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Many real-world phenomena exhibit limited or statistical fractal properties and fractal dimensions that have been estimated from sampled data using computer based fractal analysis techniques. Practically, measurements of fractal dimension are affected by various methodological issues, and are sensitive to numerical or ...
Fractal dimension
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The model was initially developed by Beddoes and Leishman&Beddoes and refined by Leishman and Tyler&Leishman.The model consists of three distinct sub-systems for describing the dynamic stall physics: Attached flow model for the unsteady (linear) airloads (with compressibility effects included) using the compressible in...
Dynamic stall on helicopter rotors
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Domination of the vortex-shedding phenomenon; High deviations of airloads and large hysteresis; Extension of the viscous zone to the order of airfoil chord; Less sensitivity to airfoil geometry, reduced frequency and Mach number; Rapid overshoots of airloads after stall.
Dynamic stall on helicopter rotors
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The effect of airfoil geometry on dynamic stall is quite intricate. As is shown in the figure, for a cambered airfoil, the lift stall is delayed and the maximum nose-down pitch moment is significantly reduced. On the other hand, the inception of stall is more abrupt for a sharp leading-edge airfoil. More information is...
Dynamic stall on helicopter rotors
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Minor flow separation; Low deviations of airloads and small hysteresis; The same order of the viscous zone thickness as the airfoil thickness; Sensitivity to airfoil geometry, reduced frequency and Mach number.
Dynamic stall on helicopter rotors
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The terms fractal dimension and fractal were coined by Mandelbrot in 1975, about a decade after he published his paper on self-similarity in the coastline of Britain. Various historical authorities credit him with also synthesizing centuries of complicated theoretical mathematics and engineering work and applying them ...
Fractal dimension
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If the theoretical fractal dimension of a set exceeds its topological dimension, the set is considered to have fractal geometry.Unlike topological dimensions, the fractal index can take non-integer values, indicating that a set fills its space qualitatively and quantitatively differently from how an ordinary geometrica...
Fractal dimension
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Such familiar scaling relationships can be defined mathematically by the general scaling rule in Equation 1, where the variable N {\displaystyle N} stands for the number of measurement units (sticks, squares, etc.), ε {\displaystyle \varepsilon } for the scaling factor, and D {\displaystyle D} for the fractal dimension...
Fractal dimension
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The concept of a fractal dimension rests in unconventional views of scaling and dimension. As Fig. 4 illustrates, traditional notions of geometry dictate that shapes scale predictably according to intuitive and familiar ideas about the space they are contained within, such that, for instance, measuring a line using fir...
Fractal dimension
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In this case, a validation can also be done by comparing other than fractal properties implied by the model, with measured data. In colloidal physics, systems composed of particles with various fractal dimensions arise. To describe these systems, it is convenient to speak about a distribution of fractal dimensions, and...
Fractal dimension
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In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales...
Fractal dimension
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A view model or viewpoints framework in systems engineering, software engineering, and enterprise engineering is a framework which defines a coherent set of views to be used in the construction of a system architecture, software architecture, or enterprise architecture. A view is a representation of the whole system fr...
Viewpoint model
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Among these, the IEEE Recommended Practice for Architectural Description of Software-Intensive Systems (IEEE Std 1471-2000) established useful definitions of view, viewpoint, stakeholder and concern and guidelines for documenting a system architecture through the use of multiple views by applying viewpoints to address ...
Viewpoint model
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In the 1970s, methods began to appear in software engineering for modeling with multiple views. Douglas T. Ross and K.E. Schoman in 1977 introduce the constructs context, viewpoint, and vantage point to organize the modeling process in systems requirements definition.
Viewpoint model
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In systems engineering, a viewpoint is a partitioning or restriction of concerns in a system. Adoption of a viewpoint is usable so that issues in those aspects can be addressed separately. A good selection of viewpoints also partitions the design of the system into specific areas of expertise.Viewpoints provide the con...
