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LMIs in Control/pages/Multi-Criterion LQG

The Multi-Criterion Linear Quadratic Gaussian (LQG) linear matrix inequality will allow one to form an optimized controller, similar to that in an LQR framework, for a state space system with gaussian noise based on several different criterions defined in the Q and R matrices, that are optimized as a part of the arbitrary cost function. Just like traditional LQR, the cost matrices must be tuned in much a similar fashion as traditional gains in classical control. In the LQR and LQG framework however, the gains are more intuitive as each correlates directly to a state or an input.

The System
The system is a linear time-invariant system, that can be represented in state space as shown below:

\begin{align} \dot x &= Ax + Bu + w,\\ y &= Cx + v,\\ z &=  \begin{bmatrix} Q^{1/2} & 0 \\ 0 & R^{1/2}\end{bmatrix}\begin{bmatrix} x \\ u \end{bmatrix} \end{align}$$

where $$x \in R^{n}, y \in R^{l}, z \in R^{m}$$ represent the state vector, the measured output vector, and the output vector of interest, respectively, $$w \in R^{p}$$ is the disturbance vector, and $$A, B, C, Q, R$$ are the system matrices of appropriate dimension. To further define: $$x$$ is $$\in R^{n}$$ and is the state vector, $$A $$ is $$\in R^{n*n}$$ and is the state matrix, $$B$$ is $$\in R^{n*r}$$ and is the input matrix, $$w$$ is $$\in R^{r}$$ and is the exogenous input, $$C, Q, R $$ is $$\in R^{m*n}$$ and are the output matrices, and $$y$$ and $$z$$ are $$\in R^{m}$$ and are the output and the output of interest, respectively.

$$ Q\geq 0$$ and $$ R> 0 $$, and the system is controllable and observable.

The Data
The matrices $$ A, B, C, Q, R, W, V $$ and the noise signals $$ w, v$$.

The Optimization Problem
In the Linear Quadratic Gaussian (LQG) control problem, the goal is to minimize a quadratic cost function while the plant has random initial conditions and suffers white noise disturbance on the input and measurement.

There are multiple outputs of interest for this problem. They are defined by

\begin{align} z &=  \begin{bmatrix} Q^{1/2} & 0 \\ 0 & R^{1/2}\end{bmatrix}\begin{bmatrix} x \\ u \end{bmatrix}, Q_{i} \geq 0, R_{i}>0, i = 0,...,p. \end{align}$$

For each of these outputs of interest, we associate a cost function:

\begin{align} J^{i}_{LQG} = \lim_{t\to\infty} Ez_{i}(t)^{T}z_{i}(t), i = 0,...,p. \end{align}$$

Additionally, the matrices $$X_{LQG}$$ and $$Y_{LQG}$$ must be found as the solutions to the following Riccati equations:

\begin{align} A^{T}X_{LQG} + X_{LQG}A = X_{LQG}BR^{-1}B^{T}X_{LQG} + Q &= 0\\ AY_{LQG} + Y_{LQG}A^{T} - Y_{LQG}C^{T}V^{-1}CY_{LQG}+W &= 0\\ \end{align}$$

The optimization problem is to minimize $$J^{0}_{LQG}$$ over u subject to the measurability condition and the constraints $$J^{i}_{LQG}<\gamma_{i}, i = 0,...,p.$$. This optimization problem can be formulated as:

\begin{align} \max trace(X_{LQG}U + QY_{LQG}) - \sum_{i=1}^{p} \gamma_{i}\tau_{i}, \end{align}$$ over $$\tau_{1},...,\tau_{p}$$, with:

\begin{align} Q &= Q_{0} + \sum_{i=1}^{p} \tau_{i}Q_{i},\\ R &= R_{0} + \sum_{i=1}^{p} \tau_{i}R_{i}. \end{align}$$

The LMI: Multi-Criterion LQG

\begin{align} \max:     trace(XU + (Q_{0} + \sum_{i=1}^{p} \tau_{i} Q_{i} )Y_{LQG}) - \sum_{i=1}^{p} \gamma_{i}\tau_{i}, \end{align}$$ over $$X, \tau_1, ... \tau_{p}$$, subject to the following constraints:

\begin{align} X&>0,\\ \tau_{1} \geq 0, ..., \tau_{p} &\geq 0,\\ A^{T}X + XA - XB(R_{0} + \sum_{i=1}^{p} \tau_{i} R_{i})^{-1}B^{T}X + Q_{0} + \sum_{i=1}^{p} \tau_{i} Q_{i} &\geq 0.\\ \end{align}$$

Conclusion:
The result of this LMI is the solution to the aforementioned Ricatti equations:

\begin{align} A^{T}X_{LQG} + X_{LQG}A = X_{LQG}BR^{-1}B^{T}X_{LQG} + Q &= 0\\ AY_{LQG} + Y_{LQG}A^{T} - Y_{LQG}C^{T}V^{-1}CY_{LQG}+W &= 0\\ \end{align}$$

Implementation
This implementation requires Yalmip and Sedumi.

https://github.com/rezajamesahmed/LMImatlabcode/blob/master/multicriterionquadraticproblems.m

Related LMIs

 * Inverse Problem of Optimal Control


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LMIs in Control/pages/Nonconvex Multi-Criterion Quadratic Problems

The Non-Concex Multi-Criterion Quadratic linear matrix inequality will allow one to form an optimized controller, similar to that in an LQR framework, for a non-convex state space system based on several different criterions defined in the Q and R matrices, that are optimized as a part of the arbitrary cost function. Just like traditional LQR, the cost matrices must be tuned in much a similar fashion as traditional gains in classical control. In the LQR and LQG framework however, the gains are more intuitive as each correlates directly to a state or an input.

The System
The system for this LMI is a linear time invariant system that can be represented in state space as shown below:

\begin{align} \dot x &=Ax+Bw, x(0) = x_{0}\\ \end{align}$$ where the system is assumed to be controllable.

where $$x \in R^{n}$$ represents the state vector, respectively, $$w \in R^{p}$$ is the disturbance vector, and $$A, B$$ are the system matrices of appropriate dimension. To further define: $$x$$ is $$\in R^{n}$$ and is the state vector, $$A $$ is $$\in R^{n*n}$$ and is the state matrix, $$B$$ is $$\in R^{n*r}$$ and is the input matrix, $$w$$ is $$\in R^{r}$$ and is the exogenous input.

for any input, we define a set $$p+1$$ cost indices $$J_{0},...,J_{P}$$ by

\begin{align} J_{i}(u) = \int_{0}^{\infty}\begin{bmatrix} x^{T}&u^{T} \end{bmatrix}\begin{bmatrix} Q_i & C_i\\ C_i^T & R_i \end{bmatrix}\begin{bmatrix} x\\ u \end{bmatrix} dt,\\ i = 0,...,p \end{align}$$

Here the symmetric matrices,

\begin{align} \begin{bmatrix} Q_i & C_i\\ C_i^T & R_i \end{bmatrix}, i=0,...,p \end{align}$$,

are not necessarily positive-definite.

The Data
The matrices $$ A, B, C $$.

The Optimization Problem
The constrained optimal control problem is:

\begin{align} \max:     J_0,\\ \end{align}$$ subject to

\begin{align} J_i \leq \gamma_i, i=1,...,p, x \rightarrow 0, t \rightarrow \infty \end{align}$$

The LMI: Nonconvex Multi-Criterion Quadratic Problems
The solution to this problem proceeds as follows: We first define

\begin{align} Q = Q_{0} + \sum_{i=1}^{p} \tau_i Q_i ,\\ R = R_{0} + \sum_{i=1}^{p} \tau_i R_i ,\\ C = C_{0} + \sum_{i=1}^{p} \tau_i C_i ,\\ \end{align}$$

where $$\tau_i \geq 0$$ and for every $$\tau_i$$, we define

\begin{align} S = J_0 + \sum_{i=1}^{p} \tau_i J_i - \sum_{i=1}^{p} \tau_i \gamma_i \end{align}$$

then, the solution can be found by:

\begin{align} \max: x(0)^{T}Px(0) - \sum_{i=1}^{p} \tau_i \gamma_i \end{align}$$

subject to

\begin{align} \begin{bmatrix} A^TP + PA + Q & PQ+C^T \\ B^TP+C &R \end{bmatrix} &\geq 0\\ \tau_i &\geq 0 \end{align}$$

Conclusion:
If the solution exists, then $$ K $$ is the optimal controller and can be solved for via an EVP in P.

Implementation
This implementation requires Yalmip and Sedumi.

https://github.com/rezajamesahmed/LMImatlabcode/blob/master/multicriterionquadraticproblems.m

Related LMIs

 * Multi-Criterion LQG
 * Inverse Problem of Optimal Control
 * Nonconvex Multi-Criterion Quadratic Problems
 * Static-State Feedback Problem

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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LMIs in Control/pages/Inverse Problem of Optimal Control

In some cases, it is needed to solve the inverse problem of optimal control within an LQR framework. In this inverse problem, a given controller matrix needs to be verified for the system by assuring that it is the optimal solution to some LQR optimization problem that is controllable and detectable. In other words: in this inverse problem, the controller is known and the LQR gain matrices are to be calculated such that the controller is the optimal solution.

The System
The system is a linear time-invariant system, that can be represented in state space as shown below:

\begin{align} \dot x &= Ax + Bu,\\ z &=  \begin{bmatrix} Q^{1/2} & 0 \\ 0 & R^{1/2}\end{bmatrix}\begin{bmatrix} x \\ u \end{bmatrix} \end{align}$$ where $$x \in R^{n}, y \in R^{l}, z \in R^{m}$$ represent the state vector, the measured output vector, and the output vector of interest, respectively, $$w \in R^{p}$$ is the disturbance vector, and $$A, B, C, Q, R$$ are the system matrices of appropriate dimension. To further define: $$x$$ is $$\in R^{n}$$ and is the state vector, $$A $$ is $$\in R^{n*n}$$ and is the state matrix, $$B$$ is $$\in R^{n*r}$$ and is the input matrix, $$w$$ is $$\in R^{r}$$ and is the exogenous input, $$C, Q, R $$ is $$\in R^{m*n}$$ and are the output matrices, and $$y$$ and $$z$$ are $$\in R^{m}$$ and are the output and the output of interest, respectively.

