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Phi value analysis, φ analysis, or φ-value analysis is an experimental protein engineering technique for studying structures of the transition state and
Phi_value_analysis
Twenty-first letter in the Greek alphabet
numerals, phi has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter Ef (Ф, ф) descends from phi. Like other Greek letters, lowercase phi (encoded
Phi
British chemist (born 1943)
reagents. This procedure of studying protein engineered mutants, named Phi value analysis, was then applied to inferring the structure of transition states
Alan_Fersht
American biologist
application of phi-value analysis to the study of barnase, a bacterial RNAse used in many protein folding studies. Development of phi value analysis in combination
Andreas_Matouschek
used as a measure of the "nativeness" of folding transition states. Phi value analysis in concert with molecular dynamics has produced transition-state models
Contact_order
Change of a linear protein chain to a 3D structure
measure protein folding kinetics, generate a chevron plot and derive a Phi value analysis. Circular dichroism is one of the most general and basic tools to
Protein_folding
Technique in molecular biology
it for expression in a particular organism. Directed mutagenesis Phi value analysis Hsu PD, Lander ES, Zhang F (June 2014). "Development and applications
Site-directed_mutagenesis
Bacterial ribonuclease protein
method of characterizing protein folding transition states known as phi value analysis. Barnase catalyzes hydrolysis at diribonucleotide GpN sites. Cleavage
Barnase
Statistical measure of association for two binary variables
In statistics, the phi coefficient, also known as the mean square contingency coefficient or Yule coefficient of correlation and commonly denoted by φ
Phi_coefficient
Process in protein folding
amenable to complementary computational and experimental study using phi value analysis. Correct protein folding is integral to proper functionality within
Hydrophobic_collapse
after introducing premature stop codon. Site-directed mutagenesis Phi value analysis missense mutation nonsense mutation point mutation frameshift mutation
Mutant_protein
Various systems of symbolic logic
Value [ ⊥ ] = ∅ Value [ ⊤ ] = R Value [ A ∧ B ] = Value [ A ] ∩ Value [ B ] Value [ A ∨ B ] = Value [ A ] ∪ Value [ B ] Value [ A → B ] = int ( Value
Intuitionistic_logic
Maximized objective function of an optimization problem
x(t_{1}))=\phi (x(t_{1}))} , where ϕ ( x ( t 1 ) ) {\displaystyle \phi (x(t_{1}))} is the "scrap value". If the optimal pair of control and state trajectories is
Value_function
Decision support tool
M1 has the highest phi function value and M4 has the highest information gain value. The M1 mutation will be the root of our phi function tree and M4
Decision_tree
Statistical measure of variability
k=1/\left(\Phi ^{-1}(3/4)\right)\approx 1/0.67449\approx 1.4826,} i.e., the reciprocal of the quantile function Φ − 1 {\displaystyle \Phi ^{-1}} (also
Median_absolute_deviation
Graph of protein folding kinetics
Denaturation (biochemistry) Denaturation midpoint Equilibrium unfolding Phi value analysis Jenkins DC, Pearson DS, Harvey A, Sylvester ID, Geeves MA, Pinheiro
Chevron_plot
Statistical measure of association
(sometimes referred to as Cramér's phi and denoted as φc) is a measure of association between two nominal variables, giving a value between 0 and +1 (inclusive)
Cramér's_V
Protein domain
folding pathway of an immunoglobulin domain: structural detail from Phi value analysis and movement of the transition state". Structure. 9 (5): 355–366.
