text stringlengths 9 3.55k | source stringlengths 31 280 |
|---|---|
For example, the Reform Act 1832 radically altered the distribution of MPs and subsequent parliaments followed the new rules. However, it remains open to any successor to legislate again to change these requirements, protecting its sovereignty. Similarly, only a reconstituted House of Lords could pass a bill reversing the changes of the House of Lords Act 1999 if its consent were required (unless the Parliament Acts were used). However, the whole system of government could be abolished, and the next parliament would not be bound if it were not considered a successor. | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
Some jurists have suggested that the Acts of Union 1707 place limits on parliamentary sovereignty and its application to Scotland. Although no Scottish court has yet openly questioned the validity of an Act of Parliament, certain judges have raised the possibility. Thus, in MacCormick v. Lord Advocate, the Lord President (Lord Cooper) stated that "the principle of the unlimited sovereignty of Parliament is a distinctively English principle which has no counterpart in Scottish Constitutional Law", and that legislation contrary to the Act of Union would not necessarily be regarded as constitutionally valid. | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
Also, in Gibson v Lord Advocate, Lord Keith was circumspect about how Scottish courts would deal with an Act, which would substantially alter or negate the essential provisions of the 1707 Act, such as the abolition of the Court of Session or the Church of Scotland or the substitution of English law for Scots law.The establishment of the Scottish Parliament in 1998 has implications for parliamentary supremacy. For example, although nuclear power is not within its competence, the Scottish government successfully blocked the wishes of the UK government to establish new nuclear power stations in Scotland using control over planning applications which is devolved. While it remains theoretically possible to dissolve the Scottish Parliament, in practice such a change would be politically difficult. | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
The accepted rule is that the bill must be signed by both Houses of Parliament and be granted royal assent, unless the Parliament Act procedure has been properly enacted. The Parliament Acts create a system of passing a bill without the consent of the Lords. That system does not however, extend to private or local bills, nor bills extending the length of a parliament beyond five years. However, despite the granting of the Speaker's Certificate, certifying the act to be valid, the validity of an act passed under the Parliament Acts may still be challenged in the courts. In Jackson v Attorney General, the judges decided by a seven-to-two majority that an Act that extended the life of a parliament would be considered invalid by the courts if it had been passed under the Parliament Act procedure. | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
From 1 January 1973 to 31 January 2020, the United Kingdom was a member state of the European Union and its predecessor the three European Communities which was made up principally of the European Economic Community (EEC) which was widely known at the time as the "Common Market", the European Coal and Steel Community (ECSC) which became defunct in 2002 and the European Atomic Energy Community (EAEC or Euratom) which the UK also withdrew from in 2020. The European Communities Act 1972 gave European Union law (previously Community law) the force of law in the United Kingdom and it also incorporated the obligations of the European Treaties into UK domestic law as well. : section 2(1) reads: 2. General implementation of Treaties (1) All such rights, powers, liabilities, obligations and restrictions from time to time created or arising by or under the Treaties, and all such remedies and procedures from time to time provided for by or under the Treaties, as in accordance with the Treaties are without further enactment to be given legal effect or used in the United Kingdom shall be recognised and available in law, and be enforced, allowed and followed accordingly ; and the expression " enforceable Community right" and similar expressions shall be read as referring to one to which this subsection applies. | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
The case of R v. Secretary of State for Transport ex parte Factortame is considered decisive as to the superiority of EU law over British law. It judged that the Merchant Shipping Act 1988 and section 21 of the Crown Proceedings Act 1947 (which prevented an injunction against the Crown) should be disapplied. Alongside R v Employment Secretary, ex parte EOC, these two cases establish that any national legislation, coming into force before or after the European Communities Act 1972, cannot be applied by British courts if it contradicts Community law.The Factortame case was considered to be revolutionary by Sir William Wade, who cited in particular Lord Bridge's statement that "there is nothing in any way novel in according supremacy to rules of Community law in areas to which they apply and to insist that... national courts must not be prohibited by rules of national law from granting interim relief in appropriate cases is no more than a logical recognition of that supremacy", which Wade characterises a clear statement that parliament can bind its successors and is therefore a very significant break from traditional thinking. | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
Trevor Allan, argued, however, that the change in rule was accepted by the existing order because of strong legal reasons. Since legal reasons existed, the House of Lords had, instead, determined what the current system suggested under new circumstances and so no revolution had occurred. Section 18 of the European Union Act 2011 declared that EU law is directly applicable only through the European Communities Act or another act fulfilling the same role. | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
18. Status of EU law dependent on continuing statutory basis Directly applicable or directly effective EU law (that is, the rights, powers, liabilities, obligations, restrictions, remedies and procedures referred to in section 2(1) of the European Communities Act 1972) falls to be recognised and available in law in the United Kingdom only by virtue of that Act or where it is required to be recognised and available in law by virtue of any other Act. Parliament legislated in 2018 to repeal the 1972 Act, and in 2020 the United Kingdom ceased to be a member of the EU in accordance with and by virtue of that Act (albeit amended by further legislation of Parliament), demonstrating that the previous Parliament (of 1972) had not bound its successor with respect to leaving the EU. The European Union (Withdrawal Agreement) Act 2020 further declared that "It is recognised that the Parliament of the United Kingdom is sovereign." | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
