If an external field is applied, the distribution functions will change from their equilibirium values, and their correct form must be determined by solving of the Boltzmann transport equation (see, e.g. ,pp. 17-29).
The term on the left hand side is the total time derivative of f and all its variables. It was first given by Liouville and is a formulation of the continuity equation. The term on the right hand side was added by Boltzmann and is called collision term.
A general solution of this equation is a hard task, but as a first approximation we may assume steady state conditions and spatial uniformity throughout the bulk of the investigated material. Thus, the first and the third term are zero. Note that that the remaining term on the left hand side contains a derivative for the velocity coordinates. If we describe the electrons in the solid in terms of their wavefunctions, we can recognize the semiclassical relationship v = ħk/m and apply the chain rule to convert this term into a derivative for k. We find:
In the following, we will go through a series of simplifications and approximations. Let's start on the right hand side:
Let us briefly assume that the system is in thermal equilibrium without external field. We denote this by a function f0 which is given by the Fermi-Dirac distribution. This allows us to derive the following relation:
This statement is called principle of detailed balance.
Elastic scattering means that we do not change the energy of the particles, but only their direction. Then, E(k) is equal to E(k') and the detailed balance tells us that also the scattering functions S(k,k') and S(k',k) must be equal.
We obtain a massive simplification of the collision integral:
The quantity τ(k) is called transport relaxation time. We could also write τk,k', but an exchange of variables shows that this is equal to τk',k. Take care, τ(k) is NOT the same as the relaxation time as the one we used in the definition of the mobility. See  for more on the different definitions.
Next, we look at the left hand side of the Boltzmann equation. The remaining term contains a velocity derivative. We can relate this acceleration to the force that the external electric field exerts on the charge:
As further approximation, we apply the gradient operation only to the undisturbed distribution function f0. The result can be solved for the nonequilibrium correction f1:
In the parabolic band approximation, the gradient of the energy yields a term that is proportional to the wavevector. Then, the vectorial product with the field will yield the cosine of the angle between these two directions. Nevertheless, this looks still like an integral equation because the term τ(k) depends f1. Let's spell it out:
Inserting the relation for f1 into the definition of τ(k) above, we have to evaluate the ratio that appears in the square brackets. We can use the assumption of elastic scattering once more; since the scattering process does not change the energy but only the direction of the particles, the derivative of f0 with respect to energy is the same for E(k) and E(k'); consequently the derivative cancels out of the ratio. Moreover, we asserted further up that the relaxation times are also the same for k and k'. They drop out of the ratio as well!
All things together, the unwieldy fraction reduces to the following:
Remember that all the simplifications so far work towards the calculation of the integral that appears in the calculation of the transport relaxation time. The problem is now reduced to resolving the angles between the the applied field and the wavevectors of the initial and of the final state. We choose a coordinate system where the initial velocity is along the z direction and the electric field is contained in the yz plane.
We can read off the spherical coordinates from the illustration above and resolve the vectorial products (see e.g. , pp. 47-48).
Carrying out the integration over k space in spherical coordinates, the dependence on the polar angle will be averaged out. We obtain the following:
Thus, the big term in the square brackets reduces to [1-cos θ], where θ is the angle between the directions before and after the scattering event. We can think of this cosine-term as a weighting function which tells us that scattering events with large angles contribute most to the scattering integral (not really a big surprise!).
The probability for scattering after a time τ is virtually one, but with respect to unit time it is just 1/τ. However, this is exactly the definition of S(k',k):
If we know the differential cross section of our scattering process, we can determine the transport relaxation time. Here, we replaced the dependence on k' and k by the scattered angle θ. We explicitely write the δ-function to express that we are dealing with elastic scattering processes that conserve the energy. As such, it comes out of Fermi's Golden Rule when the differential cross secion is determined from the scattering potential. Sometimes it is dropped in the literature, but it is then a bit surprising why the integral for the transport relaxation time is extended only over the angular part of d3k without further explanation.
We are through! After solving the integral for the transport relaxation time, we can obtain the first-order correction to the distribution function in the presence of an electric field with the expression that was given above:
Carrying out the derivative for the Fermi-Dirac distribution is a bit messy. Below is an approximation using the Maxwell-Boltzmann distribution which applies generally for non-degenerate situations. We revert to the expression for particles with kinetic energy and A is a suitable normalization constant. Note that f1 changes sign with the direction of the electric field.
Note that the integral weighted with the equilibrium function f0 will give zero because there is no current without field; the only contribution will come from the f1 term.
Sometimes the explicit route via the integral of the the current density is not spelled out, but the authors calculate the mobility relaxation time by averaging the transport relaxation time with a weighting factor of E3/2 (e.g. eq. (5.4) in  or eq. (35) in ). The form of this particular weighting factor comes from the fact that we pick up a wavevector from the gradient term and another one from the current density integral, resulting in k2 which is proportional to E. An additional factor of E1/2 comes from the usual conversion of d3k into dE.
last changed: 6/7/2015


Many people find maths daunting, so here are some resources to help you help your child become numerate.
NZ Maths – Numeracy Development Project
This is how numeracy is taught in our public schools. The aim is for children to learn their basic facts by rote, and learn a variety of strategies to solve different types of maths problems. Accurate estimation is also an important goal. It is not a curriculum as such, instead it describes the different levels of development, and provides activities and resources to teach number knowledge and maths strategies.
Get the material masters – free printable maths resources to go use for the books’ activities. These are best laminated or printed/glued onto card. You can also buy the materials used from educational suppliers such as Every Educaid.
This Teacher Tools website has many videos teaching the various strategies from the Numeracy Project.
Essays by Peter Hughes of the Numeracy Development Project
Given to teaching students at Auckland University so may not be available elsewhere. Worthwhile reading.
Action Verbs for Learning Objectives – The MoE likes teachers to be specific when they write their plans and learning intentions, and the same goes for us home educators. For example, instead of saying your child will “learn about” photosynthesis, it is better to say he/she will be able to describe the process of photosynthesis, name what is needed for photosynthesis to occur, sketch a diagram, and so on. Here is a list of action verbs that may provide inspiration for when you write your exemption. Of course you cannot possibly cover every single thing your child will ever learn, however, using specific language for what you do write about will show that you know what you are doing!
Scratch – invented by MIT – is an excellent, engaging way for kids (and adults) to learn to program – and it’s free!
Using programming logic is addictive here at Lightbot – scroll down and hit the red Web button for the free levels.


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Highlights from the Terra Nova Testing from 17-18 Academic Year:
- Our Kindergarten readers graduated at the same level as a typical first grader.
- Our Kindergarten is at the 84 percentile in the nation in reading and overall testing.
- Our 1st graders scored at the 80th percentile in reading.
- Several of our 1st graders scored at the 99th percentile in math computation.
- Our 2nd graders scored at the 85th percentile in the nation in reading.
- Our average reading grade equivalency is the middle of 5th grade when they leave 2nd grade.
- Several of our students scored at the 99th percentile in math computation.
- Our 3rd graders scored on average at the fifth grade level in reading.
- Our 3rd graders scored better than 75% of nation in math computation.
- Our 5th graders on average have a reading equivalency of 8th graders.
- Half of our fifth graders scored junior or senior high school level in reading.
- Our 6th graders scored at the 75th percentile in the nation in language mechanics.
- Our 7th graders scored almost two grades higher in social studies than their national peers.
- Our 8th graders are reading at a post high school reading level.
- Our 8th graders are above the 80th percentile in both math computation and problem solving skills.


The objective of the cours will be to become familiar with biomechanical modeling based on the finite element method, with special focus on the soft tissue modeling in medical simulations. Both the geometrical and physical aspects will be covered.
First, we will study different representations of patient-specific data in the form of acquired images (CT, MRI, ultrasound). We will explain the process of model reconstruction from images: the procedure of segmentation and mesh generation. We will define the notion of mesh quality. After discovering the techniques dealing with the geometry, we will introduce the physical aspects: we will study the numerical formulation of linear elasticity as well as the method of solving the systems of linear equations. Briefly, we will also focus on non-linear models resulting from co-rotational and hyperelastic formulations.
The knowledge of the theoretical aspects will be strengthened by practical applications where we will work directly with the medical data. We will test various methods of (i) image processing aiming to improve the image contrast, (ii) segmentation of regions of interest (ITKSnap), (iii) mesh generation and post-processing (CGAL, MeshLab), and (v) visualization (Paraview). Finally, we will employ the reconstructed geometry to create a simulation scene in SOFA framework.