Immunoglobulin_C2-set_domain
Statistical concept
letting the test ϕ α {\displaystyle \phi _{\alpha }} take value in [ 0 , 1 ] {\displaystyle [0,1]} . Here, its value is interpreted as a probability with
E-values
Numerical method for solving physical or engineering problems
u} (mean value theorem) but may be proved in a distributional sense as well. We define a new operator or map ϕ ( u , v ) {\displaystyle \phi (u,v)} by
Finite_element_method
following result is stated by E. Stein: Suppose that a real-valued function ϕ ( x ) {\displaystyle \phi (x)} is smooth in an open interval ( a , b ) {\displaystyle
Van der Corput lemma (harmonic analysis)
Van_der_Corput_lemma_(harmonic_analysis)
Multivariate statistical technique
{\displaystyle K=k(\mathbf {x} ,\mathbf {y} )=(\Phi (\mathbf {x} ),\Phi (\mathbf {y} ))=\Phi (\mathbf {x} )^{T}\Phi (\mathbf {y} )} which represents the inner
Kernel principal component analysis
Kernel_principal_component_analysis
Method to estimate the components of a signal
{f}}(t)=\sum _{i=1}^{N}{\tfrac {1}{2}}A_{i}\left(e^{j\phi _{i}}e^{\lambda _{i}^{+}t}+e^{-j\phi _{i}}e^{\lambda _{i}^{-}t}\right),\end{aligned}}} where
Prony's_method
Mathematical term
In mathematical analysis, a Banach limit is a continuous linear functional ϕ : ℓ ∞ → C {\displaystyle \phi :\ell ^{\infty }\to \mathbb {C} } defined on
Banach_limit
Bayesian diagnostic threshold derived from the geometry of screening curves
positive predictive value after a positive result is: ρ ( ϕ ) = P ( D = 1 ∣ T + ) = a ϕ a ϕ + ( 1 − b ) ( 1 − ϕ ) {\displaystyle \rho (\phi )=P(D=1\mid T^{+})={\frac
Prevalence_threshold
Signal processing technique
spectral density estimate Singular spectrum analysis is a nonparametric method that uses a singular value decomposition of the covariance matrix to estimate
Spectral_density_estimation
Dimensionless parameter of the Weibull distribution
characteristic of a narrower distribution of values. Use case examples include biological and brittle material failure analysis, where modulus is used to describe
Weibull_modulus
Method of analyzing the amortized complexity of a data structure
(\Phi (S_{i})-\Phi (S_{i-1}))\right)=T_{\mathrm {actual} }(O)+C\cdot (\Phi (S_{n})-\Phi (S_{0})),} where the sequence of potential function values forms
Potential_method
Number, approximately 1.618
a>b>0, a is in a golden ratio to b if a+ba=ab=φ, where the Greek letter phi (φ or ϕ, or Φ) denotes the golden ratio. The constant φ satisfies
Golden_ratio
Branch of ordinary differential equations
solution ϕ ( t ) {\displaystyle \phi \,(t)} . Moreover, if ϕ ( t ) {\displaystyle \phi (t)} is a real matrix for every value of t {\displaystyle t} , then
Floquet_theory
Theory in soil mechanics
{\cos \beta -\left(\cos ^{2}\beta -\cos ^{2}\phi \right)^{1/2}}{\cos \beta +\left(\cos ^{2}\beta -\cos ^{2}\phi \right)^{1/2}}}*cos\beta } K p = cos β +
Rankine's_theory
Type of mathematical function
{\displaystyle \int _{\mathbf {R} ^{n}}\Phi =1} and set Φ t ( x ) = t − n Φ ( x t ) {\displaystyle \Phi _{t}(x)=t^{-n}\Phi ({\tfrac {x}{t}})} for t > 0. Then
Maximal_function
Mathematical theorem
=: m ( r ) {\displaystyle \max \,(\Phi (0),\Phi (x'))<\inf \limits _{\|x\|=r}\Phi (x)=:m(r)} . Φ {\displaystyle \Phi } satisfies weak Palais–Smale condition
Mountain_pass_theorem
Class of differential and integral operators
compactly supported in x {\displaystyle x} and Φ {\displaystyle \Phi } is real valued and homogeneous of degree 1 {\displaystyle 1} in ξ {\displaystyle
Fourier_integral_operator
Statistical model used in time series analysis
and ϕ {\displaystyle \phi } is the characteristic polynomial of the autoregressive part of the ARMA model. An appropriate value of p in the ARMA(p, q)
