When it comes to properly mean “powered by” in Spanish web pages, a lot of spanish-speaking users don’t seem to agree on how to properly mean that, as can be seen from the following links:

http://www.spanishdict.com/answers/144054/how-do-you-say-powered-by-in-espanol

http://forum.wordreference.com/showthread.php?t=329580

Not even Google and Microsoft seem to find a sounded way of meaning the above:

http://es.bab.la/diccionario/ingles-espanol/powered-by

I realized that this is an even worse problem among those hispanics and second generation latinos in the U.S. that are too “americanized” (if that is a valid term).

The Solution:

When we have problems finding terms from different languages with equivalent meanings, the best that we can do is to stop forcing translations and start describing what we want to say. This is a kind of a descriptive strategy.

For instance, according to http://arl-shipzine.com/issue-2-powered-by , “powered by” implies the notion of a service being “provided by”.

So, following the descriptive strategy, “provisto por” is a more appropriate option than ”impulsado por”, “potenciado por”, “generado por”, “auspiciado por”, “producido por” and other expressions that sound a bit ridiculous for the context in question. Of course, that’s just my opinion and you don’t have to agree with me.

“Impulsado por”…really? Are you launching a rocket?

“Potenciado por”…really? Are you a battery or power supply?

“Generado por”…really? Are you an electric generator?

“Auspiciado por”…really? Are you sponsoring something?

“Producido por”…really? Are you in a production business?

I know, I know. I’m being sarcastic. Me bad.

What is important to point out is that the above alternatives are subject to misinterpretations, while to imply “a product or service provided by”, o “un producto o servicio provisto por” has only one meaning: a product or service provided by someone, in a b2c (business-to-consumer) or b2b (business-to-business) context. 

At first glance, the above seems trivial, but is not. You would be surprised to see the faces of those latinos that read web content and creatives translated by SEO companies with no knowledge about Spanish or that use automatic translators. Bad translations can ruin any marketing, press release, or link-building campaign.

http://www.miislita.com/images-crawler/images-crawler.php

Who can benefit from this tool?

• Webmasters and designers that want to check for broken images and their resolutions across browsers.
• Site owners checking if other sites are infringing on their images, pictures, banners, logos, or icons.
• Users looking for an easy way to find images from newspapers, forums, social networks, or any site.
• Marketing researchers, psychologists, and others interested in studying the power of images.

I think this can be applied to many knowledge domains without making the same mistakes from similar services across the Web.  For now, baby steps.

http://www.miislita.com/binary-similarity-calculator/binary-similarity-calculator.php

We plan to add few more in the future, so more data miners, researchers, and students can benefit from it. We plan to make this a comprehensive project on similarity analysis. For this purposes, several doctoral theses are deployed. Any help, correction, feedback is appreciated.

Another advantage of the above strategy is this:

A set of HREFs may contain information about absolute and relative URLs, visible and hidden links, internal and external file paths, email addresses, css files, local javascript calls, and anchors (#). A subset of HREFs can also be used as pointers to anchor text information. So, a set of HREFs can be more informative than a mere set of links or URLs as it subsumes both.

(http://www.miislita.com/email-crawler/email-crawler.php)

the following features:

1. A User Tracking Session (just find the link and click on it) to view current user data.

2. Search for user email addresses in the top search engines and social networks

Give it a try.

We plan to add the tracking session feature to all our pages. This feature is now visible to gives you an idea of how it works, but can be invisible to users. Geo and search data can be added in a snap.

Why pay monthly fees when you can have your own tracking service, customized to your needs?

This tool was developed to complement The Binary Similarity Calculator, one of our popular tools.

Fractalettes: A Fractal Design Strategy to Color Mining and Learning through Discovery - Based on Fractal Geometry, fractalettes are color palettes within color palettes, where each cell contains color space information and relationships. These types of architectures engage end-users in data mining, critical thinking, and learning through discovery.

At least that’s what is claimed.

http://www.jprr.org/index.php/jprr/article/viewFile/20/8

What it is

The Binary Similarity Calculator (BSC) can be used to compare binary sets, groups consisting of only two types of items or states. These are item sets that can be represented as sequences of 1′s and 0′s.

