Detecting Complex Image Data Using Data Mining Techniques

Detecting Complex Image Data Using Data Mining Techniques Detecting complex image data using data mining techniques IMRAN KHAN ABSTRACT The Internet, computer networks and information are vital resources of current information trend and their protection has increased in importance in current existence. The intrusion detection system (IDS) plays a vital role to monitors vulnerabilities in network and generates alerts when found attacks. Today the educational network services increasing day today so that IDS becomes essential for security on internet. The Intrusion data classification and detection process is very complex process in network security. In current network security scenario various types of Intrusion attack are available some are known attack and some are unknown attack. The attack of know Intrusion detection used some well know technique such as signature based technique and rule based technique. In case of unknown Intrusion attack of attack detection is various challenging task. In current trend of Intrusion detection used some data mining technique such as classification and clustering. The process of c lassification improves the process of detection of Intrusion. In this dissertation used graph based technique for Intrusion classification and detection. This dissertation proposes efficient intrusion detection architecture which named IDS using improved ensemble techniques (IDSIET). The IDSIET contains a new improved algorithm of attribute reduction which combines rough set theory and a method of establishing multiple rough classifications and a process of identifying intrusion data. The experimental results illustrate the effectiveness of proposed architecture. Our proposed work is implemented in MATLAB .for implementation purpose write various function and script file for implementation of our proposed architecture. For the test of our hybrid method, we used DARPA KDDCUP99 dataset. This data set is basically set of network intrusion and host intrusion data. This data provided by UCI machine learning website. Proposed method compare with exiting ensemble techniques and generate the improved ensemble technique to getting better result such as detection rate, precision and recall value. Keywords- Intrusion Detection System (IDS), IDSIET, Neural Network, rough set theory, Network Security, MATALAB, KDDCUP99 Dataset. PROPOSED METHODOLOGY AND ARCHITECTURE Comparison with linear scale-space representation While not being used explicitly in SURF, we take interest here in the approximation of Gaussian kernels by box filters to understand the advantages and the limitations of the SURF approach. 3.1 Scale-space representation linear scale space The linear scale-space representation of a real valued image u : R2 7→ R defined on a continuous domain is obtained by a convolution with the Gaussian kernel uÏÆ' := GÏÆ' âˆâ€"u (1) where GÏÆ' is the centered, isotropic and separable 2-D Gaussian kernel with variance ÏÆ'2 ∀(x,y) ∈R2, GÏÆ'(x,y) := 1 2Ï€ÏÆ'2 e−x2+y2 2ÏÆ'2 = gÏÆ'(x)gÏÆ'(y) and gÏÆ'(x) = 1 √2π ·ÃÆ'e− x2 2ÏÆ'2 . (2) The variable ÏÆ' is usually referred to as the scale parameter. Discrete scale space In practice, for the processing of a numerical image u, this continuous filter is approximated using regular sampling, truncation and normalization: ∀i,j ∈J−K,KK GÏÆ'(i,j) = 1 CK GÏÆ'(i,j) , where CK = K Xi,j =−K GÏÆ'(i,j). (3) The scale variable ÏÆ' is also sampled, generally using a power law, as discussed later in  § 3.2. Discrete box space Making use of the aforementioned box filter technique, such a multi-scale representation can be (very roughly) approximated using a box filter with square domain Γ = J−Î ³,ÃŽ ³KÃâ€"J−Î ³,ÃŽ ³K uÃŽ ³ := 1 (2ÃŽ ³ + 1)2 BΓ âˆâ€"u. (4) The question now is how to set the parameter ÃŽ ³ ∈ N to get the best approximation of Gaussian zoom-out. Second moment comparison One may for instance choose to match the second order moment ÏÆ'2 of the 1D Gaussian gÏÆ' and the variance of the corresponding box filter, as suggested by [7]. This leads to the relation ÏÆ'2 ÃŽ ³ = ÃŽ ³ Xi =−Î ³ i2 2ÃŽ ³ + 1 = (2ÃŽ ³ + 1)2 −1 12 = ÃŽ ³(ÃŽ ³ + 1) 3 , (5) where ÏÆ'2 ÃŽ ³ is the variance of the centered 1D box filter with width 2ÃŽ ³ + 1. Thus, for large values of filter size (ÃŽ ³ 1), we get approximately ÏÆ'ÃŽ ³ ≈ ÃŽ ³ √3 ≈ 0.58ÃŽ ³. Since ÃŽ ³ ∈ N takes integer values, ÏÆ'ÃŽ ³and ÏÆ' cannot match exactly in general. Moreover, due to the anisotropy of the box filter in 2D, it is impossible to match the covariance matrices. SURF scale parameter analogy Note that box filters are only used to approximate first and second order of Gaussian derivatives in SURF algorithm, and not to approximate Gaussian filtering like in [7]. However, when considering the approximation of second order Gaussian derivative Dxx GÏÆ'(x,y) = Dxx gÏÆ'(x)Ãâ€"gÏÆ'(y) = 1 ÏÆ'22 ÏÆ'2 −1gÏÆ'(x)Ãâ€"gÏÆ'(y) By these condition order box filter operator DLxx, we can see that the1D Gaussian filter gÏÆ'(y) is approximated by 1D box filter with parameter ÃŽ ³ = L−1 2. The authors of SURF claim that the corresponding Gaussian scale is ÏÆ' = 1.2 3 L ≈ 0.8ÃŽ ³for ÃŽ ³ 1, which is close but dià ¯Ã‚ ¬Ã¢â€š ¬erent to the value given by Formula (5): ÏÆ'ÃŽ ³ ≈ 0.58ÃŽ ³. Other analogies could have been made for scale variables, for instance by considering zero crossing of second order derivative of Gaussians, second moment of Gaussian derivatives, mean-square error minimization, but each one provides dià ¯Ã‚ ¬Ã¢â€š ¬erent relations. In conclusion, defining a relation between the box parameters (L and `(L)) and the Gaussian scale variable ÏÆ' seems quite arbitrary. Visual comparison Figure 8 illustrates the dià ¯Ã‚ ¬Ã¢â€š ¬erence between the linear scale-space representation obtained by Gaussian filtering and the box-space, that is its approximation by box-filters when using relation (5). While being roughly similar, the approximated scale-space exhibits some strong vertical and horizontal artifacts due to the anisotropy and the high frequencies of the box kernels. Again, while it is not being used explicitly in SURF, these artifacts may explain some of the spurious detections of the SURF approach that will be exhibited later on. 3.2 Box-space sampling Because of the dentition of first and second order box filters, the