Autoregressive moving-average model
Autoregressive_moving-average_model
Characterization of distortion in map projections
{\displaystyle M={\frac {R(1-e^{2})}{(1-e^{2}\sin ^{2}(\phi ))^{\frac {3}{2}}}}} Substituting these values into the first fundamental form gives the formula
Tissot's_indicatrix
Mathematical method
f_{n}(x)=a_{1}\phi _{1}(x)+a_{2}\phi _{2}(x)+\cdots +a_{n}\phi _{n}(x),\ } with the set of functions { ϕ j ( x ) {\displaystyle \ \phi _{j}(x)} } an
Least-squares function approximation
Least-squares_function_approximation
Partial correlation of a time series with its lagged values
series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values, regressed
Partial autocorrelation function
Partial_autocorrelation_function
Multivariate functions can be written using univariate functions and summing
exist real values η , λ 1 , … , λ n {\displaystyle \eta ,\lambda _{1},\ldots ,\lambda _{n}} , a continuous function Φ : R → R {\displaystyle \Phi \colon \mathbb
Kolmogorov–Arnold representation theorem
Kolmogorov–Arnold_representation_theorem
Type of probability distribution
{1}{\sigma }}\,{\frac {\varphi ({\frac {x-\mu }{\sigma }})}{\Phi ({\frac {b-\mu }{\sigma }})-\Phi ({\frac {a-\mu }{\sigma }})}}} and by f = 0 {\displaystyle
Truncated_normal_distribution
Analytic method in statistics
In statistics, factor analysis of mixed data or factorial analysis of mixed data (FAMD, in the French original: AFDM or Analyse Factorielle de Données
Factor_analysis_of_mixed_data
learning methods. Proto-value functions are generated by spectral analysis of a graph, using the graph Laplacian. Proto-value functions were first introduced
Proto-value_function
Type of integration
a general function ϕ {\displaystyle \phi } by I + ϕ = inf f ≥ ϕ I f . {\displaystyle I^{+}\phi =\inf _{f\geq \phi }If.} The lower integral is defined in
Daniell_integral
American educator and economist
Sigma, Phi Gamma Delta, Alpha Kappa Psi, and Phi Chi Theta. At the time of his death, various editions of the book he coauthored, Security Analysis, had
David_Dodd
Diagnostic plot of binary classifier ability
it can be generalized to multiple classes) at varying threshold values. ROC analysis is commonly applied in the assessment of diagnostic test performance
Receiver operating characteristic
Receiver_operating_characteristic
Statistical measures of whether a finding is likely to be true
Predictive values". BMJ. 309 (6947): 102. doi:10.1136/bmj.309.6947.102. PMC 2540558. PMID 8038641. Fawcett, Tom (2006). "An Introduction to ROC Analysis" (PDF)
Positive and negative predictive values
Positive_and_negative_predictive_values
Ratio of void volume and total volume of a porous material
equation: ϕ ( z ) = ϕ 0 e − k z {\displaystyle \phi (z)=\phi _{0}e^{-kz}\,} where, ϕ ( z ) {\displaystyle \phi (z)} is the porosity of the sediment at a given
Porosity
Approximation whereby the Coriolis parameter, f, is set to vary linearly in space
y)|_{\phi _{0}}=2\Omega \cos(\phi _{0})/a} is the Rossby parameter, y {\displaystyle y} is the meridional distance from ϕ 0 {\displaystyle \phi _{0}}
Beta_plane
Statistical test
two-tailed p-values can be calculated as Φ ( Z ) {\displaystyle \Phi (Z)} (for lower/left-tailed tests), Φ ( − Z ) {\displaystyle \Phi (-Z)} (for upper/right-tailed
Z-test
Statistical measure of a test's accuracy
In statistical analysis of binary classification and information retrieval systems, the F-score or F-measure is a measure of predictive performance. It
F-score
{S} _{B}^{\phi }&=\left(\mathbf {m} _{2}^{\phi }-\mathbf {m} _{1}^{\phi }\right)\left(\mathbf {m} _{2}^{\phi }-\mathbf {m} _{1}^{\phi }\right)^{\text{T}}\\\mathbf
Kernel Fisher discriminant analysis
Kernel_Fisher_discriminant_analysis