The Data
The matrices $$ A, B, C $$ that define the system, and a given controller $$ K $$ for which the inverse problem is to be solved.

The Optimization Problem
In this LMI, the following cost function is to be minimized for a given controller K by finding an optimal input:

\begin{align} \int_{0}^{\infty} z^{T}z dt \end{align}$$

the solution of the problem can be formulated as a state feedback controller given as:

\begin{align} K &= -R^{-1}B^{T}P,\\ A^{T}P + PA - PBR^{-1}B^{T}P+Q &=0 \end{align}$$

The LMI: Inverse Problem of Optimal Control
the inverse problem of optimal control is the following: Given a matrix $$ K $$, determine if there exist $$ Q \geq 0 $$ and $$ R > 0 $$, such that $$ (Q, A) $$ is detectable and $$ u = Kx $$ is the optimal control for the corresponding LQR problem. Equivalently, we seek $$ R>0 $$ and $$ Q \geq 0 $$ such that there exist $$ P $$ nonnegative and $$ P_{1} $$ positive-definite satisfying

\begin{align} (A+BK)^{T}P + P(A+BK) + K^{T}RK + Q&=0\\ B^{T}P + RK &=0\\ A^{T}P_{1} + P_{1}A &< Q \end{align}$$

Conclusion:
If the solution exists, then $$ K $$ is the optimal controller for the LQR optimization on the matrices $$ Q $$ and $$ R $$

Implementation
This implementation requires Yalmip and Sedumi.

https://github.com/rezajamesahmed/LMImatlabcode/blob/master/inverseprob.m

Related LMIs

 * Multi-Criterion LQG]


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User:LBird BASc/sandbox/ATK/Seminar6/Power/Power in Airplane Boarding

Context
Most airlines use a back-to-front boarding strategy in an attempt to maximize efficiency. Most often, passengers will be divided in three groups, and these will enter the airplane separately; first the people sitting in the last 20 rows (in the case of a 60 row airplane), then the group corresponding to the people sitting between rows 20 and 40, and then the passengers of the first 20 rows will board. After all, this seems intuitive, and boarding front to back, for example, would be catastrophically slow. However, for the last 15 years, research has continuously demonstrated that this is not in fact the most efficient way to board an airplane. It has been found that an airline could reduce their turnaround time (the time between arrival and departure) by up to 20 minutes. Given that every second counts in terms of cost in airports for airplanes, why have not most airlines incorporated these new studies in their boarding strategies? To understand why, we need to take an interdisciplinary approach that explains the power inequalities between the appropriate disciplines.

Economics
From an economical point of view, it would be much cheaper for the companies to board using a window-middle-aisle boarding technique, in which first all passengers sitting near the window board, then the middle, then the aisle passengers, as this significantly reduces passenger jams which normally arise. As the aforementioned study states, airplanes could cut their boarding time by up to 20 mins, and considering that the average cost per minute for an airplane stationed at the gate comprises of both infrastructure, security, and landing costs, 20 mins could amount to an extremely significant sum, although no valid research has been done on this.

Psychology
Airlines using the window-middle-aisle technique of boarding risk disorienting passengers, as until now the tradition back to front method has dominated the airline industry. An airline suddenly switching to a new technique could potentially lose more time than the traditional way because we would have to take into account the factor of confusion which would in overall would cause more delays. Psychology tells us that the rationale so characteristic to economics is at fault here because you cannot just assume everyone will suddenly perfectly adapt to change.

Conclusion
This is an example of an interdisciplinary issue caused by power as there is a power imbalance between psychology and economics. Psychology states that the airline shouldn't switch boarding methods while economics says it should. However, as explained in the introduction, we remark that airlines in fact are not changing boarding techniques, which illustrates that in this case psychology has more to say than economics.


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Issues in Interdisciplinarity 2019-20/The Power of the Hijab

The hijab is the universally recognised symbol for Islam. This garment is at the centre of many issues regarding gender, religion, socio-economic status, and security. A new movement in the Western world has now given the hijab a different powerful role: the trademark of modern feminism.

In Early Civilizations
Islam wasn't the first religion to introduce the "veil" into Arab societies. It already existed in Hellenic, Judaic, Byzantine and Balkan cultures, for both genders. However, this piece of clothing was granted a distinct meaning in the Arab society. It originally wasn't a piece of clothing exclusive for women. Turkish and Persian civilizations often represented Prophet Muhammad with his head covered in a white veil. This "veil" wasn't even the hijab. The hijab became the frequently used term when the headscarf became the centre of nationalist and feminist speeches in Egypt during Britain's colonial rule. Only one of the Qur'an references to the hijab concerns women's clothing. As much as religion commanded women to wear a veil, it didn't alienate them from society. In fact, women in Arabo-Islamic societies held important positions, playing a role in the religious and social life of the community. The veil was a reminder of God's command and a metaphor for a sacred divide: according to the Qur'an, humans weren't naked in their beginnings. It thus separated obedience and disobedience to God, mortal from immortal, earth from heaven.

Prophet Muhammad's wives
The Prophet's wives wore a veil, like the "verse of the veil" describes: "[...] And when you ask of his wives anything, ask from behind a hijab. That is purer for your hearts and for their hearts". Men had to ask permission to talk to the Prophet's wives and if granted, it would be from behind a partition or curtain. The veil protected women from the behaviour of men, slaves of lust and desire. Given the position of the Prophet's wives: "O wives of the Prophet, you are not like other women", the separating aspect of the hijab cannot be restrained to just gender. It also separated wrongdoers from the righteous. This explains why women nowadays who wear the niqab feel more virtuous and dedicated to Islam than women who wear the hijab. The Prophet's wives were put in a particular position, regardless of their right to privacy: they were to go out only when necessary and avoid exhibitionist dresses. This pictures the restraining of Muslim women to one man only, a phenomenon embodied by the veil.

The Hijab: a garment for patriarchal domination?
Hijabs question the male-female relationship. It's a sensitive subject to analyse as there are different opinions from a country to another.

For some, hijabs are used by men to dominate females, suppressing their femininity and sexual appeal. Feminists consider that wearing the hijab isn't a free decision and is imposed by males to limit women's roles to household tasks and the education of children. Therefore, females are excluded from the labor market with no economical role to play. It creates a financial dependency that strengthens the husband's domination. Others reject the idea that it represents a blind submission to men and religion but consider it a personal choice that reflects their values and their identity. They claim the freedom to dispose of their bodies and to dress as they wish. They defend a society where everyone can display distinctive signs without being excluded from economic and social life.

The hijab issue reflects the differences between the French republican principles and the Anglo-Saxon liberal model.

Two perceptions of the Hijab
In France, society is built around the principle of republican unity and secularism. Unity doesn't accept plurality: society is built around the marginalisation of differences. The Hijab is viewed as a threat to social cohesion and has been forbidden by law in public spaces. When Decathlon launched in February 2019 its "running hijab", it triggered a national heated debate. President Macron's party spokesperson wrote: "Sport emancipates. It doesn't submit. My choice as a woman and as a citizen will be to no longer trust a brand that doesn't respect our values". The far-right called the runner's hijab a "new intrusion of Islamic communitarianism in the public space", while far-left-wing feminists declared "hijab's sole purpose is to prolong sexual apartheid". Initially Decathlon fired back, but ultimately removed it from the market.

So close yet so different, Great-Britain has another approach, considering society is a juxtaposition of communities with different values. Hijabs aren't forbidden in public spaces and diversity is considered as a social enrichment factor. Inclusion is largely promoted by social and political institutions. It's commonly accepted for individuals to display their religious affiliation in public as it supports society's cultural enrichment. Therefore, hijabs, kippahs, crosses, or any religious signs coexist in a relative harmony.

Cultural oppression behind a multicultural world
We live in a multicultural world where issues concerning women's rights are often linked with religion. Mainly, heads have turned to the muslim religion. Its sacred text indicates that women must be covered to preserve their purity. This may seem an oppressive measure in a highly patriarchal society. Therefore, headscarves have been negatively perceived in the Western world. The latter has built a social stigma around headscarves, especially after 9/11. This led to many integration problems: veiled women are less likely to find a job, to be able to send their children to schools, etc... Moreover, muslim communities are often segregated in disadvantaged neighbourhoods. Feeling left-out, they've developed a sentiment of hate towards the governments.

As national security is becoming a priority in the Western world, governments have to choose between an integrated society or a supposedly bettered national security.

The American view of Islam has created many preconceptions of the culture, turning it into an object to fear and undermine. How many times have people associated muslims with "terrorists"? However, those uneducated cannot understand the reasons behind choosing to wear the hijab.

The hijab allows you to build a stronger connection with your religion. Everyday, you are affirming your belief in God. In this multicultural world that is uniformizing, it is hard to maintain your cultural identity. The hijab is a mean to remember your roots and keep your identity.

The Hijab: a form of feminism
Nowadays, the hijab has become the symbol of a new feminism, many muslim women choose to veil themselves. In a world focused on appearances, covering yourself is a way to highlight your intellectual abilities, rejecting preconceptions based on your physique. Many women found that being veiled allowed them to have a voice in the political scene. Furthermore, the hijab projects a sense of modesty, a need to stay grounded and connected with your own culture and identity.

Many muslim women disregard the idea of submission, and consider being veiled a personal choice that reflects their values. It grants them the freedom to dispose of their bodies and to freely dress themselves. They defend a society where distinctive signs are welcomed, without any form of exclusion.

Many western countries have prohibited the hijab, claiming it is a liability to national security. However, this creates ethnic prejudices that harden the process of national integration.