The Human Rights Act 1998 confirmed the UK's commitment to the European Convention on Human Rights. In a white paper, the government expressed that "to make provision in the Bill for the courts to set aside Acts of Parliament would confer on the judiciary a general power over the decisions of Parliament which under our present constitutional arrangements they do not possess, and would be likely on occasions to draw the judiciary into serious conflict with Parliament". According to the theory that a parliament cannot bind its successors, any form of a Bill of Rights cannot be entrenched, and a subsequent parliament could repeal the act. In the government's words, " to allow any Act of Parliament to be amended or repealed by a subsequent Act of Parliament." | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
However, it would have been possible to apply human rights rules to previous (rather than future) legislation. The government also confirmed that it had no plans to devise a special arrangement for the bill.Instead, it would be for courts to interpret legislation consistently with the Convention, if such an interpretation were possible. This system confirmed the formal authority of Parliament, while allowing judicial oversight. A court cannot strike down primary legislation. | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
In Jackson v Attorney General, the appellants questioned the validity of the Parliament Act 1949. There were various arguments put forward by the appellants who were represented by Sir Sydney Kentridge QC. All nine judges accepted that the court had jurisdiction to consider whether the 1949 Act was valid. They looked to distinguish the case from that of Pickin v British Railways Board, where the unequivocal belief of the judges had been that "the courts in this country have no power to declare enacted law to be invalid". The judges believed that whereas Pickin had challenged the inner workings of Parliament, which a court could not do, Jackson questioned the interpretation of a statute. | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
The UK Supreme Court on December 1, 2010, in the Chaytor judgment, gave her first ruling on the parliamentary system. Approaching the procedural privilege of exclusivity and absolute pre-eminence of the chamber as a judge of its internal affairs (exclusive cognisance), the judges dated back to 1812 to refute the belief that the judge cannot examine in court fact happened within the House walls and to refute the belief that the contempt of Parliament is always and in any case the only way to face issues raised by the conduct of third parties not belonging to the Houses. | https://en.wikipedia.org/wiki/Parliamentary_sovereignty_in_the_United_Kingdom |
An anatomically correct doll or anatomically precise doll is a doll that depicts some of the primary and secondary sex characteristics of a human for educational purposes. A very detailed type of anatomically correct doll may be used in questioning children who may have been sexually abused. The use of dolls as interview aids has been criticized, and the validity of information obtained this way has been contested. | https://en.wikipedia.org/wiki/Anatomically_correct_doll |
Some children's baby dolls and potty training dolls are anatomically correct for educational purposes. There are also dolls that are used as medical models, particularly in explaining medical procedures to child patients. These have a more detailed depiction of the human anatomy and may include features like removable internal organs. One notable anatomically correct doll was the "Archie Bunker's Grandson Joey Stivic" doll that was made by the Ideal Toy Co. in 1976. The doll, which was modeled after infant character Joey Stivic from the Television sitcom series All In The Family, was considered to be the first anatomically correct boy doll.The dolls are also sometimes used by parents or teachers as sex education. | https://en.wikipedia.org/wiki/Anatomically_correct_doll |
A particular type of anatomically correct dolls are used in law enforcement and therapy. These dolls have detailed depictions of all the primary and secondary sexual characteristics of a human: "oral and anal openings, ears, tongues, nipples, and hands with individual fingers" for all and a "vagina, clitoris and breasts" for each of the female dolls and a "penis and testicles" for each of the male dolls.These dolls are used during interviews with children who may have been sexually abused. The dolls wear removable clothing, and the anatomically correct and similarly scaled body parts ensure that sexual activity can be simulated realistically. There is some criticism with regard to using anatomically correct dolls to question victims of sexual abuse. | https://en.wikipedia.org/wiki/Anatomically_correct_doll |
Critics argue that because of the novelty of the dolls, children will act out sexually explicit maneuvers with the dolls even if the child has not been sexually abused. Another criticism is that because the studies that compare the differences between how abused and non-abused children play with these dolls are conflicting (some studies suggest that sexually abused children play with anatomically correct dolls in a more sexually explicit manner than non-abused children, while other studies suggest that there is no correlation), it is impossible to interpret what is meant by how a child plays with these dolls. == References == | https://en.wikipedia.org/wiki/Anatomically_correct_doll |
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made, based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
Let (x1, x2, ..., xn) be independent and identically distributed samples drawn from some univariate distribution with an unknown density ƒ at any given point x. We are interested in estimating the shape of this function ƒ. Its kernel density estimator is f ^ h ( x ) = 1 n ∑ i = 1 n K h ( x − x i ) = 1 n h ∑ i = 1 n K ( x − x i h ) , {\displaystyle {\widehat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}K_{h}(x-x_{i})={\frac {1}{nh}}\sum _{i=1}^{n}K{\Big (}{\frac {x-x_{i}}{h}}{\Big )},} where K is the kernel — a non-negative function — and h > 0 is a smoothing parameter called the bandwidth. A kernel with subscript h is called the scaled kernel and defined as Kh(x) = 1/h K(x/h). Intuitively one wants to choose h as small as the data will allow; however, there is always a trade-off between the bias of the estimator and its variance. The choice of bandwidth is discussed in more detail below. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
A range of kernel functions are commonly used: uniform, triangular, biweight, triweight, Epanechnikov, normal, and others. The Epanechnikov kernel is optimal in a mean square error sense, though the loss of efficiency is small for the kernels listed previously. Due to its convenient mathematical properties, the normal kernel is often used, which means K(x) = ϕ(x), where ϕ is the standard normal density function. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
