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Measure of the level of consciousness
Perturbational Complexity Index (PCI) is a quantitative measure used in neuroscience to assess the level of consciousness based on the complexity of brain
Perturbational Complexity Index
Perturbational_Complexity_Index
Topics referred to by the same term
signalling system Pavement condition index, used in transportation civil engineering Perturbational Complexity Index, a scalar measure of consciousness
PCI
Awareness of internal and external existence
[citation needed] In 2013, the perturbational complexity index (PCI) was proposed, a measure of the algorithmic complexity of the electrophysiological response
Consciousness
State of unconsciousness
patient's awakening. In advanced cases, a technique called the Perturbational Complexity Index (PCI), which combines transcranial magnetic stimulation (TMS)
Coma
Theory within consciousness research
has found practical application in the development of the Perturbational Complexity Index (PCI), an empirical measure used in clinical neuroscience to
Integrated_information_theory
System composed of many interacting components
built by the Santa Fe Institute in 1989 and the more recent economic complexity index (ECI), introduced by the MIT physicist Cesar A. Hidalgo and the Harvard
Complex_system
Topological index in graph theory
The harmonic index is a topological index based on the degrees of vertices in a graph. Introduced by Fajtlowicz in 1987, it has become an important descriptor
Harmonic_index
Unitary transformation in quantum mechanics
W=e^{S}} being unitary, it does not change the amount of information or the complexity of the Hamiltonian. The resulting shuffle of the matrix elements creates
Schrieffer–Wolff transformation
Schrieffer–Wolff_transformation
Graph with sign-labeled edges
Finding the frustration index is an NP-hard problem. One can see the NP-hard complexity by observing that the frustration index of an all-negative signed
Signed_graph
Field of mathematics and science based on non-linear systems and initial conditions
the Future of the European Union". Chaos, complexity and leadership 2018 explorations of chaotic and complexity theory. Springer. ISBN 978-3-030-27672-0
Chaos_theory
Method for mathematical optimization
time-complexity, because its complexity is bounded by a cubic polynomial. There are examples of algorithms that do not have polynomial-time complexity. For
Criss-cross_algorithm
Computational problem of graph theory
asymptotic time complexity (using big O notation). In 1998, David Eppstein reported an approach that maintains an asymptotic complexity of O(m + n log n
K_shortest_path_routing
Method in computer science
Intuitively, h i ( x ) {\displaystyle h_{i}(x)} represents a small perturbation in the index of T {\displaystyle T} . By noting that ⌊ b i x ⌋ = b i x + (
Akra–Bazzi_method
Subset of artificial intelligence
performance in the context of generalisation, the complexity of the hypothesis should match the complexity of the function underlying the data. If the hypothesis
Machine_learning
Physics of many interacting particles
the ensemble. These ensemble evolution equations inherit much of the complexity of the underlying mechanical motion, and so exact solutions are very difficult
Statistical_mechanics
Study of uncertainty in the output of a mathematical model or system
(evaluating the f {\displaystyle f} -function) multiple times. Depending on the complexity of the model there are many challenges that may be encountered during
Sensitivity_analysis
Earth's most severe extinction event
environmental stresses also acted as a ceiling limiting the maximum ecological complexity of marine ecosystems until the Spathian. Recovery biotas appear to have
Permian–Triassic extinction event
Permian–Triassic_extinction_event
Branch of applied probability theory
concerned with decisions that are difficult simply because of their complexity, or the complexity of the organization that has to make them. Individuals making
Decision_theory
English mathematician, mathematical physicist (born 1931)
7 December 2021. Retrieved 12 October 2020. "20th WCP: Computational Complexity and Philosophical Dualism". www.bu.edu. Archived from the original on
Roger_Penrose
Theory of gravitation as curved spacetime
distinguishing marks like the hairstyles of humans. Irrespective of the complexity of a gravitating object collapsing to form a black hole, the object that