Who can benefit from it

• Marketing analysts that need to examine Yes/No-type questionnaires about products and services.

• Teachers and examiners that must score Yes/No-type exams or assess plagiarism cases.

• Engineers, mathematicians, and physicists that must evaluate On/Off-type records.

• Statisticians, bioanalysts, and others involved with sequencing analysis.

• To sum up, anyone that uses binary sets.

An editor or owner of a page (in this case, us) end a page with what we call a “Qualified Links” section. A topic to follow is specified. Interested users submit a link to complete a sentence. Then the editor or owner of the page and at its sole discretion decides whether a submission is on topic. If so, the link is promoted to a list of Qualified Links on that page.

The result: the current page becomes more on-topic centered while submitters have a chance to gain more link building real estate. Only quality links are considered using our own criteria. Sure there will be some pros and cons down the road, but at least is an interesting start. Monetization can sure follow the shake.

From the Harlem Shake to the Link Shake: Here it comes the Qualified Links Shake .

Vulnerability scans via search engines. Includes Google scans and Bing reflections.

BTW, here is a list of nice Unicode myths.

http://macchiato.com/slides/UnicodeMyths.pdf

We also found that iterating the 16-color VGA palette, with these rules, the result converges to a 42-color palette. As given below.

Advantages?

The algorithms utilized allow one to:

• reconstruct large palettes with a small set of seed colors.
• store a small set of colors instead of a large palette file.
• build basic palette generators and color tools.
• use an initial palette to discover colors or propose new ones, then use these to expand the initial palette.

For additional information and to verify these findings, visit the The Color Miner page.

The traditional way of presenting color palettes to users is by rendering these as static arrays of colors. This limits users to staring at color squares to make color-color comparisons instead of engaging them in data mining and critical thinking, activities that promotes discovery and learning—in a research or school setting.

When we developed The Color Miner, we did so with a fractal design strategy in mind. As a result, we developed a tool capable of generating what we call fractalettes or palettes within palettes. That is, each cell of a generated palette behaves as a smaller palette, containing color space information and relationships for the current color.

We could iterate the individual cells for ever, but in practice we found that a one-level iteration was a good start to encourage users to investigate color-color, space-space, and color-space relationships, to find basic trends and information patterns. In general, this architecture can be iterated to organize additional attributes and relational data.

http://www.icst.pku.edu.cn/course/ImageProcessing/2012/resource/Color78.pdf

http://en.wikipedia.org/wiki/RGB_color_space

http://www.adobe.com/digitalimag/pdfs/AdobeRGB1998.pdf

http://help.adobe.com/en_US/illustrator/cs/using/WS714a382cdf7d304e7e07d0100196cbc5f-6273a.html

Interesting Amazon-Google Comparison for the last 3 years:

Amazon: #1 in 2013, #4 in 2012, and #8 in 2011.

Google: #4 in 2013, #2 in 2012, and #1 in 2011.

1. For the data in the A1 and B1 cells, I simply entered the following formula into the C1 cell and bingo!

=CHAR(34)&A1&CHAR(34)&CHAR(61)&CHAR(62)&CHAR(34)&B1&CHAR(34)&CHAR(44)

where the unicode numbers 34, 61, 62, and 44 are used to render the double quote, equality, greater than, and comma symbols.

2. Then I just pasted the formula in the remaining cells of column C.

3. Finally, I pasted the result into a php text file, between the parentheses of

$arr=array(  );

and removed the last comma from the last array element.

I know there is an easier way by writing a short macro, but this worked for me just fine.

I hope this saves some time to others.