The construction of a kernel density estimate finds interpretations in fields outside of density estimation. For example, in thermodynamics, this is equivalent to the amount of heat generated when heat kernels (the fundamental solution to the heat equation) are placed at each data point locations xi. Similar methods are used to construct discrete Laplace operators on point clouds for manifold learning (e.g. diffusion map). | https://en.wikipedia.org/wiki/Kernel_density_estimation |
Kernel density estimates are closely related to histograms, but can be endowed with properties such as smoothness or continuity by using a suitable kernel. The diagram below based on these 6 data points illustrates this relationship: For the histogram, first, the horizontal axis is divided into sub-intervals or bins which cover the range of the data: In this case, six bins each of width 2. Whenever a data point falls inside this interval, a box of height 1/12 is placed there. If more than one data point falls inside the same bin, the boxes are stacked on top of each other. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
For the kernel density estimate, normal kernels with variance 2.25 (indicated by the red dashed lines) are placed on each of the data points xi. The kernels are summed to make the kernel density estimate (solid blue curve). The smoothness of the kernel density estimate (compared to the discreteness of the histogram) illustrates how kernel density estimates converge faster to the true underlying density for continuous random variables. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
The bandwidth of the kernel is a free parameter which exhibits a strong influence on the resulting estimate. To illustrate its effect, we take a simulated random sample from the standard normal distribution (plotted at the blue spikes in the rug plot on the horizontal axis). The grey curve is the true density (a normal density with mean 0 and variance 1). In comparison, the red curve is undersmoothed since it contains too many spurious data artifacts arising from using a bandwidth h = 0.05, which is too small. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
The green curve is oversmoothed since using the bandwidth h = 2 obscures much of the underlying structure. The black curve with a bandwidth of h = 0.337 is considered to be optimally smoothed since its density estimate is close to the true density. An extreme situation is encountered in the limit h → 0 {\displaystyle h\to 0} (no smoothing), where the estimate is a sum of n delta functions centered at the coordinates of analyzed samples. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
In the other extreme limit h → ∞ {\displaystyle h\to \infty } the estimate retains the shape of the used kernel, centered on the mean of the samples (completely smooth). The most common optimality criterion used to select this parameter is the expected L2 risk function, also termed the mean integrated squared error: MISE ( h ) = E {\displaystyle \operatorname {MISE} (h)=\operatorname {E} \!\left} Under weak assumptions on ƒ and K, (ƒ is the, generally unknown, real density function), MISE ( h ) = AMISE ( h ) + o ( ( n h ) − 1 + h 4 ) {\displaystyle \operatorname {MISE} (h)=\operatorname {AMISE} (h)+{\mathcal {o}}((nh)^{-1}+h^{4})} where o is the little o notation, and n the sample size (as above). The AMISE is the asymptotic MISE, i. e. the two leading terms, AMISE ( h ) = R ( K ) n h + 1 4 m 2 ( K ) 2 h 4 R ( f ″ ) {\displaystyle \operatorname {AMISE} (h)={\frac {R(K)}{nh}}+{\frac {1}{4}}m_{2}(K)^{2}h^{4}R(f'')} where R ( g ) = ∫ g ( x ) 2 d x {\displaystyle R(g)=\int g(x)^{2}\,dx} for a function g, m 2 ( K ) = ∫ x 2 K ( x ) d x {\displaystyle m_{2}(K)=\int x^{2}K(x)\,dx} and f ″ {\displaystyle f''} is the second derivative of f {\displaystyle f} and K {\displaystyle K} is the kernel. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
The minimum of this AMISE is the solution to this differential equation ∂ ∂ h AMISE ( h ) = − R ( K ) n h 2 + m 2 ( K ) 2 h 3 R ( f ″ ) = 0 {\displaystyle {\frac {\partial }{\partial h}}\operatorname {AMISE} (h)=-{\frac {R(K)}{nh^{2}}}+m_{2}(K)^{2}h^{3}R(f'')=0} or h AMISE = R ( K ) 1 / 5 m 2 ( K ) 2 / 5 R ( f ″ ) 1 / 5 n − 1 / 5 = C n − 1 / 5 {\displaystyle h_{\operatorname {AMISE} }={\frac {R(K)^{1/5}}{m_{2}(K)^{2/5}R(f'')^{1/5}}}n^{-1/5}=Cn^{-1/5}} Neither the AMISE nor the hAMISE formulas can be used directly since they involve the unknown density function f {\displaystyle f} or its second derivative f ″ {\displaystyle f''} . To overcome that difficulty, a variety of automatic, data-based methods have been developed to select the bandwidth. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
Several review studies have been undertaken to compare their efficacies, with the general consensus that the plug-in selectors and cross validation selectors are the most useful over a wide range of data sets. Substituting any bandwidth h which has the same asymptotic order n−1/5 as hAMISE into the AMISE gives that AMISE(h) = O(n−4/5), where O is the big o notation. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
It can be shown that, under weak assumptions, there cannot exist a non-parametric estimator that converges at a faster rate than the kernel estimator. Note that the n−4/5 rate is slower than the typical n−1 convergence rate of parametric methods. If the bandwidth is not held fixed, but is varied depending upon the location of either the estimate (balloon estimator) or the samples (pointwise estimator), this produces a particularly powerful method termed adaptive or variable bandwidth kernel density estimation. Bandwidth selection for kernel density estimation of heavy-tailed distributions is relatively difficult. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
If Gaussian basis functions are used to approximate univariate data, and the underlying density being estimated is Gaussian, the optimal choice for h (that is, the bandwidth that minimises the mean integrated squared error) is: h = ( 4 σ ^ 5 3 n ) 1 5 ≈ 1.06 σ ^ n − 1 / 5 , {\displaystyle h=\left({\frac {4{\hat {\sigma }}^{5}}{3n}}\right)^{\frac {1}{5}}\approx 1.06\,{\hat {\sigma }}\,n^{-1/5},} An h {\displaystyle h} value is considered more robust when it improves the fit for long-tailed and skewed distributions or for bimodal mixture distributions. This is often done empirically by replacing the standard deviation σ ^ {\displaystyle {\hat {\sigma }}} by the parameter A {\displaystyle A} below: A = min ( σ ^ , I Q R 1.34 ) {\displaystyle A=\min \left({\hat {\sigma }},{\frac {IQR}{1.34}}\right)} where IQR is the interquartile range.Another modification that will improve the model is to reduce the factor from 1.06 to 0.9. Then the final formula would be: h = 0.9 min ( σ ^ , I Q R 1.34 ) n − 1 5 {\displaystyle h=0.9\,\min \left({\hat {\sigma }},{\frac {IQR}{1.34}}\right)\,n^{-{\frac {1}{5}}}} where n {\displaystyle n} is the sample size. This approximation is termed the normal distribution approximation, Gaussian approximation, or Silverman's rule of thumb. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