size parameter L cannot be chosen arbitrarily. The sampling values and the corresponding variables used to mimic the linear scale space analysis. The following paragraphs give more detailed explanations. Octave decomposition Alike most multi-scale decomposition approaches (see e.g. [13, 15]), the box-space discretization in SURF relies on dyadic sampling of the scale parameter L. The box length representation is therefore divided into octaves (similarly to SIFT [14, 13]), which are indexed by parameter o ∈{1,2,3,4}, where a new octave is created for every doubling of the kernel size. Note that, in order to save computation time, the filtered image is generally sub-sampled of factor two at every octave, as done for instance by SIFT [14]. As pointed out by the author of SURF [2], sub-sampling is not necessary with the use of box filters, since the computation time complexity does not depends on scale. However, while not being explicitly stated in the original paper [2], but as done in most implementations we have reviewed (for instance, this approximation is used in [3] but not in [5]), we choose to use sub-sampling to speed up the algorithm. More precisely, instead of evaluating the multi-scale operators at each pixel, we use a sampling†step† which depends on the octave level (this sampling is detailed in the next sections). Note that this strategy is consistent with the fact that the number of features is decreasing with respect to scale. Level sampling Each octave is also divided in several levels (indexed here by the parameter i ∈ {1,2,3,4}). In the usual discrete scale space analysis, these levels correspond directly to the desired sampling of the scale variable ÏÆ', which parametrizes the discretized Gaussian kernels GÏÆ' (see definition in Eq. (16)). In SURF, the relation between scale L, octave o and level i variables is L := 2o i + 1 . (6) These values are summarized in Table 2. Note that because of the non-maxima suppression involved in the feature selection, only intermediate levels are actually used to define interest points and local descriptors (i ∈{2,3}). On comparison of the box space and the linear scale space. (Top) Convolution with squared and centered box filters with radii ÃŽ ³ = 5 and ÃŽ ³ = 20 (respectively from left to right). (Middle) Corresponding Gaussian filters with respective scales ÏÆ'5 ≈ 3.16 and ÏÆ'20 ≈ 11.83, according to formula (5). Dià ¯Ã‚ ¬Ã¢â€š ¬erence between Gaussian and Box filters (using a linear transform for visualization). We can see here that the box space is a rough approximation of the Gaussian scale space, that exhibits some artifacts due to the anisotropy and the high frequencies of the box kernels. Scale analogy with linear scale space As discussed before in Section 3.1, we can define a scale analysis variable by analogy with the linear scale space decomposition. In [2], the scale parameter ÏÆ'(L) associated with octave o and level i is obtained by the following relation ÏÆ'(L) := 1.2 3(2o Ãâ€"i + 1) = 0.4L. (7) Since the relation between the scale ÏÆ'(L) of an interest point is linear in the size parameter L of box filters operators, we shall speak indià ¯Ã‚ ¬Ã¢â€š ¬erently of the former or the latter to indicate the scale. Remark A finer scale-space representation could be obtained (i.e. with sub-pixel values of L) using a bilinear interpolation of the image, as suggested in [2]. This is not performed in the proposed implementation. 3.3 Comparison with Gaussian derivative operators 3.3.1 First order operators The first order box filters DL x and DL y defined at scale L are approximations of the first derivatives of Gaussian kernel at the corresponding scale ÏÆ'(L) (see Eq. (7)), respectively corresponding to Dx GÏÆ'(x,y) = − x ÏÆ'2(L) GÏÆ'(x,y) and Dy GÏÆ'(x,y). These operators are used for local feature description, in detailed we compares the first order box filter impulse response with the discretized Gaussian derivative kernel. DL x ÃŽ ´ (Eq. (6)) Dx GÏÆ'(L) Illustration of the discrete derivative operator DL x (defined in Section 2.3.1) and discretization of the Gaussian derivative kernel Dx GÏÆ'(L) when using scale relation ÏÆ'(L) from Eq. (7). 3.3.2 The second order operators Second order dià ¯Ã‚ ¬Ã¢â€š ¬erential operators are computed in the scale-space for the detection of interest points [9, 10]. In the linear scale-space representation, this boils down to the convolution with second derivatives of Gaussian kernels Dxx GÏÆ'(x,y) = 1 ÏÆ'22 ÏÆ'2 −1GÏÆ'(x,y), Dyy GÏÆ', and Dxy GÏÆ'(x,y) = xy ÏÆ'4 GÏÆ'(x,y). (8) In the SURF approach, the convolution with theses kernels are approximated by second order box filters, previously introduced respectively as DL xx, DL yy , and DL xy . A visual comparison between second order derivatives of Gaussian and their analogous with box filters. These operators are required for local feature selection step in section 4. 3.3.3 Scale Normalization According to [12], dià ¯Ã‚ ¬Ã¢â€š ¬erential operators have to be normalized when applied in linear scale space in order to achieve scale invariance detection of local features. More precisely, as it can be seen from Equation (21), the amplitude of the continuous second order Gaussian derivative filters decreases with scale variable ÏÆ' by a factor 1 ÏÆ'2. To balance this eà ¯Ã‚ ¬Ã¢â€š ¬ect, second order operators are usually normalized by ÏÆ'2, so that we get for instance (a) (b) (c) (d) On comparison of second order box filters and second order derivative of Gaussian kernels. (a) operator DL yy; (b) discretizedsecondorderGaussianderivative D2 y GÏÆ'; (c) operator DL xy; (d) discretized second order Gaussian derivative Dxy GÏÆ'; For comparison purpose, we used again the scale relation ÏÆ'(L) from Eq. (7). †¢ the scale-normalized determinant of Hessian operator: DoHÏÆ' (u) :=uÏÆ' −(Dxy uÏÆ')2; (9) †¢ the scale-normalized Laplacian operator: à ¢Ã‹â€ Ã¢â‚¬  ÃÆ' u := ÏÆ'2à ¢Ã‹â€ Ã¢â‚¬   uÏÆ' = ÏÆ'2à ¢Ã‹â€ Ã¢â‚¬   GÏÆ' âˆâ€"u = ÏÆ'2(Dxx + Dyy)GÏÆ' âˆâ€"u = ÏÆ'2(Dxx uÏÆ' + Dyy uÏÆ'), (10) where à ¢Ã‹â€ Ã¢â‚¬  ÃÆ' GÏÆ'(x,y) = ÏÆ'2(Dxx +Dyy)à ¢- ¦GÏÆ'(x,y) =x2+y2 ÏÆ'2 −1GÏÆ'(x,y) is the multi-scale Laplacian of Gaussian. Observe that this operator can be obtained from the Trace of the scalenormalized Hessian matrix. These two operators are widely used in computer vision for feature detection. They are also