Viewpoint model
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S2CID 123422715. Hollings, Christopher (2014). Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups.
Semigroup with zero
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Zbl 1040.20048. Hollings, Christopher (2009). "The Early Development of the Algebraic Theory of Semigroups".
Semigroup with zero
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Clifford, Alfred Hoblitzelle; Preston, Gordon Bamford (2010) . The algebraic theory of semigroups. Vol.
Semigroup with zero
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The Algebraic Theory of Semigroups. Vol. 1.
Semigroup with zero
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These results are nothing more than a particularization of the first isomorphism theorem in universal algebra. Congruence classes and factor monoids are the objects of study in string rewriting systems. A nuclear congruence on S is one which is the kernel of an endomorphism of S.A semigroup S satisfies the maximal cond...
Semigroup with zero
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Every element x has at least one inverse y satisfying xyx=x and yxy=y; the elements x and y are sometimes called "mutually inverse". Inverse semigroups are regular semigroups where every element has exactly one inverse. Alternatively, a regular semigroup is inverse if and only if any two idempotents commute. Affine sem...
Semigroup with zero
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An example of such a sheaf is that associated in algebraic geometry to an R-module M, R being any commutative ring, on the spectrum of a ring Spec(R). Another example: according to Cartan's theorem A, any coherent sheaf on a Stein manifold is spanned by global sections. (cf. Serre's theorem A below.)
Sheaf extension
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In mathematics, in the theory of several complex variables and complex manifolds, a Stein manifold is a complex submanifold of the vector space of n complex dimensions. They were introduced by and named after Karl Stein (1951). A Stein space is similar to a Stein manifold but is allowed to have singularities. Stein spa...
Levi problem
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A knowledge arena is a virtual space where individuals can manipulate concepts and relationships to form a concept map. Individuals using a computer with appropriate software can represent concepts and the relationships between concepts in a node-relationship-node formalism. The process of thinking about the concepts a...
Knowledge arena
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A fundamental barrier to making AI systems explainable is the technical complexity of such systems. End users often lack the coding knowledge required to understand software of any kind. Current methods used to explain AI are mainly technical ones, geared toward machine learning engineers for debugging purposes, rather...
Interpretable artificial intelligence
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A ligand exchange (also ligand substitution) is a type of chemical reaction in which a ligand in a compound is replaced by another. One type of pathway for substitution is the ligand dependent pathway. In organometallic chemistry this can take place via associative substitution or by dissociative substitution.
Ligand exchange reaction
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Developments in biomedical text mining have incorporated identification of biological entities with named entity recognition, or NER. Names and identifiers for biomolecules such as proteins and genes, chemical compounds and drugs, and disease names have all been used as entities. Most entity recognition methods are sup...
Biomedical text mining
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Computational frameworks have been developed to rapidly build tools for biomedical text mining tasks. SwellShark is a framework for biomedical NER that requires no human-labeled data but does make use of resources for weak supervision (e.g., UMLS semantic types). The SparkText framework uses Apache Spark data streaming...
Biomedical text mining
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Biomedical text mining (including biomedical natural language processing or BioNLP) refers to the methods and study of how text mining may be applied to texts and literature of the biomedical domain. As a field of research, biomedical text mining incorporates ideas from natural language processing, bioinformatics, medi...
Biomedical text mining
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A variety of academic journals publishing manuscripts on biology and medicine include topics in text mining and natural language processing software. Some journals, including the Journal of the American Medical Informatics Association (JAMIA) and the Journal of Biomedical Informatics are popular publications for these ...
Biomedical text mining
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Some biomedical text mining and natural language processing tools are available through application programming interfaces, or APIs. NOBLE Coder performs concept recognition through an API.
Biomedical text mining
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Text mining researchers frequently combine these corpora with the controlled vocabularies and ontologies available through the National Library of Medicine's Unified Medical Language System (UMLS) and Medical Subject Headings (MeSH). Machine learning-based methods often require very large data sets as training data to ...
