Slice Knots And Links
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Slice Knots And Links
Slice may refer to: *Cutting Food and beverage *A portion of bread, pizza, cake, meat, or other food item that is cut flat and thin: :* Sliced bread :* Pizza by the slice, a fast food dish :* Vanilla slice :*Fudge :*Toffee :* Barfi * Slice (drink), a line of fruit-flavored soft drinks *A serving or cooking utensil, such as a Fish slice In Australia and New Zealand *A category of sweet or savory dishes: :* Vanilla slice, a dessert cake similar to a brownie :* Zucchini slice, a savory dish similar to a quiche In arts and entertainment Music * ''Slice'' (album), a Five for Fighting album, 2009 ** "Slice" (song), a 2009 song by Five for Fighting *''Slice'', a 1998 album by Arthur Loves Plastic * Slices (band) * ''Slice'' (EP), 2023 by O. Other uses in arts and entertainment *Slice (TV channel), a Canadian TV channel formerly known as Life Network * Slice (2009 film), a Thai crime film * ''Slice'' (2018 film), an American horror comedy film * Slice (G.I. Joe), a fictional chara ...
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Cutting
Cutting is the separation or opening of a physical object, into two or more portions, through the application of an acutely directed force. Implements commonly used for wikt:cut, cutting are the knife and saw, or in medicine and science the scalpel and microtome. However, any sufficiently sharp object is capable of cutting if it has a hardness sufficiently larger than the object being cut, and if it is applied with sufficient force. Even liquids can be used to cut things when applied with sufficient force (see water jet cutter). Cutting is a compression (physical), compressive and shearing (physics), shearing phenomenon, and occurs only when the total stress (physics), stress generated by the cutting implement exceeds the ultimate Strength of materials, strength of the material of the object being cut. The simplest applicable equation is: :\text = or \tau=\frac The stress generated by a cutting implement is directly proportional to the force with which it is applied, and ...
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Slice (2018 Film)
''Slice'' is a 2018 American horror comedy film, written and directed by Austin Vesely. The film stars Zazie Beetz and Chance Bennett, with Rae Gray, Marilyn Dodds Frank, Katherine Cunningham, Will Brill, Y'lan Noel, Hannibal Buress, Tim Decker, Joe Keery, Chris Parnell, and Paul Scheer appearing in supporting roles. It follows the murders of several pizza deliverymen in the Ghost Town neighborhood of Kingfisher, and various townspeople's efforts to solve the crimes. It was theatrically released on September 10, 2018, by A24. Plot Kingfisher, U.S.A. is home to 40,000 ghosts — mostly victims of the former sanatorium — who live and work alongside the living, but are relocated by Mayor Tracy to an abandoned neighborhood. Perfect Pizza Base driver Sean Hammerschmidt makes a delivery to "Ghost Town", where his throat is slit by an unseen killer. ''Kingfisher Chronicle'' reporter Sadie Sheridan attends Tracy's press conference regarding Sean's murder, which is interrupted ...
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Slice Sampling
Slice sampling is a type of Markov chain Monte Carlo algorithm for pseudo-random number sampling, i.e. for drawing random samples from a statistical distribution. The method is based on the observation that to sample a random variable one can sample uniformly from the region under the graph of its density function. Motivation Suppose you want to sample some random variable ''X'' with distribution ''f''(''x''). Suppose that the following is the graph of ''f''(''x''). The height of ''f''(''x'') corresponds to the likelihood at that point. If you were to uniformly sample ''X'', each value would have the same likelihood of being sampled, and your distribution would be of the form ''f''(''x'') = ''y'' for some ''y'' value instead of some non-uniform function ''f''(''x''). Instead of the original black line, your new distribution would look more like the blue line. In order to sample ''X'' in a manner which will retain the distribution ''f''(''x''), some sampling technique must be u ...
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Slice Knot
A slice knot is a knot (mathematics), mathematical knot in 3-dimensional space that bounds an embedded disk in 4-dimensional space. Definition A knot K \subset S^3 is said to be a topologically slice knot or a smoothly slice knot, if it is the boundary of an Embedding, embedded disk in the 4-ball B^4, which is Local flatness, locally flat or Smoothness, smooth, respectively. Here we use S^3 = \partial B^4: the 3-sphere S^3 = \ is the boundary (topology), boundary of the four-dimensional ball (mathematics), ball B^4 = \. Every smoothly slice knot is topologically slice because a smoothly embedded disk is locally flat. Usually, smoothly slice knots are also just called slice. Both types of slice knots are important in 3- and 4-dimensional topology. Smoothly slice knots are often illustrated using knots diagrams of ribbon knots and it is an open question whether there are any smoothly slice knots which are not ribbon knots (′Slice-ribbon conjecture′). Cone construction The ...
