Public Articles
From idea to result 2017
How could the properties of black holes be exploited?
The possible applications of black holes are explored, with a focus on interstellar travel and energy extraction. Further to this, emphasis is placed upon Oberth manoeuvres, Hawking radiation, and the creation of black holes. An equation for the maximum ΔV from a one-stage Oberth manoeuvre is derived. A conclusion is reached that although these applications may be possible in the distant future, they are likely to have been superseded by more effective, viable alternatives that do not have the risks associated with black holes.
Utilización de IA en toma de desiciones en la Empresa SICIE
Title
An Introduction to Hummingbird Charm Algorithm
Open data in organizational research
and 1 collaborator
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Test test test. Roger roger. $\BETA=MC^2 \beta $ gjghjhgjhg
Title
DETECCIÓN DE ZONAS PRODUCTIVAS E INDENTIFICACIÓN DE FACTORES SOCIOECONÓMICOS QUE IMPIDEN LA RECONVERSIÓN DE CULTIVOS EN EL MUNICIPIO DE SOMBRERETE ZACATECAS.
GvHD/Relapse data -- issues, directions & prospects
- Either impute the missing data, or just discard it.
- Options include latent Gaussian Process priors, nonparametric hierarchical shrinkage priors, dirichlet processes etc.
- We need nonparametric models for both the baseline hazard and covariate effects.
- Simplest nonparametric model for baseline hazard is the piecewise exponential model (essentially model baseline hazard as a staircase function).
- We model the log-hazard as \(\log h(t|x) = \beta_0(t) + \sum_{j = 1}^{p}x_j \beta_j(t) \varphi(\sum_{i\neq j} w_{ij} x_i)\)
- We choose the 'activation function' \(\varphi(\cdot)\) to be a logistic sigmoid in keeping with standard NN practice; i.e. \(\varphi(\cdot) = \frac{2}{1+\exp(-x)} = 2\textrm{logit}^{-1}(x)\).
- We have additivity whenever the \(w_{ij} = 0\) and proportionality whenever the \(\beta_j\) are constant.
- This suggests a model where the \(w_{ij}\) are given LN-CASS priors, and the \(\beta_j(t)\) are modelled as basis function expansions with hierarchical LN-CASS priors on the coefficients.
- \(\beta_0(t)\) should probably also be modelled nonparametrically, although its complexity is not of great concern.
- The likelihood is then \(\prod_{i=1}^nh(t_i)^{\delta_i}S(t_i) = \prod_{i=1}^nh(t_i)^{\delta_i}\exp(-H(t_i))\).
- So in order to compute the likelihood, we need to compute the survival function, or alternatively the cumulative hazard.
- Writing out the hazard, the integral we need to compute is:
\(H(t_i) = \int_{0}^{t_i} \exp\left( \beta_0(\tau))\exp( \sum_{j = 1}^{p} \varphi_j x_j \sum_{k = 1}^{m}\omega_{jk}\psi_k(\tau) \right) d\tau\)
- Ideally we would like this integral to have a closed form representation.
- Alternatively, working with the log-likelihood:
- \(\ell(\theta) = \sum_{i = 1}^{n} \log(h(t_i)^{\delta_i}) + \log(S(t_i)) = \sum_{i = 1}^{n} \log(h(t_i)^{\delta_i}) - H(t_i)\)
- The baseline hazard can be flexibly modelled using the low-rank thin plate splines of Murray et al. (2016, Bayes. Anal.)
- Given a discretisation of the time domain \(t_1,t_2,...\),
Data Visualisation Tools
The Inchanted Hallway. Ch.2
How to write a thesis proposal and analyse data
Chemistry, OZ Revision Notes
Extends 100km above Earth
Troposphere and Stratosphere most important
90% of all molecules in troposphere
\label{Atmospheric Gases}
Gas | Concentration |
Nitrogen | 78% |
Oxygen | 21% |
Argon | 1% |
Carbon Dioxide | 400ppm |
Chemistry, ES Revision Notes
Extremely high water density
Salt is 350gdm-1
Normal is 40gdm-1
400m below sea level
Huge evaporating basin
High proportion of bromide salts
Major source of minerals
Mainly group 7 ions
Halogens are group 7 elements
All have 7 electrons in outer shell
Most reactive group of non-metals
Not found naturally in elemental form
Abundance decreases down group
All occur as diatomic molecules
In compounds, there several ways by which a halogen can achieve stability:
Gaining an electron from a metal atom, forming a halide ion in an ionic compound
Sharing an electron with a non-metal atom in a covalently bonded compound
Chemistry, EL Revision Notes
Atoms can be considered to consist of 3 sub-atomic particles
Proton, Mr 1, Charge of +1
Neutron, Mr 1, Neutral
Electron, Mr $\frac{1}{2000}$, Charge of -1
Most of the atom is empty space
Atomic Number, Z
Number of protons
Lower number
Equal to charge on Nucleus
Mass Number, A
Number of protons and neutrons
Highest number
Atoms of same element with different mass numbers
Different number of neutrons
Average of relative Isotopic Masses relative to Carbon-12
Taking abundance into account
Mass Spectrometry used to find it
Measures atomic/molecular mass of different particles, and relative abundances
Ionised to cations
Separated by mass to charge ratios
In a nuclear fusion reaction, two light atomic nuclei fuse together to form a single, heavier nuclei, releasing huge amounts of energy in the process of doing so
Impossible at normal temperature and pressure
Positive nuclei repel too strongly
Possible in stars, repulsion overcome
\begin{equation*} {^{1}_{1}H}+{^{2}_{1}H}={^{3}_{2}He}+\gamma \end{equation*}
Physics, Motion and Forces, 9-12
Scalar quantities just have magnitude
Energy
Distance
Speed
Mass
Vectors have magnitude and direction
Velocity
Displacement
Acceleration
Force
Physics, Waves and WPD, 5-8
Progressive waves transfer energy without transferring any matter. There is no net movement of the medium, although each particle does oscillate around its equilibrium position.