1. If you are using Spybot Search & Destroy on Windows32 systems, enter

C:\Windows\System32\drivers\etc\hosts

2. Spybot Search & Destroy will list all blocked connections; i.e. those that are redirected to the localhost.

3. You can manually add/delete entries.

4. It is a another layer of security!!

For details, check:

http://winhelp2002.mvps.org/hosts.htm

http://en.wikipedia.org/wiki/Spybot_%E2%80%93_Search_%26_Destroy

http://www.fb10.uni-bremen.de/homepages/wildgen/pdf/GeometryandDynamicsLeonardonew.pdf

The tool set has been around for about a week with some few speed issues, but now you can enjoy it for good. So, what you can do with it? Well, visit the site, try it, and let me know if you like it or if there is room for improvement.

With The Net Miner Tool Set, now anyone can do some basic network security tests. You would be surprise to learn of how many sites are exposing things like php.ini files, making easy the life of attackers, or leaking unnecessary information in their configuration headers.

PS.

Resolving some DNS issues and IE browser issues. Improving things. There will be few tools uploaded this week.

This prompted me to search for even a simpler solution without all the nice features of these editors, but one that just does the mere work of showing code. I came up with the following strategy, tested on recent versions of IE, Opera, Chrome, Safari, and Firefox. I haven’t tested it with older browser versions and cannot claim it will work with those. More tests are necessary to please other programming/validation requirements.

1. Place HTML code into a hidden textarea.

2. Show  it with the following javascript one-line snippet

document.getElementById(‘id’).innerHTML=”<pre><code>”+document.getElementsByTagName(‘textarea’)[index].innerHTML+”</code></pre>”;

Optionally, both the textarea and snippet can be placed right before the closing body tag.

In the snippet, id is the identifier given to a tag container used to show the html code. This container can be a division placed at will in the body section of the document and CSS styled to your heart needs. The index parameter is the index value of the textarea; i.e. [0] if there is only one textarea in the page, [1] if it is the second textarea, and so forth.

When the textarea is replaced by a noscript tag, the snippet seems to work with the above browsers, except with firefox (particularly if the html code itself contains script tags).

PS.

If you care about semantics and SEO, simply move the <pre> and <code> tags from the snippet to the division container. Then add the id to the code tag instead of to the division container, like this:

<div><pre><code id=’id’></code></pre></div>

This makes the snippet even shorter, like this:

document.getElementById(‘id’).innerHTML=document.getElementsByTagName(‘textarea’)[index].innerHTML;

This isolates programming from presentation, which is always a good practice.

PS2 I added single quotes in snippet, so if you simply copy/paste it won’t flag you an error.

Back then my SEO and marketing friends immediately started to see the next “future” for marketing and, of course, porn: teleportation for meetings, events, and SEO Conferences.

Keep these terms in mind: Teleportnication, Teleportnography => Teleportnicación, Teleportnografía

PS: Mobile apps for that, too? Probably there are some out there now or in the near future (with the right equipment in place) Portnography, anyone?

Back in 1995, I wrote in the Dedication section of my doctoral thesis:

“If I have a theory, but no experimental results, I may have nothing. And if I have a theory without practical applications, I may have an artifact.”

So, don’t give your visitors hearsays, half-lies, or misrepresentation of facts found across the Web, but things that they can really test, use, and that solve a real or urgent problem for them. Don’t waste your time repeating interesting -perhaps catchy concepts-, but that at the end of the day are just useless.

In addition to textual and audiovisual content of good quality, give them TOOLS. However, provide tools that make them interact more time with your site and that authoritative pages will recommend or link to.

This is important because the amount of time spent by users in a site is directly correlated to several web metrics/analytics like:

• frequency cap – restriction on the amount of time a specific visitor is shown a particular advertisement.
• stickiness – the amount of time spent at a site over a given time period.
• underdelivery – delivery of less impressions, visitors, or conversions than contracted for a specified period of time.
• unique visitors – individuals who have visited a site (or network) at least once during a fixed time frame.
• bandwidth – how much data (e.g., content, ads, creatives) can be transmitted in a time period over a communication channel, often expressed in kilobits per second (kbps). Data is any alphanumeric content. This includes parameters, variables or any text/pixel-based creative.

