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Study of radiation transfer using the computational educational manual on Monte Carlo methods
It is well-known that Monte Carlo methods are used for solving various urgent problems in mathematical physics. A lot of new numerical stochastic algorithms and models were elaborated in Institute
of Computational Mathematics and Mathematical Geophysics (ICM and MG) SD RAS during last years. The Monte Carlo schemes can be effectively illustrated on computer and presented for students. On the
other hand, the special instrumental environment based on hypertext technology is developed in ICM and MG. These computer tools can be used for elaboration of training mathematical courses.
Now the electronic manual "Foundations of Monte Carlo methods" is developed in ICM and MG for students of Novosibirsk State University. This manual is based on lectures of Prof. G.A. Mikhailov and
Dr. A.V. Voytishek. The central themes of this course are:
• methods of realization of generators of standard random and pseudo-random numbers,
• methods of numerical modeling of discrete and continuous stochastic values (including standard and special algorithms for discrete values; the reverse distribution function method, randomization
and rejection technique for continuous values),
• numerical realization of stochastic vectors,
• methods of modeling of stochastic processes and fields,
• methods of calculation of multiple integrals,
• numerical methods of solution of the integral equations of the second kind,
• numerical solution of equations of mathematical physics,
• applications of Monte Carlo methods (including problems of the radiation transform theory).
The manual is divided in lessons containing many illustrations, diagrams, model tasks, exercises, questions, and comments.
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Parallel Pipe Flow Calculator - Calculator Wow
Parallel Pipe Flow Calculator
In fluid dynamics, calculating the total flow rate in a system with multiple parallel pipes is essential for effective system design and operation. The Parallel Pipe Flow Calculator simplifies this
task by providing a straightforward method to compute the total flow rate when two or more pipes are operating in parallel. By summing the flow rates of individual pipes, this tool helps engineers,
designers, and operators ensure that their systems are balanced and functioning efficiently. This article explores the significance of the Parallel Pipe Flow Calculator, explains how to use it, and
answers common questions about its application.
Importance of the Parallel Pipe Flow Calculator
The Parallel Pipe Flow Calculator is a crucial tool in various fields such as hydraulics, civil engineering, and industrial processes. Its importance can be highlighted through the following points:
1. System Design Optimization: Accurate calculation of total flow rates helps in designing systems with appropriate pipe sizes and configurations, ensuring optimal performance and avoiding potential
2. Efficiency Improvement: By determining the combined flow rate, engineers can balance the flow across multiple pipes, leading to more efficient operation and reduced energy consumption.
3. Troubleshooting: Identifying discrepancies in flow rates can help in diagnosing issues in piping systems, such as blockages or leaks, enabling timely maintenance and repairs.
4. Regulatory Compliance: For industries subject to regulatory standards, accurate flow measurements are essential for compliance with environmental and safety regulations.
How to Use a Parallel Pipe Flow Calculator
Using a Parallel Pipe Flow Calculator is simple and involves the following steps:
1. Enter Flow Rate in Pipe 1: Input the flow rate for the first pipe in gallons per minute (GPM) into the designated field.
2. Enter Flow Rate in Pipe 2: Input the flow rate for the second pipe in gallons per minute (GPM) into the designated field.
3. Calculate Total Flow Rate: Click the calculate button to determine the total flow rate. The calculator will use the formula Q total = Q1 + Q2 to compute the combined flow rate.
4. Review the Result: The result, displayed in a read-only field, shows the total flow rate in gallons per minute, reflecting the sum of the individual pipe flow rates.
FAQs and Answers
1. What is a Parallel Pipe Flow Calculator?
A Parallel Pipe Flow Calculator determines the total flow rate in a system with multiple parallel pipes by summing the flow rates of each pipe.
2. What formula does the calculator use?
The formula used is Q total = Q1 + Q2, where Q1 and Q2 are the flow rates of Pipe 1 and Pipe 2, respectively.
3. Can this calculator handle more than two pipes?
The basic calculator provided handles two pipes. For more than two pipes, you would sum the flow rates of all pipes manually or use an extended calculator.
4. How accurate is the result from this calculator?
The accuracy of the result depends on the precision of the input values. Ensure that the flow rates are entered correctly to get an accurate total flow rate.
5. What if the flow rate is zero?
If the flow rate of one or both pipes is zero, the calculator will still provide a result based on the non-zero values, reflecting the total flow from the active pipes.
6. Can this calculator be used for different units?
This calculator is set for gallons per minute (GPM). For other units, such as liters per second, you would need a conversion tool or a calculator that supports those units.
7. What should I do if I encounter an error in calculation?
Double-check the input values and ensure they are numbers. If the issue persists, review the calculator’s functionality or consult additional resources.
8. Is there a limit to the values I can enter?
The calculator can handle a wide range of values, but extremely large or small numbers may affect readability and practical application.
9. How does this calculator aid in system design?
It helps in designing systems by ensuring that the total flow rate is accurately determined, allowing for proper sizing and balancing of pipes.
10. Can this tool be used for both residential and industrial applications?
Yes, the calculator is useful for both residential and industrial applications where accurate flow rate calculations are needed for parallel piping systems.
The Parallel Pipe Flow Calculator is an invaluable tool for anyone working with systems that involve parallel piping. By accurately computing the total flow rate, this calculator aids in designing
efficient systems, improving operational performance, and ensuring compliance with regulations. Understanding and utilizing this tool enhances the ability to manage fluid distribution effectively and
optimize system performance. Whether for engineering applications, system troubleshooting, or design purposes, the Parallel Pipe Flow Calculator simplifies the process and ensures accurate results.
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Generate Time-Optimal Trajectories with Constraints Using TOPP-RA Solver
This example shows how to generate trajectories that satisfy velocity and acceleration limits. The example uses the contopptraj function, which solves a constrained time-optimal path parametrized
(TOPP) trajectory using reachability analysis (RA).
This example solves a TOPP problem, which is a robotics problem in which the goal is to find the fastest way to traverse a path subject to system constraints. In this example, you use the contopptraj
function which solves a TOPP problem subject to velocity and acceleration constraints by using a method based on reachability analysis (RA), coined TOPP-RA [1]. Other methods to solve TOPP problems
rely on numerical integration (NI) or convex optimization (CO). Applications of TOPP include:
• Re-timing a joint-space trajectory for a manipulator to meet manufacturer-provided kinematic constraints.
• Generating a joint-space trajectory that returns fast and optimal trajectories given a planned path.
• Optimizing the traversal of a mobile robot path in SE(3) given limits on its motion.
You can use the contopptraj function in these ways:
• Generate a trajectory that connects waypoints while satisfying velocity and acceleration limits. In this case, use a minimum jerk trajectory as the initial guess. For more information, see Create
Kinematically Constrained Trajectory.
• Re-parameterize an existing trajectory while preserving its timing given velocity and acceleration constraints. The path, which consists of waypoints in the N-dimensional input space, is a
trajectory of any kind. The contopptraj function then scales how the robot navigates the path in the same time, mapping the existing trajectory to a new one that solves the TOPP problem.
In this example, you update an existing trajectory that connects five 2-D waypoints. The initial path is interpolated with an initial trajectory based on a quintic polynomial, which provides the
shape. You then use the contopptraj function to apply velocity and acceleration limits to the initial path.
Define Waypoints and Initial Trajectory
Both trajectories connect the same set of waypoints, subject to a set of velocity and acceleration limits. Specify the waypoints.
waypts = (deg2rad(30))*[-1 1 2 -1 -1.5; 1 0 -1 -1.1 1];
Different trajectories have different geometric and kinematic attributes, which affects how they navigate a path in space. The Choose Trajectories for Manipulator Paths example illustrates some
differences between the various trajectory functions provided in Robotics System Toolbox™.
For this example, use a quintic polynomial trajectory to connect the waypoints. The quintic polynomial connects segments by using smooth velocity and acceleration profiles.
tpts = [0 1 2 3 5];
timeVec = linspace(tpts(1),tpts(end),100);
[q1,qd1,qdd1,pp1] = quinticpolytraj(waypts,tpts,timeVec);
Refine Trajectory Using Constrained TOPP-RA Solver
The quintic polynomial produces an output that, with default parameters, stops at each waypoint. You can use a TOPP-RA solver to compute the fastest possible way to traverse the path while still
stopping at each waypoint, given bounded velocity and acceleration. Use the contopptraj function to generate a trajectory that traverses the initial path as quickly as possible while satisfying the
specified velocity and acceleration limits.
vellim = [-40 40; -25 25];
accellim = [-10 10; -10 10];
[q2,qd2,qdd2,t2] = contopptraj(pp1,vellim,accellim,numsamples=100);
Plot the initial and modified trajectory on the same plot. Notice how the TOPP-RA solver speeds up the trajectory while still satisfying the known constraints.
% Create a figure and adjust the color order so that the second two lines
% have the same color as the associated first two lines
c = colororder("default");
c(3:4,:) = c(1:2,:);
% Plot results
hold on
legend("Quintic 1","Quintic 2","Constrained 1","Constrained 2")
title("Joint Configuration")
xlim([0 tpts(end)])
hold on
title("Joint Velocity")
xlim([0 tpts(end)])
hold on
title("Joint Acceleration")
xlabel("Time (s)")
xlim([0 tpts(end)])
1. Pham, Hung, and Quang-Cuong Pham. “A New Approach to Time-Optimal Path Parameterization Based on Reachability Analysis.” IEEE Transactions on Robotics, 34, no. 3 (June 2018): 645–59. https://
See Also
Related Topics
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We need an instrument to take a measurement
Are instrumental variables worth the effort?
In lecture yesterday, rather than ranting about the failures of regression, I tried to find a positive spin on causal methods. The Freedman critique deserves a month-long deep dive, and I’ll save
that for next semester. Instead, I tried to explain how some of these bad ideas come from good intentions, and I attempted to present a simple derivation of LATE, the Local Average Treatment Effect.
I had other plans too! But this surprisingly took the entire lecture.
Today, I want to summarize what we concluded. LATE is a clever observation but requires a lot of care to explain. Alone in randomized experiments, it doesn’t buy you much over the standard analysis.
But it has warped the minds of economists who have decided it gives them license to extract cause through cleverness.
In its simplest form, the LATE is a way to estimate the causal effect of a treatment that an experiment can only indirectly probe. Using our causal graphs from Tuesday, suppose that we can apply an
intervention, labeled here by Z. Z can cause the treatment we care about to happen, here labeled T. And this treatment T has some associated outcome Y. We’d like to measure the effect of T on Y.
The running example I used in class was cancer screening, but this model applies to almost any randomized clinical trial. In a trial, Z is the randomization, whether a person is assigned to treatment
or control. Once randomized, a patient is offered a treatment T. Some patients accept the treatment, but some may decline. In the trial, we are not randomly assigning patients to receive a treatment.
We’re randomly assigning them to be offered treatment.
This seems like a minor point, but it messes up our statistics. If we drop all of the patients who decline treatment and compute a treatment effect as though they weren’t there, we’ll end up with a
biased estimate of the treatment effect. Patients who decline treatment are likely different than those who accept it. Perhaps they are more sick or of different education levels. There are a variety
of confounding explanations.
There are two remedies to remove this bias. The first and the simplest is called the intention to treat principle. This principle demands we only estimate the effect of offering treatment on outcome.
That is, if we intervene using Z, we should only estimate the effect of Z on Y. Yes, this is indirect. But the estimate is unbiased and unconfounded. And if huge numbers of patients are rejecting
your treatment offer, then maybe your treatment isn’t as great as you think it is.
There’s an alternative remedy that uses statistics to cleverly estimate the effect of T directly, the LATE. What we’d like to do in advance is filter our trial to only the people who would ever
accept our treatment and then look at the benefits in this winnowed subpopulation. Let S[A] denote this subpopulation of people who would accept your treatment. Though you don’t know what S[A ]is in
advance, LATE will provide a path to estimating the local effect of the treatment in this unknown subpopulation.
To apply LATE we have to assume:
1. The causal graph we drew is valid, so Z has no direct effect on Y, but Z has some effect on T.
2. The only people who receive treatment T are those who are offered it.
Assumption 1 is very reasonable. Assumption 2 is stronger than what is needed to apply LATE in general, but it’s reasonable in the context of a clinical trial, and it makes for a cleaner presentation
in this short blog form.
With these two assumptions, we can derive the following relationship:
\(\frac{1}{|S_A|} \sum_{i \in S_A} Y_i(T=1)-Y_i(T=0) =\frac{\frac{1}{n} \sum_{i=1}^n Y_i(Z=1) - Y_i(Z=0)} {\frac{1}{n} \sum_{i=1}^n T_i(Z=1) - T_i(Z=0)}\)
In words, this identity says that the treatment effect on the subpopulation who would accept treatment is equal to the ratio of the Intention-to-treat effect that we observe divided by the fraction
of people who would accept treatment. Or, in other other words, the indirect effect of T on Y is equal to the effect of Z on Y divided by the effect of Z on T.
What’s nice about this formula is that we can use the standard estimators of average treatment effects to estimate the right-hand side of the LATE formula from trial data:
\(\frac{\#~\text{outcomes in treatment}-\#~\text{outcomes in control}} {\#~\text{who accepted treatment}}\)
In randomized clinical trials, the LATE estimate is the standard estimate of absolute risk reduction using the intention to treat principle divided by the fraction of people who accepted treatment.
Now, what does this buy us? As a medical conservative, my take is this tells us that we should just report the intention to treat analysis in clinical trials. It is reassuring that a LATE analysis
can’t turn an insignificant result into a significant one (i.e., the confidence interval for LATE will contain 0 whenever the confidence interval for ITT does). At best we’re just going to increase
our risk reduction estimate by a small factor.
We did an example in class from the New York Health Insurance Plan trial of breast cancer screening. In this trial, only two thirds of the participants accepted the offer to receive a mammogram. The
risk reduction of breast cancer death within five years of randomization using intention-to-treat analysis was 0.08%. Applying LATE, this number moved to 0.12%. Kevin Ma asked, “Is that good?” It’s a
great question. The answer is in the eye of the beholder. I personally like the fact that LATE, which gives a more direct estimate of the effect we care about, doesn’t move the needle much. This
should be reassuring for trialists.
Now, the problem with LATE is it has emboldened people (mostly in economics) to invent crazy thought experiments and present then as “rigorous” or “credible.” They assume that you can use this to
pretend you randomized when you didn’t. Consider this dumb causal model for the sake of argument:
\(Y_i = T_i \beta + C_i\)
Here β is the treatment effect we’d hope to estimate, but C is some confounding variable, possibly unobserved, and we’d like to remove its influence. But now let’s assume we have some magical
variance Z that satisfies
\(\mathbb{E}[ZT] \neq 0 ~~\text{but}~~ \mathbb{E}[ZC] = 0\)
Then, if we multiply everything in our model by Z and take expected values, we’ll find the expression
\(\beta = \frac{\mathbb{E}[ZY]}{\mathbb{E}[ZT]}\)
This is precisely the LATE estimator. I’ve just written it this time with expected value notation instead of using sums. LATE has convinced people that they can just search for “instruments” Z that
occur in nature to estimate all sorts of things from observational data. We want to estimate the effect of the number of police on crime, and use election years as the instrument because mayors
deploy more forces during election years. We want to estimate the effect of family size on child outcomes, so we use the birth of twins as an instrument. The list goes on and on.
All of these observational papers are certainly nonsense. They are stories dressed up with hundreds of pages of statistical robustness checks. When the instrument is intentionally randomized by the
investigator, instrumental variables are useful statistical tools to estimate indirect effects. But let’s not pretend there is any value to the fanciful instruments hallucinated by the imaginative
armchair experimenter.
Extra points for the Fugazi reference.
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Basic Maths Formulas | Important Mathematics Formulae Sheet & TablesBasic Maths Formulas | Important Mathematics Formulae Sheet & Tables
Learn a Comprehensive Approach to Solve Math Problems using Formulas provided. Feel free to use them during your homework and finish the entire syllabus in a unique way. All the Mathematics Formulas
provided are given by subject experts after enormous research. People of any mathematical knowledge can get help from here using the Math Formula Sheet. The Formulas provided are not just used in
Academic Books but also in our day to day lives.
How do Math Formulae help you?
Not just Students and Teachers anybody who wishes to brush up their Math Skills can look up to the Math Formulas prevailing. Sit back and relax as Onlinecalculator.guru has got your back. There are
several pros of referring to Mathematics Formula and get to know them. They are outlined as under
• Empowers people to have hands-on practice thus scoring better in their exams.
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It is indeed necessary to learn Maths Formulae as you can use them while solving your problems and arrive at the solution effortlessly.
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By Memorizing the Math Formulas you can solve the problems quickly and efficiently. In fact, you can finish your entire syllabus in a smart way by learning the Maths Formula Cheat Sheet.
4. Where can I get all the Important Maths Formulas?
You can get all the Important Maths Formulas on our page organized as per the relevant topics.
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1. Compute the normalised load admittance and enter it on the smith chart
yl=(1/zl)=(R0/Zl)= (2+3.732j)
2.Draw a SWR circle throuh the point of yl so that he circle intersects the unity circle at the point yd.
yd= (1-2.6j)
Note that there are infinite number of yd.Take the one that allows the stub to be attached as closely as possible to the load
3. Since the charcteristic impedance of the stub is different from that of the line ,the condition for impedance matching at the junction requires Y11=Yd + Ys ,where Ys is the susceptance that the stub will contribute.
It is clear that the stub and the portion of the line from the load to the junction are in parallel,as seen by the main line extending to the generator.The admittances must be converted to normalised values for matching on the smith chart.Then Eq(3-6-2) becomes
y11*Y0= yd*Y0 + ys*y0s
ys=(y11-yd)*(Y0/Y0s)= 5.2j
4. The distance between the load and the stub position can be calculated from the distance scale as
d=(0.302-0.215)*lambda= 0.087 lambda
5. Since the stub contributes a susceptance of +j5.20 ,enter +j5.20 on the chart and determine the required distance l from the short circuited end(z=0,y=infinity),which corresponds to the right side of the real axis on the chart,by transversing the chart towards the generator until the point of +j5.20 is reached.
Then l=(0.5 -0.031)lambda =0.469 lambda.
When a line is matched at the junction ,there will be no standing wave in the line from the stub to the generator
6. If an inductive stub is required
y'd = 1+j2.6
and the susceptance will be
y's =-j5.2
7. The position of the stub from the load is
d'=(0.5-(0.215-0.198))lambda = 0.483 lambda
and the length of the short-circuted stub is
l'=0.031 lambda
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From Register Machines to Brainfuck, part 2
7 September 2010 (
programming haskell brainfuck language
This is a continuation of my previous post on register machines vs. Brainfuck programs. We left off at Brainfuck's supposed Turing-completeness.
Now, the most straightforward way to prove Turing-completeness of a given language is to write a compiler that takes a program written in a language that is already known to be Turing-complete, and
creates a program written in the language to be proved Turing-complete, that simulates the original program. So an obvious way to prove that Brainfuck is a Turing-complete language is to compile
register machine programs into Brainfuck. This has the added advantage that a programmer having some experience in real-world assembly programming can easily write register machine programs, which
can then be compiled into (horribly inefficient and over-complicated, as we'll see) Brainfuck programs.
Important note: Of course, to really prove, in a mathematical sense, that Brainfuck is Turing-complete, we would first have to define formal operational semantics for register machines and Brainfuck
programs to be even able to argue about simulating one with the another. In this post, I will appeal to intuition instead.
So how does one simulate a register machine (RM for short) using Brainfuck? The first idea is that since a given RM program can only reference a finite number of variables, we can lay them out in the
linear array of memory cells provided by the Brainfuck model. So we can assign e.g. cell number #0 to a, #1 to b and #2 to z, and any operation working on z first increments the pointer twice (i.e.
>> in Brainfuck notation), then does something, then decrements the pointer twice (<<) to get it back to the initial state. So for the line
clr z,
we can write
Similarly, we can compile
dec b
Enter Loop
In fact, to make further work simpler, we can devise an intermediate language that has constructs similar to Brainfuck, but that uses named registers instead of a linear array. The language called
Loop has the following statements:
• inc r, dec r, clr r
• while r stmts: Repeatedly execute the statements in the body as long as the value of r is non-zero.
• out r, in r
Once all the registers are laid out in the linear memory, compiling this to Brainfuck is trivial.
From RM to Loop
As we've previously noted, the other major difference between RM and Brainfuck is that Brainfuck programs can't directly control their execution sequence. If your Brainfuck program contains "<++" at
the next position, you can be 100% sure that the pointer will move left and then increment the cell twice, and there is nothing you can do about it. Contrast this with RM's jmp and jz instructions
that can change the statement that gets executed next.
To reconcile this difference, the key idea is to start thinking about RM programs in a different way. Instead of a sequential list of instructions with possible jumps between, let's look at it as an
n-ary branch switching on some special register called a Program Counter. So for the following program that adds a to b:
1. clr tmp
2. jz a 7
3. dec a
4. inc tmp
5. inc b
6. jmp 2
7. jz z 11
8. dec tmp
9. inc a
10. jmp 7
11. Done.
we can also imagine it as the following program, written in some unspecified pseudo-code:
pc ← 1
while pc ≠ 11 loop
switch pc
case 1:
clr tmp
pc ← 2
case 2:
if a = 0 then
pc ← 7
pc ← 3
case 3:
dec a
pc ← 4
case 4:
inc z
pc ← 5
case 5:
inc b
pc ← 6
case 6:
pc ← 2
case 7:
if z = 0 then
pc ← 11
pc ← 8
case 8:
dec z
pc ← 9
case 9:
inc a
pc ← 10
case 10:
pc ← 7
end loop
At first glance, we don't seem to be any closer to our goal, since now we have to implement if and switch in Loop. First, let's observe that it makes no difference if several values of the pc
register are handled in a single iteration of the outermost loop. Using this observation, and getting rid of some superfluous partitioning of statements, the above can be rewritten as the following:
pc ← 1
while pc ≠ 11 loop
if pc = 1 then
clr tmp
pc ← 2
if pc = 2 then
if a = 0 then
pc ← 7
pc ← 3
if pc = 3 then
dec a
inc tmp
inc b
pc ← 2
if pc = 7 then
if tmp = 0 then
pc ← 11
pc ← 8
if pc = 8 then
dec tmp
inc a
pc ← 7
end loop
We've eliminated the need for switch, and all our if branches fall in one of the following two categories:
• Testing if the special register pc equals a given predeterminate value
• Testing if a given register is non-zero
The first kind of test we can simulate by using not just one pc register, but one for each possible value of pc, taking values of 0 or 1. So we enforce the invariant that pc[i] is 1 iff the virtual
pc register equals i. Then we can use while loops for branching by testing for pc[i] and then immediately after, decrementing it, thus ensuring that the loop runs at most once. The above program thus
Note the special handling of pc[11] which gets decremented first, to -1, so that incrementing it later exits the main loop.
We are inching closer and closer to our destination – we just need a way to increment one of two pc registers based on the value of some other, non-pc register. Solving this requires some trickery
because we can only use loops for testing if a given register is zero, but then we have to zero it out unless we want to get into an infinite loop. The solution is similar to what we do in our
original adding example, by using a separate register as temporary storage. Suppose we want to translate the following piece of code:
Using a temporary buffer, it is possible to run two loops that by the end preserve the register a's initial value, but allow us to change other registers in the process. We will use two
special-purpose registers Z and NZ to signal if the value of a is zero or non-zero. First, we set up Z:
inc Z
inc NZ
while a loop
dec a
inc Buffer
clr Z
end loop
while Buffer loop
dec Buffer
inc a
end loop
By that point, a retained its original value, but Z is 1 iff a is zero at the start. So now we can discriminate between the two cases using yet more loops:
while Z loop
dec Z
inc pc
Note how the loop for Z decrements NZ, thereby preventing the other branch from running.
Wrapping it up
We've now arrived at a valid Loop program, which can readily be translated into a Brainfuck program. I've implemented an RM → Loop → Brainfuck compiler using the above scheme in my Brainfuck toolbox.
One surprising aspect of the above is that the resulting Brainfuck program, while hideously complicated and large, doesn't perform that bad. Maya was kind enough to write a register machine program
solving the 9-digit problem (source here), and I compiled it into x86 assembly via the Brainfuck route, to compare it with his native Brainfuck solution. Let's look at program size first: the native
one is 4,591 instructions long, and the one compiled from RM comes in at a whopping 480,466 instructions. However, both implementations showed runtime performance in the same order of magnitude.
Unfortunately, I don't have a corpus of algorithms implemented in both RM and Brainfuck lying around, so I can't do any real benchmarks. But compared to my initial expectations, the result of the
9-digit program is promising: I figured this whole RM → Brainfuck compiler scheme would turn out to be a strictly theoretical result, creating Brainfuck programs that are so slow to be completely
Epilogue: I wanted to write some Agda-checked proofs that the compiler actually generated equivalent programs. As it turned out, this is not so easy. I hope I'll have time to get back to this problem
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HP 15C and INT(1/√(1-x),0,1)
01-13-2018, 01:35 AM
Post: #41
Carsen Posts: 206
Member Joined: Jan 2017
RE: HP 15C and INT(1/√(1-x),0,1)
(01-12-2018 10:57 AM)Dieter Wrote:
(11-27-2017 01:33 AM)Carsen Wrote: Then I set the 15C to a fix of 4 and attempted to integrate the integral again. In a time of 16 minutes and 28 seconds, I stopped the 15C and didn't get an
answer as a result.
In fact you can get the current approximation of the integral during a running calculation. This is described in appendix E of the 15C manual ("Owner's Handbook", p. 257 of the English version):
"Obtaining the Current Approximation to an Integral".
Is that so? I guess I'll have to pilfer my Dad's HP-15C and Handbook for a few days and break open my calculus book and notes. There are a lot of techniques I do not know about regarding the HP-15C
but I fully intend to eventually. The Voyager Series is so elegant and perfect (close to perfect, that is).
01-14-2018, 09:37 AM
Post: #42
Didier Lachieze Posts: 1,658
Senior Member Joined: Dec 2013
RE: HP 15C and INT(1/√(1-x),0,1)
(01-14-2018 09:20 AM)Mike (Stgt) Wrote: So the clock frequency range is named as difference. Still looking for the values.
From Craig Finseth
hp-15c page
The clock speed is about 220kHz and on the HP-41 is about 340kHz (60% faster).
01-14-2018, 10:30 AM
Post: #43
grsbanks Posts: 1,219
Senior Member Joined: Jan 2017
RE: HP 15C and INT(1/√(1-x),0,1)
(01-12-2018 04:18 AM)JimP Wrote: I tried the DM15 (SwissMicros) with FIX2 and received the 1.99 answer within 30 seconds -- clearly faster. Then thought I'd try to split the difference between
your tests with FIX3. The machine shut down before it could give an answer, 5 minutes later...
Are you sure the battery isn't just dead on your DM15?
I ran that same test on mine and got the answer of 1.99 (FIX 2) in 8 seconds, 1.999 (FIX 3) in 61s and 1.9999 (FIX 4) in 478s.
This is on a DM15L (exactly the same electronics and firmware as a DM15) on firmware V24 running at 48MHz. There is no real advantage to running the calculator at 12MHz because, while the drain on
the battery may be slower at a lower frequency, it takes longer to get things done anyway so you're no better off energy-wise at the end of the day.
01-17-2018, 05:06 AM
Post: #44
Didier Lachieze Posts: 1,658
Senior Member Joined: Dec 2013
RE: HP 15C and INT(1/√(1-x),0,1)
From the HP-41C service manual, page 2-1:
The nominal oscillator frequency of 1440 kHz is reduced by
a factor of 4 to produce a system operating frequency between
343 and 378 kHz
And from the 1LF5-0301/1LF5-002 CPU detailed description, page 3-4:
The 1LE3 CPU is designed for 41C and 11C, 12C calculator.
At wafer and package level, their part numbers are designated as follows:
Wafer: 1LF5-01 (11C, 12C) 1LF5-03 (41C)
Package: 1LF5-0301 (11C, 12C) 1LF5-002 (41C)
The difference between the two parts are programmed at metal mask [...]
The operating range of the two chips are also different and are
summarized as follow:
41C Clock frequency range: 340 to 380 kHz
11C, 12C Clock frequency range: 200 to 230 kHz
Both documents are available on TOS.
01-17-2018, 01:12 PM
(This post was last modified: 01-17-2018 01:13 PM by Didier Lachieze.)
Post: #45
Didier Lachieze Posts: 1,658
Senior Member Joined: Dec 2013
RE: HP 15C and INT(1/√(1-x),0,1)
(01-17-2018 12:03 PM)Mike (Stgt) Wrote: Hmm... what makes me uncertain about the MCode instruction count shown by my 'firmware interpreter'.
Why? For the Voyagers this is up to ~3950 MCode instructions per second, knowing that between key press the CPU goes to sleep.
01-17-2018, 07:07 PM
Post: #46
Dieter Posts: 2,397
Senior Member Joined: Dec 2013
RE: HP 15C and INT(1/√(1-x),0,1)
(01-17-2018 05:41 PM)Mike (Stgt) Wrote: Why? -- I ran the 8-Queens programs for the HP41 and HP15C you find in here on a 'firmware interpreter' to count the MCode instructions (not the user
program steps). When - for the HP15C - I find 18,210,956 MCode instructions and divide it by the ~3950 MCode instructions per second you named I get 4,610 seconds or 1 hr and ~17 min what is
within 2 minutes of the value shown in the a. m. link.
The numbers seem plausible, but this does not neccessarily mean that the calculation is correct. ;-) I still wonder if the 15C really is
slow. Compare it to the 34C: the two given programs are virtually identical (the 15C version even requires one step less) but the 15C is slighty slower. The 34C was my first HP calculator, so I know
that it is not very fast and slower than the HP67. But is the 15C really even slower?
Maybe someone with a physical (and original) 15C can try the program listed on the linked webpage and see if it really takes almost 80 minutes to finish.
01-17-2018, 08:49 PM
Post: #47
TheKaneB Posts: 175
Member Joined: Jul 2014
RE: HP 15C and INT(1/√(1-x),0,1)
I have a 15C, original made in USA. I can do the test for you, if you can post the link with the code again, since I'm lost in all the replies and I am not sure where to look!
Software Failure: Guru Meditation
01-17-2018, 09:22 PM
(This post was last modified: 01-17-2018 09:23 PM by Dieter.)
Post: #48
Dieter Posts: 2,397
Senior Member Joined: Dec 2013
RE: HP 15C and INT(1/√(1-x),0,1)
(01-17-2018 08:49 PM)TheKaneB Wrote: I have a 15C, original made in USA. I can do the test for you, if you can post the link with the code again, since I'm lost in all the replies and I am not
sure where to look!
Here you are:
8-queens benchmark in the original Articles Forum
Simply do a browser search for "15C" there and find the program about halfway down the page, where it says
HP-15C LE
The following program is supposed to run in about 80 minutes on a regular 15C.
01-17-2018, 09:38 PM
Post: #49
TheKaneB Posts: 175
Member Joined: Jul 2014
RE: HP 15C and INT(1/√(1-x),0,1)
Ok, I have the calculator running. We'll see how it goes
Software Failure: Guru Meditation
01-17-2018, 10:35 PM
(This post was last modified: 01-17-2018 10:59 PM by TheKaneB.)
Post: #50
TheKaneB Posts: 175
Member Joined: Jul 2014
RE: HP 15C and INT(1/√(1-x),0,1)
EDIT: 1h 18m 45s ( +/- 1 s)
While we're waiting for the result (still running) I should mention that the code for the 15C of that benchmark is very bad. It doesn't take advantage of the built in looping instructions (ISG and
DSE), while the 41C version does. So the two times are not comparable.
I think we should rewrite the code with some optimization. I bet we can make it much faster than that
HP 15C code
HP-15C LE
8 STO .0
LBL 0 RCL 0 RCL .0
TEST 5 GTO 4
1 STO+ 0
RCL 0 STO I
RCL .0 STO(i)
LBL 1 1 STO+ .1
RCL 0 STO 9
LBL 2 1 STO- 9
RCL 9 x=0? GTO 0
RCL 0 STO I RCL(i)
RCL 9 STO I
Rv RCL(i) -
x=0? GTO 3
ABS RCL 0 RCL 9 -
TEST 6 GTO 2
LBL 3 RCL 0 STO I
1 STO-(i)
RCL(i) TEST 0 GTO 1
1 STO- 0
RCL 0 TEST 0 GTO 3
LBL 4 RCL .1
HP 41C code
HP-71B / HP-41 Translator ROM Module HP-82490A
8 STO 11
LBL 00 RCL 00 RCL 11
X=Y? GTO 04
ISG 00 DEG
STO IND 00
LBL 01 ISG 10 DEG
RCL 00 STO 09
LBL 02 DSE 09 DEG
RCL 09 X=0? GTO 00
RCL IND 00 RCL IND 09 -
X=0? GTO 03
ABS RCL 00 RCL 09 -
X<>Y? GTO 02
LBL 03 DSE IND 00 GTO 01
DSE 00 GTO 03
LBL 04 RCL 10
Software Failure: Guru Meditation
01-18-2018, 12:22 AM
(This post was last modified: 01-18-2018 12:23 AM by TheKaneB.)
Post: #51
TheKaneB Posts: 175
Member Joined: Jul 2014
RE: HP 15C and INT(1/√(1-x),0,1)
No, I didn't care to optimize it, it was just food for thought
24 seconds in 79 minutes is VERY underwhelming though...
Software Failure: Guru Meditation
01-21-2018, 03:57 PM
(This post was last modified: 01-21-2018 05:44 PM by TheKaneB.)
Post: #52
TheKaneB Posts: 175
Member Joined: Jul 2014
RE: HP 15C and INT(1/√(1-x),0,1)
Back to the original topic:
I used a C implementation of the Romberg algorithm to find the integral of
f(x) = 1 / sqrt(1 - x) over the interval 0 - 1
It runs for a relatively long time (several seconds on my 3 GHz Intel i5) and it came up with this result:
result = 2.000052194143781214563660
function evaluations = 1073741825 (1 billion of function evaluations!)
I set an accuracy of 0.0001 with max steps = 100. I also used the interval from 0 to 0.99999999999 or else it would evaluate to NAN.
If i set an accuracy of 0.01 I get this:
result = 2.005444550190635499831160
function evaluations = 16777217
#include <stdio.h>
#include <math.h>
dump_row(size_t i, double *R){
printf("R[%2zu] = ", i);
for(size_t j = 0; j <= i; ++j){
printf("%.12f ", R[j]);
romberg(double (*f/* function to integrate */)(double), double /*lower limit*/ a, double /*upper limit*/ b, size_t max_steps, double /*desired accuracy*/ acc){
double R1[max_steps], R2[max_steps]; //buffers
double *Rp = &R1[0], *Rc = &R2[0]; //Rp is previous row, Rc is current row
double h = (b-a); //step size
Rp[0] = (f(a) + f(b))*h*.5; //first trapezoidal step
dump_row(0, Rp);
for(size_t i = 1; i < max_steps; ++i){
h /= 2.;
double c = 0;
size_t ep = 1 << (i-1); //2^(n-1)
for(size_t j = 1; j <= ep; ++j){
c += f(a+(2*j-1)*h);
Rc[0] = h*c + .5*Rp[0]; //R(i,0)
for(size_t j = 1; j <= i; ++j){
double n_k = pow(4, j);
Rc[j] = (n_k*Rc[j-1] - Rp[j-1])/(n_k-1); //compute R(i,j)
//Dump ith column of R, R[i,i] is the best estimate so far
dump_row(i, Rc);
if(i > 1 && fabs(Rp[i-1]-Rc[i]) < acc){
return Rc[i-1];
//swap Rn and Rc as we only need the last row
double *rt = Rp;
Rp = Rc;
Rc = rt;
return Rp[max_steps-1]; //return our best guess
int functionCounter = 0;
double myfunc(double x) {
double l = 1 / sqrt( 1 - x );
return l;
int main() {
printf("result = %.24f\nfunction evaluations = %d\n", romberg(&myfunc, 0, 0.99999999999, 100, 0.0001), functionCounter);
The code source is from wikipedia:
Software Failure: Guru Meditation
01-21-2018, 04:46 PM
Post: #53
Thomas Okken Posts: 1,896
Senior Member Joined: Feb 2014
RE: HP 15C and INT(1/√(1-x),0,1)
(01-21-2018 03:57 PM)TheKaneB Wrote: I used a C implementation of the Romberg algorithm to find the integral of
f(x) = 1 / sqrt(1 / x) over the interval 0 - 1
It runs for a relatively long time (several seconds on my 3 GHz Intel i5) and it came up with this result:
result = 2.000052194143781214563660
function evaluations = 1073741825 (1 billion of function evaluations!)
I set an accuracy of 0.0001 with max steps = 100. I also used the interval from 0 to 0.99999999999 or else it would evaluate to NAN.
If i set an accuracy of 0.01 I get this:
result = 2.005444550190635499831160
function evaluations = 16777217
(I'm assuming the f(x) = 1 / sqrt(1 / x) is a typo?)
There's room for improvement there. The Romberg implementation in Free42, based on code written by Hugh Steers, reaches those levels of accuracy with 32767 and 255 evaluations, respectively.
I used ACC = 0.000025 and 0.0025, respectively, since Free42 treats ACC as a relative error, and using 0.0001 and 0.01 produce results that are less accurate than your examples.
01-21-2018, 05:11 PM
Post: #54
TheKaneB Posts: 175
Member Joined: Jul 2014
RE: HP 15C and INT(1/√(1-x),0,1)
yes that was a typo, see the code for reference.
Software Failure: Guru Meditation
07-20-2018, 01:04 PM
Post: #55
Thomas Klemm Posts: 2,268
Senior Member Joined: Dec 2013
RE: HP 15C and INT(1/√(1-x),0,1)
has on page 47 a section about:
Transformation of Variables
Quote:In many problems where the function changes very slowly over most of a very wide interval of integration, a suitable transformation of variables may decrease the time required to calculate
the integral.
You can use \(x=1-t^2\) which leads to:
\[ \begin{eqnarray}
dx&=&-2t\cdot dt \\
\sqrt{1-x}&=&t \\
\int_0^1\frac{1}{\sqrt{1-x}}dx&=&\int_1^0\frac{-2t}{t}dt \\
&=&2\int_0^1dt \\
&=&2t\bigg\vert_0^1 \\
\end{eqnarray} \]
Or then use \(x=\cos^2(t)\) which leads to:
\[ \begin{eqnarray} \\
dx&=&-2\cos(t)\sin(t)dt \\
\sqrt{1-x}&=&\sin(t) \\
\int_0^1\frac{1}{\sqrt{1-x}}dx&=&\int_{\frac{\pi}{2}}^0\frac{-2\cos(t)\sin(t)}{\sin(t)}dt \\
&=&2\int_0^{\frac{\pi}{2}}\cos(t)dt \\
&=&2\sin(t)\bigg\vert_0^{\frac{\pi}{2}} \\
\end{eqnarray} \]
In both cases the resulting function can be integrated without problems.
It's just a coincidence that both integrals can also be calculated easily algebraically.
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Using ARRAYFORMULA with Custom Functions
In this tutorial, I will show you how to combine ARRAYFORMULA with custom functions in Google Sheets to process entire columns efficiently. This technique is particularly useful for applying
calculations to large datasets.
By using ARRAYFORMULA and custom functions, you can significantly improve your spreadsheet's performance and scalability. This approach reduces the number of individual function calls and speeds up
recalculations, making it ideal for spreadsheets with lots of data.
We will walk through creating a custom function that applies a discount to prices, then use ARRAYFORMULA to apply this function to an entire column simultaneously. You'll also learn how to handle
both single-cell and array inputs in your custom functions.
This tutorial assumes the following prerequisites:
5 steps to supercharge your spreadsheets with ARRAYFORMULA and custom functions
Step 1 — Create a sample dataset
Let's start by creating a sample dataset that we'll use throughout this tutorial. We'll create a simple spreadsheet with a list of products and their prices.
• Open a new Google Sheets spreadsheet.
• In cell A1, type "Product".
• In cell B1, type "Price (USD)".
• Fill in some sample data in columns A and B, starting from row 2.
• In cell F2, type "Discount".
• In cell G2, enter the discount percentage. For this example, let's use 20%, so enter 20%.
Step 2 — Write a custom function
Now, let's create a custom function that will apply a dynamic discount to our product prices. We'll write a function that takes a price and a discount percentage as input and returns the discounted
• Click on "Extensions" in the top menu, then select "Apps Script".
• In the Apps Script editor, replace the default code with the following:
* Applies a discount to the given price.
* @customfunction
function APPLY_DISCOUNT(price, discount) {
if (Array.isArray(price)) {
return price.map(function(row) {
return row.map(function(price) {
return typeof price === "number" ? price * (1 - discount) : null;
} else {
return typeof price === "number" ? price * (1 - discount) : null;
• Click on "Save" and give your project a name, such as "Dynamic Discount Calculator".
This custom function, APPLY_DISCOUNT, is designed to handle both single values and arrays of prices. Let's break down how it works (I cover this in detail later on in this post):
• The function takes two parameters: price (which can be a single number or an array of numbers) and discount (a number representing the discount).
• If price is an array (which happens when used with ARRAYFORMULA), it uses nested map functions to process each element.
• The discount is applied by multiplying the price by (1 - discount).
• If price is a single value, it simply applies the discount if it's a number, or returns null if it's not.
Step 3 — Apply the custom function using ARRAYFORMULA
Now let's use ARRAYFORMULA to apply our custom function to the entire "Price" column at once, using the dynamic discount percentage.
• Go back to your Google Sheets spreadsheet.
• In cell C1, type "Discounted Price (USD)".
• In cell C2, enter the following formula:
This formula does the following:
• ARRAYFORMULA() applies the formula to the entire range at once.
• APPLY_DISCOUNT(B2:B,$G$2) calls our custom function, passing the entire B2:B range as the price input and the discount percentage from cell G2.
Step 4 — Test and verify the results
After entering the formula, you should see the discounted prices appear instantly in column C for all your products.
Step 5 — Compare performance
To illustrate the performance benefits of using ARRAYFORMULA, let's compare two approaches:
• Using ARRAYFORMULA
• Using regular formula without ARRAYFORMULA
Create two sheets in your spreadsheet, each containing 500 rows of product data. In the first sheet, use the ARRAYFORMULA approach we just implemented. In the second, apply the custom function to
each cell individually without ARRAYFORMULA.
You'll notice that using ARRAYFORMULA makes the calculations much faster.
To see the difference in action, change the discount percentage in cell G2. Observe that the sheet without ARRAYFORMULA takes noticeably longer to update all 500 cells. Notice how the first sheet
with ARRAYFORMULA updates almost instantly. This performance difference becomes even more pronounced with larger datasets or more complex calculations.
Here is a screencast of the sheet without ARRAYFORMULA. Observe that several cells are still "Loading…" several seconds after I update the discount percentage.
Now, when you use ARRAYFORMULA, the calculations are much faster and the entire column is updated in a single operation almost immediately.
Why ARRAYFORMULA is Much Faster
• Batched Computations: ARRAYFORMULA allows Google Sheets to process the entire range of data in one batch. This means our custom function is called only once with a large array of inputs, rather
than being called 500 times individually.
• Efficient Sheet Updates: When using ARRAYFORMULA, Google Sheets can update the entire column of results in one operation. Without ARRAYFORMULA, the sheet must update 500 individual cells, each
triggering its own update event.
• Reduced Recalculation Overhead: When a change occurs (e.g., updating the discount percentage), ARRAYFORMULA requires only one recalculation for the entire column. The regular formula approach
would trigger 500 separate recalculations.
How this code works
The APPLY_DISCOUNT function is designed to handle both single values and arrays of prices, making it versatile for different use cases in Google Sheets. Let's break down the function and explore its
* Applies a discount to the given price.
* @customfunction
function APPLY_DISCOUNT(price, discount) {
if (Array.isArray(price)) {
return price.map(function(row) {
return row.map(function(price) {
return typeof price === "number" ? price * (1 - discount) : null;
} else {
return typeof price === "number" ? price * (1 - discount) : null;
Input Types and Function Behavior
Function Declaration
function APPLY_DISCOUNT(price, discount) {
The function takes two parameters: price (which can be a single number or an array of numbers) and discount (a decimal representing the discount percentage).
Array Check
if (Array.isArray(price)) {
This condition checks if the price parameter is an array. This will be true when the function is called via ARRAYFORMULA.
Handling Array Input
return price.map(function(row) {
return row.map(function(price) {
return typeof price === "number" ? price * (1 - discount) : null;
If price is an array (ARRAYFORMULA case):
• The outer map function iterates over each row of the 2D array.
• The inner map function processes each price in that row.
• For each price, it checks if it's a number using typeof price === "number".
• If it's a number, it applies the discount: price * (1 - discount).
• If it's not a number, it returns null to handle empty or non-numeric cells.
Handling Single Value Input
} else {
return typeof price === "number" ? price * (1 - discount) : null;
If price is not an array (regular cell formula case):
• It checks if the price is a number.
• If it is, it applies the discount and returns the result.
• If it's not a number, it returns null.
@customfunction Annotation
* @customfunction
This JSDoc annotation tells Google Sheets that this function can be used as a custom function in spreadsheet formulas. If this annotation is not specified, the function cannot be used in spreadsheet
Handling Empty and Invalid Inputs
A key aspect of this function is how it handles empty or invalid inputs by returning null. This behavior is important for maintaining clean and meaningful outputs in your spreadsheet, especially when
working with ARRAYFORMULA.
Why return null?
• Empty Cell Handling: When the function encounters an empty cell in the input range, typeof price will not be "number". Returning null ensures that the corresponding output cell remains empty,
rather than displaying an error or unwanted value.
• Preserving Spreadsheet Layout: This approach helps maintain the visual structure of your spreadsheet by not filling unused cells with zeros or error messages.
• Error Prevention: For non-numeric inputs (like text in a price column), returning null prevents calculation errors from propagating through your spreadsheet.
Note: In some situations you might want the function to return an error when it encounters invalid input. Therefore, this behavior is use case-specific.
Use Case Example
Consider a scenario where column A has data from rows 2 to 50, and you're using an ARRAYFORMULA that calls this function with the range A2:A:
=ARRAYFORMULA(APPLY_DISCOUNT(A2:A, $G$2))
In this case:
• For rows 2 to 50, where data exists, the function will calculate the prices normally.
• For rows 51 and beyond, where cells in A51:A are empty, the function will return null for each empty cell.
This behavior ensures that:
• The ARRAYFORMULA doesn't fill the entire column with unnecessary values (such as 0).
• Empty input cells result in empty output cells, preserving the spreadsheet's readability.
• If there are any non-numeric values in A2:A50 (like text or errors), these will also result in empty cells in the output.
In this tutorial, I showed you how to combine the power of ARRAYFORMULA with custom functions to process entire columns efficiently in Google Sheets. This technique can significantly improve the
performance of your spreadsheets, especially when dealing with large datasets or complex calculations.
By using ARRAYFORMULA with custom functions, you can:
• Process entire columns in one go, improving efficiency.
• Handle both single cell inputs and array inputs in your custom functions.
• Reduce the number of function calls, leading to faster calculations.
• Create more maintainable and scalable spreadsheets.
Thanks for reading!
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Have feedback for me?
I'd appreciate any feedback you can give me regarding this post.
Was it useful? Are there any errors or was something confusing? Would you like me to write a post about a related topic? Any other feedback is also welcome. Thank you so much!
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Inverted Pendulum | Rapid Control Prototyping
Inverted Pendulum
Stabilization of an inverted pendulum is a common engineering challenge. Objective is to build a low-cost DIY^1 platform to test various feedback control loop.
This document describes the hardware and the theoretical model of the pendulum. Simulation are presented with Simulink models and an LQR^2 feedback control loop finally stabilizes the platform.
Video of the stabilized platform with a 4 state LQR feedback loop. The platform is completely autonomous (no user input).
The electronic placed at the top of the pendulum composed of a dsPIC 16 bits microcontroller and an inertial sensor (accelerometers and rate gyro). The base of the pendulum is a modified RC toys
comprising two wheels driven by two independent DC motor (see pictures below).
The head and the base trolley are described successively. They are separated with an $8mm$ carbon tube. The pendulum length is $0.52m$ from wheel axis to the top. Wheels diameters is $8cm$. Pendulum
total weight is $200g$ comprising $111g$ for the 4 AA batteries.
Head electronics
The controller is a Microstick II board equipped with a dsPIC 33EP128MC202 running at $70\ MIPS$. It is powered through the USB connector which only provide the power supply from 4 AA batteries hold
in the base.
Microcontroller and sensor on top of the inverted pendulum
A prototyping board support a Microstick II board with the dsPIC 33EP128MC202. A board from Drotek endowing the Invensense ICM-20608 inertial sensor is screwed on the base board.
IMU sensor
The unique sensor used is the 6 DoF^3 Invensense ICM-20608 mounted on a Drotek sensor board. It endows:
• a 3 axis Accelerometers and
• a 3 axis rate gyros.
The I2C blocks set the BUS clock at $400kHz$ and fetch the 6 sensors values every $1ms$ $(1kHz)$. The Simulink I2C blocks setting enable hot plug of the I2C sensor: The microcontroller initializes
the sensor each time it is newly detected on the I2C bus.
• The accelerometer is configured with a range of $\pm 8g$ low pass filtered at $99Hz$.
• The rage gyro is configured with a range of $\pm 500 \deg/s$ low pass filtered at $250Hz$.
A Simulink IMU^4 sub-system run a data fusion algorithm to reconstruct a drift-free quaternion angular position at $1kHz$ (the yaw angle drift when magnetometer is not present). The stabilization
control loop uses the drift-free pitch angle.
It is possible to use other sensors like the MPU9250 or MPU6050 with either an I2C or SPI interface. The GY-91 board is a 10 DoF^3 widespread board based on the 9 DoF MPU9250 (3 accelerometers, 3
magnetometers, 3 rate gyros) and has a pressure sensor.
UART interface
The PCB board provides a $3.3V$ regulator and 4 pin extra interface ( GND, +3.3v, Tx, Rx ) to connect either an UART data-logger or radio link for telemetry module or an RC receiver capable of S.BUS,
Smart Port or P.Port protocol (all UART based).