While this rule of thumb is easy to compute, it should be used with caution as it can yield widely inaccurate estimates when the density is not close to being normal. For example, when estimating the bimodal Gaussian mixture model 1 2 2 π e − 1 2 ( x − 10 ) 2 + 1 2 2 π e − 1 2 ( x + 10 ) 2 {\displaystyle {\frac {1}{2{\sqrt {2\pi }}}}e^{-{\frac {1}{2}}(x-10)^{2}}+{\frac {1}{2{\sqrt {2\pi }}}}e^{-{\frac {1}{2}}(x+10)^{2}}} from a sample of 200 points, the figure on the right shows the true density and two kernel density estimates — one using the rule-of-thumb bandwidth, and the other using a solve-the-equation bandwidth. The estimate based on the rule-of-thumb bandwidth is significantly oversmoothed. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
Given the sample (x1, x2, ..., xn), it is natural to estimate the characteristic function φ(t) = E as φ ^ ( t ) = 1 n ∑ j = 1 n e i t x j {\displaystyle {\widehat {\varphi }}(t)={\frac {1}{n}}\sum _{j=1}^{n}e^{itx_{j}}} Knowing the characteristic function, it is possible to find the corresponding probability density function through the Fourier transform formula. One difficulty with applying this inversion formula is that it leads to a diverging integral, since the estimate φ ^ ( t ) {\displaystyle \scriptstyle {\widehat {\varphi }}(t)} is unreliable for large t’s. To circumvent this problem, the estimator φ ^ ( t ) {\displaystyle \scriptstyle {\widehat {\varphi }}(t)} is multiplied by a damping function ψh(t) = ψ(ht), which is equal to 1 at the origin and then falls to 0 at infinity. The “bandwidth parameter” h controls how fast we try to dampen the function φ ^ ( t ) {\displaystyle \scriptstyle {\widehat {\varphi }}(t)} . | https://en.wikipedia.org/wiki/Kernel_density_estimation |
We can extend the definition of the (global) mode to a local sense and define the local modes: M = { x: g ( x ) = 0 , λ 1 ( x ) < 0 } {\displaystyle M=\{x:g(x)=0,\lambda _{1}(x)<0\}} Namely, M {\displaystyle M} is the collection of points for which the density function is locally maximized. A natural estimator of M {\displaystyle M} is a plug-in from KDE, where g ( x ) {\displaystyle g(x)} and λ 1 ( x ) {\displaystyle \lambda _{1}(x)} are KDE version of g ( x ) {\displaystyle g(x)} and λ 1 ( x ) {\displaystyle \lambda _{1}(x)} . Under mild assumptions, M c {\displaystyle M_{c}} is a consistent estimator of M {\displaystyle M} . Note that one can use the mean shift algorithm to compute the estimator M c {\displaystyle M_{c}} numerically. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
A non-exhaustive list of software implementations of kernel density estimators includes: In Analytica release 4.4, the Smoothing option for PDF results uses KDE, and from expressions it is available via the built-in Pdf function. In C/C++, FIGTree is a library that can be used to compute kernel density estimates using normal kernels. MATLAB interface available. In C++, libagf is a library for variable kernel density estimation. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
In C++, mlpack is a library that can compute KDE using many different kernels. It allows to set an error tolerance for faster computation. Python and R interfaces are available. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
in C# and F#, Math.NET Numerics is an open source library for numerical computation which includes kernel density estimation In CrimeStat, kernel density estimation is implemented using five different kernel functions – normal, uniform, quartic, negative exponential, and triangular. Both single- and dual-kernel density estimate routines are available. Kernel density estimation is also used in interpolating a Head Bang routine, in estimating a two-dimensional Journey-to-crime density function, and in estimating a three-dimensional Bayesian Journey-to-crime estimate. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
In ELKI, kernel density functions can be found in the package de.lmu.ifi.dbs.elki.math.statistics.kernelfunctions In ESRI products, kernel density mapping is managed out of the Spatial Analyst toolbox and uses the Quartic(biweight) kernel. In Excel, the Royal Society of Chemistry has created an add-in to run kernel density estimation based on their Analytical Methods Committee Technical Brief 4. In gnuplot, kernel density estimation is implemented by the smooth kdensity option, the datafile can contain a weight and bandwidth for each point, or the bandwidth can be set automatically according to "Silverman's rule of thumb" (see above). | https://en.wikipedia.org/wiki/Kernel_density_estimation |
In Haskell, kernel density is implemented in the statistics package. In IGOR Pro, kernel density estimation is implemented by the StatsKDE operation (added in Igor Pro 7.00). | https://en.wikipedia.org/wiki/Kernel_density_estimation |
Bandwidth can be user specified or estimated by means of Silverman, Scott or Bowmann and Azzalini. Kernel types are: Epanechnikov, Bi-weight, Tri-weight, Triangular, Gaussian and Rectangular. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
In Java, the Weka (machine learning) package provides weka.estimators.KernelEstimator, among others. In JavaScript, the visualization package D3.js offers a KDE package in its science.stats package. In JMP, the Graph Builder platform utilizes kernel density estimation to provide contour plots and high density regions (HDRs) for bivariate densities, and violin plots and HDRs for univariate densities. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
Sliders allow the user to vary the bandwidth. Bivariate and univariate kernel density estimates are also provided by the Fit Y by X and Distribution platforms, respectively. In Julia, kernel density estimation is implemented in the KernelDensity.jl package. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
In MATLAB, kernel density estimation is implemented through the ksdensity function (Statistics Toolbox). As of the 2018a release of MATLAB, both the bandwidth and kernel smoother can be specified, including other options such as specifying the range of the kernel density. Alternatively, a free MATLAB software package which implements an automatic bandwidth selection method is available from the MATLAB Central File Exchange for 1-dimensional data 2-dimensional data n-dimensional data A free MATLAB toolbox with implementation of kernel regression, kernel density estimation, kernel estimation of hazard function and many others is available on these pages (this toolbox is a part of the book ). | https://en.wikipedia.org/wiki/Kernel_density_estimation |
In Mathematica, numeric kernel density estimation is implemented by the function SmoothKernelDistribution and symbolic estimation is implemented using the function KernelMixtureDistribution both of which provide data-driven bandwidths. In Minitab, the Royal Society of Chemistry has created a macro to run kernel density estimation based on their Analytical Methods Committee Technical Brief 4. In the NAG Library, kernel density estimation is implemented via the g10ba routine (available in both the Fortran and the C versions of the Library). | https://en.wikipedia.org/wiki/Kernel_density_estimation |