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Slice Genus
In mathematics, the slice genus of a smooth knot ''K'' in ''S''3 (sometimes called its Murasugi genus or 4-ball genus) is the least integer g such that ''K'' is the boundary of a connected, orientable 2-manifold ''S'' of genus ''g'' properly embedded in the 4-ball ''D''4 bounded by ''S''3. More precisely, if ''S'' is required to be smoothly embedded, then this integer ''g'' is the ''smooth slice genus'' of ''K'' and is often denoted gs(''K'') or g4(''K''), whereas if ''S'' is required only to be topologically locally flatly embedded then ''g'' is the ''topologically locally flat slice genus'' of ''K''. (There is no point considering ''g'' if ''S'' is required only to be a topological embedding, since the cone on ''K'' is a 2-disk with genus 0.) There can be an arbitrarily great difference between the smooth and the topologically locally flat slice genus of a knot; a theorem of Michael Freedman says that if the Alexander polynomial of ''K'' is 1, then the topologicall ...
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Comma Category
In mathematics, a comma category (a special case being a slice category) is a construction in category theory. It provides another way of looking at morphisms: instead of simply relating objects of a Category (mathematics), category to one another, morphisms become objects in their own right. This notion was introduced in 1963 by William Lawvere, F. W. Lawvere (Lawvere, 1963 p. 36), although the technique did not become generally known until many years later. Several mathematical concepts can be treated as comma categories. Comma categories also guarantee the existence of some Limit (category theory), limits and colimits. The name comes from the notation originally used by Lawvere, which involved the comma punctuation mark. The name persists even though standard notation has changed, since the use of a comma as an operator is potentially confusing, and even Lawvere dislikes the uninformative term "comma category" (Lawvere, 1963 p. 13). Definition The most general comma ca ...
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Internet Communications Engine
The Internet Communications Engine, or Ice, is an open-source RPC framework developed by ZeroC. It provides SDKs for C++, C#, Java, JavaScript, MATLAB, Objective-C, PHP, Python, Ruby and Swift, and can run on various operating systems, including Linux, Windows, macOS, iOS and Android. Ice implements a proprietary application layer communications protocol, called the Ice protocol, that can run over TCP, TLS, UDP, WebSocket and Bluetooth. As its name indicates, Ice can be suitable for applications that communicate over the Internet, and includes functionality for traversing firewalls. History Initially released in February 2003, Ice was influenced by the Common Object Request Broker Architecture (CORBA) in its design, and indeed was created by several influential CORBA developers, including Michi Henning. However, according to ZeroC, it was smaller and less complex than CORBA because it was designed by a small group of experienced developers, instead of suffering fr ...
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Bit Slicing
Bit slicing is a technique for constructing a processor from modules of processors of smaller bit width, for the purpose of increasing the word length; in theory to make an arbitrary ''n''-bit central processing unit (CPU). Each of these component modules processes one bit field or "slice" of an operand. The grouped processing components would then have the capability to process the chosen full word-length of a given software design. Bit slicing more or less died out due to the advent of the microprocessor. Recently it has been used in arithmetic logic units (ALUs) for quantum computers and as a software technique, e.g. for cryptography in x86 CPUs. Operational details Bit-slice processors (BSPs) usually include 1-, 2-, 4-, 8- or 16-bit arithmetic logic unit (ALU) and control lines (including carry or overflow signals that are internal to the processor in non-bitsliced CPU designs). For example, two 4-bit ALU chips could be arranged side by side, with control ...
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Array Slicing
In computer programming, array slicing is an operation that extracts a subset of elements from an array and packages them as another array, possibly in a different dimension from the original. Common examples of array slicing are extracting a substring from a string of characters, the "''ell''" in "h''ell''o", extracting a row or column from a two-dimensional array, or extracting a vector from a matrix. Depending on the programming language, an array slice can be made out of non-consecutive elements. Also depending on the language, the elements of the new array may be aliased to (i.e., share memory with) those of the original array. Details For "one-dimensional" (single-indexed) arrays vectors, sequences, strings etc. the most common slicing operation is extraction of zero or more consecutive elements. If we have a vector containing elements (2, 5, 7, 3, 8, 6, 4, 1), and want to create an array slice from the 3rd to the 6th elements, we get (7, 3, 8, 6). In programming la ...
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Slice (disk)
Disk partitioning or disk slicing is the creation of one or more regions on secondary storage, so that each region can be managed separately. These regions are called partitions. It is typically the first step of preparing a newly installed disk after a partitioning scheme is chosen for the new disk before any file system is created. The disk stores the information about the partitions' locations and sizes in an area known as the partition table that the operating system reads before any other part of the disk. Each partition then appears to the operating system as a distinct "logical" disk that uses part of the actual disk. System administrators use a program called a partition editor to create, resize, delete, and manipulate the partitions. Partitioning allows the use of different filesystems to be installed for different kinds of files. Separating user data from system data can prevent the system partition from becoming full and rendering the system unusable. Partitioning can ...
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