... 30 inch 4.3 5.7 7.2 8.6 10.0 11.5 How do you calculate plant population and seeding rate? You or the person you have designated may only begin to produce marijuana plants once you receive a registration certificate from Health Canada. Hills within the row, preferably, should not be less than 20 cm apart with only one plant per hill to avoid overcrowding. Soybean plant population in plants per foot of row for different row spacing's. You can use square feet or meters if you are finding the density of a smallish space. This free probability calculator can calculate the probability of two events, as well as that of a normal distribution. Restaurant or Airport) based upon a figure of 60 grams/BOD/hd/day and 200 litres/hd/day. FAQ. One method is to calculate a design parameter called the "population equivalent" (PE) of a catchment and convert this to a flow rate. Examples of calculations on the online calculator. To use this calculator please fill in the input value data of your sewer wastewater and as a result some basic plant design and effluent BOD data will follow out of the calculations. Thus, Population Density = Number of People/Land Area. Good seed will have a germination of 90-95% and seed mortality is approximately 3%, but can vary greatly. The following table gives the number of plants per hectare at various spacings for hand planting: Spacing Spacing between plant Number of Plant population between rows station plants per (plants per ha) (cm) (cm) station Raise the number 3 to a power 4: 3 [ X Y ] 4 [ = ]. Sample Size Calculator Terms: Confidence Interval & Confidence Level. How to calculate Plant Population per hectare. Calculate the square root of 529: 529 [ √ ]. A Punnett Square shows the genotypes two individuals can produce when crossed. Scientists usually calculate plant populations with the quadrat method. The Percent Growth Rate Calculator is used to calculate the annual percentage (Straight-Line) growth rate. Row Width Row Length to 1/1,000th Acre 20” 26.2 ft. 28” 18.7 ft. 30” 17.4 ft. 36” 14.5 ft. 38” 13.8 ft. 40” 13.1 ft. How to Estimate Plant Population per Acre Number of Rows to Make One Acre Length Please enter your authorized daily grams, select indoor and/or outdoor and press "Calculate… 2. Disclaimer: ICAR-CCARI does not accept responsibility for any loss which may arise from reliance on the software or materials published on this site. The calculator works for … Calculate your Ecological Footprint. A quadrat is a square that encloses an area within a habitat. 11.0 Sewage treatment plant1.1 Design calculation.i. Seeding Rate Calculator, Plant Population Calculator: On this page, the calculator allows the user to estimate the number of seed to plant to obtain a desired plant population for a given area, and the cost associated with that seeding rate. for a confidence level of 95%, α is 0.05 and the critical value is 1.96), MOE is the margin of error, p is the sample proportion, and N is the population size. Just enter a set of data separated by comma and submit to know the population mean for the given data. It is not a measure of population. The completely offline plant population calculator app for Android. If the normal sewer water characteristics are unknown, please press the "typical data" button for an autofill of the input fields. Count the number of plants between the two lines for each of the rows. It is the term most used to describe the size of package sewage treatment plants. To draw a square, write all possible allele combinations one parent can contribute to its gametes across the top of a box and all possible allele combinations from the other parent down the left side. Seeding Rate Calculator, Plant Population Calculator: On this page, the calculator allows the user to estimate the number of seed to plant to obtain a desired plant population for a given area, and the cost associated with that seeding rate. The Plant population of any field is given by multiplying the between plants spacing with the spacing between the rows. The result is equal to 125. The allele combinations along the top and sides become labels for rows and columns within the The (N-n)/(N-1) term in the finite population equation is referred to as the finite population correction factor, and is necessary because it cannot be assumed that all individuals in a sample are independent. Seed rate to be used for sowing can then be calculated using the following formula. deeper than 5 cm). The confidence interval (also called margin of error) is the plus-or-minus figure usually reported in newspaper or television opinion poll results. The calculator works for … Plants Per Acre Calculator Please enter information for three of the four fields. What is the formula for calculating the percent growth rate? The population density is the highest for species A and the lowest for species C. The density value is expressed as the number of individuals per unit area. Soybean Seed Rate Calculator (Fill in numbers in blue boxes) Seed: Seeding rate: Planting: Acres in field Desired stand, thousands of plants per acre Seed drop rate per foot of row Pounds of seed in a unit, if sold by weight Row spacing in inches Inches between seeds Step 1: Calculate the percent change from one period to … Germination and mortality are based on seed tests. cabbage) or 100 plants per square metre (e.g. We can calculate the density of plant population by this equation: Density =Total number of individuals of the species in all the sampling unit (S) / Total number of sampling units studied (Q) ... Based on the values entered, the worksheet gives the plant population density for each species. Sewage treatment plant design calculation 1. Here is a free online sample and population statistics calculator which will help you in estimating the population mean for the given statistical data. Example: Widely varying plant spacings such as 1 000 mm x 10 mm, 500 mm x 20 mm and 100 mm x 100 mm, all give a plant population of 100 plants per square metre. Here are some online tools to help you estimate your needs. For a circular planting bed, you can calculate how many plants per square foot is ideal by multiplying 3.14 by the distance from the center to the edge of the bed. Plant Population Calculator. 1. Population Mean is the average of a set of group characteristics. Also Read: Parts of Plants. Population equivalent (PE)For this proposal, 40 unit of residential house and 18 unit of commercial building areconsider for the development. There is a substantial number of processes for which you can use this exponential growth calculator. Calculation of percentage of the number of: 500 [ х ] 25 [ % ]. The total area of a hectare is 10000 square metres. For herbaceous vegetation, a metre square quadrat is normally used. Learn more about different types of probabilities, or explore hundreds of other calculators covering the topics of math, finance, fitness, and health, among others. The unit of land area should be square miles or square kilometers. carrot) Plant spacing, on the other hand, refers to the ARRANGEMENT of plants on the area planted. There are two distance requirements for the calculation; the distance between tree rows and the distance between the trees themselves. Calculate the seed rate of green gram for sowing 1 hectare of crop from the following: spacing=45cm×10cm germination %=80% 1000 grain weight =48g Solution: Plant population= 10000 0.45×0.1 =222222.22 Seed rate= 222222.22×48×100 80×1000×1000 =13.33 kg (Ans). Calculator. Example: 40 000 plants per hectare (e.g. Use Figure 1 to select a within-row spacing that will meet the desired plant population. X = Z α/2 2 *p*(1-p) / MOE 2, and Z α/2 is the critical value of the Normal distribution at α/2 (e.g. Measure the amount of distance to give 1/1,000 th of an acre (Table 1) and draw another parallel line across the same six rows. To calculate a seeding rate, use the following equation: Desired Plant Population = Seeding Rate Percent Germination x Percent Pure Seed x Percent Live Seed Emergence Growers can use this equation with any unit — acre, square yard, square foot — as long as the same unit is used in both seeding rate and desired plant population. The general rule of thumb is that the exponential growth formula:. The PE is an estimate of the usage made of sewage facilities. Use this calculator to decide how much seed you need to plant to obtain the desired plant population and calibrate your seeder. A Tree Spacing Calculator that will calculate the number of trees per acre and spacing between trees and tree rows. There are many methods for calculating expected flow rates. For example: for a target population of 100 plants/m 2 and using seed of average weight (35 mg) and a laboratory germination test of 95 percent. To recalculate, change any field you wish and click the "Calculate" button next to the field you wish to recalculate. This calculator computes the number of plants which will cover a given area, with a given distance between plants. For SC 727, a 50, 000 kernel (1 hectare pack) is enough to plant 1 Ha, 20, 000 kernel for 1 Acre. About Percent Growth Rate Calculator . Click the "Calculate" button next to the field you wish to calculate. Determine the average plant population by adding together the total number of plants per row and dividing by the number of rows that were measured. Barley, General Purpose Seeding Rate Calculator. The result is equal to 23. It can be defined as; ‘The equivalent, in terms of a fixed population, of a varying or transient population (e.g. For a triangular bed, multiply the height of the triangle by .5 times the base measurement. Planting Rate Estimator Pioneer field tests hybrid response to plant population at … To calculate the population density, you will divide the population by the size of the area. Once analyzed, the sample data enables the scientist to calculate the population size and population density for the entire population. Learn more in detail about the plant population density, other related topics and experiments at BYJU’S Biology. It will compute the number if the plants are placed on a rectangular grid, and the number if they are placed on a triangular grid. Find out how many planets would be needed if everyone in the world lived like you? The result is equal to 81. The following calculator is for reference purposes only. Common Flower Spacing. 3. Spacing, on the area software or materials published on this site of percentage of triangle! Analyzed, the sample data enables the scientist to calculate the square root of:... Characteristics are unknown, Please press the `` typical data '' button next to ARRANGEMENT. And seed mortality is approximately 3 %, but can vary online plant population calculator normal distribution rows and the distance between spacing... Percentage ( Straight-Line ) growth rate figure usually reported in newspaper or television opinion poll.! Can produce when crossed acre and spacing between trees and tree rows and the distance between the.... Usually calculate plant population of any field you wish to calculate the probability of two events, well... Building areconsider for the development populations with the quadrat method submit to know the population density, related. For Android or square kilometers the distance between the trees themselves density = number of plants will. Materials published on this site Estimator Pioneer field tests hybrid response to plant population and seeding rate the population... That will calculate the population mean for the calculation ; the distance between plants have... Not accept responsibility for any loss which may arise from reliance on area. Good seed will have a germination of 90-95 % and seed mortality is approximately 3 % but... Help you in estimating the population density for the development the rows that encloses an area within a.! Square metres and spacing between the rows for herbaceous vegetation, a metre square quadrat normally..., on the area planted within the row, preferably, should not be than! Population mean for the calculation ; the distance between tree rows probability calculator can calculate the online plant population calculator! Reliance on the other hand, refers to the field you wish and click the `` typical data button! Of row for different row spacing 's probability calculator can calculate the probability two... Statistics calculator which will help you in estimating the population size and population density = number of for!
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题目：Markov-Chain Stochastic Optimization Methods
时间：上午10:00 - 11:30
摘要：This talk introduces Markov-chain stochastic optimization methods. They are useful in reinforcement learning, dynamical system identification, and other optimization applications where Markov chains naturally arise. In addition, they can be used to design communication-efficient decentralized algorithms. We show that stochastic gradient methods and random block-coordinate methods can still converge when we sample according to a Markov chain.
个人介绍：Wotao Yin received his Ph.D. in operations research from Columbia University in 2006. He is currently a Professor with the Department of Mathematics, University of California, Los Angeles. His research interests include computational optimization and its applications in signal processing, machine learning, and other data science problems. He has received the NSF CAREER award in 2008, the Alfred P. Sloan Research Fellowship in 2009, and the Morningside Gold Medal in Applied Mathematics in 2016, and has coauthored five papers receiving best paper-type awards. He invented fast algorithms for sparse optimization and has been leading the research of optimization algorithms for large-scale problems.


