Semantic analytics, also termed semantic relatedness, is the use of ontologies to analyze content in web resources. This field of research combines text analytics and Semantic Web technologies like RDF. Semantic analytics measures the relatedness of different ontological concepts. Some academic research groups that have active project in this area include Kno.e.sis Center at Wright State University among others. == History == An important milestone in the beginning of semantic analytics occurred in 1996, although the historical progression of these algorithms is largely subjective. In his seminal study publication, Philip Resnik established that computers have the capacity to emulate human judgement. Spanning the publications of multiple journals, improvements to the accuracy of general semantic analytic computations all claimed to revolutionize the field. However, the lack of a standard terminology throughout the late 1990s was the cause of much miscommunication. This prompted Budanitsky & Hirst to standardize the subject in 2006 with a summary that also set a framework for modern spelling and grammar analysis. In the early days of semantic analytics, obtaining a large enough reliable knowledge bases was difficult. In 2006, Strube & Ponzetto demonstrated that Wikipedia could be used in semantic analytic calculations. The usage of a large knowledge base like Wikipedia allows for an increase in both the accuracy and applicability of semantic analytics. == Methods == Given the subjective nature of the field, different methods used in semantic analytics depend on the domain of application. No singular methods is considered correct, however one of the most generally effective and applicable method is explicit semantic analysis (ESA). ESA was developed by Evgeniy Gabrilovich and Shaul Markovitch in the late 2000s. It uses machine learning techniques to create a semantic interpreter, which extracts text fragments from articles into a sorted list. The fragments are sorted by how related they are to the surrounding text. Latent semantic analysis (LSA) is another common method that does not use ontologies, only considering the text in the input space. == Applications == Entity linking Ontology building / knowledge base population Search and query tasks Natural language processing Spoken dialog systems (e.g., Amazon Alexa, Google Assistant, Microsoft's Cortana) Artificial intelligence Knowledge management The application of semantic analysis methods generally streamlines organizational processes of any knowledge management system. Academic libraries often use a domain-specific application to create a more efficient organizational system. By classifying scientific publications using semantics and Wikipedia, researchers are helping people find resources faster. Search engines like Semantic Scholar provide organized access to millions of articles.
Security of the Java software platform
The Java software platform provides a number of features designed for improving the security of Java applications. This includes enforcing runtime constraints through the use of the Java Virtual Machine (JVM), a security manager that sandboxes untrusted code from the rest of the operating system, and a suite of security APIs that Java developers can utilise. Despite this, criticism has been directed at the programming language, and Oracle, due to an increase in malicious programs that revealed security vulnerabilities in the JVM, which were subsequently not properly addressed by Oracle in a timely manner. == Security features == === The JVM === The binary form of programs running on the Java platform is not native machine code but an intermediate bytecode. The JVM performs verification on this bytecode before running it to prevent the program from performing unsafe operations such as branching to incorrect locations, which may contain data rather than instructions. It also allows the JVM to enforce runtime constraints such as array bounds checking. This means that Java programs are significantly less likely to suffer from memory safety flaws such as buffer overflow than programs written in languages such as C which do not provide such memory safety guarantees. The platform does not allow programs to perform certain potentially unsafe operations such as pointer arithmetic or unchecked type casts. It manages memory allocation and initialization and provides automatic garbage collection which in many cases (but not all) relieves the developer from manual memory management. This contributes to type safety and memory safety. === Security manager === The platform provides a security manager which allows users to run untrusted bytecode in a "sandboxed" environment designed to protect them from malicious or poorly written software by preventing the untrusted code from accessing certain platform features and APIs. For example, untrusted code might be prevented from reading or writing files on the local filesystem, running arbitrary commands with the current user's privileges, accessing communication networks, accessing the internal private state of objects using reflection, or causing the JVM to exit. The security manager also allows Java programs to be cryptographically signed; users can choose to allow code with a valid digital signature from a trusted entity to run with full privileges in circumstances where it would otherwise be untrusted. Users can also set fine-grained access control policies for programs from different sources. For example, a user may decide that only system classes should be fully trusted, that code from certain trusted entities may be allowed to read certain specific files, and that all other code should be fully sandboxed. === Security APIs === The Java Class Library provides a number of APIs related to security, such as standard cryptographic algorithms, authentication, and secure communication protocols. === The sun.misc.Unsafe class === sun.misc.Unsafe is an internal utility class in the Java programming language which is a collection of low-level unsafe operations. While it is not a part of the official Java Class Library, it is called internally by the Java libraries. It resides in an unofficial Java module named jdk.unsupported. Beginning in Java 11, it has been partially