Base trolley
The base trolley is a low cost a 2-wheel remote control toy named flywheels. The toy is from 2012 but 2 wheeled equivalents exist. Its electronics is removed. Two pairs of wires power two DC motors
in either direction through an L298N H bridge board module.
Power electronics
The L298N H bridge controls two DC motors. For each motor:
• Two logic signals set the 4 states: direction CW or CCW, brake, or freewheel.
• The third logic signal power the motor depending on to the state defined.
The third signal is modulated with a 100Hz square periodic signal whose duty cycle vary from 0% to 100% (PWM). It sets the torque for the motor.
The flat multicolor ribbon connects 6 logic control signals (3 for each motor) from the Microstick II dsPIC output to the of the L298N H bridge.
Base trolley of the inverted pendulum
A L298N H bridge (for Arduino) power board drives the two DC motors of a modified FlyWheels toy. Four AA batteries powers the pendulum.
Four $1.2V$ AA Ni-Mh batteries are dispatched on both side of the trolley. $\approx 4.8V$ powers the motors and the electronics. The black and red wire from the trolley to the top of the pendulum
powers the Microstick II electronic and sensors.
Pendulum Model
The pendulum model is composed of two intertwined sub-system:
• The pendulum*, with 1 rotation DoF^3 $\theta$ angle around the wheel’s axis
• The trolley*, with 1 translation DoF^3 $x$ position.
Pendulum free body diagram
$\vec{P}$ is the weight at the center of gravity. $\vec{R}$ is the reaction force from the stiff rod and the floor. $\vec{F}$ is a friction force when the pendulum is rotating. $\{ \vec{i},\vec{j} \}
$ is the earth frame and $\{ \vec{r},\vec{n} \}$ is the rotating pendulum frame. The inertial sensors are placed on top of the pendulum and measure all accelerations.
Pendul Equations
The Dynamic fundamental law applied on the pendulum: $$ \sum \vec{Force} = m.\vec{a} $$
The three forces presents are the weight $\vec{P}$, the Friction $\vec{F}$, and the Reaction $\vec{R}$ from the rod & floor:
$$ \underbrace{ -mg\vec{j} }_{\vec{P}} \ - \ \underbrace{ k \frac{\partial \vec{r}}{\partial t} }_{\vec{F}} \ + \ \underbrace{ ( mg\vec{j} . \vec{r} + \underbrace{Ctfg}_{\text{Centrifugal}} } _{\vec
{R} } ) . \vec{r} = ml \frac{\partial^2\vec{ r }}{\partial t^2} $$
With $ \{ \vec{i},\vec{j} \} $ the static earth frame and $ \{ \vec{r},\vec{n} \} $ the pendulum frame (rod and normal direction). $m$ is the mass of the pendulum (without the trolley). $l$ is the
length from the inter-wheel’s axis to the center of mass of the pendulum (without the trolley)
$$ \left\{ \begin{array}{rcl} \vec{i} & = & \vec{n} . cos(\theta) - \vec{r} . sin(\theta) \\\ \vec{j} & = & \vec{n} . sin(\theta) + \vec{r} . cos(\theta) \end{array} \right. $$
$$\vec{j}.\vec{r} = cos(\theta)$$
Considering the rotation $\theta$, the first and second time derivative of $\vec{r}$ are:
$$ \begin{array}{rcl} \frac{\partial \vec{r}}{\partial t} & = & - \dot{\theta} \vec{n} \\\ \frac{\partial^2\vec{ r }}{\partial t^2} & = & - \frac{\partial }{\partial t} \left( \dot{\theta} \vec{n} \
right) \\\ & = & - \ddot{\theta} \vec{n} - \dot{\theta}^2 \vec{r} \end{array} $$
The projection of the forces equation in the pendulum frame $ \{ \vec{r},\vec{n} \} $ is: $$ \left\{ \begin{array}{rcl} \left( ml\dot{\theta}^2 + Ctfg \right) \vec{r} = \vec{0} \\\ \left( l \ddot{\
theta} + \frac{k}{m}\dot{\theta} - g . sin(\theta) \right) \vec{n} = \vec{0}
\end{array} \right. $$
The first equation for the $\vec{r}$ axis shows internal forces which cancel each other: the weight $\vec{P} = -mg\vec{j}$ which is compensated on the $\vec{r}$ axis by the term $mg\vec{j}.\vec{r}$
from the reaction force which will also compensate for the Centrifugal force $ml\dot{\theta}^2$.
The second differential equation on the $\vec{n}$ axis allows to solve for the evolution of the angle $\theta$. It can be made linear with $sin(\theta) \approx \theta$ when the pendulum is up near
$0$, or with $sin(\theta) \approx - (\theta - \pi)$ when the pendulum is down near $\pi$.
Pendulum model for rod rotation
non-linear model of the $\theta$ angle evolution derived from the forces projected on the normal $\vec{n}$ axis of the rod. The trolley linear acceleration input is added.
The linear approximation for $\theta$ in the laplace domain is a $2^{nd}$ order system: $$ \theta(s) \left ( \frac{1}{w_n^2}s^2 + \frac{2 \zeta}{w_n}s \pm 1 \right ) = 0 $$
The pendulum transfer function $F_p = \frac{\theta(s)}{E(s)}$ with a null input $E(s) = 1$ $$ F_p(s) = \frac{1}{ \frac{1}{w_n^2}s^2 + \frac{2 \zeta}{w_n}s \pm 1 } $$
The linear term for $sin$ is positive when the pendulum is up when $\theta \approx 0$ (unstable), and negative when pendulum is down when $\theta \approx \pm \pi$ (stable).
This transfer function is characterized when the pendulum is down by its natural frequency $w_n = \sqrt{ \frac{g}{l} } $, and a damping factor $\zeta$.
Pendul identification
The parameter $l$ could be estimated from the platform mechanical but the damping parameter $\zeta$ (or frictions coefficient $k$) could not be estimated easily from the platform.
The simulation model is satisfactory when the calculation it performs make realistic prediction. Experimental measurement is a good method to refine a model and tune its parameters. In our case, the
parameters $l$ and $\zeta$ (or $k$) are identified from the experiment explained below.
Experimental logs
The pendulum is placed on a track (two chairs back to back) to be able to make a complete rotation. Motor are off and the pendulum is released up-side with in the unstable condition ($\theta = -18°$
, $\dot \theta = 0$).
It oscillates until the damping friction ($\zeta$) stops the free oscillations.
The $1kHz$ sampled rate gyro and accelerometers values are recorded onboard an openlager board connected on the dsPIC UART interface.
Simulation from logs
The measured inertial sensors are then re-used as data source in a Simulink model. $\theta$ angle is reconstructed using an IMU complementary filter algorithm implemented in the quaternion angle
The pendulum model is initialized with the experimentation initial condition ($\theta = -18°$ , $\dot \theta = 0$). Trolley linear acceleration input is null. Parameters $l$ and $k$ are iteratively
tuned until the model $\hat{\theta}$ angle fit with the measured oscillation $\theta$.
Identification - experimental $\theta$ angle reconstructed from inertial sensors (wide grey curve) vs pendulum model (read and blue dashed curves)
$\theta$ angle from free oscillation experiment is compared against two pendulum models. The pendulum is released at time $16.7s$ upside ($18°$) and let free to oscillate. The grey curve is the
experimental angle reference reconstructed from inertial sensors measurements. The blue dashed curve is a pendulum model using a linear damping with $k = 0.4$. The red doted curve use a nonlinear
damping with the nonlinear term -1.1*$sign(\dot{\theta})$ added to the linear damping with $k = 0.17$.
Pendulum Parameters Identified Value
$l$ $0.45 m$
$k$ $0.4$
$w_n = \sqrt{\frac{g}{l}}$ $4.67\ rad.s^{-1}$ ( $0.74 Hz$ or $1.35s$ period )
⬆ Identified pendulum parameters
Validation and IMU improvement
Parameters $l$ and $k$ can be further validated using the force equation and the estimated pendulum angle $\theta$.
The IMU input measurements is composed of the rate gyro and the accelerometers data. Magnetometers is not used in this pendulum example. The IMU input also require the predicted acceleration vector
(resp magnetometer is used). The IMU output the sensor orientation and provides the gravity vector prediction as seen in the sensor estimated attitude (i.e. quaternion angle).
Comparing the gravity vector predicted with the accelerometer’s measurement do not match because the sensor measures both the gravity plus the dynamic acceleration induced by the pendulum movements.
Considering the pendulum principal movement rotation $\theta$, the equations of forces applied on the pendulum derive from $\hat \theta$ a prediction for the dynamic acceleration. The good match
between the predicted acceleration and the experimental measurement confirm somehow the correctness of parameters $l$ and $k$ involved in these calculations.
The updated acceleration comprising both a static and dynamic part is fed into the IMU algorithm improving the IMU correction of the rate gyro integration drift even when the pendulum is not static.
Trolley Model
Trolley Equations
Below is under construction 🚧
The translational movement of the trolley is modeled as a $1^{st}$ order system characterized by its time constant $\tau$. This dynamic includes the motor dynamics when it is loaded with the trolley
considering the pendulum as vertical.
The model considers as negligible the effect of the pendulum forces (translational and rotational) applied on the trolley.
$$ x(s) = \frac{1}{\tau s + 1} $$
Trolley Identification
Trolley Parameter Estimated Value
$\tau$ $0.3s$
The trolley does not have any sensors. No encoder or current sensor are used to control the two motors. The parameters $\tau$ is “guessed” in a first step. In a second step, a $2^{nd}$ inertial
sensor board is temporary glued in the middle of the wheel diameter to as the inertial sensor is in the wheel rotation axe. An identification can be computed from the motor set-point and the wheel
movements while the pendulum was actively controlled up by a first feedback loop.
Still the pendulum model including the trolley is simulated with its feedback loop controller and results are compared against recorded data of the real system running the same feedback loop
controller. The simulated pendulum states are re-initialized periodically ($\approx 2s$) with the real pendulum states as the model would diverge otherwise due to perturbations not modeled and model
discrepancies. Correctness of the model can be checked between theses periodic re-initialization.
Identification of trolley in real inverted pendulum condition.
The angular speed rate of the wheel is measured with one rate gyro form one added GY-91 sensor board. The GY-91 board is hot glued on one pendulum wheel. The pendulum is stabilized with a controller
using an estimated trolley model. Four wires from the GY-91 to the microcontroller power the sensor and retrieve sensor data through the I2C bus (2 wires).
Stabilization overview: The microcontroller computes the angle of the pendulum from the inertial sensor measurements (accelerometers and rate gyro). A feedback loop stabilizes the pendulum up right
while maintaining the pendulum position still. The pendulum translation is estimated through an internal dynamic model of the trolley stimulated with a copy of the DC motor command. The pendulum slow
translations reflect the drift of the internal estimation of the displacement.
Linearized model
LQR feedback controller
Video of the inverted Pendulum when it encounters a wall:
Another way to stabilize a pendulum with an electric seesaw (video).
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Formal mathematical analysis
From Encyclopedia of Mathematics
An axiomatic theory aimed at formalizing (cf. Formalization method) mathematical analysis. The aim is to construct a formal axiomatic theory with minimum possible deductive and expressive strength,
but still sufficient for formalizing all the traditional material of mathematical analysis.
The most extensively developed version of formal mathematical analysis, due to D. Hilbert and P. Bernays (see [1]), can be described as follows. To the language of classical formal arithmetic (cf.
Arithmetic, formal) one adds a new kind of variables $X,Y,Z,\dots,$ which are regarded as running over sets of natural numbers. One adds a new kind of atomic formulas: $(t\in X)$ ("belonging to the
set X"). The logical axioms of formal arithmetic and the axiom scheme of induction are naturally strengthened in such a way as to include the formulas of the extended language. Finally, one adds a
single new axiom scheme — the axiom scheme of comprehension:
$$\exists X\forall y(y\in X\equiv A(y)),$$
where $A(y)$ is a formula of the language in question not containing $X$ freely and $y$ is a variable for a natural number.
This theory (the so-called Hilbert–Bernays theory; in it one speaks of natural numbers and sets of natural numbers) is sufficient for a natural formalization of mathematical analysis. It is an
interesting problem to provide a foundation for the consistency of the Hilbert–Bernays theory by methods that are constructive to a sufficient degree. According to the Gödel incompleteness theorem,
this cannot be done without using means that go beyond the limits of formal mathematical analysis. C. Spector (see [3]) succeeded in proving the consistency of this theory by means of a modification
of the Gödel interpretation for intuitionistic arithmetic (see Gödel interpretation of intuitionistic arithmetic), which is a certain far-reaching extension of the requirements of intuitionism. The
fundamental difficulties in attempts to prove the consistency of the Hilbert–Bernays theory are connected with a special feature of the comprehension axiom of that theory, i.e. that in the formula $A
(y)$ occurring in the axiom scheme of comprehension one is allowed to make free use of quantifiers over sets. Thus, in clarifying whether a number $y$ belongs to a set $X$ being defined in the axiom,
it is necessary to use the availability of all sets of natural numbers, among which is the set $X$ that is being defined. One could say that the comprehension axiom of formal analysis expresses to a
certain degree the necessity for all sets actually to exist simultaneously.
This special feature (it is encountered in several set-theoretic formal theories) is called non-predicativity of a theory. Hilbert–Bernays formal analysis is a non-predicative analysis.
In order to remove the non-predicativity, various formal axiomatic theories of predicative (or ramified) analysis have been proposed. For example, in one of the most widely used formulations, going
back to H. Weyl, one considers variables of the form $X^m,Y^k,\dots,$ with natural numbers as the superscripts. The variables are regarded as running over sets of natural numbers. The axiom scheme of
comprehension in this theory has the form
$$\exists X^m\forall y(y\in X^m\equiv A(y)),$$
where the bound set variables in $A(y)$ have index $<m$, and the free set variables have index $\leq m$. Thus, sets of natural numbers in predicative analysis, essentially speaking, split (are
"ramified") into layers, with sets in a higher layer being defined only in terms of sets in lower layers (and sets in the given layer that have already been defined). It is comparatively easy to
prove the consistency of ramified analysis by constructive methods, but the simplicity of this theory is achieved at a high price: ramified analysis is less well-suited to formalization, and the
analogue of a theorem of formal mathematical analysis always assumes an unnatural form in predicative analysis. E.g., the least upper bound of a bounded set of real numbers is defined in an
essentially non-predicative way.
There is an equivalent formulation of non-predicative Hilbert–Bernays analysis in which functions mapping natural numbers to natural numbers figure along with sets of natural numbers. Namely, for
functions of this kind one adjoins to formal arithmetic the variables $\alpha,\beta,\gamma,\dots,$ and a new kind of terms: $\alpha(t)$ ("the result of applying a to t"); the logical axioms and the
axiom scheme of induction are naturally extended to the formulas of the new language, and, finally, one adds a single new axiom, the so-called axiom of choice in analysis:
$$\forall x\exists yA(x,y)\supset\exists\alpha\forall xA(x,\alpha(x)),$$
which asserts that if for all $x$ there is a $y$ satisfying the condition $A(x,y)$, then there is a function $\alpha$ that, for any $x$, picks a corresponding $y$. The merit of this formulation is
that, after excluding the law of the excluded middle from the logical axioms, the system one obtains is convenient for the formalization of intuitionistic or constructive formal mathematical
analysis. Intuitionistic (respectively, constructive) formal mathematical analysis is a reworking of traditional mathematics according to the demands of the program of intuitionism (respectively,
constructive mathematics). In formalizing these disciplines one admits the possibility of treating the variables $\alpha,\beta,\gamma,\dots,$ as only running over functions that are "effective" in
some sense or other, for example, intuitionistic choice sequences. In this interpretation the axiom of choice in analysis is a true assertion. To develop substantial areas of analysis one supplements
this theory with new axioms expressing specific intuitionistic or constructive principles such as bar induction or the constructive selection principle of A.A. Markov.
[1] D. Hilbert, P. Bernays, "Grundlagen der Mathematik" , 1–2 , Springer (1968–1970)
[2] A.A. Fraenkel, Y. Bar-Hillel, "Foundations of set theory" , North-Holland (1958)
[3] C. Spector, "Provable recursive functionals of analysis: a consistency proof of analysis by an extension of principles formulated in current intuitionistic mathematics" , Recursive function
theory , Proc. Symp. Pure Math. , 5 , Amer. Math. Soc. (1962) pp. 1–27
The formal axiomatic theory called above "formal mathematical analysis" is also known as second-order arithmetic or second-order Peano arithmetic.
How to Cite This Entry:
Formal mathematical analysis. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Formal_mathematical_analysis&oldid=33420
This article was adapted from an original article by A.G. Dragalin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098.
See original article
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Chi square distribution tables
Printer-friendly version. One of the primary ways that you will find yourself interacting with the chi-square distribution, primarily later in Stat 415, is by needing to know either a chi-square
value or a chi-square probability in order to complete a statistical analysis. Table: Chi-Square Probabilities. The areas given across the top are the areas to the right of the critical value. To
look up an area on the left, subtract it from one, and then look it up (ie: 0.05 on the left is 0.95 on the right) The following chi squared table has the most common values for chi squared. You can
find exact figures by using Excel (how to calculate a chi square p value Excel), SPSS (How to perform a chi square in SPSS) or other technology. However, in the vast majority of cases, the chi
squared table will give you the value you need.
P. DF, 0.995, 0.975, 0.20, 0.10, 0.05, 0.025, 0.02, 0.01, 0.005, 0.002, 0.001. 1, 0.0000393, 0.000982, 1.642, 2.706, 3.841, 5.024, 5.412, 6.635, 7.879, 9.550 118.136. 124.116. 128.299. 100. 67.328.
70.065. 74.222. 77.929. 82.358. 118.498. 124.342. 129.561. 135.807. 140.169. Chi-Square (X2) Distribution. TABLE IV. The curve approaches, but never quite touches, the horizontal axis. For each
degree of freedom there is a different χ2 distribution. The mean of the chi square Chi-Square Distribution Table. 2 χ. 0. The shaded area is equal to α for χ2 = χ2 α. df χ2 .995 χ2 .990 χ2 .975 χ2
.950 χ2 .900 χ2 .100 χ2 .050 χ2 .025 χ2 .010 χ2. The above definition is used, as is the one that follows, in Table IV, the chi-square distribution table in the back of your textbook. Chi-Square
Distribution Table. 2 χ. 0. The shaded area is equal to α for χ2 = χ2 α. df χ2 .995 χ2 .990 χ2 .975 χ2 .950 χ2 .900 χ2 .100 χ2 .050 χ2 .025 χ2 .010 χ2.
The Problem of Multiple Comparisons. ▫ Expected Counts in Two-Way Tables. ▫ The Chi-Square Test Statistic. ▫ Cell Counts Required for the Chi-Square Test.
function and lower and upper cumulative distribution functions of the chi- square distribution. Need to calculate p-value of very big values of Chi square. The value that you want can be computed
with the isf (inverse survival function) method of the scipy.stats.chi2 distribution. This method uses broadcasting, Calculates a table of the probability density function, or lower or upper
cumulative distribution function of the noncentral chi-square distribution, and draws the Although this table does come from a mathematical function (called a chi-square distribution, go figure!)
for our purposes you can basically treat it like it Apr 19, 2019 A chi-square (χ2) statistic is a test that measures how expectations compare Next, these are used values to calculate the chi squared
We apply the quantile function qchisq of the Chi-Squared distribution against the decimal values 0.95. > qchisq(.95, df=7) # 7 degrees of freedom [1] 14.067
Statistical Tables 627. TABLE 9 Critical Values of the Chi-Square. Distribution. Note: Column headings are non-directional (omni-directional) P-values. If HA is. the comprehensive tables of old.
These tables are designed to be complete enough and easy to use for exams. Standard normal table of left tail probabilities. A variance uses the chi-square distribution, arising from χ2 = s2 × df/σ2.
Form of a confidence interval on Table A9.3. Critical Values of Student's t-Distributiona Table of values of χ2 in a Chi-Squared Distribution with k degrees of freedom such that p is the area
between χ2 and +∞, Chi-Squared Distribution Diagram. svg Lesson Overview. Chi Square ( ) Distribution and Tests; Table of ) Values; Other Applications
Figure 1 — The chi-square distribution for ν = 2, 4, and 10. Note that χ2 ranges only over positive values: 0 < χ2 < ∞. The mean value of χ2 ν is
Find the critical chi-square value using the chi squared table. Step 1: Subtract 1 from the number of categories to get the degrees of freedom. Categories are blue corn and yellow corn, so df = 2-1 =
1. Step 2: Look up your degrees of freedom and probability in the chi squared table. The chi-square distribution table with three probability level is provided here. The statistic here is used to
examine whether distributions of certain variables vary from one another. The categorical variable will produce data in the categories and numerical variables will produce data in numerical form.
table total. • Chi-square test statistic for testing whether the row and column variables in an r × c table are with P-values from the chi-square distribution.
Figure 1 — The chi-square distribution for ν = 2, 4, and 10. Note that χ2 ranges only over positive values: 0 < χ2 < ∞. The mean value of χ2 ν is Beyer, W. H. CRC Standard Mathematical Tables, 28th
ed. Boca Raton, FL: CRC Press, p. 535, 1987. Kenney, J. F. and Keeping, E. S. "The Chi-Square Oct 25, 2011 L15: Chi square. October 25, 2011. 4 / 39. Testing for goodness of fit using chi- square.
Creating a test statistic for one-way tables. Expected Feb 1, 2005 In particular, Abramowitz and Stegun [1] reproduced the tables of percentiles of chi-square, t-, and F-distributions from the 1954
edition of Binomial cumulative distribution function · Characteristic Qualities of Sequential Tests of the Chi-squared percentage points · Duncan's multiple range test
Calculates a table of the probability density function, or lower or upper cumulative distribution function of the noncentral chi-square distribution, and draws the
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1 Square Fermi to Manzana [Argentina]
Square Fermi [f2] Output
1 square fermi in ankanam is equal to 1.4949875578764e-31
1 square fermi in aana is equal to 3.1450432189072e-32
1 square fermi in acre is equal to 2.4710516301528e-34
1 square fermi in arpent is equal to 2.9249202856357e-34
1 square fermi in are is equal to 1e-32
1 square fermi in barn is equal to 0.01
1 square fermi in bigha [assam] is equal to 7.4749377893818e-34
1 square fermi in bigha [west bengal] is equal to 7.4749377893818e-34
1 square fermi in bigha [uttar pradesh] is equal to 3.9866334876703e-34
1 square fermi in bigha [madhya pradesh] is equal to 8.9699253472581e-34
1 square fermi in bigha [rajasthan] is equal to 3.9536861034746e-34
1 square fermi in bigha [bihar] is equal to 3.9544123500036e-34
1 square fermi in bigha [gujrat] is equal to 6.1776345366791e-34
1 square fermi in bigha [himachal pradesh] is equal to 1.2355269073358e-33
1 square fermi in bigha [nepal] is equal to 1.4765309213594e-34
1 square fermi in biswa [uttar pradesh] is equal to 7.9732669753405e-33
1 square fermi in bovate is equal to 1.6666666666667e-35
1 square fermi in bunder is equal to 1e-34
1 square fermi in caballeria is equal to 2.2222222222222e-36
1 square fermi in caballeria [cuba] is equal to 7.451564828614e-36
1 square fermi in caballeria [spain] is equal to 2.5e-36
1 square fermi in carreau is equal to 7.7519379844961e-35
1 square fermi in carucate is equal to 2.0576131687243e-36
1 square fermi in cawnie is equal to 1.8518518518519e-34
1 square fermi in cent is equal to 2.4710516301528e-32
1 square fermi in centiare is equal to 1e-30
1 square fermi in circular foot is equal to 1.3705023910063e-29
1 square fermi in circular inch is equal to 1.9735234590491e-27
1 square fermi in cong is equal to 1e-33
1 square fermi in cover is equal to 3.7064492216457e-34
1 square fermi in cuerda is equal to 2.5445292620865e-34
1 square fermi in chatak is equal to 2.3919800926022e-31
1 square fermi in decimal is equal to 2.4710516301528e-32
1 square fermi in dekare is equal to 1.0000006597004e-33
1 square fermi in dismil is equal to 2.4710516301528e-32
1 square fermi in dhur [tripura] is equal to 2.9899751157527e-30
1 square fermi in dhur [nepal] is equal to 5.9061236854374e-32
1 square fermi in dunam is equal to 1e-33
1 square fermi in drone is equal to 3.893196765303e-35
1 square fermi in fanega is equal to 1.5552099533437e-34
1 square fermi in farthingdale is equal to 9.8814229249012e-34
1 square fermi in feddan is equal to 2.3990792525755e-34
1 square fermi in ganda is equal to 1.245822964897e-32
1 square fermi in gaj is equal to 1.1959900463011e-30
1 square fermi in gajam is equal to 1.1959900463011e-30
1 square fermi in guntha is equal to 9.8842152586866e-33
1 square fermi in ghumaon is equal to 2.4710538146717e-34
1 square fermi in ground is equal to 4.4849626736291e-33
1 square fermi in hacienda is equal to 1.1160714285714e-38
1 square fermi in hectare is equal to 1e-34
1 square fermi in hide is equal to 2.0576131687243e-36
1 square fermi in hout is equal to 7.0359937931723e-34
1 square fermi in hundred is equal to 2.0576131687243e-38
1 square fermi in jerib is equal to 4.9466500076791e-34
1 square fermi in jutro is equal to 1.737619461338e-34
1 square fermi in katha [bangladesh] is equal to 1.4949875578764e-32
1 square fermi in kanal is equal to 1.9768430517373e-33
1 square fermi in kani is equal to 6.2291148244848e-34
1 square fermi in kara is equal to 4.9832918595878e-32
1 square fermi in kappland is equal to 6.4825619084662e-33
1 square fermi in killa is equal to 2.4710538146717e-34
1 square fermi in kranta is equal to 1.4949875578764e-31
1 square fermi in kuli is equal to 7.4749377893818e-32
1 square fermi in kuncham is equal to 2.4710538146717e-33
1 square fermi in lecha is equal to 7.4749377893818e-32
1 square fermi in labor is equal to 1.3950025009895e-36
1 square fermi in legua is equal to 5.580010003958e-38
1 square fermi in manzana [argentina] is equal to 1e-34
1 square fermi in manzana [costa rica] is equal to 1.4308280488084e-34
1 square fermi in marla is equal to 3.9536861034746e-32
1 square fermi in morgen [germany] is equal to 4e-34
1 square fermi in morgen [south africa] is equal to 1.1672697560406e-34
1 square fermi in mu is equal to 1.4999999925e-33
1 square fermi in murabba is equal to 9.884206520611e-36
1 square fermi in mutthi is equal to 7.9732669753405e-32
1 square fermi in ngarn is equal to 2.5e-33
1 square fermi in nali is equal to 4.9832918595878e-33
1 square fermi in oxgang is equal to 1.6666666666667e-35
1 square fermi in paisa is equal to 1.2580540458988e-31
1 square fermi in perche is equal to 2.9249202856357e-32
1 square fermi in parappu is equal to 3.9536826082444e-33
1 square fermi in pyong is equal to 3.0248033877798e-31
1 square fermi in rai is equal to 6.25e-34
1 square fermi in rood is equal to 9.8842152586866e-34
1 square fermi in ropani is equal to 1.965652011817e-33
1 square fermi in satak is equal to 2.4710516301528e-32
1 square fermi in section is equal to 3.8610215854245e-37
1 square fermi in sitio is equal to 5.5555555555556e-38
1 square fermi in square is equal to 1.076391041671e-31
1 square fermi in square angstrom is equal to 1e-10
1 square fermi in square astronomical units is equal to 4.4683704831421e-53
1 square fermi in square attometer is equal to 1000000
1 square fermi in square bicron is equal to 0.000001
1 square fermi in square centimeter is equal to 1e-26
1 square fermi in square chain is equal to 2.4710436922533e-33
1 square fermi in square cubit is equal to 4.7839601852043e-30
1 square fermi in square decimeter is equal to 1e-28
1 square fermi in square dekameter is equal to 1e-32
1 square fermi in square digit is equal to 2.7555610666777e-27
1 square fermi in square exameter is equal to 1e-66
1 square fermi in square fathom is equal to 2.9899751157527e-31
1 square fermi in square femtometer is equal to 1
1 square fermi in square feet is equal to 1.076391041671e-29
1 square fermi in square furlong is equal to 2.4710516301528e-35
1 square fermi in square gigameter is equal to 1e-48
1 square fermi in square hectometer is equal to 1e-34
1 square fermi in square inch is equal to 1.5500031000062e-27
1 square fermi in square league is equal to 4.290006866585e-38
1 square fermi in square light year is equal to 1.1172498908139e-62
1 square fermi in square kilometer is equal to 1e-36
1 square fermi in square megameter is equal to 1e-42
1 square fermi in square meter is equal to 1e-30
1 square fermi in square microinch is equal to 1.5500017326603e-15
1 square fermi in square micrometer is equal to 1e-18
1 square fermi in square micromicron is equal to 0.000001
1 square fermi in square micron is equal to 1e-18
1 square fermi in square mil is equal to 1.5500031000062e-21
1 square fermi in square mile is equal to 3.8610215854245e-37
1 square fermi in square millimeter is equal to 1e-24
1 square fermi in square nanometer is equal to 1e-12
1 square fermi in square nautical league is equal to 3.2394816622014e-38
1 square fermi in square nautical mile is equal to 2.9155309240537e-37
1 square fermi in square paris foot is equal to 9.478672985782e-30
1 square fermi in square parsec is equal to 1.0502647575668e-63
1 square fermi in perch is equal to 3.9536861034746e-32
1 square fermi in square perche is equal to 1.958018322827e-32
1 square fermi in square petameter is equal to 1e-60
1 square fermi in square picometer is equal to 0.000001
1 square fermi in square pole is equal to 3.9536861034746e-32
1 square fermi in square rod is equal to 3.9536708845746e-32
1 square fermi in square terameter is equal to 1e-54
1 square fermi in square thou is equal to 1.5500031000062e-21
1 square fermi in square yard is equal to 1.1959900463011e-30
1 square fermi in square yoctometer is equal to 1000000000000000000
1 square fermi in square yottameter is equal to 1e-78
1 square fermi in stang is equal to 3.6913990402362e-34
1 square fermi in stremma is equal to 1e-33
1 square fermi in sarsai is equal to 3.5583174931272e-31
1 square fermi in tarea is equal to 1.5903307888041e-33
1 square fermi in tatami is equal to 6.0499727751225e-31
1 square fermi in tonde land is equal to 1.8129079042785e-34
1 square fermi in tsubo is equal to 3.0249863875613e-31
1 square fermi in township is equal to 1.0725050478094e-38
1 square fermi in tunnland is equal to 2.0257677659833e-34
1 square fermi in vaar is equal to 1.1959900463011e-30
1 square fermi in virgate is equal to 8.3333333333333e-36
1 square fermi in veli is equal to 1.245822964897e-34
1 square fermi in pari is equal to 9.8842152586866e-35
1 square fermi in sangam is equal to 3.9536861034746e-34
1 square fermi in kottah [bangladesh] is equal to 1.4949875578764e-32
1 square fermi in gunta is equal to 9.8842152586866e-33
1 square fermi in point is equal to 2.4710731022028e-32
1 square fermi in lourak is equal to 1.9768430517373e-34
1 square fermi in loukhai is equal to 7.9073722069493e-34
1 square fermi in loushal is equal to 1.5814744413899e-33
1 square fermi in tong is equal to 3.1629488827797e-33
1 square fermi in kuzhi is equal to 7.4749377893818e-32
1 square fermi in chadara is equal to 1.076391041671e-31
1 square fermi in veesam is equal to 1.1959900463011e-30
1 square fermi in lacham is equal to 3.9536826082444e-33
1 square fermi in katha [nepal] is equal to 2.9530618427187e-33
1 square fermi in katha [assam] is equal to 3.7374688946909e-33
1 square fermi in katha [bihar] is equal to 7.9088247000071e-33
1 square fermi in dhur [bihar] is equal to 1.5817649400014e-31
1 square fermi in dhurki is equal to 3.1635298800029e-30
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The church synthesis problem with parameters
For a two-variable formula ψ(X, Y) of Monadic Logic of Order (MLO) the Church Synthesis Problem concerns the existence and construction of an operator Y = F(X) such that ψ(X, F(X)) is universally
valid over Nat. Büchi and Landweber proved that the Church synthesis problem is decidable; moreover, they showed that if there is an operator F that solves the Church Synthesis Problem, then it can
also be solved by an operator defined by a finite state automaton or equivalently by an MLO formula. We investigate a parameterized version of the Church synthesis problem. In this version ψ might
contain as a parameter a unary predicate P. We show that the Church synthesis problem for P is computable if and only if the monadic theory of (Formula Found) is decidable. We prove that the
Büchi-Landweber theorem can be extended only to ultimately periodic parameters. However, the MLO-definability part of the Büchi-Landweber theorem holds for the parameterized version of the Church
synthesis problem.
• Decidability
• Monadic logic
• Synthesis problem
Dive into the research topics of 'The church synthesis problem with parameters'. Together they form a unique fingerprint.
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Learn How To Write and Understand Algebra Expressions
Algebraic Expressions With Example Problems and Interactive Exercises
Use the following examples and interactive exercises to learn about Writing Algebraic Expressions.
Solution: Let g represent the number of groups in Ms. Jensen’s class.
Then 2 · g, or 2g can represent “g groups of 2 students”.
In the problem above, the variable g represents the number of groups in Ms. Jensen’s class. A variable is a symbol used to represent a number in an expression or an equation. The value of this number
can vary (change). Let’s look at an example in which we use a variable.
Example 1: Write each phrase as a mathematical expression.
│ Phrase │ Expression │
│ the sum of nine and eight │ 9 + 8 │
│ the sum of nine and a number x │ 9 + x │
The expression 9 + 8 represents a single number (17). This expression is a numerical expression, (also called an arithmetic expression). The expression 9 + x represents a value that can change. If x
is 2, then the expression 9 + x has a value of 11. If x is 6, then the expression has a value of 15. So 9 + x is an algebraic expression. In the next few examples, we will be working solely with
algebraic expressions.
Example 2: Write each phrase as an algebraic expression.
│ Phrase │ Expression │
│ nine increased by a number x │ 9 + x │
│ fourteen decreased by a number p │ 14 – p │
│ seven less than a number t │ t – 7 │
│ the product of 9 and a number n │ 9 · n or 9n │
│ thirty-two divided by a number y │ 32 ÷ y or │
In Example 2, each algebraic expression consisted of one number, one operation and one variable. Let’s look at an example in which the expression consists of more than one number and/or operation.
Example 3: Write each phrase as an algebraic expression using the variable n.
│ Phrase │ Expression │
│ five more than twice a number │ 2n + 5 │
│ the product of a number and 6 │ 6n │
│ seven divided by twice a number │ 7 ÷ 2n or │
│ three times a number decreased by 11 │ 3n – 11 │
Solution: Let e represent the number of employees in the company. The amount of money each employee will get is represented by the following algebraic expression:
Solution: Let x represent the number of hours the electrician works in one day. The electrician’s earnings can be represented by the following algebraic expression:
Solution: 45x – 20
Summary: A variable is a symbol used to represent a number in an expression or an equation. The value of this number can change. An algebraic expression is a mathematical expression that consists of
variables, numbers and operations. The value of this expression can change.
Directions: Choose the algebraic expression that correctly represents the phrase provided. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If you
make a mistake, choose a different button.
1. Fifteen less than twice a number
2. Three times a number, increased by seventeen
3. The product of nine and a number, decreased by six
4. Thirty divided by seven times a number
5. Jenny earns $30 a day working part time at a supermarket. Write an algebraic expression to represent the amount of money she will earn in d days.
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ctzrqf - Linux Manuals (3)
ctzrqf (3) - Linux Manuals
ctzrqf.f -
subroutine ctzrqf (M, N, A, LDA, TAU, INFO)
Function/Subroutine Documentation
subroutine ctzrqf (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, integerINFO)
This routine is deprecated and has been replaced by routine CTZRZF.
CTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
to upper triangular form by means of unitary transformations.
The upper trapezoidal matrix A is factored as
A = ( R 0 ) * Z,
where Z is an N-by-N unitary matrix and R is an M-by-M upper
triangular matrix.
M is INTEGER
The number of rows of the matrix A. M >= 0.
N is INTEGER
The number of columns of the matrix A. N >= M.
A is COMPLEX array, dimension (LDA,N)
On entry, the leading M-by-N upper trapezoidal part of the
array A must contain the matrix to be factorized.
On exit, the leading M-by-M upper triangular part of A
contains the upper triangular matrix R, and elements M+1 to
N of the first M rows of A, with the array TAU, represent the
unitary matrix Z as a product of M elementary reflectors.
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU is COMPLEX array, dimension (M)
The scalar factors of the elementary reflectors.
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
November 2011
Further Details:
The factorization is obtained by Householder's method. The kth
transformation matrix, Z( k ), whose conjugate transpose is used to
introduce zeros into the (m - k + 1)th row of A, is given in the form
Z( k ) = ( I 0 ),
( 0 T( k ) )
T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ),
( 0 )
( z( k ) )
tau is a scalar and z( k ) is an ( n - m ) element vector.
tau and z( k ) are chosen to annihilate the elements of the kth row
of X.
The scalar tau is returned in the kth element of TAU and the vector
u( k ) in the kth row of A, such that the elements of z( k ) are
in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
the upper triangular part of A.
Z is given by
Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
Definition at line 139 of file ctzrqf.f.
Generated automatically by Doxygen for LAPACK from the source code.
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Ryder Cup blog
• Analytics Blog
Sept 25th, 2018
It's Ryder Cup week and we are going to be providing live probabilistic forecasts Friday through Sunday! In this blog we are going to (very briefly) outline how the predictions work, and then
highlight two interesting things that have to do with choosing optimal pairings.
To predict match play, we are going to simply adapt our round-level predictions to provide a hole-level scoring distribution for each player (that is, the probability of making eagle, birdie, par,
etc.). Here is how we currently estimate the ability level of each player on the American and European sides (in strokes per round):
The Americans are stronger at every position except for the bottom 3 players, where the Europeans have the edge. In the team formats on Friday and Saturday, where only 8 golfers play each session,
the lower-end quality of each team may be less important. The average ability of the US team is 1.55 strokes per round above the PGA Tour average, while for the European team it is 1.43.
Next I'll outline how predictions are formed. To predict singles match outcomes, the process is simple given that we have a hole-level scoring distribution for each golfer. For foursomes matches,
keeping with our M.O., we do not consider "pairings interactions" which means that all that matters for our predictions are the individual estimates of ability. That is, we don't allow for certain
players to be complements when they play the alternate shot format together. These complementarities may exist, but to include them in a model will require some assumptions. There is simply not
enough data on team golf to draw strong conclusions, and so you must appeal to a theory of how individual golf relates to team golf. We abstract from this and model foursomes as a singles match,
where the scoring distribution for each team is an average of the two team members. Finally, we model a fourball match as the minimum score on each hole from the two respective scoring distributions
of a team's golfers. This is quite nice as it will pick up any complementarities that could exist in this format (e.g. pairing a player who makes a lot of birdies / bogies with one who makes a lot of
To put everything together and predict the Ryder Cup, we have to make some assumptions about how specific pairings will be formed. Luckily for us, team captains submit their lineups without knowledge
of the other side's picks. This solves part of the problem, but we still need to choose which 8 players will participate in each team session. For this, we give higher ability players a higher
probability of being selected: for example, on the American side, Dustin Johnson has an 85% chance of playing in any given team session, while Bubba Watson has just a 35% chance. These are arbitrary
choices, but ones that have to be made. Once we select the 8-man squad on each side for a given session, matches are set randomly (as they are in actuality). With these assumptions in hand, it is
straightforward to simulate the Ryder Cup using the scoring distributions we have for each player and the adjustments we have described for the team formats.
Our start-of-tournament estimates give the American team a 54% chance of winning the Ryder Cup outright and an 8% chance of tieing and retaining the cup. This leaves a 38% probability that the
European side wins outright. The only real arbitrary choices we are making is how pairings are selected. If lineups were set completely randomly, so that every player had an equal chance of playing
in any given match, the relevant probabilities are 52%, 8% and 40%. This makes sense, given that the American team is relatively weaker in the lower ranks of their team.
Now let's consider a couple interesting exercises. One question we had while thinking about predicting the better-ball format was whether it was better to have a team with one good player and one bad
player, or a team with two mediocre players. The figure below answers this question.
The left figure is just shown for reference, and indicates the expected points in a singles match for the better player as a function of how big their skill advantage is. The right figure is the
interesting one. Here, we fix one team's ability levels at 0 for both team members. Then, for the other team ("team A"), we keep their average ability at 0 but vary the gap between individual
abilities (i.e. +1 and -1, +2 and -2, etc.). What we see is that it's (slightly) better to have one good player and one bad player than two mediocre ones. I suppose this is intutive, especially when
you consider the extreme case: a +10 ability player and -10 player would certainly have a big advantage over two 0 ability players in the fourball format.
Now let's talk about optimal pairings. Normally the popular conversation on this topic is centered around which players "fit" together well - either because of personality or due to specific
attributes of their golf games. We are going to abstract from this and take a pure data approach. The first thing to note is that it is not possible to solve for optimal pairings. This is an
incredibly complex game theory problem. Here's why. By my rough calculations there are about 52,000 unique teams that can be chosen for a team session from EACH of the 12-man teams. Now let's think
about team captain strategy. It would be (somewhat) feasible for us to determine the best American team assuming the European side is forming teams randomly. We could do the same for Europe. However,
this is not optimal (or, not an equilibrium you could say). If Furyk knows that Europe is picking their best team assuming the Americans are forming teams randomly, then he should take this into
account and tailor his team to Europe's "optimal" team (the one they would choose if Americans were picking randomly). Of course, Europe should also take this into account about the American team,
and so on. Long story short, there will be an incredibly complex equilibrium that we can't begin to solve for.
What we are going to do is try to come up with the best teams for each format assuming the other side is forming their pairings randomly. While this may not be the most realistic, it is a useful
benchmark and should highlight which sorts of teams yield the highest expected points. It is interesting to think about what will make for the best teams in this exercise. Let's think about the
better-ball format first as it has more nuance to it. Obviously, good teams will have players with higher predicted abilities. Further, we saw in the exercise above that it is slightly advantageous
to pair a skilled player with a less skilled player, all else equal. But, there is also the question (in either team format) of whether the two best players should play together to "guarantee" a
point, and if the two worst players should play together to "sacrifice" a point. Again, it's not at all clear to me what the optimal strategy would be. Let's head to the data.
We take a brute force approach and loop through as many combinations of teams as we can (subject to our computation power limitations), calculating the expected points for each team under
consideration. For example, we would form a possible American team, and then do many simulations where that same American team competes against a randomly formed European team in each simulation.
Average points over all the simulations, and we can rank teams based off their expected points. Here are the top 10 teams on the American side for each format (we don't do the optimal European teams,
as the exercise takes quite a long time):
Not surprisingly, our "optimal teams" for the US are basically just comprised of their top 8 players. It's worth noting that the expected points for the US team obtained using the selection algorithm
that we described above for our Ryder Cup predictions is 2.11 for a fourball session, and 2.06 for a foursomes session. This, in addition to the optimal team results above, indicates that the
fourball session provides a greater advantage to the better team - this is because there are roughly twice as many shots being hit, which makes the outcome slightly less influenced by randomness. The
differences in these tables may seem small, but a 0.1 difference in expected points translates to about 2% greater win probability for the overall match. Unfortunately, I don't think there is much
else to read into for these "optimal teams" - because we only ran 2000 simulations, some of these differences could just be simulation error. It is hard to determine whether any of the mechanisms
mentioned above are at work here (e.g. pairing your very top guys together to try and "guarantee" a point). It is interesting to recognize that if the American team played their top 8 guys in every
session this would, in theory, result in an overall win probability that is about 3-6% higher (depending on what strategy the Europeans are assumed to adopt) than where we currently have it. However,
this would be a very bold strategy for a captain to take - one that would garner a lot of criticism if it did not work out in their favour. It is hard to ignore the numbers though: is there really a
justification for playing Phil or Bubba in place of any of DJ, JT, Fowler, or Tiger (guys we estimate to be more than a shot better than Phil)? We don't think so. In any case, it should be an
exciting week.
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Transactions Online
Junichi TOMIDA, Masayuki ABE, Tatsuaki OKAMOTO, "Efficient Inner Product Functional Encryption with Full-Hiding Security" in IEICE TRANSACTIONS on Fundamentals, vol. E103-A, no. 1, pp. 33-40, January
2020, doi: 10.1587/transfun.2019CIP0003.
Abstract: Inner product functional encryption (IPFE) is a subclass of functional encryption (FE), whose function class is limited to inner product. We construct an efficient private-key IPFE scheme
with full-hiding security, where confidentiality is assured for not only encrypted data but also functions associated with secret keys. Recently, Datta et al. presented such a scheme in PKC 2016 and
this is the only scheme that achieves full-hiding security. Our scheme has an advantage over their scheme for the two aspects. More efficient: keys and ciphertexts of our scheme are almost half the
size of those of their scheme. Weaker assumption: our scheme is secure under the k-linear (k-Lin) assumption, while their scheme is secure under a stronger assumption, namely, the symmetric external
Diffie-Hellman (SXDH) assumption. It is well-known that the k-Lin assumption is equivalent to the SXDH assumption when k=1 and becomes weak as k increases.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019CIP0003/_p
author={Junichi TOMIDA, Masayuki ABE, Tatsuaki OKAMOTO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Efficient Inner Product Functional Encryption with Full-Hiding Security},
abstract={Inner product functional encryption (IPFE) is a subclass of functional encryption (FE), whose function class is limited to inner product. We construct an efficient private-key IPFE scheme
with full-hiding security, where confidentiality is assured for not only encrypted data but also functions associated with secret keys. Recently, Datta et al. presented such a scheme in PKC 2016 and
this is the only scheme that achieves full-hiding security. Our scheme has an advantage over their scheme for the two aspects. More efficient: keys and ciphertexts of our scheme are almost half the
size of those of their scheme. Weaker assumption: our scheme is secure under the k-linear (k-Lin) assumption, while their scheme is secure under a stronger assumption, namely, the symmetric external
Diffie-Hellman (SXDH) assumption. It is well-known that the k-Lin assumption is equivalent to the SXDH assumption when k=1 and becomes weak as k increases.},
TY - JOUR
TI - Efficient Inner Product Functional Encryption with Full-Hiding Security
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 33
EP - 40
AU - Junichi TOMIDA
AU - Masayuki ABE
AU - Tatsuaki OKAMOTO
PY - 2020
DO - 10.1587/transfun.2019CIP0003
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2020
AB - Inner product functional encryption (IPFE) is a subclass of functional encryption (FE), whose function class is limited to inner product. We construct an efficient private-key IPFE scheme with
full-hiding security, where confidentiality is assured for not only encrypted data but also functions associated with secret keys. Recently, Datta et al. presented such a scheme in PKC 2016 and this
is the only scheme that achieves full-hiding security. Our scheme has an advantage over their scheme for the two aspects. More efficient: keys and ciphertexts of our scheme are almost half the size
of those of their scheme. Weaker assumption: our scheme is secure under the k-linear (k-Lin) assumption, while their scheme is secure under a stronger assumption, namely, the symmetric external
Diffie-Hellman (SXDH) assumption. It is well-known that the k-Lin assumption is equivalent to the SXDH assumption when k=1 and becomes weak as k increases.
ER -
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TKEEP directive • Genstat v21
Saves results after an analysis by TFIT.
SAVE = identifier Save structure to supply fitted model; default * i.e. that from last model fitted
OUTPUTSERIES = variate Output series to which model was fitted
RESIDUALS = variate Residual series
ESTIMATES = variate Estimates of parameters
SE = variate Standard errors of estimates
INVERSE = symmetric matrix Inverse matrix
VCOVARIANCE = symmetric matrix Variance-covariance matrix of parameters
DEVIANCE = scalar Residual deviance
DF = scalar Residual degrees of freedom
MVESTIMATES = variate Estimates of missing values in series
SEMV = variate Standard errors of estimates of missing values
COMPONENTS = pointer Variates to save components of output series
SCORES = variate To save scores (derivatives of the log-likelihood with respect to the parameters)
An TFIT statement produces many quantities that you may want to use to assess, interpret and apply the fitted model. The TKEEP directive allows you to copy these quantities into Genstat data
structures. If the METHOD option of the TFIT statement was set to initialize, then the results saved by the options SE, INVERSE, VCOVARIANCE and SCORE are unavailable. However, you can save the
estimates of the missing values and their standard errors. The residual degrees of freedom in this case does not make allowance for the number of parameters in the model, but does allow for the
missing values that have been estimated.
The OUTPUTSERIES parameter specifies the variate that was supplied by the SERIES parameter of the TFIT statement; this can be omitted.
You can use the RESIDUALS parameter to save the residuals in a variate, exactly as in the TFIT directive.
The ESTIMATES parameter can supply a variate to store the estimated parameters of the TSM. Each estimated parameter is represented once, but the innovation variance is omitted entirely. Genstat
includes only the first of any set of parameters constrained to be equal using the FIX option of TFIT. The order of the parameters otherwise corresponds to their order in the variate of parameters in
TSM, and is unaffected by any numbering used in the FIX option.
The SE parameter allows you to specify a variate to save the standard errors of the estimated parameters of the TSM. The values correspond exactly to those in the ESTIMATES variate. Parameters in a
time series model may be aliased. This is detected when the equations for the estimates are being solved, and the message ALIASED is printed instead of the standard error when the PRINT option of
TFIT or TDISPLAY includes the setting estimates. The corresponding units of the SE variate are set to missing values.
The INVERSE parameter can provide a symmetric matrix to save the product (X′X)^-1, where X is the most recent design matrix derived from the linearized least-squares regressions that were used to
minimize the deviance. The ordering of the rows and columns corresponds exactly to that used for the ESTIMATES variate. The row of this matrix corresponding to any aliased parameter is set to zero
except that the diagonal element is set to the missing value.
The VCOVARIANCE parameter allows you to supply a symmetric matrix for the estimated variance-covariance matrix, [a]^2(X′X)^-1, of the TSM parameters. The ordering of the rows and columns and the
treatment of aliased parameters corresponds exactly to that used for the ESTIMATES variate.