Class of analytical partial differential equation-solving processes
{c}}_{n}\phi _{n}(x)} For simplicity, let the basis be orthogonal and normalized, ⟨ ϕ n , ϕ m ⟩ = δ n m {\displaystyle \langle \phi _{n},\phi _{m}\rangle
Pseudo-spectral_method
Solution to partial differential equation
function ϕ {\displaystyle \phi } such that ϕ ( x 0 ) = u ( x 0 ) {\displaystyle \phi (x_{0})=u(x_{0})} and ϕ ≥ u {\displaystyle \phi \geq u} in a neighborhood
Viscosity_solution
Mathematical operation
Let ϕ : M → N {\displaystyle \phi :M\to N} be a smooth map between smooth manifolds M {\displaystyle M} and N {\displaystyle N} . Then there is an associated
Pullback (differential geometry)
Pullback_(differential_geometry)
American mathematician (1852–1926)
and his Ph.D. (1894) from Syracuse University. A member of Sigma Xi and Phi Beta Kappa, he was tutor at the Department of Mathematics of Wesleyan University
Clarence_Abiathar_Waldo
Angle between the zenith and the centre of the Sun's disc
{V} _{oz}=\sin \phi _{o}\sin \phi _{s}+\cos \phi _{o}\cos \phi _{s}\cos(\lambda _{s}-\lambda _{o}).} Note that ϕ s {\displaystyle \phi _{s}} is the same
Solar_zenith_angle
Statistical measure of the magnitude of a phenomenon
values of EHBG have been interpreted using the following empirical bands. Commonly used measures of association for the chi-squared test are the Phi coefficient
Effect_size
Table that displays the frequency of variables
measure, applicable only to the case of 2 × 2 contingency tables, is the phi coefficient (φ) defined by ϕ=±χ2N, where χ2 is computed as in Pearson's chi-squared
Contingency_table
Two propositions or events that cannot both be true
3 ) {\displaystyle \lnot (\phi _{1}\land \phi _{2})\land \lnot (\phi _{1}\land \phi _{3})\land \lnot (\phi _{2}\land \phi _{3})} is a tautology" (it is
Mutual_exclusivity
Rise of water due to wind blowing over the water surface
= 3.3*10−6 ϕ {\displaystyle \phi } = angle of the wind relative to the coast g = acceleration of gravity cw has a value between 0.8*10−3 and 3.0*10−3
Wind_setup
Province of Thailand
islands, Ko Phi Phi Le stands out for its recognition as a filming location for the movie The Beach. Other significant islands include Ko Phi Phi Don, a part
Krabi_province
Rating system for players of skill-based games
{e^{x}(\Delta ^{2}-\phi ^{2}-v-e^{x})}{(\phi ^{2}+v+e^{x})^{2}}}-{\frac {x-\ln({\sigma ^{2}})}{\tau ^{2}}},} we need to find the value A {\displaystyle A}
Glicko_rating_system
Type of boundary condition in mathematics
Robin boundary conditions on the electrostatic potential ϕ {\displaystyle \phi } naturally appear when efficiently modelling electrostatic capacitance or
Robin_boundary_condition
Part of the porosity in which a given fluid can flow
ϕ e 1 {\displaystyle \phi _{e1}} The sum of all the interconnected pore space. In the vast majority of cases, this core analysis and Petroleum Engineering
Effective_porosity
Mathematical concept
(\phi )&=\operatorname {Rot} (\theta +\phi ),\\[4pt]\operatorname {Ref} (\theta )\,\operatorname {Ref} (\phi )&=\operatorname {Rot} (2\theta -2\phi )
Rotations and reflections in two dimensions
Rotations_and_reflections_in_two_dimensions
Sine wave used to approximate data
of spectral density estimation and least-squares spectral analysis. A good starting value for c {\displaystyle c} can be obtained by calculating the
Sinusoidal_model
Statistics function
{1}{x^{2}}}\right)\phi (u)\,du>\int _{x}^{\infty }\left(1+{\frac {1}{u^{2}}}\right)\phi (u)\,du=-{\biggl .}{\frac {\phi (u)}{u}}{\biggr |}_{x}^{\infty }={\frac {\phi (x)}{x}}
Q-function
Equation relating to oscillating systems
A-{\frac {l}{2}}A|A|^{2}.} where A = | A | e i ϕ {\displaystyle A=|A|e^{i\phi }} is a complex quantity describing the disturbance, σ = σ r + i σ i {\displaystyle
