For instance, a basic property of sets is that disjointness from a given set is preserved by unions:Īpplying the dictionary in the reverse direction, one might now conjecture that if was independent of and was independent of, then should also be independent of, and furthermore thatīut these statements are well known to be false (for reasons related to pairwise independence of random variables being strictly weaker than joint independence). On the other hand, not every assertion about cardinalities of sets generalises to entropies of random variables that are not arising from restricting random boolean functions to sets. Which (together with non-negativity of conditional mutual information) implies the data processing inequality, and this identity is in turn easily established from the definition of mutual information. Using the dictionary in the reverse direction, one is then led to conjecture the identity Firstly, if and are not necessarily disjoint outside of, then a consideration of Venn diagrams gives the more general inequalityĪnd a further inspection of the diagram then reveals the more precise identity This dictionary also suggests how to prove the data processing inequality using the existing Shannon inequalities. Specialising to sets, this now says that if are disjoint outside of, then this can be made apparent by considering the corresponding Venn diagram. For instance, the Shannon inequality becomes the union bound, and the definition of mutual information becomes the inclusion-exclusion formulaįor a more advanced example, consider the data processing inequality that asserts that if are conditionally independent relative to, then. If one discards the normalisation factor, one then obtains the following dictionary between entropy and the combinatorics of finite sets: Random variablesĮvery (linear) inequality or identity about entropy (and related quantities, such as mutual information) then specialises to a combinatorial inequality or identity about finite sets that is easily verified. If is the restriction of to, and is the restriction of to, then the joint variable is equivalent to the restriction of to. In this case, has the law of a random uniformly distributed boolean function from to, and the entropy here can be easily computed to be, where denotes the cardinality of. One can get some initial intuition for these information-theoretic quantities by specialising to a simple situation in which all the random variables being considered come from restricting a single random (and uniformly distributed) boolean function on a given finite domain to some subset of : In a related vein, if and are equivalent in the sense that there are deterministic functional relationships, between the two variables, then is interchangeable with for the purposes of computing the above quantities, thus for instance, ,, , etc. At the other extreme, is a measure of the extent to which fails to depend on indeed, it is not difficult to show that if and only if is determined by in the sense that there is a deterministic function such that. Similarly, vanishes if and only if and are conditionally independent relative to. The mutual information is a measure of the extent to which and fail to be independent indeed, it is not difficult to show that vanishes if and only if and are independent. More generally, given three random variables, one can define the conditional mutual informationĪnd the final of the Shannon entropy inequalities asserts that this quantity is also non-negative. So we can define some further nonnegative quantities, the mutual information Given two random variables taking on finitely many values, the joint variable is also a random variable taking on finitely many values, and also has an entropy. (In some texts, one uses the logarithm to base rather than the natural logarithm, but the choice of base will not be relevant for this discussion.) This is clearly a nonnegative quantity. Given a random variable that takes on only finitely many values, we can define its Shannon entropy by the formula
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You can indent elements by moving them two spaces to the right. When writing HTML it is important to properly format your code using good indentation. This is much easier to read and now we can see all of the nested child elements inside their parent elements and understand what the code is doing. Now I am going to take that exact same code and properly indent it to show you the difference. If you tried to submit something like this in a professional developer setting, your team would not be happy with you at all. This is not good HTML practice at all because it is really difficult to read and understand what the code is doing. In this example, I have copied all of the code from the Learn HTML by Building a Cat Photo App project and removed all of the indentation to show you what poor code formatting looks like. A large part of readability is properly indenting your HTML. When you are writing code, it is important to write code that is readable by other developers. ĭrive 1.2 miles and turn left on Cherry laneĭrive 4.5 miles and turn right on Sycamore Rd. The ol element is the parent of the li elements. The li elements are indented two spaces to the right and nested inside the ol element. The ul element is the parent of the li elements. The li elements are indented two spaces to the right and nested inside the ul element. Commonly Used Examples of Indentation in HTML Unordered lists The h2 and p elements are children of the main element. īut if I edit the code by moving the h2 and p elements two spaces to the right, now we have proper indentation. In this next example, I have an h2 and p element nested inside a main element without indentation. Now we can see that the p element is nested inside its parent element which is the div. This is considered best practice and will make your code more readable by other developers. This is what indentation looks like for HTML To indent the p element, I will move it two spaces to the right. In this example, I have a p element nested inside a div element. Nested elements are known as children of their parent element. Whenever you have HTML elements nested inside other HTML elements, it's best to use indentation. In this article, I will show you how to properly indent your HTML files and explain why it is important to properly format your code. But how do you do that in HTML and why is it important? This ability to perceive as a paragraph break provides for continuity with HTML, and allows authors to graduate to treating it as a container in their own time.When you are building out HTML files, it's really important to indent your code. If the paragraph style includes a blank line between paragraphs, then additional care is needed after headers and other major elements *2 to avoid inserting an unwanted blank line, e.g. Note that when using explicit line breaks (see Section 5.12) you may wish to switch off word wrap with WRAP=OFF.