approximatedinSURF,asdetailedinthenextsections. Asaconsequence, suchascale-normalization is also required with box filters to achieve similar invariance in SURF. To do so, the authors proposed that amplitude of operators DL xx , DL yy , and DL xy should be reweighted so that the l2 norms of normalized operators become constant over scales. The quadratic l2 norm of operators are estimated from the squared Frobenius norm of impulse responses kDL xxk2 2 := kDL xx ÃŽ ´k2 F = kDL yy ÃŽ ´k2 F =1 + 1 + (−1)2L(2L−1) = 6L(2L−1), so that kDL xxk2 2 ≈ 12L2 when L=1, and kDL xyk2 2 := kDL xy ÃŽ ´k2 F =1 + 1 + (−1)2 + (−1)2LÃâ€"L = 4L2. This means that box filters responses should be simply divided by the scale parameter L to achieve scale invariance detection. Interest point detection: In the previous sections, second order operators based on box filters have been introduced. These operators are multi-scale and may be normalized to yield scale invariant response. We will now take interest in their use for multi-scale local feature detection. Once the integral image has been computed, three consecutive steps are performed which are detailed in the following sections: 1. Feature filtering based on a combination of second order box filters; 2. Feature selection is combining non-maxima suppression and thresholding; 3. Scale-space location refinement ( § 4.3) using second order interpolation. This interest point detection task is summarized in Algorithm 1. Step-1 Filtering Image by Integration: Integral image and box filters Let u be the processed digital image defined over the pixel grid à ¢Ã¢â‚¬Å¾Ã‚ ¦ = [0,N-1]Ãâ€"[0.M-1], where M and N are positive integers. In the following, we only consider quantized gray valued images (taking values in the range [0; 255]), which is the simplest way to achieve robustness to color modifications, such as a white balance correction. The integral image of I for(x,y) à Ã¢â‚¬Å¾ à ¢Ã¢â‚¬Å¾Ã‚ ¦ is Flow Diagram: Figure3.1: showing the flow chart of the process for object detection Step 2: Point Detection: During the detection step, the local maxima in the box-space of the determinant of Hessian† operator are used to select interest point candidates. These candidates are then validated if the response is above a given threshold. Both the scale and location of these candidates are then refined using quadratic fitting. Typically, a few hundred interest points are detected in a megapixel image. input: image u, integral image U, octave o, level i output: DoHL(u) function Determinant_of_Hessian (U; o; i) L 2oi + 1 (Scale variable, Eq. (19)) for x := 0 to M à ´Ã¢â€š ¬Ã¢â€š ¬Ã¢â€š ¬ 1, step 2oà ´Ã¢â€š ¬Ã¢â€š ¬Ã¢â€š ¬1 do (Loop on columns) for y := 0 to N à ´Ã¢â€š ¬Ã¢â€š ¬Ã¢â€š ¬ 1, step 2oà ´Ã¢â€š ¬Ã¢â€š ¬Ã¢â€š ¬1 do (Loop on rows) DoHL(u)(x; y) Formula (24) (with (4), (10) and (11)) end for end for return DoHL(u) end function Algo input: image u output: listKeyPoints (Initialization) U IntegralImage(u) (Eq. (1)) (Step 1: filtering of features) for L 2 f3; 5; 7; 9; 13; 17; 25; 33; 49; 65g do (scale sampling) DoHL(u) Determinant_of_Hessian (U; L) end for (Step 2: selection and refinement of keypoints) for o := 1 to 4 do (octave sampling) for i := 2 to 3 do (levels sampling for maxima location) L -> 2o i + 1 listKeyPoints -> listKeyPoints + KeyPoints(o; i;DoHL(u)) end for end for return listKeyPoints So that the scale normalization factor C(L) for second order box filters should be proportional to 1 L2 However, the previous normalization is only true when L1. Indeed, while we have kDxxGÏÆ'k2 2 kDxyGÏÆ'k2 2 = 3 at any scale ÏÆ', this is not exactly true with box filters, where: kDL xxk2 2 kDL xyk2 2 = 3(2L−1) 2L ≈ 3 when L1. To account for this dià ¯Ã‚ ¬Ã¢â€š ¬erence in normalization for small scales, while keeping the same (fast) un-normalized box filters, the author of SURF introduced in Formula (24) a weight factor: w(L) = kDL xxk2 kDL xyk2  ·kDxyGÏÆ'k2 kDxxGÏÆ'k2 =r2L−1 2L . (26) The numerical values of this parameter are listed in the last column of Table 2. As noticed by the authors of SURF, the variable w(L) does not vary so much across scales. This is the resaon why the weighting parameter w in Eq. (10) is fixed to w(3) = 0.9129. Feature selection: In our methodology, interest points are defined as local maxima of the aforementioned DoHL operator applied to the image u. These maxima are detected by considering a 3 Ãâ€" 3 Ãâ€" 3 neighborhood, andperforminganexhaustivecomparisonofeveryvoxelofthediscretebox-spacewith its 26 nearest-neighbors. The corresponding feature selection procedure is described in Algorithm 3. Algorithm 3 Selection of features input: o,i,DoHL(u) (Determinant of Hessian response at octave o and level i) output: listKeyPoints (List of keypoints in box space with sub-pixel coordinates (x,y,L)) function KeyPoints (o,i,DoHL(u)) L ↠ 2oi + 1 for x := 0 to M −1, step 2o−1 do (Loop on columns) for y = 0 to N −1, step 2o−1 do (Loop on rows) if DoHL(u)(x,y) > tH then (Thresholding) if isMaximum (DoHL(u),x,y) then (Non-maximum suppression) if isRefined (DoHL(u),x,y,L) then addListKeyPoints (x,y,L) end if end if end if end for end for return listKeyPoints end function Remark A faster method has been proposed in [21] to find the local maxima without exhaustive search, which has been not implemented for the demo. Thresholding: Using four octaves and two levels for analysis, eight dià ¯Ã‚ ¬Ã¢â€š ¬erent scales are therefore analyzed (see Table 2 in Section 3.2). In order to obtain a compact representation of the image -and also to cope with noise perturbation- the algorithm selects the most salient features from this set of local maxima. This is achieved by using a threshold tH on the response of the DoHL operator DoHL(u)(x,y) > tH . (27) Note that, since the operator is scale-normalized, the threshold is constant. In the demo, this threshold has been set to 10 assuming that the input image u takes values in the intervalJ0,255K. This setting enables us to have a performance similar to the original SURF algorithm [2, 1] (see Section 6 for more details). Figure 13 shows the set of interest points detected as local box-space maxima of the DoHL operator, and selected after thresholding. For visualization purpose, the radii of the circles is set as 2.5 times the box scale L of the corresponding interest points.

The Life And Work Of Euclid