In Nuklei, C++ kernel density methods focus on data from the Special Euclidean group S E ( 3 ) {\displaystyle SE(3)} . In Octave, kernel density estimation is implemented by the kernel_density option (econometrics package). In Origin, 2D kernel density plot can be made from its user interface, and two functions, Ksdensity for 1D and Ks2density for 2D can be used from its LabTalk, Python, or C code. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
In Perl, an implementation can be found in the Statistics-KernelEstimation module In PHP, an implementation can be found in the MathPHP library In Python, many implementations exist: pyqt_fit.kde Module in the PyQt-Fit package, SciPy (scipy.stats.gaussian_kde), Statsmodels (KDEUnivariate and KDEMultivariate), and scikit-learn (KernelDensity) (see comparison). KDEpy supports weighted data and its FFT implementation is orders of magnitude faster than the other implementations. The commonly used pandas library offers support for kde plotting through the plot method (df.plot(kind='kde')). | https://en.wikipedia.org/wiki/Kernel_density_estimation |
The getdist package for weighted and correlated MCMC samples supports optimized bandwidth, boundary correction and higher-order methods for 1D and 2D distributions. One newly used package for kernel density estimation is seaborn ( import seaborn as sns , sns.kdeplot() ). A GPU implementation of KDE also exists. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
In R, it is implemented through density in the base distribution, and bw.nrd0 function is used in stats package, this function uses the optimized formula in Silverman's book. bkde in the KernSmooth library, ParetoDensityEstimation in the DataVisualizations library (for pareto distribution density estimation), kde in the ks library, dkden and dbckden in the evmix library (latter for boundary corrected kernel density estimation for bounded support), npudens in the np library (numeric and categorical data), sm.density in the sm library. For an implementation of the kde.R function, which does not require installing any packages or libraries, see kde.R. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
The btb library, dedicated to urban analysis, implements kernel density estimation through kernel_smoothing. In SAS, proc kde can be used to estimate univariate and bivariate kernel densities. In Apache Spark, the KernelDensity() class In Stata, it is implemented through kdensity; for example histogram x, kdensity. Alternatively a free Stata module KDENS is available allowing a user to estimate 1D or 2D density functions. In Swift, it is implemented through SwiftStats.KernelDensityEstimation in the open-source statistics library SwiftStats. | https://en.wikipedia.org/wiki/Kernel_density_estimation |
In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms. | https://en.wikipedia.org/wiki/Learnable_function_class |
Let Ω = X × Y = { ( x , y ) } {\displaystyle \Omega ={\mathcal {X}}\times {\mathcal {Y}}=\{(x,y)\}} be the sample space, where y {\displaystyle y} are the labels and x {\displaystyle x} are the covariates (predictors). F = { f: X ↦ Y } {\displaystyle {\mathcal {F}}=\{f:{\mathcal {X}}\mapsto {\mathcal {Y}}\}} is a collection of mappings (functions) under consideration to link x {\displaystyle x} to y {\displaystyle y} . L: Y × Y ↦ R {\displaystyle L:{\mathcal {Y}}\times {\mathcal {Y}}\mapsto \mathbb {R} } is a pre-given loss function (usually non-negative). | https://en.wikipedia.org/wiki/Learnable_function_class |
Given a probability distribution P ( x , y ) {\displaystyle P(x,y)} on Ω {\displaystyle \Omega } , define the expected risk I P ( f ) {\displaystyle I_{P}(f)} to be: I P ( f ) = ∫ L ( f ( x ) , y ) d P ( x , y ) {\displaystyle I_{P}(f)=\int L(f(x),y)dP(x,y)} The general goal in statistical learning is to find the function in F {\displaystyle {\mathcal {F}}} that minimizes the expected risk. That is, to find solutions to the following problem: f ^ = arg min f ∈ F I P ( f ) {\displaystyle {\hat {f}}=\arg \min _{f\in {\mathcal {F}}}I_{P}(f)} But in practice the distribution P {\displaystyle P} is unknown, and any learning task can only be based on finite samples. Thus we seek instead to find an algorithm that asymptotically minimizes the empirical risk, i.e., to find a sequence of functions { f ^ n } n = 1 ∞ {\displaystyle \{{\hat {f}}_{n}\}_{n=1}^{\infty }} that satisfies lim n → ∞ P ( I P ( f ^ n ) − inf f ∈ F I P ( f ) > ϵ ) = 0 {\displaystyle \lim _{n\rightarrow \infty }\mathbb {P} (I_{P}({\hat {f}}_{n})-\inf _{f\in {\mathcal {F}}}I_{P}(f)>\epsilon )=0} One usual algorithm to find such a sequence is through empirical risk minimization. | https://en.wikipedia.org/wiki/Learnable_function_class |
We can make the condition given in the above equation stronger by requiring that the convergence is uniform for all probability distributions. That is: The intuition behind the more strict requirement is as such: the rate at which sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} converges to the minimizer of the expected risk can be very different for different P ( x , y ) {\displaystyle P(x,y)} . Because in real world the true distribution P {\displaystyle P} is always unknown, we would want to select a sequence that performs well under all cases. However, by the no free lunch theorem, such a sequence that satisfies (1) does not exist if F {\displaystyle {\mathcal {F}}} is too complex. | https://en.wikipedia.org/wiki/Learnable_function_class |
This means we need to be careful and not allow too "many" functions in F {\displaystyle {\mathcal {F}}} if we want (1) to be a meaningful requirement. Specifically, function classes that ensure the existence of a sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} that satisfies (1) are known as learnable classes.It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies (1). Thus in these settings not only do we know that the problem posed by (1) is solvable, we also immediately have an algorithm that gives the solution. | https://en.wikipedia.org/wiki/Learnable_function_class |
If the true relationship between y {\displaystyle y} and x {\displaystyle x} is y ∼ f ∗ ( x ) {\displaystyle y\sim f^{*}(x)} , then by selecting the appropriate loss function, f ∗ {\displaystyle f^{*}} can always be expressed as the minimizer of the expected loss across all possible functions. That is, f ∗ = arg min f ∈ F ∗ I P ( f ) {\displaystyle f^{*}=\arg \min _{f\in {\mathcal {F}}^{*}}I_{P}(f)} Here we let F ∗ {\displaystyle {\mathcal {F}}^{*}} be the collection of all possible functions mapping X {\displaystyle {\mathcal {X}}} onto Y {\displaystyle {\mathcal {Y}}} . f ∗ {\displaystyle f^{*}} can be interpreted as the actual data generating mechanism. However, the no free lunch theorem tells us that in practice, with finite samples we cannot hope to search for the expected risk minimizer over F ∗ {\displaystyle {\mathcal {F}}^{*}} . | https://en.wikipedia.org/wiki/Learnable_function_class |
Thus we often consider a subset of F ∗ {\displaystyle {\mathcal {F}}^{*}} , F {\displaystyle {\mathcal {F}}} , to carry out searches on. By doing so, we risk that f ∗ {\displaystyle f^{*}} might not be an element of F {\displaystyle {\mathcal {F}}} . This tradeoff can be mathematically expressed as In the above decomposition, part ( b ) {\displaystyle (b)} does not depend on the data and is non-stochastic. | https://en.wikipedia.org/wiki/Learnable_function_class |