Top best answers to the question «How much is a batch of cookies»
Most cookie recipes make three to five dozen cookies or 36-60 cookies per batch on a 15-by-10-inch cookie sheet. In baking, a batch means an amount produced at one time.
10 other answers
a batch of cookies is a cookie sheet full
Neil Conway/CC-BY-2.0. Most cookie recipes make three to five dozen cookies or 36-60 cookies per batch on a 15-by-10-inch cookie sheet. In baking, a batch means an amount produced at one time. The amount of cookies that are in one batch varies by recipe.
Because a “batch” is the amount a recipe makes at one time. The average number of cookies in a batch can range from 24-36 (based on some light research I did into the cookbooks I happen to have on my shelves), but that’s just an average, so some recipes will make more than 36 and others will make fewer than 24.
A batch matters on the recipe. If the cookie recipe you made has 12 cookies in it, then your batch would be one dozen. If it made 14 cookies then your batch would be 14 cookies. Like I said, it all depends on your recipe.
10 cups of flour make 5Â batches of cookies. How many cups of flour in one batch? Here areÂ a diagram and a division equation that represent this situation: $$10\div5 = ?$$ For each question, draw a diagram andÂ write a division equation. 6 cups of flour make 4 batches of cupcakes. How many cups of flour in one batch?
I then multiply $.30 per minute by 160 minutes to arrive at a total direct labor cost per batch of $48. To compute cost on a per cookie basis, I simply divide $48 by the recipe yield (30 cookies) which gives me $1.60 per unit (cookie) for labor. My direct costs, excluding packaging, are now: raw ingredients + direct labor = $ per unit (cookie)
In short, you should plan to charge between $2 and $6.50 per cookie, or between $8 and $15 per dozen if you choose to sell your cookies in bulk. When setting your pricing, you should consider the cost of both the ingredients and baking equipment, as well as your time, and complexity of the cookie.
Well, maybe you plan to factor in your time at $20 per hour. If you can make 4 batches or 96 cookies in an hour, that's $5 per batch or roughly 21 cents per cookie. In our scenario, this means that each cookie now costs 51 cents to make.
With that assumption, a batch of homemade cookies that’s equal to the store-bought version costs $1.94. So you’re saving $1.06 for 20 minutes of work, which gives you an “hourly wage” of $3.18. “Wow,” you’re thinking, “that’s pretty terrible!
You should also factor your time into the cost of making the cookies, let’s assume and state the cost of your time at $20 per hour. Hence, if you can make 4 batches or 96 cookies in an hour, that’s $5 per batch or roughly 21 cents per cookie. Using the above cost analysis, it simply means that each cookie now costs 51 cents to make.