Conclusion
Islam relies on the subjugation of women on many levels, but the veil should not be seen as the perfect representation of it. It deprives women of their autonomy as much as it grants them power. Women who grew up in Western countries claim that it's their choice to wear the veil, as a protection in public settings. Nevertheless, there's an obvious hint of patriarchy in this religious obligation imposed on women—it marks their belonging to one man only. This asymmetry is the key of gender inequalities in Islam.


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User:Eftekhar Naeem

Welcome To wikibook

title: User:Eftekhar Naeem


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IGCSE Information and Communication Technology/6. ICT applicatiolns

ICT, Information and Communication Technology and how we can apply them to our lives:

1. Communication for both personal and business reasons. There are 2 types of communication: -paper-based communication -digital-based communication

We can use our ICT skills to create documents, presentations, excel worksheets, databases to provide and produce a visual representation of data we want to convey. Additionally, ICT can be used to create posters, newsletters and flyers to target a certain audience depending on the visual attractiveness.

In the digital world with the huge presence of the Internet, ICT can be applied to create websites, multimedia presentations, animations and many more.


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User:Katieghhad/sandbox

=Truth Work (Environmental Science Bit)= https://en.wikibooks.org/wiki/User:LGreg/sandbox/Approaches_to_Knowledge_(LG_seminar)/_Group_2/Truth/Philosophy_%26_Environmental_Science

Environmental Science

What are its truths (if it has any)?

Truth in environmental science is under a lot of controversy. Environmental science aims to study human relationships with the natural environment, and as a result, also aims to tackle the current environmental crisis. However, the shared truth as regarded by environmental scientists is that climate change is unpredictable but it is happening and is heavily influenced by humans. That said, another truth shared by environmental scientists are that humans do have an impact on the climate, and over the last few hundred years, have been overall having a negative impact Other than that general idea, the findings about specific problems can vary largely or minimally but all focus on the truth that humans are negatively influencing the environment and that there must be action taken for humans to either or both adapt and mitigate.

However, these empirical truths shared by scientists and a large majority of the world aren't necessarily considered truth by others.

How does it come to realise/evaluate truth?

Truth in environmental science involves studying the impact changes have on different ecosystems. Although there are multiple types of environmental science, most of them follow the same idea of studying relationships and correlations between physical characteristics of the environment / physical changes in the environment (either human or naturally caused) and it's impact on different species or organisms. This is usually done by looking at trends of different environmental changes, such as atmospheric greenhouse gases.

Is truth important to the discipline?

Truth is important to this discipline in terms of actually creating productive change and acting upon the data. As a result, it can eb said that the truth from this discipline is needed to become universally truth.

The shared truths by scientists in this field focuses on the human impact in the environment. However, due to people - especially those in power- preferring their "personal truths" of climate change not being real, being natural, or not being our responsibility, the findings and potential solutions created by this scientists are rendered useless. For example, with all the climate change denial by people in power (such as Donald Trump ), there is still a lack of action to combat and the negative impacts and mitigate the causes of climate change, as seen by the Trump administration suing California as they attempt to tackle climate change.

Therefore, it can be said that shared truths in this field is imperative in order to make the discipline's findings useful in the real world.

=Group Brainstorming for Wikibooks= EVIDENCE: Surrogacy → who’s the mother? Biological perspectives (intention versus the actual DNA) legal perspectives (legal documents) psychological (if something is inherited or taught through social environment → parental investment theory)

Legalisation of euthanasia in the UK → ethical perspectives (is it ethical?, who’s allowed to get euthanized?), philosophy/religious perspectives (suicide → is looked down upon?) → religious texts biological perspectives (suffering, signing your life away and who has the right to say you can be euthanized- ethics of medicine, etc) , legal perspectives (complications of consent → pain combined with anaesthesia and pain killers),

Legalisation of recreational use of marijuana in the UK→ sociological perspective (crime rate etc) → correlation graphs, looking at relations Interviews (for stereotypes and to look at the relationships within the community) Content analysis → how it’s played in the media → positive view vs negative view medical perspective (medicinal applications of marijuana, lack of evidence for long term effects) → empirical evidence/positivist evidence religious/historica perspectives (role marijuana has played in religions) → content analysis/biblical texts; historical perspective (e.g. historical reasons for alcohol being legal and weed not) → anecdotal evidence political perspective (what’s better for a city → drug crime, what’s considered “safe”) → other countries’ laws → business perspective, hemp as wood alternative, CBD

title: User:Katieghhad/sandbox


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Issues in Interdisciplinarity 2019-20/Evidence in the Afterlife

=Introduction= Any argument made on the existence of an afterlife requires an extent of conjecture due to the nature of death itself prohibiting first-hand accounts of afterlife experiences. Evidence found within one discipline also often contradicts that of another. It is therefore necessary to take a critical and interdisciplinary approach to explore the evidence used to debate the existence of an afterlife.

=Across the Disciplines=

Religion

Most evidence for the afterlife in Religion rely on interpretations from works of art, literature, or teachings, such as artwork found in churches (like the Chatres) depicting images of an afterlife and literature that alludes to heaven, hell, or reincarnation. Some examples include the Ancient Egyptian portrayals of afterlives through “The Coffin Texts” and “The Pyramid Texts”. In religions like hinduism and buddhism, the afterlife is dominantly portrayed by art, like the wheel of rebirth which “visually communicates... the realms of reincarnation”, and their practices. Other notable examples are the Holy Bible, prayers and fables, and anecdotes from those claiming to have experienced an afterlife.

However, it is acknowledged that since there is little non-human-made evidence within religion (most coming from texts or art), different biases can influence the interpretations of evidence. For example, the most cited anecdotal interviews for reincarnation are from children, universally known for their imagination and creativity. Moreover, this evidence may have been manipulated by religious leaders in order to influence followers.

Religious evidence therefore tends to lack a sense of objectivity due to being interpretivist and more prevalent in pieces of art and literature, and can lack a sense of credibility due to the potential use of fiction, imagination, or hyperbole.

Anthropology
Anthropological evidence can be construed from cultural and archaeological perspectives. The existence of an afterlife is closely integrated with anthropology because, although the biological inevitability of death is shared by all species, humans are the primary origin of death concerns and are the initial creators of heterogeneous systems of afterlife beliefs. Qualitative social research methods are essential for making an ethnographic approach towards collecting cultural evidence of an afterlife’s existence, focusing on observing and interpreting contemporary societies and their cultures, namely death rituals and ceremonies. The evidence is highly interpretivist and empirical. Many global indigenous tribes still exercise systems of afterlife beliefs, which act as a relief for ambivalence and fear toward death. Especially for less developed societies, the existence of the afterlife affects a society's cooperation, both culturally and economically. It is important to note that anthropology originated in the West in the 19th century. Therefore, when interpreting evidence of an afterlife in native societies, it is often done under the influence of imperialism. Charles Eastman wrote regarding an afterlife among plains Indians: “The idea of a ‘happy hunting-ground’ is modern and probably borrowed, or invented by the white man”; which also suggests the cross-cultural nature of the evidence of afterlife belief and how it is closely linked with other disciplines such as religion, history and sociology. For archaeological anthropology, there exists physical evidence such as artefacts, architecture and texts that were used in the afterlife rituals. With the help of other disciplines, anthropologists can examine and analyze these using advanced technologies, thus providing a more detailed insight into ancient afterlife beliefs.

Physics
An empirically supported idea within physics is the law of conservation of energy, claiming that energy and matter can only be transferred Consequently, a deceased human’s matter only transfers through decomposition. This suggests that the Christian belief of resurrected bodies being of “incorruptible matter” is an “oxymoron and impossibility in our universe”. Moreover, Galileo and Newton demonstrated that matter remains constant throughout the “observable universe”, evident through the observation of “spectral lines of light”. This questions a physical difference between life and the afterlife, suggesting life after death remains on this plane of existence. Evidence from physics, which tends to be more objective, conflict with the interpretivist religious evidence. Overall, positivist evidence can be used from physics to suggest life after death is the entropy of nutrients from decomposing bodies rather than another conscious state of being.

Psychology
In psychology, evidence surrounding the afterlife is generally interpretivist, dealing with investigating origins of belief in the concept, the development of such thoughts, and near death experiences (NDEs). Belief in the afterlife has been proposed as a means of dealing with individual mortality: while enhancing positive death perspective, such beliefs also allow an acceptance of the negative aspects of death. The idea of immortality of the soul may also be an intuitive religious concept. Hence, some psychological evidence suggests that the idea of an afterlife has been constructed to ease the human experience as opposed to arguing for its existence.

NDEs are often characterized by the sensation of being in a different dimension, where the usual perception of space-time disappears while the physical dimension vanishes. Psychologist Emily Williams Kelly states that NDEs show that a form of consciousness exists even after brain activity becomes abnormal. Kelly argues that “if our conscious experience totally depends on the brain, then there can’t be an afterlife -- when the brain is gone, the mind is gone. But [...] when the brain seems to be virtually disabled, people are still having these experiences.”. NDEs can also be reproduced by drugs such as ketamine making further psychological study more accessible. However, subjects are not definitively (irreversibly) dead during NDEs, making the NDE argument for the existence of the afterlife potentially less credible. However, research conducted by the Loyola University Medical Center shows that even after being clinically diagnosed as brain dead, some patients continued to show electroencephalographic activity for 36.6 hours. This is an example of empirical evidence that exists even in situations of definitive death, although the necessity for an interpretivist approach in such cases must be noted.

Evidence for the afterlife in psychology can vary between working towards understanding the nature of human belief in the afterlife and personal accounts; it therefore combines both empirical and subjective evidence. As the concept of the afterlife is an inherently human idea, taking a psychological approach to investigating its evidence is appropriate since psychology is the science of the human mind/behaviour. However, it requires the use of perspectives from other disciplines such as philosophy, making such investigation interdisciplinary.