General_relativity
Solution concept of a non-cooperative game
because, even though the equilibrium must exist, it is unknown due to the complexity of the game, for instance in Chinese chess. Or, if known, it may not be
Nash_equilibrium
Organic compounds containing amine and carboxylic groups
example, lysine and arginine are present in large amounts in the low-complexity regions of nucleic-acid binding proteins. There are various hydrophobicity
Amino_acid
Something that communicates meaning
relations are structured to perpetuate themselves leads to a level of complexity not usually experienced in the routine of message creation and interpretation
Sign_(semiotics)
Matrix decomposition
represents the time modulation (or vice versa). One may then define an index of separability α = σ 1 2 ∑ i σ i 2 , {\displaystyle \alpha ={\frac {\sigma
Singular_value_decomposition
Method for computing topological features of a space at different spatial resolutions
canonical form by upper-triangular matrices and runs in worst-case cubical complexity in the number of simplices. The fastest known algorithm for computing
Persistent_homology
Numerical linear algebra algorithm
{\displaystyle (i,m_{i})} . Also the updating of the index array can be done in O(n) average-case complexity: First, the maximum entry in the updated rows k
Jacobi_eigenvalue_algorithm
Interventions to prevent injury in domestic settings
S328423. PMC 8843349. PMID 35173427. Camerlingo, Claudia (2023-05-15). "The complexity of basophobia and aging: covariates and consequences". European Review
Fall_prevention
Scientific field of study
quantum, and astronomical physics, many everyday phenomena involving complexity, chaos, or turbulence are still poorly understood. Complex problems that
Physics
optimization techniques into simulation modeling and analysis. Because of the complexity of the simulation, the objective function may become difficult and expensive
Simulation-based_optimization
Graph representation in quantum mechanics
edge joining two vertices represents an index that is summed over, and an open edge represents a free index of the resulting object; the dimension of
Tensor_network
Class of artificial neural network
that are differentiable and trained. In this way, they are similar in complexity to recognizers of context free grammars (CFGs). Recurrent neural networks
Recurrent_neural_network
Branch of engineering
these technologies is known as aerospace engineering. Because of the complexity and number of disciplines involved, aerospace engineering is carried out
Aerospace_engineering
DC linear voltage regulator
another inverting amplifier is required to control it, increasing circuit complexity compared to simple linear regulator.[citation needed] Power FETs may be
Low-dropout_regulator
Primary male sex hormone
PMID 30381580. Berenbaum SA (March 2018). "Beyond Pink and Blue: The Complexity of Early Androgen Effects on Gender Development". Child Development Perspectives
Testosterone
Theoretical description of motion of Earth's moon
account for the motions of the Moon. There are many small variations (or perturbations) in the Moon's motion, and many attempts have been made to account for
Lunar_theory
Community of living organisms together with the nonliving components of their environment
and earthworms, which consume detritus). Real systems, with all these complexities, form food webs rather than food chains which present a number of common
Ecosystem
Sense of position of one's own body parts
feedback in neuromechanical simulations. Various proprioceptor models of complexity have been developed. They range from simple phenomenological models to
Proprioception
Rapidly rotating storm system
The lack of improvement in intensity forecasting is attributed to the complexity of tropical systems and an incomplete understanding of factors that affect
Tropical_cyclone
Species of owl
lower-branch density to impede hunting (and perhaps superior structural complexity to aid hunting), greater security from mobbing, and perhaps greater thermoregulation
Barred_owl
Optimality criterion in phylogeny
(4): 581–587. doi:10.1093/sysbio/42.4.581. Day WH (1987). "Computational complexity of inferring phylogenies from dissimilarity matrices". Bulletin of Mathematical
Maximum_parsimony
Worldwide glaciation episodes during the Proterozoic eon
environments at least, life did not suffer any perturbation. Instead life developed a trophic complexity and survived the cold period unscathed. Proponents