Biomedical text mining
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Large annotated corpora used in the development and training of general purpose text mining methods (e.g., sets of movie dialogue, product reviews, or Wikipedia article text) are not specific for biomedical language. While they may provide evidence of general text properties such as parts of speech, they rarely contain...
Biomedical text mining
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The discrete ordinates method, or some variation of it, is applied for solving radiation intensities in several physics and engineering simulation programs, such as COMSOL Multiphysics or the Fire Dynamics Simulator.
Discrete Ordinates Method
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Shellsort is an optimization of insertion sort that allows the exchange of items that are far apart. The idea is to arrange the list of elements so that, starting anywhere, taking every hth element produces a sorted list. Such a list is said to be h-sorted. It can also be thought of as h interleaved lists, each individ...
Shellsort
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The nano-FTIR technology has been commercialized by neaspec – a Germany-based spin-off company of the Max Planck Institute of Biochemistry founded by Ocelic, Hillenbrand and Keilmann in 2007 and based on the original patent by Ocelic and Hillenbrand. The detection module optimized for broadband illumination sources was...
Nano-FTIR
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The availability of both amplitude and phase of the scattered field and theoretically well understood signal formation in nano-FTIR allow for the recovery of both real and imaginary parts of the dielectric function, i.e. finding the index of refraction and the extinction coefficient of the sample. While such recovery f...
Nano-FTIR
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Significant efforts have been put towards simulating nano-FTIR electric field and complex scattering signal through numerical methods (using commercial proprietary software such as CST Microwave Studio, Lumerical FDTD, and COMSOL Multiphysics) as well as through analytical models (such as through finite dipole and poin...
Nano-FTIR
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Nano-FTIR systems can be easily integrated into synchrotron radiation beamlines. The use of synchrotron radiation allows for acquisition of an entire mid-infrared spectrum at once. Synchrotrons radiation has already been utilized in synchrotron infrared microscopectroscopy - the technique most widely used in bioscience...
Nano-FTIR
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Nano-FTIR has a plenitude of applications, including polymers and polymer composites, organic films, semiconductors, biological research (cell membranes, proteins structure, studies of single viruses), chemistry and catalysis, photochemistry, minerals and biominerals, geochemistry, corrosion and materials sciences, low...
Nano-FTIR
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{\displaystyle \|x-y\|=\|x-z\|+\|z-y\|{\text{ for all }}x,y\in X{\text{ and }}z\in .} Two norms ‖ ⋅ ‖ α {\displaystyle \|\cdot \|_{\alpha }} and ‖ ⋅ ‖ β {\displaystyle \|\cdot \|_{\beta }} on a vector space X {\displaystyle X} are called equivalent if they induce the same topology, which happens if and only if there ex...
L2 distance
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{\displaystyle n\to \infty .} Equivalently, the topology consists of all sets that can be represented as a union of open balls. If ( X , ‖ ⋅ ‖ ) {\displaystyle (X,\|\cdot \|)} is a normed space then ‖ x − y ‖ = ‖ x − z ‖ + ‖ z − y ‖ for all x , y ∈ X and z ∈ .
L2 distance
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The topology thus defined (by either a norm or a seminorm) can be understood either in terms of sequences or open sets. A sequence of vectors { v n } {\displaystyle \{v_{n}\}} is said to converge in norm to v , {\displaystyle v,} if ‖ v n − v ‖ → 0 {\displaystyle \left\|v_{n}-v\right\|\to 0} as n → ∞ .
L2 distance
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The concept of unit circle (the set of all vectors of norm 1) is different in different norms: for the 1-norm, the unit circle is a square oriented as a diamond; for the 2-norm (Euclidean norm), it is the well-known unit circle; while for the infinity norm, it is an axis-aligned square. For any p {\displaystyle p} -nor...
L2 distance
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The source coding theorem states that for any ε > 0 {\displaystyle \varepsilon >0} and any discrete-time i.i.d. source such as X {\displaystyle X} and for any rate less than the entropy of the source, there is large enough n {\displaystyle n} and an encoder that takes n {\displaystyle n} i.i.d. repetition of the source...
