The isopleth crosses the scale for T at just under 4.65; a larger figure printed in high resolution on paper would yield T = 4.64 to three-digit precision. Note that any variable can be calculated from values of the other two, a feature of nomograms that is particularly useful for equations in which a variable cannot be algebraically isolated from the other variables. Straight scales are useful for relatively simple calculations, but for more complex calculations the use of simple or elaborate curved scales may be required. Nomograms for more than three variables can be constructed by incorporating a grid of scales for two of the variables, or by concatenating individual nomograms of fewer numbers of variables into a compound nomogram.
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The user does not have to know how to solve algebraic equations, look up data in tables, use a slide rule, or substitute numbers into equations to obtain results. The user does not even need to know the underlying equation the nomogram represents. In addition, nomograms naturally incorporate implicit or explicit domain knowledge into their design. For example, to create larger nomograms for greater accuracy the nomographer usually includes only scale ranges that are reasonable and of interest to the problem.
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Nomograms are typically used in applications where the level of accuracy they offer is sufficient and useful. Alternatively, a nomogram can be used to check an answer obtained from another, more exact but possibly error-prone calculation. Other types of graphical calculators such as intercept charts, trilinear diagrams and hexagonal charts are sometimes called nomograms. Other such examples include the Smith chart, a graphical calculator used in electronics and systems analysis, thermodynamic diagrams and tephigrams, used to plot the vertical structure of the atmosphere and perform calculations on its stability and humidity content.
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He introduced nomograms into physiology and biology as well. The consequential inter-relations of various factors were shown in his book Blood in more than one hundred nomograms. In 1913, Henderson wrote The Fitness of the Environment, one of the first books to explore concepts of fine tuning in the Universe. Henderson discusses the importance of water and the environment with respect to living things, pointing out that life depends entirely on the very specific environmental conditions on Earth, especially with regard to the prevalence and properties of water.
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The pair of nomograms at the top of the image determine the probability of occurrence and the availability, which are then incorporated into the bottom multistage nomogram. Lines 8 and 10 are ‘tie lines’ or ‘pivot lines’ and are used for the transition between the stages of the compound nomogram. The final pair of parallel logarithmic scales (12) are not nomograms as such, but reading-off scales to translate the risk score (11, remote to extremely high) into a sampling frequency to address safety aspects and other ‘consumer protection’ aspects respectively. This stage requires political ‘buy in’ balancing cost against risk.
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Various types of tools have been invented and widely used to assist in numeric calculations. Before Renaissance, they were various types of abaci. More recent examples include slide rules, nomograms and mechanical calculators, such as Pascal's calculator. At present, they have been supplanted by electronic calculators and computers.
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In patients who undergo treatment, the most important clinical prognostic indicators of disease outcome are the stage, pretherapy PSA level, and Gleason score. The higher the grade and the stage, the poorer the prognosis. Nomograms can be used to calculate the estimated risk of the individual patient. The predictions are based on the experience of large groups of patients.
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Combinations of disorders can be complex and difficult to interpret, so calculators, \- Online arterial blood gas analysis nomograms, and rules of thumb are commonly used. ABG samples originally were sent from the clinic to the medical laboratory for analysis. Newer equipment lets the analysis be done also as point-of-care testing, depending on the equipment available in each clinic.
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He wrote the Henderson equation in 1908 to describe the use of carbonic acid as a buffer solution. Karl Albert Hasselbalch later expressed the equation in logarithmic terms, creating the Henderson–Hasselbalch equation. In addition, he described blood gas transport and the general physiology of blood as physico-chemical system (1920–1932). He invented and constructed new charts, nomograms, with the help of Maurice d'Ocagne.
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Between 35-50% of the calcium in plasma is protein-bound, and 5-10% is in the form of complexes with organic acids and phosphates. The remainder (50-60%) is ionized. The ionized calcium can be determined directly by colorimetry, or it can be read off from nomograms, though the usefulness of the latter is limited when the pH and protein content of the plasma deviate widely from the normal.
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Food risk assessment nomogram Although nomograms represent mathematical relationships, not all are mathematically derived. The following one was developed graphically to achieve appropriate end results that could readily be defined by the product of their relationships in subjective units rather than numerically. The use of non- parallel axes enabled the non-linear relationships to be incorporated into the model. The numbers in square boxes denote the axes requiring input after appropriate assessment.
