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Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics, numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology.
Public-key cryptography, or asymmetric cryptography, is a cryptographic system that uses pairs of keys. Each pair consists of a public key and a private key. The generation of such key pairs depends on cryptographic algorithms which are based on mathematical problems termed one-way functions. Effective security requires keeping the private key private; the public key can be openly distributed without compromising security.
A key in cryptography is a piece of information, usually a string of numbers or letters that are stored in a file, which, when processed through a cryptographic algorithm, can encode or decode cryptographic data. Based on the used method, the key can be different sizes and varieties, but in all cases, the strength of the encryption relies on the security of the key being maintained. A key’s security strength is dependent on its algorithm, the size of the key, the generation of the key, and the process of key exchange.
A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature, where the prerequisites are satisfied, gives a recipient very strong reason to believe that the message was created by a known sender (authenticity), and that the message was not altered in transit (integrity).
Round-robin (RR) is one of the algorithms employed by process and network schedulers in computing. As the term is generally used, time slices are assigned to each process in equal portions and in circular order, handling all processes without priority. Round-robin scheduling is simple, easy to implement, and starvation-free. Round-robin scheduling can be applied to other scheduling problems, such as data packet scheduling in computer networks. It is an operating system concept.
In the field of databases in computer science, a transaction log is a history of actions executed by a database management system used to guarantee ACID properties over crashes or hardware failures. Physically, a log is a file listing changes to the database, stored in a stable storage format.
In numerical analysis, hill climbing is a mathematical optimization technique which belongs to the family of local search. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by making an incremental change to the solution. If the change produces a better solution, another incremental change is made to the new solution, and so on until no further improvements can be found.
Checkpointing is a technique that provides fault tolerance for computing systems. It basically consists of saving a snapshot of the application's state, so that applications can restart from that point in case of failure. This is particularly important for the long running applications that are executed in the failure-prone computing systems.
In computer science, a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems.
In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation, computational differentiation, auto-differentiation, or simply autodiff, is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations and elementary functions. By applying the chain rule repeatedly to these operations, derivatives of arbitrary order can be computed automatically, accurately to working precision, and using at most a small constant factor more arithmetic operations than the original program.
Harmonic Vector Excitation Coding, abbreviated as HVXC is a speech coding algorithm specified in MPEG-4 Part 3 standard for very low bit rate speech coding. HVXC supports bit rates of 2 and 4 kbit/s in the fixed and variable bit rate mode and sampling frequency 8 kHz. It also operates at lower bitrates, such as 1.2 - 1.7 kbit/s, using a variable bit rate technique. The total algorithmic delay for the encoder and decoder is 36 ms.
Quicksort is an in-place sorting algorithm. Developed by British computer scientist Tony Hoare in 1959 and published in 1961, it is still a commonly used algorithm for sorting. When implemented well, it can be somewhat faster than merge sort and about two or three times faster than heapsort.
In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points higher than the adjacent points are reduced, and points that are lower than the adjacent points are increased leading to a smoother signal. Smoothing may be used in two important ways that can aid in data analysis (1) by being able to extract more information from the data as long as the assumption of smoothing is reasonable and (2) by being able to provide analyses that are both flexible and robust. Many different algorithms are used in smoothing.
In mathematics, binary splitting is a technique for speeding up numerical evaluation of many types of series with rational terms. In particular, it can be used to evaluate hypergeometric series at rational points.
Cryptography, or cryptology, is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages; various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, electrical engineering, communication science, and physics. Applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.
Desmond is a software package developed at D. E. Shaw Research to perform high-speed molecular dynamics simulations of biological systems on conventional computer clusters. The code uses novel parallel algorithms and numerical methods to achieve high performance on platforms containing multiple processors, but may also be executed on a single computer.
In cryptography, post-quantum cryptography refers to cryptographic algorithms that are thought to be secure against a cryptanalytic attack by a quantum computer. The problem with currently popular algorithms is that their security relies on one of three hard mathematical problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve discrete logarithm problem. All of these problems can be easily solved on a sufficiently powerful quantum computer running Shor's algorithm.
F2FS is a flash file system initially developed by Samsung Electronics for the Linux kernel.
Michel Raynal, is a French informatics scientist, professor at IRISA, University of Rennes, France. He is known for his contributions in the fields of algorithms, computability, and fault-tolerance in the context of concurrent and distributed systems. Michel Raynal is also Distinguished Chair professor at the Hong Kong Polytechnic University and editor of the “Synthesis Lectures on Distributed Computing Theory” published by Morgan & Claypool. He is a senior member of Institut Universitaire de France and a member of Academia Europaea.
References
- ↑ D. K. Pradhan and N. H. Vaidya, "Roll-forward checkpointing scheme: a novel fault-tolerant architecture," in IEEE Transactions on Computers, vol. 43, no. 10, pp. 1163-1174, Oct. 1994, doi: 10.1109/12.324542.