identification may result in unreliable prediction for complex systems where our understanding of the physics of the system is insufficient. Here we used a non-parametric approach as control of walking in humans is a complex task involving many degrees of freedom. We chose to perturb the system using visual perturbations as the input since the optic flow has a profound effect on the perception of speed. We measured muscle activations and kinematics as the output of the system. In linear time invariant (LTI) systems the relationship between the input and the output could be described in the frequency domain through frequency response functions (FRFs). In these systems an input with the frequency of f1 creates an output at frequency f2. The gain function of FRFs describes the relationship between input and output amplitudes and the phase function describes the timing information (i.e. lead or lag). Periodic systems like locomotion however are not LTI. Close to their point of operation these…
John Gutmann was one of America’s most distinctive photographers. Gutmann was born in Germany where he became an artist. He later fled Germany due to the Nazi’s because he was a Jew. Gutmann moved to San Francisco and re-established himself as a photojournalist captivating the lives of Americans. He mainly took photographs of people who were imperfect like himself because of his Jewish nationality. Gutmann targeted the poor, circus folk, the gay community and the rich. Two of Gutmann’s works are…
The fundamental theorem of Calculus: The fundamental theorem of calculus asserts the interrelated properties of integration and differentiation. It says that a function when differentiated, can be brought back by integrating (anti-derivative) or a function when integrated, can be brought back by differentiation. First theorem: Let f be a function that is integrable on [a,x] for each x in [a,b], then let c be such that a≤c≤b and define a new function A as follows, A(x)=∫_c^x▒f(x)dt, if a≤x≤b.…
Fundamental Theorem of Calculus The Fundamental Theorem of Calculus evaluate an antiderivative at the upper and lower limits of integration and take the difference. This theorem is separated into two parts. The first part is called the first fundamental theorem of calculus and states that one of the antiderivatives of some function may be obtained as the integral of the function with a variable bound of integration. The second part of the theorem, called the second fundamental theorem of…
Memory and personal identity are an integral part of our lives. These characteristics and traits assist us in the way we make decisions and approach situations. Memory in relation to personal identity is a topic that has been studied by several Philosophers. The question of whether or not memory presupposes identity is a circular one, and therefore makes this question important. To study this, I looked at Parfits theory of Psychological continuity, and how it was seen as problematic due to its…
Materiality and Identity Megan Holmes’s “Miraculous Images in Renaissance Florence” examines many of the ramifications of materiality. The materiality, an image’s physical properties, has direct impacts on the expression and popularity of immagini miracolose. These sacred images are subjects of miracles throughout the late 13th to 16th centuries. Two of the most important ramifications of materiality include the accessibility of the religious images and manifestation of the miracles. In this…
1. Henri Lebesgue [8] Lebesgue is credited for many amazing discoveries to different areas of mathematics. In the area of topology, Lebesgue is known for his covering theorem which is used for finding the dimensions of a set. He is also credited for his work on the Fourier series. He was able to demonstrate that using term by term integration of a series that were Lebesgue integrable functions was always valid and therefore, gave validation to Fourier’s proof of his series. What is now…
1. What are the least, and most, amount of distinct zeroes of a 7th degree polynomial, given that at least one root is a complex number? Answer: If the equation is 7th degree then it has 7 roots. Those roots can be complex or real. Complex roots always come in pairs, so if it has one, then it has 2, the other one being the conjugate of the first one. This in other words, if one complex root is a + bi, then the other complex root is a – bi. If at least one root were complex, then we would have a…
II INTRODUCTION The purpose of this lab was to demonstrate and observe the effect a large focal spot and a small focal spot will have on the resolution of the image. Chapter 3 of Practical Radiographic Imaging states that resolution is “the ability to distinguish two adjacent details as being separate and distinct from each other” (Carrol, 2007, p. 48). This definition of resolution helps to explain what will be looking for to retrieve the data for this lab. As stated in Chapter 16 of…
A ball, and a feather dropped at the same height will hit the ground at the same time when placed in a vacuum space. This is because acceleration of motion is the same for both object, and in this experiment, we are going to calculate accelerated motion using inclined planes. In this experiment, we will see whether “distance traveled is directly proportional to the square of the time”, and “if speed of a falling object depend only on the height from which it falls”. This experiment will give us…