=Evaluation= Evidence for or against the existence of an afterlife can be seen to be very speculative, with evidence either being very interpretivist or positivist. While more positivist evidence decreases the influences of biases, afterlife is closely associated to wellbeing and choice and as such, subjectivity is necessary. Although both are needed for a more holistic understanding, conclusions from the different evidence conflict. This questions the credibility of each discipline’s evidence and questions the superior way into continuing to study this debate.

=References=


text:
Talk:Issues in Interdisciplinarity 2019-20/Evidence in the Afterlife

=GROUP BRAINSTORMING= Brainstorming of topics

TRUTH
Conspiracy theories - flat earth → business perspective and marketing the “truth”, personal truths versus group truths

POWER
Art → but which issues?

Surrogacy → who’s the mother? Biological perspectives (intention versus the actual DNA) versus legal perspectives versus psychological (if something is inherited or taught through social environment)

Euthanasia → ethical perspectives (is it ethical?), philosophy/religious perspectives (suicide → is looked down upon?), biological perspectives, legal perspectives

EVIDENCE
Legalisation of recreational use of marijuana in the UK→ sociological perspective (crime rate etc) → correlation graphs, looking at relations Interviews (for stereotypes and to look at the relationships within the community) Content analysis → how it’s played in the media → positive view vs negative view medical perspective (medicinal applications of marijuana, lack of evidence for long term effects) → empirical evidence/positivist evidence religious/historical perspectives (role marijuana has played in religions) → content analysis/biblical texts; historical perspective (e.g. historical reasons for alcohol being legal and weed not) → anecdotal evidence political perspective (what’s better for a city → drug crime, what’s considered “safe”) → other countries’ laws → business perspective, hemp as wood alternative, CBD

the existence of an afterlife: the Religion -Different religions → Heaven vs Hell, Christianity / Catholicism, Buddhism (reincarnation) science Psychedelic drug experiences Neuroscience: Brain is still alive after death; analysis of brain activity Law of conservation of energy (can link to environmental science) Philosophy Different philosophical persepectives on existence/non-existence of afterlife

Anthropology Ancient Egyptian cultures different fields: Sociocultural, biological, Archaeological, linguistic


text:
Issues in Interdisciplinarity 2019-20/Evidence of Vichy France after World War Two

Introduction
From 1940 to 1945, the French State committed to a collaboration with Germany under the Vichy-Regime which lead to a division of beliefs in society in the post-war period. There was a lack of ‘official truth’ in France during that somber period as a result of the privatization of the main sources of evidence, such as official archives. This paper aims to study evidence used to shape the truth in that time, and how interdisciplinary research helped set the collective memory of the French people.

Construction of the collective memory
To unify its post-war divided country, the French government constructed a new collective memory. One of their methods was to restructure the geographical evidence of the war. As De Gaulle led the government, he proliferated the myth of the Résistancialisme and thus, funded several museums and memorials dedicated to the resistance and deportation during the WW2. However, official museums appeared later in history as a result of the founding of the an official branch of the government which managed the construction of memorial sites. Before that only a few small and private ones where disseminated across the country. The territorial distribution of these museums is interesting as most of them are settled in the former Vichy area which collaborated the most during the war.

The "Les Lieux de Mémoire" have shaped the french landscape and urbanism. Plaques, streets renamed after soldiers, memorials, among other symbols were built throughout the country and significant places of the resistance where actively highlighted. These evidence of the glorification of war heroes were geographically surrounding the people. Hence, it strongly influenced their psychology and reconstructed their memories of the conflict. Geographical evidence of the jewish memory (i.e. memorials, museums, etc.) arose several decades later, as the government and the country faced their role in the shoah. The first proper important museums dedicated to the jewish memory were opened in the 1990s and many were only inaugurated in the beginning of the 21st century. The role of museums and all other "lieux de mémoires" illustrates the government's aim to conceive a collective memory, leaving out sometimes the dark sides of their history.

Museums are also used as a pedagogical tool. Evidence-based education uses evidence to identify starting points for teaching and learning. Information of past experiences from teachers are points used as evidence to establish academic curriculums. Duty of remembrance designates a moral obligation to commemorate a tragic historical event to prevent its reproduction. Politics impact what evidence is taken into consideration to expand throughout education.

In the case study, duty of remembrance influences the evidence French education is based on. Consequently, pedagogy allows scholars to acquire constructed memory thus considered as an 'official truth'.

Law and justice, presumed as a moral concept within judiciary, approach evidence epistemologically. Validity and justification as well as truth are crucial elements when considering evidence in a legal sense. However, approaches to evidence in justice and the law vary distinctively with respect to different legislatures. Even if there is no consensus concerning its definition, evidence in a legal sense has to be viewed as an independent concept. It is primarily seen as a means in the process of proving a claim or accusation to be true or false. When referring to evidence in a court case, this is the most common meaning. In this particular sense evidence can be oral in the form of testimonies, visual as in documents or physical with regard to objects. Evidence in the law has to be factual and valid.

Under the rule of the Vichy-Regime, France’s legislation changed drastically. Whilst collaborating with Germany, France’s defeat was mainly believed to be the fault of Jews and foreigners which prompted several anti-Semitic statues and xenophobic laws to be imposed. These statues led to the deportation and mass-murder of many French Jews as they were being denaturalized as citizens. Proving the Vichy-Regime’s complicity with Germany after the war was deemed difficult as there was a lack of legal evidence. The first time France admitted to being partially at fault for deportations and the genocide of WW2 was 1995 by then president Chirac. This period of failed recognition of France's fault was crucial in shaping the collective memory, as the lack of evidence meant that living in denial was easy. Despite Vichy France’s undeniable antisemitism, they did not actively want to aid the Germans in their crimes against French Jews. Regardless, the issue itself was that they discriminated against a minority and thus singled them out, which consequently enabled the Germans even further.

Construction of the individual memory
Testimonies found in literature, art and documentaries are considered as some of the most controversial pieces of evidence. After WW2, testimonies and personal pieces played a crucial role in forging a collective truth and giving a voice to victims of the collaboration. Because it was based on deeply personal experiences, artwork from this period became persuasive and forceful evidence. Art, literature and film making from this period all approach evidence in a similar manner, namely by looking at the human experience and trying to convey their reality and emotions. However, memories are subjective and can be hard to deem viable in other disciplines, such as justice and sciences. This leads to them being less respected in terms of classifying evidence. During psychological resilience, expressing lived phenomena through art allows to uncover the truthful events. This resulted in the creation of many pieces of evidence such as books, films, paintings, etc. For example, a long investigation consisting of survivors describing their different coping processes was conducted. Moreover, these documentaries were often censored by the government. The movie "The Sorrow and the Pity” by Marcel Ophuls which described the life of the French during the occupation and showed that they were very few to resist, for instance, was censored until 1981.

Phenomenology uses qualitative research methodologies concerning experimental psychology and the experience of the French people through memory. It aims to enlighten how people understand and comprehend phenomena and lived experiences. Phenomenological methods include oral history, diary methods and qualitative interviews paying particular attention to individuality. Oral history allows to subjectively and realistically describe an event as lived by an individual for instance, whereas interviews supply information on the perception on concepts such as forgiveness and reconciliation. The evidence provided by phenomenology is subjective. These methods are critiqued for their lack of quantitative research methods resulting in a low generalizability.

Conclusion
Regardless of the Vichy-Regime’s collaboration with the National Socialist Germany and thus its liability for many crimes, deportations and murders, committed during that period, it seemed rather difficult to find evidence of any misconduct. Interdisciplinary work, encompassing evidence approached by law, arts and education among others, the truth was finally established and malpractice during the collaboration was acknowledged. This case study illustrates the value of interdisciplinary methods. Indeed, there is an obligation to understand complex problems and gain adequate understanding of issues, often englobing different disciplines. The importance of variability in approaches to knowledge, especially when dealing with such a delicate situation is considerable in terms of taking into account all aspects of the victims thus in finding an adequate and more truthful response.


text: Issues in Interdisciplinarity 2019-20/The issue of History in the 2013 - 2016 EVD Epidemic


text:
Issues in Interdisciplinarity 2019-20/The issue of History in the 2013 - 2016 EVD epidemic

Introduction
The first outbreaks of the Ebola Virus Disease were in 1976 in the DRC and Sudan. The subsequent West African Epidemic reached mortality rates of up to 90%, more specifically in Liberia, Guinea, Mali, Sierra Leon, Nigeria and Senegal. The epidemic had devastating social, political impacts on the countries’ economies and healthcare systems.

The death toll by October 2015, 11,323, begs us to question methods employed to end the outbreak. Medical and biological sciences are needed to explain the origin and treatment of diseases, while understanding the cultural practices that prevented the containment of EVD requires anthropological perspectives. However, the history of these different disciplines is problematic in tackling the crisis, as scientific procedure tends to take precedence. We will therefore explore different disciplinary approaches to the 2013-2016 Ebola crisis, illustrating the benefits of interdisciplinary thinking.

Biology and Virology
Zaire Ebolavirus is one of the most virulent pathogens within the hemorrhagic fevers. The virus spreads through contact with bodily fluids. The incubation period is 21 days, during which the patient may inadvertently cause propagation. Symptoms are similar to other diseases found in West Africa such as malaria, Lassa fever and typhoid, resulting in frequent misdiagnosis.

Its genome consists of non-segmented, negative-sense, and single-stranded RNA molecule. After contagion, the virus targets and weakens the immune system, specifically dendritic cells. In a study published by  'Cell Host & Microbe' , research found that the VP24 protein on Ebola inhibits the production of antibodies. Toxins trigger the release of proinflammatory cytokine and nitric oxide, which damage the endothelial lining of blood vessels. Then, the repeated coagulation reduces blood supply resulting in fatal organ failure.

No cure exists for EVD, but in 2016 the rVSV-ZEBOV vaccine was found to be 70-100% effective.

1. Medical
The primary aim of medical practitioners was to interrupt transmission chains by quarantining patients. The EVD response privileged the work of scientists often overlooking social and cultural factors. Medical intervention was highly individualistic and included enforced quarantines, movement prohibition, traveller test points, and mandated cremation. Unsurprisingly, the effectiveness of such measures increased the stigmatisation surrounding the disease. Medical practitioners used IgM ELISA tests, RT-PCR tests, biopsy samples and viral cultures to diagnose patients and limit the spread of ebola.