Snowball_Earth
Study involving matter and electromagnetic radiation
D'Emilio, Emilio (2011). "Perturbation Theory in Quantum Mechanics". In Meyers, Robert A. (ed.). Mathematics of Complexity and Dynamical Systems. Springer
Spectroscopy
Vehicle propelled by ejection of gases
seen in more pedestrian manufacturing. Amongst liquid-fuelled rockets, complexity can be influenced by how much hardware must be lightweight, like pressure-fed
Rocket
Reconstruction of binary images from a small number of their projections
mathematical fields, such as number theory, discrete mathematics, computational complexity theory and combinatorics. In fact, a number of discrete tomography problems
Discrete_tomography
Computer approximation for real numbers
as though it had computed the infinitely precise result. The enormous complexity of modern division algorithms once led to a famous error. An early version
Floating-point_arithmetic
Mathematical model of the time dependence of a point in space
Tools and Applications for Economic Modelling. Springer Proceedings in Complexity. 2016. doi:10.1007/978-3-319-33276-5. ISBN 978-3-319-33274-1.[page needed]
Dynamical_system
Multi-dimensional generalization of triangle
takes O ( n log n ) {\displaystyle O(n\log n)} complexity, which can be improved to O(n) complexity via median-finding algorithms. Projecting onto the
Simplex
Chemical reaction between a fuel and oxygen
perturbation and p' is the pressure fluctuation. When the heat release oscillations are in phase with the pressure oscillations, the Rayleigh Index is
Combustion
Theory of stochastic partial differential equations
is an ordered phase—a perspective anticipated in early discussions of complexity: as pointed out in the context of STS: ... chaos is counter-intuitively
Supersymmetric theory of stochastic dynamics
Supersymmetric_theory_of_stochastic_dynamics
Study of chemical processes of living organisms
Many other pioneers in the field who helped to uncover the layers of complexity of biochemistry have been proclaimed founders of modern biochemistry.
Biochemistry
Russian mathematician (1937–2010)
investigated in 1983 the dynamo property of the ABC flow. The Arnold complexity in dynamical systems theory, and the Arnold's stability theorems in analysis
Vladimir_Arnold
Bhatt, Rajen B., et al. "Efficient skin region segmentation using low complexity fuzzy decision tree model." India Conference (INDICON), 2009 Annual IEEE
List of datasets in computer vision and image processing
List_of_datasets_in_computer_vision_and_image_processing
Civilization in southern Peru, c. 100 BC–800 AD
Anthropology 35, no. 5 (December 1994): 675–679 "Cahuachi: Non-Urban Cultural Complexity on the South Coast of Peru" by Helaine Silverman, Journal of Field Archaeology
Nazca_culture
Rain that is unusually acidic
an increase in community dominants, and a reduction in the food web complexity. In 1980, the US Congress passed an Acid Deposition Act in the 100th Congress
Acid_rain
domain, using heat kernels directly as features would lead to a high complexity. HKS instead restricts itself to just the temporal domain by considering
Heat_kernel_signature
Layer of fluid in the immediate vicinity of a bounding surface
This can reduce drag, but is usually impractical due to its mechanical complexity and the power required to move the air and dispose of it. Natural laminar
Boundary_layer
Hypothesis that planets with complex life are extremely rare
hypothesis argues that the origin of life and the evolution of biological complexity, such as sexually reproducing, multicellular organisms on Earth, and subsequently
Rare_Earth_hypothesis
Measure of connection disorder in a network
characterize real complex networks and can also be used to quantify network complexity According to a 2018 publication by Zenil et al. there are several formulations
Network_entropy
chip. Due to rapid MOSFET scaling, MOS IC chips rapidly increased in complexity at a rate predicted by Moore's law, leading to large-scale integration
History_of_computing_hardware
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
methods for solving quantum problems where the perturbation cannot be considered small in perturbation theory and where quantum numbers are large. Correlating
Quantum_chaos
Degree to which a correct prediction of a system's state can be made
could be caused by factors such as a lack of information or excessive complexity. In experimental physics, there are always observational errors determining