The Life And Work Of Euclid While studying geometry with Euclid a youth inquired after having learned the first proposition, What do I get by learning these things? Euclid called a slave to them and said, Give him threepence, since he must make a gain out of what he learns. [8] Euclid, a Greek mathematician and teacher, changed the course of the world. Euclids work not only affected the work of other prominent scientists to come after him, but also the lives of ordinary people, which contributed to the rise of modern science in western civilization. What is perplexing is that despite him changing the course of world, we know very little about him. Unlike some other well-known historical figures, Euclids influence did not spread simply by fame. Historians dont even know his exact date of birth. To this day, we do not know which continent he was born on, much less the city. Of the little we do know about Euclid, we know that he taught in Alexandria around 300 B.C. [9], and that he wrote, amongst approximately 10 other books, arguably one of the greatest mathematical textbooks in history, The Elements. The Elements is a geometry textbook that unified all of the previously known principles of geometry. It was unique in that it was constructive in its delivery of its principles. Basically, it explained mathematic principles from the ground up and added onto what was already established. Imagine trying to study science if one concept didnt flow into the next and everything was garbled and out of order. The Elements solved this problem through careful organization and logical delivery of its principles. The Elements wasnt a revolutionary observation or a new and exciting revelation, but rather a book of brilliant deductive reasoning, analysis, and organization. The Elements was explained so well that every Geometry textbook preceding it was practically discarded, and because of this the term Euclidean wasnt necessary or used for over two thousand years because there was no other known form of geometry[17]. Concerning Euclids deductive reasoning and analysis, his axiomatic systems are most prominent. His axiomatic systems are considered to be constructive. [18] This means that he never reached any conclusions or spoke about concepts that he did not yet explain to the reader. He arranged the geometric theorems so that they flowed logically from one to the next. [9] For example, he started with the simplest of concepts such as describing a geometric point and worked his way into derived propositions. [16] More specifically he took a small number of axioms (self-evident logical truths) and deduced many other theorems from them. He even filled in the blanks whenever it was necessary by filling in the missing steps absent from others processes, and even by developing his own proofs [9]. For example, Euclid proved that it is impossible to find the largest prime number. He proved that if you were to take the largest known prime number and 1 to the product of all the prime numbers leading up to it and including it then you will get another prime number. This is accepted as being one of the classics proofs in mathematics because of how clear and concise it is. [5] Euclid put a lot of effort into making it possible for common people to understand geometry rather than just professional mathematicians. How the natural flow and style of explanation of The Elements affected the world is self-evident. Since it is easier to understand scientific concepts when they are communicated clearly and concisely and delivered in a logical order, Euclids book made it much easier for the people to acquire a complete understanding of geometry. As newborns in this world often one of the first things we get to play with are blocks of different geometric shapes. This helps us to develop our minds both visually and mathematically. Euclidean shapes are quite literally everywhere in our society. Unlike Calculus where there is usually a fixed method for solving a given problem, when it comes to geometry, using Euclidean axioms allows people to solve any one problem in several different ways. It also inspires development of problem solving skills. One of the ways Euclidean geometry has been applied and influences our day to day lives is through construction and architecture. For example, if somebody wants to construct a wooden table. If they wanted to figure out if it was square or not they could measure each corner of the table to see if it was at a 90 angle. With Euclidean Geometry, however, they would need only to measure two of the corners. The properties of right triangles within The Elements tells us that if two corners are square then the whole shape is square. This is probably very obvious to a person of our modern day, but it was not at the tme. Unless you are a mathematician you may not even know who such properties can be attributed to and just consider them common knowledge. Another, less obvious way they could have done this is to have measured the distance between two diagonal corners of the table. If the two distances are the same then the table must be a square. The latter method I have described is a common wa y for construction workers or home-improvement workers to check their work. There are countless examples of this that common people can utilize in their everyday lives with the principles of Euclidean Geometry. Euclids influence doesnt end there. Examples of Euclidean geometry can be found in modern day computer graphics. It is used in mesh generation. A mesh is basically a combination of geometric polygons or polyhedrons that create the illusion of a curve. Although the Euclidean Geometry may be widespread within western civilization, in some third world countries there are houses are constructed as lop-sided indeterminate shapes. This is a real-life example of what our architecture would have looked like without Euclids influence.