It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{*}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to put enough restrictions on F {\displaystyle {\mathcal {F}}} will cause it to be not learnable, and part ( a ) {\displaystyle (a)} will not stochastically converge to 0. This is the well-known overfitting problem in statistics and machine learning literature. | https://en.wikipedia.org/wiki/Learnable_function_class |
A good example where learnable classes are used is the so-called Tikhonov regularization in reproducing kernel Hilbert space (RKHS). Specifically, let F ∗ {\displaystyle {\mathcal {F^{*}}}} be an RKHS, and | | ⋅ | | 2 {\displaystyle ||\cdot ||_{2}} be the norm on F ∗ {\displaystyle {\mathcal {F^{*}}}} given by its inner product. It is shown in that F = { f: | | f | | 2 ≤ γ } {\displaystyle {\mathcal {F}}=\{f:||f||_{2}\leq \gamma \}} is a learnable class for any finite, positive γ {\displaystyle \gamma } . The empirical minimization algorithm to the dual form of this problem is arg min f ∈ F ∗ { ∑ i = 1 n L ( f ( x i ) , y i ) + λ | | f | | 2 } {\displaystyle \arg \min _{f\in {\mathcal {F}}^{*}}\left\{\sum _{i=1}^{n}L(f(x_{i}),y_{i})+\lambda ||f||_{2}\right\}} This was first introduced by Tikhonov to solve ill-posed problems. | https://en.wikipedia.org/wiki/Learnable_function_class |
Many statistical learning algorithms can be expressed in such a form (for example, the well-known ridge regression). The tradeoff between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in (2) is geometrically more intuitive with Tikhonov regularization in RKHS. We can consider a sequence of { F γ } {\displaystyle \{{\mathcal {F}}_{\gamma }\}} , which are essentially balls in F ∗ {\displaystyle {\mathcal {F^{*}}}} with centers at 0. | https://en.wikipedia.org/wiki/Learnable_function_class |
As γ {\displaystyle \gamma } gets larger, F γ {\displaystyle {\mathcal {F}}_{\gamma }} gets closer to the entire space, and ( b ) {\displaystyle (b)} is likely to become smaller. However we will also suffer smaller convergence rates in ( a ) {\displaystyle (a)} . The way to choose an optimal γ {\displaystyle \gamma } in finite sample settings is usually through cross-validation. | https://en.wikipedia.org/wiki/Learnable_function_class |
Part ( a ) {\displaystyle (a)} in (2) is closely linked to empirical process theory in statistics, where the empirical risk { ∑ i = 1 n L ( y i , f ( x i ) ) , f ∈ F } {\displaystyle \{\sum _{i=1}^{n}L(y_{i},f(x_{i})),f\in {\mathcal {F}}\}} are known as empirical processes. In this field, the function class F {\displaystyle {\mathcal {F}}} that satisfies the stochastic convergence are known as uniform Glivenko–Cantelli classes. It has been shown that under certain regularity conditions, learnable classes and uniformly Glivenko-Cantelli classes are equivalent. | https://en.wikipedia.org/wiki/Learnable_function_class |
Interplay between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in statistics literature is often known as the bias-variance tradeoff. However, note that in the authors gave an example of stochastic convex optimization for General Setting of Learning where learnability is not equivalent with uniform convergence. == References == | https://en.wikipedia.org/wiki/Learnable_function_class |
Microbial intelligence (known as bacterial intelligence) is the intelligence shown by microorganisms. The concept encompasses complex adaptive behavior shown by single cells, and altruistic or cooperative behavior in populations of like or unlike cells mediated by chemical signalling that induces physiological or behavioral changes in cells and influences colony structures.Complex cells, like protozoa or algae, show remarkable abilities to organize themselves in changing circumstances. Shell-building by amoebae reveals complex discrimination and manipulative skills that are ordinarily thought to occur only in multicellular organisms. Even bacteria can display more behavior as a population. | https://en.wikipedia.org/wiki/Microbial_intelligence |
These behaviors occur in single species populations, or mixed species populations. Examples are colonies or swarms of myxobacteria, quorum sensing, and biofilms.It has been suggested that a bacterial colony loosely mimics a biological neural network. The bacteria can take inputs in form of chemical signals, process them and then produce output chemicals to signal other bacteria in the colony. Bacteria communication and self-organization in the context of network theory has been investigated by Eshel Ben-Jacob research group at Tel Aviv University which developed a fractal model of bacterial colony and identified linguistic and social patterns in colony lifecycle. | https://en.wikipedia.org/wiki/Microbial_intelligence |
Bacterial biofilms can emerge through the collective behavior of thousands or millions of cells Biofilms formed by Bacillus subtilis can use electric signals (ion transmission) to synchronize growth so that the innermost cells of the biofilm do not starve. Under nutritional stress bacterial colonies can organize themselves in such a way so as to maximize nutrient availability. Bacteria reorganize themselves under antibiotic stress. Bacteria can swap genes (such as genes coding antibiotic resistance) between members of mixed species colonies. | https://en.wikipedia.org/wiki/Microbial_intelligence |
Individual cells of myxobacteria coordinate to produce complex structures or move as social entities. Myxobacteria move and feed cooperatively in predatory groups, known as swarms or wolf packs, with multiple forms of signalling and several polysaccharides play an important role. Populations of bacteria use quorum sensing to judge their own densities and change their behaviors accordingly. | https://en.wikipedia.org/wiki/Microbial_intelligence |
This occurs in the formation of biofilms, infectious disease processes, and the light organs of bobtail squid. For any bacterium to enter a host's cell, the cell must display receptors to which bacteria can adhere and be able to enter the cell. Some strains of E. coli are able to internalize themselves into a host's cell even without the presence of specific receptors as they bring their own receptor to which they then attach and enter the cell. | https://en.wikipedia.org/wiki/Microbial_intelligence |
Under nutrient limitation, some bacteria transform into endospores to resist heat and dehydration. A huge array of microorganisms have the ability to overcome being recognized by the immune system as they change their surface antigens so that any defense mechanisms directed against previously present antigens are now useless with the newly expressed ones. In April 2020 it was reported that collectives of bacteria have a membrane potential-based form of working memory. When scientists shone light onto a biofilm of bacteria optical imprints lasted for hours after the initial stimulus as the light-exposed cells responded differently to oscillations in membrane potentials due to changes to their potassium channels. | https://en.wikipedia.org/wiki/Microbial_intelligence |