migrated to jdk.internal.misc.Unsafe (which resides in module java.base). Its primary feature is to allow direct memory management (similar to C memory management) and memory address manipulation, manipulating objects and fields, thread manipulation, and concurrency primitives. Its declaration is: public final class Unsafe;, and it is a singleton class with a private constructor. It contains the following methods, many of which are declared native (invoking Java Native Interface): static Unsafe getUnsafe(): retrieves the Unsafe instance. It uses sun.reflect.Reflection to do so. int getInt(Object o, long offset): fetches a value (a field or array element) in the object at the given offset. (There are corresponding getBoolean(), getByte(), getShort(), getChar(), getLong(), getFloat(), and getDouble() methods as well.) void putInt(Object o, long offset, int x): stores a value into an object at the given offset. (There are corresponding putBoolean(), putByte(), putShort(), putChar(), putLong(), putFloat(), and putDouble() methods as well.) Object getObject(Object o, long offset): fetches a reference value from an object at the given offset. void putObject(Object o, long offset, Object x): stores a reference value into an object at the given offset. int getInt(long address): fetches a value at the given address. (There are corresponding getBoolean(), getByte(), getShort(), getChar(), getLong(), getFloat(), and getDouble() methods as well.) void putInt(long address, int x): stores a value into the given address. (There are corresponding putBoolean(), putByte(), putShort(), putChar(), putLong(), putFloat(), and putDouble() methods as well.) long getAddress(long address): fetches a native pointer from a given address. void putAddress(long address, long x): stores a native pointer into a given address. long allocateMemory(long bytes): allocates a block of native memory of the given size (similar to malloc()). long reallocateMemory(long address, long bytes): resizes a block of native memory to the given size (similar to realloc()). void setMemory(Object o, long offset, long bytes, byte value), void setMemory(long address, long bytes, byte value): sets all bytes in a block of memory to a fixed value (similar to memset()). void copyMemory(Object srcBase, long srcOffset, Object destBase, long destOffset, long bytes), void copyMemory(long srcAddress, long destAddress, long bytes): sets all bytes in a given block of memory to a copy of another block (similar to memcpy()). void freeMemory(long address): deallocates a block of native memory obtained from allocateMemory() or reallocateMemory(), similar to free()). long staticFieldOffset(Field f): obtains the location of a given field in the storage allocation of its class. long objectFieldOffset(Field f): obtains the location of a given static field in conjunction with staticFieldBase(). Object staticFieldBase(Field f): obtains the location of a given static field in conjunction with staticFieldOffset(). void ensureClassInitialized(Class c): ensures the given class has been initialized. int arrayBaseOffset(Class arrayClass): obtains the offset of the first element in the storage allocation of a given array class. int arrayIndexScale(Class arrayClass): obtains the scale factor for addressing elements in the storage allocation of a given array class. static int addressSize(): obtains the size (in bytes) of a native pointer. int pageSize(): obtains the size (in bytes) of a native memory page. Class defineClass(String name, byte[] b, int off, int len, ClassLoader loader, ProtectionDomain protectionDomain): signals to the JVM to define a class without security checks. Class defineAnonymousClass(Class hostClass, byte[] data, Object[] cpPatches): signals to the JVM to define a class but do not make it known to the class loader or system directory. Object allocateInstance(Class cls) throws InstantiationException: allocates an instance of a class without running its constructor. void monitorEnter(Object o): locks an object. void monitorExit(Object o): unlocks an object. boolean tryMonitorEnter(Object o): tries to lock an object, returning whether the lock succeeded. void throwException(Throwable ee): throws an exception without telling the verifier. final boolean compareAndSwapInt(Object o, long offset, int expected, int x): updates a variable to x if it is holding expected, returning whether the operation succeeded. (There are corresponding compareAndSwapLong() and compareAndSwapObject() methods as well.) int getIntVolatile(Object o, long offset): volatile version of getInt(). (There are corresponding getBooleanVolatile(), getByteVolatile(), getShortVolatile(), getCharVolatile(), getLongVolatile(), getFloatVolatile(), getDoubleVolatile(), and getObjectVolatile() methods as well.) void putIntVolatile(Object o, long offset, int x): volatile version of putInt(). (There are corresponding putBooleanVolatile(), putByteVolatile(), putShortVolatile(), putCharVolatile(), putLongVolatile(), putFloatVolatile(), putDoubleVolatile(), and putObjectVolatile() methods as well.) void putOrderedInt(Object o, long offset, int x): version of putIntVolatile() not guaranteeing immediate visibility of storage to other threads. (There are corresponding putOrderedLong() and putOrderedObject() methods as well.) void unpark(Object thread): unblocks a thread. void park(boolean isAbsolute, long time): blocks the current thread. int getLoadAverage(double[] loadavg, int nelems): gets the load average in the system run queue assigned to available processors averaged over various periods of time. void invokeCleaner(ByteBuffe
Vans challenge
The Vans challenge is a viral internet challenge that began in March 2019 where people show their Vans shoes landing right-side up after tossing them in the air. The viral sensation reportedly started after a Twitter user shared a video of the occurrence, which was captioned: “Did you know it doesn’t matter how you throw your Vans they will land facing up.” Since then, multiple people on social media posted similar videos of them throwing their Vans in the air and landing right-side up, along with Crocs, UGG boots, and other popular shoes. This theory proved false, as these shoes have not always landed facing up after tossing them.