[4] It is fair to say that the study of Euclids book was one of the main contributing factors to the Scientific Revolution and subsequently the rise of science in Europe rather than in Asia. The Elements made the concept of one principle being built upon another glaringly obvious and, over the course of time, it became considered common knowledge in western civilization. Of course, scientists such as Newton, Copernicus, Kepler, and Galileo played significant roles as well [9], but as Sir Isaac Newton said If I have seen further it is by standing on the shoulders of giants [21]. Euclids book provided for us, not just a shoulder, but an entire foundation built of giants shoulders that would have otherwise been scattered and disorganized. This solid base of knowledge allowed western civilization to reach new heights. For example, when it came to Isaac Newton and his book, Principles Of Natural Philosophy, many of his proofs were set in a geometric form similar to those found in The Elements . [12] As it is with any great work of science, The Elements allows others to build upon it or advance into new areas of discovery. Some men, such as Girolamo Saccehri, have tried to disprove or find flaws in Euclids axioms. Saccehri was an Italian mathematician who in 1733 almost discovered a form of non-Euclidean geometry. He studied for years to find a flaw in Euclids work. He was supposedly on the verge of a breakthrough but gave up before his work came to fruition. It wasnt until about a hundred years later in 1899 that a German mathematician by the name of David Hilbert found another set of geometric axioms that differed from Euclid. [13] Non-Euclidean geometry allows us to describe physical space in new ways. Following Hilbert came another German, by the name of Albert Einstein. Einstein recalls receiving two gifts that had particular influence on him as a child, one a magnetic compass, and the other Euclids The Elements. He referred to The Elements as the holy little geometry book. [3] Another example of a great scientist that was influenced by Euclid is Galileo Galilei. In his old age Galileo told his biographers that while attending the University of Pisa he would nose-drop in on lectures being given by Ostilio Ricci to the court pages on Euclid. These lectures were only available to members of the court so he would try to stay quiet whenever he attended them. His interest in Euclid got the better of him after a while and he approached Ricci to ask him questions on Euclid. Ricci noticed Galileos talent for math and eventually became his teacher. Although Galileo was supposed to be going to college to study medicine, (Galen) he secretly studied mathematics (Euclid) instead. Galileo later used Euclids Book Five, Definition Five, to show how bodies of certain arbitrary weight have weights directly proportional to their volumes. [2] This is one of the best examples how influential Euclids work was to anybody with a mind for mathematics and how he changed the course o f history by capturing the interest of a man such as Galileo. Euclids work also influenced philosophers such as Benedict Spinoza. Benedict Spinoza was a prominent philosopher of 17th century. He wrote the ambitious philosophicical book Ethics where he attempts to provide us with a coherent view of the universe and our place in it. To explain such concepts he used Euclids style of delivery complete with axioms and propositions. Speaking of the system within his book and the style in which he chose to present it in Spinoza said that it was demonstrated in geometrical order. [23] Usually philosophical books were written differently, such as Rene Descartes Meditations that was written like a diary. When it comes to mathematicians I think every mathematician alive since the time of Euclid had to have been influenced by his work in some form or another, but, of some of the most prominent mathematicians, Euclid specifically influenced the work of Bertrand Rusell, Alred North Whitehead, Blaise Pascal, Marin Mersenne , and Adrien-Marie Legendre. Interestingly enough Bertrand Russell, an English 20th century mathematician and logician, used Euclids work to push mathematics into the next level by explaining to people in his book An Essay On The Foundations Of Geometry [11] how Euclidean Geometry was being replaced by more advanced forms of geometry. Both Russell and Whitehead were co-authored the epoch Principia Mathmatica in which they referenced Euclid a number of times as evidence in their work. Pascal, a 17th century French mathematician, received a copy of Euclids Elements as a boy and before the age of 13 he had proven the 32nd proposition of Euclid and discovered a flaw in Rene Descartes geometry [25]. Mersenne, also a 17th century French mathematician, used Euclids proof on prime numbers to develop his own ways or forms as they are called, making it even easier to find large prime numbers. Prime numbers are important to modern day society because they are used in cryptographic software security systems. Basically, large prime numbers can be implemented into coding schemes that are difficult to break. Legendre, a 19th century French mathematician, wrote his most famous book Elà ©ments de Gà ©omà ©trie based entirely off of The Elements. In it he sought to simplify Euclids propositions even further. Elà ©ments de Gà ©omà ©trie was used in elementary school classrooms for over a 100 years. [13][24][6] Euclid influenced politicians such as Abraham Lincoln. Lincoln, as a lawyer traveling on horseback would carry a copy of Euclids Elements in his saddlebag. According to his law partner, at night Lincoln would lay on the floor for hours at night studying Euclids Elements by lamplight. [5] He was a great admirer of the logical delivery of information that The Elements contained and used Euclids systematic approach in many of his speeches. It is no coincidence that the phrase dedicated to the proposition bears such striking similarities to Euclids axioms. Lincoln, speaking of his study of Euclid, said, In the course of my law reading I constantly came upon the word demonstrate. I thought at first that I understood its meaning, but soon became satisfied that I did not. I said to myself, What do I do when I demonstrate more than when I reason or prove? How does demonstration differ from any other proof? I consulted Websters Dictionary. They told of certain proof, proof beyond the possibility of doubt; but I could form no idea of what sort of proof that was. I thought a great many things were proved beyond the possibility of doubt, without recourse to any such extraordinary process of reasoning as I understood demonstration to be. I consulted all the dictionaries and books of reference I could find, but with no better