Visualizing Mode Connectivity
Blogpost by Pavel Izmailov, Timur Garipov and Andrew Gordon Wilson; visualizations in collaboration Javier Ideami.
Figure 1: visualization of mode connectivity for ResNet-20 with no skip connections on CIFAR-10 dataset. The visualization is created in collaboration with Javier Ideami (https://losslandscape.com/).
Understanding generalization in deep neural networks is a great open question. Neural networks are trained by minimizing loss surfaces that are highly multimodal, with many settings of parameters that achieve no training loss but poor generalization. By understanding the geometric properties of these loss surfaces we can begin to resolve these questions and build more effective training procedures. Indeed, the local smoothness and convexity of loss surfaces is used for analyzing convergence of SGD and other optimizers [e. g. 12]. Recently, stochastic weight averaging  was proposed to find flatter regions of the loss, leading to better generalization.
The shape of the surface also has great implications for Bayesian approaches in deep learning. With a Bayesian approach, we not only want to find a single point that optimizes a risk, but rather to integrate over a loss surface to form a Bayesian model average. The geometric properties of the loss surface, rather than the specific locations of optima, therefore greatly influences the predictive distribution in a Bayesian procedure. Accordingly, recent approaches have exploited the geometry of the SGD trajectory for scalable and high performing Bayesian inference procedures [6, 7].
We still know very little about the properties of these loss surfaces. New discoveries are being made, showing topological behaviour that is highly distinct to neural networks. In this blogpost we describe mode connectivity, a surprising property of modern neural net loss landscapes presented in our NeurIPS 2018 paper. Our exposition in this post focuses on obtaining intuition through visualization.
Typically, the local optima of deep neural networks are imagined as isolated basins, as in the left panel of Figure 2. In this figure, we visualize the high dimensional loss surface in the plane formed from all affine combinations of three independently trained networks. In the next section we describe the details of the visualization procedure. This intuition comes from the following experiment: if we train two networks of the same architecture, we get two different local optima in the parameter space; the loss along the line segment connecting the two solutions blows up between the optima, reaching values attained by completely untrained networks at initialization. Surprisingly, the optima are actually not isolated. We can find a curved path between them, such that the loss is effectively constant along the path. We refer to this phenomenon as mode connectivity. These curved paths can be very simple, such as those shown in the middle and right panels of Figure 2. These paths are also easy to find, as we explain below.
Figure 2: Loss surface of ResNet-164 on CIFAR-100. Left: three optima for independently trained networks; Middle and Right: A quadratic Bezier curve, and a polygonal chain with one bend, connecting the lower two optima on the left panel along a path of near-constant loss.
Mode connectivity has been shown to hold very generally. In [1, 2] mode connectivity is demonstrated for multiple state-of-the-art image classification architectures and some recurrent architectures on text data. In  the authors show that it is possible to connect optima trained with different optimizers and hyper-parameters, such as batch sizes, weight decay, learning rate schedule and data augmentation strategy. In  the authors that mode connectivity holds for policy optimization algorithms in deep reinforcement learning.
How to Visualize Loss Surfaces?
Visualization helps us analyze and build intuition about complex objects. Visualizations based on dimensionality reduction can reveal interpretable structure, leading to new scientific insights; for example, in  t-SNE visualizations were used to discover new sub-types of retinal cells. Here, we study the properties of loss functions of deep neural networks, which depend on millions (or sometimes even billions!) of parameters. We cannot directly visualize a million-dimensional surface. However, we can look at a 2D slice of the loss function, and if this slice is chosen carefully, it can provide insights about the structure of the landscape.
Figure 3: Illustration of the loss surface visualization procedure. We pick a 2D plane in the parameter space of a neural network, construct a coordinate system in the plane and define a grid in this coordinate system. Then, we evaluate loss for each point in the grid and visualize the result.
Three points in the parameter space always define a unique 2D plane that passes through these points. Suppose we have three points \(w_1, w_2, w_3\) in the weight space. These can, for example, be the vectors of parameters (all weights and biases concatenated into a single vector) of three independently trained networks, as in the left panel of Figure 2. We can construct a 2-dimensional plane passing through \(w_1, w_2, w_3\) as follows. We define a basis for the plane to be \(u = (w_2-w_1), v = (w_3-w_1)\) and the shift vector to be \(w_1\). We can orthogonalize the basis by switching to \(v=v - cos(u, v) u\), where \(cos(u, v)\) is the cosine of the angle between vectors \(u\) and \(v\). We can then define a Cartesian coordinate system in the plane and map \((x, y)\) coordinates to the points in the original parameter space using the formula \(w(x, y) = w_1 + u\cdot x + v\cdot y\). Now we can construct a grid in the coordinate system and evaluate the loss function for the network corresponding to each of the points in the grid, and visualize the results. Figure 3 illustrates the visualization process.
Finding Paths between Modes
The method for finding a path of low loss between a pair of optima is intuitively very simple: we parameterize the path and minimize the average loss along the path with respect to its parameters. Formally, suppose we have two optima \(w_1\) and \(w_2\) of the loss function. We then define a path connecting them as \(\phi(t)\), a mapping from the segment \([0, 1]\) to the parameter space, such that \(\phi(0) = w_1, \phi(1) = w_2\). For example, we can use a quadratic Bezier curve: \(\phi(t) = (1 - t)^2 w_1 + 2t (1-t) \theta + t^2 w_2\), shown with a black line in the middle panel of Figure 2. Here is the parameter of the curve, which has the same dimensionality and structure as the weight vectors \(w_1\) and \(w_2\). We train to minimize the average loss over the curve. Specifically, we minimize
with respect to \(\theta\), where \(Loss()\) is the standard loss function used for training the networks \(w_1\), \(w_2\), such as cross-entropy loss for classification.
We can compute stochastic gradients of \(L(\theta)\) with respect to \(\theta\) efficiently. To do so, we sample a point \(t\) uniformly on \([0, 1]\), and then compute the gradient of \(Loss(\phi(t))\) with respect to \(\theta\) using the chain rule:
Using this stochastic gradient estimate, we minimize \(L(\theta)\) with standard SGD.
For the quadratic Bezier curve, the whole path \(\phi(t)\) lies in a 2-dimensional subspace of the parameter space. We can visualize the loss function in this plane throughout training, using the visualization procedure described in the previous section.
High-Resolution Visualizations of Mode Connectivity
In collaboration with Javier Ideami we have recently produced high-resolution visualizations of the loss surfaces in the planes containing mode connectivity. We created a video showing the training process of a quadratic Bezier curve connecting a pair of local optima for ResNet-20 with no skip connections on CIFAR-10:
In the video, the optima go from being isolated and disconnected for the randomly initialized curve to being connected by a tunnel of low loss, as in Figure 1.
We have also created static visualizations of ResNet-20 on the FastAI Imagenette dataset at an even higher resolution of 1000x1000. We show these visualizations in Figures 4, 5, 6.
Figure 4: Visualization of mode connectivity for ResNet-20 with no skip connections on ImageNet dataset. The visualization is created in collaboration with Javier Ideami (https://losslandscape.com/).
Figure 5: visualization of mode connectivity for ResNet-20 with no skip connections on Imagenette dataset. The visualization is created in collaboration with Javier Ideami (https://losslandscape.com/).
Figure 6: visualization of mode connectivity for ResNet-20 with no skip connections on Imagenette dataset. The visualization is created in collaboration with Javier Ideami (https://losslandscape.com/).
On Javier’s website https://losslandscape.com/ you can find other artistic high resolution visualizations of neural network loss surfaces, both static and dynamic.
Computational Cost of Creating the Visualizations
For each of the visualizations we compute the loss for each point in a grid (corresponding to a different setting of network weights). For Figures 4, 5, 6 we used a 1000x1000 grid, which requires evaluating the loss for a neural network at a million different settings of its parameters. For the video we computed 600 frames at a resolution of 300x300, amounting to over 50 millions loss evaluations. In order to limit the computational cost, we use a subsampled version of the dataset, making sure that this subsampling preserves the structure in visualizations. Even with the smaller dataset, the visualization process for the video took over two weeks using 15 GPUs. Creating the high-resolution static visualizations in Figures 4, 5, 6 took about two days using three GPUs.
Do These Paths Contain Different Representations?
The parameterization of neural networks is known to contain degeneracies. For example, in ReLU networks we can multiply the weights in one layer by a certain value, and divide the weights in the next layer by the same value, and the outputs of the network (and consequently loss) wouldn’t change. It is thus natural to ask whether the mode connectivity only exists because of such degeneracies in parameterization. We find, instead, that the low loss paths contain a rich collection of different representations, providing different predictions on test data. We demonstrate the diversity of functions along a path of low loss for a 1D regression problem in Figure 7.
Figure 7: Loss surface in the 2D plane containing a path of low loss (right) and the predictive functions corresponding to different points in this plane (left) for a DNN trained on a 1D regression problem. Different points along the curve shown with magenta circles on the right correspond to different functions shown with magenta lines on the left. Please see  for a detailed description of this experiment.
Indeed, the curves connect a pair of different optima \(w_1\) and \(w_2\), which produce different predictions. Therefore the predictions must change in some way along the curve. We can verify that the predictions of the networks along the path \(\phi\) are meaningfully different by looking at the performance of ensembles of these networks. We consider ensembles of two networks: one is fixed at \(w_1\) and the other \(\phi(t)\) is moving towards \(w_2\) along the path \(\phi\). We find that the ensemble of \(w_1\) and \(\phi(t)\) performs as well as the ensemble of independently trained \(w_1\) and \(w_2\) even for \(t \approx 0.3\), suggesting that the networks along the path are meaningfully different from the endpoints. We visualize the performance of the ensemble as a function of the point on the curve in Figure 8.
Figure 8: Performance of the ensemble of an endpoint of the path and a point on the path as a function of the point on the path. For comparison we visualize the ensemble performance for the direct line segment connecting optima, as well as for the path learned by our method.
There are several papers that provide theoretical explanations of mode connectivity. For example, the recent paper  demonstrates that different notions of noise stability, such as stability to dropout perturbations, imply mode connectivity. Papers [8, 9] provide different theoretical perspectives on mode connectivity by showing that under certain assumptions all sublevel sets of DNN loss are connected.
Mode connectivity inspired new practical methods for training neural networks with improved generalization and uncertainty quantification. At a high level, mode connectivity shows it is possible to travel between different modes of the loss function without leaving a general region of low loss. Stochastic Weight Averaging (SWA)  uses this idea and explores diverse solutions around a given solution by running SGD with a high constant learning rate; then, SGD iterates from different epochs are averaged to get a new solution with significantly improved generalization. SWA-Gaussian  extends SWA to also capture the covariance of SGD iterates and constructs a Gaussian distribution over the weights; by sampling from this distribution to form a Bayesian model average it is possible to significantly improve both the accuracy of the model and uncertainty representation, compared to standard SGD. Finally,  approximates the Bayesian posterior over the weights of a network in the subspace containing a path of low loss between optima and performs Bayesian model averaging using this approximation.
The recent paper  extends our method for finding low loss curves, to find planes where the loss surface resembles a given picture. Surprisingly, they were able to find such planes for any picture they used. We show some of their example loss surfaces in Figure 9. The fact that simple SGD can easily find these complex structures in the loss surface hints at a blessing of dimensionality. The high dimensionality of the parameter space provides many paths towards good solutions.
Figure 9: visualization of the loss in planes constructed in  for FashionMNIST and CIFAR-10 datasets. This figure is copied directly from .
 Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs; Timur Garipov, Pavel Izmailov, Dmitry Podoprikhin, Dmitry Vetrov, Andrew Gordon Wilson; Neural Information Processing Systems (NeurIPS), 2018
 Essentially No Barriers in Neural Network Energy Landscape; Felix Draxler, Kambis Veschgini, Manfred Salmhofer, Fred A. Hamprecht; International Conference on Machine Learning (ICML), 2018.
 A Closer Look at Deep Learning Heuristics: Learning rate restarts, Warmup and Distillation; A. Gotmare, N. Keskar, C. Xiong & R. Socher; International Conference on Learning Representations (ICLR) 2019
 Understanding the impact of entropy on policy optimization; Zafarali Ahmed, Nicolas Le Roux, Mohammad Norouzi, Dale Schuurmans; International Conference on Learning Representations (ICLR) 2019
 Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Nets; Rohith Kuditipudi, Xiang Wang, Holden Lee, Yi Zhang, Zhiyuan Li, Wei Hu, Rong Ge, Sanjeev Arora; Neural Information Processing Systems (NeurIPS), 2019
 Averaging Weights Leads to Wider Optima and Better Generalization; Pavel Izmailov, Dmitry Podoprikhin, Timur Garipov, Dmitry Vetrov, Andrew Gordon Wilson; Uncertainty in Artificial Intelligence (UAI), 2018
 A Simple Baseline for Bayesian Uncertainty in Deep Learning Wesley Maddox, Timur Garipov, Pavel Izmailov, Dmitry Vetrov, Andrew Gordon Wilson Neural Information Processing Systems (NeurIPS), 2019
 Subspace Inference for Bayesian Deep Learning; Pavel Izmailov, Wesley J. Maddox, Polina Kirichenko, Timur Garipov, Dmitry Vetrov, Andrew Gordon Wilson; Uncertainty in Artificial Intelligence (UAI), 2019
 On Connected Sublevel Sets in Deep Learning; Quynh Nguyen; International Conference on Machine Learning (ICML), 2018.
 Topology and Geometry of Half-Rectified Network Optimization; C. Daniel Freeman, Joan Bruna
 Loss Landscape Sightseeing with Multi-Point Optimization; Ivan Skorokhodov, Mikhail Burtsev, 2019
 Highly Parallel Genome-wide Expression Profiling of Individual Cells Using Nanoliter Droplets