Error exponent
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Many of the information-theoretic theorems are of asymptotic nature, for example, the channel coding theorem states that for any rate less than the channel capacity, the probability of the error of the channel code can be made to go to zero as the block length goes to infinity. In practical situations, there are limita...
Error exponent
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The channel coding theorem states that for any ε > 0 and for any rate less than the channel capacity, there is an encoding and decoding scheme that can be used to ensure that the probability of block error is less than ε > 0 for sufficiently long message block X. Also, for any rate greater than the channel capacity, th...
Error exponent
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CLAIRE regularly provides feedback to the European Commission on matters pertaining to Artificial Intelligence including the CLAIRE's "Response to the European Commission White Paper on Artificial Intelligence – A European approach to excellence and trust" and the "Response to the European Commission’s Proposal for AI ...
Confederation of Laboratories for Artificial Intelligence Research in Europe
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CLAIRE has the support of more than 4,000 people, representing the vast majority of Europe’s AI community, spanning academia and industry, research and innovation, including 2295 AI experts (PhD-level expertise in AI or equivalent) and 1126 supporters in industry.Furthermore, nine advisory groups with 48 members from 1...
Confederation of Laboratories for Artificial Intelligence Research in Europe
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The Confederation of Laboratories for Artificial Intelligence Research in Europe (CLAIRE) is a European organisation, created to strengthen artificial intelligence (AI) and human-centred AI research and innovation, in Europe. CLAIRE is referred to as the world's largest network for artificial intelligence research.CLAI...
Confederation of Laboratories for Artificial Intelligence Research in Europe
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The CLAIRE Network consists of the Research, the Innovation and the Rising Researchers Networks and collectively creates the world‘s largest AI network of labs and institutions, companies and start-ups, and graduate students involved in AI research, that are committed to working together towards developing European sov...
Confederation of Laboratories for Artificial Intelligence Research in Europe
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For instance, when a variable is binary, the messages over the edges incident to the corresponding vertex can be represented as vectors of length 2: the first entry is the message evaluated in 0, the second entry is the message evaluated in 1. When a variable belongs to the field of real numbers, messages can be arbitr...
Factor graph
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A factor graph is a bipartite graph representing the factorization of a function. In probability theory and its applications, factor graphs are used to represent factorization of a probability distribution function, enabling efficient computations, such as the computation of marginal distributions through the sum-produ...
Factor graph
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This algorithm is somewhat analogous to a neural network with a single hidden layer. The internal nodes are represented by the clusters c j {\displaystyle c_{j}\,} and the first and second layers of network weights are the conditional probabilities p ( c j | x i ) {\displaystyle p(c_{j}|x_{i})\,} and p ( y k | c j ) {\...
Information bottleneck method
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The information bottleneck method is a technique in information theory introduced by Naftali Tishby, Fernando C. Pereira, and William Bialek. It is designed for finding the best tradeoff between accuracy and complexity (compression) when summarizing (e.g. clustering) a random variable X, given a joint probability distr...
Information bottleneck method
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It has been mathematically proven that controlling information bottleneck is one way to control generalization error in deep learning. Namely, the generalization error is proven to scale as O ~ ( I ( X , T ) + 1 n ) {\displaystyle {\tilde {O}}\left({\sqrt {\frac {I(X,T)+1}{n}}}\right)} where n {\displaystyle n} is the ...
Information bottleneck method
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Theory of Information Bottleneck is recently used to study Deep Neural Networks (DNN). Consider X {\displaystyle X} and Y {\displaystyle Y} respectively as the input and output layers of a DNN, and let T {\displaystyle T} be any hidden layer of the network. Shwartz-Ziv and Tishby proposed the information bottleneck tha...