Other time-based metrics inherited from traditional media (TV, radio) and that are based on the time spent by users viewing a communication channel can be applied to web channels and sites; among others:

• average audience – the average number of people who tuned into the given time selected and expressed in thousands or as a percentage (also known as a Rating) of thetotal potential audience of the demographic selected. It is also known as a T.A.R.P -Targeted Audience Rating Point.
• channel share – the share one channel has of all viewing for a particular time period. The share, expressed as a percentage, is calculated by dividing the channel’s average audience by the average audience of all channels (PUTs) (It is held in higher esteem by networks than media buyers on a day to day basis and is only referred to by the latter group when apportioning budgets and evaluating a programme for sponsorship).
• cummulative audience or reach – the total number of different people within the selected demographic who tuned into the selected time period for 8 minutes or more (i.e., reached at least once by a specific schedule or advertisement).
• frequency – the average number of times that a person within the target audience has had the opportunity to see an advertisement over the campaign period.
• time spent viewing or TVS – how many minutes/hours an audience has viewed a particular channel.

[Sources: WebSiteMagazine, WebMediaSolutions, NielsenMedia].

So, any tool that helps your visitors to wisely improve their time spent on your site -in an effective manner, of course- cannot hurt you. For this to be true, however, the tool provided must be engaging, useful, effortless, and with a minimum learning curve; otherwise the user experience of your visitors can be frustrating and a waste of time.

The 2012 Elections are over.

We have a political change in Puerto Rico.

http://www.miislita.com site is back to business.

Things to come:

A work and tests in progress:

How to enable JavaScript-only external web pages to execute server-side scripts.

The abstract says:

“As smartphones become more pervasive, they are increasingly targeted by malware. At the same time, each new generation of smartphone features increasingly powerful onboard sensor suites. A new strain of `sensor malware’ has been developing that leverages these sensors to steal information from the physical environment | e.g., researchers have recently demonstrated how malware can `listen’ for spoken credit card numbers through the microphone, or `feel’ keystroke vibrations using the accelerometer. Yet the possibilities of what malware can `see’ through a camera have been understudied.”

“This paper introduces a novel `visual malware’ called PlaceRaider, which allows remote attackers to engage in remote reconnaissance and what we call \virtual theft.” Through completely opportunistic use of the phone’s camera and other sensors, PlaceRaider constructs rich, three dimensional models of indoor environments. Remote burglars can thus `download’ the physical space, study the environment carefully, and steal virtual objects from the environment (such as nancial documents, information on computer monitors, and personally identi able information). Through two human subject studies we demonstrate the e ectiveness of using mobile devices as powerful surveillance and virtual theft platforms, and we suggest several possible defenses against visual malware.”

In this tutorial, you will determine if a data set is normally distributed by comparing its quantiles against those of a theoretical normal distribution. You will also learn how to make a data set nearly normally distributed.

http://www.miislita.com/statistics/quantile-quantile-plot-tutorial.pdf

Oct 3, 2012 Update: I’ve added a new figure to the article and reworked few lines.

He writes:

“A less profound application of the less-is-more principle
is to our habits of reporting numerical results. There
are computer programs that report by default four, five,
or even more decimal places for all numerical results.
Their authors might well be excused because, for all the
programmer knows, they may be used by atomic scientists.
But we social scientists should know better than to
report our results to so many places. What, pray, does an
r = .12345 mean? or, for an IQ distribution, a mean of
105.6345? For N = 100, the standard error of the r is
about . 1 and the standard error of the IQ mean about
1.5. Thus, the 345 part of r = .12345 is only 3% of its
standard error, and the 345 part of the IQ mean of
105.6345 is only 2% of its standard error. These superfluous
decimal places are no better than random numbers.
They are actually worse than useless because the clutter
they create, particularly in tables, serves to distract the
eye and mind from the necessary comparisons among the
meaningful leading digits. Less is indeed more here.”

End of the quote.

So, r = 0.12 is good enough.

Some statistical tables use more than 2 decimal places, but then is up to the writer to use two decimal places in the actual experimental results.

It reminds me of Jacob Cohen’s Things I have learned (So Far) article.

Yes, beware of the so-called sample-size-of-30 “magic” number.