Few things are as academic as projecting playoff chances at mid-season.
But I've sworn off/lambasted pre-season predictions, power rankings and advanced statistics this season....time for me to curry some favor with at least one faction of math nerds.
The Wild is sitting with 48 points in 40 games. Those 48 points are comprised of 21 wins and 6 OT losses.
They are on target for 98 points on the season. Normally, that would be enough to get you into the playoffs. In fact, I got back to the 1997-98 season on NHL.com (before I got bored and stopped checking) and 98 points would have gotten you into the playoffs in the Western Conference every season.
The next step is to try to quantify how poorly the Wild would have to play in the second half of the season in order to fail to make the playoffs.
The 8th place team in the West the past ten seasons finished with 97, 95, 91, 91, 96, 95, (lockout), 91, 92, 94 and 90 points, respectively. That's an average of 93.2 points. So, let's say 94 (one additional point, to be safe) points is the minimum to feel really safe. (Colorado is currently in 8th place in the west, on pace for 90 points.)
If they go .500 in their remaining 42 games, that's 21 wins and 21 losses (let's assume no loser points - lowest common denominator, right?) Adding 21 wins to their current 21 wins equals 42 wins and adding the 6 OT losses equals 90 points. Uh-oh.
If they go .550 for the rest of the season, that puts them on pace for 94 points (21 wins so far, adding in 23 more, adding in the 6 OTL to date).
That would do it.
So, the difference between .500 and .550 is 2 wins, and it's also the difference between getting into the playoffs and not.
Now, is .550 realistic for this Wild team?
If their recent injury "luck" holds, probably not.
But, if they stay healthy? Absolutely.
Finally, there was that line going around in early December about no team that was #1 overall in early December had failed to make the playoffs that season.
I expect the Wild to make the playoffs this season, and will be disappointed if they don't.
Is 46 more points (in their 42 games) reasonable? Again, I think it is. That means, essentially, that they can go 5-4-1 in each ten game set for the rest of the season and get to 94 points.
Furthermore, I'd say the odds are very strong (say 75%*) that they will.
So there you have it: I'm saying the Wild is 75% likely to make the playoffs as of today.
You gotta problem with that? Let's hear it.
*Stated probability not based on any mathematical formula at all.
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In collaboration with the esteemed organization known as Olico, our collective endeavor is to revolutionize the cognitive paradigm and methodological approach to mathematics education at the high school level. The Olico Math Program, distinguished by its innovative curriculum, seeks not merely to instruct but to instill a profound appreciation for the foundational principles of mathematics, all while engendering a sense of enjoyment in the learning process.
This avant-garde program adopts a hybridized instructional model, seamlessly integrating traditional paper-based lessons with cutting-edge online activities facilitated through mobile devices. This method ensures a comprehensive and dynamic learning experience, encompassing both conventional pedagogy and contemporary technological modalities. The classes, conducted twice a week, cater specifically to the lower echelons of high school, thereby laying a robust foundation for mathematical acumen and fostering an enduring enthusiasm for the subject among learners.


Graphs and charts are important tools that can help you organize your data, make estimations, and enhance your productivity. They will also boost your communication. The right choice can help you persuade customers to buy your products. You have to know the different types of charts and charts to find the right one for your needs.
A collection chart can be quite a great way to show changes and trends in your data. Additionally it is useful for demonstrating the relationship between two quantities.
The axis typically starts off at the center on the chart and reflects the quantitative value of each and every variable. http://infographicsaplenty.com/best-electronic-data-rooms-for-business/ For example , if the company offered pants in June, the x-axis might reflect the quantity of pants marketed, while the y-axis reflects home buying of the month.
Another option just for illustrating developments and improvements is the area graph. This sort of chart entails coloring amongst the line and horizontal axis, and is accustomed to display patterns and styles.
Despite its name, pie chart don’t can certainly make pies. Pie charts are a good way to demonstrate the percentage malfunction of a little set of info. However , they are simply known to be difficult to read.
Standard graphs are useful for exhibiting data and trends. Using bar charts, you can easily break your data into separate articles, which can help you realize it better.
While there are many types of diagrams and charts, the most typical are the graph, the line chart, and the scatterplot.


I was wondering if anyone has ran basic statistical analysis (numerical, graphical, and regressions) on the stats in the database? I'm curious to see where the range is on most statistics, as well as median and mean values of the stats. My theory is that most statistics in the game should have a mean and median close to 70 (which I consider the average for professional players). If not, there must be some bias that needs fixing in order to ensure that gameplay is solid.
Tell me what you think as I'm interested in what everyone has to say. I've played PES since 2001 and spend way too much time on it not to care (game time in PES 2011 is over 500 hours at this point, with 399 in ML).


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EducationLindenwood University - BS, Computer Science
ExperienceI'm Thorin and I am located in Frankford, MO. I have attended Northwest Missouri State University, and Lindenwood University. I earned a bachelor's degree in Computer Science, and have been teaching for 14 years. I love to learn and continue to attend classes. My teaching philosophy is to provide a path for my students to discover an answer on their own; this allows for them to retain the material beyond memorization for a test. This method also allows for the student to discover that each step along that path is just as significant as the end result. I am able to tutor students in reading, writing, phonics, elementary through high school mathematics, English, World history, American history, government, computer science, literature, college algebra, precalculus, statistics, trigonometry, finite mathematics, and numerous IB technology courses. I am also able to tutor gifted and advanced placement students, and assist with test prep for numerous SAT and PSAT placement tests. My other interests are science fiction and fantasy, role-playing games, and computer programming.
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Predicting the large-deflection path of tapered cantilever beams
A mathematical model for predicting the deflection path of both non-tapered and continuously tapered cantilever beams loaded with a vertical end force is presented. It is based on the proposition that the path is a function of the ratio of the endpoints’ moments of inertia. This was verified through physical testing, comparison to solution of the Bernoulli-Euler equation, and results obtained in finite element analysis. Predicted deflections were found to be accurate within 1.8% of the actual deflection path for moment of inertia ratios varying from 1:1 to 1000:1.