Information bottleneck method
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The equilibrium probability vector p ( ∞ ) {\displaystyle p(\infty )\,} given, in the usual way, by the dominant eigenvector of matrix P {\displaystyle P\,} which is independent of the initialising vector p ( 0 ) {\displaystyle p(0)\,} . This Markov transition method establishes a probability at the sample points which...
Information bottleneck method
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In the following soft clustering example, the reference vector Y {\displaystyle Y\,} contains sample categories and the joint probability p ( X , Y ) {\displaystyle p(X,Y)\,} is assumed known. A soft cluster c k {\displaystyle c_{k}\,} is defined by its probability distribution over the data samples x i: p ( c k | x i ...
Information bottleneck method
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When the scientific method employs statistics as a key part of its arsenal, there are mathematical and practical issues that can have a deleterious effect on the reliability of the output of scientific methods. This is described in a popular 2005 scientific paper "Why Most Published Research Findings Are False" by John...
Scientific methodology
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James D. Watson, Francis Crick, and others hypothesized that DNA had a helical structure. This implied that DNA's X-ray diffraction pattern would be 'x shaped'. This prediction followed from the work of Cochran, Crick and Vand (and independently by Stokes). The Cochran-Crick-Vand-Stokes theorem provided a mathematical ...
Scientific methodology
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The other approach, "top down", takes into account the emergence of unpredictable phenomena through the reductionist approach. Thus, the experimental evidence showing that carcinogenesis is a process bound to emerge a break geometry of the tissue architecture requires abandoning the genetic level or above genetics to g...
Physical oncology
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The soft material that transmits the mechanical signals is therefore pre-stressed and this allows the transmission of forces in the body with a quantitative distribution according to the scale: the skeleton, a macroscopic structure, will transmit much greater forces than an isolated organ. On the scale of a tissue of a...
Physical oncology
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But this shift from the physical sciences to the biological sciences is problematic, in the absence of any bridge between these two sciences, one quantitative, physics based on mathematical language and the other qualitative, based on the laws of genetics and molecular biology. OP aims to study the effect of a mechanic...
Physical oncology
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Biology / Mechanics comparison Some differences between biological and physical signals The use of mechanical signals is therefore also the support of mechanobiology whose objective is very different from the PO. Indeed, as shown in the table above, the study of mechanotransduction, which is the support of mechanobiolo...
Physical oncology
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Any theory of carcinogenesis must explain cancerization since its onset, dysplasia, in situ, then crossing of the basement membrane, the growth of the primary tumor and the appearance of metastases. Let us quote DW Smithers (1962): "cancer is no more a disease of the cells than a traffic jam is a disease of cars". We t...
Physical oncology
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The diagnosis of cancer is made by looking under the microscope a fragment of the tumor (biopsy). The tissue phenotype - here cancerous tissue - is the sum of the cellular and tissue phenotype. The phenotype of the cell is supposed to be the translation of the genotype (and of the environment: epigenetics) expressed in...
Physical oncology
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The cancer is fractal and this in all its components and at different scales micro/meso and macroscopic. This geometry is recent and still little integrated in our mental representations.The first observation was the fractal nature of microcalcifications linked to breast cancer on a mammogram.Then the fractality of the...
Physical oncology
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Several teams, in the USA in particular, had maintained an expertise in the study of non-biological signals in oncology (Donald Ingber, Mina Bissell then Valerie Weaver, Rakesh J Jain among others).But the absolute dominance of genetics and molecular biology since the middle of the 20th century had marginalized this ap...
Physical oncology
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Popularized by Pierre Gilles de Gennes the term soft matter refers to the study of materials between solid and liquid; at ambient temperature, that of biology, thermal energy (kT) is of the same order of magnitude as the interaction energies between the various components. Due to this entropy / enthalpy balance these b...
Physical oncology
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Barclay recovers, but the crew finds him much more intelligent than before. His IQ continues to increase, and La Forge finds that he has spent the night in a holodeck arguing quantum physics with Albert Einstein.