īrowsers, when parsing paragraphs, can choose to simply treat the tag as denoting a paragraph break. This attribute is a hint and may be ignored by some browsers. Other possibilities are ALIGN=left (the default), ALIGN=right, ALIGN=justify and ALIGN=indent. The ALIGN attribute can be used to center a paragraph, e.g. You can force line breaks in normal paragraph text with the element, but the browser may wrap lines arbitrarily at window margins prior to reaching the element. In some situations you will want to preserve the original line breaks and spacing, for this you should use the LIT or PRE elements, these are described in a later section. The following samples of HTML+ all produce exactly the same results when displayed: This works since HTML+ formally doesn't require you to wrap text up as paragraphs. If you wish, you may think of the tag as a paragraph separator. You don't need to give the end tag as it is implied by the context, e.g. The P element acts as a container for the text between the start tag and the end tag. This works since HTML+ formally doesn't require you to wrap If you wish, you may think of thetag as a paragraph Tag as it is implied by the context, e.g. The P element acts as container for the text between the start The text is generally shown in a proportional font: Normal text is automatically wrapped by the browser at the current window margin and adapts to changes in window size. Identity and access management refers to the framework of processes and technologies used by IT organizations to grant permission for network use. They discussed the need for consistent protection standards and how generative AI will change security work in the enterprise. Kovar spoke with theCUBE industry analyst Dave Vellante at the Supercloud 3: Security, AI and the Supercloud event, during an exclusive broadcast on theCUBE, SiliconANGLE Media’s livestreaming studio. It’s really understanding what the events are that are going to cause you the most pain and then trying to write universal detections as much as possible that hits across all those different places.” The strategy always starts with looking at the identity and access management plane and trying to figure out the ways you can best secure your assets through there. “The user is what allows them to have credentials, and those credentials are how they log in to the cloud. “People don’t hack the cloud they hack the user,” said Ryan Kovar (pictured), distinguished security strategist and leader of SURGe at Splunk. Its approach provides a realistic view of vulnerabilities, starting with access management. built its platform around enterprise resilience and keeping data secure. the time from the moment when peer detects a new / changed file to the moment when any peer gets this updated data).Į="" | transaction startswith=eval('event.event_type'="file_added" OR 'event.event_type'="file_modified") endswith=eval('event.Splunk Inc. Use next query to see your data delivery latency (i.e. If you choose a real-time sliding window, Splunk will show you what happens in real-time:Į="" | stats latest(event.event_type) as latest_event, latest(_time) as event_time_e by peer | convert ctime(event_time_e) AS event_time | table peer latest_event event_time In this case, you'll be able to see the latest event reported by each peer for the selected folder.
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The US Open men's final is today (Sunday 11th September) at 9pm BST and 4pm local time (ET). Can wunderkind Alcaraz win his first-ever grand slam title? It's looking promising. Carlos Alcaraz had to go all the way once more to beat Frances Tiafoe in a run to the final that has seen the 19-year-old go to five sets in more rounds than not. With an injury-ravaged Nadal suffering a shock defeat to Frances Tiafoe, and reigning champion Daniil Medvedev dethroned by the now departed Nick Kyrgios, this has become a year for a rookie winner, given that Novak Djokovic was not there to compete either.Ĭasper Ruud brushed past Karen Khachanov in his semi. UK stream: Amazon Prime Video (free 30-day trial) Venue: USTA Billie Jean King National Tennis Center The couple had eight children together: Geraldine, Michael, Josephine, Victoria, Eugene, Jane, Annette, and Christopher, and they remained married until Chaplin's death in 1977. But for Chaplin this was the happy union he had been waiting for all his life. "e at last found true happiness, and it seems they had both found their soul mates, despite the fact that Oona was only 18, and Charlie was 53," according to the Chaplin Office.Īlthough O'Neill was older than both of his first two wives when they married, the couple's age gap raised eyebrows. They hit it off immediately, becoming inseparable, and married the following year. Oona O\’neill chaplin circa 1943 George Karger/Pix Inc./The LIFE Images Collection/Getty ImagesĬhaplin met O'Neill in 1942 when he was considering her for a role in one of his films. They were married from 1936 to 1942 and divorced amicably. Chaplin's third wife was the actress Paulette Goddard, who appeared in several his films and was 21 when they wed. In 1924, Chaplin quietly married another 16-year-old actress, Lita Grey, whom he met on the set of The Gold Rush. He married his first wife, actress Mildred Harris, after a pregnancy scare when she was just 16 years old. Unfortunately, real-life scandals too often overshadowed Chaplin's on-screen triumphs. His most enduring films include The Kid (1921), The Gold Rush (1925), City Lights (1931), Modern Times (1936), and The Great Dictator (1940). Griffith to found the United Artists Corp. Chaplin launched his silent movie career in 1913.Ĭhaplin increasingly became involved in the writing and directing side of moviemaking and later joined forces with fellow actors Mary Pickford and Douglas Fairbanks, and director/producer D.W. Chaplin was a hit with audiences and the fledgling Hollywood film industry took notice. However, "the early death of his father and the subsequent illness of his mother made it necessary for Charlie and his brother, Sydney, to fend for themselves" before Chaplin was 10 years old, notes the Chaplin Office, which represents the Chaplin rights-holding companies and the Chaplin family.Ī part in a stage show at age 12 started Chaplin's career as a vaudeville comedian, which eventually took him to the United States in 1912. I wish I could write more about this, but it involves love, and perfect love is the most beautiful of all frustrations because it is more than one can express."įor a long time, it seemed unlikely Chaplin would ever find lasting love.Ĭharles Spencer Chaplin was born in London on April 16, 1889, to parents who pursued careers as actors and singers. "I have the good fortune to be married to a wonderful wife. Chaplin and O\’neill the day after their jwedding Getty Images |
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