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A DePriester Chart DePriester Charts provide an efficient method to find the vapor-liquid equilibrium ratios for different substances at different conditions of pressure and temperature. The original chart was put forth by C.L. DePriester in an article in Chemical Engineering Progress in 1953. These nomograms have two vertical coordinates, one for pressure, and another for temperature. "K" values, representing the tendency of a given chemical species to partition itself preferentially between liquid and vapor phases, are plotted in between.
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The result is obtained by laying a straightedge across the known values on the scales and reading the unknown value from where it crosses the scale for that variable. The virtual or drawn line created by the straightedge is called an index line or isopleth. Nomograms flourished in many different contexts for roughly 75 years because they allowed quick and accurate computations before the age of pocket calculators. Results from a nomogram are obtained very quickly and reliably by simply drawing one or more lines.
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An observed value of 81 would use the tick mark above 81 in range E, and curved scale E would be used for the expected value. This allows five different nomograms to be incorporated into a single diagram. In this manner, the blue line demonstrates the computation of :(9 − 5)2/ 5 = 3.2 and the red line demonstrates the computation of :(81 − 70)2 / 70 = 1.7 In performing the test, Yates's correction for continuity is often applied, and simply involves subtracting 0.5 from the observed values.
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If the cancer has spread beyond the prostate, treatment options change significantly, so most doctors who treat prostate cancer use a variety of nomograms to predict the probability of spread. Treatment by watchful waiting/active surveillance, HIFU, external-beam radiation therapy, brachytherapy, cryosurgery, and surgery are, in general, offered to men whose cancer remains within the prostate. Clinicians may reserve hormonal therapy and chemotherapy for disease that has spread beyond the prostate. However, there are exceptions: radiation therapy can treat some advanced tumors, and hormonal therapy some early-stage tumors.
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Components of a parallel-scale nomogram A nomogram for a three-variable equation typically has three scales, although there exist nomograms in which two or even all three scales are common. Here two scales represent known values and the third is the scale where the result is read off. The simplest such equation is u1 \+ u2 \+ u3 = 0 for the three variables u1, u2 and u3. An example of this type of nomogram is shown on the right, annotated with terms used to describe the parts of a nomogram.
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The user specifies any two of these three quantities and the program derives the third. A description of each calculation, written in English, is generated and may be copied into the user's documents. Interactive help is available. The program provides methods that are appropriate for matched and independent t-tests, survival analysis,Schoenfeld DA, Richter JR: "Nomograms for Calculating the Number of Patients Needed for a Clinical Trial With Survival as an Endpoint" Biometrics 1982; 38:163-170. matchedDupont, WD: "Power Calculations for Matched Case-Control Studies", Biometrics, 1988; 44:1157-1168.
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The field of nomography was invented in 1884 by the French engineer Philbert Maurice d'Ocagne (1862–1938) and used extensively for many years to provide engineers with fast graphical calculations of complicated formulas to a practical precision. Nomograms use a parallel coordinate system invented by d'Ocagne rather than standard Cartesian coordinates. A nomogram consists of a set of n scales, one for each variable in an equation. Knowing the values of n-1 variables, the value of the unknown variable can be found, or by fixing the values of some variables, the relationship between the unfixed ones can be studied.
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Many nomograms include other useful markings such as reference labels and colored regions. All of these provide useful guideposts to the user. An impedance Smith chart (with no data plotted) Like a slide rule, a nomogram is a graphical analog computation device, and like the slide rule, its accuracy is limited by the precision with which physical markings can be drawn, reproduced, viewed, and aligned. While the slide rule is intended to be a general-purpose device, a nomogram is designed to perform a specific calculation, with tables of values effectively built into the construction of the scales.
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Brachydactyly can also be a signal that one will be at risk for heart problems as they age. Nomograms for normal values of finger length as a ratio to other body measurements have been published. In clinical genetics the most commonly used index of digit length is the dimensionless ratio of the length of the 3rd (middle) finger to the hand length. Both are expressed in the same units (centimeters, for example) and are measured in an open hand from the fingertip to the principal creases where the finger joins the palm and where the palm joins the wrist.