Stuart–Landau_equation
Statistical data type
_{k}+\phi _{k}\mathbf {\beta } ^{T}\mathbf {x} } where the score parameters are constrained such that 0 = ϕ 1 ≤ ϕ 2 ≤ ⋯ ≤ ϕ q = 1 {\displaystyle 0=\phi _{1}\leq
Ordinal_data
Concept in statistics
) ≈ 0.000010997 {\displaystyle \mathrm {ApEn} =\phi ^{2}(3)-\phi ^{3}(3)\approx 0.000010997} The value is very small, so it implies the sequence is regular
Approximate_entropy
Information theorem
σ ′ {\displaystyle \sigma '} if Φ σ ′ ⊂ Φ σ {\displaystyle \Phi _{\sigma '}\subset \Phi _{\sigma }} Blackwell's theorem states that, given two information
Blackwell's informativeness theorem
Blackwell's_informativeness_theorem
Dimensionality of space at which the character of the phase transition changes
P}=\int d^{d}x\left\{{\frac {1}{2}}\left(\nabla ^{2}\phi \right)^{2}+u\phi ^{3}\nabla ^{2}\phi +w\phi ^{6}\right\},} see also the figure on the right. This
Critical_dimension
a_{N}\phi _{N}\,=a_{R}\phi _{R}+a_{L}\phi _{L}} {\displaystyle \;} (11) where, In the Upwind scheme we replace the value at the face with the value at the
Hybrid_difference_scheme
Theorem in convex analysis
{\displaystyle \phi (\cdot ,z)} is differentiable. Instead it assumes that ϕ ( ⋅ , z ) {\displaystyle \phi (\cdot ,z)} is an extended real-valued closed proper
Danskin's_theorem
Mathematical analysis
constructive analysis can be framed in terms of the weakness of propositions of the logically negative form ¬ ¬ ϕ {\displaystyle \neg \neg \phi } , which
Constructive_analysis
Dividing things between two categories
Other metrics include Youden's J statistic, the uncertainty coefficient, the phi coefficient, and Cohen's kappa. Statistical classification is a problem studied
Binary_classification
Signal processing algorithm
)e^{j\phi _{\tau }(\omega )}\end{aligned}}} where M t ( ω ) {\displaystyle M_{t}(\omega )} is the magnitude, and ϕ τ ( ω ) {\displaystyle \phi _{\tau
Reassignment_method
Phenomena in quantum physics
value of an operator O {\displaystyle O} given by ⟨ O ⟩ w = ⟨ ϕ | O | ψ ⟩ ⟨ ϕ | ψ ⟩ , {\displaystyle \langle O\rangle _{\rm {w}}={\frac {\langle \phi
Quantum_Cheshire_cat
Rectangle with side lengths in the golden ratio
Livio 2002, p. 61. Livio, Mario (2002). The Golden Ratio: The Story of Phi, The World's Most Astonishing Number. New York: Broadway Books. p. 136. ISBN 0-7679-0816-3
Golden_rectangle
Theory of molecular orbitals by Erich Hückel
_{-}={\frac {1}{\sqrt {2}}}(\phi _{1}-\phi _{2})\,} is the LUMO energy. If, contrary to the Hückel treatment, a positive value for S := S 12 = S 21 {\displaystyle
Hückel_method
Instruction set extension by Intel
proposed by Intel in July 2013, and first implemented in the 2016 Intel Xeon Phi x200 (Knights Landing), and then later in a number of AMD and other Intel
AVX-512
SAT solving algorithm
{\displaystyle \Phi } and neither l {\displaystyle l} nor ¬ l {\displaystyle \neg l} is in A {\displaystyle A} , then decide on the truth value of l {\displaystyle
Conflict-driven clause learning
Conflict-driven_clause_learning
United States federal law concerning health information
stated, "HONI did not conduct an accurate and thorough risk analysis to the confidentiality of ePHI [electronic Protected Health Information] as part of its
Health Insurance Portability and Accountability Act
Health_Insurance_Portability_and_Accountability_Act
Mathematical model used for classification or regression
{\displaystyle \phi (x,y)} , the decision function is defined as: f ( x ; w ) = arg max y w T ϕ ( x , y ) {\displaystyle f(x;w)=\arg \max _{y}w^{T}\phi (x,y)}
Discriminative_model
Probability distribution