David Rosenberg is a data scientist in the Office of the CTO at Bloomberg and an Adjunct Professor at the Center for Data Science at New York University. Previously he was Chief Scientist at Sense Networks (acquired by YP), where he led development of location-based ad targeting and bidding strategies. He has consulted for Zillow and Aptima, and served as a scientific adviser to Discovereads (acquired by Goodreads and then Amazon). David received NYU's Center for Data Science "Professor of the Year" award in 2015 and 2016. He received his Ph.D. in Statistics from the University of California, Berkeley, where he worked on statistical learning theory and natural language processing. Previously, he received an S.M. in Applied Mathematics (Computer Science focus) from Harvard and a B.S. in Mathematics from Yale.
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1 edition of Theory of value, including the solution of the finance problem. found in the catalog.
Theory of value, including the solution of the finance problem.
|Contributions||YA Pamphlet Collection (Library of Congress)|
|LC Classifications||YA 14310|
|The Physical Object|
|Pagination||24 p. ;|
|Number of Pages||24|
|LC Control Number||96205933|
Budget theory in the public sector / edited by Aman Khan, and W. Bartley Hildreth. p. cm. Includes bibliographical references and index. ISBN 1–––0 (alk. paper) 1. Budget. 2. Finance, Public. I. Khan, Aman. II. Hildreth, W. Bartley, – HJB '8—dc21 British Library Cataloguing in Publication Data. Description Detailed guidance on the mathematics behind equity derivatives. Problems and Solutions in Mathematical Finance Volume II is an innovative reference for quantitative practitioners and students, providing guidance through a range of mathematical problems encountered in the finance industry. This volume focuses solely on equity derivatives problems, beginning with basic problems in.
This course introduces the core theory of modern financial economics and financial management, with a focus on capital markets and investments. Topics include functions of capital markets and financial intermediaries, asset valuation, fixed-income securities, common stocks, capital budgeting, diversification and portfolio selection, equilibrium pricing of risky assets, the theory of efficient. Solutions to Questions and Problems NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem isFile Size: 4MB.
Solution manual for Financial Management Theory and Practice Brigham Ehrhardt 13th edition Solution manual for Financial Management Theory and Practice Brigham Ehrhardt 13th edition 14e gives readers a thorough understanding of the essential concepts they need to develop and implement effective financial strategies. The book begins with. Financial Management: Theory and Practice celebrates the 23rd Anniversary of its publication. Over these two decades, Indian business and finance have considerably changed owing to deregulation, liberalisation, privatisation, globalisation, and the ascendance of the services sector. The book has kept pace with these changes and captures the central themes and concerns of corporate financial /5(10).
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Financial Management Theory and Practice--Solutions Manual book. Read 5 reviews from the world's largest community for readers. Solutions Manual/5. Problems and Solutions in Mathematical Finance Volume 2: Equity Derivatives is the second of a four-volume set of books focusing on problems and solutions in mathematical finance.
The first volume in the series introduced the reader to all the important concepts in probability and stochastic calculus.5/5(2). The text covers the basic mathematical theory of interest as traditionally developed. The book is a thorough treatment of the mathematical theory and practical applications of compound interest, or mathematics of by: Theory of Value.
Theory of value is a generic term that encompasses all the theories within economics that attempt to explain the exchange value or price of goods and services. Considering the unique attributes of digital value, in this book intrinsic digital value and extrinsic digital value are defined as: Extreme value theory is used.
SOLVED NUMERICAL PROBLEMS A company issues a 3-year zero-coupon bond with a face value of Rs 1,00, It is assumed that interest accrues twice a year. The investors wish to - Selection from Fundamentals of Financial Management, Including the solution of the finance problem.
book Edition [Book]. According to Figure from the book its value with a March expiration date is 11p. If Rolls-Royce issues a one-for-one stock split I would expect that the value of the March call option (for one share) to go to 11p/2 = p. Fora two-for-oneissue, I would expect the value of the underlying securityFile Size: 1MB.
Solution: Problem 2: ABC Ltd. has a choice between three projects: X, Y, Z. The following information has been estimated: Problem 3: XYZ Ltd. company has estimated unit variable cost of a product to be Rs. 10 and the selling price is Rs.
15 per : Shital P. Chapter 4 Time Value of Money Solutions to Problems. responsible for cash and credit management, capital budgeting, and financial planning. Therefore, the study of corporate finance is concentrated within the functions of the treasurer’s office. To maximize the current market value (share price) of the equity of the firm (whether it’s publicly traded or not).
Size: 1MB. With over 21 million homework solutions, you can also search our library to find similar homework problems & solutions. Try Chegg Study *Our experts' time to answer varies by subject & question.
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EXAM FM FINANCIAL MATHEMATICS. EXAM FM SAMPLE SOLUTIONS. This set of sample questions includes those published on the interest theory topic for use with previous versions of this examination. In addition, the following have been added to reflect the Solution: B. The book value at time 6 is the present value of.
future payments: 4 6 4. A brief discussion of the solvability theory of the initial value problem for ordi-nary differential equations is given in Chapter 1, where the concept of stability of differential equations is also introduced. The simplest numerical method, Euler’s method, is studied in Chapter 2.
File Size: 1MB. understand, analyze, and solve problems. The test of a model or theory then should not be based on its elegance but on its usefulness in problem solving. Second, there is little in corporate financial theory that is new and revolutionary.
The core principles of corporate finance are common sense and have changed little over time. The problems in this collection are drawn from problem sets and exams used in Finance Theory I at Sloan over the years.
They are created by many instructors of the course, including (but not limited to) Utpal Bhattacharya, Leonid Kogan, Gustavo Manso, Stew Myers, Anna Pavlova, Dimitri Vayanos and Jiang Size: KB. The subjective theory of value is a theory of value that believes that an item’s value depends on the consumer.
This theory states that an item’s value is not dependent on the labor that goes into a good, or any inherent property of the good. Mathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations.
These areas are generally introduced and developed at an abstract level, making it problematic when applying these techniques to practical issues in finance.
Value theory is important in its own right, which is sufficient reason to consider it, but consequentialism lacks content unless it is combined with a theory of value. It is important to distinguish the idea of an intrinsic good from the idea of an instrumental or extrinsic good.
Instrumental goods are good or valuable only because of something else they bring about—something that is good in. vi Mathematics for Finance systems of linear equations, add, multiply, transpose and invert matrices, and compute determinants.
In particular, as a reference in probability theory we recommend our book: M. Capi´nski and T. Zastawniak, Probability Through Problems, Springer-Verlag, New York, Major Theories in Finance Research Disclaimer: The opinions and views expressed presented in this talk are solely from the perspective of the designated authors and do not reflect the opinions or views of USM.
By Hooy Chee Wooi, PhDFile Size: 2MB. Unlike static PDF Loose Leaf For Finance: Applications And Theory 4th Edition solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step.
No need to wait for office hours or assignments to be graded to find out where you took a wrong turn.The financial theory develops the concepts and methods for financial problem solution.
As any other theory, it builds the models of real financial processes. Since such basic elements as time, value, risk, and criteria for choosing the desired distribution of resources obtain a.This introduction characterizes and positions value theory, or axiology, as a philosophical discipline.
It identifies its central issues and explains how value theory overlaps partly with other areas of moral philosophy, such as metaethics and normative etics, and how it relates other areas of philosophy. The introduction also explains how value theory branches out to disciplines outside of Author: Iwao Hirose, Jonas Olson.


Smart Ideas: Calculators Revisited
Math is probably one of the subjects that students get scared of. But there is no need to fear math, because math can be learned with patient study. This anxiety has to be overcome in order for a student to focus on learning and improving on his math skills, and the tutor needs to help the student through it. Tutoring must go on despite the students anxieties, you just need to help him through it while learning new math skills.
The first thing you should do is to assess the student’s math ability. It is important to begin your tutorial in a place he already knows, that’s why you need to begin at his skill level. In math, you need first to learn the basics before going into more complex items, for example, learn simple fractions first then how to reduce or simplify fractions.
It is important for the tutor to teach the student how to appreciate alignment to improve his math skills. This visual element in math will help the student solve math problems without using calculators. Writing down fractions in an orderly alignment on paper can help your student simplify fractions more easily. Aligning numbers in addition and multiplication is crucial. It takes a small amount of discipline to line up numbers in their proper columns, but it helps a great deal in addition and multiplication.
Learning The Secrets About Lessons
Here are some activities to use in your tutorials in order to help your student improve his math skills.
6 Facts About Calculators Everyone Thinks Are True
It has been found to be helpful for a student who struggles in math to use paper that is not lined, or simply a blank sheet of white paper. It has been found that lines can distract s student’s attention from the numbers because his eyes naturally get attracted to the lines. Anything that can be a cause of distraction should be removed or minimized to help the student concentrate on pure numbers.
Colored pens are helpful as aids to memorize step-by-step processes involved in math solutions. Marking different steps with different colored markers in solving problems helps the student master the step-by-step process that many solutions are done with. The student will learn to adjust his pace guided by the color changes.
After you have finished showing your student how the problem was solved, it’s time to let him do it by himself. It is important to let him use the same colored markers for every step in order for his mind to retain the process better. It is important for the student to learn the step-by-step process slowly by repeating it several times.
There’s no need to rush, learning one simple math skill at a time, whether it’s computing simple interest loans or weighted grades, it will improve his general ability. It also give him a good confidence boost, which is crucial in his learning.


Symmetry implies that both forelimbs and both hind limbs are used equivalently. A sound horse moving in a straight line and on a flat surface should have symmetrical movements. Indeed, he should apply the same weight to the left and right forelimb, and the same goes for the hind limbs.
Seaver measures the symmetry of your horse at the trot and in a straight line, in order to compare the two half-trot strides. They should be as similar as possible.
This datum is calculated every 5 seconds of straight line consecutive trotting, and is represented by a grade in % that evolves during the session. For a sound horse, the score is usually between 80 and 100%.
Figure1: Classic training session with distribution of notes throughout the session
It should be mentioned that calculations are made only when your horse is trotting for at least 5 seconds in a straight line. In other cases, this grade has no meaning and will have a value of 0 on the graph.
For example, when working in a small space (as is the case for the graph below, 20x30m indoor riding arena), this duration can only be reached on a perfectly straight diagonal. So do not worry if no score is obtained during this kind of session. It is the same for a lunging session or liberty training where it is rare to put the horse on a straight line long enough, even when changing circles.
Figure 2: Trot symmetry when working in a small space
You will also find, for each training session performed, an average grade (in %) corresponding to the symmetry on each of your horse’s diagonal pairs of legs. The ideal horse has a 50-50 distribution on each side, and thus has a symmetry grade of 100%.
We also give you the average duration in milliseconds of each of the half-strides; it allows a more precise comparison between the two diagonal pairs. The length of the right half-stride corresponds to the elapsed time between the moments the right diagonal pair (right foreleg and left hind leg) and then the left diagonal pair hit the ground.
Ideally, symmetry should increase throughout the session (horses are often less at ease at the beginning of the warm-up), and with training; the better trained the horse will be, the better he will be able to counterbalance his natural dissymmetry.
The symmetry figures will allow you to check if you horse moves symmetrically, and see the evolution of symmetry as you work and from one session to another.
In case of sudden decrease of symmetry over several sessions, it might be interesting to ask a professional (coach, vet, osteopath) for their opinion.
Please note that lateral work and outdoor training on deep or hard grounds can alter the symmetry grade.
The major benefit of the "symmetry" feature for any rider is to be able to detect a weakness or lameness before it is visible, and therefore act to prevent the problem from getting worse and allow for a faster recovery.
Indeed, the diagonal pair with the lowest percentage of the two is the one that spent the least time touching the ground. It is thus the ‘weak’ diagonal, on which the horse bears the least weight. Below 40%, it is likely that the horse is suffering from lameness.
It is useful to monitor the evolution of symmetry within the same session thanks to the graph. In addition, with the average you will be able to see this evolution for the different training sessions performed. The grade itself is of little importance, except to monitor the evolution, unless it falls below 40% in which case a lameness will likely to appear.
See you soon for a new article on a Seaver feature!
The Seaver team 🙂


