| This is a suite of algorithms implemented in delphi that demonstrate simple high-capacity fragile watermarking algorithms and how they can be implemented on loss-less format images. The algorithms implement LSB watermarking on 1st, 2nd and 3rd bits, and have been optimised to be run in parallel. Due to the high data storing capacity of the algorithms they can also be used as steganographic tools for storing hidden data. |  |
 | FastGEO is a library written in object pascal that contains a wide range of highly optimized vector based geometrical algorithms and routines for many different types of geometrical operations such as geometrical primitives and predicates, hull construction and triangulation, clipping, rotations and projections. |
| This is a fully scalable particle engine, that has the capabilities of running on clusters that run MPI and Open-MPI protocols. Currently the system simulates mass-spring systems, and visualizes the result via OpenGL 3D graphics and GLUT windowing interface.At the moment the system uses very primitive ODEs such as Euler, Extended Euler and Runge-Kutta algorithms. PES has been successfully compiled and run under both Unix and Windows systems, however under Windows MPI capabilities are not available. |  |
 | This is a simulation of the N-Mice problem, which is presented as the paths that "N" mice which are standing evenly distributed around a circle with a particular radius would take if they were all trying to reach the mouse on their right hand side. It turns out that mathematically they never reach each other, however physically they do. The paths they create are in spiral form, This application can simulate up to 20 mice, in theory it could do much more, however the visual effect of the nice spirals really begin to dissipate after about 20 mice. The simulation assumes each mouse as being an independent particle in 2D space, each particle (mouse) follows the particle on its right hand side, with an attraction force that is calculated via Newton's formula of matter to matter attraction. There are many other ways to implement this problem, a full mathematical definition of the problem and other possible solutions can be found at mathworld. |
| This is a signal generation and processing application. It is capable of producing many different types of commonly used wave forms such as square, saw-tooth and triangular wave forms, it can also take an algebraic expression representing a continuous analog signal and turn it into a useable digital wave form. The application also has a rendering system which applies different types of smoothing and noise reduction algorithms. I hope to add Fourier and Hadamard transformations to future versions of this application. (If I get the time...) |  |
 | This is my contribution to the plethora of mathematical applications on the web. I wrote this to prove to myself I could write and implement a grammar, and once I had achieved that I saw many different areas in which I could use the grammar. The application does function graphing, solution to expressions, integration in 2D and 3D and it also does simple series calculations. Its a very simple program and was only intended on demonstrating the speed and capabilities of the parser engine I had developed. A note on the parser engine is its unique ability to simplify expressions and re-order them so that they are executed as a list of sequential operations rather than a tree of prioritized expression this functionality leads to great decrease in time needed to evaluate a particular expression which makes it ideal for repetitive evaluations of expressions where only the variables change value and not the expression itself, such as graphing a function or integrating an area. |
| This is a particle simulation with a cooling algorithm implemented as the particles move within the 2D space. The particles follow a very simple parametric equation and the space that they have traveled on begins to cool down with regards to Newton's differential equation for the cooling of matter. What is interesting here is if another particle intersects the path of a particle which has just passed the space where the intersection occurs heats up more than what the second particle would have heated it up normally. This is due to the remaining heat that was already there being summed up by the new heat that is arriving. This simulation makes for some very interesting eye-candy . |  |
 | This is a simple java applet implementation of a paint-brush style program. It has the basic drawing tools such as pen, line, filled and non-filed rectangles and ellipses and color manipulation options, other than that its really boring, but a good example of how to use java's graphics libraries. |
| A simple library written in the C++ language for performing arithmetic over Galois fields. The arithmetic can be in the form of either elements or polynomials over a specified Galois field. The library is optimised to run in one of two modes, normal or LUT mode. In the LUT mode performance is increased dramatically at the cost of large consumption of memory. The library can be used in but not limited to such fields as cryptography, error correcting codes and computational analysis. |  |
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| 1905 | Ph.D. | Einstein received his doctorate from the University of Zurich for a theoretical dissertation providing a new way of calculating the size of molecules. | |
| 1905 | Brownian Motion | In 1827 the botanist Robert Brown observed under the microscope the movement or motion of plant spores floating in water and moving about randomly all the time. The explanation for this was already thought to be the random motion of molecules "hitting" the spores. But the first satisfactory theoretical treatment of the Brownian motion was made by Albert Einstein in 1905. Einstein's theory enabled significant statistical predictions about the motion of particles that are randomly distributed in a fluid. These predictions were later confirmed by experiment. | |
| 1905 | Photoelectric Effect | It was known that when light was shone on certain substances, the substances gave out electrons, but that only the number of electrons emitted, and not their energy, was increased when the strength of the light was increased. According to classical theory, when light, thought to be composed of waves, strikes substances, the energy of the liberated electrons ought to be proportional to the intensity of light. In other words, the energy emitted by the irradiated substance is changing in a discrete quantities rather than in a continuous manner. Einstein proposed that under certain circumstances light can be considered as consisting of particles, but he also hypothesized that the energy carried by any light particle, called a photon, is proportional to the frequency of the radiation. This proposal, that the energy contained within a light beam is transferred in individual units, or quanta, contradicted a hundred-year-old tradition of considering light energy a manifestation of a continuous processes or of its wave nature. Virtually no one accepted Einstein's proposal until a decade later when the American physicist Robert Andrews Millikan experimentally confirmed the theory. This Einstein's efforts helped out with the development of the quantum theory (mechanics). For this contribution, Einstein was awarded the Nobel Prize in physics for 1921 (see below). | |