Signals intelligence
Signals intelligence (SIGINT) is the act and field of intelligence-gathering by interception of signals, whether communications between people (communications intelligence—abbreviated to COMINT) or from electronic signals not directly used in communication (electronic intelligence—abbreviated to ELINT). As classified and sensitive information is usually encrypted, signals intelligence may necessarily involve cryptanalysis (to decipher the messages). Traffic analysis—the study of who is signaling to whom and in what quantity—is also used to integrate information, and it may complement cryptanalysis. == History == === Origins === Electronic interceptions appeared as early as 1900, during the Boer War of 1899–1902. The British Royal Navy had installed wireless sets produced by Marconi on board their ships in the late 1890s, and the British Army used some limited wireless signalling. The Boers captured some wireless sets and used them to make vital transmissions. Since the British were the only people transmitting at the time, the British did not need special interpretation of the signals that they were. The birth of signals intelligence in a modern sense dates from the Russo-Japanese War of 1904–1905. As the Russian fleet prepared for conflict with Japan in 1904, the British ship HMS Diana stationed in the Suez Canal intercepted Russian naval wireless signals being sent out for the mobilization of the fleet, for the first time in history. === Development in World War I === Over the course of the First World War, a new method of signals intelligence reached maturity. Russia's failure to properly protect its communications fatally compromised the Russian Army's advance early in World War I and led to their disastrous defeat by the Germans under Ludendorff and Hindenburg at the Battle of Tannenberg. In 1918, French intercept personnel captured a message written in the new ADFGVX cipher, which was cryptanalyzed by Georges Painvin. This gave the Allies advance warning of the German 1918 Spring Offensive. The British in particular, built up great expertise in the newly emerging field of signals intelligence and codebreaking (synonymous with cryptanalysis). On the declaration of war, Britain cut all German undersea cables. This forced the Germans to communicate exclusively via either (A) a telegraph line that connected through the British network and thus could be tapped; or (B) through radio which the British could then intercept. Rear Admiral Henry Oliver appointed Sir Alfred Ewing to establish an interception and decryption service at the Admiralty; Room 40. An interception service known as 'Y' service, together with the post office and Marconi stations, grew rapidly to the point where the British could intercept almost all official German messages. The German fleet was in the habit each day of wirelessing the exact position of each ship and giving regular position reports when at sea. It was possible to build up a precise picture of the normal operation of the High Seas Fleet, to infer from the routes they chose where defensive minefields had been placed and where it was safe for ships to operate. Whenever a change to the normal pattern was seen, it immediately signalled that some operation was about to take place, and a warning could be given. Detailed information about submarine movements was also available. The use of radio-receiving equipment to pinpoint the location of any single transmitter was also developed during the war. Captain H.J. Round, working for Marconi, began carrying out experiments with direction-finding radio equipment for the army in France in 1915. By May 1915, the Admiralty was able to track German submarines crossing the North Sea. Some of these stations also acted as 'Y' stations to collect German messages, but a new section was created within Room 40 to plot the positions of ships from the directional reports. Room 40 played an important role in several naval engagements during the war, notably in detecting major German sorties into the North Sea. The battle of Dogger Bank was won in no small part due to the intercepts that allowed the Navy to position its ships in the right place. It played a vital role in subsequent naval clashes, including at the Battle of Jutland as the British fleet was sent out to intercept them. The direction-finding capability allowed for the tracking and location of German ships, submarines, and Zeppelins. The system was so successful that by the end of the war, over 80 million words, comprising the totality of German wireless transmission over the course of the war, had been intercepted by the operators of the Y-stations and decrypted. However, its most astonishing success was in decrypting the Zimmermann Telegram, a telegram from the German Foreign Office sent via Washington to its ambassador Heinrich von Eckardt in Mexico. === Postwar consolidation === With the importance of interception and decryption firmly established by the wartime experience, countries