Under the pipeline, I’m planning to publish online a tutorial on Q-Q Normality tests using just Excel. The procedure is pretty much straightforward and can be used to optimize power transformations (Tukey, Box-Cox, etc).

Ha, Ha. More power to the people.

A current claim is that a 16-year old kid that goes by the name of Shouryya Ray solved a 350-year old problem allegedly formulated by Sir Isaac Newton.

An article putting in the right perspective Ray’s solution is given here.

Still, Ray must be praised for solving what old school-trained mathematicians and physicists were not able to solve.

The simplest solution. Visit http://www.dns-ok.us and if you see a green background, you are ok. If the background is red, you might be in trouble.

Want to do the check manually? Do this

Open a command window and at the prompt, type or paste:

ipconfig/allcompartments/all

The output will probably be very long. Look for the IPv4 information under “Ethernet adapter…” Then Look for the “DNS Servers line, and write down these numbers. “Compare them with the IP numbers of the malicious Rove DNS changer listed in http://www.dcwg.org/detect/checking-windows-7-for-infections/

If a match, you might be in trouble.

In general, if x is a non-additive variable, we cannot:

• obtain a mean (arithmetic average) x value from a set of x’s.
• calculate a standard deviation from a set of x’s.
• mean-center a set of x’s by subtracting a mean score from each x.
• standardize a set of x’s by subtracting a mean score from each x and dividing each by a standard deviation score (i.e., convert each x into a z score) .
• compute the L1-norm (Manhattan, taxicab distance) from a vector whose elements are a set of x’s.

[Added on 6-21-2012] In addition for said variable, we cannot:

• take the difference between any two pairs of x values.
• compute a coefficient of variation (standard deviation/mean), from a set of x values.
• compute a mean difference from any two sets of x values.
• compute a pooled standard deviation from any two sets of x values.
• compute a Cohen’s d (mean difference/pooled standard deviation) from any two sets of x values.

In a math/statistics scenario, the following are non-additive: slopes, cosines, sines, tangents, and ratios (e.g., standard deviations, correlation coefficients, beta coefficients, coefficients of variations, Cohen’s d, etc).

In an experimental sciences scenario, the following are non-additive: any intensive property, any ratio of extensive properties (e.g., density = mass/volume), any dissimilar ratio, etc.

The information presented in the aforementioned seminar is applicable to many dissimilar fields, including web analytics, data mining, information retrieval, and almost any research field that requires of numerical analysis of experimental variables.

Unfortunately, from time to time we see research articles published wherein the additivity/non-additivity nature of variables is ignored and data crunching and analysis is arbitrarily carried out. The result: sloppy approximations, invalid models, and erroneous forecasts.

PS. There might be counterexamples to the notion of classifying properties as intensive or extensive. Very few properties are neither one. There are also some cases wherein instrumental lectures (not properties) are subtracted in order to compute signal responses or signal-to-noise ratios, derivatives, numerical analysis, etc, but for the most part the above holds in the physical world.

My response is always the same: Think like a referee/editor. Here is a list of items that they want to see accomplished:

Referees/editors like to see that the content and format of the title, abstract, document body, tables, images, graphics, appendices, and references follow their journal guidelines.

In general, referees/editors like to see in the first page of the printed version of an article:

1. Statement of the problem – what is the problem to be solved.
2. Purpose of the article – how the present research solves the problem.
3. Organization – how the article is organized and what is covered in each section.

This is a general practice across scientific journals. So, whenever possible, I try to accomplish 1 – 3 in the first three paragraphs of the first page of the printed article. To do this, you need to avoid lengthy introductions and wordiness. Be concise and ‘go the point’.

Referees/editors also like to see the article as a whole semantic unit. So they like to see:

Transitional statements; i.e., sections ending as an introduction to the next section.

1. One paragraph, one idea; i.e., each paragraph discussing one main idea.
2. Short paragraphs; i.e., each paragraph of about five sentences or less, where sentences are of appropriate length. This provides a natural stop to the reading. In general, short paragraphs and sentences are easier to read than the long ones. Use compound sentences with caution.
3. Facts supported by pertinent references.
4. Opinion written as opinions, not as facts.