The Nth Degree (Star Trek: The Next Generation)
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The special homeomorphisms described above or their inverses provide piecewise linear homeomorphisms which carry the interior of the larger polygon onto the polygon with the free triangle removed. Iterating this process it follows that there is a piecewise linear homeomorphism of compact support carrying the original p...
Schönflies problem
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Given a simple closed polygonal curve in the plane, the piecewise linear Jordan–Schoenflies theorem states that there is a piecewise linear homeomorphism of the plane, with compact support, carrying the polygon onto a triangle and taking the interior and exterior of one onto the interior and exterior of the other.The i...
Schönflies problem
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By the polygonal Jordan-Schoenflies theorem, each of these homeomorphisms extends to the interior of the polygon. Together they yield a homeomorphism F2 of the closure of the interior of Γ2 onto the closure of the interior of Δ2; F2 extends F1. Continuing in this way produces polygonal curves Γn and triangles Δn with a...
Schönflies problem
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Let Di be the points at the intersection of the radius through f(Ai) and the smaller triangle. There is a piecewise linear homeomorphism F1 of the polygonal curve onto the smaller triangle carrying Ci onto Di. By the Jordan-Schoenflies theorem it extends to a homeomorphism F1 between the closure of their interiors.
Schönflies problem
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By construction these two disjoint open path-connected sets fill out the complement of the curve in the plane. Given the Jordan curve theorem, the Jordan-Schoenflies theorem can be proved as follows. The first step is to show that a dense set of points on the curve are accessible from the inside of the curve, i.e. they...
Schönflies problem
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The Jordan curve theorem is first deduced by this method. The Jordan curve is given by a continuous function on the unit circle.
Schönflies problem
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The Jordan-Schoenflies theorem for continuous curves can be proved using Carathéodory's theorem on conformal mapping. It states that the Riemann mapping between the interior of a simple Jordan curve and the open unit disk extends continuously to a homeomorphism between their closures, mapping the Jordan curve homeomorp...
Schönflies problem
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The Schoenflies problem can be posed in categories other than the topologically locally flat category, i.e. does a smoothly (piecewise-linearly) embedded (n − 1)-sphere in the n-sphere bound a smooth (piecewise-linear) n-ball? For n = 4, the problem is still open for both categories. See Mazur manifold. For n ≥ 5 the q...
Schönflies problem
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There does exist a higher-dimensional generalization due to Morton Brown (1960) and independently Barry Mazur (1959) with Morse (1960), which is also called the generalized Schoenflies theorem. It states that, if an (n − 1)-dimensional sphere S is embedded into the n-dimensional sphere Sn in a locally flat way (that is...
Schönflies problem
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In mathematics, the Schoenflies problem or Schoenflies theorem, of geometric topology is a sharpening of the Jordan curve theorem by Arthur Schoenflies. For Jordan curves in the plane it is often referred to as the Jordan–Schoenflies theorem.
Schönflies problem
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The third category is online interaction; for example, websites, blogs, wikis and podcasts can be used for science communication, as can other social media or forms of artificial intelligence like AI-Chatbots. Online methods of communicating science have the potential to reach huge audiences, can allow direct interacti...
Science communication
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Science popularization figures such as Carl Sagan and Neil deGrasse Tyson are partly responsible for the view of science or a specific science discipline within the general public. However, the degree of knowledge and experience a science popularizer has can vary greatly. Because of this, some science communication can...
Science communication
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21,183
Anchoring and adjustment: used when making judgments with uncertainties. One will start with an anchoring point, then adjust it to reach an assumption. For example, if you are asked to estimate how many people will take Dr. Smith's biology class this spring, you may recall that 38 students took the class in the fall, a...
Science communication
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There is nothing wrong with hypothesis testing and p-values per se as long as authors, reviewers, and action editors use them correctly." Some statisticians prefer to use alternative measures of evidence, such as likelihood ratios or Bayes factors. Using Bayesian statistics can avoid confidence levels, but also require...