results. You might as well have defined blue to a blind man. At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my fathers house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies. [1][5] The astronomers Johannes Kepler and Nicolaus Copernicus were also influenced by Euclids work. When it came to Keplers approach to astronomy he depended almost entirely on Euclid. Kepler, much like Galileo studied Euclid while attending a university (Tà ¼bingen). Kepler was a devout Lutheran and considered Euclid geometry to be the only geometry that could be applied to the heavens and refused to use any other form of geometry because he considered such forms to be heretical. He developed a proof of concerning planetary motion based entirely off propositions found in The Elements [22]. Copernicus used Euclids work on optics as evidence in his book On The Revolutions Of The Celestial Spheres which was considered the starting point of modern astronomy and the defining epiphany that began the scientific revolution. All these great men of science were not able to use Euclids work as evidence simply because he was well known or famous for doing something exciting and spectacular. It was the intellectual quality of Euclids work that made the difference. We dont know enough about Euclid to either love him nor hate him and unless you happen to be a mathematician, his work is undoubtedly not awe inspiring. Nevertheless, Euclid still managed to affect some of the most important figures of the Scientific Revolution by setting the foundations necessary for the development of modern science. Sources: 1. The Lincoln year book, written by Abraham Lincoln, 1809-1865, passage 32 2. Galileo at Work: His Scientific Biography, written by Stillman Drake, pages 2-3 3. Einstein as a Student, written by Dudley Herschbach, page 3 4. How To Use Euclidean Geometry, written by Henri Bauholz, http://www.ehow.com/how_4461018_use-euclidean-geometry.html 5. Euclid, Math Open Reference, http://www.mathopenref.com/euclid.html 6. Great Scientists: from Euclid to Stephen Hawking, written by John Farndon, 2007 7. A Chronicle of Mathematical People, written by Robert A. Nowlan 8. Geometry Quotes, History of Mathematics Archive, http://www-history.mcs.st-and.ac.uk/~john/MT4521/Lectures/Q1.html 9. The 100: A Ranking Of The Most Influential Persons In History, written by Michael H. Hart, 2000 10. Encyclopedia of World Biography. Euclid 11. The Teaching of Euclid, written by Bertrand Russell, http://www-history.mcs.st-and.ac.uk/Extras/Russell_Euclid.html 12. Isaac Newton, Wikipedia, http://en.wikipedia.org/wiki/Isaac_Newton 13. Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, written by Luetta Reimer Wilbert Reimer, 1990 14. The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, Prehistory to A.D. 1450, written by David C. Lindberg, 2008 15. Mathematics: From the Birth of Numbers, written by Jan Gulberg, 1996 16. Euclids Elements, written by D.E. Joyce, http://aleph0.clarku.edu/~djoyce/java/elements/elements.html 17. Euclid, Wikipedia, http://en.wikipedia.org/wiki/Euclid 18. Axiomatic Systems for Geometry, written by George Francis, 2002 19. The Thirteen Books of the Elements, written by Euclid / Thomas L. Heath 20. Mathmatical Thought, University of Arkansas, http://math2033.uark.edu/wiki/index.php/EuclidHYPERLINK http://math2033.uark.edu/wiki/index.php/Euclids_ElementsHYPERLINK http://math2033.uark.edu/wiki/index.php/Euclids_Elementss_Elements 21. Newton: Understanding the Cosmos, New Horizons, Letter from Isaac Newton to Robert Hooke, 1676, as transcribed by Jean-Pierre Maury, 1992 22. KEPLERS PLANETARY LAWS, written by A. E. Davis, http://www-history.mcs.st-and.ac.uk/HistTopics/Keplers_laws.html 23. Spinoza and Jefferson, The Teaching Community, http://teachingcompany.12.forumer.com/viewtopic.php?t=2147 24. A History of Mathematics, written by Carl B. Boyer, 1985 25. The History of Computing Project, Blaise Pascal, http://www.thocp.net/biographies/pascal_blaise.html

Domestic Violence Amd Women :: Violence Against Women Essays

Domestic violence is a terrible problem that we all must face, not only the people who are victims. We need to stop this before the problem develops into anything bigger than it already is. The battered woman, it has been said, lives in a world of terror and her home is her prison (Berger, 1990, pg. 35). For many hundreds of years people weren't worried about domestic violence. In fact, a popular family journal, the Journal of Marriage and Family, did not include a single article on domestic from 1932 to 1969 (Berger, 1990, pg. 27). Suddenly, more women came out and told of the abuse they had once suffered. Researchers report that 1.8-2.9 million women are battered yearly. Not only do the victims suffer physical pain, but they also have to deal with emotional and psychological pain. The victim may have to face reoccurring nightmares, and may never want to trust another man. Much too frequently, the victim blames themselves. The typical response of an abused/battered woman is, "I provoked him . . . I was being a bad wife, mother, and housekeeper," (Peled, 1995, pg. 141). The very sad part about the violence, beside the physical and emotional stress, is that most likely they know the offender or abuser. So, why, why would a person who is loved, want to abuse their spouse or girlfriend? One of the key responses . . . Jealousy. The husband may become very suspicious, afraid of losing his wife. The abuser sees his wife or girlfriend as a possession. The only way, they think, to relieve this built up anger is aggression. To improve their self-esteem, they abuse the victim physically, emotionally, and sometimes, sexually. Another key factor in wife abuse is alcohol. When the man is stressed, he turns to alcohol to relieve it. Little does he know, that the alcohol makes him more irritable. "He started really drinking excessively and that is when the abuse started. He had been drinking . . . I sat down to read the paper and he wanted his supper . . . he kicked the cat to the ceiling . . . he started slapping my face with both hands," (Berger, 1990, pg. 42). Research shows that men who abuse their wives, often saw their own mother abused. Do to witnessing this, the children of battered families usually grow up to have low self-esteem and believe that hitting is right.