While there were no approved treatments, supportive care like the one recommended by the CDC was applied to alleviate the patients' suffering. This included: oral rehydration therapy, intravenous fluids, oxygen therapy, treating other infections if they occurred, and disinfecting surfaces with (>70%) alcohol wipes. Conventional medicine was used to relieve the symptoms (high blood pressure, vomiting, fever and pain). Medical workers used experimental treatments such as immune serums, antiviral drugs and possible blood transfusions to impede the disease from victimising others. To provide relief, the doctors deployed in the infected areas set up treatment and isolation centres rather than search for a cure. Containment was the main concern so medical action was largely unquestioned.

Yet this approach was occasionally met with hostility for example when 8 health workers attempting to raise awareness about EVD in a village in Guinea were murdered. While historically very effective at minimising physical suffering, the massacre of health workers made it painfully clear that this historical authority is not universal. Therefore, medics must turn to anthropologists to understand the important cultural dynamics present in diverse African societies.

2. Anthropological Approach
Anthropological research illustrates how social and cultural factors contributed to the biological transmission of EVD during the 2013 West Africa outbreak and interfered with the corresponding medical response. Many of the affected countries suffer from poverty and the recent civil wars in Guinea, Liberia, and Sierra Leone left behind fragile health care systems and physician shortages regionally. The consequent challenged quarantine, ineffective alerts and pleas for assistance facilitated further infection.

Understanding cultural practices in infected regions is integral to tackling the EVD crisis effectively. Cultural differences between health practitioners and locals was problematic in dealing with the outbreak. The WHO’s retrospective analysis of the outbreak showed locals feared how much western treatment contradicted traditional practices regarding the dying or diseased. Ancestral funeral rites such as sleeping next to an infectious corpse of the community and bathing in water used to rinse corpses were attributable to 80% of cases in Sierra Leone by WHO estimates. The stigma around these cultural practices drove families to hide symptomatic relatives, leading to infection of their households. Traditions of returning dying patients to their native village elevated the risk of transmission through cross-border movement.

Fear of physicians was another barrier to its eradication. In Guinea, rumours of health workers disinfecting a market contaminating people led to riots. Proving that health care responses require communication between medical practitioners and community leaders. A post-colonial reading of western aid sees imperialistic thinking that disregards customs. Doctors often see locals' apprehension of western medicine as backwards tradition and the work of well-respected African healers is disregarded. Biology failed to provide a complete explanation nor complete response to EVD epidemic. Anthropological research is needed to provide culturally-sensitive aid. Moreover, theology could further inform anthropology in local religious customs.

3. Theological Approach
Burials according to biomedicine and theology present contradictory practices. Biomedicine, a Western discipline, institutionalises quarantines in burials, whereas West African religious preach religious inquires into pathology during burials.

Burials are important in many West African religions, as the time for the deceased to enter the afterlife, join their ancestors, and overlook the living. Ill-performed rituals could trap the spirits in the living realm and taunt loved ones. Bodies are cleansed and foetuses are removed from pregnant bodies to uphold natural cycles and ensure the wellbeing of both alive and dead. Thus, religious procedures concerning remains are strictly adhered to. Disagreements over how burials should be performed have arisen during the outbreak because the meaning of burials diverges between biomedicine and West African theology. An example of this is, in Guinea, a burial was brought to standstill amidst disagreements between a Kissi family and the medical team on how to handle the remains. The body rotted as the dispute carries on, which risked further infections upon leakage. Meanwhile, another team in Guinea substituted old repatriation rituals for the foetus’ removal, and successfully buried the pregnant body to everyone’s satisfaction. This underpins the importance of theology in complementing biomedicine and anthropology to understand, manage, and quell epidemics like Ebola in West Africa.

Conclusion
The 2013-2016 Ebola epidemic captured the world’s attention, and experts from a diverse range of disciplines sprang into West Africa’s aid; with medics handling the majority of ailments, while anthropologists liaised with communities, and religious leaders encouraging cooperation.

Unfortunately, due to the complex lexicon, disciplinary boundaries, and historical paradigms behind these disciplines; their ideas diverge on many seemingly intuitive concepts like burials, and could not communicate effectively. An interdisciplinary approach bridging knowledge between disciplines in their interpretation of treatment, healing, and well-being, could converge the efforts with synergetic effects.

Further disciplines may also be introduced, such as mathematical models of disease transmission, governance theories of public healthcare, and psychological perspectives on trauma. While each discipline has developed distinct metrics and criteria for what a good approach is, coherence could be achieved between these knowledge frameworks if differences are proactively reconciled.


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text:
LMIs in Control/pages/DARE

The System
Consider a Discrete-Time LTI system

\begin{align} x_{k+1} = A_dx_k + B_du_k \end{align}$$

\begin{align} y_k = C_dx_k \end{align}$$

Consider Ad ∈ $$\begin{align}\mathbb{R}\end{align}$$nxn ; Bd ∈ $$\begin{align}\mathbb{R}\end{align}$$nxm

The Data
The Matrices Ad, Bd , Cd , Q, R are given

Q and R should necessarily be Hermitian Matrices.

A square matrix is Hermitian if it is equal to its complex conjugate transpose.

The Optimization Problem
Our aim is to find

P - Unique solution to the discrete-time algebraic Riccati equation, returned as a matrix.

K - State-feedback gain, returned as a matrix.

The algorithm used to evaluate the State-feedback gain is given by

\begin{align} K = (R+B_d^TPB_d)^{-1}B_d^TPA_d \end{align}$$

L - Closed-loop eigenvalues, returned as a matrix.

The LMI: Discrete-Time Algebraic Riccati Inequality (DARE)
An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time

The Discrete-Time Algebraic Riccati Inequality is given by

\begin{align} A_d^TPA_d - A_d^TPB_d (R + B_d^TPB_d)^{-1} B_d^TPA_d + Q - P \geq 0 \end{align}$$

P, Q ∈ $$\begin{align}\mathbb{S}\end{align}$$n and R ∈ $$\begin{align}\mathbb{S}\end{align}$$m where P > 0, Q ≥ 0, R > 0

P is the unknown n by n symmetric matrix and A, B, Q, R are known real coefficient matrices.

The above equation can be rewritten using the Schur Complement Lemma as :

\begin{bmatrix} A_d^TPA_d-P+Q & A_d^TPB_d \\ B_d^TPA_d & R+B_d^TPB_d \end{bmatrix}$$$$\begin{align}\geq 0\end{align}$$

Conclusion:
Algebraic Riccati Inequalities play a key role in LQR/LQG control, H2- and H∞ control and Kalman filtering. We try to find the unique stabilizing solution, if it exists. A solution is stabilizing, if controller of the system makes the closed loop system stable.

Equivalently, this Discrete-Time algebraic Riccati Inequality is satisfied under the following necessary and sufficient condition:

\begin{bmatrix} Q & 0 & A_d^TP & P\\ 0 & R & B_d^TP & 0\\ PA_d & PB_d & P & 0\\ P & 0 & 0 & P \end{bmatrix}$$$$\begin{align}\geq 0\end{align}$$

Implementation
( X in the output corresponds to P in the LMI )

A link to the Matlab code for a simple implementation of this problem in the Github repository:

https://github.com/yashgvd/LMI_wikibooks

Related LMIs
LMI for Continuous-Time Algebraic Riccati Inequality

LMI for Schur Stabilization

title: LMIs in Control/pages/DARE


text:
LMIs in Control/pages/H2-OSE

The H2 norm of a stable system H is the root-mean-square of the impulse response of the system. The H2 norm measures the steady-state covariance (or power) of the output response to unit noise input. In this module, the goal of H2 optimal state estimation is to design an observer that minimizes the H2 norm of the closed loop transfer matrix

The System
Consider the continuous-time generalized plant P with state-space realization

\begin{align} \dot x(t)&=Ax(t)+B_1u(t)+B_2w(t) & x(0)=x_0\\ y(t)&=C_1x(t)+D_{1}u(t)+D_2w(t)\\ &z(t) = C_2x(t) \end{align}$$

where it is assumed that (A,C2) is detectable. An observer of the form

The Data
output vector, and the output vector of interests
 * $$x$$ ∈ $$\begin{align}\mathbb{R}\end{align}$$n, $$y$$ ∈ $$\begin{align}\mathbb{R}\end{align}$$l , $$z$$ ∈ $$\begin{align}\mathbb{R}\end{align}$$m are respectively the state vector, the measured

respectively
 * $$w$$ ∈ $$\begin{align}\mathbb{R}\end{align}$$p and $$u$$ ∈ $$\begin{align}\mathbb{R}\end{align}$$r are the disturbance vector and the control vector,

appropriate dimensions
 * A, B1, B2, C1, C2, D1, and D2 are the system coefficient matrices of

The Optimization Problem
Given the system and a positive scalar $$\gamma$$ we have to find the matrix L such that

|| $$G_{zw}(s)$$ || 2 < $$\gamma$$

An observer of the form

\begin{align} \dot x(t) = Ax(t) + (Ly - Ly) + B_1u(t) + B_2w(t)\\ \dot x(t)=(A+LC_1)x(t) - Ly + (B_1+LD_1)u(t) \\+ (B_2+LD_2)w(t) \end{align} $$ is to be designed, where L is the observer gain. Defining the error state as  $$e = x - \hat x$$ The break dynamics are found to be
 * $$\begin{align}

\dot e = (A+LC_1)e + (B_2+LD_2)w\\ \bar z(t) = C_2e \end{align} $$

For the system we introduce a full state observer in the following form: $$ \dot \hat x = (A+LC_1)\hat x - Ly + (B_1+LD_1)u$$ $$ \hat x, L$$ are the observation vector and the observer gain. The transfer function for this case is $$ G_{zw}(s) = C_2(sI-A-LC_1)^{-1}(B_2+LD_2)$$ and thus the problem of $$H_2$$ state observer design is to find L such that ||$$G_{zs}(s)||_2 < \gamma $$

The LMI: LMI for H2 Observer estimation
The H2 state observer problem has a solution if and only if there exists a matrix $$W$$, a symmetric matrix $$Q$$ and a symmetric matrix $$X$$ such that

\begin{bmatrix} XA + WC_1 + (XA+WC_1)^T & XB_2 +WD_2 \\ (XB_2 +WD_2)^T & -I \end{bmatrix}$$$$\begin{align}< 0\end{align}$$

\begin{bmatrix} -Q & C_2 \\ C_2^T & -X \end{bmatrix}$$$$\begin{align}< 0\end{align}$$

\begin{align} trace(Q)< \gamma^2 \end{align} $$

and from the solution of the above LMIs we can obtain the observer matrix as

L = X^{-1}W $$

Conclusion
Thus by formulation, we have converted the problem of H2 state observer design into an LMI feasibility problem by optimizing the above LMIs. In application we are often concerned with the problem of finding the minimal attenuation level  $$\gamma$$  On implementation and optimization of the above LMI using YALMIP and MOSEK (or) SeDuMi we get 3 matrices as output, $$X,W and Q$$ and also $$\rho$$ which is used to calculate $$\gamma$$ which is the H2 norm of the system.