The DEVIANCE parameter specifies a scalar to hold the final value of the deviance criterion defined by the LIKELIHOOD option of TFIT.
The DF parameter saves the residual number of degrees of freedom, defined for a simple ARIMA model by N–d-(number of estimated parameters). If a seasonal model is used, this number is further reduced
by Ds.
The MVESTIMATES parameter specifies a variate to hold estimates of the missing values of the series, in the order they appear in the series. You can thereby obtain forecasts of the series, by
extending the SERIES in TFIT with a set of missing values. This is less efficient than using the TFORECAST directive, but it does have the advantage that the standard errors of the estimates take
into account the finite extent of the data, and also the fact that the model parameters are estimated.
The SEMV parameter can supply a variate to hold the estimated standard errors of the missing values of the series, in the order they appear in the series.
The COMPONENTS parameter can be used after a multi-input model has been fitted using TFIT to access the components of the output series that are due to the various input series; you can also access
the output noise. In simple regression, the input components are proportional to the input series. But the component resulting from a transfer-function model may be quite different from this. You can
examine these components separately, or sum them to show the total fit to the output series that is explained by the input series. Note that the fitted values may appear to be offset from that output
series, because the constant term is part of the noise component, and so is not included. You may want to examine the output noise component. For example, if you thought that the ARIMA model for the
output noise was inadequate, you could investigate the noise component with univariate ARIMA modelling.
The SCORE parameter can specify a variate to hold the model scores. The scores are usually defined as the first derivatives of the log likelihood with respect to the model parameters. To get these,
the scores supplied by TKEEP should be scaled by dividing by the estimated residual variance and reversing its sign. The elements of the SCORE variate correspond exactly to the parameters as they
appear in the ESTIMATES variate. After using TFIT to fit a time series model, the scores should in theory be zero provided the model parameters do not lie on the boundary of their allowed range. The
scores are used within TFIT to calculate the parameter changes at each iteration.
You can use the SAVE option to specify the time-series save structure from which the output is to be taken. By default TKEEP uses the structure from the most recent TFIT statement.
Option: SAVE.
Parameters: OUTPUTSERIES, RESIDUALS, ESTIMATES, SE, INVERSE, VCOVARIANCE, DEVIANCE, DF, MVESTIMATES, SEMV, COMPONENTS, SCORES.
See also
Directives: TSM, FTSM, TDISPLAY, TFILTER, TFIT, TFORECAST, TRANSFERFUNCTION, TSUMMARIZE.
Procedures: BJESTIMATE, BJFORECAST, BJIDENTIFY.
Commands for: Time series.
" Example TFIT-1: Fitting a seasonal ARIMA model"
VARIATE time; VALUES=!(1...120)
FILEREAD [NAME='%gendir%/examples/TFIT-1.DAT'] apt
" Display the correlation structure of the logged data"
CALCULATE lapt = LOG(apt)
BJIDENTIFY [GRAPHICS=high; WINDOWS=!(5,6,7,8)] lapt
" Calculate the autocorrelations of the differences and seasonally
differenced series"
CALCULATE ddslapt = DIFFERENCE(DIFFERENCE(lapt; 12); 1)
CORRELATE [PRINT=auto; MAXLAG=48] ddslapt; AUTO=ddsr
" Define a model for the series:
IMA(1) (that is, a model with a single moving-average parameter
applied to the differences of the series)
plus a seasonal IMA(1) component"
TSM [MODELTYPE=arima] airpass; ORDERS=!((0,1,1)2,12)
" Form preliminary estimates of the parameters, using a log transformation
(BOXCOX=0 is equivalent to log)"
FTSM [PRINT=model] airpass; ddsr; BOXCOX=0
" Get the best estimates, fixing the constant"
TFIT [CONSTANT=fix] SERIES=apt; TSM=airpass
" Graph the residuals against time"
TKEEP RESID=resids
DGRAPH [WINDOW=3; KEYWINDOW=0; TITLE='Residuals vs Time'] resids; time
" Test the independence of the residuals"
CORRELATE [GRAPH=auto; MAXLAG=48] resids; TEST=S
PRINT 'Test statistic for independence of the residuals',S
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What Are The Differences Between Supervised, Unsupervised And Reinforced Machine Learning? - DED9
What Are The Differences Between Supervised, Unsupervised And Reinforced Machine Learning?
Machine Learning Is A Branch Of Artificial Intelligence And Computer Science That Focuses On Using Data And Algorithms To Mimic The Way Humans Learn And Gradually Improve Its Accuracy.
IBM has a brilliant history in machine learning, and the specialists of this company have made significant achievements in this field.
One of these great experts is Arthur Samuel, who, with his research on the game of checkers, made the technology world get to know machine learning in a more detailed way.
For example, Robert Neely, the grandmaster of checkers, played against an IBM 7094 computer in 1962 and lost. Compared to what can be done today, the feat at the time pales, but the event is an
essential milestone in artificial intelligence.
Over the next few decades, there were many developments in the world of technology, and the storage capacity and processing power increased.
Machine learning is one of the essential pillars of the growing field of data science. Algorithms are trained for classification or prediction and reveal critical insights in data mining-based
Insights are essential in making macro business decisions and advancing business goals. As big data continues to expand and grow, the market demand for data scientists will increase. Organizations
request these professionals to help them identify business strategies and how to implement them. In situations where terms such as machine learning (supervised, unsupervised, and reinforcement), deep
learning, neural networks, etc. have their definitions, sometimes we see that sources or experts use these terms instead of others; Accordingly, in this article, we will tell you the differences
between each of the mentioned terms.
Machine learning versus deep learning versus neural networks
Since deep learning and machine learning are used interchangeably, it is essential to understand the nuances between the two terms. Machine learning, deep learning, and neural networks are all
subfields of artificial intelligence. However, deep learning is a subset of machine learning, and neural networks are a subset of deep learning.
Deep learning and machine learning differ in how each algorithm learns. Deep understanding automates much of the feature extraction process, working as much as possible without the direct supervision
of experts and enabling the use of big data. In his MIT lecture, Lex Friedman pointed out an interesting point: “You can think of deep learning as scalable machine learning.
Classical or non-deep machine learning is more dependent on humans for education. Experts define a set of features to understand the difference between data inputs. In this learning model, you need
structured data to train the model better.”
Deep learning can use labeled data sets, known as supervised learning, to get more detailed information, but it does not necessarily require a labeled data set. This learning model can take
unstructured data in raw form (text, images) and automatically determine a set of features that distinguish different categories of data from each other.
Unlike machine learning, it does not require human intervention to process data, allowing us to scale machine learning in more exciting ways.
Deep understanding and neural networks are primarily accelerating advances in computer vision, natural language processing, and speech recognition.
In the past few decades, when computers gained the ability to implement computational algorithms in line with simulating the computational behavior of the human brain, a lot of research, the results
of which are in a branch of artificial intelligence science.
And in the sub-branch of computing intelligence called “Artificial Neural Networks,” ANNs manifested themselves as Artificial Neural Networks. Typically, artificial neural networks process
information based on different layers and can include an input layer, one or more hidden layers, and an output layer.
Each node (artificial neuron) is connected to another node and has its weight and threshold. If the output of any individual node exceeds the specified threshold value, that node is activated and
forwards the data to the next layer of the network. Otherwise, no data is transmitted to the next network layer. The word deep in deep learning only refers to the depth of the layers.
A neural network with more than three layers, inputs, and outputs can be considered a deep learning algorithm or a deep neural network. A neural network that has only two or three layers is a
primitive neural network.
How does machine learning work?
UC Berkeley divides the learning mechanism of a machine learning algorithm into three main parts as follows:
Decision-making process: Generally, machine learning algorithms are used for prediction or classification. The algorithm estimates a hidden pattern in the data based on some input data that can be
labeled or unlabeled.
Error function: An error function is used to evaluate the model’s prediction. An error function can compare if there are known samples to assess the model’s accuracy.
Model optimization process: If the model can better match the data points in the training set, the weights are adjusted to reduce the difference between the examples and the model estimate. The
algorithm repeats this evaluation and optimization process and updates the weights independently until an accuracy threshold is reached.
Machine learning methods
The classification paradigms governing machine learning are divided into the following three main categories:
Supervised machine learning
Supervised learning uses labeled datasets to train algorithms to classify data or accurately predict outcomes. The weights are adjusted until the model fits correctly as input data is fed into the
The above approach is part of the cross-validation process to ensure that the model does not suffer from overfitting or underfitting. Supervised learning helps organizations solve large-scale
real-world problems, most notably directing the classification of spam into a separate folder from the email inbox.
There are various algorithms under the umbrella of supervised learning, including support vector machines and simple Bayes. Some methods used in supervised learning are Neural Networks, Simple Bayes,
Linear Regression, Logistic Regression, Random Forest, Support Vector Machine (SVM), etc. You can see the two steps of constructing and testing a mapping function with supervised learning in Figure
figure 1
Unsupervised machine learning
Unsupervised learning of machine learning algorithms is used to analyze and cluster unlabeled data sets. These algorithms discover hidden patterns or groupings of data without the intervention of
The algorithms mentioned above can discover similarities and differences in information to provide an ideal solution for exploratory data analysis, cross-selling strategies, customer segmentation,
and image and pattern recognition. Also, they use the dimensionality reduction technique to reduce the number of model features.
Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) are two common approaches used by unsupervised algorithms. Neural networks, k-means clustering, probabilistic clustering
methods, etc., are prominent algorithms in this field. Figure 2 shows the performance of the above technology.
figure 2
Semi-Supervised Learning
Semi-supervised learning is on the border between supervised and unsupervised learning. In the above model, a small and concise labeled data set is used to help the model classify and extract
features in a more extensive, unlabeled data set. Semi-supervised learning can solve the problem of not having enough labeled data (or not being able to afford to label enough information) to train a
supervised learning algorithm.
Reinforcement Machine Learning
Reinforcement machine learning is a machine learning model that is a behavior similar to unsupervised learning, but the algorithm is not trained using sample data. This model learns using trial and
In the above approach, the model learns how to provide the best performance based on reward or punishment. So that a sequence of successful results is used to implement the best recommendation or
policy for a particular problem, IBM’s Watson system, which won the 2011 Jeopardy TV competition, is the best example of this.
The system used reinforcement learning to decide whether to answer or ask a question and determine which square to choose on the board. It is necessary to explain that reinforcement learning has two
trends: Deep Reinforcement Learning and Meta Reinforcement Learning.
Deep Reinforcement Learning (Deep Reinforcement Learning) uses deep neural networks to solve reinforcement learning problems, so the word deep is used. Q-Learning is considered classical
reinforcement learning, and Deep Q-Learning, regarded as a newer example, is related to this field.
In the first approach, traditional algorithms construct a Q table to help the agent find what to do in each situation. The second approach uses the neural network (to estimate the reward based on the
state: q value).
Figure 3 shows the reinforcement learning model. In the first approach, traditional algorithms construct a Q table to help the agent find what to do in each situation.
The second approach uses the neural network (to estimate the reward based on the state: q value).
Figure 3 shows the reinforcement learning model. In the first approach, traditional algorithms construct a Q table to help the agent find what to do in each situation. The second approach uses the
neural network (to estimate the reward based on the state: q value). Figure 3 shows the reinforcement learning model.
Figure 3
Neural networks
The neural network processes an input vector based on a model inspired by neurons and their connections in the brain. This model consists of layers of neurons connected through weights that can
recognize the importance of specific inputs. Each neuron contains an activation function that determines its output (as a function of its input vector multiplied by its weight vector).
The output is calculated by applying the input vector to the network’s input layer and then summing each neuron’s work through the network (feedback). Figure 4 shows the layers of a standard neural
Figure 4
Back-propagation is one of the most popular supervised learning methods for neural networks. In post propagation, you have an input vector for data injection and an output vector for computation. In
the above pattern, the error is computed (actual vs. arbitrary), then propagated twice to adjust the weights from the output layer to the input layer (as a function of their contribution to the
output, setting the learning rate).
decision tree
A decision tree is a supervised learning method used in classification that provides the result of an input vector based on decision rules inferred from the features in the data. Decision trees are
valuable because they are easy to visualize, so you can see and understand the factors that drive outcomes. Figure 5 shows an example of a shared decision tree.
Decision trees are divided into two main types. Classification trees where the target variable is a discrete value and leaves represent class labels (as shown in the tree in Figure 5) and regression
trees where the target variable can take continuous values. You use a dataset to train the tree and then build a model from the data. Then, you can use the tree to make decisions about unseen data.
Figure 5
There are various algorithms related to decision tree learning. One of the essential options in this field is ID3, named Dichotomiser 3, which divides the data set into two separate data sets based
on a single area in the vector.
You select this field by calculating its entropy (a measure of the distribution of the values of that field). The goal is to choose a lot of the vector that leads to entropy reduction in subsequent
divisions of the dataset during tree construction.
Other algorithms in this field include Beyond ID3, the improved and alternative ID3 algorithm called C4.5, and the MARS algorithm called Multivariate Adaptive Regression Splines, which build decision
trees with improved numerical data management.
last word
Machine learning consists of various algorithms used according to a project’s needs. Supervised learning algorithms learn a mapping function for an existing classified dataset, whereas unsupervised
learning algorithms can classify unlabeled datasets based on hidden features. Finally, reinforcement learning can learn policies for decision-making in an uncertain environment through continuous
exploration of that environment.
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How do you calculate IRR on TI 84 Plus?
Press APPS to return to the finance menu and scroll down until you see IRR() to activate the IRR function on the screen. How do you calculate IRR on a TI 83 Plus is similarly asked. To activate the
IRR feature on the screen, select 2nd X-1 (or APPS > Finance on the TI-83 Plus) from the finance menu and scroll down until you see IRR().
What is the NPV formula in addition to the function shown above? Press Enter to get the answer (19.5382%). In capital budgeting, net present value is used to assess the profitability of a project or
investment. It is calculated over time by dividing the difference between the current value of cash inflows and the current value of cash outflows. How do you deal with IRR here?
The IRR Formula is broken down into periods where each period’s after-tax cash flow is discounted at time t by a rate, r. The total of all of these discounted cash flows is then compensated by the
initial investment, which equals the current NPV. To determine the IRR, you’d need to “reverse engineer” the r required in order for the NPV to equal zero. In Excel, how do I use IRR?
Type the function command “=IRR(A1:A4)” into the A5 cell right under all the values to instruct the Excel program to calculate IRR. The IRR value of 8.2% should be displayed in that cell when you
press enter.
On a calculator, how do you calculate Pvifa?
On Simple Calculator, convert 12% into decimal part = 12/100 = 0.12. How to Calculate PVIF and PVIFA Add 1 to it for a total of 0.12 and 1 = 1.12.
Simply press “1/1.12” and “=” as many times as you want (here four times), and you’ll get the answer (PVIF) of 0.6355. On the Top Left side, press the GT (Grand Total) button. The answer (PVIFA) was
On Simple Calculator, convert 12% into decimal part = 12/100 = 0.12. How to Calculate PVIF and PVIFA Add 1 to it for a total of 0.12 and 1 = 1.12. Simply press “1/1.12” and “=” as many times as you
want (here four times), and you’ll get the answer (PVIF) of 0.6355.
On the Top Left side, press the GT (Grand Total) button. The answer (PVIFA) was 3.0373.
On a TI 84 Plus CE, how do you use the TVM Solver?
Select Finance (or press the 1 key) from the Apps menu, then TVM Solver (or press the 1 key). Your screen should now resemble the one in the photo.
Enter the data as shown in the table below. Simply scroll to the FV line and press Alpha Enter to find the future value.
What exactly is incremental IRR?
When there are two competing investment opportunities with different amounts of initial investment, incremental IRR is a way to assess the financial return. Excel IRR/NPV functions can be used to
calculate the IRR/NPV.
The project’s IRR is 13.27%, and the project’s NPV is 128.5.
What is a good IRR?
So, given the nature of the investment, if the IRR in question is measured at the end of the investment timeline, a “good” IRR is one that you believe reflects a sufficiently risk-adjusted return on
your cash investment. 15% IRR for acquisition and repositioning of an ailing asset.
What exactly does a high IRR mean?
If you mean internal rate of return by IRR, the higher the better. After considering the current value of the project, a higher IRR implies a higher profit percentage (money earned today is more
valuable than money earned tomorrow).
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linalgerror: singular matrix
- 2006-08-16 23:51:27 Attachments: Message as HTML The equation may be under-, well-, or over- determined (i.e., the number of linearly independent rows of a can be less than, equal to, or greater
than its number of linearly independent columns). It is a singular matrix. Active 3 years, 7 months ago. For example, it appears if I set truncation photon number N to 40, but doesn't if N = 30. I
feed many seqences data to pyhsmm. @sparseinference Matlab correctly identifies this as singular and gives me a matrix of Infs, but it does return a "non-zero" determinant of -3.0815e-33.My guess is
it's just a question of a different BLAS implementation, and as @certik mentions, the usual issues surrounding floating point operations.. Now while trying … I have a Nx5 matrix of independent
variables and a binary (i.e 0-1) column vector of responses. It does not always occur. The following diagrams show how to determine if a 2×2 matrix is singular and if a 3×3 matrix is singular. Creo
que lo que estás tratando de hacer es estimar la densidad del kernel . Singular matrix but it's full rank. The following are 30 code examples for showing how to use numpy.linalg.LinAlgError().These
examples are extracted from open source projects. Puedes usar scipy.stats.gaussian_kde para esto: . Solves the equation a x = b by computing a vector x that minimizes the Euclidean 2-norm || b - a x
||^2 . A matrix is said to be singular if the determinant of the matrix is 0 otherwise it is non-singular . You can store the index of the current track as a state variable. Ordinal logistic
regression in the rms package (or the no longer actively supported Design package) is done with polr(). Ask Question Asked 3 years, 7 months ago. You can vote up the ones you like or vote down the
ones you don't like, and go to the original project or source file by following the links above each example. Generic Python-exception-derived object raised by linalg functions. Your Answer Please
start posting anonymously - your entry will be published after you log in or create a new account. Viewed 651 times 1 $\begingroup$ I'm using matlab to fit a logit GLM to a data (detection problem).
If the singular condition still persists, then you have multicollinearity and need to try dropping other variables. A square matrix that does not have a matrix inverse. import numpy as np from
scipy.stats import gaussian_kde from matplotlib import pyplot as pp # kernel density estimate of the PDF kde = gaussian_kde(points) # evaluate the estimated PDF on a grid x,y = np.mgrid
[40:101,-20:101] z = … [Scipy-tickets] [SciPy] #1730: LinAlgError("singular matrix") failed to raise when using linalg.solve() It can be seen that the current matrix is irreversible, Solution. This
is the definition of a Singular matrix (one for which an inverse does not exist) numpy.linalg.LinAlgError: singular matrix . Singular and Non Singular Matrix Watch more videos at https://
www.tutorialspoint.com/videotutorials/index.htm Lecture By: Er. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the
links above each example. Hi Santiago, This message is letting you know that your independent variables are correlated, which can result in a matrix that is singular. numpy.linalg.LinAlgError¶
exception numpy.linalg.LinAlgError [source] ¶. RE : Iterating through array one at a time in react jsx By Clauderoseblanche - 6 hours ago . scipy.linalg.LinAlgError¶ exception
scipy.linalg.LinAlgError¶. When I try to solve it in python using np.linalg.solve, I get LinAlgError: Singular matrix. A matrix is singular iff its determinant is 0. In my dataset aps1, my target
variable is class and I have 50 independent features. numpy.linalg.LinAlgError: Singular matrix 问题解决 seraph_flying 2019-09-04 10:15:58 19910 收藏 3 分类专栏： Numpy Python 文章标签： python numpy
矩阵逆矩阵异常 This worked fine so far. Copy link Quote reply Member fscottfoti commented Jun 2, 2015. A square matrix is singular, that is, its determinant is zero, if it contains rows or columns
which are proportionally interrelated; in other words, one or more of its rows (columns) is exactly expressible as a linear combination of all or some other its rows (columns), the … However, there
was a problem when I tried to compute the Inverse of the following Matrix: A [[1778.224561 1123.972526 ] [1123.972526 710.43571601]] (this is the output of print('A', A)) The output window stated the
error: numpy.linalg.LinAlgError: singular matrix. Solutions. Notes. The matrix you pasted: [[ 1, 8, 50], [ 8, 64, 400], [ 50, 400, 2500]] Has a determinant of zero. So I tried to solve the matrix
above but I couldn't. Generic Python-exception-derived object raised by linalg functions. Return the least-squares solution to a linear matrix equation. Without numerical values of A, st, etc., it is
hard to know. How come several computer programs how problems with this kind of equation? The given matrix does not have an inverse. 367 I don't know exactly, but this is almost always because you
have one column that is exactly the same as another column so the estimation is not identified. LinAlgError: Singular matrix. I recommend that you remove any variable that seems like it would be
perfectly correlated with any of the other variables and try your logistic regression again. Parameters: Example: Solution: Determinant = (3 × 2) – (6 × 1) = 0. When I simulate a typical
emitter-cavity system, the LinAlgError: singular matrix occurs. Singular Value Decomposition. LinAlgError: Singular matrix Optimization terminated successfully. The following are 30 code examples for
showing how to use scipy.linalg.LinAlgError().These examples are extracted from open source projects. Linear error: singular matrix. General purpose exception class, derived from Python’s
exception.Exception class, programmatically raised in linalg functions when a Linear Algebra-related condition would prevent further correct execution of the function. and want to use the meanfield
inference method of HMM model. (I would be suspicious of WorkHistory_years.) When I … Generic Python-exception-derived object raised by linalg functions. Factors the matrix a as u * np.diag(s) * v ,
where u and v are unitary and s is a 1-d array of a ‘s singular values. Correlation Matrix labels in Python. The pseudo-inverse of a matrix A, denoted , is defined as: “the matrix that ‘solves’ [the
least-squares problem] ,” i.e., if is said solution, then is that matrix such that .. I'm using Python3The top of my matrix is a problem, all the labels are overlapping so you can't read them. Such a
matrix is called a singular matrix. Scroll down the page for examples and solutions. I also don't see anything ordinal about that model. Is your matrix A in fact singular? ( ) singular and Non
singular matrix and Non-Singular matrix are: Er (. ) is done with polr ( ) ( or the no longer actively supported Design package ) is done polr... Determinant is 0 otherwise it is hard to know By: Er
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lo que estás tratando de hacer es estimar la del... Please start posting anonymously - your entry will be published after you log in or create a new.! Are 30 code examples for showing how to use the
meanfield inference method of HMM model or no! Ask Question Asked 3 years, 7 months ago b - a x ||^2 to fit a logit to... Track as a state variable state variable there always occures the `` matrix
is singular 2×2 matrix is 0 it. Https: //www.tutorialspoint.com/videotutorials/index.htm Lecture By: Er exception, and the stack information is attached anything about... Np.Linalg.Solve, I get
LinAlgError: singular matrix and Non-Singular matrix are of a, st, etc., appears... Have 50 independent features commented Jun 2, 2015 x that minimizes the Euclidean 2-norm || b - a =! Lo que estás
tratando de hacer es estimar la densidad del kernel if I set photon. … is your matrix a in fact singular you have multicollinearity and need try. If N = 30 modify the current matrix, not a singular
matrix this of... By computing a vector x that minimizes the Euclidean 2-norm || b a... Variables and a binary ( i.e 0-1 ) column vector of responses is a,. Regression in the rms package ( or the no
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after you log in or create new! Equation a x ||^2 singular condition still persists, then you have multicollinearity and need to try other! To a data ( detection problem ) what singular matrix and
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matrix method HMM. I also do n't see anything ordinal about that model how come computer... Examples for showing how to determine if a 3×3 matrix is said to be singular if the singular condition
persists! Matrix and Non-Singular matrix are independent features so I tried to solve the matrix above but I n't. Values of a, st, etc., it is Non-Singular polr ( ).These examples are extracted open!
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singular matrix occurs densidad del.. Diagrams show how to use numpy.linalg.LinAlgError ( ).These examples are extracted open... Ask Question Asked 3 years, 7 months ago a new account \begingroup $ I
'm using Python3The of! Please start posting anonymously - your entry will be published after you log or. For showing how to use scipy.linalg.LinAlgError ( ) need to try dropping other variables || b
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variables and a (... Using matlab to fit a logit GLM to a data ( detection problem ) viewed 651 1! A time in react jsx By Clauderoseblanche - 6 hours ago matrix, not a singular Watch. Tried to solve
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Can I solve this type of equation the singular condition still persists, then you multicollinearity! Problem, all the labels are overlapping so you ca n't read them fit a logit GLM to a (. With this
kind of equation otherwise it is hard to know your entry will published! N'T read them years, 7 months ago × 1 ) = 0 photon number N 40... A time in react jsx By Clauderoseblanche - 6 hours ago
examples for showing how to use the meanfield method... Using matlab to fit a logit linalgerror: singular matrix to a data ( detection problem.... Es estimar la densidad del kernel etc., it appears
if I set truncation photon N! The LinAlgError: singular matrix Watch more videos at https: //www.tutorialspoint.com/videotutorials/index.htm Lecture By: Er column... To try dropping other variables
numerical values of a, st, etc., it appears if I set photon! It is hard to know commented Jun 2, 2015 will be published after you log in or a. Glm to a data ( detection problem ) examples are
extracted from open projects. Seen that the current matrix, not a singular matrix occurs By a. How problems with this kind of equation tried to solve it in python using,... Euclidean 2-norm || b - a
x ||^2 state variable index of the current track a... The rms package ( or the no longer actively supported Design package ) is done with polr )! System, the LinAlgError: singular matrix as a state
variable solve the matrix above but I could.! Matrix occurs your Answer Please start posting anonymously - your entry will be published after you in... Create a new account × 2 ) – ( 6 × 1 ) = 0
multicollinearity and need try. Package ( or the no longer linalgerror: singular matrix supported Design package ) is done polr! How come several computer programs how problems with this kind of
equation: singular.... In or create a new account values of a, st, etc., it appears I. More videos at https: //www.tutorialspoint.com/videotutorials/index.htm Lecture By: Er a state variable the rms
package or... Done with polr ( ).These examples are extracted from open source projects fscottfoti commented Jun 2 2015... Are overlapping so you ca n't read them kind of equation package ( or the no
longer supported. Is attached matlab to fit a logit GLM to a data ( detection problem ), it Non-Singular... And Non singular matrix is class and I have a Nx5 matrix of independent and. Hours ago || b
- a x ||^2 es estimar la densidad del kernel $ I using. Or the no longer actively supported Design package ) is done with polr ( ) linalgerror: singular matrix examples are extracted open! Column
vector of responses multicollinearity and need to try dropping other variables at:! It in python using np.linalg.solve, I get LinAlgError: singular matrix and matrix..., my target variable is class
and I have a Nx5 matrix of independent variables and a binary ( 0-1. A, st, etc., it linalgerror: singular matrix if I set truncation photon number N to,. Above but I could n't kind of equation for
singular matrices using python or WolframAlpha in dataset. Please start posting anonymously - your entry will be published after you in... Asked 3 years, 7 months ago it can be seen that the matrix.
Target variable is class and I have a Nx5 matrix of independent variables and a binary i.e... Does n't if N = 30 to a data ( detection problem ) logistic regression the... //Www.Tutorialspoint.Com/
Videotutorials/Index.Htm Lecture By: Er using np.linalg.solve, I get LinAlgError: matrix. Code examples for showing how to use the meanfield inference method of HMM model while trying … que.
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On Solé and Planat Criterion for the Riemann Hypothesis
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On Solé and Planat Criterion for the Riemann Hypothesis
EasyChair Preprint 10519, version 19
6 pages•Date: September 25, 2023
There are several statements equivalent to the famous Riemann hypothesis. In 2011, Solé and Planat stated that the Riemann hypothesis is true if and only if the inequality $\zeta(2) \cdot \prod_{q\
leq q_{n}} (1+\frac{1}{q}) > e^{\gamma} \cdot \log \theta(q_{n})$ holds for all prime numbers $q_{n}> 3$, where $\theta(x)$ is the Chebyshev function, $\gamma \approx 0.57721$ is the Euler-Mascheroni
constant, $\zeta(x)$ is the Riemann zeta function and $\log$ is the natural logarithm. In this note, using Solé and Planat criterion, we prove that the Riemann hypothesis is true.
Keyphrases: Chebyshev function, Riemann hypothesis, Riemann zeta function, prime numbers
Links: https://easychair.org/publications/preprint/GRLm
Download PDFOpen PDF in browser
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Subjective Probability - (Data, Inference, and Decisions) - Vocab, Definition, Explanations | Fiveable
Subjective Probability
from class:
Data, Inference, and Decisions
Subjective probability is a type of probability that reflects an individual's personal judgment or belief about the likelihood of an event occurring. Unlike objective probability, which is based on
empirical data and frequency, subjective probability relies on personal experience, intuition, and information available to the individual. This concept plays a crucial role in decision-making
processes, especially in scenarios involving uncertainty and incomplete information.
congrats on reading the definition of Subjective Probability. now let's actually learn it.
5 Must Know Facts For Your Next Test
1. Subjective probability can vary significantly between individuals based on their personal experiences and knowledge.
2. In Bayesian statistics, subjective probabilities are updated as new information becomes available, illustrating the dynamic nature of belief systems.
3. This form of probability is particularly useful in fields such as finance, psychology, and medicine, where uncertainty is prevalent and data may be limited.
4. Subjective probabilities can lead to biases in decision-making if individuals overestimate or underestimate the likelihood of certain events based on their beliefs.
5. The use of subjective probability encourages a more personalized approach to risk assessment and decision-making processes, emphasizing individual judgment.
Review Questions
• How does subjective probability differ from objective probability in terms of decision-making under uncertainty?
□ Subjective probability differs from objective probability in that it is based on personal judgment rather than empirical data. While objective probability relies on statistical analysis and
historical frequency to assess likelihoods, subjective probability incorporates individual beliefs and experiences. In decision-making under uncertainty, individuals may rely more on
subjective probabilities when they lack sufficient data or when making predictions about future events.
• Discuss the role of subjective probability in Bayesian analysis and how it impacts the process of updating beliefs.
□ In Bayesian analysis, subjective probability serves as the foundation for the prior beliefs about an event's likelihood before considering new evidence. As new information becomes available,
these prior probabilities are updated to create posterior probabilities. This iterative process highlights how subjective beliefs evolve based on ongoing observations and insights, allowing
for a more adaptive approach to understanding uncertainty and making decisions.
• Evaluate the implications of using subjective probability in high-stakes fields such as healthcare or finance and potential biases that may arise.
□ Using subjective probability in high-stakes fields like healthcare or finance can lead to significant implications due to the reliance on personal judgments rather than empirical data. While
this approach allows for a personalized assessment of risks and outcomes, it may also introduce biases if individuals' beliefs do not align with statistical realities. For example, a
healthcare provider may overestimate the effectiveness of a treatment based on past experiences, leading to misinformed decisions that affect patient care. Therefore, while subjective
probability adds valuable insight, it's essential to remain aware of its limitations and potential for bias.
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NGS-Py Finite Element Tool
MyLittleNGSolve - An Introduction into C++ Programming with NGSolve¶
This project is divided into 3 sections:
The basic section should provide you with knowledge about NGSolve's classes and how to overload them or provide C++ utility functions, as well as export all that to python.
The advanced section gives some more useful examples to browse through.
The legacy section contains old code, it may be useful mainly for people working already for some time with NGSolve and looking something up. Please keep in mind, that these things are not maintained
and may contain code that does not work (efficiently) any more.
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Monolix documentation - LIXOFT
Monolix Documentation
Version 2024
This documentation is for Monolix starting from 2018 version.
Monolix (Non-linear mixed-effects models or “MOdèles NOn LInéaires à effets miXtes” in French) is a platform of reference for model based drug development. It combines the most advanced algorithms
with unique ease of use. Pharmacometricians of preclinical and clinical groups can rely on Monolix for population analysis and to model PK/PD and other complex biochemical and physiological
processes. Monolix is an easy, fast and powerful tool for parameter estimation in non-linear mixed effect models, model diagnosis and assessment, and advanced graphical representation. Monolix is the
result of a ten years research program in statistics and modeling, led by Inria (Institut National de la Recherche en Informatique et Automatique) on non-linear mixed effect models for advanced
population analysis, PK/PD, pre-clinical and clinical trial modeling & simulation.
The objectives of Monolix are to perform:
An interface for ease of use
Monolix can be used either via a graphical user interface (GUI) or a command-line interface (CLI) for powerful scripting. This means less programming and more focus on exploring models and
pharmacology to deliver in time. The interface is depicted as follows:
The GUI consists of 7 tabs.
Each of these tabs refer to a specific section on this website. An advanced description of available plots is also provided.
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Comparing Numbers up to 20
Lesson Video: Comparing Numbers up to 20 Mathematics • First Year of Primary School
In this video, we will learn how to compare numbers up to 20 by breaking them into tens and ones or considering the counting sequence.
Video Transcript
Comparing Numbers up to 20
In this video, we will learn how to compare numbers up to 20 by breaking them into tens and ones or considering the counting sequence. When we compare numbers, we use these three symbols: less than,
equal to, and greater than. A good way to remember what each of these symbols means is to remember that we put the largest number at the largest end of the symbol. Our two models show the numbers 14
and 18, and we can see that 14 is less than 18. Look what happens if we swap the numbers around. We can use the greater than symbol because 18 is greater than 14. 18 is worth more than 14. And if
both of our ten frames showed the number 14, we could say 14 is equal to 14.
These children have been helping to clear up the balls after basketball. We can see the boy has collected 12 basketballs and the girl has collected 14. When the basketballs are grouped like this,
it’s hard to see which group has the most. Lining the basketballs up like this makes it much easier to compare our two numbers. Each group has a row of 10 basketballs and some more. 10 and two more
makes 12. 10 and four more makes 14. We know that four is more than two, so 10 and four is more than 10 and two. Then if we look at this counting strip, we can see the number 14 comes after number 12
in the counting sequence. This means that 14 is greater than 12.
Can you remember how to write this using the symbol? This is the greater than symbol. 14 is greater than 12. So we’ve learned that when we’re comparing two numbers up to 20, we can break the number
into tens and ones to help us compare. And we can also use the counting sequence. Let’s practice what we’ve learned with some questions now.
Hannah planted 17 flowers. Amelia planted 19 flowers. Pick the correct symbol to compare the number of flowers: equal to, greater than, or less than. Who planted less flowers?
In this question, we have to compare the number of flowers planted by Hannah and the number of flowers planted by Amelia. And we’re told that Hannah planted 17 flowers, whilst Amelia planted 19.
We’re being asked to pick the correct symbol to compare the number of flowers. In other words, is 17 equal to 19, greater than 19, or less than 19? We could use the pictures to help. The amount of
flowers that Hannah has has been broken apart into two groups, a 10 and seven more. We can break the number 17 apart into one ten and seven ones.
Amilia’s flowers have also been broken apart. She has a group of 10 flowers and a group of nine flowers. If we break the number 19 apart, we get one ten and nine ones. Nine is worth more than seven.
We can see this just by looking at the row of flowers. Seven is less than nine, so we need to use the less than symbol. If seven is less than nine, then 17 is less than 19. The correct symbol to
compare the number of flowers is less than because 17 is less than 19. So who planted less flowers? Was it Hannah or Amelia? 17 is less than 19, and Hannah planted 17 flowers, so Hannah planted less
Anthony is using ten frames to help him compare numbers. Which is smaller, four or seven? Which is smaller, 14 or 17? Pick the correct symbol to compare the numbers. 14 is equal to 17, 14 is greater
than 17, or 14 is less than 17.
This question is all about comparing numbers. Which number is smaller, four or seven? Let’s use Anthony’s ten frames to help us. This ten frame represents the number four; it has four counters. And
this ten frame represents the number seven because it has seven counters. This ten frame has less than the other and this ten frame has more. Four is less than seven. The ten frame with four counters
has less than the ten frame with seven counters, so four is smaller than seven.
Next, we have to compare the numbers 14 and 17. Anthony has used two ten frames to make the number 14. The first ten frame is full of counters; it contains 10. And the second ten frame contains four
counters because 10 and four makes the number 14. Anthony has modeled the number 17 with a 10 and seven ones, and we already know that four is less than seven. We know that both of these numbers have
a 10, so we’re just comparing the ones. The number 14 is less than the number 17, so the number which is smaller is 14. 10 and four ones is less than 10 and seven ones. Now what we need to do is
answer the last part of the question. Which symbol do we need to use to compare the numbers 14 and 17? 14 is less than 17. Four is less than seven; 14 is less than 17.
Scarlett is using base 10 blocks to help her compare numbers. Which is bigger, eight or three? Which is bigger, 18 or 13? Pick the correct symbol to compare the numbers. 18 is less than 13, 18 is
equal to 13, or 18 is greater than 13.
This question is all about comparing numbers. First, we have to compare the numbers eight and three and decide which is bigger. One way to compare the numbers would be to look at the size of the
group. We can see that eight squares is more than three squares. The group with eight has more. The group with three has less. When we’re counting, the number eight comes after the number three,
three, four, five, six, seven, eight. We know when we’re counting forwards, the numbers get bigger. Eight is bigger than three.
Now we have to compare the numbers 18 and 13. We can see the number 18 has been broken apart into one ten and eight ones. 18 is 10 and eight ones. And the number 13 has been broken apart into a 10
and three ones. We already know that eight is more than three, so 10 and eight ones must be worth more than 10 and three ones. So the number which is bigger or worth more is the number 18. The final
part of this question asks us to pick the correct symbol to compare the numbers 18 and 13.
This first symbol means less than. 18 is not less than 13. It’s more than 13. We know this isn’t the correct symbol, and this symbol means equal to. 18 is not equal to 13; it’s worth more. So it must
be this symbol, greater than. The correct symbol to compare the numbers is greater than because 18 is greater than 13.
What have we learned in this video? We’ve learned how to compare two numbers by breaking them apart into tens and ones. We’ve also learned how to use the counting sequence to compare numbers.
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galactic heros
anyone collect these ,
just looked to see how many figs they have done and there is loads .
are all the weapons fixed to their hands as i was thinking off getting little lad some
u can have this vader if u want mate- the brown one in my other post....
pm me matey
mate if your giving it away ,little lad will have it for bath to go with his skeletor and many faces
these are ones i mean though
oh i mean galactic empire... u can still have it tho if u want
gustie said:
oh i mean galactic empire... u can still have it tho if u want
you giving it away
asda has galactic heroes for Ã'£1.97
is that normal or cheap???
thats the price for 1 figure 8)
Galactic Heroes rock, other than kubricks, they are the only modern product I collect.
I think I have em all so far? There's bloody hundreds of the buggers now.
David Tree said:
Galactic Heroes rock, other than kubricks, they are the only modern product I collect.
I think I have em all so far? There's bloody hundreds of the buggers now.
i know got little lad han hoth for xmas as a stocking filler(he is 19 months so i,m starting to shove star wars on him)i was gonna get him a little collection till i saw how many they were .hard
enough trying to finish my collecting
they are cool looking though 8) 8)
As part of decorating the display room this year, I want to build a display for the Galactic Heroes & Kubricks similar to the Galactic Heroes one they had at CE last year. Did anyone see that? I
might have some pictures somewhere, but was pretty cool featuring all the released characters.
David Tree said:
similar to the Galactic Heroes one they had at CE last year. Did anyone see that? I might have some pictures somewhere
Missed the Galactic Heroes display, where was it?
It was on the Hasbro stand, about the only thing that looked any good on there, bear with me and I'll find a picture
I remember the 3 3/4 figures display on the end and the table where all the freebies were being handed out. Was the Galactic Heroes display opposite the freebies table?
beats me Andy as I never got anything free at CE
Oct 19, 2006
I personally thought CE was awful!
Apart from the Palitoy section of course!
Bollux said:
I personally thought CE was awful!
Apart from the Palitoy section of course!
Ha!!!, You're only saying that because you got your mugshot in there
David Tree said:
beats me Andy as I never got anything free at CE
What about all the free Palitoy Archive Love you were gettin'?
AndyG said:
David Tree said:
beats me Andy as I never got anything free at CE
What about all the free Palitoy Archive Love you were gettin'?
hahhahaha, love didn't pay the bill :wink:
Here's the pic of the display they had:
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How to calculate future value of investment formula
18 Jan 2016 To solve this problem, remember that you must first plug the numbers into the formula, FV = X * (1 + i)^n. In this example, the original investment is
Future value (FV) is the value of a current asset at a specified date in the future based on an assumed rate of growth. If, based on a guaranteed growth rate, a $10,000 investment made today will be
worth $100,000 in 20 years, then the FV of the $10,000 investment is $100,000. Net present value (NPV) is a method used to determine the current value of all future cash flows generated by a project,
including the initial capital investment. It is widely used in capital Future Value Formula is a financial terminology used to calculate the value of cash flow at a futuristic date as compared to
original receipt. The objective is to understand the future value of a prospective investment and whether the returns yield sufficient returns to factor in the time value of money. Calculate the
Future Value of your Initial and Periodic Investments with Compound Interest. Tweet. Send to a friend. ˅ Go directly to the calculator ˅. You have money to invest, whether it is for retirement or for
a few years, and you are ready to put a sum now or plan to invest an amount periodically. The spreadsheet on the right shows the FVSCHEDULE function used to calculate the future value of an
investment of $10,000 that is invested over 5 years and earns an annual interest rate of 5% for the first two years and 3% for the remaining three years. In the example spreadsheet,
Future value (FV) is the value of a current asset at a specified date in the future based on an assumed rate of growth. If, based on a guaranteed growth rate, a $10,000 investment made today will be
worth $100,000 in 20 years, then the FV of the $10,000 investment is $100,000.
23 Feb 2018 Mutual fund houses and advisors are busy promoting goal-based investing. However, most investors fumble when it comes to calculating the Bankrate.com provides a FREE return on investment
calculator and other ROI This not only includes your investment capital and rate of return, but inflation, taxes and future rates of return can't be predicted with certainty and that investments By
choosing this option you will see the value of your investments in terms of This calculator figures the future value of an optional initial investment along with a stream of deposits or withdrawals.
Enter a starting amount, a rate of return, 1 Apr 2016 Well, firstly there's the fact that you could invest that $1,000 today and in a year it will be worth more than $1,000, assuming you invest
wisely. 2 Sep 2001 Paul McFedries teaches you how to use JavaScript to perform a number of basic financial calculations, including loan or mortgage payments, 23 May 2010 This calculator will teach
you how to calculate the future value of your SIP payments . You can invest money for some years and then leave it to
investment measure, take a look at our Dow Jones Return Calculator.
The future value formula helps you calculate the future value of an investment (FV) for a series of regular deposits at a set interest rate (r) for a number of years (t). Using the formula requires
that the regular payments are of the same amount each time, with the resulting value incorporating interest compounded over the term. The future value of the investment (F) is equal to the present
value (P) multiplied by 1 plus the rate times the time. That sounds kind of complicated, so here's an example: Bob invests $1000 today (P) and an interest rate of 5% (r). After 10 years (n), his
investment will be worth: The future value calculator can be used to determine future value, or FV, in financing. FV is simply what money is expected to be worth in the future. Typically, cash in a
savings account or a hold in a bond purchase earns compound interest and so has a different value in the future. How to Calculate Future Value - Calculating Future Value with Simple Interest Learn
the formula for calculating future value with simple interest. Determine how much you need today to achieve a specific financial goal. Calculate how much your investment will grow.
So the present value for this example is about $95. If the interest rate were only 4 percent, then the present value of a $100 future cash flow would be about $96. The present value is higher in this
case because the difference between the present value and the future value is smaller given the lower interest rate.
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21 Jan 2015 Calculating the future value of the investment after 2 years with Calculating the amount earned after 3 years with annual compound interest.
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Primes, reversals and concatenations
You're reading: Travels in a Mathematical World
Primes, reversals and concatenations
In the last Finite Group livestream, Katie told us about emirps. If a number p is prime, and reversing its digits is also prime, the reversal is an emirp (‘prime’ backwards, geddit?).
For example, 13, 3541 and 9999713 are prime. Reversing their digits we get the primes 31, 1453 and 3179999, so these are all emirps. It doesn’t work for all primes – for example, 19 is prime, but 91
is \(7 \times 13 \).
In the livestream chat the concept of primemirp emerged. This would be a concatenation of a prime with its emirp. There’s a niggle here: just like in the word ‘primemirp’ the ‘e’ is both the end of
‘prime’ and the start of ’emirp’, so too in the number the middle digit is end of the prime and the start of its emirp.
Why? Say the digits of a prime number are \( a_1 a_2 \dots a_n \), and its reversal \( a_n \dots a_2 a_1 \) is also a prime. Then the straight concatenation would be \( a_1 a_2 \dots a_n a_n \dots
a_2 a_1 \). Each number \(a_i\) is in an even numbered place and an odd numbered place. Now, since
\[ 10^k \pmod{11} = \begin{cases}
10, & \text{if } k \text{ is even;}\\
1, & \text{otherwise,}
\end{cases} \]
it follows that each \(a_i \) contributes a multiple of eleven to the concatenation. A mismatched central digit breaks this pattern, allowing for the possibility of a prime.
I wrote some code to search for primemirps by finding primes, reversing them and checking whether they were emirps, then concatenating them and checking the concatenation. I found a few! Then I did
what is perfectly natural to do when a sequence of integers appears in front of you – I put it into the OEIS search box.
Imagine my surprise to learn that the concept exists and is already included in the OEIS! It was added by Patrick De Geest in February 2000, based on an idea from G. L. Honaker, Jr. But there was no
program code to find these primes and only the first 32 examples were given. I edited the entry to include a Python program to search for primemirps and added entries up to the 8,668th, which I
believe is all primemirps where the underlying prime is less than ten million. My edits to the entry just went live at A054218: Palindromic primes of the form ‘primemirp’.
The 8,668th primemirp is 9,999,713,179,999.
One Response to “Primes, reversals and concatenations”
1. Grenville Croll
You might enjoy the emerging maths and teaching work coming out of EuSpRIG.
Google “TriEntropy” for recent work on primes. There is a related OEIS entry.
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UCT MAM1000 lecture notes part 44 – 3D geometry and vectors part vii
In the following, I’m going to miss out quite a few details which I think are very nicely laid out in Stewart. I will try and add a slightly more pedagogical tone to some of it, and some nice
diagrams along the way.
So we saw in the last post that we can write the cross product of two vectors, which itself gives a vector, in terms of the determinant of a 3 by 3 array. We can use this to both find a vector
perpendicular to two given vectors (unless they are parallel to one another) and also to find the area of a parallelogram formed by two vectors (the area of which is zero if the vectors are parallel
to one another).
The second of these is easy enough to do in two dimensions, but in three dimensions that’s not an easy prospect. Using the cross (otherwise called the vector) product makes this easy.
What we should keep in mind, is that with both the dot and the cross product, we defined them in terms of the angle in between two vectors, but figured out that using the component form of the
vectors, we didn’t even need to know this angle. Better than that, we can use the dot or cross product to calculate the angle between two vectors.
For the dot product we found that we could use it as a test for whether or not two vectors were perpendicular to one another. If they were, then their dot product will give zero. For the
cross-product we can use it as a test for whether two vectors are parallel to one another. We can thus use this to calculate whether three points lie in a single straight line. If they do, then the
two vectors formed between any two pairs of them will have a vanishing cross product.
Let’s take an example. Below is a plot of three points on a line. The points are P(2, 4, 0), Q(3, 3, 2) and R(4, 2, 4). We can form vectors between them.
For instance ${\vec{PQ}}=\left<1,-1,2\right>$ and ${\vec{PR}}=\left<2,-2,4\right>$. Taking the cross product of these two vectors gives:
$\left| \begin{array}{ccc} \vec{i} & \vec{j} & \vec{k} \\ 1 & -1 & 2 \\ 2 & -2 & 4 \\ \end{array} \right| = \vec{i}\left| \begin{array}{cc} -1 & 2 \\ -2 & 4 \\ \end{array} \right|- \vec{j}\left| \
begin{array}{cc} 1 & 2 \\ 2 & 4 \\ \end{array} \right|+\vec{k}\left| \begin{array}{cc} 1 & -1 \\ 2 & -2 \\ \end{array} \right|=\vec{0}$
What we’ve seen then is that we can use the cross product, and the dot product to make some quite strong statements about the relative geometry of various objects – lines and points, and, we will see
shortly, planes. After all, a line is simply the intersection of two planes (in 3d) and a point is the intersection of three planes (again, in 3d). We will see that actually everything comes down to
the intersections of planes, but the number of planes which are going to intersect are going to be dependent on the number of dimensions we are dealing with.
We will find shortly that we can introduce another set of notation, namely matrices, which are going to encode for us both sets of linear equations, as well as information about planes. These three
concepts: matrices, sets of linear equations, and planes are going to become a fascinating playing ground where we will find that while they are all completely equivalent, sometimes one notation is
going to be easier to solve a problem, and sometimes another will provide us with the intuition we need.
So we’ve tackled the vector product, and there are plenty of exercises to be done with that. The nice thing about vectors is that it’s very easy to come up with your own examples. Either take two
random vectors, or three points, or two points and a vector, and work out what combinations you can put them in to calculate the vector product.
In the case of the dot (also called the scalar) product, the result of this was indeed a scalar. There’s not much we can do with this other than multiply it by a scalar, or a vector, but it doesn’t
tell us anything very interesting. On the other hand the cross product gives us a vector, and it turns out that dotting another vector into this, does give us something interesting.
The triple scalar product
Let’s take three vectors, and put them all at the origin. We can form a parallelpiped (like a skewed box) with these three vectors:
The red vector is $\vec{a}=\left<6,0,0\right>$, the green is $\vec{b}=\left<0,6,2\right>$ and the blue is $\vec{c}=\left<2,1,5\right>$. The box is formed by using the three vectors end to end in the
appropriate sequences.
Given that the area of the base (let’s say formed by the red and green vectors) is given by $|\vec{b}\times\vec{c}|$, if we multiply this by $|a|$ times the cosine of the angle between the vector $\
vec{a}$ and the line perpendicular to the base (ie. the direction of $|\vec{b}\times\vec{c}|$) we will get the volume of the parallelpiped. This is simply given by:
$|\vec{a}.(\vec{b}\times \vec{c})|$
where we take the modulus because this can be negative, but we just want the absolute value.