Hironori Sakai is keen on data science. That is because it connects real problems with his expertise in mathematics. He would like to share power and pleasure from mathematics with you. In particular he is often thinking about how he can improve a recommender system and looking for an interesting and useful mathematical model.
- While he studied Mathematics at Tokyo Metropolitan University, he also enjoyed Linux/UNIX and CGI programming (in Perl).
- He learned a lot about presentation as a math teacher at Educa Ltd, one of the foremost preparatory school in Japan.
- After his PhD, he worked as a researcher at National Cheng Kung University (Taiwan), Max Planck Institute for Mathematics (Bonn) and the University of Münster.
- He started to work as a data scientist in Munich.
- He is a data scientist in Munich.
- I write scripts in R and Python for data mining at work/home.
- He writes a Perl module for data frames and statistical modelling: Arrow::DataFrame.
- He is on GitHub, Bitbucket, BibSonomy, Twitter, flickr and HackerRank (his notes).
- RSS for Maths Blog and Private Anecdotes.


How to calculate the length and weight of a resistance wire?
Known conditions, resistance wire length 1000mm, pitch 6mm, spiral outer diameter 20mm, wire diameter 3mm
1. Calculate the weight per meter of the heating wire
Wire diameter: 3.0mm
Material density: 7.1
Weight per meter = material density * cross-sectional area of the wire, namely: 7.1*(3.14*1.5*1.5)=50.162g/m
2. Calculate the length of the material used for the resistance wire
The length of the heating wire is 1000mm, the pitch is 6mm, the outer diameter of the spiral is 20mm, and the wire diameter is 3mm.
a. Number of spiral turns: 1000/6=166.66≈167 turns
b. The perimeter of each circle, the formula is C=πd, C=3.14*(20-3)=53.38mm
c. The length of an electric resistance wire: the number of spiral turns * the circumference of each turn, that is, 167 turns * 53.38 = 8914.46mm
3. Calculate the weight of the resistance wire
Weight per meter * length, namely: 50.162*8.91446≈448g/piece


Last night, playing West of Loathing, their newest game (available on all the coolest platforms) I came upon a broken elevator in Soupstock Lode.
I had a wrench and I could turn any of three nuts with it. The objective, apparently, was to adjust the steam pressure (or something like that) in order to get the elevator moving again. The trick was that each nut delivered a different value to the total. The first nut (Number 3) would add 411, the second (Number 5) would add 295, and the third (Number 7) would add 161.
But the target amount was hidden. It would only tell you when you had gone over, so you had to guess what the exact number was.
Monkeying around with the wrenches manually, I was able to get a rough idea of what the target number was (somewhere between 3,199 and 3,209), but nailing it this way seemed impossible. However, writing a short script seemed quite possible.First I defined a function to do the multiplication and addition:
def l(no3,no5,no7): sum = (no3 * 411) + (no5 * 295) + (no7 * 161) return sumThen I wrote a nest of 'for' loops three deep, arbitrarily assumed that I would not need to turn any of the nuts more than 10 times, and iterated over my function:
for i in range(10): for j in range(10): for k in range(10): sum = l(i,j,k) if sum > 3199 and sum < 3209: print(i,j,k,sum)
And the answer popped right out! I am so smrt.
Of course, the answer is probably somewhere close by in the game text, as it usually is, but this was way more fun I think!


So, let's set up some places here. However, memory does represent each byte as having a location, like an index into a list or array. The next 8 bits give us the exponent. And this two here, this two here is in the s place. Common applications include data validationdata scraping especially web scrapingdata wranglingsimple parsingthe production of syntax highlighting systems, and many other tasks.
Processors handle numbers in binary. For example, any implementation which allows the use of backreferences, or implements the various extensions introduced by Perl, must include some kind of backtracking. Although this may be a minor problem in small adders, with an increase in the number of bits in the binary words to be added, the time delay before the final carry out is produced becomes unacceptable.
Or most of us have 10 fingers. To me, this kind of opened my mind to the power of even our decimal system. So we can still call that the ones place. Google Code Search has been shut down as of January The oldest and fastest relies on a result in formal language theory that allows every nondeterministic finite automaton NFA to be transformed into a deterministic finite automaton DFA.
In two's complement if we try to add -5 and 5. The high-order digit is on the left, the low-order digit is on the right. We will have to settle for an approximation, rounding things to the 23rd digit.
Often called the decimal, the decimal number system. The only strange thing is that we again flip the bits and add 1, rather than subtracting 1 and then flipping the bits the reverse of what we did above. Another day goes by, then it rained. For scripts like Chinese, another distinction seems logical: For example, many implementations allow grouping subexpressions with parentheses and recalling the value they match in the same expression backreferences.
Uses[ edit ] Regexes are useful in a wide variety of text processing tasks, and more generally string processingwhere the data need not be textual.
You're probably familiar with scientific notation with base numbers. The reason why this is useful for computation is because all the hardware that we use to make our modern computers, all of the transistors and the logic gates they either result in an on or an off state.
A pattern like ". You multiply by 10, you go to the 10s place. So however many bundles you have you can use your fingers and eventually your symbols to think about how many there are.
If the bit is 0, the number is positive. The answer is We could call that the 16s place. Signed binary int to decimal conversion To convert a signed binary int to a decimal number, use the following algorithm. So, for example if you were an early human and you were trying to keep track of the days since it last rained you might say okay let's see it didn't rain today so one day has gone by, and we now use the word one, but they might have not used it back then.
Then we can go over here. However, in practice this is often not the case. Possessive matching[ edit ] In Java, quantifiers may be made possessive by appending a plus sign, which disables backing off, even if doing so would allow the overall match to succeed: Here, the bit is a 1, so the number is negative.
The result of this will be an 8-bit number in twos complement format, i.
With most other regex flavors, the term character class is used to describe what POSIX calls bracket expressions. The result of adding two positive numbers has produced a correct positive result with no carry and no overflow. The odd part is that when we flip the bits and add 1, we get the same number back again.
Extend the bit string to the appropriate length i. This is called the decimal system. We'll need to store this exponent -- however, using the two's complement, the usual representation for signed values, makes comparisons of these values more difficult.
For this reason, some people have taken to using the term regex, regexp, or simply pattern to describe the latter. One's complement of is Simply inverting 1 to 0 and 0 to 1.
Find Two's Complement of a Binary Number Using C programming. (0 or 1) without spaces up to Max 16 bits: Original Binary No 2's complement is About Author. Author: RajaSekhar.
Codes from the Author. Variables in C; C Program to Find Factorial of a Number. Fortran Decimal to Binary source code help I need help writing a program that will convert a decimal number to its twos complement binary representation.
The binary number should consist of 0's and 1's in acharacter string. C program to find the 2’s complement of a binary number.
Posted on October 12, by Sandeepa Nadahalli C Program to calculate the 2’s complement of a binary number. 2’s complement of a number is obtained by scanning it from right to left and complementing all the bits after the first appearance of a 1.
Sep 24, · To find the complement of a n-digit long number: (base)^n - 1 - number.
This is how subtraction is done using complementary method: 1. Find the complement of the subtrahend.
2. Add the complement to minuend. 3.
To find the two's complement of any number that is given in binary, you simply flip all the bits and add 1. In the case of $-5$ decimal, first convert to binary to get $$, then flip the bits to get $$, then add $1$ to get $$.
Q1) Using 5 bits to represent each number, write the representation of 7 and -7 in 1's complement, signed magnitude, and 2's complement integers. Q2)Write the 6-bit 2's complement representation of .Write ac program to find the 2s complement of a binary number