There exists another set of LMIs which holds true for the same optimization problem as above.

\begin{align} A^TY+C_1^TV^T+YA+VC_1+C_2^TC_2 < 0\\ \end{align}$$

\begin{bmatrix} -Z & YB_2 +VD_2 \\ (YB_2 +VD_2)^T & -Y \end{bmatrix}$$$$\begin{align}< 0\end{align}$$ '''$$ \begin{align} trace(Z)< \gamma^2 \end{align} $$'''

When a minimal $$\rho$$ is obtained, the minimal attenuation level is

$$\gamma = \sqrt\rho$$

Implementation
A link to the Matlab code for a simple implementation of this problem in the Github repository:

https://github.com/yashgvd/ygovada

Related LMIs
H$\infty$ State Observer Design

Discrete time H2 State Observer Design

title: LMIs in Control/pages/H2-OSE


text:
LMIs in Control/Controller Synthesis/Continuous Time/Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

If the system is quadratically stable, then there exists some $$\mu \geq 0, P > 0,$$ and $$Z$$ such that the LMI is feasible. The $$Z$$ and $$P$$ matrices can also be used to create a quadratically stabilizing controller.

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t)+Mp(t),&&p(t) = \Delta (t)q(t),\\ q(t) &= Nx(t)+Qp(t)+D_{12}u(t),&&\Delta \in \mathbf{\Delta} \; := \{\Delta \in \mathbb{R}^{n \times n} : \| \Delta \| \leq 1 \}\\ \end{align}$$

The Data
The matrices $$ A,B,M,N,Q,D_{12} $$.

The LMI:

\begin{align} \text{Find} \; &P>0,\mu \geq 0, \text{ and } Z:\\ \begin{bmatrix} AP+BZ+PA^T+Z^TB^T & PN^T+Z^TD_{12}^T \\ NP+D_{12}Z & 0\end{bmatrix} + \mu \begin{bmatrix} MM^T & MQ^T \\ QM^T & QQ^T - I \end{bmatrix} < 0\\ \end{align}$$

Conclusion:
There exists a controller for the system with $$ u(t) = Kx(t) $$ where $$ K = ZP^{-1} $$ is the quadratically stabilizing controller, if the above LMI is feasible.

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
H-infinity Optimal Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

Stabilizing State-Feedback Controllers with Structured Norm-Bounded Uncertainty

Optimal State-Feedback Controllers with Structured Norm-Bounded Uncertainty


text:
LMIs in Control/Controller Synthesis/Continuous Time/H-inf Optimal Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

If there exists some $$\mu \geq 0, P>0$$, and $$Z$$ such that the LMI holds, then the system satisfies $$\|y\|_{L_2} \leq \gamma \|u\|_{L_2}.$$ There also exists a controller with $$u(t) = Kx(t).$$

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t)+Mp(t)+B_2w(t),&&p(t) = \Delta (t)q(t),\\ q(t) &= Nx(t)+D_{12}u(t),&&\Delta \in \mathbf{\Delta} \; := \{\Delta \in \mathbb{R}^{n \times n} : \| \Delta \| \leq 1 \}\\ y(t) &= Cx(t)+D_{22}u(t)\\ \end{align}$$

The Data
The matrices $$ A,B,M,B_2,N,D_{12},C,D_{22} $$.

The Optimization Problem
Minimize $$ \gamma $$ subject to the LMI constraints below.

The LMI:

\begin{align} \text{Find} \; &P>0,\mu \geq 0, \text{ and } Z:\\ \begin{bmatrix} AP+BZ+PA^T+Z^TB^T+B_2B_2^T+\mu MM^T & (CP+D_{22}Z)^T & PN^T+Z^TD_{12}^T \\ CP+D_{22}Z & -\gamma ^2I & 0 \\ NP+D_{12}Z & 0 & -\mu I \end{bmatrix} < 0\\ \end{align}$$

Conclusion:
The controller gains, K, are calculated by $$ K = ZP^{-1} $$.

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

Stabilizing State-Feedback Controllers with Structured Norm-Bounded Uncertainty

Optimal State-Feedback Controllers with Structured Norm-Bounded Uncertainty


text:
LMIs in Control/Controller Synthesis/Continuous Time/Stabilizing State-Feedback Controllers with Structured Norm-Bounded Uncertainty

$$ \begin{align} \text{The system is quadratically stable if and only if there exists some } \Theta \in P \Theta, P>0, \text{ and } Z \text{ such that the LMI is feasible.} \text{ Furthermore, there exists a quadratically stabilizing controller with } u(t) = Kx(t). \end{align} $$

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t)+Mp(t),&&p(t) = \Delta (t)q(t),\\ q(t) &= Nx(t)+Qp(t)+D_{12}u(t),&&\Delta \in \bf{\Delta} \;, || \Delta || \leq 1 \\ \end{align}$$

The Data
The matrices $$ A,B,M,N,Q,D_{12} $$.

The LMI:

\begin{align} \text{Find} \; &P>0,Z:\\ \begin{bmatrix} AP+BZ+PA^T+Z^TB^T & PN^T+Z^TD_{12}^T \\ NP+D_{12}Z & 0\end{bmatrix} + \begin{bmatrix} M \Theta M^T & M \Theta Q^T \\ Q \Theta M^T & Q \Theta Q^T - \Theta \end{bmatrix} < 0\\ \end{align}$$

Conclusion:
If the LMI is feasible, the controller, K, is calculated by $$ K = ZP^{-1} $$.

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

H-infinity Optimal Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

Optimal State-Feedback Controllers with Structured Norm-Bounded Uncertainty


text:
LMIs in Control/Controller Synthesis/Continuous Time/Optimal State-Feedback Controllers with Structured Norm-Bounded Uncertainty

$$ \begin{align} \text{If there exists some } \Theta \in P \Theta, P>0, \text{ and } Z \text{ such that the LMI is feasible, then the system satisfies } ||y||_{L_2} \leq \gamma ||u||_{L_2}. \text{ There also exists a controller with } u(t) = Kx(t). \end{align} $$

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t)+Mp(t)+B_2w(t),&&p(t) = \Delta (t)q(t),\\ q(t) &= Nx(t)+D_{12}u(t),&&\Delta \in \bf{\Delta} \;, || \Delta || \leq 1 \\ y(t) &= Cx(t)+D_{22}u(t)\\ \end{align}$$

The Data
The matrices $$ A,B,M,B_2,N,D_{12},C,D_{22} $$.

The Optimization Problem
$$ \text{Minimize } \gamma $$ subject to the LMI constraints.

The LMI:

\begin{align} \text{Find} \; &P>0,Z:\\ \begin{bmatrix} AP+BZ+PA^T+Z^TB^T+B_2B_2^T+M \Theta M^T & (CP+D_{22}Z)^T & PN^T+Z^TD_{12}^T \\ CP+D_{22}Z & -\gamma ^2 I & 0 \\ NP+D_{12}Z & 0 & -\Theta\end{bmatrix} < 0\\ \end{align}$$

Conclusion:
The controller is $$ K = ZP^{-1} $$.

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

H-infinity Optimal Quadratically Stabilizing Controllers with Parametric Norm-Bounded Uncertainty

Stabilizing State-Feedback Controllers with Structured Norm-Bounded Uncertainty


text:
LMIs in Control/Matrix and LMI Properties and Tools/Continuous Time/Structured Singular Value

The LMI can be used to find a $$ \Theta $$ that belongs to the set of scalings $$ P\Theta $$. Minimizing $$ \gamma $$ allows to minimize the squared norm of $$ \Theta M \Theta^-1 $$.

The System

\begin{align} M \text{ with transfer function } \hat M(s) = C(sI-A)^{-1}B+D,&& \hat M \in H_\infty \end{align}$$

The Data
The matrices $$ A \in R^{n \times n}, B \in R^{n \times m}, C \in R^{o \times n}, D \in R^{o \times m} $$.

The Optimization Problem
$$ \begin{align} \text{There exists } \Theta \in \Theta \text{ such that } ||\Theta M \Theta ^{-1} ||^2 < \gamma. \end{align} $$

The LMI:

\begin{align} \text{Find} \; &X>0:\\ \begin{bmatrix} A^TX+XA & XB \\ B^TX & -\Theta \end{bmatrix} + \gamma ^{-2} \begin{bmatrix} C^T \\ D^T \end{bmatrix} \Theta \begin{bmatrix} C & D \end{bmatrix} < 0\\ \end{align}$$

Conclusion:
$$ \text{The optimization problem and the LMI are equivalent. } \gamma \text{ must be optimized using bisection.} $$

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
Eigenvalue Problem


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LMIs in Control/Matrix and LMI Properties and Tools/Continuous Time/Eigenvalue Problem

The maximum eigenvalue of a matrix is going to have the most impact on system performance. This LMI allows for minimization of the maximum eigenvalue by minimizing $$ \gamma $$.