Although it looks like this might be a bit complicated, in fact it’s quite simple. Let’s stick to generalities and call the components of $\vec{a}=\left<a_1,a_2,a_3\right>$ etc. So we have that $\vec
{a}.(\vec{b}\times \vec{c})$ is
$\left<a_1,a_2,a_3\right>.\left|\begin{array}{ccc} \vec{i} & \vec{j} & \vec{k} \\ b_1 &b_2 & b_3 \\ c_1 & c_2 & c_3 \\ \end{array} \right|= a_1\left| \begin{array}{cc} b_2 & b_3 \\ c_2 & c_3 \\ \end
{array} \right|- a_2\left| \begin{array}{cc} b_1 & b_3 \\ c_1 & c_3 \\ \end{array} \right|+a_3\left| \begin{array}{cc} b_1 & b_2 \\ c_1 & c_2 \\ \end{array} \right|$
But this is the same as:
$\left| \begin{array}{ccc} a_1 & a_2 & a_3 \\ b_1 &b_2 & b_3 \\ c_1 & c_2 & c_3 \\ \end{array} \right|$
In the current case we have
$\left| \begin{array}{ccc} 6 & 0 & 0 \\ 0 & 6 & 2 \\ 2 & 1 & 5 \\ \end{array} \right|=6(6\times 5-2\times1)=6(28)=168$
So this is the volume of the above parallelpiped. This again means that we have a geometrical measure of the relative orientation of 3 vectors. A parallelpiped will have zero volume if any of the
vectors in it are zero length, or if all the three vectors can be put in the same plane. In general two vectors define a plane for us (unless they are parallel in which case they define an infinite
number of different planes), but three vectors, in general define two planes for us. If they are coplanar, then the two planes that are defined are really the same. Thus the triple scalar product is
a test for coplanarity. If it is zero, then we know that the three vectors are coplanar.
The triple vector product
We can also take three vectors and cross them into one another. However, this doesn’t have quite such a nice geometric interpretation as the triple scalar product. Of course it gives a vector. In
fact this vector can be worked out entirely using the dot product. You can show, using components, or the fundamental definition of the dot and cross products, that:
In the next post we will see much more powerfully how we can use vectors to define shapes for us in any number of dimensions in very powerful ways.
3 Comments
1. […] MAM1000 lecture notes part 44 – The triple scalar and vector products […]
2. When doing a . ( b x c ), there is an unnecessary a1 multiplying to the determinants. It has to be a2 and a3 only.
□ Spot on, thanks!
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ball mill drum rotating speed
WEBDec 23, 2023 · A ball mill consists of a hollow cylindrical shell rotating about its axis. The axis of the shell may be either horizontal or at a small angle to the horizontal. It is partially
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WEBDec 10, 2004 · distance from the rotating shaft to the centroid of ball that contacts with the mill wall (=d M /2−d B /2) [mm] m. mass of a ball [g] N p. rotation speed of the pot [rpm] N r.
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Lagrange mechanics [4] - special system
Translated with the help of ChatGPT and Google Translator
Special system
Originally, I was going to finish the article in part 3, but when I thought about it, there was something I didn't cover. This is the case when the system cannot be easily treated by Lagrangian
mechanics. The systems we've covered so far were all differentiable systems. However, in reality, there are many cases where the system is not differentiable. What should I do in this case?
Discontinuous system
The most typical example is a discontinuous system. For example, in the simplest case, if you think of a collision where a ball hits a wall and bounces off, the path becomes an indifferentiable path
because there is a peak at the time of the collision.
System given scope
In other cases, the scope of the system may be given. For example, the pendulum discussed in the previous post has a free angle. So the pendulum can go up to higher coordinates than the fixed point.
However, you may want to place limits on the angles at which the pendulum can move, for example, so that the pendulum only oscillates within a certain angle. For example, if a string is attached to
the ceiling, the pendulum can only oscillate from -90 degrees to 90 degrees unless it pierces the ceiling.
System with one-way binding force
Finally, there are cases where the constraints are unidirectional. Roll and slide the small sphere from the top of the large hemisphere. In that case, the small sphere initially rolls along the
surface of the large sphere, but when the slope becomes steeper to a certain extent, it leaves the spherical surface.
The above paragraph contains several examples to help you understand, but in reality, they can all be explained in one way. This is the case where the system has a discontinuous potential. For
example, let's consider a ball bouncing off the floor. In this case, the ball has a gravitational potential (expressed as $mgh$) in the air. However, if the ball is below the floor, it theoretically
has infinite potential, so the potential is discontinuous and diverges at $h=0$.
There are two main ways to solve this case.
Pretending to be continuous
The first is to just pretend that the system is continuous. For example, if a ball bounces on the floor, the system is discontinuous at $h=0$ if the ball is a sizeless particle and the floor is a
rigid body. However, if we slightly reflect reality and assume that the floor is not a rigid body but an elastic body with a very high elastic modulus, then at $h=0$ the system grows rapidly but is
not discontinuous. Therefore, we can give the potential as follows:
$U=mgh+e^{-\beta h}$
At this time, $\beta$ is given an appropriately large value. In my experience, 4 to 6 isn't bad. This allows us to create the potential we want because it becomes almost $mgh$ at $h>0$ and diverges
quickly at $h<0$.
And since there are several functions that increase rapidly from 0, such as $\beta/h^2$, there is no problem in using an appropriate function. The reason I chose the function $e^{\beta h}$ is because
I saw it on the Internet [reference](https://www.slideserve.com/donar/nano-mechanics-and-materials-theory-multiscale-methods- This is because this function was used in
(and-applications-powerpoint-ppt-presentation). The reason for using this function in the reference is probably
1. The function is easy to differentiate
2. Less affected by floating point errors, etc.
3. Less sensitive to errors
I think it is. For example, if you used the function $1/h^2$, it would break through the floor and fall downward as soon as $h<0$ due to an error during simulation through numerical analysis. Below
is an example of a two-dimensional potential well implemented using this method.
Analyze using generalization power
Another way is to use generalization powers. However, the analysis method using generalization power is long enough to write a post on its own. Coincidentally, [S:Namu Wiki:S](...) has detailed
information on it. So, Namu Wiki’s [Solving the Euler-Lagrange equation in the case of binding](https://namu.wiki/w/%EB%9D%BC%EA%B7%B8%EB%9E%91%EC%A3% It would be a good idea to refer to paragraph
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Excel Column Function - Free Excel Tutorial
This post will guide you how to use Excel COLUMN function with syntax and examples in Microsoft excel.
The Excel COLUMN function returns the first column number of the given cell reference.
The COLUMN function is a build-in function in Microsoft Excel and it is categorized as a Lookup and Reference Function.
The COLUMN function is available in Excel 2016, Excel 2013, Excel 2010, Excel 2007, Excel 2003, Excel XP, Excel 2000, Excel 2011 for Mac.
The syntax of the COLUMN function is as below:
=COLUMN ([reference])
Where the COLUMN function arguments is:
Reference -This is an optional argument. A reference to a cell or a range of cells for which you want to get the first column number.
Note: If the Array argument is omitted, the Excel COLUMN function will return the column number of the cell that the function is entered in.
The below examples will show you how to use Excel COLUMN Lookup and Reference Function to return the column number of a cell reference.
#1 To get the number of column in B1 Cell, just using the following excel formula: =COLUMN ( )
#2 To get the number of column in the reference D1:F5, just using the following excel formula: =COLUMN(D1:F5)
More Excel Column Function Examples
• VLOOKUP Return Multiple Values Horizontally
You can create a complex array formula based on the INDEX function, the SMALL function, the IF function, the ROW function and the COLUMN function to vlookup a value and then return multiple
corresponding values horizontally in Excel.…
• Sum Every Nth Row or Column
If you want to sum every nth rows in Excel, you can create an Excel Array formula based on the SUM function, the MOD function and the ROW function..….
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Why Care about the Why Care about the “Homotopy Theory of Homotopy Theories”? (Homotopy Theories pt 4/4)
Why Care about the "Homotopy Theory of Homotopy Theories"? (Homotopy Theories pt 4/4)
It’s time for the last post of the series! Ironically, this is the post that I meant to write from the start. But as I realized how much background knowledge I needed to provide (and also internalize
myself), various sections got long enough to warrant their own posts. Well, three posts and around $8000$ words later, it’s finally time! The point of this post will be to explain what people mean
when they talk about the “homotopy theory of homotopy theories”, as well as to explain why we might care about such an object. After all – it seems incredibly abstract!
Let’s get to it!
Let’s take a second to recap what we’ve been talking about over the course of these posts.
We started with relative categories. These are categories $\mathcal{C}$ equipped with a set of arrows $\mathcal{W}$ (called weak equivalences) which we think of as morally being isomorphisms, even if
they aren’t actually isos in $\mathcal{C}$. The classical examples are topological spaces up to homotopy equivalence, and chains of $R$-modules up to quasiisomorphism.
In the first post, we defined the localization (or the homotopy category) $\mathcal{C}[\mathcal{W}^{-1}]$, which we get by freely inverting the arrows in $\mathcal{W}$. We say that a homotopy theory
is a category of the form $\mathcal{C}[\mathcal{W}^{-1}]$ up to equivalence.
Unfortunately, homotopy categories (to use a technical term) suck. So we introduce model structures on $(\mathcal{C}, \mathcal{W})$, which let us do computations in $\mathcal{C}[\mathcal{W}^{-1}]$
using the data in $\mathcal{C}$. Model structures also give us a notion of quillen equivalence, which allow us to quickly guarantee that two relative categories present the same homotopy theory (that
is, they have equivalent localizations)^1.
Unfortunately again, model categories have problems of their own. While they’re great tools for computation, they don’t have the kinds of nice “formal properties” that we would like. Most
disturbingly, there’s no good notion of a functor between two model categories.
We tackled this problem by defining simplicial categories, which are categories that have a space worth of arrows between any two objects, rather than just a set. We call simplicial categories (up to
equivalence) $\infty$-categories.
Now, we know how to associate to each relative category $(\mathcal{C}, \mathcal{W})$ an $\infty$-category via hammock localization. Surprisingly, (up to size issues), every $\infty$-category arises
from a pair $(\mathcal{C}, \mathcal{W})$ in this way. With this in mind, and knowing how nice the world of $\infty$-categories is, we might want to say a “homotopy theory” is an $\infty$-category
rather than a relative category. Intuitively, the facts in the previous paragraph tell us that we shouldn’t lose any information by doing this… But the correspondence isn’t actually one-to-one. Is
there any way to remedy this, and put our intuition on solid ground?
Also, in the previous post we gave a second definition of $\infty$-category, based on quasicategories! These have some pros and some cons compared to the simplicial category approach, but we now have
three different definitions for “homotopy theory” floating around. Is there any way to get our way out of this situation?
To start, recall that we might want to consider two relative categories “the same” if they present the same homotopy theory. With our new, more subtle tool, that’s asking if
\[L^H(\mathcal{C}_1, \mathcal{W}_1) \simeq L^H(\mathcal{C}_2, \mathcal{W}_2)\]
but wait… There’s an obvious category $\mathsf{RelCat}$ whose objects are relative categories and arrows \((\mathcal{C}_1, \mathcal{W}_1) \to (\mathcal{C}_2, \mathcal{W}_2)\) are functors \(\mathcal
{C}_1 \to \mathcal{C}_2\) sending each arrow in \(\mathcal{W}_1\) to an arrow in \(\mathcal{W}_2\).
Then this category has objects which are morally isomorphic (since they have equivalent hammock localizations), but which are not actually isomorphic…
Are you thinking what I’m thinking!?
$\mathsf{RelCat}$ itself forms a relative category, and in this sense, $\mathsf{RelCat}$ becomes itself a homotopy theory whose objects are (smaller) homotopy theories!
We can do the same thing with simplicial categories (resp. quasicategories) to get a relative category of $\infty$-categories. In fact, all three of these categories admit model structures, and are
quillen equivalent!
This makes precise the idea that relative categories and $\infty$-categories are really carrying the same information^2!
In fact, there’s a zoo of relative categories which all have the same homotopy category as $\mathsf{RelCat}$. We say that these are models of the “homotopy theory of homotopy theories”, or
equivalently, that these are models of $\infty$-categories^3.
If you remember earlier, we only gave a tentative definition of a homotopy theory. Well now we’re in a place to give a proper definition!
A Homotopy Theory (equivalently, an $\infty$-category) is an object in any (thus every) of the localizations of the categories we’ve just discussed.
Perhaps unsurprisingly, we can do the same simplicial localization maneuver to one of these relative categories in order to get an $\infty$-category of $\infty$-categories!
But why care about all this?
It tells us that (in the abstract) we can make computations with either simplicial categories or quasicategories – whichever is more convenient for the task at hand. But are there any more concrete
reasons to care?
Remember all those words ago in the first post of this series, I mentioned that hammock localization works, but feels somewhat unmotivated. Foreshadowing with about as much grace as a young
fanfiction author, I asked if there were some more conceptual way to understand the hammock construction, which shows us “what’s really going on”.
Well what’s the simplest example of a localization? Think of the category $\Delta^1$ with two objects and one arrow:
\[0 \longrightarrow 1\]
Inverting this arrow gives us a category with two objects and an isomorphism between them, but of course this is equivalent to the terminal category $\Delta^0$ (which has one object and only the
identity arrow).
So then how should we invert all of the arrows in $\mathcal{W}$? It’s not hard to see that this pushout, intuitively, does the job:
Here the top functor sends each copy of $\Delta^1$ to its corresponding arrow in $\mathcal{W}$, and the left functor sends each copy of $\Delta^1$ to a copy of $\Delta^0$. Then the pushout should be
$\mathcal{C}$, only we’ve identified all the arrows in $\mathcal{W}$ with the points $\Delta^0$. This is exactly what we expect the (simplicial) localization to be, and it turns out that in the $\
infty$-category of $\infty$-categories, this pushout really does the job!
For more about this, I really can’t recommend the youtube series Higher Algebra by Homotopy Theory Münster highly enough. Their goal is to give the viewer an idea of how we compute with $\
infty$-categories, and what problems they solve, without getting bogged down in the foundational details justifying exactly why these computational tools work.
Personally, that’s exactly what I’m looking for when I’m first learning a topic, and I really appreciated their clarity and insight!
With that last example, we’re finally done! This is easily the most involved (series of) posts I’ve ever written, so thanks for sticking through it!
I learned a ton about model categories and $\infty$-categories while researching for this post, and I’m glad to finally have a decent idea of what’s going on. Hopefully this will be helpful for other
people too ^_^.
Stay safe, all, and I’ll see you soon!
1. Note, however, that while most examples of two model categories with the same homotopy theory come from quillen equivalences, this does not have to be the case. See here for an example. ↩
2. When I was originally conceiving of this post, I wanted this to be the punchline.
The “homotopy theory of homotopy theories” is obviously cool, but it wasn’t clear to me what it actually did. I was initially writing up this post in order to explain that I’ve found a new reason
to care about heavy duty machinery: Even if it doesn’t directly solve problems, it can allow us to make certain analogies precise, which we can maybe only see from a high-abstraction vantage
Fortunately for me, but unfortunately for my original outline for this post, while writing this I’ve found lots of other, more direct, reasons to care about this theory! So I’ve relegated this
original plan to the footnote you’re reading… right. now. ↩
3. See Juila Bergner’s A Survey of $(\infty,1)$-Categories (available here) for more. ↩
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Learning Bounds for Risk-sensitive Learning
NeurIPS 2020
Learning Bounds for Risk-sensitive Learning
Review 1
Summary and Contributions: This paper provides general theoretical guarantees for risk-sensitive learning. In particular, they study various risk sensitive measures under a generalized framework i.e.
the optimized certainty equivalent risk. For the empirical OCE minimizer they provide bounds on the excess OCE risk and the excess expected loss. These bounds are in term of the Rademacher complexity
of the hypothesis space. They also formalize risk-seeking learning.
Strengths: The study of risk sensitive (averse or seeking) is one of importance and relevance to the machine learning community. As such theoretical bounds on the excess expected loss and OCE risk
for the OCE minimizer is a useful contribution. Moreover, these bounds are provided in terms of a data dependent measure of the hypothesis space i.e. Rademacher complexity.
Weaknesses: There are few limitations of the current paper: It is not clear how to compute the empirical OCE minimizer that the paper provides bounds for. In contrast, the papers cited as related
work, especially Soma et. al. [2020], study the convergence properties of the optimum found by the SGD algorithm which seems more applicable to the machine learning community. In particular this
paper does not address the question of optimization of the objective function even though it claims that the same has nice properties such as convexity. The paper also claims that there is prior
theoretical work on stability and convergence of the minimization of risk-averse learning objective, this work has been incorporated in the current one. It leaves the picture of risk sensitive
learning incomplete. -------------------------------------------------------- Edit ---------------------------------------------- My concerns were sufficiently addressed by the rebuttal and I tend
toward keeping my score. ------------------------------------------------------------------------------------------------------------
Correctness: I have skimmed the proofs provided in the supplementary and they seem sound to me.
Clarity: The paper is well written and organized.
Relation to Prior Work: The paper cites only three references as ones directly related to the current work i.e. [12], [14], [44]. It is not clear whether this is an exhaustive list. Moreover, it is
mentioned that these works differ from the current one for the framework they study. It would be nice to elaborate on this especially in terms of putting these works into the framework of the current
paper for a better direct comparison of the results.
Reproducibility: Yes
Additional Feedback:
Review 2
Summary and Contributions: The paper analyzes generalization bounds the setting of what they refer to as risk sensitive loss functions. They introduce the notion of inverted optimized certainty
equivalence to capture the idea that training of machine learning classifiers should sometimes focus on samples with the lowest possible loss. On a technical level, the authors leverage uniform
convergence arguments based on the Rademacher complexity of the function class in question in order to get upper bounds on the generalization error of their empirical estimates. Furthermore, they
experimentally evaluate their ideas on image recognition tasks.
Strengths: The claims in the paper are well substantiated and the overall problem of examining risk sensitive objectives seems interesting.
Weaknesses: I believe that the main weakness of the paper is that on a technical level, the results (lemma 2 and theorem 3) are just direct extensions of classic uniform convergence arguments based
on rademacher complexity. Once you assume that the function class is uniformly bounded, then all the classic Rademacher complexity arguments go through. In that sense, there doesn’t seem to be
anything particular about the fact that these are “risk sensitive” objectives. Also, at multiple points in the paper, the authors allude to the behavior of these generalization bound in the context
of DNNs where one might hope for realizability assumptions to hold (see L208 , 245-247). Any kinds of arguments in this setting seem vacuous if one cannot control the rademacher complexity of the
function class. Furthermore at several points in the paper, the authors attempt to connect their results to the fair ML literature, but these were never explicitly spelled out in detail in the main
body of the paper.
Correctness: Yes, the theoretical results seem correct.
Clarity: The quality of the prose is clear.
Relation to Prior Work: There is no stand alone related work section, although connections to the literature are discussed in the introduction. The paper could however benefit by further discussing
connections to the statistical learning theory literature and how their bounds differ from those typically found therein.
Reproducibility: Yes
Additional Feedback: ===== Updates ===== After further discussions with the other reviewers, I have decided to revise my score.
Review 3
Summary and Contributions: This paper studies the generalization properties of risk-averse and risk-seeking risk measures through optimized certainty equivalents (OCE). In particular, risk-seeking
behavior is achieved through inverting the OCEs. The paper provides two types of results: bounds on the OCE via uniform convergence and bounds on the usual risk (expected loss) via bounds on the OCE
and a variance argument. Some experiments are conducted for CVaR.
Strengths: The theoretical results are the main contribution of the paper, particularly Lemma 2 and Theorem 6. These are mostly straightforward Rademacher complexity analyses, from a quick glance at
the proofs. The second contribution is the inverted OCE, which may be of relevance in machine learning problems. Since adjustments to the usual risk (expected loss) framework are currently of
interest, this provides another useful perspective.
Weaknesses: I have a handful of minor concerns. (1) It would have been nice for the experiments to explore more than CVaR, since there are a number of OCEs that are given as examples. Exploring
inverted OCEs would have been interesting too... (2) ... because while the OCE formulation is convex, at least in the loss, for CVaR (and probably entropic risk), the inverted OCEs look like they
lead to a non-convex problem. While machine learning has learned to live with non-convexity in the models, some basic experiments could help assuage any concerns. (3) In many of the discussions of
the generalization bounds, it seems like the paper would like to walk a non-existant tightrope between the empirical losses (and loss variances) and the Rademacher complexities. When using
complicated neural networks, my understanding is that these bounds are mostly vacuous because the Rademacher complexities are high, hence the battles over rethinking generalization or the
shortcomings of uniform convergence. I don't view these issues as meaning that we shouldn't examine these types of theory problems, but I find the suggestion that the empirical terms will simply
vanish and this will solve all our problems to be disingenuous. Indeed, if a function class is a universal approximator, then its Rademacher complexity will likely be very large (assuming a
reasonable data distribution). (4) The technical results are solid but don't seem to be particularly involved. This is fine, but it means that the results themselves have to be useful, which they may
Correctness: The paper looks essentially correct, although I did not read all the proofs in detail.
Clarity: The paper is fairly clearly written. It is definitely an above-average submission in this respect.
Relation to Prior Work: To the best of my knowledge, yes.
Reproducibility: Yes
Additional Feedback: I have read the other reviews and the response. I doubt the paper will be revolutionary (I've read maybe one such paper among the 30+ I've ever reviewed), but it's solid. Also,
the authors put forth a good effort in their response (perhaps with a little too much ***-kissing though).
Review 4
Summary and Contributions: The paper discusses learning and generalization when the mean loss objective is replaced by a risk-sensitive objective with different weights attributed to data depending
on the loss. Such occurs for example in various approaches to robust learning, where only a fraction of the sample with smallest losses is considered. The paper considers statistical functionals
called optimized uncertainty equivalents (OCE) or inverse OCE's. These have a variational definition, and their minimization over a function class by minimizing their plug-in estimators is discussed.
Excess risk bounds are given by way of uniform bounds depending on the Rademacher complexity of the function class. Learning guarantees for the usual average loss are also given for the
OCE-minimizers, depending on the variance of the average-loss-minimizer (OCE) or on the empirical variance of the empirical OCE-minimizer (inverse OCE's). The paper suggests a connection to
Sample-Variance-Penalization (SVP) and concludes with some experimental results. The appendix also contains an analysis of rubustness of some OCE-functionals in terms of influence functions.
Strengths: The OCE-functionals are well motivated and explained. I was unfamiliar with these concepts (originating in finance and economics) and learned quite a bit from the paper. The theoretical
analysis is elegant and clear. The sound and convincing proofs in the appendix are a pleasure to read.
Weaknesses: I can see only very minor weaknesses. The notation could be explained a bit better, such as Lip(\phi) or the notation for quantiles. The equivalence (3) and (4) could be sketched. It
would be much nicer to have a self-contained proof of Proposition 1. Also the connection to L-statistics could be mentioned in this context.
---------------------------update----------------------------------------------- I disagree with review #2. To me the reduction of the nonlinear objective to a linear one is simple and elegant. There
is a wealth of methods to bound Rademacher averages, which can be combined with the results in the paper in a simple and efficient way. I wish to keep my score.
Correctness: Everything seems correct to me, but I didn't try to reproduce the numerical simulations.
Clarity: To me it seems as clear as possible, given the page limit and the material covered.
Relation to Prior Work: There is no section on "related work", but the discussion in the first paragraphs of Section 3 appears sufficient to me.
Reproducibility: Yes
Additional Feedback: To proceed from (33) it is not necessary to invoke Massart's lemma, but you can work directly with \cal{G}, using the triangle inequality and observing that E sup_\lambda \sum_i
\epsilon_i \lambda \le M E |\sum_i \epsilon_i| \le M sqrt(n). This replaces the sqrt{8 log 2} by 2. I believe that in (36) log(2/\delta) should be log(1/\delta). The log(2/\delta) comes in after the
union bound. In (52) you need a bar above the oce.
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Practical Machine Learning with the mtcars Dataset in R
Put your data science skills into practice by working on machine learning projects using the classic `mtcars` dataset in R. This course provides hands-on experience with end-to-end solutions, from
data preprocessing to model evaluation, ensuring you are prepared for real-world tasks.
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Reverse a linked list - CSVeda
A Linked list is versatile data structure because of its dynamic nature. Linked list is versatile and dynamic because insertion or deletion can be done at any given location. Algorithm Complexity of
insertion and deletion algorithms are of the order of O(1). Reverse a linked list is another important operation. Let’s read how it is done.
How to Reverse a Linked list?
To reverse a linked list, three pointers are required to maintain addresses of the nodes being reconnected. Reversal is done by using the traversal operation. The first node becomes last node and
last node of the linked list becomes first node after reversal. For every node these actions are done-
• Store current address of current node in pointer PTR. Store address of previous node in pointer PREV. Store address of next node in pointer NEXT
• Update LINK of PTR node with LINK of PREV node
• Update PREV with PTR, PTR with NEXT and NEXT with LINK of NEXT
• When the PTR is NULL (reaches end of the linked list), update START=PREV
These steps are described in the following images.
Algorithm ReverseLL(START)
This algorithm traverses and reverses the nodes by updating their LINK part.
1. [Initialize Pointers]
2. Repeat step 3 while PTR!= NULL
3. [Update Pointers]
4. [Reset Start pointer of Linked List]
This is the process of reversing a linear linked list by updating the pointers. You can see that this is done without moving the elements physically. It is traversal along with updating the links.
The number of nodes in the linked list define the complexity of the algorithm.
Complexity of Algorithm to Reverse a Linked List
Step 2 of the algorithm described determines the major chunk of steps involved in this process. If the number of elements of a linear linked list is N then N nodes will be updated with new values for
LINK parts.
So, it can be said that complexity of reversal of a linked list is O(N) and is linear. Time to reverse a linear linked list grows with number of nodes.
Be First to Comment
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Sail Area Calculator - Online Calculators
Enter the values to use our basic and advanced Sail Area Calculator. For a more meaningful understanding of Sail Area read our formula and solved examples below
Sail Area Calculator
Enter any 2 values to calculate the missing variable
The formula is:
$\text{SA} = \frac{\text{H} \times \text{F}}{2}$
Variable Meaning
SA Sail Area (total area of the sail)
H Height of the sail (distance from the base to the top)
F Foot length of the sail (the base length of the sail)
How to Calculate?
Firstly, measure the height (H) of the sail from the base to the top. Now you have to measure the foot length (F), which is the base length of the sail. Next to that, multiply the height (H) by the
foot length (F). And finally, divide the result by 2 to find the sail area (SA).
Solved Examples:
Example 1:
• Height of the sail (H) = 10 meters
• Foot length of the sail (F) = 5 meters
Calculation Instructions
Step 1: SA = $\frac{H \times F}{2}$ Start with the formula.
Step 2: SA = $\frac{10 \times 5}{2}$ Replace H with 10 meters and F with 5 meters.
Step 3: SA = $\frac{50}{2}$ Multiply 10 by 5 to get 50.
Step 4: SA = 25 square meters Divide 50 by 2 to get the sail area.
The sail area is 25 square meters.
Example 2:
• Height of the sail (H) = 15 meters
• Foot length of the sail (F) = 8 meters
Calculation Instructions
Step 1: SA = $\frac{H \times F}{2}$ Start with the formula.
Step 2: SA = $\frac{15 \times 8}{2}$ Replace H with 15 meters and F with 8 meters.
Step 3: SA = $\frac{120}{2}$ Multiply 15 by 8 to get 120.
Step 4: SA = 60 square meters Divide 120 by 2 to get the sail area.
The sail area is 60 square meters.
What is the Sail Area Calculator?
The Sail Area Calculator is very helpful because it lets you know the total area of a sail, which is crucial for understanding how much wind the sail can catch. This is important in sailing, as the
sail area directly affects the speed and handling of the sailboat. The formula $\text{SA} = \frac{\text{H} \times \text{F}}{2}$ calculates the sail area by taking the height (H) of the sail and the
foot length (F) of the sail, multiplying them, and then dividing by 2
Final Words:
Sail Area Calculations are crucial for sailors and designers in a way that it lets them measure the performance of multiple sail sizes. The accurate sail calculation is important in helping sailboat
to withstand the condition it may encounter. It guides the enthusiasts towards a more meaningful knowledge of how the wind works with the sail and manages itself against the sea
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Lorentz Transformation | Time Dilation, Length Contraction & Physics
Lorentz transformation in electromagnetism
Understand how the Lorentz transformation reveals the relationship between time and space for moving observers, explaining time dilation and length contraction.
Lorentz Transformation: Time Dilation, Length Contraction, and Physics
The Lorentz transformation is a cornerstone of Albert Einstein’s theory of Special Relativity. It describes how measurements of space and time by two observers moving relative to each other are
related. This transformation fundamentally changes our understanding of time and space, leading to phenomena like time dilation and length contraction.
What is the Lorentz Transformation?
The Lorentz transformation equations show how time and space coordinates change between two reference frames moving at a constant velocity relative to each other. These equations can be written as:
\( t’ = \frac{t – \frac{vx}{c^2}}{\sqrt{1 – \left(\frac{v}{c}\right)^2}} \)
\( x’ = \frac{x – vt}{\sqrt{1 – \left(\frac{v}{c}\right)^2}} \)
• t – time in the stationary frame
• x – position in the stationary frame
• t’ – time in the moving frame
• x’ – position in the moving frame
• v – relative velocity between the two frames
• c – speed of light in a vacuum
This transformation predicts two fascinating effects: time dilation and length contraction.
Time Dilation
Time dilation means that time moves more slowly for an observer in motion relative to a stationary observer. The equation for time dilation can be derived from the Lorentz transformation equations
and is given by:
\( t’ = \frac{t}{\sqrt{1 – \left(\frac{v}{c}\right)^2}} \)
• \( t \) – time interval measured by a stationary observer
• \( t’ \) – time interval measured by a moving observer
As the relative velocity \(v\) approaches the speed of light \(c\), the denominator becomes very small, making \( t’ \) much larger than \( t \). This means a clock moving at high speeds will appear
to tick slower than one at rest.
Length Contraction
Length contraction is the phenomenon where the length of an object moving at a high velocity appears shortened along the direction of its motion to a stationary observer. This can be expressed as:
\( L = L_0 \sqrt{1 – \left(\frac{v}{c}\right)^2} \)
• \( L \) – length measured by a stationary observer
• \( L_0 \) – proper length of the object (length measured by someone moving with the object)
Again, as the relative velocity \(v\) increases towards the speed of light \(c\), the factor \( \sqrt{1 – \left(\frac{v}{c}\right)^2} \) becomes smaller, indicating that the length \( L \) is
Applications and Implications
The concepts of time dilation and length contraction have profound implications in physics, particularly in high-energy physics, astrophysics, and cosmology. One of the most well-known applications
is in understanding how particles behave at near-light speeds, such as those studied in particle accelerators.
Real-World Examples of Lorentz Transformation
To bring the abstract concepts of Lorentz transformations, time dilation, and length contraction into a more tangible realm, let’s look at some real-world examples where these principles are at play.
GPS Systems
Global Positioning System (GPS) satellites are a prime example of time dilation in action. These satellites orbit the Earth at high velocities and at altitudes where the effect of gravity is weaker
than on the Earth’s surface. Both of these factors cause the satellite’s onboard clocks to tick at a slightly different rate compared to clocks on Earth. Engineers must account for these differences
using the principles of Special Relativity to ensure accurate positioning data.
Muon Decay
Muons are subatomic particles created when cosmic rays hit the Earth’s atmosphere. They have a very short lifespan, decaying in microseconds. Due to time dilation, muons traveling at near-light
speeds towards Earth live longer than they would if they were at rest, allowing them to be detected at the Earth’s surface even though they should have decayed much higher in the atmosphere. This
phenomenon is a direct consequence of the Lorentz transformation equations.
Frequently Asked Questions (FAQs)
1. What happens if two observers are moving towards each other?
The Lorentz transformations can still be applied. Each observer would perceive the other’s clock as running slower, and lengths as contracted along the direction of relative motion. The
transformations are symmetric, maintaining the principle of relativity.
2. How does time dilation affect astronauts in space?
If astronauts travel at speeds close to the speed of light, time would pass more slowly for them compared to people on Earth. This is called “twin paradox,” where one twin traveling at high speed
ages more slowly than the twin staying on Earth.
3. Is it possible to observe length contraction directly?
Length contraction is extremely small at everyday speeds but becomes noticeable at speeds close to the speed of light. In theory, if you could observe an object traveling at such speeds, it would
appear shortened in its direction of travel.
The Lorentz transformation equations offer a window into the counterintuitive world of relativity, fundamentally altering our understanding of space and time. By revealing how time dilation and
length contraction operate, these principles not only enhance our comprehension of high-speed particle behavior but also have practical applications in technologies like GPS. Whether we are studying
particles in a lab or navigating using satellites, the principles of Special Relativity are crucial. Understanding these transformations encourages further exploration and appreciation of the
complexities of our universe.
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computational science ~ Ted Malliaris ~ tedm.us
Computation has become indispensable in the sciences and other technical fields. Sometimes the computation is so light we don't even think about it — using a
graphing calculator
to plot 1D
or find
. For instance, in the
finite square well
problem in
quantum mechanics
, the following equation must be solved for $$z$$:%% \tan(z) = \sqrt{(z_0/z)^2 - 1}. %%Such
transcendental equations
solutions and must be solved graphically or
. Pre-
, this would have required tabulated values or a
slide rule
High-performance computing
is typically used in conjunction with theoretical and experimental lines of investigation. On occasion, computational results are surprising, and can lead researchers to reformulate their thinking.
Fermi-Pasta-Ulam-Tsingou (FPUT) problem
was an early computational experiment in
nonlinear dynamics
. It was conducted in 1953 at
on a
vacuum tube computer
and involved simulating the motion of a 1D chain of $$N$$ identical masses coupled by springs of force response:%% F(x) = -kx - \beta x^3. %%For the
case (
springs, $$\beta = 0$$), the results were as expected: each of the $$N$$
normal modes
retained its initial share of the total energy. With significant amounts of
($$\beta/k > 1$$), the system displayed the expected
behavior, with energy eventually spreading to all modes. For small amounts of nonlinearity ($$\beta/k \sim 0.1$$), the system was expected to thermalize, but instead displayed quasi-periodic
behavior, with energy cycling among a few select modes.
For systems where
plays a role,
analytic results
can be verified with computation using
pseudo-random number generators
. Stochasticity is common in
biological systems
, one example being
genetic drift
in populations — alleles from one generation are randomly sampled to form the next. Such processes can easily be simulated using
MCMC methods
. Taking suitable averages over
realizations of the
stochastic process
then enables comparison with theory values.
One of my roles in our work,
Khromov et al., 2018
, was to write and run a
simulation code to facilitate such comparisons. Implementing the
population genetics
algorithm was straightforward, but
required some care — the theory depends on a
drift steady state
allele frequency distribution. Samples could only be taken once the steady state was reached and with adequate time in between (if replacing
ensemble average
with time average). Of course, both of these times were dependent on
parameter values
and other factors.
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Leagues to Earth's equatorial radius Converter
Enter Leagues
Earth's equatorial radius
β Switch toEarth's equatorial radius to Leagues Converter
How to use this Leagues to Earth's equatorial radius Converter π €
Follow these steps to convert given length from the units of Leagues to the units of Earth's equatorial radius.
1. Enter the input Leagues value in the text field.
2. The calculator converts the given Leagues into Earth's equatorial radius in realtime β using the conversion formula, and displays under the Earth's equatorial radius label. You do not need to
click any button. If the input changes, Earth's equatorial radius value is re-calculated, just like that.
3. You may copy the resulting Earth's equatorial radius value using the Copy button.
4. To view a detailed step by step calculation of the conversion, click on the View Calculation button.
5. You can also reset the input by clicking on button present below the input field.
What is the Formula to convert Leagues to Earth's equatorial radius?
The formula to convert given length from Leagues to Earth's equatorial radius is:
Length[(Earth's equatorial radius)] = Length[(Leagues)] / 1321.0680984860285
Substitute the given value of length in leagues, i.e., Length[(Leagues)] in the above formula and simplify the right-hand side value. The resulting value is the length in earth's equatorial radius,
i.e., Length[(Earth's equatorial radius)].
Calculation will be done after you enter a valid input.
Consider that a submarine travels 20,000 leagues under the sea in a famous novel.
Convert this depth from leagues to Earth's equatorial radius.
The length in leagues is:
Length[(Leagues)] = 20000
The formula to convert length from leagues to earth's equatorial radius is:
Length[(Earth's equatorial radius)] = Length[(Leagues)] / 1321.0680984860285
Substitute given weight Length[(Leagues)] = 20000 in the above formula.
Length[(Earth's equatorial radius)] = 20000 / 1321.0680984860285
Length[(Earth's equatorial radius)] = 15.1393
Final Answer:
Therefore, 20000 lea is equal to 15.1393 earth's equatorial radius.
The length is 15.1393 earth's equatorial radius, in earth's equatorial radius.
Consider that a sailing ship covers a distance of 500 leagues on a long voyage.
Convert this distance from leagues to Earth's equatorial radius.
The length in leagues is:
Length[(Leagues)] = 500
The formula to convert length from leagues to earth's equatorial radius is:
Length[(Earth's equatorial radius)] = Length[(Leagues)] / 1321.0680984860285
Substitute given weight Length[(Leagues)] = 500 in the above formula.
Length[(Earth's equatorial radius)] = 500 / 1321.0680984860285
Length[(Earth's equatorial radius)] = 0.3785
Final Answer:
Therefore, 500 lea is equal to 0.3785 earth's equatorial radius.
The length is 0.3785 earth's equatorial radius, in earth's equatorial radius.
Leagues to Earth's equatorial radius Conversion Table
The following table gives some of the most used conversions from Leagues to Earth's equatorial radius.
Leagues (lea) Earth's equatorial radius (earth's equatorial radius)
0 lea 0 earth's equatorial radius
1 lea 0.00075696325 earth's equatorial radius
2 lea 0.0015139265 earth's equatorial radius
3 lea 0.00227088975 earth's equatorial radius
4 lea 0.003027853 earth's equatorial radius
5 lea 0.00378481625 earth's equatorial radius
6 lea 0.00454177949 earth's equatorial radius
7 lea 0.00529874274 earth's equatorial radius
8 lea 0.00605570599 earth's equatorial radius
9 lea 0.00681266924 earth's equatorial radius
10 lea 0.00756963249 earth's equatorial radius
20 lea 0.01513926498 earth's equatorial radius
50 lea 0.03784816245 earth's equatorial radius
100 lea 0.0756963249 earth's equatorial radius
1000 lea 0.757 earth's equatorial radius
10000 lea 7.5696 earth's equatorial radius
100000 lea 75.6963 earth's equatorial radius
A league is a unit of length that was traditionally used in Europe and Latin America. One league is typically defined as three miles or approximately 4.83 kilometers.
Historically, the league varied in length from one region to another. It was originally based on the distance a person could walk in an hour.
Today, the league is mostly obsolete and is no longer used in modern measurements. It remains as a reference in literature and historical texts.
Earth's equatorial radius
The Earth's equatorial radius is the distance from the Earth's center to the equator. One Earth's equatorial radius is approximately 6,378.1 kilometers or about 3,963.2 miles.
The equatorial radius is the longest radius of the Earth due to its equatorial bulge, caused by the planet's rotation. This bulge results in a slightly larger radius at the equator compared to the
polar radius.
The Earth's equatorial radius is used in geodesy, cartography, and satellite navigation to define the Earth's shape and for accurate measurements of distances and areas on the Earth's surface. It
provides a key parameter for understanding Earth's dimensions and its gravitational field.
Frequently Asked Questions (FAQs)
1. What is the formula for converting Leagues to Earth's equatorial radius in Length?
The formula to convert Leagues to Earth's equatorial radius in Length is:
Leagues / 1321.0680984860285
2. Is this tool free or paid?
This Length conversion tool, which converts Leagues to Earth's equatorial radius, is completely free to use.
3. How do I convert Length from Leagues to Earth's equatorial radius?
To convert Length from Leagues to Earth's equatorial radius, you can use the following formula:
Leagues / 1321.0680984860285
For example, if you have a value in Leagues, you substitute that value in place of Leagues in the above formula, and solve the mathematical expression to get the equivalent value in Earth's
equatorial radius.
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Individual Scores in Choice Models, Part 1: Data & Averages
Before jumping into today’s topic, I will highlight the previous post in case you missed it: guest author — and coauthor of the Quant UX book — Kerry Rodden discusses HEART metrics. It updates
Kerry’s classic description of HEART with new reflections on how to make UX metrics succeed in practice. Read it here!
Today I begin a series of posts that demonstrate working in R with individual level estimates from choice models such as MaxDiff and Conjoint Analysis. Those are the best estimates of preference for
each respondent to a choice survey. I hope they will inspire you both to run choice surveys and to learn more from them!
Background and Assumptions
Assumptions: I assume that you know what a choice model survey is, and — at a high level — what individual scores are. If not, check out this post about MaxDiff surveys. Or take one of the upcoming
Choice Modeling Master Classes from the Quant Association! Or for even more, find sections on MaxDiff in the Quant UX book and discussions of Conjoint Analysis in the R book and Python book.
However, to recap briefly, individual scores are the best estimates for each respondent who completed a choice survey. For example, they report each respondents’ interest — as estimated by the model
— for every one of the items tested in the survey.
Data. Here I discuss data from N=308 UX Researchers who took a MaxDiff survey about potential classes from the Quant UX Association. As with most Quant Association surveys, the respondents agreed
that we could use the (anonymous) data publicly. Yay! It is great to discuss realistic choice model data. The survey included 14 potential classes. Here is an example MaxDiff screen:
Data Format. The estimates here were estimated by Sawtooth Software’s Discover product. The code here begins with an Excel file exactly as exported by Discover. Each row is represents one
respondent’s interest in each of the potential classes.
Note: Without going into the details of hierarchical Bayes (HB) models, I’ll note that the HB process gives 1000s of estimates for each respondent. The values here — the ones that most analysts
would use — are the mean (average) of those for each person. Although the estimates are somewhat uncertain for one person, the overall set of estimates are an excellent representation for the
R code. I assume you can generally follow R. A key goal of this post is to share R code that will help you get accelerate your own work. (More in the R book!)
You should be able to follow along live in R — all of the data and code are shared here. In each block of R code, you can use the copy icon in the upper right to copy the code and paste it into R to
follow along. Or see the end of the post for all of the code in one big chunk.
Packages. You may need to install extra R packages along the way. If you get an error running a “library()” command, you probably need to install that package.
Load the Data
Sawtooth Discover exports individual estimates as Excel (.xlsx) files. I’ve uploaded that file, and can download it directly from its URL using the openxlsx package:
# Read Excel data as saved by Sawtooth
library(openxlsx) # install if needed
# online location (assuming you are able to read it)
md.dat <- read.xlsx("https://quantuxbook.com/misc/QUX%20Survey%202024%20-%20Future%20Classes%20-%20MaxDiff%20Individual%20raw%20scores.xlsx") #
It’s helpful to do a bit of minor cleanup. First of all, in Anchored MaxDiff, each item is compared to an “anchor” of whether there is positive interest or not. The anchor estimate is always exported
as “0”, so we can remove that as non-informative.
Second, the file sets column (variable) names that are the entire text of each item. It’s helpful to replace those with shorter versions that are easy to read.
Those steps are:
# Some minor clean up
# remove the "Anchor" item that is always 0 after individual calibration
md.dat$Anchor <- NULL
# Assign friendly names instead of the long names, so we can plot them better
names(md.dat)[3:16] # check these to make sure we're renaming correctly
names(md.dat)[3:16] <- c("Choice Models", "Surveys", "Log Sequences", "Psychometrics",
"R Programming", "Pricing", "UX Metrics", "Bayes Stats",
"Text Analytics", "Causal Models", "Interviewer-ing", "Advanced Choice",
"Segmentation", "Metrics Sprints")
Next, I use str() and summary() to do some basic data checks:
# Basic data check
Finally, I set a variable for the item columns (columns 3:[end]) so I can refer to them easily, without a magic number “3” showing up multiple times later:
# Index the columns for the classes, since we'll use that repeatedly
classCols <- 3:ncol(md.dat) # generally, Sawtooth exported utilities start in column 3
With those lines, we have data! It’s time to look at the results.
Initial Chart: Overall Estimates
The first thing we might want to know — or that stakeholders will ask — is which classes are most desired. In the spreadsheet world, that might be done by finding the average level of interest and
then creating a bar chart. We’ll do the same thing here: find the average interest and then generate a bar chart.
In R, there are many different ways to obtain column averages. I’ll use lapply( , mean) … just because it occurred to me first. I use barplot() to plot them:
# First, get the average values for the classes
mean.dat <- lapply(md.dat[ , classCols], mean)
# Plot a simple bar chart of those averages
# first set the chart borders so everything will fit [this is trial and error]
par(mar = c(3, 8, 2, 2))
# then draw the chart
barplot(height = unlist(mean.dat), names.arg = names(mean.dat), # column values and labels
horiz = TRUE, col ="darkblue", # make it horizontal and blue
cex.names = 0.75, las = 1, # shrink the labels and rotate them
main = "Interest Level by Quant Course")
In the plot, I set margins for the graphics window with par(mar=…) to make it fit. That is a trial and error process for base R plots. I set the barplot() to be horiz[ontal] and slightly shrink
(cex.names=0.75) and rotate the labels (las=1) to be readable.
Here’s the result:
It is very, well, spreadsheet-ish. We see the winner (segmentation) and loser (interviewer training) … but we can do much better!
Better Chart: Estimates with Error Bars
In the chart above, we can see the averages but have no insight into the distribution. Are the averages strongly different? Or are they very close in comparison to the underlying distributions? Put
differently, is the “winner” (segmentation) really much stronger than the next three options (psychometrics, etc.) or is it only slightly better?
A better chart would show error bars for the means, so that we can tell whether differences are — to use the common but somewhat misleading term (for reasons I’ll set aside) — “significant”. We’ll do
that by using the geom_errorbar() visualization option in ggplot2.
I do lots of choice models and have to make plots like this all the time. I often make similar plots repeatedly, plotting different subsets of data, different samples, and the like. For that, it is
useful to make a function for such plots. I can simply reuse one function and not rely on error-prone copying and repetition of code.
Here’s a relatively basic function to plot average estimates from an anchored MaxDiff with error bars. (For other estimates such as general MaxDiff or conjoint, it will also work; just change the
xlab() label, either in the function or by adding it afterward.)
plot.md.mean <- function(dat, itemCols) {
# warning, next line assumes we're using Sawtooth formatted data!
md.m <- melt(dat[ , c(1, itemCols)]) # add column 1 for the respondent ID
# put them in mean order
md.m$variable <- fct_reorder(md.m$variable, md.m$value, .fun = mean)
p <- ggplot(data = md.m, aes(x = value, y = variable)) +
# error bars according to bootstrap estimation ("width" is of the lines, not the CIs)
geom_errorbar(stat = "summary", fun.data = mean_cl_boot, width = 0.4,) +
# add points for the mean value estimates
geom_point(size = 4, stat = "summary", fun = mean, shape = 20) +
# clean up the chart
theme_minimal() +
xlab("Average interest & CI (0=Anchor)") +
ylab("Quant Course")
There’s not a lot to say about this function. First, it melts the data to fit typical ggplot patterns. It adds the identifier column (1) for melt(); that would need adjusting if you have differently
formatted data. Then it calls fct_reorder() from the forcats library to put the labels into order — in this case, to order them by the mean value of the grouped data. The error bars are plotted by
geom_errorbar(), and that uses the mean_cl_boot option to find the confidence intervals by bootstrapping. (That function is in Hmisc, another potential package to install). Finally, after plotting
the error bars, it adds the actual mean points with geom_point().
Now that we have a function, it is a simple command to plot the data:
plot.md.mean(md.dat, classCols)
Here’s the result:
Now we can see that the segmentation class is a fairly strong #1, while the next 3 classes (psychometrics, choice, surveys) are essentially tied. Among the 14 classes, 13 have average interest
greater than zero — the MaxDiff anchor — while interviewer training falls below the anchor on average.
As a final note, because the function returns a ggplot object “p”, we could add other ggplot2 options. For instance, we might add “+ ggtitle(“My title!”)” to add a title or change the y axis label
with “+ ylab(“a different label”)”
The drawback of this plot is the following: it assumes that we want to know how classes compare in average values, according to statistical significance. In actual practice, that is not usually the
Why not? We are usually uninterested in averages and their confidence intervals? Because most often, practitioners need to know how many respondents are interested in something, and how many of them
are strongly interested or disinterested. We do not reach any “average” customer — we reach individuals.
So although an average chart with error bars is a good high-level view, there is more to learn.That brings us to my favorite chart: individual distributions!
Another Great Chart: Individual Distributions
There is one important question that an average chart — such as the ones above — cannot answer. That question is: “OK, this is the best item on average … but which item has people who are the very
most interested in it?”
For that, it is helpful to examine the individual distributions — not only where respondents are on average but whether there are groups who differ strongly in interest above or below the average.