x ) {\displaystyle \phi (x)} denote the standard normal probability density function ϕ ( x ) = 1 2 π e − x 2 2 {\displaystyle \phi (x)={\frac {1}{\sqrt
Skew_normal_distribution
Statistical method that summarizes and/or integrates data from multiple sources
and Other Spin-Offs of Meta-analysis: Shift from P-Values to Effect Sizes of any Scientific Issue", Modern Meta-Analysis, Cham: Springer International
Meta-analysis
Mathematical function
and complex analysis. The coefficient p ( k ) {\displaystyle p(k)} in the formal power series expansion for 1 / ϕ ( q ) {\displaystyle 1/\phi (q)} gives
Euler_function
Concept in machine learning
automatically construct better basis function Φ {\displaystyle \Phi } which can represent the value function well. A good construction method should have the
Automatic basis function construction
Automatic_basis_function_construction
Theorized increase of longevity with age
− Φ ′ ( t ) Φ ( t ) = ϵ t = 1 + p p 1 t . {\displaystyle -{\frac {\Phi '(t)}{\Phi (t)}}={\frac {\epsilon }{t}}={\frac {1+p}{p}}{\frac {1}{t}}.} This means
Lindy_effect
Distance measured along the surface of the Earth
meridian, or the value of ϕ m {\displaystyle \phi _{\mathrm {m} }\!} ("mid-latitude") for the two positions ( ϕ 1 {\displaystyle \phi _{1}\!} =89°, λ 1
Geographical_distance
Model in physics
}}E_{0}\cos \theta _{i}\left(C_{1}+C_{2}\cos(\phi _{i}-\phi _{r})\tan \beta +C_{3}(1-|\cos(\phi _{i}-\phi _{r})|)\tan {\frac {\alpha +\beta }{2}}\right)
Oren–Nayar_reflectance_model
Fission from a high energy neutron
\phi (E)_{\text{fuel}}\,dE}{\int \Sigma _{\text{f}}(E')_{\text{fuel}}\,\phi (E')_{\text{fuel}}\,dE'}}\times \left({\frac {\phi _{{\text{fE}}'}}{\phi
Fast_fission
Root-finding algorithm
\kappa _{2}\in \left[1,1+\phi \right)} and n 0 ∈ [ 0 , ∞ ) {\displaystyle n_{0}\in [0,\infty )} where ϕ {\displaystyle \phi } is the golden ratio 1 2
ITP_method
Aspect of a numerical matrix
the mathematical field of linear algebra and convex analysis, the numerical range or field of values or Wertvorrat or Wertevorrat of a complex n × n {\displaystyle
Numerical_range
Class of mathematical problems
{\displaystyle \phi :{\bar {\mathcal {S}}}\to \mathbb {R} } satisfies ϕ ∈ C ( S ¯ ) ∩ C 1 ( S ) ∩ C 2 ( S ∖ ∂ D ) {\displaystyle \phi \in C({\bar {\mathcal
Optimal_stopping
Goods used to create other goods
mean double counting, because the value of the intermediate good is included in the value of the final good. The value-added method can be used to calculate
Intermediate_good
Number with a real and an imaginary part
value |z| of the corresponding z is the amplitude and the argument arg z is the phase. If Fourier analysis is employed to write a given real-valued signal
Complex_number
Set of methods in numerical analysis
Nonstandard finite difference schemes is a general set of methods in numerical analysis that gives numerical solutions to differential equations by constructing
Nonstandard finite difference scheme
Nonstandard_finite_difference_scheme
Variant of cubic interpolation that preserves monotonicity
In the mathematical field of numerical analysis, monotone cubic interpolation is a variant of cubic interpolation that preserves monotonicity of the data
Monotone_cubic_interpolation
Statistical model written in multiple levels
evidence. The usual starting point of a statistical analysis is the assumption that the n values y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots
Bayesian hierarchical modeling
Bayesian_hierarchical_modeling
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PHI VALUE-ANALYSIS
PHI VALUE-ANALYSIS
PHI VALUE-ANALYSIS
PHI VALUE-ANALYSIS
PHI VALUE-ANALYSIS
PHI VALUE-ANALYSIS
PHI VALUE-ANALYSIS
PHI VALUE-ANALYSIS
PHI VALUE-ANALYSIS
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