Predictability
Altered state of consciousness
the "inner world" behind the eyelids. These visual effects increase in complexity with higher dosages, and also when the eyes are closed. The visual alteration
Psychedelic_experience
Wei-Yin; Shih, Yu-Shan (2000). "A comparison of prediction accuracy, complexity, and training time of thirty-three old and new classification algorithms"
List of datasets for machine-learning research
List_of_datasets_for_machine-learning_research
Method of analyzing electrochemical reactions
certain compounds. This approach is optimal to use since samples of high complexity can be analyzed with high cross-selectivity. Thus, the sensors can be
Cyclic_voltammetry
Approach to understanding the human brain
network representations is that they can describe and uncover higher-level complexity in terms of the interaction perspective and further identify the overall
Network_neuroscience
Numerical method for solving physical or engineering problems
independent as possible of the geometric description and minimize the complexity of mesh generation, while retaining the accuracy and robustness of a standard
Finite_element_method
Austrian philosopher of science (1924–1994)
might include recalcitrant evidence, theoretical paradoxes, mathematical complexity, or inconsistency with neighboring theories. Feyerabend learned of this
Paul_Feyerabend
Specific aspects of Benjamin Banneker's life and legacy
works into a colonial cabinet, which was typical considering the cost and complexity of the mechanical components, Bagnall created the works himself with parts
Mythology of Benjamin Banneker
Mythology_of_Benjamin_Banneker
Special function occurring in problems possessing elliptic symmetry
eigenvalue problem, or implementing a backwards recurrence algorithm. The complexity of the three-term recurrence relation is one of the reasons there are
Mathieu_function
Polish-born American physical chemist
Reviews. 94 (7): 1887–1930. doi:10.1021/cr00031a008. ""Physicists wipe away complexity for a clearer view of heavy nuclei", AAAS EurekAlert, March 14, 2007"
Piotr_Piecuch
Active volcanic belt that covers central-southern Mexico
to the general position of the arc. In addition to the physiographic complexities, igneous compositions vary—dominant subduction-related products contrast
Trans-Mexican_Volcanic_Belt
Obtaining information through non-contact sensors
developed for school lessons has not yet been implemented due to its complexity. Thereby, the subject is either not at all integrated into the curriculum
Remote_sensing
Mathematical structures that allow quantum mechanics to be explained
formal mathematical analysis, beginning with calculus, and increasing in complexity up to differential geometry and partial differential equations. Probability
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Interdisciplinary field of research
methodology, the use of computer simulations to study problems in social complexity, interest in micro–macro linkage and the problem of emergence, and ever-increasing
Mathematical_sociology
convergence Superconvergence Discretization Difference quotient Complexity: Computational complexity of mathematical operations Smoothed analysis — measuring
List of numerical analysis topics
List_of_numerical_analysis_topics
Solving multiple machine learning tasks at the same time
superior to regularization that prevents overfitting by penalizing all complexity uniformly. One situation where MTL may be particularly helpful is if the
Multi-task_learning
Ordered arrangement of atoms, ions, or molecules in a crystalline material
powerful algorithms and high-performance computing, structures of medium complexity can be predicted using such approaches as evolutionary algorithms, random
Crystal_structure
Decrease of pH levels in the ocean
Wing, Scott L. (30 May 2011). "The Paleocene-Eocene Thermal Maximum: A Perturbation of Carbon Cycle, Climate, and Biosphere with Implications for the Future"
Ocean_acidification
Schadt, Eric; Zhang, Bin; Zhu, Jun. "Integrative Biology Approach to Complexity of Alzheimer's Disease". Grantome. "Integrated understanding of complex
Sam_Gandy
Family of iterative methods
Journal on Optimization. 19 (4): 1574. doi:10.1137/070704277. Problem Complexity and Method Efficiency in Optimization, A. Nemirovski and D. Yudin, Wiley
Stochastic_approximation
Surgical process