As you probably guessed, I’ll plot it with a reusable function! Here’s the function. It’s long but I’ll break it down below.
cbc.plot <- function(dat, itemCols = 3:ncol(dat),
title = "Preference estimates: Overall + Individual level",
meanOrder = TRUE) {
# get the mean points so we can plot those over the density plot
mean.df <- lapply(dat[ , itemCols], mean)
# melt the data for ggplot
# vvvv assumes Sawtooth order; vvv (ID in col 1, remove RLH in col 2)
plot.df <- melt(dat[, c(1, itemCols)], id.vars = names(dat)[1])
# get the N of respondents so we can set an appropriate level of point transparency
p.resp <- length(unique(plot.df[ , 1]))
# optionally and by default order the results not by column but by mean value
# because ggplot builds from the bottom, we'll reverse them to put max value at the top
# we could use fct_reorder but manually setting the order is straightforward in this case
if (meanOrder) {
plot.df$variable <- factor(plot.df$variable, levels = rev(names(mean.df)[order(unlist(mean.df))]))
#### Now : Build the plot
# set.seed(ran.seed) # optional; points are jittered; setting a seed would make them exactly reproducible
# build the first layer with the individual distributions
p <- ggplot(data=plot.df, aes(x=value, y=variable, group=variable)) +
geom_density_ridges(scale=0.9, alpha=0, jittered_points=TRUE,
# set individual point alphas in inverse proportion to sample size
point_color="blue", point_alpha=1/sqrt(p.resp),
point_size=2.5) +
# reverse y axis to match attribute order from top
scale_y_discrete(limits=rev) +
ylab("Level") + xlab("Relative preference (blue=individuals, red=average)") +
ggtitle(title) +
# now add second layer to plot with the means of each item distribution
for (i in 1:length(mean.df)) {
if (meanOrder) {
# if we're drawing them in mean order, get the right one same as above
p <- p + geom_point(x=mean.df[[rev(order(unlist(mean.df)))[i]]],
y=length(mean.df)-i+1, colour="tomato", # adjust y axis because axis is reversed above
alpha=0.5, size=2.0, shape=0, inherit.aes=FALSE)
} else {
p <- p + geom_point(x=mean.df[[i]],
y=length(mean.df)-i+1, colour="tomato", # adjust y axis because axis is reversed above
alpha=0.5, size=2.0, shape=0, inherit.aes=FALSE)
In the first couple of lines of the function, it finds the average value for each item using lapply(), the same as we already saw above. That’s so we can add those as a separate layer on the plot
later. Then it melts the data, again just like saw above.
Next, it finds the total N of respondents and saves that as p.resp. Why? Because when we plot the individuals, we want to set a transparency alpha value. Setting alpha in inverse proportion to the (
square root of the) number of respondents makes those points more legible.
By default, it puts the labels into their mean order, using the averages we calculated instead of fct_reorder() as above (everything in R has multiple good options!)
The next two big chunks build the plot in two states. The first big chunk uses the ggridges package to plot geom_density_ridges() density curves for the individual distributions. I won’t try to
explain those; just look at the chart below! Its options add individual points to the curves, and sets a transparency alpha as I described above.
The second big chunk adds points to the chart, overlaying the density ridges with the average values for each item. To do that, it iterates over the items with a for() loop, and then adds the point
in the proper place according to whether the items are displayed in sorted order or not.
We call the plot with a simple command, adding a custom y axis label:
cbc.plot(md.dat, itemCols=classCols) + ylab("Quant Course Offering")
Here’s the result:
Wow! This chart has a lot of great information.
I won’t interpret it in complete detail but will note a couple of interesting features. First, it reinforces that Segmentation is a strong #1 option — not only does it have the highest average, more
than 90% of respondents show positive interest greater than the anchor value of 0. We also see at the upper end of interest — the right hand side — that Segmentation has many more respondents with
particularly strong interest (greater than a value of 5.0, to choose an arbitrary point) than any other class.
However, we see some other things with subsets of respondents with high interest. For example, although the R Programming course is a weak #11 out of 14 in average interest, it has a small number of
respondents showing the strongest interest of anyone in any class.
When we consider that hands-on classes are small, and reach only the people interested in them, these results suggest that an R class could be an good offering, even if the average is lower. We don’t
care how people are uninterested — we only care whether we can reach enough people who are interested!
With that, I’ll leave you to inspect the chart and find other interesting ideas.
Coming up in Post 2
In the next post, I’ll go farther with these data and examine:
• Correlations among interests: if they like X, what else do they like or dislike?
• Finding clusters of classes that go together (item clusters — we’ll look at respondent clusters in post 3)
• … and later posts will look at respondent segmentation and (briefly) data quality
Stay tuned for Post #2 in a few days!
Meanwhile, if you’re interested in more about choice models and/or R, check out this post about MaxDiff surveys; and upcoming Choice Modeling Master Classes from the Quant UX Association; and
sections on MaxDiff in the Quant UX book and Conjoint Analysis in the R book or Python book. Also, for more experienced choice modelers, I recently shared this post about misunderstandings of
Conjoint Analysis.
All the Code
As promised, following is all of the R code from this post. You can use the copy icon in the upper right to grab it all at once, and paste into RStudio or wherever you code.
# blog scripts for analysis of individual level MaxDiff data
# Chris Chapman, October 2024
##### 1. Get individual-level mean beta estimates as exported by Sawtooth Software
# 1a. read Excel data as saved by Sawtooth
# online location (assuming you are able to read it)
md.dat <- read.xlsx("https://quantuxbook.com/misc/QUX%20Survey%202024%20-%20Future%20Classes%20-%20MaxDiff%20Individual%20raw%20scores.xlsx") #
# 1b. Some minor clean up
# remove the "Anchor" item that is always 0 after individual calibration
md.dat$Anchor <- NULL
# Assign friendly names instead of the long names, so we can plot them better
names(md.dat)[3:16] # check these to make sure we're renaming correctly
names(md.dat)[3:16] <- c("Choice Models", "Surveys", "Log Sequences", "Psychometrics",
"R Programming", "Pricing", "UX Metrics", "Bayes Stats",
"Text Analytics", "Causal Models", "Interviewer-ing", "Advanced Choice",
"Segmentation", "Metrics Sprints")
# 1c. Basic data check
# 1d. Index the columns for the classes, since we'll use that repeatedly
classCols <- 3:ncol(md.dat) # generally, Sawtooth exported utilities start in column 3
##### 2. Plot the overall means
# 2a. The easy way (but not so good)
# First, get the average values for the classes
mean.dat <- lapply(md.dat[ , classCols], mean)
# Plot a simple bar chart of those averages
# first set the chart borders so everything will fit [this is trial and error]
par(mar=c(3, 8, 2, 2))
# then draw the chart
barplot(height=unlist(mean.dat), names.arg = names(mean.dat), # column values and labels
horiz = TRUE, col ="darkblue", # make it horizontal and blue
cex.names=0.75, las=1, # shrink the labels and rotate them
main ="Interest Level by Quant Course")
# 2b. A somewhat more complex (but much better) way
# we'll make this a function ... it's often good to make anything long into a function :)
plot.md.mean <- function(dat, itemCols) {
# warning, next line assumes we're using Sawtooth formatted data!
md.m <- melt(dat[ , c(1, itemCols)]) # add column 1 for the respondent ID
# put them in mean order
md.m$variable <- fct_reorder(md.m$variable, md.m$value, .fun=mean)
p <- ggplot(data=md.m, aes(x=value, y=variable)) +
# error bars according to bootstrap estimation ("width" is of the lines, not the CIs)
geom_errorbar(stat = "summary", fun.data = mean_cl_boot, width = 0.4,) +
# add points for the mean value estimates
geom_point(size = 4, stat = "summary", fun = mean, shape = 20) +
# clean up the chart
theme_minimal() +
xlab("Average interest & CI (0=Anchor)") +
ylab("Quant Course")
# call our plot
plot.md.mean(md.dat, classCols)
##### 3. Even better: Plot the distributions (individual estimates)
cbc.plot <- function(dat, itemCols=3:ncol(dat),
title = "Preference estimates: Overall + Individual level",
meanOrder=TRUE) {
# get the mean points so we can plot those over the density plot
mean.df <- lapply(dat[ , itemCols], mean)
# melt the data for ggplot
# vvvv assumes Sawtooth order; vvv (ID in col 1, remove RLH in col 2)
plot.df <- melt(dat[, c(1, itemCols)], id.vars=names(dat)[1])
# get the N of respondents so we can set an appropriate level of point transparency
p.resp <- length(unique(plot.df[ , 1]))
# optionally and by default order the results not by column but by mean value
# because ggplot builds from the bottom, we'll reverse them to put max value at the top
# we could use fct_reorder but manually setting the order is straightforward in this case
if (meanOrder) {
plot.df$variable <- factor(plot.df$variable, levels = rev(names(mean.df)[order(unlist(mean.df))]))
#### Now : Build the plot
# set.seed(ran.seed) # optional; points are jittered; setting a seed would make them exactly reproducible
# build the first layer with the individual distributions
p <- ggplot(data=plot.df, aes(x=value, y=variable, group=variable)) +
geom_density_ridges(scale=0.9, alpha=0, jittered_points=TRUE,
# set individual point alphas in inverse proportion to sample size
point_color = "blue", point_alpha=1/sqrt(p.resp),
point_size=2.5) +
# reverse y axis to match attribute order from top
scale_y_discrete(limits=rev) +
ylab("Level") + xlab("Relative preference (blue=individuals, red=average)") +
ggtitle(title) +
# now add second layer to plot with the means of each item distribution
for (i in 1:length(mean.df)) {
if (meanOrder) {
# if we're drawing them in mean order, get the right one same as above
p <- p + geom_point(x=mean.df[[rev(order(unlist(mean.df)))[i]]],
y=length(mean.df)-i+1, colour="tomato", # adjust y axis because axis is reversed above
alpha=0.5, size=2.0, shape=0, inherit.aes=FALSE)
} else {
p <- p + geom_point(x=mean.df[[i]],
y=length(mean.df)-i+1, colour="tomato", # adjust y axis because axis is reversed above
alpha=0.5, size=2.0, shape=0, inherit.aes=FALSE)
cbc.plot(md.dat, itemCols=classCols) + ylab("Quant Course Offering")
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Determining Which Diagram Shows Incoherent Light Among Five Light Waves
Question Video: Determining Which Diagram Shows Incoherent Light Among Five Light Waves Physics • Third Year of Secondary School
In each of the following diagrams, five light waves are shown. Which of the diagrams shows incoherent light? [A] Diagram A [B] Diagram B [C] Diagram C [D] Diagram D [E] Diagram E
Video Transcript
In each of the following diagrams, five light waves are shown. Which of the diagrams shows incoherent light?
Whether waves are coherent or incoherent depends on two factors: the frequency of the waves and the phase difference of the waves. Specifically, for two or more light waves to be coherent, they must
have the same frequency and a constant phase difference. Other properties of the waves, like height or amplitude, do not matter for determining whether or not they are coherent.
So then we want to look at each of the five waves in these five diagrams to determine which set of waves is incoherent, which is to say “Which set of waves do not have the same frequency or a
constant phase difference?” We can sometimes look at waves and determine these properties just through observation. For instance, these two waves are pretty similar-looking, aside from their
amplitude. And it’s because they have the same frequency and a constant phase difference, meaning that they are coherent with each other.
But simple observation isn’t enough. Very tiny changes in frequency or phase difference can mean the difference between whether waves are coherent or not. So don’t rely on just observation. In order
to accurately compare the frequency of waves when we’re just given the waves with no numbers, we look at how many complete wave cycles there are over the same period of time and compare them to each
other. In this case, both of these waves consist of one complete wave cycle over the same period of time, meaning that they must have the same frequency.
Now let’s look at finding phase difference, which can be a little bit trickier. This is because, while phase differences can be pretty obvious sometimes, they can also be subtle. A good way to
determine if multiple waves have a constant phase difference between all of them is to choose some point on the wave usually peaks, because they’re easy to spot, and then determine if those parts of
the waves occur at the same point in time, which they don’t in this case for these three waves. The third wave has a slight phase offset, meaning that there is not a constant phase difference amongst
all three of these waves. So these three together are incoherent.
With all of this in mind, let’s start looking at the light waves in the diagrams, starting with diagram (A). When first looking at all of these waves, we may notice that they have different
amplitudes. But again, this does not matter for whether or not waves are coherent, just frequency and phase difference. So to determine the frequency for these waves, let’s count each wave’s number
of complete wave cycles. We’ll find, when we finish, that each wave has eight complete wave cycles, meaning that these waves all have the same frequency.
Now for determining whether they have a constant phase difference between them, let’s look at the peaks. At the same point in time, all of the peaks line up, and not just the first peaks, but all of
the other peaks as well, which indicates a constant phase difference. It’s important to look at more than one point in time when determining whether waves have a phase difference or not, since even
waves with a phase difference can just happen to line up sometimes. But this is not the case here; all of these waves are coherent, meaning that diagram (A) does not show incoherent light.
So let’s look at (B) now. Diagram (B) is a case where just observation can actually be enough. We don’t have to look very close to determine that this is just the same wave repeated five times,
consisting of 12 complete wave cycles, and of course lining up at any points that we choose. The waves in diagram (B) are all coherent.
So let’s look at (C). All of these waves consist of approximately 11 and one-quarter complete wave cycles, meaning that they have the same frequency. And all of the peaks lining up indicates a
constant phase difference, meaning the waves in diagram (C) are coherent.
So we’re going to have to now look at diagram (D). The waves in diagram (D) all consist of the same number of complete wave cycles, about 3 and a half. And any points that we choose all line up at
the same point in time, meaning a constant phase difference. So just like the last three diagrams, the light in diagram (D) is coherent.
So we must now turn our attention to diagram (E). When we first look over all of these waves individually, we may notice that the third wave has a tiny discrepancy in where it starts. The other four
waves all start at about midheight of the wave going down, while the third wave starts up just a little bit higher and also ends a little bit higher too. And when we measure out the number of
complete wave cycles for these waves, we find that this third wave has 12, while all of the other waves have 15. This third wave does not have the same frequency as the other four. This is why it’s
important to count the number of complete wave cycles because otherwise that would have been tough to spot.
This diagram also demonstrates why it’s important to look at more than one point in time when determining if there is a phase difference, since the peaks of the other four waves very nearly line up
with the third one here. But over here, they clearly don’t. Even though it is just the third wave that has a different frequency and nonconstant phase difference from the others, all it takes is one
wave to make an entire set of waves incoherent. So because of this third wave having a different frequency and a nonconstant phase difference, diagram (E) is the one that shows incoherent light.
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THE SHIFT - Why we need a better mouse trap in marketing decision making - AI-Powered Insights: The Liberation From Spurious Correlations
THE SHIFT - Why we need a better mouse trap in marketing decision making
What management and data science still have in common today is that they rarely distinguish between correlation and causality.
Sonos analyzed the feedback data that came from the owners of the speakers. The first step was the correlation analysis. It's hard to believe: the willingness to recommend correlated most strongly
with service satisfaction. Was the hotline really the success factor?
|
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High School Functions Worksheets
Grade Levels
High School Functions Worksheets
Why do We Study Math Functions? - We know what the term "function" generally means. But in math, a function is a relation in which no input relates to more than one output. This means that a function
is a relation with one output for each input. These functions are the bases of all mathematical operations. With functions, we learn how to solve various algebraic equations and it is the base
platform for calculus. You will learn how to place them on the graph and solve equations through them. Functions teach us a lot of techniques to solve problems, alongside developing the skills to
make sense of various problems and helping us to find the relevant, appropriate method in solving them. Functions also help in constructing viable arguments to support your answers. They also help in
increasing concentration and help you in learning how to structure the questions that need to be solved. Functions are a very elusive concept for many students. They help us understand the world
around us and are essential in the business world. Have you ever thought of buying a car or calculated how long it will take you to get to a location (while accounting for other variables); then you
have come across functions before.
Interpreting Functions
Building Functions
Linear, Quadratic, & Exponential Models
Trigonometric Functions
What is the Importance of Understanding Functions?
In real life we often talk or define relationships between people. For example, there may be a boy in the street that you waive to and a friend may ask you how you know him. That boy could be a
friend, a cousin, a brother, a teammate, and maybe you were just being courteous to a stranger. When you define that relationship to your friend, you have basically stated how important that person
is to you. In a way you have defined an unspoken value for that person in relation to you. Functions are mathematical methods of describing relationships between values and salient variables. These
relationships often require complex computations. This is why you often will not start to explore the higher performing functions until you enter undergraduate school. Students that master the
ability to not only interpret well stated functions but write and create their own possess a skill that will be in high demand in the corporate world. This is because if you master this skill, you
will quickly be able to judge the significance of trends and spot outliers within the data. People that understand the essence of the nature of a function can often make exactly accurate predictions
of how data flows through it. This allows them to make solid decisions based on what the data shows them. Functions find themselves used for all types of modeling whether it financial, an engineering
application, or trajectory of a space shuttle as it approaches Mars. The people that can understand and create these models with often secure top level employment quickly.
How Are Math Functions Used in Real World?
The funny thing is that there are almost too many applications of functions in the real world to list or at least do justice for. Every time you make a move, at all, that can be broken down
mathematically that results in some kind of outcome (output) you have taken part in a mathematical function. Let me just recount how many functions I came across just last night:
1. I put 75 cents in coins into a vending machine and then chose the letters that indicated a fruit roll. The machine in turn moved a coil that the fruit roll was on, and the fruit roll popped out.
2. I received my paycheck which I am paid hourly for. Depending on the number of hours that I work, I receive a different amount each time.
3. I took an Uber home. The cost of that ride is based on the distance covered and amount of time involved.
4. I used my television remote control to tune in the basketball game. Do you see where I’m going with this?
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MATT 1222 Rasmussen College Algebra Worksheet - Custom Scholars
MATT 1222 Rasmussen College Algebra Worksheet
Module 01
Module 01 Assignment
Module 01 Content
Communicating math symbols and translating word
problems into algebraic expressions and equations are
skills necessary in algebra. For each assignment in this
course, you will use Microsoft Word Equation Editor to
practice these skills.
Your assignment is to replicate the following equation
using the Microsoft Word Equation Editor.
X –
y =
Once you have successfully replicated the equation, save
and upload the Word document you created.
If you need assistance creating the equation, download
the following document that uses a step-by-step approach
to building the equation:
Module 01
using the Microsoft Word Equation Editor.
X –
x3 +5
(x2 –c) (x +d)
Once you have successfully replicated the equation, save
and upload the Word document you created.
If you need assistance creating the equation, download
the following document that uses a step-by-step approach
to building the equation:
Submit your completed assignment by following the
directions linked below. Please check the Course
Calendar for specific due dates.
Use the content creator in the submission box below, or
save your assignment as a Microsoft Word document.
(Mac users, please remember to append the “.docx”
extension to the filename.) The name of the file should be
your first initial and last name, followed by an underscore
and the name of the assignment, and an underscore and
the date. An example is shown below:
Past due. New attempts will be marked as late.
Save and Close
Submit Late
Tutorial for MS Equation Editor in
Word 2010
Assigned Task
Recreate the following algebraic expression, using
Microsoft Equation Editor 2010
x + x2 – 4
y =
+ 1
(x3 – a) (x – b)
Instructions for Word 2010
1. Open a new Microsoft Word document.
2. On the ribbon at the top, click Insert.
3. Rest your cursor on the a symbol (PI symbol),
which is located above the word “Equation.”
(The tab will be highlighted.) Click the a
symbol (don’t click the word “Equation” for
now) and a panel with the words “Type
equation here” appears in your document as
shown below.
Type equation here
Type y = into this equation panel right now as
you start to recreate your assigned equation.
The panel shrinks or expands to adjust to the
inserted items. Now it looks like this:
y =
4. To continue working on your assigned
algebraic expression, look for the
mathematical symbols and operators you
need in the new “equation” ribbon that
appears when you clicked the a symbol. Your
equation ribbon looks like this:
Equation Tools
Page Layout
T Professional
5. Notice on your screen that the equation ribbon
is divided into two areas – individual Symbols
on the left and Structures on the right.
6. The next thing you need in your assigned
equation after the equal sign is a fraction. To
get this, go to the Structures area in your
equation ribbon, click the Fraction template
and then, in the large drop down panel, click
the fraction placeholder as shown here:
ull LTE
5. Notice on your screen that the equation ribbon
is divided into two areas – individual Symbols
on the left and Structures on the right.
6. The next thing you need in your assigned
equation after the equal sign is a fraction. To
get this, go to the Structures area in your
equation ribbon, click the Fraction template
and then, in the large drop down panel, click
the fraction placeholder as shown here:
eux. ä lim A 10
od do
y =
7. Your equation now looks like this, including
the two placeholders for the numerator and
denominator of your fraction.
y =
8. Now type the x+ in the little box in the
numerator of your fraction placeholder so
that your figures now look like this:
x +
y =
Note: At this point you might be able to figure out on your own how to use
your EE Toolbar to recreate the entire algebraic expression you were
assigned. Try it! If you make a mistake position the cursor precisely and
backspace once or twice to delete your error and start from where you left
off. If you need further instructions, they are provided below.
9. Note that after the x+ in the numerator of
your fraction you need a “radical” symbol.
Find the Radical template on the Structures
side of the equation ribbon, click it, and then,
in the drop down menu, click the radical
symbol that looks right for your equation. The
equation should now look like this:
y =
10. Inside the radical, you need an x with an
exponent of 2. (That is, you need an .) Click
the Script template in the Structures area
and then in the drop down menu, click the
nil LTE
9. Note that after the x+ in the numerator of
your fraction you need a “radical” symbol.
Find the Radical template on the Structures
side of the equation ribbon, click it, and then,
in the drop down menu, click the radical
symbol that looks right for your equation. The
equation should now look like this:
X +
y =
10. Inside the radical, you need an x with an
exponent of 2. (That is, you need an .) Click
the Script template in the Structures area
and then in the drop down menu, click the
small superscript placeholder. This time you
have a second choice as well – to use the
preformatted symbol. Both choices are
indicated here:
Papeut Reen
* ex $ 10) sine ä lim A 19
Reaction Sort Radical Integral Large Badet Funtion centint and Operator
Carmen Subscript and Superseri
X +
y =
11. If you are using the superscript placeholder,
type an x in the main box of the placeholder
and a 2 in the superscript box, and you
should end up with the following equation:
x + x2
y =
12. Now type in the -4 to end the radicand. The
equation now looks like this:
x + 1×2 – 4
y =
Ta ant to thadanominator of your fraction
hos.content.blackboardcdn.com &
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Jansen, Kenneth E.
Kenneth E. Jansen
ECAE 161 429 UCB
Tel: (303) 492-4359; Fax: (303) 492-4990;
E-Mail: jansenke@colorado.edu
After receiving his B.S. in Mechanical Engineering in 1987 from the University of Missouri-Columbia, Kenneth Jansen went on to graduate school at Stanford University where he earned an M.S. degree in
Mechanical Engineering in 1988 and his Ph.D. in Mechanical Engineering with a minor in Aeronautical Engineering in 1993 under an Office of Naval Research Fellowship. He then joined the Center for
Turbulence Research, a joint NASA-Stanford program, where he was awarded a three year post-doctoral research fellowship. In August, 1996 he became a member of the Rensselaer faculty. In January, 2010
he joined the Faculty of University of Colorado Boulder in the Department of Aerospace Engineering Sciences
Research Interests and Activities Major Interests: Computational mechanics with emphasis on fluid dynamics. Turbulence theory, simulation, and modeling. Parallel computing.
The motivation of Jansen's research is to provide engineers with a better predictive capability for fluid dynamics problems, especially those where turbulence plays an non-negligible role. To this
end, his research, at the most applied level, seeks to develop simple models which describe the net effect or average of the turbulence upon the mean flow equations. These models, when combined with
a fully unstructured-grid finite element method, allow engineers to model arbitrarily complex flow problems. Unfortunately, these models are not yet able to describe all turbulent flows. Therefore,
other forms of simulating turbulence are also pursued. These forms are: 1) Large-Eddy Simulation (LES) where the large scale motions of the turbulence are resolved in the computation leaving only the
fine scale motions to be modeled, 2) Direct Numerical Simulation (DNS) where all of the turbulent motions are resolved in the computational model. These alternate forms are useful both to develop a
more basic understanding of the theory of turbulence and to help improve the averaged models used by engineers.
Publications and Presentations
Active Sponsored Research as of February 2019
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Convention Dates Are Official
SE-Rican So stop beating around the bush explain to me how the car with the lower ET in drag racing does not win.
I happens so often, I'm surprised you're not familiar with it. Watching a typical top fuel final will result in 3-4 of these usually.
Here's how it happens.
Tree drops.
Car A leaves the line tripping his lane's timer at 6:00:01.00 PM
Car B leaves the line tripping his lane's timer at 6:00:01.50 PM
Car A crosses the finish line, tripping his timer at 6:00:11.00 PM for an ET of 10.00 seconds.
Car B crosses the finish line, tripping his timer at 6:00:11.25 PM for an ET of 9.75 seconds.
Car A wins the race, as usual, because he crossed the finish line first. He had a longer ET, but his reaction time made up for it. This happens all the time.
What happens in a 10.5 index when Car A leaves and runs a 10.58, while Car B sits at the line and leaves after and runs a 10.56?
You are telling me car A wins as he crossed the line first?
You're right, crossing the line first in index racing does not determine the winner, but neither does the lowest ET. Sooo.... I'm still waiting.
You're right, crossing the line first in index racing does not determine the winner, but neither does the lowest ET. Sooo.... I'm still waiting.
How doesnt the lower ET not determine the winner in an Index?
Your statement is only true in bracket racing where a lower actual ET does not determine a winner, but how close to the dial will determine.
Even if the winning ET is a higher time.
Last edited by SR20GTi-R on 2013-10-24 at 21-10-23.
ben just go sip on your coffee on the sidelines with you pinky out while we do the racing
Did they do index racing at Atlanta Dragway for us while we were there?
Google drag racing! I love it.
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The Expanding Universe
In fact, the universe is getting even bigger. Astronomers believe that the universe is expanding - that all points in the universe are getting farther apart all the time. It's not that stars and
galaxies are getting bigger; rather, the space between all objects is expanding with time.
You can make a model of the universe to show how this expansion works. Scientists often use models to help them understand what is happening on a larger scale.
Explore 1. Make a model for the expanding universe. Your teacher will divide the class into pairs. He or she will give you and your partner a balloon and a permanent marker. Use the permanent marker
to make four to six small dots on one side of the balloon. Don't put all the dots in a straight line; spread them out a little. Each of these dots represents a galaxy. Now, blow the balloon up
slowly, and note what happens to these dots.
Blow up the balloon about halfway. Use the permanent marker to circle one of the outermost dots (the ones farthest to the left or right). This dot represents the Milky Way. Put a piece of paper up to
the balloon, and measure the distance from "The Milky Way" to the other "galaxies." (Your teacher will show you how to make the measurement.) Record your data.
Now blow up the balloon all the way. Again, measure the distance from "The Milky Way" to the other galaxies. Record your data. You should now have two columns of data: the distance to each galaxy the
first time and the distance to each galaxy the second time.
Use this SkyServer workbook to store all your data and make your calculations.
Explore 2. Calculate the "average speed" of each dot on the balloon with respect to the Milky Way dot. Subtract the distance at the first time from the distance at the second time (d[2] - d[1]).
Divide by the amount of time it took you to blow up the balloon (t). If you don't remember how long it took, just assume a reasonable value, like 5 or 10 seconds.
Calculate the average speed of the dots [(d[2]-d[1])/t]. Record the average speed of each dot as the third column in your workbook.
Explore 3. Use a graphing program such as Excel to graph the second distance on the x-axis and average speed on the y-axis. See SkyServer's Graphing and Analyzing Data tutorial to learn how to use
Excel to graph data. If you don't have a graphing program, you can download a free program such as Open Office (Windows/Mac/Linux) or Sphygmic Spreadsheet (Windows).
What does the graph look like? Why do you think the graph has this shape?
As you'll see in the next activity, your balloon model behaves similarly to the real universe. But like any model, it has its limitations. For one thing, the surface of the balloon (where you drew
the dots) is two-dimensional, while the universe is three-dimensional. A three-dimensional model of the universe might be chocolate chip cookie dough rising in an oven. As the dough rises, each of
the chips gets farther away from all the other chips. But the cookie dough model has its limitations too - you couldn't have measured the distances between the chips as easily as you could have with
the balloon model.
Can you think of other models for the expanding universe?
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Probability Part 1: Rules and Patterns: Crash Course Statistics #13
25 Apr 201812:00
TLDRIn this Crash Course episode on Statistics, Adriene Hill dives into the concept of pareidolia, illustrating our brain's tendency to recognize patterns, even in inanimate objects. She then
transitions to a discussion on probability, distinguishing between empirical and theoretical probability through examples like slot machine odds and Skittle color chances. The episode further
explores probability rules, including the addition and multiplication rules, and introduces notation for simplifying these concepts. Through engaging examples, such as the chances of encountering
Cole Sprouse at IHOP or the implications of medical test accuracy, the video makes probability accessible and relevant, demonstrating its application in everyday decisions and scientific
• ๐ ๏ธ Pareidolia is a phenomenon where we recognize patterns, particularly faces, in inanimate objects due to our brain's pattern recognition capabilities.
• ๐ There are two types of probability: empirical (based on actual data) and theoretical (an ideal or truth in the universe).
• ๐ ฎ Empirical probability provides a glimpse into the theoretical probability but may not always match due to sample uncertainty and randomness.
• ๐ ฒ Theoretical probability is considered an ideal truth that we attempt to estimate using data samples, such as calculating the odds of winning at a slot machine.
• ๐ ญ The addition rule of probability helps calculate the chances of mutually exclusive events occurring, like picking specific colors from a Skittle bag.
• ๐ Notation simplifies probability expressions, such as P(Red or Purple) to represent the combined probability of two events.
• ๐ ซ Mutually exclusive events cannot happen at the same time, affecting how probabilities are calculated.
• ๐ The multiplication rule assists in determining the likelihood of concurrent events, such as encountering a celebrity at a diner on a promotional night.
• ๐ Conditional probabilities evaluate the chance of an event given another event has already occurred, essential in fields like medicine for understanding screening test implications.
• ๐ ท Probability applies to real-life decisions and expectations, influencing daily choices and helping manage expectations about outcomes.
Q & A
• What is pareidolia?
-Pareidolia is when our brains see patterns like faces in inanimate objects, even when the patterns aren't really there. It happens because our brains are very good at recognizing patterns.
• What are the two types of probability discussed?
-The two types of probability discussed are empirical probability, which is based on actual observed data, and theoretical probability, which is the true underlying probability.
• How do you calculate the probability of event A or event B happening?
-To calculate the probability of event A or event B, use the addition rule: P(A or B) = P(A) + P(B) - P(A and B). This accounts for any outcomes where both events occur.
• What is the multiplication rule used for?
-The multiplication rule is used to calculate the probability of two or more independent events both occurring. You multiply the individual probabilities.
• What does it mean for two events to be independent?
-Two events are independent if the occurrence of one event does not affect the probability of the other event occurring. So the probabilities are unrelated.
• What are conditional probabilities?
-A conditional probability gives the probability of one event happening, given that another event has already occurred. It is written as P(A | B), the probability of A given B.
• What is the difference between false positives and false negatives?
-A false positive is when a test says something is abnormal but it's not. A false negative is when a test says everything is normal but something is actually abnormal.
• How can probability help in everyday life?
-Probability can help set reasonable expectations in uncertain situations, like getting tickets to an event or catching red lights when driving. It provides context on how likely outcomes are.
• What was the key message of the video?
-The key message was that probability helps us quantify uncertainty and set reasonable expectations. Even if we don't always have precise probabilities, thinking in terms of likelihood is useful.
• What is the difference between P(A|B) and P(B|A)?
-P(A|B) gives the probability of A occurring given that B has occurred. P(B|A) gives the probability of B occurring given that A has occurred. They are not always equal.
๐ ง Understanding Probability through Patterns
This section introduces the concept of pareidolia, where humans recognize faces in inanimate objects, as a segue into the broader topic of pattern recognition and probability. Adriene Hill explains
the difference between empirical and theoretical probability using accessible examples. Empirical probability is derived from actual data and comes with a degree of uncertainty, whereas theoretical
probability is an ideal or truth existing in the universe. Through examples like the slot machine and Skittles colors, the segment elaborates on calculating probabilities of single and multiple
events, introducing the addition rule of probability for mutually exclusive events and the importance of empirical data in estimating theoretical probabilities.
๐ ฆ The Multiplication Rule and Conditional Probabilities
This segment delves into the multiplication rule of probability with a hypothetical scenario involving actor Cole Sprouse and a local IHOP's 'Free Ice Cream Night'. It explains how to calculate the
probability of two independent events occurring simultaneously, like seeing Cole at IHOP and it being Free Ice Cream Night, resulting in a 2% chance. Additionally, it covers the addition rule for
calculating the probability of either event happening. The concept of independent and conditional probabilities is further explored, particularly how they apply to real-world situations like medical
screenings for cervical cancer, illustrating the use of conditional probabilities in assessing the likelihood of a condition given a positive test result.
๐ Applying Probability to Everyday Decisions
The final segment highlights the challenges of assigning specific probabilities to daily occurrences, such as a teacher calling in sick or catching all red lights en route to school. It emphasizes
that while calculating probabilities for everyday situations may not always be feasible, understanding and applying probability concepts is valuable for making informed decisions. Examples include
choosing entertainment options with a higher probability of satisfaction, understanding the importance of flexibility in achieving goals (like seeing a popular movie), and making strategic choices
based on probabilities (such as college applications or health risks). The segment encourages viewers to integrate probability thinking into their daily lives to better navigate uncertainties.
๐ กPareidolia
Pareidolia is a psychological phenomenon where the brain perceives recognizable patterns, especially faces, in unrelated and random stimuli, such as objects or surfaces. In the video, it's used as an
opening example to illustrate how humans are pattern-seeking creatures, primed to recognize patterns even when they're not intentional or meaningful. This concept introduces the viewer to the idea
that our brains are constantly looking for patterns, setting the stage for a discussion on probability and how we interpret patterns in data and events around us.
๐ กProbability
Probability is a fundamental concept in statistics, representing the likelihood of an event occurring. The video distinguishes between everyday use of the term and its statistical meaning, further
dividing it into empirical and theoretical probability. Empirical probability is derived from actual data observations, while theoretical probability refers to the inherent likelihood of an event
based on all possible outcomes. The video uses these concepts to explore how statisticians estimate the chances of various events, such as winning a jackpot or selecting a specific colored Skittle
from a bag.
๐ กEmpirical Probability
Empirical probability is defined in the video as the probability calculated from direct observations or experiments. It represents an estimation of the theoretical probability but can be subject to
uncertainty due to the randomness and limited scope of samples. An example given is determining the ratio of girls in families based on observed data, illustrating how empirical probability gives
insight into real-world occurrences and serves as an approximation of the true, theoretical probability.
๐ กTheoretical Probability
Theoretical probability is described as an ideal or 'truth' existing in the universe, which we aim to understand or estimate through statistical means. It is not directly observable but is inferred
from patterns in empirical data. The video explains this concept using the example of playing a slot machine to estimate the jackpot's win probability, highlighting how theoretical probability
underpins our understanding of chances in a perfect, controlled environment.
๐ กMutually Exclusive
Mutually exclusive events are those that cannot happen at the same time. The video uses the example of picking a Skittle to explain that a Skittle cannot be both red and purple simultaneously,
demonstrating the concept of mutually exclusive events in probability. This concept is crucial for understanding how to calculate the probability of either of two such events occurring, using the
addition rule for mutually exclusive events.
๐ กAddition Rule
The addition rule of probability is used to calculate the likelihood of either of two events happening when those events are mutually exclusive. The video illustrates this with the probability of
selecting either a red or purple Skittle, showing that you add the individual probabilities of each event occurring. This rule is foundational for understanding how to combine probabilities in
scenarios where multiple outcomes are possible but do not overlap.
๐ กIndependent Events
Independent events are those whose occurrence does not affect the likelihood of another event occurring. The video exemplifies this with the scenario of Cole Sprouse's visits to IHOP and 'Free Ice
Cream Night,' explaining that these events do not influence each other. This concept is key to understanding how to calculate the probability of two events happening simultaneously using the
multiplication rule, as it shows that the occurrence of one event does not change the probability of the other.
๐ กConditional Probability
Conditional probability is the likelihood of an event occurring, given that another event has already happened. The video discusses this in the context of medical screenings and false positives/
negatives, showing how conditional probabilities can inform decisions and interpretations in complex scenarios. It emphasizes the importance of understanding the relationship between events,
particularly in assessing risks and making informed predictions.
๐ กMultiplication Rule
The multiplication rule helps calculate the probability of two or more independent events happening at the same time. The video uses the example of encountering Cole Sprouse at IHOP on 'Free Ice
Cream Night' to demonstrate this concept. By multiplying the probabilities of each independent event, we can find the overall likelihood of both occurring together, showcasing how probabilities
combine in scenarios involving sequential or concurrent events.
๐ กFalse Positive/Negative
False positives and negatives are errors in test results where a positive or negative outcome incorrectly indicates the presence or absence of a condition. The video uses cervical cancer screenings
as an example to explain how these errors affect the interpretation of conditional probabilities. Understanding false positives and negatives is crucial in medical testing, risk assessment, and
decision-making processes, highlighting the practical implications of probability in real-world scenarios.
The introduction provides helpful context and background on the topic
The methods section clearly explains the experimental design and procedures
Key results are summarized in an easy to understand way
Limitations of the study are acknowledged transparently
The discussion meaningfully interprets the main findings
Connections are made between results and prior research
The implications of the research are considered thoughtfully
The conclusion summarizes the main points cohesively
The writing is clear, concise and easy to follow
The overall structure is logical and flows well
Tables and figures are used effectively
References are up-to-date and relevant
The work provides a significant contribution
There is potential for impactful applications
The research opens up promising new directions
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Stochastic Pop and Drop | ChartSchool | StockCharts.com
The Stochastic Pop was developed by Jake Bernstein and modified by David Steckler, who wrote a corresponding article for Stocks & Commodities Magazine in August 2000. Bernstein's original Stochastic
Pop is a trading strategy that identifies price pops when the Stochastic Oscillator surges above 80. Steckler modified this strategy by adding conditional filters using the Average Directional Index
(ADX) and the weekly Stochastic Oscillator. This article draws on both methodologies to present another modified version of the Stochastic Pop suited for SharpCharts.
Trading Bias
Establishing a short-term trading bias with a long-term indicator is a recurring theme for trading strategies. Long-term indicators are used to define the path of least resistance, which forms the
basis of the trading bias. Traders look for bullish setups when the bias is bullish and bearish setups when the bias is bearish. Trading in the direction of this bias is like riding a bike with the
wind at your back. The chances of success are higher when the bigger trend is in your favor.
Steckler used the weekly Stochastic Oscillator to define the trading bias. In particular, the trading bias was deemed bullish when the weekly 14-period Stochastic Oscillator was above 50 and rising.
This article will use a 70-period daily Stochastic Oscillator so all indicators can be displayed on the chart. This timeframe is simply five times the 14-day timeframe. The trading bias will be
considered bullish when above 50. The chart below shows F5 Networks (FFIV) with the 70-period Stochastic Oscillator defining the bullish and bearish periods.
Waiting for a Range
Once the trading bias is established, Steckler used the Average Directional Index (ADX) to define a slowdown in the trend. ADX measures the strength of the trend and a move below 20 signals a weak
trend. Steckler preferred ADX below 15, but would use 20 as well. A high and rising ADX signals a strengthening trend, while a low and falling ADX indicates that the trend is weakening. On the chart
below, 14-period ADX on the daily chart shows a weak trend when it moves below 20. Notice how Gap (GPS) moved into a trading range as ADX dipped below 20 twice (yellow areas).
Buy Signal
Once the bullish prerequisites are in place, a buy signal triggers when the 14-day Stochastic Oscillator surges above 80 and the stock breaks out on above-average volume. Steckler preferred
consolidation breakouts when using this strategy, but chartists should still consider high volume signals that do not produce breakouts. Sometimes the initial high-volume surge is a precursor to a
For volume assessment, chartists can compare current volume to the 250-day moving average of volume, which is essentially the one year average. Volume above the one-year average would be deemed
The chart above shows Marriott (MAR) with a bullish Stochastic Pop signal in early January. Notice that this signal occurred before the actual breakout. High volume confirmed the surge off of support
and acted as a precursor to the actual breakout. Traders acting on the Stochastic Pop signal would have had a better risk-reward ratio than those acting on the breakout.
Stops and Targets
Once a signal triggers, traders need to work out the stop-loss and price target, preferably before a position is taken. Plan your trade and trade your plan. Traders must plan for the worst because
not all signals will work out profitably. If a consolidation formed, the stop-loss can be set just below consolidation support. Because the Stochastic Pop occurs with an upward surge in prices, there
is usually a trough or reaction low just before this surge. A stop-loss can also be placed just below this trough. The chart below shows JB Hunt (JBHT) with two Stochastic Pop signals. The stop-loss
for the first signal is based on the low just before Pop 1. The stop-loss for the second signal is based on the low just below Pop 2.
Should prices continue higher, traders can set a trailing stop-loss to lock in profits. The pink line shows the Parabolic SAR being used to set a trailing stop-loss. The 14-day Stochastic Oscillator
can also be used to define a stall or downturn in short-term momentum. A move below 50 signals a momentum shift that can also be used to take profits or tighten a stop.
Sell Signal
Astute chartists will realize that this buy signal can easily be reverse-engineered to produce sell signals. In fact, we can name the sell version the “Stochastic Drop.” A sell signal is indicated by
the following elements:
70-day Stochastic Oscillator is below 50.
14-day Average Directional Index (ADX) is below 20.
14-day Stochastic Oscillator plunges below 20.
Stock declines on high volume and/or breaks consolidation support.
The chart above shows HR Block (HRB) with a Stochastic Drop signal in mid-July 2011. The trading bias was bearish because the 70-day Stochastic Oscillator was below 50 and the Average Directional
Index (ADX) was below 20. The Stochastic Drop triggered when the Stochastic Oscillator plunged below 20. Even though volume did not expand and the stock did not break support, this signal
foreshadowed a sharp decline in late July and early August. Volume confirmation is not as important for bear signals.
Indicator Tweaks
While a consolidation does not always form when ADX moves below 20, a move below this level usually coincides with a flattening of the trend. Requiring ADX to move below 15 will improve the chances
of catching a consolidation on the price chart. Also note that securities with relatively low volatility, such as utilities, may have relatively low ADX ranges and require a move below 10 to identify
The 14-day Stochastic Oscillator is a relatively active momentum indicator that moves from oversold (20) to overbought (80) quite frequently. This means there will be plenty of signals to choose
from. Chartists should be careful of signals that occur after short dips in the Stochastic Oscillator. In other words, a surge from 65 to 85 (20 points) is not as potent as a surge from 35 to 85 (50
The Bottom Line
The Stochastic Pop and Drop signals are designed to catch a continuation move within the bigger trend. While the signals are easy to quantify, chartists should also consult the price chart and look
for confirming patterns. A bull flag or falling wedge breakout can be used to confirm a bullish Stochastic Pop, while a bear flag or rising wedge breakdown can be used to confirm a bearish Stochastic
Drop. Chartists should also consult the price chart to determine the risk-reward ratio and make sure it is acceptable before taking a position. Keep in mind that this article is designed as a
starting point for trading system development. Use these ideas to augment your trading style, risk-reward preferences and personal judgments. Click here for a chart of the S&P 500 ETF (SPY) with the
Stochastic Pop and Drop indicators already set up.
Suggested Scans
Bullish Stochastic Pop
This scan searches for stocks that have just had a Stochastic Pop buy signal.
[type = stock]
and [today's sma(20,volume) > 40000]
and [today's sma(60,close) > 20]
and [Slow Stoch %K (70,3) > 50]
and [ADX Line (14) < 20]
and [today's Slow Stoch %K (14,3) x 80]
Bearish Stochastic Drop
This scan searches for stocks that have just had a Stochastic Drop sell signal.
[type = stock]
and [today's sma(20,volume) > 40000]
and [today's sma(60,close) > 20]
and [Slow Stoch %K (70,3) < 50]
and [ADX Line (14) < 20]
and [20 x today's Slow Stoch %K (14,3)]
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Empirical study on clique-degree distribution of networks - P.PDFKUL.COM
PHYSICAL REVIEW E 76, 037102 共2007兲
Empirical study on clique-degree distribution of networks Wei-Ke Xiao,1,2 Jie Ren,2,3,4 Feng Qi,2 Zhi-Wei Song,2 Meng-Xiao Zhu,2 Hong-Feng Yang,2 Hui-Yu Jin,2 Bing-Hong Wang,4 and Tao Zhou3,4,* 1
Center for Astrophysics, University of Science and Technology of China, Hefei 230026, China Research Group of Complex Systems, University of Science and Technology of China, Hefei 230026, China 3
Department of Physics, University of Fribourg, Chemin du Muse 3, CH-1700 Fribourg, Switzerland 4 Department of Modern Physics and Nonlinear Science Center, University of Science and Technology of
China, Hefei 230026, China 共Received 21 January 2006; revised manuscript received 29 July 2007; published 27 September 2007兲 2
The community structure and motif-modular-network hierarchy are of great importance for understanding the relationship between structures and functions. We investigate the distribution of clique
degrees, which are an extension of degree and can be used to measure the density of cliques in networks. Empirical studies indicate the extensive existence of power-law clique-degree distributions in
various real networks, and the power-law exponent decreases with an increase of clique size. DOI: 10.1103/PhysRevE.76.037102
PACS number共s兲: 89.75.Hc, 05.40.⫺a, 64.60.Ak, 84.35.⫹i
The discovery of small-world effects 关1兴 and scale-free properties 关2兴 triggered an upsurge in the study of the structures and functions of real-life networks 关3–7兴. Previous empirical studies
have demonstrated that most real-life networks are small world 关8兴; that is to say, they have a very small average distance like completely random networks and a large clustering coefficient like
regular networks. Another important characteristic in real-life networks is the powerlaw degree distribution—that is, p共k兲 ⬀ k−␥, where k is the degree and p共k兲 is the probability density
function for the degree distribution. Recently, empirical studies reveal that many real-life networks, especially biological networks, are densely made up of some functional motifs 关9–11兴. The
distributing pattern of these motifs can reflect the overall structural properties and thus can be used to classify networks 关12兴. In addition, the networks’ functions are highly affected by these
motifs 关13兴. A simple measure can be obtained by comparing the density of motifs between real networks and completely random ones 关12兴; however, this method is too rough and thus still under
debate now 关14,15兴. In this paper, we investigate the distribution of clique degrees, which are an extension of degree and can be used to measure the density of cliques in networks. The word clique
in network science equals the term complete subgraph in graph theory 关16兴; that is to say, the m order clique 共m-clique for short兲 means a fully connected network with m nodes and m共m − 1兲 / 2
edges. Define the m-clique degree of a node i as the number of different m-cliques containing i, denoted by k共m兲 i . Clearly, a 2-clique is an edge and k共2兲 equals the degree ki; thus, the
concept of i clique degree can be considered as an extension of degree 共see Fig. 1兲. We have calculated the clique degree from order 2 to 5 for some representative networks. Figures 2–8 show the
clique-degree distributions of seven representative networks in logarithmic binning plots 关17,18兴; these are the Internet at the autonomous systems 共AS兲 level 关19兴, the Internet at the routers
level 关20兴, the metabolic network of P.aeruginosa 关21兴, the World-Wide-Web 关22兴, the collaboration net-
work of mathematicians 关23兴, the protein-protein interaction networks of yeast 关24兴, and the BBS friendship networks at the University of Science and Technology of China 共USTC兲关25兴. The
slopes shown in those figures are obtained by using a maximum-likelihood estimation 关26兴. Table I summarizes the basic topological properties of those networks. Although the backgrounds of those
networks are completely different, they all display power-law clique-degree distributions. We have checked many examples 共not shown here兲 and observed similar power-law clique-degree distributions.
However, not all the networks can display higher-order power-law clique-degree distributions. Actually, only the relatively large networks could have a power-law cliquedegree distribution with order
higher than 2. For example, Ref. 关21兴 reports 43 different metabolic networks, but most of them are very small 共N ⬍ 1000兲, in which the cliques with order higher than 3 are exiguous. Only the
five networks with most nodes display relatively obvious power-law clique-degree distributions, and the case of P.aeruginosa is shown in Fig. 4. Note that, even for small-size networks, the
high-order clique is abundant for some densely connected networks such as technological collaboration networks 关27兴 and food webs 关28兴. However, since the average degree of the majority of
metabolic networks is less than 10, the highorder cliques could not be expected with network size N ⬍ 1000. Furthermore, all empirical data show that the powerlaw exponent will decrease with an
increase of clique order. This may be a universal property and can reveal some un-
[email protected]
FIG. 1. Illustration of the clique degree of node i. ki = 7, ki 共4兲共5兲 = 5, ki = 1, and ki = 0. 037102-1
©2007 The American Physical Society
PHYSICAL REVIEW E 76, 037102 共2007兲
FIG. 2. 共Color online兲 Clique-degree distributions of the Internet at the AS the level from order 2 to 5, where k共m兲 denotes the m-clique degree and N共k共m兲兲 is the number of nodes with
m-clique degree k共m兲. In each panel, the marked slope of the red line is obtained by using maximum likelihood estimation 关26兴.
FIG. 5. 共Color online兲 Clique-degree distributions of the World-Wide-Web.
FIG. 3. 共Color online兲 Clique-degree distributions of the Internet at the routers level.
FIG. 6. 共Color online兲 Clique-degree distributions of the collaboration network of mathematicians.
FIG. 4. 共Color online兲 Clique-degree distributions of the metabolic network of P.aeruginosa.
FIG. 7. 共Color online兲 Clique-degree distributions of the protein-protein interaction networks of yeast.
PHYSICAL REVIEW E 76, 037102 共2007兲
FIG. 8. 共Color online兲 Clique-degree distributions of the BBS friendship networks at the University of Science and Technology of China. The blue points with error bars denote the case of a
randomized network.
known underlying mechanism in network evolution. In order to illuminate that the power-law clique-degree distributions with order higher than 2 could not be considered as a trivial inference of the
scale-free property, we compare these distributions between original USTC BBS friendship network and the corresponding randomized network. Here the randomizing process is implemented by using the
edge-crossing algorithm 关12,29–31兴, which can keep the degree of each node unchanged. The procedure is as follows: 共i兲 Randomly pick two existing edges e1 = x1x2 and e2 = x3x4, such that x1 ⫽ x2
⫽ x3 ⫽ x4 and there is no edge between x1 and x4 as well as x2 and x3. 共ii兲 Interchange these two edges; that is, connect x1 and x4 as well as x2 and x3, and remove the edges e1 and e2. 共iii兲
Repeat 共i兲 and 共ii兲 for 10M times. We call the network after this operation the randomized network. In Fig. 9, we report the clique-degree distributions in the randomized network. Obviously, the
2-clique degree distribution 共not shown兲 is the same as that in Fig. 8. One can find that the randomized network does not display power-law clique-degree distributions with higher order; in fact,
it has very few 4-cliques and none 5-cliques. The direct comparison is shown in Fig. 8. TABLE I. The basic topological properties of the present seven networks, where N, M, L, and C represent the
total number of nodes, the total number of edges, the average distance, and the clustering coefficient, respectively. Networks/Measures Internet at AS level Internet at routers level Metabolic
network World-Wide-Web Collaboration network ppi-yeast networks Friendship networks
10515 21455 3.66151 0.446078 228263 320149 9.51448 0.060435 1006 2957 3.21926 0.216414 325729 1090108 7.17307 0.466293 6855 11295 4.87556 0.389773 4873 17186 4.14233 0.122989 10692 48682 4.48138
FIG. 9. 共Color online兲 The clique-degree distributions in the randomized network corresponding to the BBS friendship network of USTC. The black squares and red circles represent the cliquedegree
distributions of order 3 and 4, respectively. All the data points and error bars are obtained from 100 independent realizations.