Significance level
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In specific fields such as particle physics and manufacturing, statistical significance is often expressed in multiples of the standard deviation or sigma (σ) of a normal distribution, with significance thresholds set at a much stricter level (for example 5σ). For instance, the certainty of the Higgs boson particle's e...
Significance level
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Clinical Biochemistry is a peer-reviewed scientific journal covering the analytical and clinical investigation of laboratory tests in humans used for diagnosis, molecular biology and genetics, prognosis, treatment and therapy, and monitoring of disease ; the discipline of clinical biochemistry. It is the official journ...
Clinical Biochemistry
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Clinical Biochemistry. 40 (12): 893–899. doi:10.1016/j.clinbiochem.2007.04.017. PMID 17543295.
Clinical Biochemistry
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Clinical Biochemistry. 40 (5–6): 383–391. doi:10.1016/j.clinbiochem.2006.10.026.
Clinical Biochemistry
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According to SCOPUS, the following three articles have been cited most often (>70 times): Herget-Rosenthal, S.; Bökenkamp, A.; Hofmann, W. (2007). "How to estimate GFR-serum creatinine, serum cystatin C or equations?". Clinical Biochemistry.
Clinical Biochemistry
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Researchers at the University of North Carolina published an article in Clinical Biochemistry which found Baby wash products could cause false drug test results. Newborn drug screening has a significant implications in both the healthcare and legal domains, on occasion resulting in involvement by social services or fal...
Clinical Biochemistry
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21,191
Pharmacodynamics (PD) is the study of the biochemical and physiologic effects of drugs (especially pharmaceutical drugs). The effects can include those manifested within animals (including humans), microorganisms, or combinations of organisms (for example, infection). Pharmacodynamics and pharmacokinetics are the main ...
Pharmacodynamics
0.81042
21,192
Most people are neither evening nor morning types but lie somewhere in between. Estimates vary, but a 2007 survey of over 55,000 people by Roenneberg et al. showed that morningness–eveningness tends to follow a normal distribution. People who share a chronotype, morningness or eveningness, have similar activity-pattern...
Diurnal variation
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21,193
Descriptive Complexity is a book in mathematical logic and computational complexity theory by Neil Immerman. It concerns descriptive complexity theory, an area in which the expressibility of mathematical properties using different types of logic is shown to be equivalent to their computability in different types of res...
Descriptive Complexity
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It includes Fagin's theorem characterizing nondeterministic polynomial time in terms of existential second-order logic, the Cook–Levin theorem on the existence of NP-complete problems, and extensions of these results to the polynomial hierarchy. Chapter eight uses games to prove the inexpressibility of certain language...
Descriptive Complexity
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21,195
The term data model can have two meanings: A data model theory, i.e. a formal description of how data may be structured and accessed. A data model instance, i.e. applying a data model theory to create a practical data model instance for some particular application.A data model theory has three main components: The stru...
Structured data
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21,196
The Unified Modeling Language (UML) is a standardized general-purpose modeling language in the field of software engineering. It is a graphical language for visualizing, specifying, constructing, and documenting the artifacts of a software-intensive system. The Unified Modeling Language offers a standard way to write a...
Structured data
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21,197
Noncoding RNA molecules play many essential roles in cells, especially in the many reactions of protein synthesis and RNA processing. Noncoding RNA include tRNA, ribosomal RNA, microRNA, snRNA and other non-coding RNA genes including about 60,000 long non-coding RNAs (lncRNAs). Although the number of reported lncRNA ge...
Human genome sequence map
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Although the sequence of the human genome has been completely determined by DNA sequencing in 2022 (including methylation), it is not yet fully understood. Most, but not all, genes have been identified by a combination of high throughput experimental and bioinformatics approaches, yet much work still needs to be done t...
Human genome sequence map
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21,199
Optimization comes at a price and it is important to be sure that the investment is worthwhile. An automatic optimizer (or optimizing compiler, a program that performs code optimization) may itself have to be optimized, either to further improve the efficiency of its target programs or else speed up its own operation. ...
Premature optimization
0.81041