HNC Managing People Essay -- GCSE HNC Managing People Assignment

HNC Managing People Assignment Responsible for: Â · Recruitment, selection, training, and development of all staff. Â · The Management and Leadership of a team of 5 people. Â · The overall training budget of the Company. Â · Company Legislation appertaining to HR. Management and Employee Welfare. Duties include: Â · To produce accurate conditions of service contracts and process instructions for all aspects of salary payments for employee starters and leavers. Â · To issue accurate pay instructions to organisational pay services, ensuring information is received and processed, chasing queries as and when necessary. Â · To liaise with pay services on discrepancies, etc and inform members of staff of responses, ensuring all issues are dealt with in a timely manner. Â · To distribute pay slips to all employees on payroll. Â · To monitor and accurately maintain sick leave records for all staff, liaising with managers and the welfare service where appropriate. Â · To update and maintain the computerised Personnel system, ensuring data is accurate at all times. Â · To administer the recruitment process in an efficient and effective manner ensuring timescales and procedures are adhered to. Â · To act as an usher and provide assistance at interviews, selection tests and other assessments when required. Â · To act as HR representative on recruitment boards, as and when necessary. Â · To provide ‘first day’ induction to new employees in line with corporate policy. Â · To administer the flexible working scheme for staff. Â · To request references, health clearance, and security clearance for potential employees. Â · To fulfil the requirements of equal opportunities policy and procedures and implement equality principles and practices within the context of the job. The successful candidate must be able to prioritise work and meet deadlines, communicate effectively and have attention to detail. It essential that the successful candidate has intermediate to advanced MS Office skills and, ideally you will have a personnel qualification or be willing to study for the Certificate in Personnel Practice. Task 2 Interviews Interviews are a good way of the interviewer and interviewee of getting to known more information about the job and suitability of each other for the job, it is seen to be a... ... * Define the priority of each job responsibility and goal. * Define performance standards for key components of the job. * Hold discussions and provide feedback about employee performance, * Maintain a record of performance. * Provide the opportunity for broader feedback. Use a 360-degree performance feedback system that incorporates feedback from the employee's peers, customers, and people who may report to them * Develop and administer a coaching and improvement plan if the employee is not meeting expectations. Task 7 - Delegation Before delegating your workload you must identify a suitable person for the task. Prepare the person. Explain the task clearly. Make sure that you are understood. Make sure the person has the necessary authority to do the job properly. State reasons as to why the job needs delegating and when it needs to be done by. After the work has been delegated you should keep in touch with the person for support and monitoring progress. . Accept alternative approaches if they are necessary and Praise / Acknowledge a job well done. You should give the individual feedback on how they are doing and deal with any issues that do occur.

The Ice Storm Book Vs. Movie C Essay -- essays research papers

There are many ways to tell a story. Back before there were books there as the actual storyteller who could speak out a story. There is also acting where people physically perform a story. Books are another storytelling device that is more permanent, the words are kept and they can be reviewed again and again. Now there are movies, which provide story telling with more an emphasis on visual effects. The question is which way is the best to present a certain type of story. The Ice Storm by Rick Moody was in such a position that one could actually look at both the modern movie and the book version.   Ã‚  Ã‚  Ã‚  Ã‚  The story is a realistic story about the Hoods and the Willams. Both of these families were affluent families that lived in New Canaan. The book centers around Wendy and the events that take place during the their thanksgiving in the 70s. The story is pretty simple and is about family strife. Wendy is a typical adolescent exploring her sexuality. At the same time her parents, Ben and Elena are having marital differences. Ben is cheating on his wife with Janey, the wife of his close friend Jim. The irony comes up with Wendy who is has sexual relations with Janey and Jim's son Mikey and his younger brother Sandy. Wendy's older brother Paul who goes to boarding school returns home and is sexual inexperienced he desires to be with a girl named Libbets. The story centers around a key party that both the Hood's and Willams' attend. The highlight of the key party is where people place their keys into a jar and people pick up the keys of different people to have sex with the owner of the keys. At this party Ben expects to have sex with Janey, but instead Janey blows him off and has sex with someone else. This night Elena also finds out about the affair and has an affair with Jim, Janey's wife. Now while both of the parents are away Mikey wants to see Wendy, but instead Wendy fools around with Sandy. Mikey ends up wandering during the ice storm to get electrocuted by a live wire. At the same time Paul is with Libbets drinking and taking drugs. All of this is happening simultaneously on one fortuitous night.   Ã‚  Ã‚  Ã‚  Ã‚  Though the events and a lot of the dialogue are the same in both the book and the movie the crux of the two are completely different. The book focuses a lot more on sexual tension and sexual exploration. The... ...modems'; (3). It's much longer than that, but the jist of it captures the period of the sixties, which is a completely different time period with different morals and different problems. The movie should have started with Paul on the train and going through that speech, it was really well written.   Ã‚  Ã‚  Ã‚  Ã‚  The book and the movie are two different things both are remarkable in their own way. The book captures the period of adolescence and the sexual tension extremely well. It also captures the time period of the seventies well too. The movie has really good acting and the emotion of a family. It's realistic and the dialogue seems typical of an average family, which is what the movie is trying to portray. The movie and the book are two perspectives looking at the same story. It's impossible to judge which is better, but instead respect them both for their merit. The story behind both the book and movie is excellent. What makes it extraordinarily good is that all characters seem so real. Moody did a stellar job of humanizing the characters. This makes the story behind the book and movie so easy to relate to. The Ice Storm in any form of media is time well spent.