Individual cells of cellular slime moulds coordinate to produce complex structures or move as multicellular entities. Biologist John Bonner pointed out that although slime molds are “no more than a bag of amoebae encased in a thin slime sheath, they manage to have various behaviors that are equal to those of animals who possess muscles and nerves with ganglia -- that is, simple brains.” The single-celled ciliate Stentor roeselii expresses a sort of "behavioral hierarchy" and can 'change its mind' if its response to an irritant does not relieve the irritant, implying a very speculative sense of 'cognition'. Paramecium, specifically P. caudatum, is capable of learning to associate intense light with stimulus such as electric shocks in its swimming medium; although it appears to be unable to associate darkness with electric shocks. | https://en.wikipedia.org/wiki/Microbial_intelligence |
Protozoan ciliate Tetrahymena has the capacity to 'memorize' the geometry of its swimming area. Cells that were separated and confined in a droplet of water, recapitulated circular swimming trajectories upon release. This may result mainly from a rise in intracellular calcium. | https://en.wikipedia.org/wiki/Microbial_intelligence |
Bacterial colony optimization is an algorithm used in evolutionary computing. The algorithm is based on a lifecycle model that simulates some typical behaviors of E. coli bacteria during their whole lifecycle, including chemotaxis, communication, elimination, reproduction, and migration. | https://en.wikipedia.org/wiki/Microbial_intelligence |
Logical circuits can be built with slime moulds. Distributed systems experiments have used them to approximate motorway graphs. The slime mould Physarum polycephalum is able to solve the Traveling Salesman Problem, a combinatorial test with exponentially increasing complexity, in linear time. | https://en.wikipedia.org/wiki/Microbial_intelligence |
Microbial community intelligence is found in soil ecosystems in the form of interacting adaptive behaviors and metabolisms. According to Ferreira et al., "Soil microbiota has its own unique capacity to recover from change and to adapt to the present state capacity to recover from change and to adapt to the present state by altruistic, cooperative and co-occurring behavior is considered a key attribute of microbial community intelligence. "Many bacteria that exhibit complex behaviors or coordination are heavily present in soil in the form of biofilms. | https://en.wikipedia.org/wiki/Microbial_intelligence |
Micropredators that inhabit soil, including social predatory bacteria, have significant implications for its ecology. Soil biodiversity, managed in part by these micropredators, is of significant importance for carbon cycling and ecosystem functioning.The complicated interaction of microbes in the soil has been proposed as a potential carbon sink. Bioaugmentation has been suggested as a method to increase the 'intelligence' of microbial communities, that is, adding the genomes of autotrophic, carbon-fixing or nitrogen-fixing bacteria to their metagenome. | https://en.wikipedia.org/wiki/Microbial_intelligence |
The COVID-19 pandemic has impacted the mental health of people across the globe. The pandemic has caused widespread anxiety, depression, and post-traumatic stress disorder symptoms. According to the UN health agency WHO, in the first year of the COVID-19 pandemic, prevalence of common mental health conditions, such as depression and anxiety, went up by more than 25 percent. The pandemic has damaged social relationships, trust in institutions and in other people, has caused changes in work and income, and has imposed a substantial burden of anxiety and worry on the population. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Women and young people face the greatest risk of depression and anxiety.COVID-19 triggered issues caused by substance use disorders (SUDs). The pandemic disproportionately affects people with SUDs. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
The health consequences of SUDs (for example, cardiovascular diseases, respiratory diseases, type 2 diabetes, immunosuppression and central nervous system depression, and psychiatric disorders), and the associated environmental challenges (such as housing instability, unemployment, and criminal justice involvement), are associated with an increased risk for contracting COVID-19. Confinement rules, as well as unemployment and fiscal austerity measures during and following the pandemic period, can also affect the illicit drug market and patterns of use among consumers of illicit drugs drastically. Mitigation measures (i.e. physical distancing, quarantine, and isolation) can worsen loneliness, mental health symptoms, withdrawal symptoms, and psychological trauma. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
The known causes of mental health issues during the pandemic included fear of infection, stigma associated with infection, isolation (imposed by individuals sheltering on their own or in compliance with lockdowns), and masks. Billions of people shifted to remote work, temporary unemployment, homeschooling or distance education, and lack of physical contact with family members, friends and colleagues. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
As the pandemic began, the risks were uncertain. As sick people flooded into hospitals and official advice evolved, the lack of information increased stress and anxiety. Many uncertainties surrounded the beginning of the pandemic, including estimating infection risk, symptom overlap between COVID-19 and other health problems.Covid-19 also caused many mental health problems. Patients experienced unfavorable psychological effects such as post-traumatic stress symptoms, disorientation, and rage when exposed to Covid-19. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
During the first wave of the epidemic, critical supplies were quickly exhausted. The most prominent items were personal protective equipment (PPE) for hospital workers and ventilators for treatment. At the onset of the pandemic in early 2020, a national survey found that many medical facilities were running out of PPE supplies, including one third of the surveyed medical facilities reporting being out of face masks and a quarter reporting a shortage or almost shortage of gowns. Another study reported that 63.3% of nurses agreed with the statement, “I am worried about inadequate personal protective equipment for healthcare personnel (PPE)”. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