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t), \\ y(t) &= Cx(t) \end{align}$$

The Data
The matrices $$ A \in R^{n \times n}, B \in R^{n \times m}, C \in R^{o \times n} $$.

The Optimization Problem
$$ \text{ Minimize } \gamma \text{ subject to the LMI below.} $$

The LMI:

\begin{align} \text{Find} \; &P>0:\\ \begin{bmatrix} -A^TP-PA-C^TC & PB \\ B^TP & \gamma I\end{bmatrix} > 0\\ \end{align}$$

Conclusion:
The eigenvalue problem can be utilized to minimize the maximum eigenvalue of a matrix that depends affinely on a variable.

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
Structured Singular Value


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LMIs in Control/Stability Analysis/Continuous Time/Parametric, Norm-Bounded Uncertain System Quadratic Stability

Given a system with matrices A,M,N,Q the quadratic stability of the system with parametric, norm-bounded uncertainty can be determined by the following LMI. The feasibility of the LMI tells if the system is quadratically stable or not.

The System

\begin{align} \dot x(t)&=Ax(t)+Mp(t),&&p(t) = \Delta (t)q(t),\\ q(t) &= Nx(t)+Qp(t),&&\Delta \in \mathbf{\Delta} \; := \{\Delta \in \mathbb{R}^{n \times n} : \| \Delta \| \leq 1 \}\\ \end{align}$$

The Data
The matrices $$ A,M,N,Q $$.

The LMI:

\begin{align} \text{Find} \; &P>0,\mu \geq 0:\\ \begin{bmatrix} AP+PA^T & PN^T \\ NP & 0\end{bmatrix} + \mu \begin{bmatrix} MM^T & MQ^T \\ QM^T & QQ^T - I \end{bmatrix} < 0\\ \end{align}$$

Conclusion:
The system above is quadratically stable if and only if there exists some mu >= 0 and P > 0 such that the LMI is feasible.

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
Stability of Structured, Norm-Bounded Uncertainty

Stability under Arbitrary Switching

Quadratic Stability Margins


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LMIs in Control/Stability Analysis/Continuous Time/Stability of Structured, Norm-Bounded Uncertainty

Given a system with matrices A,M,N,Q with structured, norm-bounded uncertainty, the stability of the system can be found using the following LMI. The LMI takes variables P and $$ \Theta $$ and checks for a feasible solution.

The System

\begin{align} \dot x(t)&=Ax(t)+Mp(t),&&p(t) = \Delta (t)q(t),\\ q(t) &= Nx(t)+Qp(t),&&\Delta \in \bf{\Delta} \;, || \Delta || \leq 1 \\ \end{align}$$

The Data
The matrices $$ A,M,N,Q $$.

The LMI:

\begin{align} \text{Find} \; &P>0:\\ \begin{bmatrix} AP+PA^T & PN^T \\ NP & 0\end{bmatrix} + \begin{bmatrix} M \Theta M^T & M \Theta Q^T \\ Q \Theta M^T & Q \Theta Q^T - \Theta \end{bmatrix} < 0\\ \end{align}$$

Conclusion:
$$ \begin{align} \text{The system above is quadratically stable if and only if there exists some } \Theta \in P \Theta \text{ and } P > 0 \text{ such that the LMI is feasible.} \end{align} $$

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
Parametric, Norm-Bounded Uncertain System Quadratic Stability

Stability under Arbitrary Switching

Quadratic Stability Margins


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LMIs in Control/Stability Analysis/Continuous Time/Stability under Arbitrary Switching

LMIs in Control/Stability Analysis/Continuous Time/Stability under Arbitrary Switching

Using the LMI below, find a P matrix that fits the constraints. If there exists one, then the system can switch between subsystems $$ A_1 $$ and $$ A_2 $$ arbitrarily and remain stable.

The System

\begin{align} \dot x(t) \in \{ A_1x(t),A_2x(t) \} \end{align}$$

The Data
The matrices $$ A_1 \in R^{n \times n} ,A_2 \in R^{n \times n} $$.

The LMI

\begin{align} \text{Find} \; &P>0:\\ A_1^TP+PA_1 < 0 \text{ and }\\ A_2^TP+PA_2 < 0 \end{align}$$

Conclusion
The switched system is stable under arbitrary switching if there exists some P > 0 such that the LMIs hold.

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
Parametric, Norm-Bounded Uncertain System Quadratic Stability

Stability of Structured, Norm-Bounded Uncertainty

Quadratic Stability Margins


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LMIs in Control/Stability Analysis/Continuous Time/Quadratic Stability Margins

$$ \begin{align} \text{The quadratic stability margin of the system is defined as the largest } \alpha \geq 0 \text{ for which the system is quadratically stable.} \text{This LMI applies for systems with norm-bounded uncertainty.} \end{align} $$

The System

\begin{align} \dot x(t)&=Ax(t)+B_pp(t),&&p^Tp \leq \alpha ^2 x^TC_q^TC_qx\\ \end{align}$$

The Data
The matrices $$ A,B_p,C_q $$.

The Optimization Problem
$$ \text{Maximize } \beta = \alpha^2 \text{ subject to the LMI constraint.} $$

The LMI:

\begin{align} \text{Find} \; &P,\lambda, \text{ and } \beta = \alpha ^2:\\ \begin{bmatrix} A^TP+PA+ \beta \lambda C_q^TC_q & PB_p \\ B_p^TP & -\lambda I \end{bmatrix} < 0\\ \end{align}$$

Conclusion:
If there exists an $$ \alpha \geq 0 $$ then the system is quadratically stable, and the stability margin is the largest such $$ \alpha $$.

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
Parametric, Norm-Bounded Uncertain System Quadratic Stability

Stability of Structured, Norm-Bounded Uncertainty

Stability under Arbitrary Switching


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IGCSE Information and Communication Technology/4. Networks and the effects of using them

networks are:a group or system of interconnected people or things. Networks Understand how a router works and its purpose Understand the use of other common network devices, including: network interface cards, hubs, bridges, switches, modems Understand the use of WiFi and Bluetooth in networks Understand how to set up and configure a small network, including: access to the internet, the use of a browser, the use of email, access to an ISP Understand the characteristics and purpose of common network environments, such as intranets and the internet Understand the advantages and disadvantages of using different types of computer to access the internet 4.2 Network issues and communication Describe security issues regarding data transfer Network communication


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IGCSE Information and Communication Technology/1. Types and components of computer systems

The written theory exam is 2 hours long and covers a wide range of topics. Questions range from simple true/false ones, to ones requiring long, extended answers.

Like any other IGCSE subject, ICT theory requires you to understand and learn the facts.

There is no shortcut... you will have to REVISE!

But, hopefully, these notes will help you to gain the understanding required. Stacks Image 235 If you're trying to find out about a particular topic, rather than a syllabus section, try looking here: Topic List Before you start reading the notes for each of the syllabus sections, read this introductory section: Some General Concepts The notes are divided into the following sections to match the theory section of the syllabus: Types and Components of Computer Systems Input and Output Devices Storage Devices and Media Computer Networks Data Type and Organisation The Effects of Using IT ICT Use in Everyday Life, ICT Use in the Workplace Systems Analysis and Design


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IGCSE Information and Communication Technology/2. Input and output devices

The course syllabus states that you should be able to: (a) Identify the following input devices: Keyboards, Numeric Keypads, Pointing Devices (including mouse, touch pad and tracker ball), Remote Controls, Joysticks, Touch Screens, Magnetic Stripe Readers, Chip Readers, PIN Pads, Scanners, Digital Cameras, Microphones, Sensors, Graphics Tablet, MICR, OMR, OCR, Barcode Readers, Video Cameras, Web Cams, Light Pens. (b) Identify suitable uses of the input devices stating the advantages and disadvantages of each. (c) Identify the uses of the following sensors: Temperature Sensor, Pressure Sensor, Light Sensor. (d) Identify the following output devices: Monitors (CRT, TFT), Projectors, Printers (laser, ink jet and dotmatrix), Plotters, Speakers. (e) Identify suitable uses of the output devices stating the advantages and disadvantages of each. (f) Identify the following control devices in control applications: Motors, Buzzers, Heaters, Lights/Lamps (g) Identify suitable uses of the control devices stating the uses of each.

WHAT IS AN INPUT DEVICE? An input device is any hardware device that sends data to a computer, allowing you to interact with and control it.


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IGCSE Information and Communication Technology/9. Audience

Information Communication and Technology is a subject which can give an IGCSE a strong base of knowledge in which you can apply to your studies or work all over the world. All over the world daily people apply their skills based on what they have learnt in ICT. Ones' skills can be very useful as you can learn how to spread information not just to the world wide web, but the whole world. ICT skills have an international effect expanding your chances to travel to different places of the world as a person that has a rich knowledge in ICT can easily find a job wherever they look throughout the world(you can find more advanced jobs in that field later in your carreer). Unlike subjects like Computer Science which requires a level of advanced math skills ICT is a subject that requires limited math skills especially for an IGCSE student. If you can complete IGCSE maths successfully the


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User:Itsyunotyou/sandbox

Social theory

Durkehim
 'In fact, in nature everything is so closely interconnected that there can be neither a complete division, nor too precise boundaries, between the various sciences.'

 * The difficulty of isolating disciplines

 'Even if they conform to my own sentiments and I feel their reality subjectively, this reality is still objective, for I did not create them, I merely received them through my education.

 * Truth is subjective and according to personal experience
 * Relationship between empirical knowledge and subjectivity
 * The fragility of objectivity

 'The intensity of punishment is greater to the degree that a society belongs to a less developed type - and to the degree that the central power has a more absolute character.'

