Analysis and Numerics of the Chemical Master Equation
... is dimensionally exponential. For example, the state space of a system with 10 different types of particles, where each particle can be alive or dead, is the size of 210 . The state space for biological systems with more than 10 varieties of species becomes too large to compute. As larger dimensiona ...
... is dimensionally exponential. For example, the state space of a system with 10 different types of particles, where each particle can be alive or dead, is the size of 210 . The state space for biological systems with more than 10 varieties of species becomes too large to compute. As larger dimensiona ...
Using extended feature objects for partial similarity
... therefore determine the extended feature objects which correspond to the polygon sections starting anywhere on the first edge and ending anywhere on the last edge. Since we have two continuous parameters, the extended feature objects are 2D objects in multidimensional feature space. The 2D feature o ...
... therefore determine the extended feature objects which correspond to the polygon sections starting anywhere on the first edge and ending anywhere on the last edge. Since we have two continuous parameters, the extended feature objects are 2D objects in multidimensional feature space. The 2D feature o ...
Availability-aware Mapping of Service Function Chains
... wide area network, primary VNFs of a service chain may be implemented in one single data center for low latency [20], [18] or distributed at geographically different locations [25] for reasons [2], [1], [21], [8], such as 1) some data centers may only implement limited types of network functions to ...
... wide area network, primary VNFs of a service chain may be implemented in one single data center for low latency [20], [18] or distributed at geographically different locations [25] for reasons [2], [1], [21], [8], such as 1) some data centers may only implement limited types of network functions to ...
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... fault-tolerant programs using their existing fault-intolerant version and a partially available specification. In [8], the authors introduce a synthesis algorithm that adds UNITY properties [9] such as leads-to (which is an unbounded liveness property) to untimed programs. Synthesis of real-time pro ...
... fault-tolerant programs using their existing fault-intolerant version and a partially available specification. In [8], the authors introduce a synthesis algorithm that adds UNITY properties [9] such as leads-to (which is an unbounded liveness property) to untimed programs. Synthesis of real-time pro ...
Querying Large Collections of Semistructured Data
... We focus first on mathematics retrieval, which is appealing in various domains, such as education, digital libraries, engineering, patent documents, and medical sciences. Capturing the similarity of mathematical expressions also greatly enhances document classification in such domains. Unlike text r ...
... We focus first on mathematics retrieval, which is appealing in various domains, such as education, digital libraries, engineering, patent documents, and medical sciences. Capturing the similarity of mathematical expressions also greatly enhances document classification in such domains. Unlike text r ...
Stochastic Search and Surveillance Strategies for
... 5.2 Knapsack Problem with Sigmoid Utility . . . . . . . . . . . 5.2.1 KP with Sigmoid Utility: Problem Description . . . . 5.2.2 KP with Sigmoid Utility: Approximation Algorithm . 5.3 Generalized Assignment Problem with Sigmoid Utility . . . 5.3.1 GAP with Sigmoid Utility: Problem Description . . . ...
... 5.2 Knapsack Problem with Sigmoid Utility . . . . . . . . . . . 5.2.1 KP with Sigmoid Utility: Problem Description . . . . 5.2.2 KP with Sigmoid Utility: Approximation Algorithm . 5.3 Generalized Assignment Problem with Sigmoid Utility . . . 5.3.1 GAP with Sigmoid Utility: Problem Description . . . ...
Algorithm
In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ AL-gə-ri-dhəm) is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning.An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing ""output"" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.The concept of algorithm has existed for centuries, however a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the ""decision problem"") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define ""effective calculability"" or ""effective method""; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's ""Formulation 1"" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.