company will determine how much the patient will pay in copays. Despite the complexity of the procedure and numerous doctor's visits involved, 80–90% of patients
Anterior cruciate ligament reconstruction
Anterior_cruciate_ligament_reconstruction
Excessive displeasing noise
invertebrates have been represented in the research. A variation in the complexity of their sensory systems exists, which allows scientists to study a range
Noise_pollution
Analysis of datasets using techniques from topology
configurations analog to homotopical links. Because of its combinatorial complexity, only the simplicial subcase of the cohomology and of information structure
Topological_data_analysis
Computational method
dimension and huge entries, which makes the computation slow. The exponential complexity in the Zassenhaus algorithm comes from a combinatorial problem: how to
Factorization_of_polynomials
the observation that genome size does not correlate with the perceived complexity of organisms, nor necessarily with the number of genes they possess; for
Glossary of cellular and molecular biology (0–L)
Glossary_of_cellular_and_molecular_biology_(0–L)
Graph where most nodes are reachable in a small number of steps
large average clustering is constructed. A fast algorithm of constant complexity is given, along with measurements of the robustness of the resulting graphs
Small-world_network
both length and width), which offers high storage capacity and lower complexity of device construction and operation if precise time control of droplets
Droplet-based_microfluidics
Family of machine learning techniques
counts as hard depends on the model complexity: a high-complexity model treats most examples as easy, while a low-complexity model treats most as hard. Hard
Hard_negative_mining
some researches into the laws of induced currents, but owing to their complexity of the investigation it was not productive of very notable results. Around
History of electromagnetic theory
History_of_electromagnetic_theory
Philosophical concept
(2009). "Coordination dynamics". In R. A. Meyers (ed.). Encyclopedia of complexity and system science. pp. 1537–1564. doi:10.1007/978-0-387-30440-3_101.
Enactivism
Pollution around Earth by defunct artificial objects
commercial actor since the earliest days of spaceflight due to the cost and complexity of achieving direct retrieval, but the ESA has scheduled a 2026 demonstration
Space_debris
Form of adaptive capacity for a socio-ecological system
measure resilience in rural development contexts share two shortcomings: complexity and high cost. USAID published a field guide for assessing climate resilience
Climate_resilience
Branch of statistical computational learning theory
Vladimir; Papadopoulos, Harris; Gammerman, Alexander (eds.), Measures of Complexity, Cham: Springer International Publishing, pp. 11–30, doi:10.1007/978-3-319-21852-6_3
Vapnik–Chervonenkis_theory
Analytical framework to study life history strategies used by organisms
life. It serves as a method to investigate further the "many layers of complexity of organisms and their worlds". Organisms have evolved a great variety
Life_history_theory
Wildland-ocean interface
and stakeholders, often with conflicting interests. To adapt to such complexity coastal ocean observing system must be an integrated, multidisciplinary
Marine_coastal_ecosystem
Application of statistical techniques to biological systems
relates data from DDBJ, EMBL-EBI, and NCBI. Nowadays, increase in size and complexity of molecular datasets leads to use of powerful statistical methods provided
Biostatistics
Examines sequence information from individual cells
approaches. Cancer scDNAseq is particularly useful for examining the depth of complexity and compound mutations present in amplified therapeutic targets such as
Single-cell_sequencing
American biologist
hot paper) Yuan et al. 2021. Climate Warming Enhances Microbial Network Complexity and Stability. Nature Climate Change, 11:343-348. (top 1% highly cited)
Jizhong_Zhou
Proposed cloud-seeding technique
nuclei particles precipitate naturally. A 2024 study used a unique reduced complexity modeling framework to evaluate the effectiveness of marine cloud brightening
Marine_cloud_brightening
Study of threats to biological diversity
worth noting that there are no models in existence that account for the complexity of unpredictable factors like species movement, a non-analog climate,
Conservation_biology
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