established permanent agencies dedicated to this task in the interwar period. In 1919, the British Cabinet's Secret Service Committee, chaired by Lord Curzon, recommended that a peace-time codebreaking agency should be created. The Government Code and Cypher School (GC&CS) was the first peace-time codebreaking agency, with a public function "to advise as to the security of codes and cyphers used by all Government departments and to assist in their provision", but also with a secret directive to "study the methods of cypher communications used by foreign powers". GC&CS officially formed on 1 November 1919, and produced its first decrypt on 19 October. By 1940, GC&CS was working on the diplomatic codes and ciphers of 26 countries, tackling over 150 diplomatic cryptosystems. The US Cipher Bureau was established in 1919 and achieved some success at the Washington Naval Conference in 1921, through cryptanalysis by Herbert Yardley. Secretary of War Henry L. Stimson closed the US Cipher Bureau in 1929 with the words "Gentlemen do not read each other's mail." === World War II === The use of SIGINT had even greater implications during World War II. The combined effort of intercepts and cryptanalysis for the whole of the British forces in World War II came under the code name "Ultra", managed from Government Code and Cypher School at Bletchley Park. Properly used, the German Enigma and Lorenz ciphers should have been virtually unbreakable, but flaws in German cryptographic procedures, and poor discipline among the personnel carrying them out, created vulnerabilities which made Bletchley's attacks feasible. Bletchley's work was essential to defeating the U-boats in the Battle of the Atlantic, and to the British naval victories in the Battle of Cape Matapan and the Battle of North Cape. In 1941, Ultra exerted a powerful effect on the North African desert campaign against German forces under General Erwin Rommel. General Sir Claude Auchinleck wrote that were it not for Ultra, "Rommel would have certainly got through to Cairo". Ultra decrypts featured prominently in the story of Operation SALAM, László Almásy's mission across the desert behind Allied lines in 1942. Prior to the Normandy landings on D-Day in June 1944, the Allies knew the locations of all but two of Germany's fifty-eight Western Front divisions. Winston Churchill was reported to have told King George VI: "It is thanks to the secret weapon of General Menzies, put into use on all the fronts, that we won the war!" Supreme Allied Commander, Dwight D. Eisenhower, at the end of the war, described Ultra as having been "decisive" to Allied victory. Official historian of British Intelligence in World War II Sir Harry Hinsley argued that Ultra shortened the war "by not less than two years and probably by four years"; and that, in the absence of Ultra, it is uncertain how the war would have ended. At a lower level, German cryptanalysis, direction finding, and traffic analysis were vital to Rommel's early successes in the Western Desert Campaign until British forces tightened their communications discipline and Australian raiders destroyed his principal SIGINT Company. == Technical definitions == The United States Department of Defense has defined the term "signals intelligence" as: A category of intelligence comprising either individually or in combination all communications intelligence (COMINT), electronic intelligence (ELINT), and foreign instrumentation signals intelligence (FISINT), however transmitted. Intelligence derived from communications, electronic, and foreign instrumentation signals. Being a broad field, SIGINT has many sub-disciplines. The two main ones are communications intelligence (COMINT) and electronic intelligence (ELINT). == Disciplines shared across the branches == === Targeting === A collection system has to know to look for a particular signal. "System", in this context, has several nuances. Targeting is the process of developing collection requirements: "1. A
Signals intelligence
Signals intelligence (SIGINT) is the act and field of intelligence-gathering by interception of signals, whether communications between people (communications intelligence—abbreviated to COMINT) or from electronic signals not directly used in communication (electronic intelligence—abbreviated to ELINT). As classified and sensitive information is usually encrypted, signals intelligence may necessarily involve cryptanalysis (to decipher the messages). Traffic analysis—the study of who is signaling to whom and in what quantity—is also used to integrate information, and it may complement cryptanalysis. == History == === Origins === Electronic interceptions appeared as early as 1900, during the Boer War of 1899–1902. The British Royal Navy had installed wireless sets produced by Marconi on board their ships in the late 1890s, and the British Army used some limited wireless signalling. The Boers captured some wireless sets and used them to make vital transmissions. Since the British were