| 1905 | Special Theory of Relativity | This theory provides a consistent explanation for the way radiation (light, for example) and matter interact when viewed from different inertial frames of reference, that is, an interaction viewed simultaneously by an observer at rest and an observer moving at uniform speed. Einstein based this theory on two postulates: the principle of relativity, that physical laws are the same in all inertial reference systems, and the principle of the invariance of the speed of light, that the speed of light in a vacuum is a universal constant for all observers regardless of the motion of the observer or of the source of the light. He was thus able to provide a consistent and correct description of physical events in different inertial frames of reference without making special assumptions about the nature of matter or radiation, or how they interact. Among the theory's main assertions and consequences are the propositions that the maximum velocity attainable in the universe is that of light; that objects appear to contract in the direction of motion and vice versa; that the rate of a moving clock seems to decrease as its velocity increases; the results of observers in different systems are equally correct; and that mass and energy are equivalent and interchangeable properties according to Einstein's famous formula: | |
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| 1911 | Why Is The sky Blue? | The case, "Why is the sky blue?", was finally settled by Einstein in 1911, who calculated the detailed formula for the scattering of light from molecules; and this was found to be in agreement with experiment. | |
| 1916 | General Theory of Relativity | Einstein expanded the special theory of relativity into the general theory of relativity that applies to systems in nonuniform (accelerated) motion as well as to systems in uniform motion (like in the special theory of relativity). The general theory is principally concerned with the large-scale effects of gravitation and therefore is an essential ingredient in theories of the universe as a whole, or cosmology. The theory recognizes the equivalence of gravitational and inertial mass. It asserts that material bodies produce curvatures in space-time that form a gravitational field and that the path of a body in the field is determined by this curvature. In other words, according to this theory, space becomes curved in the vicinity of matter (this is the meaning of gravity); the greater the concentration of matter, the greater the curvature and the greater the gravity. The geometry of a given region of space and the motion in the field can be predicted from the equations of the general theory. | |
| 1922 | Nobel Prize | On December 10, 1922, Einstein received the Nobel prize in physics for the year 1921, especially for his discovery of the law of the photoelectric effect (see above). | |
| 1924 | Bose-Einstein Condensate | The Bose-Einstein condensate (BEC) is a phase of matter, in the sense that solid, liquid, gas and plasma are phases of matter. In 1924 the Indian physicist Satyendra Nath Bose sent Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein generalized Bose's theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved and, in the same year, predicted that at sufficiently low temperatures the particles would become locked together, or overlap, in the lowest quantum state of the system. The result of Einstein's and Bose's efforts is the so called Bose Einstein statistics. We now know that this phenomenon, (BEC), only happens for "bosons". What does it mean to say that atoms overlap? The coins in a stack of pennies don’t overlap, and neither do the gas molecules in the air we breathe. As a gas becomes colder and colder, quantum mechanics tells us that the wavelike behavior of the atoms becomes more and more important. At the lowest temperatures, within a few hundred billionths of absolute zero (-273.15°C), the waves of the atoms in a gas can overlap and create, in effect, one super-atom. In this state, it hardly even makes sense to talk about individual atoms because they all behave as one collective object. This is much like the output of a laser, since all the light is the same wavelength (same color) and the waves are all in step and you can’t tell one light particle (a photon) from another. In recent developments, BECs are being used to create atom lasers, the equivalent of a laser made of light; in the study of superconductivity (the ability of some materials to conduct electrical current without any resistance); superfluidity (the ability of some materials to flow without resistance) and in refining measurements of time and distance. | |
| 1926 | Einstein Refrigerator | Only few know that Albert Einstein was also a practical man and invented a refrigerator. The Einstein refrigerator is an absorption refrigerator which has no moving parts and requires only a heat source to operate - it does not require electricity to operate, needing only a heat source, e.g. a small gas burner, suitable for poor countries and outdoor activities. It was jointly invented in 1926 by Albert Einstein and his former student Leó Szilárd and patented in the US on November 11, 1930 (U.S. Patent 1,781,541). | |
| 1945 | The First Atomic Bomb Was Dropped | The first atomic bomb, nicknamed "Little Boy", was dropped on Hiroshima on August 6, 1945. Although Einstein did not invent the bomb and did not participate in the Manhattan Project, his theories laid the foundation for it. The Relativity Theory showed that mass could be converted directly into energy (E=mc²), and that a minute piece of mass could release a vast amount of energy. In 1939 Einstein collaborated with several other physicists in writing a letter to President Franklin D. Roosevelt, pointing out the possibility of making an atomic bomb and the likelihood that the German government was embarking on such a course. The letter, which bore only Einstein's signature, helped lend urgency to efforts in the U.S. to build the atomic bomb, but Einstein himself played no role in the work and knew nothing about it at the time. Source:http://www.juliantrubin.com/einsteininvent.html | |