Article About Advantage Phone in School

According to a 2008 study by the Pew Research Center, 75 percent of teenagers ages 12 to 17 own a mobile phone and use that phone for daily communication through talking and text messaging. Although mobile phones may be a distraction in schools, there are many advantages to teenagers keeping and using their mobile phones–among them a number of educational and informational smartphone applications and the ability to pinpoint a missing teenager's location via GPS tracking.One of the biggest advantages to a teenager having a mobile phone is the ability to call an emergency service in case of an accident or a towing service in case of a tire blowout while driving. According to the 2008 study conducted by the Pew Research Center, 75 percent of Americans claim to have used their mobile phones in emergency situations. Emergency agencies also support the use of mobile phones during an emergency by urging people to add the letters ICE (for â€Å"in case of emergency†) in front o f certain names in their mobile phone directory to designate who should be called in case of an emergency.Many new phones also include GPS location technology, allowing parents to pinpoint the location of their teens or to locate lost or stolen phones. Smartphones allow teenagers to keep in touch not only with their friends, but also with family members, schools and emergency services. Facebook and other social media applications allow for instant updates on a teenager's status, and mobile phones have revolutionized long-distance communication by including long-distance calling options in their service plans.The ability to send instant text messages is an added advantage, though it should be avoided while driving. According to the Pew Research Center's 2008 study, an estimated 88 percent of teenage mobile phones users use their phones to connect through text messaging. Smartphones enable teenagers and college students alike to download course lectures, lesson plans and other applica tions designed to aid in education.Many applications provide books in digital format, much like a Kindle, while other applications, such as the USA Today or the New York Times app, condense every aspect of the print newspaper so it fits in the palm of a teenager's hand. In addition, a number of informational and educational podcasts, as well as classes recorded in podcast format, are available for instant download to most smartphones. main idea 1. Cell Phones as an Aid in Emergency Situations * ability to call an emergency service in case of an accident or a towing service include GPS location technology, allowing parents to pinpoint the location of their teens or to locate lost or stolen phones. 2. Cell Phones as a Means to Connect * allow teenagers to keep in touch not only with their friends, but also with family members, schools and emergency services. 3. Cell Phones as Wellness and Educational Tools * enable teenagers and college students alike to download course lectures, less on plans and other applications designed to aid in education.

Like Stars on Earth Essay

Every Child is Special is a Hindi films directed by Amir Khan .The story is about an 8-year-old boy named Ishaan who cannot cope with the academic demands in school. He once complained that The letters are dancing!† when he was asked to read. Teacher threw him out of the class and the students who passed by the hall mocked him for being punished. Moreover, Ishaanreversed letters when he wrote and demonstrated a poor understanding of mathematical concepts. Sometimes if he commits mistakes everybody laughs at him or will shout on him just like what his father or even his mother did. He always find ways to laugh after evrybody laugh bout what his diong. He was at the risk of repeating a grade level again because of his poor scholastic performance.Too often, he may be caught by his teacher daydreaming and getting low grades. see more:every child is special characters Ishaan began to evade homework and cutting classes because of his discouragement over his failings. Sometimes his father shouts and doing harsh against Ishaan. When his teachers advised his parents to avail of special education services, his family decided to send him to a boarding school instead in the hopes that the highly structured environment will straighten out his â€Å"behavioral problems†. But the academic status of Ishaan was not improve. Alternatively, he became withdrawn and lonely, far from the Ishaan who was active and fun-loving. Ishaan continued struggling with the same problems in his new school. When he was finally on the brink of suicide,Then came an alternative art teacher Ram Nikumbh discovered that he had dyslexia and consequently turned his life around. Ram Nikumbh change the best way Ishaan would act towards school and figure out how to appreciate himself even more, his art teacher who pay attention to Ishaan and to understand Ishaan whom his parents never finds what ishaan is. Towards the end of the school year Nikumbh organises an art fair for the staff and students. The competition is judged by artist Lalita Laimi, who portrays herself in the film. Ishaan, with his strikingly creative style, is declared the winner and Nikumbh, who paints Ishaan’s portrait, the runner-up. When Ishaan’s parents meet his teachers on the last day of school they are left speechless by the transformation they see in him. Overcome with emotion, Ishaan’s father thanks Nikumbh. As Ishaan is getting into the car to leave with his parents, he turns around and runs toward Nikumbh. The film ends with a freeze frame shot of Nikumbh tossing Ishaan into the air.