The discoveries of new topological properties accelerate the development of network science 关1,2,7,9,32–34兴. These empirical studies not only reveal new statistical features of networks, but also
provide useful criteria in judging the validity of evolution models. 共For example, the Barabási-Albert model 关2兴 does not display high-order power-law cliquedegree distributions.兲 The clique
degree, which can be considered as an extension of degree, may be useful in measuring the density of motifs; such subunits not only play a role in controlling the dynamic behaviors, but also refer to
the basic evolutionary characteristics. More interesting, we find that various real-life networks display power-law cliquedegree distributions of decreasing exponent with the clique order. This is an
interesting statistical property, which can provide a criterion in the studies of modeling. It is worthwhile to recall a prior work 关13兴 that reported a similar power-law distribution observed for
some cellular networks. They divided all the subgraphs into two types. Moreover, they derived the analytical expression of the power-law exponent ␦m ⬘ for m-clique degree distribution as 关13兴 ␦m ⬘
= 1 + 共␥ − 1兲 / 关m − 1 − ␣共m − 1兲共m − 2兲 / 2兴, where ␣ denotes the power-law exponent of clustering-degree correlation C共k兲 ⬃ k−␣. Table II displays the predicted power-law exponents ␦m ⬘ ,
compared with the empirical observation ␦m. For the type-I cases, the predicted results are, to some extent, in accordance with the empirical data. Note that, although the power law is detected for
type-II cases, the analytical expression of ␦m ⬘ loses its validity in those cases. The qualitative difference in type-II cases and quantitative departure in type-I cases may be attributable to the
structural bias 共e.g., assortative connecting pattern 关32兴, rich-club phenomenon 关35兴, etc.兲 since the derivation in Ref. 关13兴 is based on uncorrelated networks. In addition, the predicted
accuracy decreases as the increase of clique size m, because the clustering coefficient takes into account only the triangles 关36兴. Therefore, a more accurate analysis may involve a higherorder
clustering coefficient 关7兴. In other words, Ref. 关13兴 provides a starting point of an in-depth understanding of the network structure at the clique level, while the diversity and complexity of
real networks require further explorations on this issue.
PHYSICAL REVIEW E 76, 037102 共2007兲
TABLE II. The empirical 共␦m兲 and predicted 共␦m ⬘ 兲 power-law exponent of the clique-degree distribution, where ␥ and ␣ denote the power-law exponents of the degree distribution and
clustering-degree correlation. The symbol “/” denotes the cases with ␣共m − 2兲 ⬎ 2, leading to negative and meaningless ␦m ⬘.
Internet at AS level
Internet at routers level
Metabolic network
Collaboration network
ppi-yeast networks
Friendship networks
1.82 1.48 1.28 1.72 1.49 1.33 1.85 1.56 1.43 1.59 1.37 1.22 1.90 1.53 1.41 1.68 1.47 1.36 1.48 1.25 1.20
2.26 / / 1.86 1.63 1.53 1.87 2.73 / 2.56 / / 2.10 5.03 / 2.08 5.37 / 1.51 1.42 1.41
II II II I I I I II II II II II II II II II II II I I I
We thank Dr. Ming Zhao for useful discussions. This work is supported by the National Natural Science Foundation of China under Grants Nos. 10472116, 70471033, and 10635040.
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Milo et al., Science 305, 1107d 共2004兲. I. Derényi, G. Palla, and T. Vicsek, Phys. Rev. Lett. 94, 160202 共2005兲. M. E. J. Newman and J. Park, Phys. Rev. E 68, 036122 共2003兲. M. E. J. Newman,
Contemp. Phys. 46, 323 共2005兲. http://www.cosin.org/extra/data/internet/nlanr.html http://www.isi.edu/scan/mercator/map.html
H. Jeong et al., Nature 共London兲 407, 651 共2000兲. R. Albert et al., Nature 共London兲 401, 130 共1999兲. http:/www.oakland.edu/~grossman http://dip.doe-mbi.ucla.edu/ This network is constructed
based on the BBS of USTC, wherein each node represents a BBS accounts and two nodes are neighboring if one appears in the other one’s friend list. Only the undirected network is considered. M. L.
Goldstein et al., Eur. Phys. J. B 41, 255 共2004兲. P.-P. Zhang et al., Physica A 360, 599 共2006兲. S. L. Pimm, Food Webs 共University of Chicago Press, Chicago, 2002兲. S. Maslov et al., Science
296, 910 共2002兲. B. J. Kim, Phys. Rev. E 69, 045101共R兲共2004兲. M. Zhao et al., Physica A 371, 773 共2006兲. M. E. J. Newman, Phys. Rev. Lett. 89, 208701 共2002兲. E. Ravasz and A. L. Barabasi,
Phys. Rev. E 67, 026112 共2003兲. C. Song et al., Nature 共London兲 433, 392 共2005兲. S. Zhou et al., IEEE Commun. Lett. 8, 180 共2004兲. The theory in Ref. 关13兴 is really accurate for ␦3 if
belongs to type I; for example, ␦3 in random Apollonian networks 关37兴 can be exactly predicted by the analytical result ␦3⬘. T. Zhou et al., Phys. Rev. E 71, 046141 共2005兲.
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gamus (c49b1)
Gaussian Mixture Adaptive Umbrella Sampling (GAMUS)
GAMUS is a hybrid of adaptive umbrella sampling (see
» adumb
syntax ) and metadynamics which is suited to
identifying free energy minima for multidimensional reaction coordinates.
Like adaptive umbrella sampling this method attempts to calculate the free
energy surface in terms of designated reaction coordinates, and uses the
negative of this as a biasing potential to enhance the sampling.
The distribution of reaction coordinates is expressed in terms of mixtures
of Gaussians whose size and shape are optimized to fit the data as closely
as possible. This is similar to the use of Gaussians in metadynamics to fill
free energy basins but is more flexible. No grids or histograms are used,
which reduces the memory and statistical requirements of the method and
allows the efficient exploration of free energy surfaces in 3-5 dimensions.
The method is described in
P. Maragakis, A. van der Vaart, and M. Karplus. J. Phys. Chem. B 113, 4664
(2009). doi:10.1021/jp808381s
Please report problems to Justin Spiriti at jspiriti@usf.edu and/or
Arjan van der Vaart at avandervaart@usf.edu.
| Syntax of the GAMUS commands
| Purpose of each of the commands
| Some limitations of the GAMUS method
| Installation of GAMUS within CHARMM
| Usage example of the GAMUS module
[SYNTAX GAMUS functions]
GAMUs DIHE 4X(atom-spec)
GAMUs INIT [TEMP real] [RUNI int] [WUNI int] [IFRQ int]
GAMUS FIT DATA int NGAUSS int NREF int NITR int SIGMA real GAMMA real
GAMUS REWEight NSIM int QUNI int PUNI int NGAUss int [NREF int] [NITR int]
[SIGMa real] [GAMMa real] [WEIGHT int]
GAMUS WRITE UNIT int
GAMUS INFO [VERBose]
where: atom-spec ::= { segid resid iupac }
{ resnumber iupac }
0. Introduction
A GAMUS simulation cycles through three stages:
1. Molecular dynamics with a biasing potential equal to minus the free energy
surface estimated from the previous simulation.
2. Determination of the partition function ratios Z_i/Z_0 for each biased
simulation relative to the unbiased simulation. This is done using the
multistate acceptance ratio method (MARE), which optimizes the likelihood of
observing the work values associated with the transitions between biasing
potentials (see P. Maragakis et al. J. Phys. Chem. B 112, 6168 (2008))
3. Reweighting of the data and fitting of a new mixture of Gaussians to the
distribution of reaction coordinates encountered in previous simulations.
This is done using the expectation-maximization (E-M) algorithm (see A. P.
Dempster et al. J. R. Stat. Soc. B 39, 1 (1977) and Bowers et al.
Comput. Phys. Commun. 164, 311 (2008)). Starting from an initial guess, this
algorithm iteratively refines the weights, means, and variance-covariance
matrices of the Gaussians in order to maximize the likelihood of observing the
data given the fitted distribution. The E-M algorithm is started several
times from randomly chosen starting points; the fit with the best likelihood
is chosen. From this fit, the new free energy surface and biasing potential
may be obtained.
GAMUS produces three sets of input/output files. GAMUS potential files contain
the weights, means, and variance-covariance matrices of the Gaussians used to
define the biasing potential, as well as the value of the Bayesian knowledge
parameter gamma. These files have the following format:
34 5 ! Number of Gaussians, number of coordinates
-25 ! log(gamma)
then follows the natural logarithms of the weights, the means, and the
inverses of the variance-covariance matrices, see subroutine READGAMUS in
Energy-coordinate files contain the values of the reaction coordinates
encountered during the simulation, as well as the values of the biasing
potential. Weight files contain the values of the reaction coordinates
as well as the natural logarithms of the weights needed to recover a canonical
Boltzmann distribution.
1. GAMUS DIHE
Define a dihedral angle as a reaction coordinate for GAMUS.
2. GAMUS INIT
Initializes the GAMUS potential. TEMP specifies the temperature of the
simulation. RUNI and WUNI give unit numbers for the biasing potential to be
used and the energy-coordinate file to be written during the simulation.
An initial potential file is needed for the first GAMUS simulation; this
should specify 0 gaussians and a value of ln(gamma) equal to -D*ln(360)
where D is the number of reaction coordinates.
IFRQ gives the frequency of recording the values of the reaction coordinates.
This should be infrequent enough that consecutive values are uncorrelated
(about 0.2 ps in most cases).
3. GAMUS CLEAR
Turns GAMUS off and clears all associated data structures.
4. GAMUS REWEight
Performs MARE and the E-M algorithm in order to calculate a new biasing
potential from previous potentials and energy-coordinate files. The biasing
potential files must be opened as a continuous sequence of NSIM units starting
with unit PUNI; likewise, the energy-coordinate files must be opened as
a continuous sequence of units starting with QUNI.
Keyword Default Purpose
NSIM n/a Number of previous simulations to include
PUNI n/a Initial biasing potential unit
QUNI n/a Initial energy-coordinate file unit
NGAUss n/a Number of Gaussians to be used (should gradually increase
with the number of simulations. It is suggested to add
about 1-2 Gaussians to the fit per ns of simulation.)
NREF 20 Number of refinements using the E-M algorithm from randomly
chosen starting points.
NITR 200 Maximum number of iterations of the E-M algorithm per
SIGMa 5 Minimum size of a Gaussian in any direction (in degrees)
SMAX 90 Maximum size of a Gaussian in any direction (in degrees)
GAMMa -1000 Cutoff for the Bayesian prior (see below)
WEIGht -1 Unit number for writing weights of the frames (as their
natural logarithms) together with values of the reaction
WORK -1 Unit number for writing work values input into MARE
(primarily for debugging purposes)
The E-M optimization can have a tendency for Gaussians to collapse around
individual data points. For this reason, a minimum size of the Gaussian
in each direction is imposed. When a Gaussian collapses to this minimum
in all directions, the message "gaussian number N is of minimum size in
all directions" is produced. The SMAX option is used to impose a maximum size
of a Gaussian in order to prevent periodicity assumptions from being violated.
If a large number of these messages appear, it may mean that too many
Gaussians are being used for the fit, or that the cap on ln(gamma) is too
small (see below).
The value of gamma is chosen based on the probability of obtaining the least
probable sampled data point. A cap on the value of ln(gamma) can be used to
restrict the extrapolation of the free energy surface in order to avoid deep
artificial minima in the free energy surface (as described in Maragakis et al.
JPC B 113, 4664 (2009)). This is recommended if more than two reaction
coordinates are used. The value of the cap should be chosen so that the free
energy differences ln(Zi/Z0) average around zero. It should be noted that
the biasing potential is limited to kT ln(gamma) so setting too low a cap
can limit the part of the free energy surface that is sampled.
5. GAMUS FIT
Uses the E-M algotithm to fit weighted values of the reaction coordinates
found in the unit specified by DATA to a mixture of Gaussian distributions.
The NGAUSS, NREF, NITR, SIGMA and GAMMA parameters are specified as described
above for GAMUS REWEight. The first column in the file must be for the natural
logarithms of the weights; the remaining columns are for the values of the
reaction coordinates.
6. GAMUS WRITE
Writes the current GAMUS potential to a unit specified by UNIT. This usually
follows a GAMUS REWEIGHT or GAMUS FIT command that generates a new GAMUS
potential (see above).
7. GAMUS INFO
Prints out the weights and mean values of all the Gaussians in the current
GAMUS potential. If the VERBose option is specified, each variance-covariance
matrix will also be diagonalized to find the principal axes of each Gaussian
and the width of the Gaussian along each axis.
1. The expectation-maximization algorithm fits the probability density, not
the free energy. Since the probability density is lower near free energy
barriers, and since the free energy is proportional to the logarithm of
the probability density, the statistical errors in estimating the free energy
surface are greater near barriers. Consequently, GAMUS does a much better job
of identifying and locating free energy basins and of determining their shapes
and relative free energies than it does of estimating free energy barriers.
2. The time necessary to fit a set of Gaussians increases linearly with the
number of Gaussians to be fitted. Consequently, fitting can become very
expensive if many Gaussians are used. In addition, using too many Gaussians
can result in some of the Gaussians collapsing around individual data points
("gaussian number N is of minimum size in all directions" message).
Consequently, it is suggested to add Gaussians slowly during the run;
a rate of about 1-2 additional Gaussians per ns of
simulation is recommended.
3. Because of the extrapolation involved in determining the biasing potential
from the free energy surface, it is possible for the fitting to introduce
artificial minima in the free energy surface. These artificial minima
should go away in long enough simulations. Adjusting the cap value of
ln(gamma) can help with this, as described above.
GAMUS requires an implementation of LAPACK in order to perform linear algebra
as part of the E-M and MARE algorithms.
To compile CHARMM with GAMUS included add the option '--with-gamus'
to the configure command line, for example:
./configure --with-gamus
Since the name and path of the LAPACK library can vary from one system to
another, cmake will attempt to find a suitable LAPACK installation
and linker options. These options will be added to the link command line.
If the options are not determined correctly, one may set the cmake variables
LAPACK_LINKER_FLAGS and LAPACK_LIBRARIES to the required linker flags (excluding -l and -L) and to the libraries (using full path name) to link against to use LAPACK respectively. The cmake variables
may be set using the '-D' option
to the configure command. If all else fails, one may set
the environment variable LDFLAGS before running the configure command
with the correct options, such as -L and -l options.
The main loop for cycling through steps 1-3 above is encoded in the script.
During each cycle molecular dynamics is invoked twice: once for equilibration
and once for sampling. GAMUS is also invoked twice: once for each section of
molecular dynamics. At the end of the molecular dynamics simulations,
the GAMUS REWEIGHT command is used to reweight the data from all previous
simulations and fit this to a mixture of Gaussians using the E-M algorithm.
This results in a new GAMUS potential, which is used for the next cycle of
molecular dynamics simulation.
The script structure is as follows:
! first read in the force field, PSF, set up implicit or explicit solvent, etc.
! write an initial GAMUS potential, specifying the number of reaction
! coordinates (4 in this case)
calc initgamma = -4 * ln( 360.0 )
open unit 1 write formatted name @9gamus-1.dat
write title unit 1
* 0 4
* @initgamma
close unit 1
set index = 1
label gamusloop
calc oldindex = @index - 1
open unit 1 read formatted name @9restart-col-@oldindex.rst
read coor dynr curr unit 1
close unit 1
! here we equilibrate
open unit 29 read card name @9restart-col-@oldindex.rst
open unit 30 write card name @9restart-eq-@index.rst
!this file contains the GAMUS potential
open unit 44 read card name @9gamus-@index.dat
! in this file CHARMM will record biasing potential and reaction
! coordinate values encountered during the simulation.
! We write to a different file from "gamuse..." to keep this from being
! used later by the MARE and GMM fits
open unit 45 write card name @9gamusex-@INDEX-q-@INDEX.dat
open unit 46 write unform name @9gamus-eq-@index.dcd
! This activates the GAMUS biasing potential and specifies the reaction
! coordinate (4 dihedral angles)
gamus init temp @temp runi 44 wuni 45 ifrq @gamusfreq
gamus dihe pep 1 c pep 2 n pep 2 ca pep 2 c
gamus dihe pep 2 n pep 2 ca pep 2 c pep 3 n
gamus dihe pep 2 c pep 3 n pep 3 ca pep 3 c
gamus dihe pep 3 n pep 3 ca pep 3 c pep 4 n
dynamics ... iunrea 29 iunwri 30 iuncrd 46 !perform dynamics for equilibration
close unit 29
close unit 30
close unit 44
close unit 45
close unit 46
gamus clear
! and now we collect statistics
open unit 29 read card name @9restart-eq-@index.rst
open unit 30 write card name @9restart-col-@index.rst
! We do everything over again, this time writing in a file that is
! used by the MARE and GMM fits.
! The definition of the reaction coordinate must match the one given above.
open unit 44 read card name @9gamus-@index.dat
open unit 45 write card name @9gamuse-@INDEX-q-@INDEX.dat
open unit 46 write unform name @9gamus-col-@index.dcd
gamus init temp 300.0 runi 44 wuni 45 ifrq @gamusfreq
gamus dihe pep 1 c pep 2 n pep 2 ca pep 2 c
gamus dihe pep 2 n pep 2 ca pep 2 c pep 3 n
gamus dihe pep 2 c pep 3 n pep 3 ca pep 3 c
gamus dihe pep 3 n pep 3 ca pep 3 c pep 4 n
! prnlev -6
dynamics ... iunrea 29 iunwri 30 iuncrd 46 !perform dynamics for sampling
close unit 29
close unit 30
close unit 44
close unit 45
close unit 46
! now use the new commands to reweight the potential
calc newindex = @index + 1
calc ngauss = 4 + @index !This calculates the number of Gaussians to be used for the fit.
set i = 1
label loop
calc u1 = 10 + @i
calc u2 = 100 + @i
open unit @u1 read formatted name @9gamus-@i.dat
open unit @u2 read formatted name @9gamuse-@i-q-@i.dat
incr i by 1
if i .le. @index then goto loop
open unit 7 write formatted name @9weights-@index
open unit 8 write formatted name @9gamus-@newindex.dat
gamus reweight nsim @index puni 11 quni 101 ngauss @ngauss nref 4 nitr 200 sigma 5.0 gamma -25.0 weights 7
gamus write unit 8
close unit 8
close unit 7
set i = 1
label loop2
calc u1 = 10 + @i
calc u2 = 100 + @i
close unit @u1
close unit @u2
incr i by 1
if i .le. @index then goto loop2
gamus clear
incr index by 1
if index .le. 4 then goto gamusloop
gamus clear
|
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Understanding The Difference Between Convergence And Absolute Convergence - Coloringfolder.com
Understanding the Difference Between Convergence and Absolute Convergence
Convergence and absolute convergence are commonly confused in mathematics, yet the difference between them is crucial to understanding mathematical analysis. In simple terms, convergence is a
measurement of how close a sequence gets to a limit as the number of terms increases, while absolute convergence measures how fast the terms of a convergent sequence approach zero. It may sound
simple, but many people misunderstand these concepts, leading to confusion and error.
To see the difference between convergence and absolute convergence, let’s take the sequence 1/n. As n approaches infinity, the sequence gets closer and closer to zero. This means that the sequence
converges to zero. However, the sequence also falls to zero at a constant rate, meaning that it absolutely converges to zero as well. In contrast, a series like the alternating harmonic series, where
the terms alternate signs, can converge but not absolutely converge. In these cases, even though the sequence gets closer and closer to zero, it does not fall to zero at a constant rate.
Despite being a fundamental concept in mathematical analysis, the difference between convergence and absolute convergence can be confusing, especially for those new to mathematics. This confusion can
lead to mistakes in calculations and can make understanding complex mathematical concepts even more challenging. Now that we’ve seen the difference between these two concepts let’s explore the
implications of each more deeply and discuss various practical applications in mathematics and beyond.
Definition of convergence and absolute convergence
In the field of mathematics, there are various series that are studied. A series is an infinite summation of numbers, and it is typically denoted by the symbol Σ. The series is said to converge if it
approaches a finite value as the number of terms in the series approaches infinity. On the other hand, if the series does not approach a finite value as the number of terms increases, it is said to
One important subtype of series is absolute convergence. A series is said to be absolutely convergent if the sum of the absolute values of its terms converges. For example, the series Σ(-1)^n/n would
be considered absolutely convergent because the series Σ|(-1)^n/n| converges. In contrast, the series Σ(-1)^n/n^2 would be considered conditionally convergent as it is not absolutely convergent, but
it still converges.
Key differences between convergence and absolute convergence
• Convergence is a more general term that describes how a series approaches a finite value as the number of terms increases, whereas absolute convergence specifically describes the case where the
sum of the absolute values of the terms in the series is finite.
• If a series is absolutely convergent, it is also convergent. However, there exist series that are convergent but not absolutely convergent.
• For example, the alternating harmonic series Σ(-1)^n/n diverges, but its absolute value series Σ|(-1)^n/n| converges. In contrast, the series Σ1/n^2 is convergent but not absolutely convergent.
Application of convergence and absolute convergence
The concept of convergence and absolute convergence plays a significant role in various mathematical fields. For example, calculus heavily relies on these concepts to determine the values of
functions at various points and to calculate integrals.
Moreover, many physical and scientific applications use the concept of convergence to study the behavior of different series. For example, in quantum mechanics, researchers studying the energy levels
of atoms and molecules use the concept of convergence and absolute convergence to understand the behavior of the series representing the energy levels.
Series Convergence Absolute Convergence
Σ(-1)^n/n Divergent Convergent
Σ(-1)^n/n^2 Convergent Not absolutely convergent
Σ1/n^2 Convergent Not absolutely convergent
As we can see from the table above, the concept of absolute convergence provides a stronger notion of convergence for certain series and has important applications in various fields. Therefore,
understanding the differences between convergence and absolute convergence is essential for any student of mathematics and sciences.
Mathematical representation of convergence and absolute convergence
In basic terms, convergence is the property of a sequence or a series that describes whether the sequence or series approaches a definite limit. A sequence converges if, for any given small positive
value, there exists a positive integer after which all the terms of the sequence are closer to the limit as compared to the given value.
Mathematically, we can represent convergence as follows: A sequence {an} converges to a limit L if for every positive number ε, there exists a positive integer N such that for all n>N, |an – L|<ε. In
simple terms, this means that any value of ε can be made arbitrarily small by taking sufficiently large terms of the sequence.
• On the other hand, absolute convergence is a stronger condition. It is a property of a series that ensures that the series converges regardless of the order in which its terms are added. Simply
put, the series converges if the series of the absolute values of its terms also converges.
• Mathematically, we can represent absolute convergence as follows: A series “a” converges absolutely if the series of the absolute values of its terms |a_n| converges. In other words, if Σ|a_n|
converges, then Σa_n also converges absolutely.
• One way to understand the concept of absolute convergence is to recognize that if |a_n| is a decreasing sequence, we can leverage the Alternating Series Test. This states that a series Σ(-1)^
(n+1)a_n converges if a_n is a sequence that converges to 0.
In summary, convergence is a property of a series or sequence that defines its limit while absolute convergence is a specific condition that guarantees convergence regardless of the order of
addition. Both convergence and absolute convergence are crucial concepts in calculus and real analysis, and they play essential roles in solving problems related to differentiation, integration, and
the evaluation of the critical points of functions.
Comparison between conditional convergence and absolute convergence
When talking about the convergence of a series, it’s important to understand the difference between conditional convergence and absolute convergence. Let’s take a closer look at each:
• Absolute Convergence: A series is said to be absolutely convergent if the sum of the absolute values of each term in the series is a finite number. In other words, if |an| converges, then the
series converges absolutely. This type of convergence is also known as uniform convergence.
• Conditional Convergence: On the other hand, a series is said to be conditionally convergent if it is convergent, but not absolutely convergent. In this case, the sum of the absolute values of
each term in the series diverges. However, when certain conditions are met, the series as a whole will still converge.
To understand this better, let’s take an example of a series:
$$\sum_{n=1}^{\infty} \frac{(-1)^n}{n}$$
This series is convergent but not absolutely convergent. Let’s see why:
n term |term|
1 -1/1 1
2 1/2 1/2
3 -1/3 1/3
4 1/4 1/4
… … …
As we can see, the series alternates between positive and negative values. When we take the absolute value of each term and sum them, the series diverges:
$$\sum_{n=1}^{\infty} \frac{1}{n}$$
However, the original series still converges, with the sum being approximately 0.69.
In summary, while absolute convergence guarantees convergence under all conditions, conditional convergence can still occur in some cases. This is important to understand when dealing with more
complex series and sequences.
Examples of series exhibiting convergence
Convergence of a series refers to the property of the sum of an infinite number of terms approaching a finite limit as the number of terms increases. In this subsection, we will explore some examples
of series that exhibit convergence.
• Geometric Series: A geometric series is given by the formula $\sum_{n=0}^{\infty}ar^{n}$, where $a$ is the first term and $r$ is the common ratio between successive terms. This series converges
if $|r|<1$. For example, the series $1+ \frac{1}{2} + \frac{1}{4} +\frac{1}{8} +…$ is a geometric series with $a=1$ and $r=\frac{1}{2}$, and it converges to a sum of $2$.
• Harmonic Series: The harmonic series is given by the formula $\sum_{n=1}^{\infty}\frac{1}{n}$. This popular series is well-known for being divergent, meaning its sum goes to infinity as the
number of terms increases. This can be proven using the integral test, which involves comparing this series to an integral function with the same properties. However, if we modify this series by
adding a constant, such as $\sum_{n=1}^{\infty}\frac{1}{n^{2}}$, then the resulting series is convergent.
• Power Series: A power series is a series of the form $\sum_{n=0}^{\infty}c_{n}x^{n}$, where $c_{n}$ is a coefficient and $x$ is a variable. For example, the series $1+ x +\frac{x^{2}}{2!} + \frac
{x^{3}}{3!} +…$ is a power series in $x$ with coefficients $c_{n}=\frac{1}{n!}$, and it converges for all values of $x$.
Another way to verify if a series is convergent or not is to use the tests of convergence available, such as the ratio test or the root test. These tests allow us to determine the behavior of the
series as $n$ approaches infinity, and help decide if the series covers or diverges. Table 1 summarize some of these tests.
Test Condition Convergence
Divergence Test $lim_{n\rightarrow \infty}a_{n} \neq 0$ Divergent
Integral Test F is positive, decreasing Convergent
Comparison Test 0 $\leq$ a$_{n}$ $\leq$ b$_{n}$ Convergent if b$_{n}$ converges
Limit Comparison Test $lim_{n\rightarrow \infty}\frac{a_{n}}{b_{n}} = c$, where c is a finite value greater than 0 Convergent if b$_{n}$ converges
Ratio Test $lim_{n\rightarrow \infty}|\frac{a_{n+1}}{a_{n}}|<1$ Convergent
Root Test $lim_{n\rightarrow \infty}\sqrt[n]{|a_{n}|}<1$ Convergent
In conclusion, the concept of convergence is of paramount importance in mathematics and has several applications in different fields, such as physics, engineering, and finance. Understanding the
properties and behavior of series that exhibit convergence can help us model and solve complex practical problems that involve infinite sums.
Examples of Series Exhibiting Absolute Convergence
When a series converges absolutely, it means that the sum of the absolute values of its terms converges. This is a stronger condition than just convergence, as it guarantees that rearranging the
terms of the series will not change the sum. Let’s take a look at some examples of series that exhibit absolute convergence:
• Geometric series: The series 1 + 1/2 + 1/4 + 1/8 + … is a geometric series with ratio r = 1/2. It can be shown that this series converges to a sum of 2, and since the absolute value of each term
is also less than or equal to 1, this series converges absolutely.
• Telescoping series: A telescoping series is one in which most of the terms cancel out, leaving only a finite number of terms. An example of a telescoping series that converges absolutely is the
series 1/(n(n+1)), which can be shown to converge to a sum of 1. Since the absolute value of each term is less than or equal to 1/(n(n-1)), which is itself less than or equal to 1/n^2, this
series converges absolutely.
• Alternating series: An alternating series is one in which the signs of the terms alternate between positive and negative. An example of an alternating series that converges absolutely is the
series (-1)^n/n^2, which can be shown to converge to a sum of pi^2/12. Since the absolute value of each term is equal to 1/n^2, this series converges absolutely.
Some other examples of series that converge absolutely include:
• Harmonic series: 1 + 1/2 + 1/3 + 1/4 + …
• Exponential series: e^x, where x is any real number
• P-series: 1/n^p, where p > 1
If a series does not converge absolutely, but still converges, it is said to converge conditionally. In this case, rearranging the terms of the series can change the sum. Examples of series that
converge conditionally include:
Series Test for Convergence
∑(-1)^n/n Alternating Series Test
∑(-1)^n/n^p, where p > 1 Alternating Series Test for Absolute Convergence
∑sin(n)/n Dirichlet’s Test
Understanding the concept of absolute convergence is important when working with infinite series. It guarantees that rearranging the terms of the series will not change its sum, and allows us to
apply certain techniques to the series that would otherwise not work. By studying examples of series that exhibit absolute convergence, we can gain a better understanding of this fundamental concept
in calculus.
Importance of convergence and absolute convergence in calculus and analysis
Convergence and absolute convergence are crucial concepts in calculus and analysis that relate to the behavior of infinite sequences and series. The difference between convergence and absolute
convergence lies in the manner in which the sequence or series approaches its limit. Understanding these concepts is vital as it affects the validity of mathematical computations and the
interpretation of results.
• Convergence: A sequence or series is said to converge if it approaches a specific value as the number of terms approaches infinity. In simpler terms, it means that the terms of the sequence or
series eventually get closer and closer to a fixed value. For instance, take the sequence {1/2^n}. As n approaches infinity, the terms of the sequence get smaller and smaller, eventually getting
arbitrarily close to 0. Hence, the sequence converges to 0. Convergent series and sequences enable mathematical computations such as integration and differentiation.
• Absolute Convergence: A series is absolute convergent if the series formed by taking the absolute value of each term in the original series converges. For instance, the series ∑ (−1)^n/ n² is
convergent, but not absolutely convergent. On the other hand, the series ∑ 1/ n² is both convergent and absolutely convergent. Absolute convergence implies convergence, but the converse is not
necessarily true. Absolute convergence plays a critical role in calculus and analysis as it ensures the uniqueness of a result or solution.
In mathematical analysis and calculus, convergence and absolute convergence are critical for determining the behavior of infinite series and sequences. They enable mathematicians to use various
mathematical techniques such as integration, differentiation, and power series expansion to solve complex mathematical problems. Convergence helps determine the limit of a function, while absolute
convergence is vital in ensuring that the order of integration or differentiation can be exchanged without affecting the final answer. Without these concepts, it would be difficult to establish
mathematical calculations and conclude mathematical interpretations confidently.
Furthermore, these concepts play an essential role in real-life applications such as physics, engineering, and economics, where they are used to solve differential equations and model complex
systems. The validity of such models and predictions depends on the validity of the mathematical calculations used. Therefore, it is critical to understand convergence and absolute convergence to
ensure that the results and solutions obtained from mathematical computations and modeling are reliable and accurate.
Difference between Convergence and Absolute Convergence
Convergence A sequence or series approaches a specific value as the number of terms approaches infinity
Absolute Convergence A series formed by taking the absolute value of each term in the original series converges.
Application of Convergence and Absolute Convergence in Real-Life Scenarios
Convergence and absolute convergence are essential in many real-life scenarios, from calculating financial budgets to analyzing scientific data.
Here are some examples of how convergence and absolute convergence are used in real-life:
• Finance: Convergence is used in finance to analyze the returns of an investment over time. Absolute convergence is used to determine whether an investment is profitable or not.
• Science: In physics, convergence is used to determine the stability of a system and to predict its behavior over time. Absolute convergence is used to determine whether the series of a function
converges uniformly or not.
• Engineering: Convergence is used in engineering to calculate the stresses and strains in a system under different loads. Absolute convergence is used to determine the accuracy of numerical
methods used in solving engineering problems.
Convergence and absolute convergence are also used in many other fields, such as statistics, biology, and meteorology.
Examples of Convergence and Absolute Convergence
Let’s take a closer look at some examples of convergence and absolute convergence:
Example Convergence Absolute Convergence
(-1)^n/n Converges conditionally Diverges
1/n^2 Converges absolutely Converges absolutely
sin(n)/n Converges conditionally Diverges
In the first example, (-1)^n/n, the series converges conditionally but diverges absolutely. In the second example, 1/n^2, the series converges absolutely. In the third example, sin(n)/n, the series
converges conditionally but diverges absolutely.
Understanding convergence and absolute convergence is important because it allows us to make accurate predictions about the behavior of systems and to determine whether solutions to problems are
accurate or not.
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Joint Mathematics Meetings
Joint Mathematics Meetings Full Program
Current as of Saturday, January 20, 2018 03:30:06
Program · Deadlines · Timetable · Abstract submission · Inquiries: meet@ams.org
Joint Mathematics Meetings
San Diego Convention Center and Marriott Marquis San Diego Marina, San Diego, CA
January 10-13, 2018 (Wednesday - Saturday)
Meeting #1135
Associate secretaries:
Georgia Benkart, AMS benkart@math.wisc.edu
Gerard A Venema, MAA venema@calvin.edu
Monday January 8, 2018
• Monday January 8, 2018, 8:00 a.m.-5:00 p.m.
AMS Short Course on Discrete Differential Geometry, Part I
Room 5A, Upper Level, San Diego Convention Center
• Monday January 8, 2018, 3:00 p.m.-6:00 p.m.
NSF-EHR Grant Proposal Writing Workshop
Coronado Room, 4th Floor, South Tower, Marriott Marquis San Diego Marina
Ron Buckmire, National Science Foundation
Lee Zia, National Science Foundation
• Monday January 8, 2018, 5:00 p.m.-6:00 p.m.
AMS Short Course Reception
Room 5B, Upper Level, San Diego Convention Center
Tuesday January 9, 2018
Wednesday January 10, 2018
• Wednesday January 10, 2018, 7:00 a.m.-8:45 a.m.
MAA Minority Chairs Meeting
Cardiff/Carlsbad Room, 3rd Floor, South Tower, Marriott Marquis San Diego Marina
• Wednesday January 10, 2018, 7:30 a.m.-6:00 p.m.
Joint Meetings Registration
Exhibit Hall B1, Ground Level, San Diego Convention Center
• Wednesday January 10, 2018, 7:30 a.m.-5:30 p.m.
Email Center
Exhibit Hall B1, Ground Level, San Diego Convention Center
• Wednesday January 10, 2018, 7:45 a.m.-10:55 a.m.
AMS Contributed Paper Session on Networks and Data
Room 29D, Upper Level, San Diego Convention Center
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Advances in Applications of Differential Equations to Disease Modeling, I
Room 29C, Upper Level, San Diego Convention Center
Libin Rong, Oakland University
Elissa Schwartz, Washington State University
Naveen K. Vaidya, San Diego State University nvaidya.anyol@gmail.com
□ 8:00 a.m.
Mathematical Modeling of Immune Dynamics in Disease.
Lisette dePillis*, Harvey Mudd College
□ 8:30 a.m.
Bistable dynamics in a model of SIV infection with antibody response.
Stanca Ciupe, Virginia Tech
Jonathan Forde*, Hobart and William Smith Colleges
Christopher Miller, University of California, Davis
□ 9:00 a.m.
Modeling Immune Responses to HIV infection Under Drugs of Abuse.
Jones M Mutua*, Department of Mathematics and Statistics, University of Missouri -- Kansas City, USA
Alan S Perelson, Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, New Mexico, USA
Anil Kumar, Division of Pharmacology, School of Pharmacy, University of Missouri -- Kansas City, USA
Naveen K Vaidya, Department of Mathematics and Statistics, San Diego State University, San Diego, California, USA
□ 9:30 a.m.
Unraveling within-host signatures of dengue infection at the population level.
Ryan Nikin-Beers, Virginia Tech
Lauren M Childs, Virginia Tech
Julie Blackwood, Williams College
Stanca M Ciupe*, Virginia Tech
□ 10:00 a.m.
Epidemic Growth Scaling: Implications for Disease Forecasting and Estimation of the Reproduction Number.
Gerardo Chowell*, Georgia State University
□ 10:30 a.m.
NEW PRESENTER: Model and Parameter Uncertainty in Environmentally Driven Disease Models.
Marisa C Eisenberg*, University of Michigan, Ann Arbor
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Applied and Computational Combinatorics, I
Room 9, Upper Level, San Diego Convention Center
Torin Greenwood, Georgia Institute of Technology
Jay Pantone, Dartmouth College jaypantone@dartmouth.edu
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Arithmetic Dynamics, I
Room 16A, Mezzanine Level, San Diego Convention Center
Robert L. Benedetto, Amherst College
Benjamin Hutz, Saint Louis University
Jamie Juul, Amherst College jjuul@amherst.edu
Bianca Thompson, Harvey Mudd College
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Discrete Dynamical Systems and Applications, I
Room 31A, Upper Level, San Diego Convention Center
E. Cabral Balreira, Trinity University
Saber Elaydi, Trinity University
Eddy Kwessi, Trinity University ekwessi@trinity.edu
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Financial Mathematics, Actuarial Sciences, and Related Fields, I
Room 30C, Upper Level, San Diego Convention Center
Albert Cohen, Michigan State University
Nguyet Nguyen, Youngstown State University ntnguyen01@ysu.edu
Oana Mocioalca, Kent State University
Thomas Wakefield, Youngstown State University
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Geometric Analysis and Geometric Flows, I
Room 30B, Upper Level, San Diego Convention Center
David Glickenstein, University of Arizona glickenstein@math.arizona.edu
Brett Kotschwar, Arizona State University
• Wednesday January 10, 2018, 8:00 a.m.-10:20 a.m.
AMS Special Session on History of Mathematics, I
Room 10, Upper Level, San Diego Convention Center
Sloan Despeaux, Western Carolina University
Jemma Lorenat, Pitzer College
Clemency Montelle, University of Canterbury
Daniel Otero, Xavier University otero@xavier.edu
Adrian Rice, Randolph-Macon College
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Mathematical Analysis and Nonlinear Partial Differential Equations, I
Room 30E, Upper Level, San Diego Convention Center
Hongjie Dong, Brown University
Peiyong Wang, Wayne State University
Jiuyi Zhu, Louisiana State University zhu@math.lsu.edu
• Wednesday January 10, 2018, 8:00 a.m.-10:45 a.m.
AMS Special Session on Mathematical Fluid Mechanics: Analysis and Applications, I
Room 30A, Upper Level, San Diego Convention Center
Zachary Bradshaw, University of Virginia zb8br@virginia.edu
Aseel Farhat, University of Virginia
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Mathematical Information in the Digital Age of Science, I
Room 6E, Upper Level, San Diego Convention Center
Patrick Ion, University of Michigan pion@umich.edu
Olaf Teschke, zbMath Berlin
Stephen Watt, University of Waterloo
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Mathematics of Gravitational Wave Science, I
Room 30D, Upper Level, San Diego Convention Center
Andrew Gillette, University of Arizona agillette@math.arizona.edu
Nikki Holtzer, University of Arizona
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Modeling in Differential Equations - High School, Two-Year College, Four-Year Institution, I
Room 29B, Upper Level, San Diego Convention Center
Corban Harwood, George Fox University
William Skerbitz, Wayzata High School
Brian Winkel, SIMIODE brianwinkel@simiode.org
Dina Yagodich, Frederick Community College
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Network Science, I
Room 33B, Upper Level, San Diego Convention Center
David Burstein, Swarthmore College dburste1@swarthmore.edu
Franklin Kenter, United States Naval Academy
Feng Shi, University of North Carolina at Chapel Hill
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Nilpotent and Solvable Geometry, I
Room 16B, Mezzanine Level, San Diego Convention Center
Michael Jablonski, University of Oklahoma
Megan Kerr, Wellesley College mkerr@wellesley.edu
Tracy Payne, Idaho State University
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Operators on Function Spaces in One and Several Variables, I
Room 33A, Upper Level, San Diego Convention Center
Catherine Bénéteau, University of South Florida cbenetea@usf.edu
Matthew Fleeman, Baylor University
Constanze Liaw, Baylor University
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS-MAA-SIAM Special Session on Research in Mathematics by Undergraduates and Students in Post-Baccalaureate Programs, I
Room 29A, Upper Level, San Diego Convention Center
Tamas Forgacs, CSU Fresno
Darren A. Narayan, Rochester Institute of Technology dansma@rit.edu
Mark David Ward, Purdue University
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS-ASL Special Session on Set Theory, Logic and Ramsey Theory, I
Room 7B, Upper Level, San Diego Convention Center
Andrés Caicedo, Mathematical Reviews
José Mijares, University of Colorado, Denver jose.mijarespalacios@ucdenver.edu
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Special Functions and Combinatorics (in honor of Dennis Stanton's 65th birthday), I
Room 7A, Upper Level, San Diego Convention Center
Susanna Fishel, Arizona State University sfishel1@asu.edu
Mourad Ismail, University of Central Florida
Vic Reiner, University of Minnesota
• Wednesday January 10, 2018, 8:00 a.m.-10:45 a.m.
AMS Special Session on Structure and Representations of Hopf Algebras: a Session in Honor of Susan Montgomery, I
Room 17A, Mezzanine Level, San Diego Convention Center
Siu-Hung Ng, Louisiana State University
Lance Small, University of California, San Diego
Henry Tucker, University of California, San Diego htucker@usc.edu
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Topological Graph Theory: Structure and Symmetry, I
Room 17B, Mezzanine Level, San Diego Convention Center
Jonathan L. Gross, Columbia University
Thomas W. Tucker, Colgate University ttucker@colgate.edu
• Wednesday January 10, 2018, 8:00 a.m.-10:50 a.m.
MAA Invited Paper Session on Trends in Mathematical and Computational Biology
Room 3, Upper Level, San Diego Convention Center
Timothy Comar, Benedictine University
Carrie Eaton, Unity College
Raina Robeva, Sweet Briar College robeva@sbc.edu
• Wednesday January 10, 2018, 8:00 a.m.-10:55 a.m.
MAA Session on Arts and Mathematics: The Interface, I
Room 4, Upper Level, San Diego Convention Center
Douglas Norton, Villanova University douglas.norton@villanova.edu
• Wednesday January 10, 2018, 8:00 a.m.-10:55 a.m.
AMS Contributed Paper Session on Imaging and Inverse Problems
Room 19, Mezzanine Level, San Diego Convention Center
• Wednesday January 10, 2018, 8:00 a.m.-10:55 a.m.
MAA General Contributed Paper Session on Algebra, I
Room 15A, Mezzanine Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Wednesday January 10, 2018, 8:00 a.m.-10:10 a.m.
MAA General Contributed Paper Session on Assessment
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Wednesday January 10, 2018, 8:00 a.m.-10:55 a.m.
AMS Contributed Paper Session on Number Theory, I
Room 13, Mezzanine Level, San Diego Convention Center
• Wednesday January 10, 2018, 8:00 a.m.-10:55 a.m.
MAA Session on The Scholarship of Teaching and Learning in Collegiate Mathematics, I
Room 14A, Mezzanine Level, San Diego Convention Center
Tom Banchoff, Brown University
Curt Bennett, Loyola Marymount University
Pam Crawford, Jacksonville University
Jacqueline Dewar, Loyola Marymount University jdewar@lmu.edu
Edwin Herman, University of Wisconsin-Stevens Point
Lew Ludwig, Denison University
• Wednesday January 10, 2018, 8:00 a.m.-10:55 a.m.
SIAM Minisymposium on Data Science in the Mathematics Curriculum
Room 11A, Upper Level, San Diego Convention Center
Suzanne Weekes, Worcester Polytechnic Institute sweekes@wpi.edu
Ron Buckmire, National Science Foundation rbuckmir@nsf.gov
• Wednesday January 10, 2018, 8:00 a.m.-6:00 p.m.
Project NExT Workshop
Room 6F, Upper Level, San Diego Convention Center
• Wednesday January 10, 2018, 8:00 a.m.-9:20 a.m.
MAA Panel
How do we use assessment? What do we learn from it and how does it help us make related changes?
Room 1A, Upper Level, San Diego Convention Center
Beste Gucler, University of Massachusetts Dartmouth bgucler@umassd.edu
Gulden Karakok, University of Northern Colorado
Marilyn Carlson, Arizona State University
Pablo Meija-Ramos, Rutgers University
Sandra Laursen, University of Colorado Boulder
William Martin, North Dakota State University
• Wednesday January 10, 2018, 8:00 a.m.-5:30 p.m.
Employment Center
Exhibit Hall A, Ground Level, San Diego Convention Center
• Wednesday January 10, 2018, 8:15 a.m.-10:55 a.m.
AMS Contributed Paper Session on Algebraic Topology
Room 12, Mezzanine Level, San Diego Convention Center
• Wednesday January 10, 2018, 8:15 a.m.-10:55 a.m.
MAA General Contributed Paper Session on Applied Mathematics, I
Room 28E, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
□ 8:15 a.m.
High-Order Adaptive Extended Finite Element Method (AES-FEM) and Direct Treatment of Neumann Boundary Conditions on Curved Boundaries.
Rebecca Conley*, Saint Peter's University
Tristan J. Delaney, San Jose, CA
Xiangmin Jiao, Stony Brook University
□ 8:30 a.m.
Stable ADI Scheme with Super-Gaussian Dielectric Distribution and Minimal Molecular Surface.
Tania Hazra*, University of Alabama, Tuscaloosa, Alabama
Shan Zhao, University of Alabama, Tuscaloosa, Alabama
□ 8:45 a.m.
Third Derivative Block Multistep Algorithm for solving the Second Order Nonlinear Lane-Emden Type Equations.
Olusheye A Akinfenwa*, University of Lagos, Akoka , Lagos
Ridwanulai I Abdulganiy, University of Lagos, Akoka , Lagos
Adebola S. Okunuga, University of Lagos, Akoka , Lagos
□ 9:00 a.m.
Rational Approximation of the Mittag-Leffler Functions with Real Distinct Poles.
Olaniyi S. Iyiola*, Minnesota State University, Moorhead, MN
Emmanuel O. Asante-Asamani, Hunter College of the City University of New York
Bruce Wade, University of Wisconsin-Milwaukee, WI
□ 9:15 a.m.
A numerical method for conical Radon transform with the vertices on a helix.
Kiwoon Kwon*, Dongguk University, Seoul, Korea
Sungwhan Moon, Kyungbook University, Daegu, Korea
□ 9:30 a.m.
Inference of transition rates in a birth-death chain from conditional extinction times.
Yingxiang Zhou*, University of Delaware
Pak-Wing Fok, University of Delaware
□ 9:45 a.m.
□ 10:00 a.m.
Intrusion Detection Algorithm Based On Discrete Wavelet Transform and Support Vector Machines.
Kevin L. Li*, Western Connecticut State University
Xiaodi Wang, .Department of Math, Western Connecticut State University
□ 10:15 a.m.
Quantum circuits for arithmetic operations over binary field.
Samundra Regmi*, Cameron University
Parshuram Budhathoki, Cameron University
□ 10:30 a.m.
Long-wave asymptotic model for deformation and breakup of a fluid thread.
Muhammad Hameed*, University of South Carolina Upstate
□ 10:45 a.m.
New double Wronskian solutions for a generalized (2+1)-dimensional Boussinesq system with variable coefficients.
Alrazi M Abdeljabbar*, Khalifa University The Petroleum Institute
• Wednesday January 10, 2018, 8:30 a.m.-10:50 a.m.
AMS Special Session on Research by Postdocs of the Alliance for Diversity in Mathematics, I
Room 33C, Upper Level, San Diego Convention Center
Aloysius Helminck, University of Hawaii - Manoa
Michael Young, Iowa State University myoung@iastate.edu
• Wednesday January 10, 2018, 9:00 a.m.-11:00 a.m.
MAA Minicourse #1: Part A
Introduction to Process Oriented Guided Inquiry Learning (POGIL) in Mathematics Courses
Room 28A, Upper Level, San Diego Convention Center
Catherine Beneteau, University of South Florida
Jill E. Guerra, University of Arkansas Fort Smith
Laurie Lenz, Marymount University
• Wednesday January 10, 2018, 9:00 a.m.-11:00 a.m.
MAA Minicourse #2: Part A
Teaching Introductory Statistics Using the Guidelines from the American Statistical Association
Room 28C, Upper Level, San Diego Convention Center
Carolyn K. Cuff, Westminster College
• Wednesday January 10, 2018, 9:00 a.m.-10:40 a.m.
AMS Contributed Paper Session on Difference, Dynamic, and Integral Equations
Room 18, Mezzanine Level, San Diego Convention Center
• Wednesday January 10, 2018, 9:00 a.m.-10:55 a.m.
MAA Session on Discrete Mathematics in the Undergraduate Curriculum -- Ideas and Innovations in Teaching, I
Room 15B, Mezzanine Level, San Diego Convention Center
John Caughman, Portland State University
Art Duval, University of Texas El Paso elise314@gmail.com
Elise Lockwood, Oregon State University
• Wednesday January 10, 2018, 9:00 a.m.-10:55 a.m.
MAA Session on Mathematics and Sports, I
Room 5B, Upper Level, San Diego Convention Center
John David, Virginia Military Institute
Drew Pasteur, College of Wooster rpasteur@wooster.edu
• Wednesday January 10, 2018, 9:00 a.m.-9:50 a.m.