As the pandemic began, anyone who interacted with infected people had to address the possibility that they might have been infected themselves and might therefore present an unknown risk to their family and others. In some cases, they were initially stigmatized. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Many care homes subjected their residents to enforced isolation. They were locked into their rooms around the clock, including at mealtimes when their meals were delivered to their doors. Visitors were not allowed, nor was any socialization among the residents. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Nurses worked longer hours during the pandemic, which increased anxiety in many. Many patients rapidly progressed once in the hospital to the ICU and ultimately, death. The absence of approved therapeutics meant that palliative care (supplemental oxygen, ventilators and extracorporeal membrane oxygenation) were the only options. In some cases, this stimulated frustration and a sense of powerlessness. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Those caring for COVID-19 patients were subject strict biosecurity measures, consigned to wearing gowns, uncomfortable masks and face shields at work. After returning home, many changed clothes before entering and isolated themselves, in an attempt to protect their families. Their jobs demanded constant awareness and vigilance, reduced their autonomy, reduced access to social support, reduced self-care, uncertainty about the effects of long-term exposure to COVID-19 patients, and fear of infecting others.In some jurisdictions, schools were closed during the early months of the pandemic. Such closures increased anxiety, loneliness, stress, sadness, frustration, indiscipline, and hyperactivity among children. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
The Guidelines on Mental Health and Psychosocial Support of the Inter-Agency Standing Committee of the United Nations recommends that mental health support during an emergency "do no harm, promote human rights and equality, use participatory approaches, build on existing resources and capacities, adopt multi-layered interventions and work with integrated support systems. "One author suggested implementing habits that act as "psychological PPE". These habits include healthy eating, healthy coping mechanisms, and practicing mindfulness and relaxation methods.Another method that many companies followed for their employees was to provide the employees with specific mental health improvement programs in order to increase the morale of the employees and improve their mental health. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
WHO and CDC issued guidelines for minimizing mental health issues during the pandemic. The summarized guidelines are: | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Be empathetic to affected individuals. Use people-first language while describing infected individuals. (for example, instead of saying "a schizophrenic person, say "a person with schizophrenia"). Minimize watching the news to reduce anxiety. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Seek information only from trusted sources, preferably once or twice a day. Protect yourself and be supportive to others. Amplify positive stories of local infected people. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Honor healthcare workers who are caring for those with COVID-19. Implement positive thinking. Engage in hobbies. Avoid negative coping strategies, such as avoidance of crowds and pandemic news coverage. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
What are health care workers experiencing? Feeling pressure is normal in a crisis. Mental health is as important as physical health. Nurses face higher rates of fatigue, sleep problems, depressive disorders, PTSD, and anxiety. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Personal Protective Equipment shortages leaving nurses feeling unsafe. Frontline health care works experience higher levels of stress Nurses expressed elevated stress. Hands-on patient care increased risk perception. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Vaccinated nurses were less fatigued than others. Nurses working with infected patients faced more anxiety, depression, and distress. Non-frontline nurses exhibited less depression.What actions can healthcare workers take? | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Adopt coping strategies, get sufficient rest, eat healthy food, be physically active, avoid tobacco, alcohol, or drugs. Stay connected with loved ones, including digitally. Use understandable ways to share messages with people with disabilities. Know how to link people with available resources. Online counseling can reduce the risk of insomnia, anxiety, and depression/burnout. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Focus on long-term occupational capacity rather than short term results. Ensure good quality communication and accurate updates. Ensure that staff are aware of mental health resources. Orient staff on how to provide psychological first aid to the affected. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Ensure that mental health emergencies are managed in healthcare facilities. Ensure availability of essential psychiatric medications at all levels of health care. Offset feelings of anxiety and depression using strong leadership and clear, honest, and open communication. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Use widespread screening to identify workers in need of mental health support. Provide organizational support Facilitate peer support. Rotate work schedules to mitigate stress. Implement interventions tailored to local needs and provide positive, supportive environments. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Role model healthy behaviors, routines, and coping skills. Use a positive parenting approach based on communication and respect. Maintain family routines and provide age-appropriate activities to teach children responsibility. Explain COVID-19 and required interventions in age-appropriate ways. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Monitor children's social media. Validate children's thoughts and feelings and help them find positive ways to express emotions. Avoid separating children from their parents/caregivers as much as possible. Ensure regular contact with parents and caregivers, for children in isolation. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Older adults, those especially in isolation or suffering from pre-existing conditions, may become more anxious, angry, or withdrawn. Provide practical and emotional support through caregivers and healthcare professionals. Share facts on the crisis and give clear information about how to reduce infection risk. Maintain access to current medications. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Find out in advance where and how to get practical help. Learn and perform daily home exercises. Keep regular schedules. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Keep in touch with loved ones. Continue hobbies or regular tasks. Talk on the phone or online or do a fun online activity with others. Help your community, e.g., by providing food/meals to others. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Stay connected and maintain social networks. Pay attention to your needs and feelings. Engage in relaxing activities. Avoid listening to rumors. | https://en.wikipedia.org/wiki/Mental_health_during_the_COVID-19_pandemic |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.