the only people transmitting at the time, the British did not need special interpretation of the signals that they were. The birth of signals intelligence in a modern sense dates from the Russo-Japanese War of 1904–1905. As the Russian fleet prepared for conflict with Japan in 1904, the British ship HMS Diana stationed in the Suez Canal intercepted Russian naval wireless signals being sent out for the mobilization of the fleet, for the first time in history. === Development in World War I === Over the course of the First World War, a new method of signals intelligence reached maturity. Russia's failure to properly protect its communications fatally compromised the Russian Army's advance early in World War I and led to their disastrous defeat by the Germans under Ludendorff and Hindenburg at the Battle of Tannenberg. In 1918, French intercept personnel captured a message written in the new ADFGVX cipher, which was cryptanalyzed by Georges Painvin. This gave the Allies advance warning of the German 1918 Spring Offensive. The British in particular, built up great expertise in the newly emerging field of signals intelligence and codebreaking (synonymous with cryptanalysis). On the declaration of war, Britain cut all German undersea cables. This forced the Germans to communicate exclusively via either (A) a telegraph line that connected through the British network and thus could be tapped; or (B) through radio which the British could then intercept. Rear Admiral Henry Oliver appointed Sir Alfred Ewing to establish an interception and decryption service at the Admiralty; Room 40. An interception service known as 'Y' service, together with the post office and Marconi stations, grew rapidly to the point where the British could intercept almost all official German messages. The German fleet was in the habit each day of wirelessing the exact position of each ship and giving regular position reports when at sea. It was possible to build up a precise picture of the normal operation of the High Seas Fleet, to infer from the routes they chose where defensive minefields had been placed and where it was safe for ships to operate. Whenever a change to the normal pattern was seen, it immediately signalled that some operation was about to take place, and a warning could be given. Detailed information about submarine movements was also available. The use of radio-receiving equipment to pinpoint the location of any single transmitter was also developed during the war. Captain H.J. Round, working for Marconi, began carrying out experiments with direction-finding radio equipment for the army in France in 1915. By May 1915, the Admiralty was able to track German submarines crossing the North Sea. Some of these stations also acted as 'Y' stations to collect German messages, but a new section was created within Room 40 to plot the positions of ships from the directional reports. Room 40 played an important role in several naval engagements during the war, notably in detecting major German sorties into the North Sea. The battle of Dogger Bank was won in no small part due to the intercepts that allowed the Navy to position its ships in the right place. It played a vital role in subsequent naval clashes, including at the Battle of Jutland as the British fleet was sent out to intercept them. The direction-finding capability allowed for the tracking and location of German ships, submarines, and Zeppelins. The system was so successful that by the end of the war, over 80 million words, comprising the totality of German wireless transmission over the course of the war, had been intercepted by the operators of the Y-stations and decrypted. However, its most astonishing success was in decrypting the Zimmermann Telegram, a telegram from the German Foreign Office sent via Washington to its ambassador Heinrich von Eckardt in Mexico. === Postwar consolidation === With the importance of interception and decryption firmly established by the wartime experience, countries established permanent agencies dedicated to this task in the interwar period. In 1919, the British Cabinet's Secret Service Committee, chaired by Lord Curzon, recommended that a peace-time codebreaking agency should be created. The Government Code and Cypher School (GC&CS) was the first peace-time codebreaking agency, with a public function "to advise as to the security of codes and cyphers used by all Government departments and to assist in their provision", but also with a secret directive to "study the methods of cypher communications used by foreign powers". GC&CS officially formed on 1 November 1919, and produced its first decrypt on 19 October. By 1940, GC&CS was working on the diplomatic codes and ciphers of 26 countries, tackling over 150 diplomatic cryptosystems. The US Cipher Bureau was established in 1919 and achieved some success at the Washington Naval Conference in 1921, through cryptanalysis by Herbert Yardley. Secretary of War Henry L. Stimson closed the US Cipher Bureau in 1929 with the