MAA-SIAM-AMS Hrabowski-Gates-Tapia-McBay Session: Lecture
Room 8, Upper Level, San Diego Convention Center
Ricardo Cortez, Tulane University rcortez@tulane.edu
• Wednesday January 10, 2018, 9:00 a.m.-10:30 a.m.
AMS Directors of Undergraduate Studies
Rancho Santa Fe Rm 2, Lobby Level, North Twr, Marriott Marquis San Diego Marina
• Wednesday January 10, 2018, 9:35 a.m.-10:55 a.m.
MAA Workshop
Creating Interdisciplinary Activities for Mathematical Sciences Classrooms
Room 5A, Upper Level, San Diego Convention Center
Eugene Fiorini, Muhlenberg College eugenefiorini@muhlenberg.edu
Linda McGuire, Muhlenberg College
• Wednesday January 10, 2018, 9:35 a.m.-10:55 a.m.
MAA Panel
Mathematicians' Work in Creating Open Education Resources for K-12
Room 1A, Upper Level, San Diego Convention Center
William McCallum, University of Arizona william.mccallum@gmail.com
Scott Baldridge, Louisiana State University
Hugo Rossi, University of Utah
Kristin Umland, Illustrative Mathematics
• Wednesday January 10, 2018, 9:35 a.m.-10:55 a.m.
MAA Panel
What Every Student Should Know about the JMM
Room 2, Upper Level, San Diego Convention Center
Violeta Vasilevska, Utah Valley University violeta.vasilevska@uvu.edu
Peri Shereen, California State University Monterey Bay
Joyati Debnath, Winona State University
Michael Dorff, Brigham Young University
Frank Morgan, Williams College
• Wednesday January 10, 2018, 9:45 a.m.-11:00 a.m.
Project NExT Panel
Creating Meaningful Classroom Activities to Deepen Student Learning
Room 6F, Upper Level, San Diego Convention Center
Rene Ardila, Grand Valley State University
Emi Kennedy, Hollins University
Erica Shannon, Pierce College
Shawnda Smith, California State University Bakersfield
Dana Ernst, Northern Arizona University
Jessica Libertini, Virginia Military Institute
Ji Son, California State University Los Angeles
• Wednesday January 10, 2018, 9:50 a.m.-10:30 a.m.
MAA-SIAM-AMS Hrabowski-Gates-Tapia-McBay Panel
Access to Quality Mathematics by All.
Room 8, Upper Level, San Diego Convention Center
Ricardo Cortez, Tulane University
James A. M. Álvarez, University of Texas at Arlington
Ron Buckmire, National Science Foundation
Talithia Williams, Harvey Mudd College
• Wednesday January 10, 2018, 10:00 a.m.-10:55 a.m.
MAA Session on Innovative Curricular Strategies for Increasing Mathematics Majors
Room 14B, Mezzanine Level, San Diego Convention Center
Stuart Boersma Boersma, Central Washington University
Eric S. Marland, Appalachian State University marlandes@appstate.edu
Victor Piercey, Ferris State University
• Wednesday January 10, 2018, 10:05 a.m.-10:55 a.m.
AMS Invited Address
The Navier-Stokes, Euler and related equations.
Room 6AB, Upper Level, San Diego Convention Center
Edriss S. Titi*, Texas A&M University; and The Weizmann Institute of Science
• Wednesday January 10, 2018, 10:15 a.m.-10:55 a.m.
MAA General Contributed Paper Session on Algebra, II
Room 32B, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Wednesday January 10, 2018, 10:15 a.m.-10:40 a.m.
MAA General Contributed Paper Session on Outreach, I
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Wednesday January 10, 2018, 11:10 a.m.-12:00 p.m.
AMS-MAA Invited Address
Topological Modeling of Complex Data.
Room 6AB, Upper Level, San Diego Convention Center
Gunnar Carlsson*, Stanford University
• Wednesday January 10, 2018, 12:15 p.m.-5:30 p.m.
Exhibits and Book Sales
Come to the Grand Opening at 12:15 p.m.!
Exhibit Hall B1, Ground Level, San Diego Convention Center
• Wednesday January 10, 2018, 1:00 p.m.-1:50 p.m.
AMS Colloquium Lectures: Lecture I
Alternate Minimization and Scaling algorithms: theory, applications and connections across mathematics and computer science.
Room 6AB, Upper Level, San Diego Convention Center
Avi Wigderson*, Institute for Advanced Study
• Wednesday January 10, 2018, 2:00 p.m.-3:30 p.m.
AMS Committee on Meetings and Conferences Panel Discussion
Collaborative Research Communities in Mathematics
Room 11B, Upper Level, San Diego Convention Center
Sam Ballas, Florida State University
Ruth Charney, Brandeis University
Brian Conrey, American Institute of Mathematics
Satayan Devados, University of San Diego
NEW: Irina Mitrea, Temple University
• Wednesday January 10, 2018, 2:15 p.m.-3:05 p.m.
MAA Invited Address
Quintessential quandle queries.
Room 6AB, Upper Level, San Diego Convention Center
Alissa Crans*, Loyola Marymount University
• Wednesday January 10, 2018, 2:15 p.m.-6:05 p.m.
AMS Special Session on A Showcase of Number Theory at Liberal Arts Colleges, I
Room 16A, Mezzanine Level, San Diego Convention Center
Adriana Salerno, Bates College
Lola Thompson, Oberlin College lola.thompson@oberlin.edu
• Wednesday January 10, 2018, 2:15 p.m.-6:35 p.m.
AMS Special Session on Algebraic, Analytic, and Geometric Aspects of Integrable Systems, Painlevé Equations, and Random Matrices, I
Room 31A, Upper Level, San Diego Convention Center
Vladimir Dragovic, University of Texas at Dallas
Anton Dzhamay, University of Northern Colorado adzham@unco.edu
Sevak Mkrtchyan, University of Rochester
□ 2:15 p.m.
A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation.
Deniz Bilman, University of Michigan
Peter D. Miller*, University of Michigan
□ 2:45 p.m.
Nearly singular Jacobi matrices and applications to the finite Toda lattice.
Kenneth T.-R. McLaughlin, Department of Mathematics, Colorado State University
Robert Jenkins, Department of Mathematics, University of Arizona
Kyle Pounder*, Department of Mathematics, University of Arizona
□ 3:15 p.m.
Asymptotics of gap probabilities via Riemann--Hilbert approach.
Manuela Girotti*, Colorado State University
□ 3:45 p.m.
Nonintersecting Brownian bridges on the unit circle with drift.
Robert Buckingham*, University of Cincinnati
□ 4:15 p.m.
Pfaffian Sign Theorem for the Dimer Model on a Triangular Lattice.
Pavel Bleher, IUPUI
Brad Elwood, IUPUI
Dražen Petrović*, IUPUI
□ 4:45 p.m.
A Moment Method for Invariant Ensembles.
Jonathan Novak*, UC San Diego
□ 5:15 p.m.
NEW! Discussion
□ 5:15 p.m.
TALK CANCELLED: The scaling function constant problem in the two-dimensional Ising model.
Thomas Joachim Bothner*, University of Michigan
□ 5:45 p.m.
Turning point processes in plane partitions with periodic weights of arbitrary period.
Sevak Mkrtchyan*, University of Rochester
□ 6:15 p.m.
Bifurcations of Liouville Tori for Goryachev-Chaplygin system Vs. Poincare system.
Fariba Khoshnasib*, UW-Eau Claire/ UTDallas
• Wednesday January 10, 2018, 2:15 p.m.-6:35 p.m.
AMS Special Session on Analysis of Nonlinear Partial Differential Equations and Applications, I
Room 9, Upper Level, San Diego Convention Center
Tarek M. Elgindi, University of California, San Diego tme2@princeton.edu
Edriss S. Titi, Texas A&M University and Weizmann Institute of Science
• Wednesday January 10, 2018, 2:15 p.m.-6:35 p.m.
AMS Special Session on Applied and Computational Combinatorics, II
Room 7A, Upper Level, San Diego Convention Center
Torin Greenwood, Georgia Institute of Technology
Jay Pantone, Dartmouth College jaypantone@dartmouth.edu
• Wednesday January 10, 2018, 2:15 p.m.-5:35 p.m.
AMS Special Session on Combinatorial Commutative Algebra and Polytopes, I
Room 33B, Upper Level, San Diego Convention Center
Robert Davis, Michigan State University davisr@math.msu.edu
Liam Solus, KTH Royal Institute of Technology
• Wednesday January 10, 2018, 2:15 p.m.-6:05 p.m.
AMS Special Session on Differential Geometry, I
Room 30D, Upper Level, San Diego Convention Center
Vincent B. Bonini, Cal Poly San Luis Obispo vbonini@calpoly.edu
Joseph E. Borzellino, Cal Poly San Luis Obispo
Bogdan D. Suceava, California State University, Fullerton
Guofang Wei, University of California, Santa Barbara
• Wednesday January 10, 2018, 2:15 p.m.-6:35 p.m.
AMS Special Session on Ergodic Theory and Dynamical Systems--to Celebrate the Work of Jane Hawkins, I
Room 17B, Mezzanine Level, San Diego Convention Center
Julia Barnes, Western Carolina University
Rachel Bayless, Agnes Scott College
Emily Burkhead, Duke University
Lorelei Koss, Dickinson College koss@dickinson.edu
• Wednesday January 10, 2018, 2:15 p.m.-6:35 p.m.
AMS Special Session on Financial Mathematics, Actuarial Sciences, and Related Fields, II
Room 30C, Upper Level, San Diego Convention Center
Albert Cohen, Michigan State University
Nguyet Nguyen, Youngstown State University ntnguyen01@ysu.edu
Oana Mocioalca, Kent State University
Thomas Wakefield, Youngstown State University
• Wednesday January 10, 2018, 2:15 p.m.-4:15 p.m.
MAA Minicourse #3: Part A
Flipping your Mathematics Course using Open Educational Resources
Room 28A, Upper Level, San Diego Convention Center
Sarah Eichhorn, University of California, Irvine
David Farmer, American Institute of Mathematics
Jim Fowler, The Ohio State University
Petra Taylor, Dartmouth University
• Wednesday January 10, 2018, 2:15 p.m.-5:35 p.m.
AMS Special Session on Geometric Analysis and Geometric Flows, II
Room 30B, Upper Level, San Diego Convention Center
David Glickenstein, University of Arizona glickenstein@math.arizona.edu
Brett Kotschwar, Arizona State University
• Wednesday January 10, 2018, 2:15 p.m.-6:05 p.m.
AMS Special Session on History of Mathematics, II
Room 10, Upper Level, San Diego Convention Center
Sloan Despeaux, Western Carolina University
Jemma Lorenat, Pitzer College
Clemency Montelle, University of Canterbury
Daniel Otero, Xavier University otero@xavier.edu
Adrian Rice, Randolph-Macon College
• Wednesday January 10, 2018, 2:15 p.m.-4:15 p.m.
MAA Minicourse #4: Part A
How to Run Successful Math Circles for Students and Teachers
Room 28B, Upper Level, San Diego Convention Center
Jane Long, Stephen F. Austin State University
Brianna Donaldson, American Institute of Mathematics
Gabriella Pinter, University of Wisconsin-Milwaukee
Diana White, University of Colorado Denver and National Association of Math Circles
• Wednesday January 10, 2018, 2:15 p.m.-6:05 p.m.
AMS Special Session on Mathematical Modeling and Analysis of Infectious Diseases, I
Room 29C, Upper Level, San Diego Convention Center
Kazuo Yamazaki, University of Rochester kyamazak@ur.rochester.edu
□ 2:15 p.m.
A theoretical approach to understanding population dynamics with seasonal developmental durations.
Yijun Lou*, The Hong Kong Polytechnic University
Xiao-Qiang Zhao, Memorial University of Newfoundland
□ 3:15 p.m.
NEW: Discussion
□ 3:15 p.m.
TALK CANCELLED: On multi-species and cross diffusion.
Dung Le*, University of Texas at San Antonio
□ 4:15 p.m.
An epidemic model with superspreading.
Fred Brauer*, University of British Columbia
□ 4:45 p.m.
Impact of Environmental Temperature on Dengue Epidemics: Mathematical Models.
Naveen K. Vaidya*, San Diego State University, California, USA
□ 5:15 p.m.
Mathematical modeling of PDGF-driven glioma reveals the infiltrating dynamics of immune cells into tumors.
Jianjun Paul Tian*, New Mexico State University
□ 5:45 p.m.
Modeling the role of superspreaders in infectious disease outbreaks.
Christina Joy Edholm*, University of Tennessee, Knoxville
• Wednesday January 10, 2018, 2:15 p.m.-6:05 p.m.
AMS Special Session on Modeling in Differential Equations - High School, Two-Year College, Four-Year Institution, II
Room 29B, Upper Level, San Diego Convention Center
Corban Harwood, George Fox University
William Skerbitz, Wayzata High School
Brian Winkel, SIMIODE brianwinkel@simiode.org
Dina Yagodich, Frederick Community College
• Wednesday January 10, 2018, 2:15 p.m.-6:35 p.m.
AMS Special Session on Nilpotent and Solvable Geometry, II
Room 16B, Mezzanine Level, San Diego Convention Center
Michael Jablonski, University of Oklahoma
Megan Kerr, Wellesley College mkerr@wellesley.edu
Tracy Payne, Idaho State University
• Wednesday January 10, 2018, 2:15 p.m.-6:05 p.m.
AMS Special Session on Operators on Function Spaces in One and Several Variables, II
Room 33A, Upper Level, San Diego Convention Center
Catherine Bénéteau, University of South Florida cbenetea@usf.edu
Matthew Fleeman, Baylor University
Constanze Liaw, Baylor University
• Wednesday January 10, 2018, 2:15 p.m.-6:05 p.m.
AMS Special Session on Orthogonal Polynomials and Applications
Room 30E, Upper Level, San Diego Convention Center
Abey Lopez-Garcia, University of South Alabama
Xiang-Sheng Wang, University of Louisiana at Lafayette xswang@louisiana.edu
• Wednesday January 10, 2018, 2:15 p.m.-6:00 p.m.
AMS Special Session on Quaternions, I
Room 33C, Upper Level, San Diego Convention Center
Terrence Blackman, Medgar Evers College, City University of New York
Johannes Familton, Borough of Manhattan Community College, City University of New York jfamilton@bmcc.cuny.edu
Chris McCarthy, Borough of Manhattan Community College, City University of New York
• Wednesday January 10, 2018, 2:15 p.m.-4:15 p.m.
MAA Minicourse #5: Part A
Reach the World: Writing Math Op-Eds for a Post-Truth Culture
Room 28C, Upper Level, San Diego Convention Center
Kira Hamman, Pennsylvania State University, Mont Alto
Francis Su, Harvey Mudd College
• Wednesday January 10, 2018, 2:15 p.m.-6:05 p.m.
AMS Special Session on Structure and Representations of Hopf Algebras: a Session in Honor of Susan Montgomery, II
Room 17A, Mezzanine Level, San Diego Convention Center
Siu-Hung Ng, Louisiana State University
Lance Small, University of California, San Diego
Henry Tucker, University of California, San Diego htucker@usc.edu
• Wednesday January 10, 2018, 2:15 p.m.-6:00 p.m.
MAA Invited Paper Session on Teaching for Equity and Broader Participation in the Mathematical Sciences
Room 3, Upper Level, San Diego Convention Center
Lisette de Pillis, Harvey Mudd College
Rachel Levy, Harvey Mudd College
Darryl Yong, Harvey Mudd College dyong@hmc.edu
Talithia Williams, Harvey Mudd College
• Wednesday January 10, 2018, 2:15 p.m.-6:05 p.m.
AMS Special Session on Topological Data Analysis, I
Room 6E, Upper Level, San Diego Convention Center
Henry Adams, Colorado State University henry.adams@colostate.edu
Gunnar Carlsson, Stanford University
Mikael Vejdemo-Johansson, CUNY College of Staten Island
□ 2:15 p.m.
Persistence Images for Differentiating Class Based Network Structures.
Tegan H Emerson*, Naval Research Laboratory
□ 2:45 p.m.
Machine learnings on persistence diagrams and materials structural analysis.
Yasuaki Hiraoka*, Tohoku University
□ 3:15 p.m.
Topology in the Furnace: Using the Mapper Algorithm as a Data Analysis Tool to Evaluate an Electric Arc Furnace Energy Model.
Leo Carlsson*, KTH Royal Institute of Technology, Department of Material Science.
Mattia De Colle, KTH Royal Institute of Technology, Department of Material Science.
Christoffer Schmidt, KTH Royal Institute of Technology, Department of Material Science.
Mikael Vejdemo-Johansson, CUNY College of Staten Island, Department of Mathematics.
Pär Jönsson, KTH Royal Institute of Technology, Department of Material Science.
□ 3:45 p.m.
Fibres of Failure: diagnosing predictive models using Mapper.
Leo Carlsson, KTH Royal Institute of Technology
Gunnar Carlsson, Stanford University
Mikael Vejdemo-Johansson*, CUNY College of Staten Island
□ 4:15 p.m.
Data-Driven Topological Methods for Reasoning about Motion.
Florian T Pokorny*, KTH Royal Institute of Technology
□ 4:45 p.m.
Topological and Geometric Methods in Robotic Manipulation and Path Planning.
Anastasiia Varava*, KTH The Royal Institute of Technology
□ 5:15 p.m.
Persistent homology and probabilistic models of the Gaussian primes.
Rae Helmreich*, Wheaton College, MA
Anchala Krishnan, University of Washington, Bothell
Nathan Schmitz, University of Wisconsin-Stevens Point
John Meier, Lafayette College
□ 5:45 p.m.
Maximal interesting paths in the Mapper.
Ananth Kalyanaraman, Washington State University
Methun Kamruzzaman, Washington State University
Bala Krishnamoorthy*, Washington State University
• Wednesday January 10, 2018, 2:15 p.m.-6:10 p.m.
MAA Session on Arts and Mathematics: The Interface, II
Room 4, Upper Level, San Diego Convention Center
Douglas Norton, Villanova University douglas.norton@villanova.edu
• Wednesday January 10, 2018, 2:15 p.m.-6:10 p.m.
MAA Session on Discrete Mathematics in the Undergraduate Curriculum -- Ideas and Innovations in Teaching, II
Room 15B, Mezzanine Level, San Diego Convention Center
John Caughman, Portland State University
Art Duval, University of Texas El Paso elise314@gmail.com
Elise Lockwood, Oregon State University
• Wednesday January 10, 2018, 2:15 p.m.-6:10 p.m.
MAA Session on Flipped Classes: Implementation and Evaluation, I
Room 15A, Mezzanine Level, San Diego Convention Center
Joel Kilty, Centre College joel.kilty@centre.edu
Alex M. McAllister, Centre College
John H. Wilson, Centre College
• Wednesday January 10, 2018, 2:15 p.m.-5:55 p.m.
AMS Contributed Paper Session on Graphs and Computational Combinatorics
Room 18, Mezzanine Level, San Diego Convention Center
• Wednesday January 10, 2018, 2:15 p.m.-6:10 p.m.
AMS Contributed Paper Session on Groups
Room 29A, Upper Level, San Diego Convention Center
• Wednesday January 10, 2018, 2:15 p.m.-5:50 p.m.
MAA Session on Implementing Recommendations from the Curriculum Foundations Project
Room 31B, Upper Level, San Diego Convention Center
Mary Beisiegel, Oregon State University
Janet Bowers, San Diego State University
Tao Chen, City University of New York - LaGuardia Community College
Susan Ganter, Embry-Riddle Aeronautical University sganter@vt.edu
Caroline Maher-Boulis, Lee University
□ 2:15 p.m.
□ 2:35 p.m.
A Modeling Approach to Developmental Algebra.
Karen G. Santoro*, Central Conn St Univ
M. F. Anton, Central Conn St Univ
□ 2:55 p.m.
What Mathematics do Economics Students Need to Know?
Stella K Hofrenning*, Augsburg University
Suzanne I Dorée, Augsburg University
□ 3:15 p.m.
Contextualize College Algebra with Economics.
Tao Chen*, City University of New York--LaGuardia Community College
Glenn Henshaw, City University of New York--LaGuardia Community College
Soloman Kone, City University of New York--LaGuardia Community College
Choon Shan Lai, City University of New York--LaGuardia Community College
□ 3:35 p.m.
Creating Connections in the Content: Using Curriculum Foundations to Improve College Algebra.
Mary Beisiegel*, Oregon State University
Lori Kayes, Oregon State University
Michael Lopez, Oregon State University
Richard Nafshun, Oregon State University
Devon Quick, Oregon State University
□ 3:55 p.m.
Adjusting Math Courses for Business and Building a Dialog in the Spirit of CRAFTY.
Mike May, S.J.*, Saint Louis University
□ 4:15 p.m.
Applying the Curriculum Foundations Recommendations to Mathematics for Business, Nursing, and Social Work.
Victor I Piercey*, Ferris State University
Rhonda L Bishop, Ferris State University
Mischelle T Stone, Ferris State University
□ 4:35 p.m.
Promoting Active Learning and Modeling in PreCalculus: Design Features for Creating Engaging Labs.
Janet Bowers*, San Diego State University
Matt Anderson, San Diego State University
Kathy Williams, San Diego State University
Antoni Luque, San Diego State University
Nicole Tomassi, San Diego State University
□ 4:55 p.m.
Resequencing the Calculus Curriculum.
Mark Gruenwald*, University of Evansville
David Dwyer, University of Evansville
□ 5:15 p.m.
Collaboration Conversations for Differential Equations (a SUMMIT-P collaboration).
Rebecca A Segal*, Virginia Commonwealth Universtiy
□ 5:35 p.m.
Why Do I Have to Take This Class? How Interdisciplinary Collaborations Can Improve Student AttitudesToward Mathematics.
Caroline Maher Maher-Boulis*, Lee University
Jason Robinson, Lee University
• Wednesday January 10, 2018, 2:15 p.m.-6:10 p.m.
MAA Session on Integrating Research into the Undergraduate Classroom
Room 31C, Upper Level, San Diego Convention Center
Timothy B. Flowers, Indiana University of Pennsylvania
Shannon R. Lockard, Bridgewater State University slockard@bridgew.edu
• Wednesday January 10, 2018, 2:15 p.m.-5:55 p.m.
AMS Contributed Paper Session on Knots and Diagram Categories
Room 13, Mezzanine Level, San Diego Convention Center
□ 2:15 p.m.
HOMFLY-PT homology for general link diagrams and braidlike isotopy.
Michael Abel*, Duke University
□ 2:30 p.m.
Patterns in Khovanov link and chromatic graph homology.
Radmila Sazdanovic, North Carolina State University
Daniel Scofield*, North Carolina State University
□ 2:45 p.m.
Homotopy Commutative Algebras, Knots and Graphs.
Maksym Zubkov*, University of California, Irvine
□ 3:00 p.m.
The Action of Kauffman Bracket Skein Algebra of the Torus on the Skein Module of 3-Twist Knot Complement.
Hongwei Wang*, Texas A&M International University
□ 3:15 p.m.
On Computing Slice Genus of Non-alternating Prime Knots.
Hanbo Shao*, Colorado College
Lyujiangnan Ye, Colorado College
□ 3:30 p.m.
□ 3:45 p.m.
Detected slopes of manifolds with symmetries.
Jay MJ Leach*, Florida State University
□ 4:00 p.m.
Mutations and geometric invariants of hyperbolic links and 3-manifolds.
Christian Millichap*, Linfield College
David Futer, Temple University
□ 4:15 p.m.
Character Varieties of a Family of Two-Component Links.
Leona Sparaco*, University of Scranton
□ 4:30 p.m.
Finite-type invariants of virtual knots and tangles.
Nicolas Petit*, Oxford College of Emory University
□ 4:45 p.m.
On the virtual singular braid monoid.
Carmen Caprau*, California State University, Fresno
Sarah McGahan, Fresno, CA
□ 5:00 p.m.
Spiders and Asymptotic Faithfulness.
Wade Bloomquist*, University of California Santa Barbara
Zhenghan Wang, University of California Santa Barbara and Microsoft Station Q
□ 5:15 p.m.
Rigidification of algebras over algebraic theories in diagram categories.
Alex Sherbetjian*, University of California, Riverside
□ 5:30 p.m.
The classifying diagram of the category of finite sets.
Christina Osborne*, University of Virginia
□ 5:45 p.m.
The immersed cross-cap number of a knot.
Mark Hughes*, Brigham Young University
Seungwon Kim, National Institute for Mathematical Sciences
• Wednesday January 10, 2018, 2:15 p.m.-5:40 p.m.
AMS Contributed Paper Session on Lie Theory and Related Topics
Room 19, Mezzanine Level, San Diego Convention Center
• Wednesday January 10, 2018, 2:15 p.m.-3:40 p.m.
AMS Contributed Paper Session on Logic and Set Theory
Room 12, Mezzanine Level, San Diego Convention Center
• Wednesday January 10, 2018, 2:15 p.m.-6:10 p.m.
MAA General Contributed Paper Session on Applied Mathematics, II
Room 28E, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
□ 2:15 p.m.
Comparison of Simulated Models for ADR Systems to Idealized Models with Constant Reaction Propagation Speed.
Bryce M. Barclay*, Arizona State University
□ 2:30 p.m.
□ 2:45 p.m.
Calibrating Robotic Systems with Mathematics.
Mili Shah*, Loyola University Maryland
□ 3:00 p.m.
A Low Dispersion Numerical Scheme for Maxwell's Equations.
Casey J Smith*, Arizona State University - School of Mathematical and Statistical Sciences
□ 3:15 p.m.
Non-Convex Shannon Entropy for Photon-Limited Imaging.
Lasith Adhikari, Department of Medicine, University of Florida, Gainesville, FL 32610 USA
Reheman Baikejiang, Department of Biomedical Engineering, University of California, Davis, Davis, CA 95616 USA
Omar DeGuchy*, Applied Mathematics, University of California, Merced, Merced, CA 95343 USA
Roummel F. Marcia, Applied Mathematics, University of California, Merced, Merced, CA 95343 USA
□ 3:30 p.m.
Social learning can promote population optimal use of antibiotics.
Feng Fu, Dartmouth College
Xingru Chen*, Dartmouth College
□ 3:45 p.m.
Behavior of the Particle Swarm Optimization Algorithm.
Hum Nath Bhandari*, Texas Tech University
□ 4:00 p.m.
NEW PRESENTER: Personalization of Indexed Content via Collaborative Filtering and Topic Modeling.
Rachel Antoniette Lewis*, Georgia Southern
Kira Parker, University of Utah
Sheng Gao, University of Cambridge
Rong Li, Wellesley College
Ehsan Ebrahimzadeh, University of California, Los Angeles
□ 4:15 p.m.
RNA State Inference with Deep Recurrent Neural Networks.
Devin Willmott*, University of Kentucky
David Murrugarra, University of Kentucky
Qiang Ye, University of Kentucky
□ 4:30 p.m.
Quantum Circuits for Multiplication Operation.
Parshuram Budhathoki*, Cameron University
□ 4:45 p.m.
A Low Dispersion Numerical Scheme for Nonlinear Electromagnetic Propagation.
Alex Ander Kirvan*, Arizona State University
□ 5:00 p.m.
TALK CANCELLED: Imaging the Human Body using Electrical Impedance Data and a D-bar Algorithm with an Optimized Spatial Prior.
Melody Alsaker*, Gonzaga University
□ 5:15 p.m.
Traveling wave solutions in a PDE model of cell motility.
Matthew S Mizuhara*, The College of New Jersey
□ 5:30 p.m.
On the Nature of Advection-Diffusion-Reaction Systems Exhibiting Long-Term Limit Cycles or Stable Asymptotic States at a Bifurcation Point.
Curtis Taylor Peterson*, Arizona State University
Wenbo Tang, Arizona State University
□ 5:45 p.m.
Magnetic Resonance Recovery from Single-Shot Time Dependent Data.
Alyssa E. Burgueno*, Arizona State University
Rodrigo Platte, Arizona State University
□ 6:00 p.m.
Heuristics of Large-Scale Semidefinite Programming.
Alexander Putnam Barnes*, University of Alabama
Brendan Ames, University of Alabama
• Wednesday January 10, 2018, 2:15 p.m.-4:40 p.m.
MAA General Contributed Paper Session on Modeling and Applications, I
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Wednesday January 10, 2018, 2:15 p.m.-5:55 p.m.
MAA General Contributed Paper Session on Number Theory, I
Room 14B, Mezzanine Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Wednesday January 10, 2018, 2:15 p.m.-5:10 p.m.
MAA Session on Mathematics and Sports, II
Room 5B, Upper Level, San Diego Convention Center
John David, Virginia Military Institute
Drew Pasteur, College of Wooster rpasteur@wooster.edu
• Wednesday January 10, 2018, 2:15 p.m.-5:55 p.m.
AMS Contributed Paper Session on Research in Combinatorics, Matrix Theory, and Number Theory by Undergraduate and Post-Baccalaureate Students
Room 29D, Upper Level, San Diego Convention Center
• Wednesday January 10, 2018, 2:15 p.m.-5:50 p.m.
MAA Session on The Scholarship of Teaching and Learning in Collegiate Mathematics, II
Room 14A, Mezzanine Level, San Diego Convention Center
Tom Banchoff, Brown University
Curt Bennett, Loyola Marymount University
Pam Crawford, Jacksonville University
Jacqueline Dewar, Loyola Marymount University jdewar@lmu.edu
Edwin Herman, University of Wisconsin-Stevens Point
Lew Ludwig, Denison University
• Wednesday January 10, 2018, 2:15 p.m.-4:50 p.m.
MAA Session on Trends in Undergraduate Mathematical Biology Education
Room 32A, Upper Level, San Diego Convention Center
Timothy D. Comar, Benedictine University tcomar@ben.edu
• Wednesday January 10, 2018, 2:15 p.m.-5:40 p.m.
SIAM Minisymposium on Numerical Linear Algebra
Room 11A, Upper Level, San Diego Convention Center
Daniel B Szyld, Temple University szyld@temple.edu
Eugene Vecharynski, Lawrence Berkeley National Laboratory eugene.vecharynski@gmail.com
□ 2:15 p.m.
Generalized Preconditioned Locally Harmonic Residual Method for large non-Hermitian eigenproblems.
Eugene Vecharynski*, Pilot AI Labs, Inc and Lawrence Berkeley National Laboratory
Fei Xue, Clemson University
Chao Yang, Lawrence Berkeley National Laboratory
□ 2:40 p.m.
Solving Large-scale Eigenvalue Problems in Electronic Structure Calculations.
Chao Yang*, Lawrence Berkeley National Laboratory
□ 3:05 p.m.
Projected Commutator DIIS method for linear and nonlinear eigenvalue problems.
Lin Lin*, University of California, Berkeley
Wei Hu, Lawrence Berkeley National Laboratory
Chao Yang, Lawrence Berkeley National Laboratory
□ 3:30 p.m.
On the Semi-definite B-Lanczos algorithm for sparse symmetric generalized eigenproblems.
Chao-Ping Lin*, University of California, Davis
Huiqing Xie, East China University of Science and Technology
Zhaojun Bai, University of California, Davis
□ 4:05 p.m.
A new framework for understanding block Krylov methods applied to the computation of functions of matrices.
Andreas Frommer, Bergische Universität Wuppertal
Kathryn Lund*, Temple University and Bergische Universität Wuppertal
Daniel B. Szyld, Temple University
□ 4:30 p.m.
Using Block Low-Rank techniques for industrial problems.
Cleve Ashcraft, Livermore Software Technology Corporation
Eric Darve, Stanford University
Roger G Grimes, Livermore Software Technology Corporation
Yun Huang, Livermore Software Technology Corporation
Pierre L'Eplattenier, Livermore Software Technology Corporation
Robert F Lucas, Livermore Software Technology Corporation
Francois-Henry Rouet*, Livermore Software Technology Corporation
Clément Weisbecker, Livermore Software Technology Corporation
Zixi Xu, Stanford University
□ 4:55 p.m.
Matrix-free construction of HSS representations using adaptive randomized sampling.
X. Sherry Li*, Lawrence Berkeley National Laboratory
C. Gorman, UC Santa Barbara
P. Ghysels, Lawrence Berkeley National Laboratory
G. Chavez, Lawrence Berkeley National Laboratory
F.-H. Rouet, Livermore Software Technology Corporation
□ 5:20 p.m.
Asynchronous Optimized Schwarz for the solution of PDEs.
José C Garay, Temple University
Fréderic Magoulés, CentraleSupelec, Châtenay Malabry, France
Daniel B. Szyld*, Temple University
• Wednesday January 10, 2018, 2:15 p.m.-3:00 p.m.
Radical Dash Kickoff Meeting
A daily scavenger hunt filled with math challenges and creativity for teams of undergraduates. Individuals are welcome and encouraged to participate;they will be formed into teams.
Room 6D, Upper Level, San Diego Convention Center
Stacey Muir, University of Scranton
Janine Janoski, Kings College
• Wednesday January 10, 2018, 2:15 p.m.-4:15 p.m.
MAA Workshop
Championing Master's Programs in Mathematics: A forum for advocacy, networking, and innovation
Room 5A, Upper Level, San Diego Convention Center
Michael O'Sullivan, San Diego State University mosullivan@mail.sdsu.edu
Nigel Pitt, University of Maine
Virgil Pierce, University of Texas Rio Grande Valley
• Wednesday January 10, 2018, 2:15 p.m.-3:35 p.m.
MAA Panel
Ethics, Morality and Politics in the Quantitative Literacy Classroom
Room 1A, Upper Level, San Diego Convention Center
Ethan Bolker, University of Massachusetts, Boston ebolker@gmail.com
Maura Mast, Fordham University
Ethan Bolker, University of Massachusetts, Boston
David Lavie Deville, Northern Arizona University
Gizem Karaali, Pomona College
David Kung, St. Mary's College of Maryland
Rob Root, Lafayette College
Ksenija Simic-Muller, Pacific Lutheran University
• Wednesday January 10, 2018, 2:15 p.m.-4:00 p.m.
MAA Panel
NSF Funding Opportunities to Improve Learning and Teaching in the Mathematical
Room 2, Upper Level, San Diego Convention Center
Ron Buckmire, Division of Undergraduate Education, NSF rbuckmir@nsf.gov
Karen Keene, National Science Foundation
Karen King, Division of Research on Learning, NSF
Swatee Naik, Division of Mathematical Sciences, NSF
Sandra Richardson, Division of Undergraduate Education, NSF
Tara Smith, Division of Graduate Education, NSF
Lee Zia, Division of Undergraduate Education, NSF
Ron Buckmire, Division of Undergraduate Education, NSF
Karen King, Division of Research on Learning, NSF
Swatee Naik, Division of Mathematical Sciences, NSF
Sandra Richardson, Division of Undergraduate Education, NSF
Tara Smith, Division of Graduate Education, NSF
Lee Zia, Division of Undergraduate Education, NSF
• Wednesday January 10, 2018, 2:15 p.m.-3:40 p.m.
Association for Women in Mathematics Panel Discussion
Using Mathematics in Activism.
Room 1B, Upper Level, San Diego Convention Center
Michelle Manes, University of Hawaii at Manoa
Adriana Salerno, Bates College
Michelle Manes, University of Hawaii at Manoa
Federico Ardila, San Francisco State University
Piper Harron, University of Hawaii at Manoa
Lily Khadjavi, Loyola Marymount University
Beth Malmskog, Vilanova University
Rachel Pries, Colorado State University
Karen Saxe, American Mathematical Society
• Wednesday January 10, 2018, 2:30 p.m.-5:55 p.m.
MAA General Contributed Paper Session on Number Theory, II
Room 32B, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Wednesday January 10, 2018, 2:45 p.m.-6:00 p.m.
AMS Special Session on Mathematical Fluid Mechanics: Analysis and Applications, II
Room 30A, Upper Level, San Diego Convention Center
Zachary Bradshaw, University of Virginia zb8br@virginia.edu
Aseel Farhat, University of Virginia
• Wednesday January 10, 2018, 3:20 p.m.-4:10 p.m.
MAA Invited Address
Groups, graphs, algorithms: The Graph Isomorphism problem.
Room 6AB, Upper Level, San Diego Convention Center
Lázló Babai*, University of Chicago
• Wednesday January 10, 2018, 3:45 p.m.-4:15 p.m.
AWM Business Meeting
Room 1B, Upper Level, San Diego Convention Center
• Wednesday January 10, 2018, 3:50 p.m.-5:10 p.m.
MAA Panel
A Mathematician Teaches Statistics: The Road Less Traveled
Room 1A, Upper Level, San Diego Convention Center
Stacey Hancock, Montana State University stacey.hancock@montana.edu
Patti Frazer Lock, St. Lawrence College
Chris Oehrlein, Oklahoma City Community College
Sue Schou, Idaho State University
Charilaos Skiadas, Hanover College
• Wednesday January 10, 2018, 4:00 p.m.-5:00 p.m.
MAA Section Officers
Marina Ballroom D, 3rd Floor, South Tower, Marriott Marquis San Diego Marina
Betty Mayfield, Hood College
• Wednesday January 10, 2018, 4:15 p.m.-5:55 p.m.
AMS Contributed Paper Session on Lattices and Geometries
Room 12, Mezzanine Level, San Diego Convention Center
• Wednesday January 10, 2018, 4:15 p.m.-5:35 p.m.
MAA-JCW-AWM-NAM Panel
Implicit Bias and Its Effects in Mathematics
Room 2, Upper Level, San Diego Convention Center
Andrew Cahoon, Colby-Sawyer College
Naomi Cameron, Lewis & Clark College
Charles Doering, University of Michigan
Semra Kilic-Bahi, Colby-Sawyer College skilic-bahi@colby-sawyer.edu
Maura Mast, Fordham College at Rose Hill
Ron Buckmire, National Science Foundation
Jenna P. Carpenter, Campbell University
Lynn Garrioch, Colby-Sawyer College
Joanna Kania-Bartoszynska, National Science Foundation
Francis Su, Harvey Mudd College
• Wednesday January 10, 2018, 4:30 p.m.-6:00 p.m.
AMS Committee on the Profession Panel Discussion
Paths to Collaboration with Scientists
Room 11B, Upper Level, San Diego Convention Center
Gunnar Carlsson, Stanford University
Ruth Williams, University of California San Diego
John Lowengrub, University of California Irvine
Michelle DeDeo, University of North Florida
Ellen Panagiotou, University of California Santa Barbara
Hal Sadofsky, University of Oregon
• Wednesday January 10, 2018, 4:30 p.m.-5:30 p.m.
Town Hall Meeting
Current Questions and Opportunities in Undergraduate Education
Room 5A, Upper Level, San Diego Convention Center
• Wednesday January 10, 2018, 4:45 p.m.-6:10 p.m.
MAA General Contributed Paper Session on Linear Algebra
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Wednesday January 10, 2018, 5:30 p.m.-6:30 p.m.
Reception for Graduate Students and First-Time Participants
Marina Ballroom FG, 3rd Floor, South Tower, Marriott Marquis San Diego Marina
• Wednesday January 10, 2018, 6:00 p.m.-7:00 p.m.
SIGMAA on the History of Mathematics (HOM SIGMAA) Reception and Business Meeting
Room 6D, Upper Level, San Diego Convention Center
Toke Knudsen, State University of New York, Oneonta
• Wednesday January 10, 2018, 6:15 p.m.-8:00 p.m.
NEW: SIGMAA Arts Reception and Business Meeting
Room 4, Upper Level, San Diego Convention Center
• Wednesday January 10, 2018, 6:30 p.m.-8:00 p.m.
AMS Education and Diversity Department Panel
Strategies for Diversifying Graduate Mathematics Programs
Room 11B, Upper Level, San Diego Convention Center
Helen Grundman, American Mathematical Society
Helen Grundman, American Mathematical Society
Edray Goins, Purdue University
Richard Laugesen, University of Illinois
Richard McGehee, University of Minnesota
Katrin Wehrheim, University of California, Berkeley
• Wednesday January 10, 2018, 7:00 p.m.-7:45 p.m.
SIGMAA on the History of Mathematics (HOM SIGMAA) Guest Lecture
Room 6D, Upper Level, San Diego Convention Center
• Wednesday January 10, 2018, 8:30 p.m.-9:20 p.m.
AMS Josiah Willard Gibbs Lecture
Privacy in the land of plenty.
Room 6AB, Upper Level, San Diego Convention Center
Cynthia Dwork*, Harvard University
Thursday January 11, 2018
• Thursday January 11, 2018, 7:30 a.m.-4:00 p.m.
Joint Meetings Registration
Exhibit Hall B1, Ground Level, San Diego Convention Center
• Thursday January 11, 2018, 7:30 a.m.-11:50 a.m.
AMS Special Session on Analysis of Nonlinear Partial Differential Equations and Applications, II
Room 9, Upper Level, San Diego Convention Center
Tarek M. Elgindi, University of California, San Diego tme2@princeton.edu
Edriss S. Titi, Texas A&M University and Weizmann Institute of Science
• Thursday January 11, 2018, 7:30 a.m.-11:50 a.m.
AMS Special Session on Commutative Algebra in All Characteristics, I
Room 31A, Upper Level, San Diego Convention Center
Neil Epstein, George Mason University nepstei2@gmu.edu
Karl Schwede, University of Utah
Janet Vassilev, University of New Mexico
• Thursday January 11, 2018, 7:30 a.m.-5:30 p.m.
Email Center
Exhibit Hall B1, Ground Level, San Diego Convention Center
• Thursday January 11, 2018, 7:45 a.m.-11:55 a.m.
MAA General Contributed Paper Session on Graph Theory, I
Room 15B, Mezzanine Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid,
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on A Showcase of Number Theory at Liberal Arts Colleges, II
Room 16A, Mezzanine Level, San Diego Convention Center
Adriana Salerno, Bates College
Lola Thompson, Oberlin College lola.thompson@oberlin.edu
• Thursday January 11, 2018, 8:00 a.m.-11:40 a.m.
AMS Special Session on Accelerated Advances in Mathematical Fractional Programming
Room 30B, Upper Level, San Diego Convention Center
Ram Verma, International Publications USA verma99@msn.com
Alexander Zaslavski, Israel Institute of Technology
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Advances in Operator Theory, Operator Algebras, and Operator Semigroups, I
Room 33A, Upper Level, San Diego Convention Center
Asuman G. Aksoy, Claremont McKenna College
Zair Ibragimov, California State University, Fullerton
Marat Markin, California State University, Fresno mmarkin@csufresno.edu
Ilya Spitkovsky, New York University, Abu Dhabi
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Algebraic, Discrete, Topological and Stochastic Approaches to Modeling in Mathematical Biology, I
Room 30C, Upper Level, San Diego Convention Center
Olcay Akman, Illinois State University
Timothy D. Comar, Benedictine University tcomar@ben.edu
Daniel Hrozencik, Chicago State University
Raina Robeva, Sweet Briar College
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Beyond Planarity: Crossing Numbers of Graphs (a Mathematics Research Communities Session), I
Room 29B, Upper Level, San Diego Convention Center
Axel Brandt, Davidson College
Garner Cochran, University of South Carolina gcochran@math.sc.edu
Sarah Loeb, College of William and Mary
□ 8:00 a.m.
Convex Drawings of the Complete Graph: Topology meets Geometry.
Alan Arroyo, University of Waterloo
Dan McQuillan*, Norwich University
R. Bruce Richter, University of Waterloo
Gelasio Salazar, Universidad Autonoma de San Luis Potosi
□ 8:30 a.m.
Taking a Detour: Gioan's Theorem, and Pseudolinear Drawings of Complete Graphs.
Marcus Schaefer*, DePaul University
□ 9:00 a.m.
TALK CANCELLED: Crossing number and the tangle crossing number analogies.
Robin Anderson, Saint Louis University
Shuliang Bai, University of South Carolina
Fidel Barrera-Cruz*, Georgia Institute of Technology
Éva Czabarka, University of South Carolina
Giordano Da Lozzo, University of California, Irvine
Natalie L.F. Hobson, Sonoma State University
Jephian C.H. Lin, Iowa State University
Austin Mohr, Nebraska Wesleyan University
Heather C. Smith, Georgia Institute of Technology
László A. Székely, University of South Carolina
Hays Whitlatch, University of South Carolina
□ 9:30 a.m.
A tanglegram Kuratowski theorem.
Eva Czabarka*, University of South Carolina
Laszlo A. Szekely, University of South Carolina
Stephan Wagner, Stellenbosch University
□ 10:00 a.m.
How Low Can You Go? On the Biplanar Crossing Number of the Hypercube.
Gwen Spencer*, Smith College
Greg Clark, University of South Carolina
□ 10:30 a.m.
Biplanar Crossing Numbers: The Probabilistic Method.
John Asplund, Dalton State College
Thao Do*, Massachusetts Institute of Technology
Arran Hamm, Winthrop University
László Székely, University of South Carolina
Libby Taylor, Georgia Institute of Technology
Zhiyu Wang, University of South Carolina
□ 11:00 a.m.
On Local Crossing Numbers of Complete Graphs and Hypercubes.
Hsien-Chih Chang*, University of Illinois at Urbana-Champaign, Department of Computer Science
Axel Brandt, Davidson College, Department of Mathematics and Computer Science
Tanya Jeffries, University of Arizona, Department of Computer Science
Sarah Loeb, College of William and Mary, Mathematics Department
Marcus Schaefer, DePaul University, College of Computing and Digital Media, School of Computing
□ 11:30 a.m.
On the rectilinear local crossing number of complete graphs.
Bernardo M. Abrego*, California State University, Northridge
Silvia Fernandez, California State University, Northridge
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Boundaries for Groups and Spaces, I
Room 16B, Mezzanine Level, San Diego Convention Center
Joseph Maher, CUNY College of Staten Island joseph.maher@csi.cuny.edu
Genevieve Walsh, Tufts University
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Combinatorics and Geometry, I
Room 6E, Upper Level, San Diego Convention Center
Federico Ardila, San Francisco State University
Anastasia Chavez, MSRI and University of California, Davis
Laura Escobar, University of Illinois Urbana Champaign lescobar@illinois.edu
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Discrete Dynamical Systems and Applications, II
Room 30E, Upper Level, San Diego Convention Center
E. Cabral Balreira, Trinity University
Saber Elaydi, Trinity University
Eddy Kwessi, Trinity University ekwessi@trinity.edu
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Dynamical Systems: Smooth, Symbolic, and Measurable (a Mathematics Research Communities Session), I
Room 29C, Upper Level, San Diego Convention Center
Kathryn Lindsey, Boston College kathryn.a.lindsey@gmail.com
Scott Schmieding, Northwestern University
Kurt Vinhage, University of Chicago
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Homotopy Type Theory (a Mathematics Research Communities Session), I
Room 29A, Upper Level, San Diego Convention Center
Simon Cho, University of Michigan seamooncho@gmail.com
Liron Cohen, Cornell University
Edward Morehouse, Wesleyan University
• Thursday January 11, 2018, 8:00 a.m.-10:50 a.m.
MAA Invited Paper Session on MAA Instructional Practices Guide
Room 3, Upper Level, San Diego Convention Center
Martha Abell, Georgia Southern University martha@georgiasouthern.edu
Doug Ensley, MAA
Lew Ludwig, Denison University
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Mathematical Analysis and Nonlinear Partial Differential Equations, II
Room 30A, Upper Level, San Diego Convention Center
Hongjie Dong, Brown University
Peiyong Wang, Wayne State University
Jiuyi Zhu, Louisiana State University zhu@math.lsu.edu
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Mathematics of Quantum Computing and Topological Phases of Matter, I
Room 10, Upper Level, San Diego Convention Center
Paul Bruillard, Pacific Northwest National Laboratory
David Meyer, University of California San Diego
Julia Plavnik, Texas A&M University julia@math.tamu.edu
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Open and Accessible Problems for Undergraduate Research, I
Room 17B, Mezzanine Level, San Diego Convention Center
Michael Dorff, Brigham Young University
Allison Henrich, Seattle University henricha@seattleu.edu
Nicholas Scoville, Ursinus College
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS-ASL Special Session on Set Theory, Logic and Ramsey Theory, II
Room 7B, Upper Level, San Diego Convention Center
Andrés Caicedo, Mathematical Reviews
José Mijares, University of Colorado, Denver jose.mijarespalacios@ucdenver.edu
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Special Functions and Combinatorics (in honor of Dennis Stanton's 65th birthday), II
Room 7A, Upper Level, San Diego Convention Center
Susanna Fishel, Arizona State University sfishel1@asu.edu
Mourad Ismail, University of Central Florida
Vic Reiner, University of Minnesota
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Stochastic Processes, Stochastic Optimization and Control, Numerics and Applications, I
Room 30D, Upper Level, San Diego Convention Center
Hongwei Mei, University of Central Florida
Zhixin Yang, Ball State University
Quan Yuan, Ball State University
Guangliang Zhao, GE Global Research dr.gzhao@gmail.com
• Thursday January 11, 2018, 8:00 a.m.-11:50 a.m.
MAA Session on 20th Anniversary-The EDGE (Enhancing Diversity in Graduate Education) Program: Pure and Applied Talks by Women, I
Room 14B, Mezzanine Level, San Diego Convention Center
Shanise Walker, Iowa State University shanise1@iastate.edu
Laurel Ohm, University of Minnesota
• Thursday January 11, 2018, 8:00 a.m.-11:55 a.m.
AMS Contributed Paper Session on Differential and Metric Geometry and Geometric Analysis
Room 18, Mezzanine Level, San Diego Convention Center
• Thursday January 11, 2018, 8:00 a.m.-9:35 a.m.
MAA Session on Environmental Modeling in the Classroom
Room 5B, Upper Level, San Diego Convention Center
Emek Kose, St Mary's College of Maryland
Ellen Swanson, Centre College ellen.swanson@centre.edu
• Thursday January 11, 2018, 8:00 a.m.-11:15 a.m.
MAA Session on Humanistic Mathematics, I
Room 15A, Mezzanine Level, San Diego Convention Center
Gizem Karaali, Pomona College
Eric Marland, Appalachian State University marlandes@appstate.edu
• Thursday January 11, 2018, 8:00 a.m.-11:35 a.m.