Of course, there are other tips to think about, but in my opinion, the above can make a difference… well, in my opinion

The hilarious picture above shows how some SEOs look when playing to be scientists. This often occurs when interpreting big data.

Few specific scenarios:

1. Applying the statistical theory of small samples to extremely large samples, like …
2. …using large amount of data to force very small correlation coefficients to become statistically significant.
3. Trying to arithmetically average ratios (like correlation coefficients, standard deviations, slopes, and cosine similarities).
4. Mistaking Cauchy Distributions for Normal Distributions.
5. Adding together intensive properties.

Fortunately, I know of good folks that are doing a great job at educating their search marketing peers (Mike Grehan, Bruce Clay, Danny Sullivan, etc) without playing to be scientists.

In it I expand on the mathematics behind SWM to show why one should never try to compute arithmetic averages from ratios of the a/b form and similar forms. There are many reasons against doing this: Cauchy Distributions, additivity arguments, Hölder’s Inequality concepts, etc.

The paper kills for good the notion of arithmetically averaging correlation coefficients and other type of ratios frequently encountered in statistical analysis.

Part of this will be part of my presentation on Data Mining for Clinical Trials before Fundación de Investigación.

I’ll be presenting on Data Mining in Clinical Trials and how we can use the Self-Weighting Model for modeling the extracted data. The audience will be medical doctors, medical technologists, and chemists.

As we can see, data mining is not just about crunching numbers for search engines and search marketing. It is all about using the same models, but for solving different problems.

Unlike other so-called “entrepreneur experts” the speakers were the real deal. I’m glad I attended the event and learned about great success stories such as CDI-Lab, Fundacion de Investigacion, JumpStart, and other movers and shakers at the intersection of Science and Entrepreneurship.

Hats off to the Trust’s director, speakers, and organizers. BTW, great red wine and “sangria”.

http://irthoughts.wordpress.com/2012/05/22/understanding-the-lhopital-rule/

http://irthoughts.wordpress.com/2012/01/23/lhopitals-rule-and-the-00-power-controversy/

This time we show how to use the L’Hôpital Rule to derive the geometric mean from the power mean.

Deriving the Geometric Mean

The power mean from a set of n numbers of x values is defined as

Power mean = [(sum of x^p)/n]^1/p

where p is any real number.

Taking natural logs,

ln(Power mean) = [ln(sum of x^p) – ln(n)]/p

With respect to p, the right side of this expression is of the form

f(p)/g(p)

where

f(p) = ln(sum of x^p) – ln(n)

g(p) = p

So, for p = 0,

f(p)/g(p) = 0/0

This indeterminate form asks for applying the L’Hôpital Rule, which reduces to evaluating

f(p)/g(p) = f’(p)/g’(p) in the limit where p vanishes (approaches zero).

Proceeding with the derivation,

f’(p) = (1/sum of x^p) [sum of (x^p)ln(x)]

g’(p) = 1

f’(p)/g’(p) = (1/sum of x^p) [sum of (x^p)ln(x)]

Now when p = 0,

f’(p)/g’(p) = (1/n) [sum of ln(x)]

However, since

sum of ln(x) = ln(product of x)

then

f’(p)/g’(p) = (1/n) [ln(product of x)] = ln(product of x)^1/n

Therefore, taking the antilog, we obtain the geometric mean,

Geometric mean = (product of x)^1/n

Limitations of the geometric mean

Evidently, to compute the geometric mean from n numbers of x values these must be positive, greater than zero, and not written as percentages.

In the next section, we describe workarounds for circumventing these limitations.

Circumventing the limitations of the geometric mean

For a dataset with a zero value, we may add a positive value, k, calculate the geometric mean and substract k to the result. We may use a similar approach for a dataset with a negative, but insuring that k is greater than the largest negative value of the set.