 * Qualitative approach
 * Scale is crucial to making decisions

'' 'This hierarchy of social types does not imply, however, that the development of societies forms a single and linear sequence. On the contrary, it is certain that it should rather be portrayed as a tree having many branches which differ in greater or lesser degree. But societies are situated at varying heights on this tree, and at variable distances from the common trunk.'''

 * Non-linear thinking
 * New perspective on social structure not as a hierarchy

 'In effect, the degree of objectivity of a sensation is proportionate to the degree of stability of its object; for objectivity depends upon the existence of a constant and identical point of reference to which the representation can be referred, and which makes it possible to eliminate everything which is variable and subjective.'

title: User:Itsyunotyou/sandbox


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Talk:Issues in Interdisciplinarity 2019-20/Power in Pornography

to do : define as many terms as possible link as many terms to external pages/ Wikipedia pages as possible make sure we don't forget to fill in the group sheets thingy/ find out when the deadline for it is

also guys! we need to keep reminding the reader our link to power i.e. the power that pornography has or doesn't have is refleected in its economy, its social dynamics, in its access to health (or lack thereof) etc .......

need to be careful with the requested type of referencing (check moodle)

Lauren said we need to ensure that the conclusion really pulls all the disciplinary strands together i.e. the conclusion makes highlights the interdisciplinarity

increase number of academic papers

conclusion should be more related to the notion of power + improve the relation with interdisciplinarity

Last thing to check: proof-read and make sure every part is linked back to power!!


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User:LBird BASc/sandbox/ATK/Seminar6/Truth/gsdddsbss

This Wikibook chapter explores how the truth about the Facebook–Cambridge Analytica data scandal is presented/portrayed in different disciplines and why these contrasting truths create an interdisciplinary issue: when the meta-knowledge integrated from various disciplines is influenced by knowledge contradictions between the disciplines themselves.

Introduction and Case Study: The Facebook-Cambridge Analytica Scandal
This scandal came out in 2018 when Cambridge Analytica was reported to have been harvesting data from Facebook profiles in order to sway the 2016 United States presidential campaign in favour of Republican candidate Ted Cruz. Upon further investigation, Cambridge Analytica was found to have influenced more than 200 elections worlwide, including Donald Trump's 2016 campaign , resulting in the scrutiny and revisiting of policies regarding data usage and protection. It was revealed that in total the data of up to 87 million Facebook profiles were exploited for mainly political reasons. How exactly did Cambridge Analytica accomplish this extraordinary feat?

Context
In 2013, the data scientist Aleksandr Kogan, in the context of his academic work linking Facebook profiles to personality traits, developed a personality quiz app called "thisisyourdigitallife", which paid people to answer a 120 question personality test. However, in order to be paid for completing the survey, users had to log on to their Facebook profile, and allow the app to access to their Facebook activity : Kogan was trying to deduce personality traits based on Facebook activity, and to verify his hypotheses, he would use the personality test the people took to confirm whether his prediction was accurate. Later that year, Kogan was contacted by the firm SCL Group, a parent company of CA, with a business proposal: SCL would pay Kogan and provide him extra money, which he would use as an incentive to get more people to take the survey, and in exchange Kogan would provide the data gathered to SCL. The reason for SCL interest's was that the app in question not only gathered data on the individual who answered the survey, but on all of their friends's data as well, such as likes, posts, comments, location, and even private messages. An estimated number of 270 000 people took the survey, amounting up to the data of up to 87 million people and the extremely specific personality profiles of the people that took the survey being thus shared with SCL.

Law
Under 2013 Terms of Service, Facebook's API (Application Programming Interface) Version 1 allowed developers to access the data of an individual in question and their friends given that the user consented, and before signing up for Facebook, users accepted these terms and conditions: when in 2013 Kogan's app launched, its operations were completely legal. However, Facebook changed its API version in April 2014, limiting the data scope new developer apps could have, but giving pre-existing apps a one year enforcement delay to redesign their software to match the new API : Kogan had legally the right to keep harvesting data under the 2013 API for one more year. In 2015, thisismydigitallife ceased its operations as it no longer fit Facebook's terms and conditions, but was allowed to keep all the data it had harvested. The data of up to 87 million people had been obtained by Kogan under entire legality. Under the initial agreement between Kogan and Facebook with the regards to the application, Kogan explicitely states his possible intention to sell, to which Facebook knowingly agreed, although it conflicted with sections 3.3, 3.9, 3.10, and 7.4 of Facebook's Platform Policy. This means that the data gathered by Cambridge Analytica was legally obtained: Kogan, under the agreement signed by Facebook, was allowed to sell the information he had gathered, and that is what he did.

Ethics
From ethical perspective it was unrighteous to gather users' personal data without an actual consent. Personal information should be strictly secured, because easily accessible intimate information can be used for manipulating people, therefore, we have data protection policies or when personal data is exposed for third parties people should be aware and give consent for that. Indeed it is why Facebook was fined £500,000,000 by the Information Commissioner's Office in the UK: Facebook supposedly breached British Privacy Law section DPP1 (Data Privacy Principles), as the means of collection of data was done unfairly.

Conclusion
We clearly see that the data of 87 million people gathered by Cambridge Analytica was legally obtained and sold by Kogan. However, Facebook had a security hole which did not secure users' privacy.

Context
CA's job as a political consulting firm, once they had acquired the data, was to provide information to their employers in regards to the best way to target individual Facebook profiles in order to swing the elections for their employer's side.

Psychology
To do this, CA first had to match a personality profile to each of their 87 million users they had acquired the data on: they decided to use an OCEAN (The Big Five Personality Traits) model in this purpose. This model attempts to quantify the presence of 5 different traits in a person: their openness (willingness to explore, curiosity, flexibility), their conscientiousness (self-discipline, goal-orientation, planning skills), their extraversion (leadership, social confidence), their agreeableness (empathy, kindness, cooperative, generosity), and their neuroticism (irritability, insecurity, anxiety).

Using Machine Learning, they were able to match each person to their corresponding model, and use this information to manipulate people's opinions on a particular political party. For example, on the topic of creation of jobs, CA could draft a different Republican Party advertisement for two swing voters that scored differently on the OCEAN model: a person scoring high on the O part would receive an ad on how more jobs allows people to expand their knowledge and grow, whilst a person scoring high on the N part would receive a different ad detailing how more jobs allows people to receive security and emotional stability. This micro-targeting of voters is much more efficient as it appeals specifically to someone's personality, rather than a mass distribution of one ad that is less likely to appeal in large numbers.

Machine Learning/ Data Science
To convert the raw data CA had into individual OCEAN profiles for all 87 million Facebook profiles, CA used a process called data mining, which attempts to predict information based on current one. CA began by developing a training data set (the initial Facebook and personality data obtained through the survey responses), on which they could then base the target variable data set (the Facebook data they wanted to make predictions on) on. Using artificial neural networks, the CA team linked the Facebook data info of the 270 000 people that took the personality test to their personality attributes through a supervised learning method that determined the mathematical connections between these two pieces of information. This method essentially works by continually adjusting the weight of the neural connections to optimize the prediction process. Once this training data set perfected, they applied the technique to the target variable set. To obtain a near perfect predictive process, CA used an ensemble model: they used 253 different types of training sets, which resulted in individual OCEAN personality predictions at an extremely high confidence level. This is how CA figured out the personalities and extremely private information of 87 million people.

Once the psychographic information discovered, CA took advantage of Facebook's extremely lenient Advertisement Policy, which allows political parties to target extremely specific voter groups through microtargeting. To fabricate their ads, CA used another algorithm which created different advertisements for each one of the 87 million people, appealing to their OCEAN traits. Then they sent out these individual ads through Facebook.

Ethics and Politics
The scandal is a major problem in the realm of politics since it was an invasion of privacy, which was used for political means. Democracy is a political system, which enforces the freedom of its citizens. Social media and data analytics firms are being used more frequently in electoral campaigns and targeted advertisements, which in many cases is starting to undermine democracy as a concept. For example, in the case of Cambridge Analytica scandal, it was carried out using Facebook's business model. In the Trump Campaign citizens’ data was used without authorisation and for personal gains, however Cambridge Analytica deleted all their data before the 2016 election which raises questions about the actual effects on the campaign. Nevertheless, from an idealist perspective of a normative truth the use of personal data was both unethical and manipulative. Furthermore, the issue extends beyond the Trump campaign as new investigations are being carried out regarding its effects on Brexit and EU campaign. Overall, this raises questions about the need of governments to pass laws for greater regulation of online political advertisements and data use.

Law
In legal terms, the exploitation of the data in political campaigns does not have any significant legal consequences. Data driven political campaigns have existed for a long time, however the extent of micro-targeting and profiling populations has become a lot more privacy invasive. The majority of countries lack the regulation and laws to protect such personal data as well as transparency on how it is gathered and used. From the perspective of the discipline of law and the empirical truth gathered from the American Law, the use of data in Cambridge Analytica scandal was not a legal issue. There is no single data protection legislation, but rather many small sector-specific laws on state and federal levels. However, in Europe steps have been taken through the General Data Protection Regulation from May 2018, showing how data exploitation is seen more of an issue with legal consequences.

The truth about the presentation of the scandal
The scandal is presented subjectively compared to what happened in 2012. Then there was a similar case when an Obama campaign took an advantage of Facebook users data. Around 1 million of supporters signed up for an Obama campaign's Facebook app, where users gave permission to access their and their list of friends personal data. The issue was identical, as programmers could get data of users' friends without their actual consent. Thus, the campaign gathered data of around 200 millions of users, most of them were not aware of their data being given to the campaign. . However, media perspective was very different on Obama and Trump campaigns. As Cambridge Analytica caused a huge outrage and Obama's breach did not cause any scandal it was even complimented. Also, Facebook was not fined for the security holes of giving personal information without actual consent of that person, thus, it did not solve the bug of exposing personal information from one's friends list. Therefore, it seems media is being biased on different campaigns even though the privacy of people was violated in both cases.


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User:Jewel Sharif

Know the Unkhown

title: User:Jewel Sharif