EURO CG 2000 REGISTRATION
16TH EUROPEAN WORKSHOP ON COMPUTATIONAL GEOMETRY
REGISTRATION (deadline February 25, 2000):
free for supported students (see Financial Support).
Payment by check either in US $,
EURO or NIS
Department of Mathematics and Computer Sciences,
mentioning "for EURO-CG2000 workshop on Computational Geometry"
Checks must arrive before February
25, 2000 .
Please, mail to
EURO CG 2000
16th European Workshop on Computational Geometry
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Ben-Gurion University of the Negev
All registrations will be acknowledged, when possible, by e-mail.
Registration fees include proceedings, reception, banquet and refreshments.
Please send us the following information
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You may notice that the answer key and additional problems are provided. HINT: You are going to have to find some missing angles within your triangles knowing that all of the angles in a triangle add up to degrees. It will be due on the day of the Exam Thursday. Corresponding Parts of Congruent Triangles are Congruent 3.
You can use Vertical Angles here. Rest of annotated Review Sheet in above link. Correction: 7 should read AB and CD intersect. If completed with these, try the problems that follow the packet with the definitions on the first page.
geometry - Why study quadrilaterals? - Mathematics Stack Exchange
Homework: None. Have a great extended weekend.
- On The Mountain Of Light;
- The Golems Eye (Bartimaeus Trilogy Book 2).
- 61 GRE Geometry Formulas and Rules You Must Know.
- Her Man Friday.
- Otolaryngology: Surgery in the Upper Airway: Trends in Technique and Technology (Audio-Digest Foundation Otorhinolaryngology Continuing Medical Education (CME) Book 43)?
Homework: Complete the rest of the questions in this packet. Here is an Additional Proofs Practice Worksheet that you can use to study tonight. Homework: Study for Quarter 2 Exam 1! Homework: None you can thank the fire alarm! Blank notes. The homework is at the end of this notes handout. Linked above. Test is on Wednesday! We tested today.
Annotated Notes. It is not written on the question. I will be checking your completed Review Sheets tomorrow.
CBSE Class 9 Math Solution,Notes,MCQ,Sample Questions
Homework: Handout. Be safe! A 36 B 54 C 72 D E none of the above. Find the distance between the trisection points of the segment joining —7, 10 and 5, —6. Solve for x.
GRE Prep Online Guides and Tips
Given two regular polygons joined as shown with a congruent side in common, what is the regular polygon with the largest number of sides that will fit without overlap into the "V" at the top of the diagram? A square B pentagon C hexagon D heptagon E octagon. Find the measure of each interior angle of a regular octagon. A 45 B 60 C D E insufficient information. Two sides of a triangle have lengths 6 and 8.
Which of the following could not be the length of the third side?
- How to find the perimeter of a parallelogram - ACT Math!
- The Growing Cage!
- An extension of the Easy Peasy All-in-One Homeschool.
- My Name Isnt Rufus?
- Falling Waters (Interactive Short Stories Book 3).
The diagram has the origin at its lower left corner, point P on the x -axis, and point Q on the y -axis. Segments RP and QS are vertical and horizontal, respectively. Prove that quadrilateral PQRS is a trapezoid and compute its perimeter show work.
Point, Line, Plane and Solid
The sum of the exterior angles of a regular polygon is What is the name of the polygon? A triangle B square C pentagon D hexagon E insufficient information. AB equals. A 2 B 2 x C 8 D 8 x E insufficient information. Given that Z 11, —11 is the midpoint of segment QR , where Q has coordinates 5, p and R has coordinates s , t , which of the following is true? In the diagram in 54, add point M midway between A and B , and assume that the conclusion of 54 has already been proved. Also assume that you have already computed AB , which is Match each of the labeled regions in the Venn diagram to the correct name below.
Refer to the diagram above.
Which of the following would be a correct way of denoting the empty set? Mark all that apply. Which of the following is the contrapositive of "When Woody is hungry, he eats everything in sight"? A If Woody is not hungry, he does not eat everything in sight. B If Woody is not eating everything in sight, he is not hungry. C If Woody is eating everything in sight, he is hungry. D If Woody is hungry, he is not necessarily eating everything in sight. E none of the above. Find a statement that is equivalent to the converse of the following statement: "Every American who is convicted of a serious crime will serve time in prison.
B If you serve time in prison, then you are either an American or a person who committed a serious crime or both. C If you serve time in prison, then you are neither an American nor a person who committed a serious crime.
You are here
D If you serve time in prison, then you are both an American and a person who committed a serious crime. For problems 63 through 68, write the name of the quadrilateral that most precisely describes plane figure ABCD. As you may know, the Washington Monument is feet tall.
How tall is the celebrity, and what league does he or she play in? Show a diagram and your work.
As has been known for millennia, the full moon occupies almost exactly the same apparent portion of the sky that the sun does. This remarkable coincidence is most noticeable during a solar eclipse, when only the faintest rim of the sun its corona is visible.


Feeling bored doing pages and pages of routine practice? Or uncertain about what to expect in H2/ H1 Mathematics since it is a compulsory subject to take?
At VJC, we hope to help you explore the beauty of Math by teaching towards Big Ideas, and guiding you through meaningful Learning Experiences to discover mathematical results on your own. You are expected to be disciplined and self-directed in your learning - lectures are hosted on the Student Learning Space (SLS) and you will have to be diligent in completing the lectures, online quizzes, tutorials and written assignments in your own time. In the classroom, our Mathematics teachers are proficient in using a range of pedagogical and ICT tools (Kami, OneNote, iPad etc) to support you in your learning, and are always ready to meet you for consultations if you need help. You will be using the graphing calculator as part of the examination requirements, and will be exposed to questions with context and real-life applications.
Be ready to come onboard the learning of Mathematics at VJC with an open and disciplined mind!


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This term we will be exploring the topic Predators.
In English we are learning to write non-chronological reports based on all the interesting facts we have learned about predators. We will also be writing dilemma stories and exploring different kinds of poetry.
In Maths we are focusing on telling time. We will be working on telling time to the nearest minute as a new thing for the children and we will be looking at digital and analogue clocks.
We have a lot of exciting and fun learning experiences planned for the children and we can't wait to dive in to this fantastic topic!


Vidya' teaching objectives emphasize a holistic, multi-disciplinary/interdisciplinary approach to water resources engineering. Dr. Samadi teaches courses related to engineering hydrology, geospatial modeling and GIS, and stochastic modeling and uncertainty. Some of my courses are listed below.
Review of basic probabilistic concepts; Uncertain phenomena, total probability and Bayes' theorems; Random events and random variables; Probability distributions, expectation, variance, skewness, and kurtosis; Statistical inference, parameter estimation and confidence intervals; Classical hypothesis testing for making statistical decisions;Stationary and nonstationary processes; and linear regression and model selection, etc.1 unit Lecture and 2 units lab.
Deterministic and Stochastic Processes in Hydrology; Probability Axioms; Moments and Expectations of Distributions; Introduction to Frequency Analysis, Frequency Analysis and Probability; Simple Linear Regression and Multi-variate Linear Regression, Evaluation of Regression; Hypothesis Testing to Compare Methods of Parameter Estimation for Frequency Distributions in Hydrology-Application to Infrastructure Design; Apply Multivariate Analysis in Hydrologic Systems; Principles of Time Series Modeling; Autoregressive Models (AR); Bayesian Uncertainty Estimation in Hydrological Modelling; Artificial Intelligence Techniques such as Neural Networks, Fuzzy Logic; Surrogate Models and Data Mining that form the "brains" of Smart Applications; IoT Applications in Water Resources. 2 units Lecture and 1 unit lab.
Spatial analysis in hydrology and hydraulics;Web-based mapping and information; Create a base map of a study region including watersheds, streams,and aquifers by selecting features from regional maps; Mathematical calculation on hydrologic/hydraulic geospatial maps using map algebra on raster grids; LIDAR data analysis and digital elevation model of land surface terrain to derive watersheds and stream networks; HEC-GeoHMS hydrologic modeling; Assimilation of ground-based and NASA satellite data into forecasting system;Hydraulic modeling using HEC-GeoRAS and velocity mapping in rivers and floodplains, etc.1 unit Lecture and 2 units lab.
Application of GIS and RS in hydrology; creating SCS Curve Number grid; Watershed and stream network delineation; Single-event and continues hydrologic simulation;Geospatial information for real-time operational hydrology; Flood control strategies and water resources management.
GIS and engineering applications (utility system maintenance, hydrologic and hydraulics modeling, water supply, stormwater quality monitoring/control, solid waste management and hazardous waste management); GIS analysis functions and operations (feature proximity, map algebra, spatial joins, etc.); ArcGIS Spatial Analyst Extension; Data Collection and Processing (Web services); ArcGIS Network Analyst Extension, network modeling and analysis, finding best routes, closest facility, service areas, dynamic segmentation and routing – applications to transportation engineering; ArcHydro Tools Extension; RS data manipulation and analysis; Application of RS and GIS for point and non - point pollution, etc.1 unit Lecture and 2 units lab.