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Venda presented a new type of graphical nomograms, quadrangles with four quadrants that allow the representation of any experimental polycyclic processes, including mutual adaptation processes, and subsequently substantiated the possibility of their application in psychology, physiology, mathematics and other sciences. The variant of the quadrigram structure is shown in Fig. 4. The places of particular models in quadrants and the direction of transitions can vary depending on the research tasks, the features of the environment, and the system. An example of constructing the dynamics of a medium system on a quadrigram is shown in Fig. 5.
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A page from the Bombardier's Information File (BIF) that describes the components and controls of the 356x356px 347x347px An analog computer or analogue computer is a type of computer that uses the continuously changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude. Analog computers can have a very wide range of complexity. Slide rules and nomograms are the simplest, while naval gunfire control computers and large hybrid digital/analog computers were among the most complicated.
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The size and complexity of combisystems, and the number of options available, mean that comparing design alternatives is not straightforward. Useful approximations of performance can be produced relatively easily, however accurate predictions remain difficult. Tools for designing solar combisystems are available, varying from manufacturer's guidelines to nomograms (such as the one developed for IEA SHC Task 26) to various computer simulation software of varying complexity and accuracy. Among the software and packages are CombiSun (released free by the Task 26 team, which can be used for basic system sizing) and the free SHWwin (Austria, in German ).
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Typically, the ammonium sulfate concentration is increased stepwise, and the precipitated protein is recovered at each stage. This is usually done by adding solid ammonium sulfate; however, calculating the amount of ammonium sulfate that should be added to add to a solution to achieve the desired concentration may be difficult because the addition of ammonium sulfate significantly increases the volume of the solution. The amount of ammonium sulfate that should be added to the solution can be determined from published nomograms or by using an online calculator. Each protein precipitate can be dissolved individually in a standard buffer and assayed to determine the total protein content.
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Most metalworking books have nomograms or tables of spindle speeds and feed rates for different cutters and workpiece materials; similar tables are also likely available from the manufacturer of the cutter used. The spindle speeds may be calculated for all machining operations once the SFM or MPM is known. In most cases, we are dealing with a cylindrical object such as a milling cutter or a workpiece turning in a lathe so we need to determine the speed at the periphery of this round object. This speed at the periphery (of a point on the circumference, moving past a stationary point) will depend on the rotational speed (RPM) and diameter of the object.
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Quantum occupancy nomograms. The fundamental feature of quantum mechanics that distinguishes it from classical mechanics is that particles of a particular type are indistinguishable from one another. This means that in an assembly consisting of similar particles, interchanging any two particles does not lead to a new configuration of the system (in the language of quantum mechanics: the wave function of the system is invariant up to a phase with respect to the interchange of the constituent particles). In the case of a system consisting of particles of different kinds (for example, electrons and protons), the wave function of the system is invariant up to a phase separately for both assemblies of particles.
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For patients such as those treated on RTOG 0129 with primary chemoradiation, detailed nomograms have been derived from that dataset combined with RTOG 0522, enabling prediction of outcome based on a large number of variables. For instance, a 71 year old married non-smoking high school graduate with a performance status (PS) of 0, and no weight loss or anaemia and a T3N1 HPV+OPC would expect to have a progression-free survival of 92% at 2 years and 88% at 5 years. A 60 year old unmarried nonsmoking high school graduate with a PS of 1, weight loss and anaemia and a T4N2 HPV+OPC would expect to have a survival of 70% at two years and 48% at five years.
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Men with prostate cancer may be characterized as low-, intermediate-, or high-risk for having/developing metastatic disease or dying of prostate cancer. PSA level is one of three variables on which the risk-stratification is based; the others are the grade of prostate cancer (Gleason grading system) and the stage of cancer based on physical examination and imaging studies. D'Amico Criteria for each risk category are as follows: :Low-risk: PSA < 10, Gleason score ≤ 6, AND clinical stage ≤ T2a :Intermediate-risk: PSA 10-20, Gleason score 7, OR clinical stage T2b/c :High-risk: PSA > 20, Gleason score ≥ 8, OR clinical stage ≥ T3 Given the relative simplicity of the 1998 D'Amico criteria (above), other predictive models of risk stratification based on mathematical probability constructs exist or have been proposed to allow for better matching of treatment decisions with disease features. Studies are being conducted into the incorporation of multiparametric MRI imaging results into nomograms that rely on PSA, Gleason grade and tumor stage.
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