For example, to calculate the geometric mean of the values +12%, -8%, and +2%, we may add 1 to remove the negative value and calculate the geometric mean of their decimal multiplier equivalents of 1.12, 0.92, and 1.02, to compute a geometric mean of 1.0167. Subtracting 1 from this value gives the geometric mean of +1.67%.

Note that for a dataset consisting of percents, we divide each percent by 100, compute the geometric mean, and multiply the result by 100.

Additional workarounds are found in:

http://www.buzzardsbay.org/geomean.htm

http://www.waterboards.ca.gov/water_issues/programs/swamp/docs/cwt/guidance/3413.pdf

Have a mean day!

PS. Sorry. I fixed the last section to add an example describing the workaround.

If you are struggling trying to understand the L’Hôpital Rule, also called the L’Hospital Rule (with the ‘s’ silent), this post if for you. I assume you know basic calculus—at least what is a derivative.

Let f(x) and g(x) be two different functions of x, where f’(x) and g’(x) are their corresponding first derivatives.

Assume that we want to evaluate the f(x)/g(x) ratio when x = c, where c can be any real number. If direct substitution of c for x yields an indeterminate form, this obstacle is circumvented by evaluating the f’(x)/g’(x) ratio when x = c.

This is the so-called L’Hôpital Rule.

If the result still is an indeterminate form, we keep applying the L’Hôpital Rule to the result until said forms no longer are. To illustrate, consider the following example, where f(x) = (1 – cos x) and g(x) = x^2. If we evaluate the ratio f(x)/g(x) when x = c = 0,

f(x)/g(x) = 0/0

and this result asks for applying the rule. It can be shown that f’(x)/g’(x) when x = c = 0 yields

f’(x)/g’(x) =  (sin x)/(2x) = 0/0

So, we keep applying the rule. Then, f’’(x)/g’’(x) when x = c = 0 yields

f’’(x)/g’’(x) = (cos x)/2 = ½.

In an upcoming post, we will explain how to use the L’Hôpital Rule to derive the geometric mean from the power mean.

How to Create Windows Metro Style Apps with JavaScript

More and more those that resist adopting JavaScript are deemed to fade away.

You can get all kind of e-drugs: from e-marihuana to e-….anything by just using earphones. A dangerous mixture if you are driving a car!

Such e-drugs are based on binaural beats, discovered in 1839 by Dove. These are slow modulations that are perceived when tones of different frequency are presented to each ear. Such auditory beats in the brain can have unexpected results, altering consciousness: A virtual LSD?

In 1973 Oster discovered that binaural beats can be detected by humans when carrier tones are below approximately 1000 Hz. According to Lane et al (see references below)

WHEN two pure auditory signals of similar frequency are mixed together, the phase interference between their waveforms produces a composite signal with a frequency midway between the upper and lower frequencies and an amplitude modulation that occurs with a frequency equal to the difference between the two original frequencies. For example, mixing tones of 100 Hz and 110 Hz yields a signal with a perceived frequency of 105 Hz that rises and falls in amplitude with a frequency of 10 Hz. The amplitude-modulated composite signal is called an auditory beat.

A similar phenomenon occurs when auditory signals of similar frequency are presented separately to the left and right ear through stereo headphones. Although each ear hears only one of the frequencies, the listener perceives the middle frequency and the amplitude modulation, even though the auditory beat does not exist in physical space. This phenomenon, called a ‘‘binaural auditory beat,’’ and described more than 25 years ago (6), is created by the brain’s processing of the two separate auditory signals at the level of the olivary nuclei of the brainstem.

It was a matter of time to see some looking for making a quick cash doing a 2 + 2 math, mixing hungry with necessity (“se juntó el hambre con la necesidad”). So now we can see low level forms of life looking for an escape to their reality through I Doser.

Hackers may soon be able to misuse these e-brain technologies to cause physical harm. A WMD in the making or accident waiting to happen?

References

Binaural Auditory Beats Affect Vigilance Performance and Mood
Auditory Beats in the Brain
Inducing Altered States Auditory and Visual Stimulation
Entraining Tones and Binaural Beats
Research_Frequencies
Audio-Visual Entrainment