words "Gentlemen do not read each other's mail." === World War II === The use of SIGINT had even greater implications during World War II. The combined effort of intercepts and cryptanalysis for the whole of the British forces in World War II came under the code name "Ultra", managed from Government Code and Cypher School at Bletchley Park. Properly used, the German Enigma and Lorenz ciphers should have been virtually unbreakable, but flaws in German cryptographic procedures, and poor discipline among the personnel carrying them out, created vulnerabilities which made Bletchley's attacks feasible. Bletchley's work was essential to defeating the U-boats in the Battle of the Atlantic, and to the British naval victories in the Battle of Cape Matapan and the Battle of North Cape. In 1941, Ultra exerted a powerful effect on the North African desert campaign against German forces under General Erwin Rommel. General Sir Claude Auchinleck wrote that were it not for Ultra, "Rommel would have certainly got through to Cairo". Ultra decrypts featured prominently in the story of Operation SALAM, László Almásy's mission across the desert behind Allied lines in 1942. Prior to the Normandy landings on D-Day in June 1944, the Allies knew the locations of all but two of Germany's fifty-eight Western Front divisions. Winston Churchill was reported to have told King George VI: "It is thanks to the secret weapon of General Menzies, put into use on all the fronts, that we won the war!" Supreme Allied Commander, Dwight D. Eisenhower, at the end of the war, described Ultra as having been "decisive" to Allied victory. Official historian of British Intelligence in World War II Sir Harry Hinsley argued that Ultra shortened the war "by not less than two years and probably by four years"; and that, in the absence of Ultra, it is uncertain how the war would have ended. At a lower level, German cryptanalysis, direction finding, and traffic analysis were vital to Rommel's early successes in the Western Desert Campaign until British forces tightened their communications discipline and Australian raiders destroyed his principal SIGINT Company. == Technical definitions == The United States Department of Defense has defined the term "signals intelligence" as: A category of intelligence comprising either individually or in combination all communications intelligence (COMINT), electronic intelligence (ELINT), and foreign instrumentation signals intelligence (FISINT), however transmitted. Intelligence derived from communications, electronic, and foreign instrumentation signals. Being a broad field, SIGINT has many sub-disciplines. The two main ones are communications intelligence (COMINT) and electronic intelligence (ELINT). == Disciplines shared across the branches == === Targeting === A collection system has to know to look for a particular signal. "System", in this context, has several nuances. Targeting is the process of developing collection requirements: "1. A
Emergent algorithm
An emergent algorithm is an algorithm that exhibits emergent behavior. In essence an emergent algorithm implements a set of simple building block behaviors that when combined exhibit more complex behaviors. One example of this is the implementation of fuzzy motion controllers used to adapt robot movement in response to environmental obstacles. An emergent algorithm has the following characteristics: it achieves predictable global effects it does not require global visibility it does not assume any kind of centralized control it is self-stabilizing Other examples of emergent algorithms and models include cellular automata, artificial neural networks and swarm intelligence systems (ant colony optimization, bees algorithm, etc.).
Tropical cryptography
In tropical analysis, tropical cryptography refers to the study of a class of cryptographic protocols built upon tropical algebras. In many cases, tropical cryptographic schemes have arisen from adapting classical (non-tropical) schemes to instead rely on tropical algebras. The case for the use of tropical algebras in cryptography rests on at least two key features of tropical mathematics: in the tropical world, there is no classical multiplication (a computationally expensive operation), and the problem of solving systems of tropical polynomial equations has been shown to be NP-hard. == Basic Definitions == The key mathematical object at the heart of tropical cryptography is the tropical semiring ( R ∪ { ∞ } , ⊕ , ⊗ ) {\displaystyle (\mathbb {R} \cup \{\infty \},\oplus ,\otimes )} (also known as the min-plus algebra), or a generalization thereof. The operations are defined as follows for x , y ∈ R ∪ { ∞ } {\displaystyle x,y\in \mathbb {R} \cup \{\infty \}} : x ⊕ y = min { x , y } {\displaystyle x\oplus y=\min\{x,y\}} x ⊗ y = x + y {\displaystyle x\otimes y=x+y} It is easily verified that with ∞ {\displaystyle \infty } as the additive identity, these binary operations on R ∪ { ∞ } {\displaystyle \mathbb {R} \cup \{\infty \}} form a semiring.