$ is shown as:
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

$$\displaystyle \begin{align} P^'_n(x)&=\sum_{i=1}^{n}\frac{x^{i-1}}{i!} \\ R^'_{n+1}(x)&=\frac{x^n}{(n+1)!}e^{\xi}, \quad \xi\in[0,x] \end{align} $$
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="center" |
 * $$\displaystyle (12)$$
 * }
 * }

Author and proof-reader
[Author] Shin

[Proof-reader] Oh

=Problem 3 - Prove IMVT= From (meeting 4 page 3)

If $$\displaystyle f(x)$$ and $$\displaystyle w(x)$$ are continuous non-negative functions $$\in [a,b]$$

Find

 * {| style="width:100%" border="0" align="left"

\int _a^bf(x) w(x)dx=f(\zeta ) \int_a^b w(x) \, dx $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

Solution
'''Solved via combination of Mean value theorems for integration, Wikipedia

and Egm6341.s10.team3.sa/HW1 '''

First, since $$\displaystyle w(x) $$ is arbitrary and non negative we will set it equal to I

 * {| style="width:100%" border="0" align="left"

I=\int_a^b w(x) \, dx $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (13)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

\int_a^b w(x) f(x) \, dx=f(\zeta ) I $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (14)
 * }
 * }

Next we will set constants at the extreme values of $$ f(x)\in [a,b]$$

 * {| style="width:100%" border="0" align="left"

M=\max (f(x)),m=\min (f(x)) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (15)
 * }
 * }

Therefore, from the Extreme Value Theorem

 * {| style="width:100%" border="0" align="left"

m I \leq \int_a^b w(x) f(x) \, dx\leq M I $$ $$ Evaluating and subsituting in from above
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (16)
 * }
 * }

 * {| style="width:100%" border="0" align="left"

m \leq \frac{1}{ I } \int_a^b w(x) f(x) \, dx\leq M $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (17)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

Z=\frac{1}{ I } \int_a^b w(x) f(x) \, dx $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (18)
 * }
 * }

 * {| style="width:100%" border="0" align="left"

\min (f(x))\leq f(\zeta )\leq \max (f(x)) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (19)
 * }
 * }

Since $$\displaystyle f(x)$$ is continous from $$\displaystyle M$$ to $$\displaystyle m$$ there exists $$\displaystyle \zeta \in [a,b]$$ at $$\displaystyle f(\zeta)=Z $$ .
 * {| style="width:100%" border="0" align="left"

$$\therefore f(\zeta)=\frac{1}{\int_a^b w(x) \, dx} \int_a^b w(x) f(x) \, dx$$
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="left" |
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="left" |

 * }
 * }
 * }

Egm6341.spring-11.5.D 19:30, 24 January 2011 (UTC)

If $$\displaystyle w(x)$$ is strictly negative

 * {| style="width:100%" border="0" align="left"

f(\zeta)=\frac{1}{(-1) \cdot \int_a^b w(x) \, dx} \cdot (-1) \cdot \int_a^b w(x) f(x) \, dx $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (20)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" align="left" |
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="left" |

$$\therefore f(\zeta)=\frac{1}{\int_a^b w(x) \, dx} \int_a^b w(x) f(x) \, dx$$

 * }
 * }
 * }

Author and proof-reader
[Author] Davis 18:28, 24 January 2011 (UTC)

[Proof-reader] cavalcanti, Oh, Raghunathan, Shin

=Problem 4 - Plot and find infinity norm of Functions= From (meeting 5 page 3)

 * If $$\displaystyle f(x)=3x-2x^3$$, where $$\displaystyle x \in[0,1]$$ and
 * if $$\displaystyle g(x)=\sinh(x)$$, where $$\displaystyle x \in[0,1]$$

Find
1. $$\displaystyle \left \| f \right \|_{\infty }\ $$, $$\displaystyle \left \| g \right \|_{\infty }\ $$ and $$\displaystyle \left \| f - g\right \|_{\infty }\ $$ 2. Plot $$\displaystyle f, g,$$ and $$\displaystyle f-g$$

Solution
1.The definition of the infinity norm is as follows:
 * {| style="width:100%" border="0" align="left"

\left \| f(x) \right \|_{\infty }\ = \max \left| f(x) \right| $$ $$ Similarly,
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (21)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\left \| g(x) \right \|_{\infty }\ = \max \left| g(x) \right| $$ $$ Also, by definition:
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (22)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

\left \| f - g\right \|_{\infty }\ = \max \left| f(x) - g(x)\right| $$ $$ 2. In the interval of $$ [0,1]$$, the norms are as follows:
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (23)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

$$ \begin{align} \left \| 3x - 2x^3 \right \|_{\infty }\ &= 1.4142 \text{ at } x = 1/\sqrt{2} \\ \left \| \sinh (x) \right \|_{\infty }\ &= 1.1752 \text{ at } x = 1 \\ \left \| f - g\right \|_{\infty }\ &= 0.739161 \text{ at } x = 0.554 \\ \end{align} $$ 3. The plot of both functions are shown in the interval $$[0,1]$$, followed by the octave code. Plot: Octave code:
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="left" |
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="left" |
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

octave-3.2.4.exe:1> x=[0:0.001:1]; octave-3.2.4.exe:2> y=(3*x)-(2*x.^3); octave-3.2.4.exe.3> y2=sinh(x); octave-3.2.4.exe:4> y3=y-y2; octave-3.2.4.exe:5> plot(x,y,"-10",x,y2,"-11", x, y3, "-12") octave-3.2.4.exe.6> legend('f(x)', 'g(x)', 'f-g')
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="left" |
 * style="width:50%; padding:10px; border:2px solid #8888aa" align="left" |
 * }
 * }
 * }

Author and proof-reader
[Author] cavalcanti, Reiss, raghunathan

[Proof-reader] Oh, Raghunathan, Shin

= References =
 * L'Hospital's Rule, WolframMathworld
 * Mean Value Theorems for integration, Wikipedia
 * Extreme Value Theorem, Wikipedia

=Contributing members=

Signatures
Oh - Solved HW1.1 and proof-read HW1.2, 1.3 and 1.4 Shin - Solved, posted HW1.2 and proof-read HW1.1, HW1.3, HW1.4 Raghunathan - Solved HW1.1,1.3,1.4 manually and reviewed HW1.1, 1.3 and 1.4 Cavalcanti - Solved problems manually, reviewed HW1.1 and posted HW 1.4 EGM6341.S11.team5.cavalcanti 02:10, 26 January 2011 (UTC)

title: User:Egm6341.s11.team5/HW1