In a transverse wave, particles oscillate at right angles to the direction of propagation.
In a longitudinal wave, particles oscillate parallel to the direction of propagation. These have compressions and rarefactions.
Mechanical waves transfer energy through a medium by the oscillation of particles, and can be transverse or longitudinal.
EM waves are not mechanical, and no not require a medium to propagate.
Linked electric and magnetic fields
Regions of space when an electric charge would experience a force
As an EM wave passes, the electric and magnetic fields oscillate
Electric field changes, inducing a magnetic filed perpendicularly
Magnetic field varies, changing electric field
Wave is self perpetuating
EM waves are always transverse
Displacement is measured from the equilibrium position, and can be positive or negative
Maximum displacement is equal to the amplitude
The amount of energy transferred by a wave is dependent on its amplitude
Wavelength sis the distance between two consecutive points with identical displacement and velocity
Two points exactly one wavelength apart are in phase - they oscillate in step with each other
Two points half a wavelength apart are in antiphase
Phase difference is dependent on the fraction of a wavelength between two points
One wavelength is represented by 360
Two points with a phase difference of 360are in phase
Two points with a phase difference of 180are in antiphase
One radian is equivalent to 180
360∘ = 2π
The time taken for one complete wave to pass a certain point is its period, T. The phase difference can then be described as the fraction of a period between two points. \begin{gather*} f=\frac{1}{T}\\ T=\frac{1}{f} \end{gather*}
The speed of a wave depends on the properties of the medium. For a mechanical wave, it depends on:
The size of the forces between oscillating particles - the elasticity of the medium
The intertia of the vibrating particles - how easy or difficult it is to accelerate each particle
Sound travels faster through solids because of the stronger forces between adjacent particles
v = fλ
Chemistry, CI Revision Notes
The low reactivity of nitrogen molecules arises from the strong triple bond between nitrogen atoms.
A2 Physics, Thermal Physics and Gravity, 3-4
Internal energy is the sum of the randomly distributed kinetic energy and the potential energy of all particles in a body.
Kinetic energy can be:
Translational
Rotational
Vibrational
The energy of a system can be increased by doing work on it or heating it.
Doing work is the energy transfer due to a force
Heating is a thermal energy transfer
A system can do work against an external force in some circumstances:
CO2 will expand rapidly if released from a high pressure container
Does work against the atmosphere, rapidly losing energy
Cools enough to solidify to dry ice
The change in the internal energy of a system is equal to the sum of the energy transferred from or to the system by heating, and the energy transferred from or to the system as a result of work being done against or by an external force.
Kinetic energy is directly related to temperature
Specific heat capacity, c, is the energy required to raise the temperature of 1kg of a material by 1K without any change of state, measured in Jkg−1K−1 \begin{equation*} Q=mc\Delta\theta \end{equation*} cwater = 4190Jkg−1K−1; a fairly large value. Hence, a large body of water will take alot of energy to heat.
Immersion heater in a block of a metal
Time and temperature change recorded
Q calculated as the energy transferred by the heater, using its current, voltage and power
Water boiled to 100∘C with object
Object placed in cool water
Temperature changes equated
If an object is dropped, and hits the ground without rebounding, all GPE will have been transferred to KE, and then to internal energy. This leads on to:
Lead shot in a tube
Length of tube and temperature of lead recorded
Tube repeatedly turned over, moving lead through length
Total GPE changes calculated, and equated to new temperature of lead
Gives a very rough estimate
Water is good for storing energy because of its high c, so it is used as a heat transfer liquid. With flow calculations, it is often used to use: \begin{gather*} \text{rate}=\frac{\Delta v}{\Delta t}=\frac{\mathrm{d} v}{\mathrm{d} t}\\ E=pt\\ \rho=\frac{m}{v}\\ \end{gather*}
When a substance changes state, work has to be done to break the intermolecular bonds. Whilst this is happening, potential energy will increase whilst kinetic energy remaincs constant. Work often has to be done against the surroundings if an object is expanding.
The energy required to change 1kg of a liquid into 1kg of a gas with no change in temperature.
The energy required to change 1kg of a liquid into 1kg of a solid with no change in temperature. For a substance of mass m, and specific latent heat of fusion l, the energy transferred is given by \begin{align*} Q=ml, \therefore l=\frac{Q}{m}. \end{align*}
Energy is supplied at a constant rate
Temperature will rise till melting point
Substance will melt at constant temperature
Temperature of liquid will rise once all melted
Liquid will boil at constant temperature
Temperature of gas will rise once all melted
Process can be recorded with a data logger
Cooling will not take place at a constant rate, as it is dependent on the temperature of the surroundings. Thermal energy will be dissipated from a substance that is cooling.