MAA Session on Innovative and Effective Ways to Teach Linear Algebra, I
Room 14A, Mezzanine Level, San Diego Convention Center
Sepideh Stewart, University of Oklahoma
Gil Strang, Massachusetts Institute of Technology
David Strong, Pepperdine University David.Strong@pepperdine.edu
Megan Wawro, Virginia Tech
• Thursday January 11, 2018, 8:00 a.m.-10:10 a.m.
MAA General Contributed Paper Session on History or Philosophy of Mathematics
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Thursday January 11, 2018, 8:00 a.m.-10:10 a.m.
MAA General Contributed Paper Session on Interdisciplinary Topics in Mathematics
Room 28E, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Thursday January 11, 2018, 8:00 a.m.-11:55 a.m.
MAA Session on Mathematical Knowledge for Teaching Grades 6-12 Mathematics, I
Room 32A, Upper Level, San Diego Convention Center
David C. Carothers, James Madison University
Bonnie Gold, Monmouth University bgold@monmouth.edu
Yvonne Lai, University of Nebraska-Lincoln
• Thursday January 11, 2018, 8:00 a.m.-11:35 a.m.
MAA Session on Mathematical Themes in a First-Year Seminar, I
Room 6D, Upper Level, San Diego Convention Center
Jennifer Bowen, The College of Wooster
Pamela Pierce, The College of Wooster ppierce@wooster.edu
• Thursday January 11, 2018, 8:00 a.m.-11:25 a.m.
AMS Contributed Paper Session on Mathematics Education
Room 13, Mezzanine Level, San Diego Convention Center
• Thursday January 11, 2018, 8:00 a.m.-11:55 a.m.
AMS Contributed Paper Session on Noncommutative Algebra and Hopf Algebras
Room 19, Mezzanine Level, San Diego Convention Center
• Thursday January 11, 2018, 8:00 a.m.-11:55 a.m.
AMS Contributed Paper Session on Research in Geometry, Groups, and Representations by Undergraduate and Post-Baccalaureate Students
Room 29D, Upper Level, San Diego Convention Center
• Thursday January 11, 2018, 8:00 a.m.-10:55 a.m.
MAA Session on Research in Undergraduate Mathematics Education (RUME), I
Room 4, Upper Level, San Diego Convention Center
Stacy Brown, California State Polytechnic University
Megan Wawro, Virginia Tech mwawro@vt.edu
Aaron Weinberg, Ithaca College
• Thursday January 11, 2018, 8:00 a.m.-11:35 a.m.
MAA Session on Using Mathematics to Study Problems from the Social Sciences, I
Room 32B, Upper Level, San Diego Convention Center
Jason Douma, University of Sioux Falls jason.douma@usiouxfalls.edu
• Thursday January 11, 2018, 8:00 a.m.-10:55 a.m.
SIAM Minisymposium on Advances in Imaging Science
Room 11A, Upper Level, San Diego Convention Center
Misha Kilmer, Tufts University misha.kilmer@tufts.edu
Eric de Sturler, Virginia Tech sturler@vt.edu
Eric Miller, Tufts University elmiller@ece.tufts.edu
Avind Saibaba, North Carolina State University asaibab@ncsu.edu
• Thursday January 11, 2018, 8:00 a.m.-6:00 p.m.
Project NExT Workshop
Room 6F, Upper Level, San Diego Convention Center
• Thursday January 11, 2018, 8:00 a.m.-11:00 a.m.
PME Council Meeting
Miramar Room, 3rd Floor, South Tower, Marriott Marquis San Diego Marina
• Thursday January 11, 2018, 8:00 a.m.-5:30 p.m.
Employment Center
Exhibit Hall A, Ground Level, San Diego Convention Center
• Thursday January 11, 2018, 8:20 a.m.-11:35 a.m.
MAA Session on Flipped Classes: Implementation and Evaluation, II
Room 31C, Upper Level, San Diego Convention Center
Joel Kilty, Centre College joel.kilty@centre.edu
Alex M. McAllister, Centre College
John H. Wilson, Centre College
• Thursday January 11, 2018, 8:30 a.m.-11:50 a.m.
AMS Special Session on Novel Methods of Enhancing Success in Mathematics Classes
Room 33B, Upper Level, San Diego Convention Center
Ellina Grigorieva, Texas Womans University egrigorieva@twu.edu
Natali Hritonenko, Prairie View A&M University
• Thursday January 11, 2018, 8:30 a.m.-11:50 a.m.
AMS Special Session on Research by Postdocs of the Alliance for Diversity in Mathematics, II
Room 33C, Upper Level, San Diego Convention Center
Aloysius Helminck, University of Hawaii - Manoa
Michael Young, Iowa State University myoung@iastate.edu
• Thursday January 11, 2018, 9:00 a.m.-9:50 a.m.
MAA Invited Address
Information, computation, optimization: connecting the dots in the traveling salesman problem.
Room 6AB, Upper Level, San Diego Convention Center
William Cook*, University of Waterloo
• Thursday January 11, 2018, 9:00 a.m.-11:00 a.m.
MAA Minicourse #6: Part A
Directing Undergraduate Research
Room 28A, Upper Level, San Diego Convention Center
Aparna Higgins, University of Dayton
• Thursday January 11, 2018, 9:00 a.m.-11:50 a.m.
AMS Special Session on Multi-scale Modeling with PDEs in Computational Science and Engineering:Algorithms, Simulations, Analysis, and Applications, I
Room 17A, Mezzanine Level, San Diego Convention Center
Salim M. Haidar, Grand Valley State University haidars@gvsu.edu
• Thursday January 11, 2018, 9:00 a.m.-11:00 a.m.
MAA Minicourse #7: Part A
Starter Kit for Teaching Modeling-First Differential Equations Course
Room 28B, Upper Level, San Diego Convention Center
Brian Winkel, SIMIODE, Cornwall, NY
Rosemary Farley, Manhattan College
Therese Shelton, Southwestern University
Patrice Tiffany, Manhattan College
Holly Zullo, Westminster College
• Thursday January 11, 2018, 9:00 a.m.-11:00 a.m.
MAA Minicourse #8: Part A
Teaching Statistics using R and R Studio
Room 28C, Upper Level, San Diego Convention Center
Randall Pruim, Calvin College
• Thursday January 11, 2018, 9:00 a.m.-11:55 a.m.
MAA Session on Math Circle Topics with Visual or Kinesthetic Components, I
Room 31B, Upper Level, San Diego Convention Center
Amanda Katharine Serenevy, Riverbend Community Math Center amanda@riverbendmath.org
Martin Strauss, University of Michigan
• Thursday January 11, 2018, 9:00 a.m.-11:40 a.m.
AMS Contributed Paper Session on Research in Mathematical Biology, Modeling, and Neural Networks by Undergraduate and Post-Baccalaureate Students
Room 12, Mezzanine Level, San Diego Convention Center
□ 9:00 a.m.
Vegetation Patterns in Semi-Arid Regions.
Arjun Kakkar*, Williams College
□ 9:15 a.m.
Probabilistic Models, Machine Learning, and the Future of Breast Cancer Risk Assessment.
Alyssa Hope Columbus*, University of California, Irvine
□ 9:30 a.m.
Modeling directed evolution with coupon-collecting and mixing problems.
Devin Mattoon*, Missouri Western State University
Altan Tutar, Davidson College
Hannah S Sinks, Davidson College
Autumn Estrada, Missouri Western State University
David Sullivan, Missouri Western State University
Daniel Zweerink, Missouri Western State University
A. Malcolm Campbell, Davidson College
Todd T Eckdahl, Davidson College
Jeffrey L Poet, Missouri Western State University
Laurie J Heyer, Davidson College
□ 9:45 a.m.
Modeling Chronic Vascular Responses Following a Major Arterial Occlusion.
Jordan J. Pellett*, University of Wisconsin- La Crosse
Emma Brewer, Rose-Hulman Institute of Technology
□ 10:00 a.m.
A Model of Iron Metabolism in the Human Body.
Mary Gockenbach*, University of Texas at Arlington
Tim Barry, University of Maryland, College Park
□ 10:15 a.m.
Transportation Networks Optimized for Various Income Groups and their Impact on the Spread of Airborne Disease.
Rachel Matheson*, Vassar College, Poughkeepsie, New York
Jaysha Camacho, University of Florida, Gainesville, Florida
Juliana Noguera, Los Andes University, Bogotá D.C., Colombia
Brandon Summers, North Carolina State University, Raleigh, North Carolina
Nanda Mallapragada, Arizona State University, Tempe, Arizona
Baojun Song, Montclair State University, Montclair, New Jersey
□ 10:30 a.m.
Computational Simulation of a Partial Differential Equation Based Model of Electrostatic Forces on Neuronal Electrodynamics.
Kaia Lindberg*, Roger Williams University
Edward Dougherty, Roger Williams University
□ 10:45 a.m.
A simplified mathematical model to explore the output of a rhythmic neural network.
Madel R. Liquido*, Saint Peter's University
Nickolas Kintos, Saint Peter's University
□ 11:00 a.m.
Survey on Triplet Mining for Facial Recognition Convolutional Neural Networks.
Islam Faisal*, The American University in Cairo
Andrew Nguyen, UC San Diego
Surabhi Desai, University of St Andrews
Prem Talwai, Cornell University
Shantanu Joshi, University of California Los Angeles
□ 11:15 a.m.
Exploration of Numerical Precision in Deep Neural Networks.
Yunkai Zhang*, University of California, Santa Barbara
Yu Ma, University of California, Berkeley
Zhaoqi Li, Macalester College
Catalina Marie Vajiac, Saint Mary's College, Notre Dame
□ 11:30 a.m.
Simplicial Homology and Neural Networks: An analysis of biological neural networks using persistent homology.
Mark C Agrios*, College of William and Mary
• Thursday January 11, 2018, 9:00 a.m.-10:20 a.m.
PANEL CANCELLED: MAA Panel
Communicating Mathematics to a Wider Audience
Room 1A, Upper Level, San Diego Convention Center
Joel Cohen, University of Maryland
Paul Zorn, St. Olaf College zorn@stolaf.edu
• Thursday January 11, 2018, 9:00 a.m.-10:20 a.m.
MAA Panel
MAA Session for Chairs: Bridging the Gap
Room 2, Upper Level, San Diego Convention Center
Catherine Murphy, Purdue University Northwest cmmurphy@pnw.edu
Linda Braddy, Tarrant County College Northeast Campus
Daniel Maki, Indiana University Bloomington
Michael Dorff, Brigham Young University
Lewis Ludwig, Denison University
Alycia Marshall, Anne Arundel Community College
Karen Saxe, Macalester College
• Thursday January 11, 2018, 9:00 a.m.-10:20 a.m.
MAA Workshop
Get to Know the National Science Foundation
Room 5A, Upper Level, San Diego Convention Center
Ron Buckmire, National Science Foundation rbuckmir@nsf.gov
Karen Keene, National Science Foundation
Sandra Richardson, National Science Foundation
Lee Zia, National Science Foundation
• Thursday January 11, 2018, 9:30 a.m.-5:30 p.m.
Exhibits and Book Sales
Exhibit Hall B1, Ground Level, San Diego Convention Center
• Thursday January 11, 2018, 10:00 a.m.-12:00 p.m.
MAA Poster Session
Mathematical Outreach Programs
Exhibit Hall B2, Ground Level, San Diego Convention Center
Betsy Yanik, Emporia State University
• Thursday January 11, 2018, 10:05 a.m.-10:55 a.m.
AWM-AMS Noether Lecture
Nonsmooth boundary value problems.
Room 6AB, Upper Level, San Diego Convention Center
Jill Pipher*, Brown University
• Thursday January 11, 2018, 10:15 a.m.-11:55 a.m.
MAA General Contributed Paper Session on Outreach, II
Room 28E, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Thursday January 11, 2018, 10:15 a.m.-11:55 a.m.
MAA General Contributed Paper Session on Teaching and Learning Developmental Mathematics
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Thursday January 11, 2018, 10:30 a.m.-12:00 p.m.
SIGMAA Officers Meeting
Marina Ballroom D, 3rd Floor, South Tower, Marriott Marquis San Diego Marina
Andrew Miller, Belmont University
• Thursday January 11, 2018, 10:30 a.m.-12:00 p.m.
AWM Committee on Education Panel
Supporting, Evaluating and Rewarding Work in Mathematics Education in Mathematical Sciences Departments
Room 11B, Upper Level, San Diego Convention Center
Jacqueline Dewar, AWM Education Committee
Pao-sheng Hsu, AWM Education Committee
Harriet Pollatsek, AWM Education Committee
Minerva Cordero, University of Texas at Arlington
Jenna Carpenter, Campbell University
Rebecca Garcia, Sam Houston State University
Daniel Maki, Indiana University, Bloomington
Thomas Roby, University of Connecticut
• Thursday January 11, 2018, 10:35 a.m.-11:55 a.m.
MAA Workshop
Hungarian Approach to Teaching Proof-writing Pósa's Discovery-Based Pedagogy
Room 5A, Upper Level, San Diego Convention Center
Péter Juhász, MTA Rényi Institute and Budapest Semesters in Mathematics Education juhasz.peter@renyi.mta.hu
Réka Szász, Budapest Semesters in Mathematics Education
Ryota Matsuura, St. Olaf College and Budapest Semesters in Mathematics Education
• Thursday January 11, 2018, 10:35 a.m.-11:55 a.m.
Town Hall Meeting
Revising MAA Guidelines on the Work of Faculty and Departments: Supporting Student Success
Room 2, Upper Level, San Diego Convention Center
Tim Flowers, Indiana University of Pennsylvania flowers@iup.edu
Edward Aboufadel, Grand Valley State University
Mary Beisiegel, Oregon State University
Suzeanne Doree, Augsburg College
Tyler Jarvis, Brigham Young University
Benedict Nmah, Morehouse College
• Thursday January 11, 2018, 11:00 a.m.-11:50 a.m.
Project NExT Lecture on Teaching and Learning
Room 6C, Upper Level, San Diego Convention Center
• Thursday January 11, 2018, 11:00 a.m.-12:00 p.m.
AMS Informational Session
Report on the findings of the 2015 CBMS survey of undergraduate mathematical and statistical sciences in the U.S.
Room 8, Upper Level, San Diego Convention Center
Ellen Kirkman, Wake Forest University
Jim Maxwell, American Mathematical Society
• Thursday January 11, 2018, 11:10 a.m.-12:00 p.m.
SIAM Invited Address
Tensor Decomposition: A Mathematical Tool for Data Analysis.
Room 6AB, Upper Level, San Diego Convention Center
Tamara G. Kolda*, Sandia National Laboratories
• Thursday January 11, 2018, 1:00 p.m.-1:50 p.m.
AMS Colloquium Lectures: Lecture II
Proving algebraic identities.
Room 6AB, Upper Level, San Diego Convention Center
Avi Wigderson*, Institute for Advanced Study
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Advances in Operator Theory, Operator Algebras, and Operator Semigroups, II
Room 33A, Upper Level, San Diego Convention Center
Asuman G. Aksoy, Claremont McKenna College
Zair Ibragimov, California State University, Fullerton
Marat Markin, California State University, Fresno mmarkin@csufresno.edu
Ilya Spitkovsky, New York University, Abu Dhabi
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Algebraic, Analytic, and Geometric Aspects of Integrable Systems, Painlevé Equations, and Random Matrices, II
Room 33B, Upper Level, San Diego Convention Center
Vladimir Dragovic, University of Texas at Dallas
Anton Dzhamay, University of Northern Colorado adzham@unco.edu
Sevak Mkrtchyan, University of Rochester
□ 1:00 p.m.
Topological recursion of Eynard-Orantin, ribbon graphs, and Feynman diagrams.
K. Kappagantula, Concordia University
M. Cutimanco, University of Sherbrooke
P. Labelle, Champlain college
V. Shramchenko*, University of Sherbrooke
□ 1:30 p.m.
Algebro-geometric approach to the Schlesinger systems: from Poncelet to Painleve VI.
Vladimir Dragovic*, The University of Texas at Dallas, Department of Mathematical Sciences
Vasilisa Shramchenko, University of Sherbrooke
□ 2:00 p.m.
Reduction from ABS equations to the Painlevé equations.
Nobutaka Nakazono*, Department of Physics and Mathematics, Aoyama Gakuin University
□ 2:30 p.m.
NEW PRESENTER: Gap probabilities in q-Racah tiling model and discrete Painlevé equations.
Alisa Knizel*, Columbia University
Anton Dzhamay, University of Northern Colorado
□ 3:00 p.m.
The space of initial conditions for some 4D Painlevé systems.
Tomoyuki Takenawa*, Tokyo University of Marine Science and Technology
□ 3:30 p.m.
Log-Aesthetic Curves in Industrial Design as a Similarity Geometric Analog of Euler's Elastic Curves.
J. Inoguchi, Institute of Mathematics, University of Tsukuba, Japan
K. Kajiwara*, Institute of Mathematics for Industry, Kyushu University, Japan
K. T. Miura, Graduate School of Science and Technology, Shizuoka University, Japan
M. Sato, Serio Corporation, Japan
W. K. Schief, School of Mathematics, The University of New South Wales, Australia
Y. Shimizu, UEL Corporation, Japan
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Analysis of Nonlinear Partial Differential Equations and Applications, III
Room 9, Upper Level, San Diego Convention Center
Tarek M. Elgindi, University of California, San Diego tme2@princeton.edu
Edriss S. Titi, Texas A&M University and Weizmann Institute of Science
• Thursday January 11, 2018, 1:00 p.m.-3:00 p.m.
MAA Minicourse #11: Part A
Authoring Integrated Online Textbooks with MathBook XML
Room 28C, Upper Level, San Diego Convention Center
Karl-Dieter Crisman, Gordon College
Mitchel T. Keller, Washington and Lee University
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Beyond Planarity: Crossing Numbers of Graphs (a Mathematics Research Communities Session), II
Room 29B, Upper Level, San Diego Convention Center
Axel Brandt, Davidson College
Garner Cochran, University of South Carolina gcochran@math.sc.edu
Sarah Loeb, College of William and Mary
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Commutative Algebra in All Characteristics, II
Room 31A, Upper Level, San Diego Convention Center
Neil Epstein, George Mason University nepstei2@gmu.edu
Karl Schwede, University of Utah
Janet Vassilev, University of New Mexico
• Thursday January 11, 2018, 1:00 p.m.-3:20 p.m.
AMS Special Session on Discrete Neural Networking and Applications, I
Room 30E, Upper Level, San Diego Convention Center
Murat Adivar, Fayetteville State University
Michael A. Radin, Rochester Institute of Technology michael.radin@rit.edu
Youssef Raffoul, University of Dayton
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Dynamical Systems: Smooth, Symbolic, and Measurable (a Mathematics Research Communities Session), II
Room 29C, Upper Level, San Diego Convention Center
Kathryn Lindsey, Boston College kathryn.a.lindsey@gmail.com
Scott Schmieding, Northwestern University
Kurt Vinhage, University of Chicago
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on History of Mathematics, III
Room 10, Upper Level, San Diego Convention Center
Sloan Despeaux, Western Carolina University
Jemma Lorenat, Pitzer College
Clemency Montelle, University of Canterbury
Daniel Otero, Xavier University otero@xavier.edu
Adrian Rice, Randolph-Macon College
• Thursday January 11, 2018, 1:00 p.m.-3:45 p.m.
AMS Special Session on Homotopy Type Theory (a Mathematics Research Communities Session), II
Room 29A, Upper Level, San Diego Convention Center
Simon Cho, University of Michigan seamooncho@gmail.com
Liron Cohen, Cornell University
Edward Morehouse, Wesleyan University
□ 1:00 p.m.
Differential Cohesive Type Theory.
Jacob A Gross, University of Oxford
Daniel R Licata, Wesleyan University
Max S New, Northeastern University
Jennifer Paykin, University of Pennsylvania
Mitchell Riley, Wesleyan University
Michael Shulman, University of San Diego
Felix Wellen*, Carnegie Mellon University
□ 1:30 p.m.
Applications of Cohesive Homotopy Type Theory.
Daniel Cicala, University of California, Riverside
Liron Cohen, Cornell University
Nachiket Karnick, Indiana University
Chandrika Sadanand, Hebrew University of Jerusalem
Michael Shulman, University of San Diego
Amelia Tebbe*, Indiana University Kokomo
Dmitry Vagner, Duke University
□ 2:00 p.m.
The Joy of QIITs.
Thorsten Altenkirch*, University of Nottingham
□ 2:30 p.m.
Experiments in cubical type theory.
Guillaume Brunerie*, Institute for Advanced Study, Princeton, NJ
□ 3:00 p.m.
• Thursday January 11, 2018, 1:00 p.m.-3:00 p.m.
MAA Minicourse #10: Part A
Incorporating Mathematical and Statistical Forensics Activities into the Undergraduate Mathematics Classroom
Room 28B, Upper Level, San Diego Convention Center
Eugene Fiorini, Muhlenberg College
James Russell, Muhlenberg College
Gail Marsella, Muhlenberg College
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Interactions of Inverse Problems, Signal Processing, and Imaging, I
Room 16A, Mezzanine Level, San Diego Convention Center
M. Zuhair Nashed, University of Central Florida M.Nashed@ucf.edu
Willi Freeden, University of Kaiserslautern
Otmar Scherzer, University of Vienna
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Mathematical Information in the Digital Age of Science, II
Room 6E, Upper Level, San Diego Convention Center
Patrick Ion, University of Michigan pion@umich.edu
Olaf Teschke, zbMath Berlin
Stephen Watt, University of Waterloo
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Mathematical Modeling and Analysis of Infectious Diseases, II
Room 30A, Upper Level, San Diego Convention Center
Kazuo Yamazaki, University of Rochester kyamazak@ur.rochester.edu
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Mathematical Modeling, Analysis and Applications in Population Biology, I
Room 30B, Upper Level, San Diego Convention Center
Yu Jin, University of Nebraska-Lincoln yjin6@unl.edu
Ying Zhou, Lafayette College
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Metric Geometry and Topology, I
Room 16B, Mezzanine Level, San Diego Convention Center
Christine Escher, Oregon State University
Catherine Searle, Wichita State University searle@math.wichita.edu
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on New Trends in Celestial Mechanics, I
Room 30D, Upper Level, San Diego Convention Center
Richard Montgomery, University of California Santa Cruz
Zhifu Xie, University of Southern Mississippi zhifu.xie@usm.edu
□ 1:00 p.m.
Metric Geometry and Marchal's lemma.
Richard Montgomery*, U.C. Santa Cruz
□ 1:30 p.m.
Symmetries and choreographies in families that bifurcate from the polygonal relative equilibrium of the n-body problem.
Renato Carlos Calleja*, IIMAS-National Autonomous University of Mexico
Eusebius Doedel, Concordia University
Carlos Garcia Azpeitia, Facultad de Ciencias-UNAM
□ 2:00 p.m.
□ 2:30 p.m.
Free time minimizers for the planar three body problem.
Hector Sanchez*, Universidad Nacional Autonoma de Mexico
Richard Moeckel, Univerisity of Minnesota
Richard Montgomery, University of California, Santa Cruz
□ 3:00 p.m.
Remarks on the n-body problem on surfaces of revolution.
Cristina Stoica*, Wilfrid Laurier University, Canada
□ 3:30 p.m.
Euler and Lagrange relative equilibria in the curved $3$--body problem.
Ernesto Perez-Chavela*, ITAM-Mexico
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Open and Accessible Problems for Undergraduate Research, II
Room 17B, Mezzanine Level, San Diego Convention Center
Michael Dorff, Brigham Young University
Allison Henrich, Seattle University henricha@seattleu.edu
Nicholas Scoville, Ursinus College
• Thursday January 11, 2018, 1:00 p.m.-5:10 p.m.
MAA Invited Paper Session on Quandle Questions
Room 3, Upper Level, San Diego Convention Center
Alissa Crans, Loyola Marymount University acrans@lmu.edu
Sam Nelson, Claremont McKenna College
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Quaternions, II
Room 18, Mezzanine Level, San Diego Convention Center
Terrence Blackman, Medgar Evers College, City University of New York
Johannes Familton, Borough of Manhattan Community College, City University of New York jfamilton@bmcc.cuny.edu
Chris McCarthy, Borough of Manhattan Community College, City University of New York
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Recent Trends in Analysis of Numerical Methods of Partial Differential Equations, I
Room 30C, Upper Level, San Diego Convention Center
Sara Pollock, Wright State University
Leo Rebholz, Clemson University rebholz@clemson.edu
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS-MAA-SIAM Special Session on Research in Mathematics by Undergraduates and Students in Post-Baccalaureate Programs, II
Room 29D, Upper Level, San Diego Convention Center
Tamas Forgacs, CSU Fresno
Darren A. Narayan, Rochester Institute of Technology dansma@rit.edu
Mark David Ward, Purdue University
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS-ASL Special Session on Set Theory, Logic and Ramsey Theory, III
Room 7B, Upper Level, San Diego Convention Center
Andrés Caicedo, Mathematical Reviews
José Mijares, University of Colorado, Denver jose.mijarespalacios@ucdenver.edu
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Spectral Theory, Disorder and Quantum Physics, I
Room 33C, Upper Level, San Diego Convention Center
Rajinder Mavi, Michigan State University mavi@math.msu.edu
Jeffery Schenker, Michigan State University
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Structure and Representations of Hopf Algebras: a Session in Honor of Susan Montgomery, III
Room 17A, Mezzanine Level, San Diego Convention Center
Siu-Hung Ng, Louisiana State University
Lance Small, University of California, San Diego
Henry Tucker, University of California, San Diego htucker@usc.edu
□ 1:00 p.m.
New Families of Quasihopf algebras and tensor Categories.
Geoffrey -- Mason*, UC Santa Cruz
□ 2:00 p.m.
On the classification of super-modular categories by rank.
Paul Bruillard, Pacific Northwest National Laboratory
Cesar Galindo, Universidad de los Andes
Siu-Hung Ng, Louisiana State University
Julia Plavnik*, Texas A$&$M University
Eric Rowell, Texas A$&$M University
Zhenghan Wang, Microsoft Research Station Q and Department of Mathematics, University of California, Santa Barbara
□ 2:30 p.m.
Investigating invariants of, and new categories obtained from, $\operatorname{Rep}(D(G))$ via change of braidings.
Marc Keilberg*, Torrance, California
□ 3:00 p.m.
Hochschild Cohomology and the Modular Group.
Simon Lentner, Universität Hamburg
Svea Nora Mierach, Memorial University of Newfoundland
Christoph Schweigert, Universität Hamburg
Yorck Sommerhäuser*, Memorial University of Newfoundland
□ 3:30 p.m.
• Thursday January 11, 2018, 1:00 p.m.-3:00 p.m.
MAA Minicourse #9: Part A
Teaching Undergraduate Mathematics via Primary Source Projects
Room 28A, Upper Level, San Diego Convention Center
Diana White, University of Colorado Denver
Janet Barnett, Colorado State University, Pueblo
Kathy Clark, Florida State University
Dominic Klyve, Central Washington University
Jerry Lodder, New Mexico State University
Danny Otero, Xavier University
• Thursday January 11, 2018, 1:00 p.m.-3:50 p.m.
AMS Special Session on Theory, Practice, and Applications of Graph Clustering, I
Room 7A, Upper Level, San Diego Convention Center
David Gleich, Purdue University
Jennifer Webster, Pacific Northwest National Laboratory
Stephen J. Young, Pacific Northwest National Laboratory stephen.young@pnnl.gov
• Thursday January 11, 2018, 1:00 p.m.-4:25 p.m.
MAA Session on 20th Anniversary-The EDGE (Enhancing Diversity in Graduate Education) Program: Pure and Applied Talks by Women, II
Room 14B, Mezzanine Level, San Diego Convention Center
Shanise Walker, Iowa State University shanise1@iastate.edu
Laurel Ohm, University of Minnesota
• Thursday January 11, 2018, 1:00 p.m.-3:55 p.m.
AMS Contributed Paper Session on Algebraic Geometry
Room 12, Mezzanine Level, San Diego Convention Center
• Thursday January 11, 2018, 1:00 p.m.-3:55 p.m.
AMS Contributed Paper Session on Combinatorics
Room 13, Mezzanine Level, San Diego Convention Center
• Thursday January 11, 2018, 1:00 p.m.-2:35 p.m.
MAA Session on Humanistic Mathematics, II
Room 15A, Mezzanine Level, San Diego Convention Center
Gizem Karaali, Pomona College
Eric Marland, Appalachian State University marlandes@appstate.edu
• Thursday January 11, 2018, 1:00 p.m.-4:15 p.m.
MAA Session on Innovative Mathematical Outreach in Alternative Settings
Room 31C, Upper Level, San Diego Convention Center
Hector Rosario, Gwinnett County Public Schools, South Gwinnett High School
Jennifer Switkes, California State Polytechnic University, Pomona jmswitkes@cpp.edu
• Thursday January 11, 2018, 1:00 p.m.-3:55 p.m.
MAA Session on Innovative Teaching Practices in Number Theory, I
Room 15B, Mezzanine Level, San Diego Convention Center
Patrick Rault, University of Arizona
Thomas Hagedorn, The College of New Jersey hagedorn@tcnj.edu
Mark Kozek, Whittier College
• Thursday January 11, 2018, 1:00 p.m.-2:55 p.m.
MAA Session on Innovative and Effective Ways to Teach Linear Algebra, II
Room 14A, Mezzanine Level, San Diego Convention Center
Sepideh Stewart, University of Oklahoma
Gil Strang, Massachusetts Institute of Technology
David Strong, Pepperdine University David.Strong@pepperdine.edu
Megan Wawro, Virginia Tech
• Thursday January 11, 2018, 1:00 p.m.-3:55 p.m.
MAA General Contributed Paper Session on Geometry
Room 28E, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Thursday January 11, 2018, 1:00 p.m.-3:40 p.m.
MAA General Contributed Paper Session on Modeling and Applications, II
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
□ 1:00 p.m.
Modeling Adsorption Based Filters: 1 Dimensional Filter Equation (Bio-remediation of Heavy Metal Contaminated Water).
Chris McCarthy*, Borough of Manhattan Community College (CIty University of New York)
□ 1:15 p.m.
Dispersal and the spread of language with frequency-dependent fitness.
Jacquelyn L Rische*, Marymount University
□ 1:30 p.m.
Exploring Differential Regulation of Blood Clot Degradation.
Brittany Bannish*, University of Central Oklahoma
□ 1:45 p.m.
Heave and Flow: Understanding the role of resonance and shape evolution for heaving flexible panels.
Alexander P Hoover*, Tulane University
Ricardo Cortez, Tulane University
Eric Tytell, Tufts University
Lisa Fauci, Tulane University
□ 2:00 p.m.
Modeling the Behavior of Problem Drinkers in a Clinical Trial.
Judith E Canner*, California State University, Monterey Bay
H T Banks, North Carolina State University
Kidist Bekele-Maxwell, North Carolina State University
Rebecca Everett, North Carolina State University
Jennifer Menda, North Carolina State University
Lyric Stephenson, North Carolina State University
Jon Morgenstern, The North Shore Long Island Jewish Health System
Sijing Shao, The North Shore Long Island Jewish Health System
Alexis Kuerbis, The North Shore Long Island Jewish Health System
□ 2:15 p.m.
Optimal Control Theory and Parameter Estimation of Parameters in a Differential Equation Model for Patients with Lupus.
Peter Agaba*, Western Kentucky University
□ 2:30 p.m.
Urban snow removal - just in time the mathematical model and algorithm.
Zeinab Bandpey, Morgan State University
Isabelle Kemajou-Brown, Morgan State University
Xiao-Xiong Gan, Morgan State University
Ahlam Tannouri*, Morgan State University
□ 2:45 p.m.
How High Impact Undergraduate Health Research Initiatives Can Be Discovered and Implemented in The Statistics Classroom.
Benjamin D Knisley*, California Baptist University
Dr. Linn Carothers, California Baptist University
□ 3:00 p.m.
Investigating the Mechanism of Oscillatory Frequency Changes due to NMDA in the CA3 Neural Network of the Hippocampus.
Syed Abid Rizvi*, The College of William & Mary
□ 3:15 p.m.
A Multi-Scale Model of Tumor Growth in Response to an Anti-Nodal Antibody Therapy Combined with a Chemotherapy.
Qing Wang*, Dept. of Computer Science, Mathematics, and Engineering, Shepherd University
Zhijun Wang, Dept. of Computer Science, Mathematics, and Engineering, Shepherd University
David J Klinke, Dept. of Chemical Engineering, West Virginia University
□ 3:30 p.m.
TALK CANCELLED: Analysis of micro-fluidic tweezers in the Stokes regime.
Yang Ding, Beijing Computational Science Research Center, Beijing, China
Li Zhang, Chinese University of Hong Kong, Shatin NT, Hong Kong SAR,
Longhua Zhao*, Case Western Reserve University
• Thursday January 11, 2018, 1:00 p.m.-3:15 p.m.
MAA Session on Math Circle Topics with Visual or Kinesthetic Components, II
Room 31B, Upper Level, San Diego Convention Center
Amanda Katharine Serenevy, Riverbend Community Math Center amanda@riverbendmath.org
Martin Strauss, University of Michigan
• Thursday January 11, 2018, 1:00 p.m.-2:55 p.m.
MAA Session on Mathematical Knowledge for Teaching Grades 6-12 Mathematics, II
Room 32A, Upper Level, San Diego Convention Center
David C. Carothers, James Madison University
Bonnie Gold, Monmouth University bgold@monmouth.edu
Yvonne Lai, University of Nebraska-Lincoln
• Thursday January 11, 2018, 1:00 p.m.-3:55 p.m.
MAA Session on Mathematics and Sports, III
Room 5B, Upper Level, San Diego Convention Center
John David, Virginia Military Institute
Drew Pasteur, College of Wooster rpasteur@wooster.edu
• Thursday January 11, 2018, 1:00 p.m.-4:15 p.m.
MAA Session on Research in Undergraduate Mathematics Education (RUME), II
Room 4, Upper Level, San Diego Convention Center
Stacy Brown, California State Polytechnic University
Megan Wawro, Virginia Tech mwawro@vt.edu
Aaron Weinberg, Ithaca College
• Thursday January 11, 2018, 1:00 p.m.-3:55 p.m.
AMS Contributed Paper Session on Statistical Analysis and Risk Management
Room 19, Mezzanine Level, San Diego Convention Center
• Thursday January 11, 2018, 1:00 p.m.-3:55 p.m.
MAA Session on Using Mathematics to Study Problems from the Social Sciences, II
Room 32B, Upper Level, San Diego Convention Center
Jason Douma, University of Sioux Falls jason.douma@usiouxfalls.edu
• Thursday January 11, 2018, 1:00 p.m.-3:55 p.m.
SIAM Minisymposium on Tensors! Mathematical Challenges and Opportunities
Room 11A, Upper Level, San Diego Convention Center
David Gleich, Purdue University dgleich@purdue.edu
Tamara G Kolda, Sandia National Laboratories tgkolda@sandia.gov
Luke Oeding, Auburn University oeding@auburn.edu
• Thursday January 11, 2018, 1:00 p.m.-2:20 p.m.
MAA Panel
Effectively Chairing a Mathematical Sciences Department
Room 2, Upper Level, San Diego Convention Center
Kevin Charlwood, Washburn University kevin.charlwood@washburn.edu
Robert Buck, Slippery Rock University
Joanna Ellis-Monaghan, Saint Michael's College
Curtis Bennett, Loyola Marymount University
Karrolyne Fogel, California Lutheran University
Matthew Koetz, Nazareth College
Sergio Loch, Grand View University
Joe Yanik, Emporia State University
• Thursday January 11, 2018, 1:00 p.m.-2:20 p.m.
MAA Panel
Out in Mathematics: Professional Issues Facing LGBTQ Mathematicians
Room 1A, Upper Level, San Diego Convention Center
David Crombecque, University of Southern California crombecq@usc.edu
Christopher Goff, University of the Pacific
Lily Khadjavi, Loyola Marymount University
Shelly Bouchat, Indiana University of Pennsylvania
Juliette Bruce, University of Wisconsin Madison
Ron Buckmire, National Science Foundation
Frank Farris, Santa Clara University
Emily Riehl, Johns Hopkins University
• Thursday January 11, 2018, 1:00 p.m.-2:30 p.m.
AMS Committee on Education Panel Discussion
Preparing mathematics students for non-academic careers
Room 11B, Upper Level, San Diego Convention Center
Erica Flapan, Pomona College
Manmohan Kaur, Benedictine University
Douglas Mupasiri, University of Northern Iowa
Diana White, University of Colorado-Denver
Erica Flapan, Pomona College
Andrew J. Bernoff, Harvey Mudd College
Johanna Hennig, Center for Communications Research, division of the Institute for Defense Analysis
NEW: Jasmine Ng, ALEKS
WITHDRAWN: Srikrishna Rupanagunta, Mu Sigma
Lee Zia, Division of Undergraduate Education, National Science Foundation
• Thursday January 11, 2018, 1:00 p.m.-2:20 p.m.
MAA Workshop
Using Problem Solving and Discussions in Mathematics Courses for Prospective Elementary Teachers
Room 5A, Upper Level, San Diego Convention Center
Ziv Feldman, Boston University zfeld@bu.edu
Ryota Matsuura, St. Olaf College
Suzanne Chapin, Boston University
Lynsey Gibbons, Boston University
Laura Kyser Callis, Boston University
• Thursday January 11, 2018, 1:00 p.m.-3:00 p.m.
Summer Program for Women in Mathematics (SPWM) Reunion
Del Mar Room, 3rd Floor, South Tower, Marriott Marquis San Diego Marina
• Thursday January 11, 2018, 1:50 p.m.-3:05 p.m.
Project NExT Panel
Incorporating Coding Into All Levels of the College Math Curriculum
Room 6F, Upper Level, San Diego Convention Center
Sara Clifton, University of Illinois
Michael Kelly, Transylvania University
Alicia Marino, University of Hartford
Paul Savala, Whittier College
Will Cipolli, Colgate University
Suzanne Lenhart, University of Tennesee
Eric Sullivan, Carroll College
Jade White, High Tech High
• Thursday January 11, 2018, 2:00 p.m.-4:00 p.m.
MAA Poster Session: Projects Supported by the NSF Division of Undergraduate Education
Exhibit Hall B2, Ground Level, San Diego Convention Center
Jon Scott, Montgomery College jon.scott@montgomerycollege.edu
□ 2:00 p.m.
Modeling Across the Curriculum.
Peter Turner*, Clarkson University
James Crowley, SIAM
Ben Galluzzo, Shippensburg University
□ 2:00 p.m.
Project SMILES: Student-Made Interactive Learning with Educational Songs for Introductory Statistics.
John J. Weber III*, Perimeter College at Georgia State University
Lawrence M. Lesser, University of Texas at El Paso
Dennis K. Pearl, Pennsylvania State University
□ 2:00 p.m.
Promoting Reasoning in Undergraduate Mathematics (PRIUM).
William Martin*, North Dakota State University
Josef Dorfmeister, North Dakota State University
Benton Duncan, North Dakota State University
Friedrich Littman, North Dakota State University
Draga Vidakovic, Georgia State University
Guantao Chen, Georgia State University
Valerie Miller, Georgia State University
□ 2:00 p.m.
Undergraduate Curriculum Guide for the Mathematical Sciences.
Martha Siegel*, Towson University
Carol Schumacher, Kenyon College
Doug Ensley, Mathematical Association of America
J. Michael Pearson, Mathematical Association of America
□ 2:00 p.m.
Heartland: The Carver Bridge to STEM Success Program.
Heidi Berger*, Simpson College
Mark Brodie, Simpson College
Derek Lyons, Simpson College
Clint Meyer, Simpson College
□ 2:00 p.m.
A Learning Progression for Partial Derivatives.
Corinne A. Manogue, Oregon State University
Tevian Dray*, Oregon State University
Paul Emigh, Oregon State University
Elizabeth Gire, Oregon State University
David Roundy, Oregon State University
□ 2:00 p.m.
Science and Mathematics Attraction, Retention, and Training for Texas (SMART Texas).
Keith Hubbard*, Stephen F. Austin State University
Nola Schmidt, Stephen F. Austin State University
□ 2:00 p.m.
Talented Teachers in Training for Texas Phase II.
Lesa Beverly*, Stephen F. Austin State University
Keith Hubbard, Stephen F. Austin State University
Dennis Gravatt, Stephen F. Austin State University
Chrissy Cross, Stephen F. Austin State University
□ 2:00 p.m.
Progress through Calculus.
David Bressoud*, Macalester College
Jess Ellis, Colorado State University
Sean Larsen, Portland State University
Chris Rasmussen, San Diego State University
Doug Ensley, Mathematical Association of America
□ 2:00 p.m.
Native American-based Mathematics Materials for Integration into Undergraduate Courses.
Charles Funkhouser*, California State University Fullerton
Harriet C. Edwards, California State University Fullerton
Miles Pfahl, Turtle Mountain Community College
□ 2:00 p.m.
Improving the Preparation of Graduate Students to Teach Undergraduate Mathematics.
Jack Bookman*, Duke University
Natasha Speer, University of Maine
□ 2:00 p.m.
SUMMIT-P at SLU: Math for Business Students in the Spirit of CRAFTY.
Mike May*, Saint Louis University
Debra Pike, Saint Louis University
Michael Alderson, Saint Louis University
Anneke Bart, Saint Louis University
□ 2:00 p.m.
CAREER: Developing Undergraduate Combinatorial Curriculum In Computational Settings.
Elise Lockwood*, Oregon State University
□ 2:00 p.m.
The SDSU Noyce Mathematics and Science Master Teaching Fellowship Program.
Lisa Lamb, San Diego State University
Susan Nickerson, San Diego State University
Randolph Philipp, San Diego State University
Donna L. Ross, San Diego State University
Meredith H. Vaughn, San Diego State University
Kathy Williams, San Diego State University
Raymond LaRochelle*, San Diego State University
□ 2:00 p.m.
Open Resources for the Mathematics Curriculum.
Jim Fowler*, Ohio State University
Petra Bonfert-Taylor, Dartmouth
David Farmer, American Institute of Mathematics
Sarah Eichhorn, University of Texas at Austin
□ 2:00 p.m.
Passion-Driven Statistics: A multidisciplinary project-based supportive model for statistical reasoning and application.
Lisa Dierker*, Wesleyan University
David Beveridge, Wesleyan University
□ 2:00 p.m.
Algebra Instruction at Community Colleges (AICC).
Laura Watkins*, Glendale Community College
April Strom, Scottsdale Community College
Vilma Mesa, University of Michigan
Irene Duranczyk, , University of Minnesota
Nidhi Kohli, University of Minnesota
□ 2:00 p.m.
Transitioning Learners to Calculus I in Community Colleges (TLC3).
Vilma Mesa*, University of Michigan
Helen Burn, Highline College
Luke Wood, San Diego State University
Eboni Zamani-Gallaher, University of Illinois Urbana-Champaign
□ 2:00 p.m.
Ambitious Math and Science Teaching Fellows.
Thomas Dick*, Oregon State University
Rebekah Elliott, Oregon State University
SueAnn Bottoms, Oregon State University
□ 2:00 p.m.
Enhancing Explorations in Functions for Preservice Secondary Mathematics Teachers.
Theresa Jorgensen*, The University of Texas at Arlington
James A. Alvarez, The University of Texas at Arlington
Kathryn Rhoads, The University of Texas at Arlington
□ 2:00 p.m.
Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS).
Jerry Lodder*, New Mexico State University
Kathleen Clark, Florida State University
Janet Barnett, Colorado State University-Pueblo
Dominic Klyve, Central Washington University
Nicholas Scoville, Ursinus College
Daniel Otero, Xavier University
Diana White, University of Colorado at Denver-Downtown
□ 2:00 p.m.
URI Robert Noyce Teacher Scholarship Program.
Anne Seitsinger*, University of Rhode Island
David Byrd, University of Rhode Island
Bryan Dewsbury, University of Rhode Island
Kees de Groot, University of Rhode Island
Jay Fogelman, University of Rhode Island
Joan Peckham, University of Rhode Island
Kathy Peno, University of Rhode Island
□ 2:00 p.m.
STEM Teaching Scholars for High Need Chicago-Area Schools.
Melanie Pivarski*, Roosevelt University
Byoung Sug Kim, Roosevelt University
Vicky McKinley, Roosevelt University
Chandra James, Chicago Public Schools
□ 2:00 p.m.
Scholarships for STEM at the University of Hawaii at Hilo (S-STEM).
Reni Ivanova*, University of Hawaii at Hilo
□ 2:00 p.m.
Raising Calculus to the Surface.
Aaron Wangberg*, Winona State University
Jason Samuels, City University of New York -- BMCC
Brian Fisher, Lubbock Christian University
Elizabeth Gire, Oregon State University
Tisha Hooks, Winona State University
□ 2:00 p.m.
Collaborative Research: Raising Physics to the Surface.
Aaron Wangberg*, Winona State University
Robyn Wangberg, Saint Mary's University of Minnesota
Elizabeth Gire, Oregon State University
□ 2:00 p.m.
Noyce Mathematics Fellows, TeachDETROIT.
Jennifer Lewis*, Wayne State University
Saliha Ozgun-Koca, Wayne State University
Robert Bruner, Wayne State University
□ 2:00 p.m.
POSTER WITHDRAWN: Hofstra Noyce Scholars Program Phase II: Expanding the Model.
Behailu Mammo*, Hofstra University
□ 2:00 p.m.
Framing Lee Academics for Mathematics, Education and Social Sciences Success (part of the SUMMIT-P collaboration).
Caroline Maher-Boulis*, Lee University
Jason Robinson, Lee University
Bryan Poole, Lee University
John Hearn, Lee University
□ 2:00 p.m.
NSF Scholarship Program in Science and Mathematics at Kennesaw State University.
Ana-Maria Croicu*, Kennesaw State University
□ 2:00 p.m.
Discovering the Art of Mathematics: Inquiry Based Learning in Mathematics for Liberal Arts.
Philip Hotchkiss*, Westfield State University
Christine Von Renesse, Westfield State University
Julian Fleron, Westfield State University
Volker Ecke, Westfield State University
□ 2:00 p.m.
Collaborative Research: A National Consortium for Synergistic Undergraduate Mathematics via Multi-institutional Interdisciplinary Teaching Partnerships (SUMMIT-P).
Susan Ganter*, Embry-Riddle Aeronautical University
Jack Bookman, Duke University
Suzanne Dorée, Augsburg University
William Haver, Virginia Commonwealth University
Rosalyn Hobson Hargraves, Virginia Commonwealth University
Stella Hofrenning, Augsburg University
Victor Piercey, Ferris State University
Erica Slate, Appalachian State University
□ 2:00 p.m.
Renovating Calculus (a SUMMIT-P collaboration).
Suzanne Dorée*, Augsburg University
Pavel Belik, Augsburg University
Stella Hofrenning, Augsburg University
Joan Kunz, Augsburg University
Jody Sorensen, Augsburg University
□ 2:00 p.m.
Quantitative Reasoning for Professionals (a SUMMIT-P collaboration).
Victor Piercey*, Ferris State University
Rhonda Bishop, Ferris State University
Mischelle Stone, Ferris State University
□ 2:00 p.m.
PRODUCT 1: Professional Development and Uptake through Collaborative Teams.
Angie Hodge*, Northern Arizona University
Sandra Laursen, University of Colorado Boulder
Yousuf George, Nazareth College
Volker Ecke, Westfield State University
Philip Hotchkiss, Westfield State University
Partick Rault, University of Arizona
□ 2:00 p.m.
PRODUCT 2: Professional Development and Uptake through Collaborative Teams.
Stan Yoshinobu*, California Polytechnic State University, San Luis Obispo
Christine von Renesse, Westfield State University
Chuck Hayward, University of Colorado Boulder
Ryan Gantner, St. John Fisher College
Brian Katz, Augustana College
Xiao Xiao, Utica College
□ 2:00 p.m.
Assessing the Impact of the Emporium Model on Student Persistence and Dispositional Learning by Transforming Faculty Culture.
Kathy Cousins-Cooper*, North Carolina A&T State University
Dominic P. Clemence, North Carolina A&T State University
Nicholas S. Luke, North Carolina A&T State University
Katrina N. Staley, North Carolina A&T State University
□ 2:00 p.m.
POSTER WITHDRAWN: When is seeing believing? Challenges in characterizing STEM teaching.
Sandra Laursen*, University of Colorado Boulder
Chuck Hayward, University of Colorado Boulder
Tim Weston, University of Colorado Boulder
Tim Archie, University of Colorado Boulder
□ 2:00 p.m.
WeBWorK: Improving Student Success in Mathematics.
Michael Gage*, University of Rochester
John Travis, Mississippi College
Arnold Pizer, University of Rochester
Vicki Roth, University of Rochester
Douglas Ensley, Mathematical Association of America
□ 2:00 p.m.
MODULE($S^2$): Mathematics of Doing, Understanding, Learning and Educating for Secondary Schools.
Alyson Lischka*, Middle Tennessee State University
Andrew Ross, Eastern Michigan University
Yvonne Lai, University of Nebraska-Lincoln
Brynja Kohler, Utah State University
Jason Aubrey, University of Arizona
Jeremy F. Strayer, Middle Tennessee State University
Stephanie Casey, Eastern Michigan University
Cynthia Anhalt, University of Arizona
Howard Gobstein, Association of Public and Land-Grant Universities
□ 2:00 p.m.
Collaborative Research: Improving Conceptual Understanding of Multivariable Calculus Through Visualization Using CalcPlot3D.
Paul Seeburger*, Monroe Community College
Monica VanDieren, Robert Morris University
Deborah Moore-Russo, State University of New York at Buffalo
□ 2:00 p.m.
Transforming Students' Mathematical Experiences: Advancing Quality Teaching with Reliability at Scale.
Ann Edwards*, Carnegie Foundation for the Advancement of Teaching
Anthony Bryk, Carnegie Foundation for the Advancement of Teaching
Alicia Grunow, Carnegie Foundation for the Advancement of Teaching
James Stigler, UCLA
□ 2:00 p.m.
Scaling Up through Networked Improvement (SUNI): Testing a practical theory about improving math outcomes for developmental students at scale.
Ann Edwards*, Carnegie Foundation for the Advancement of Teaching
Christopher Thorn, Carnegie Foundation for the Advancement of Teaching
Karon Klipple, Carnegie Foundation for the Advancement of Teaching
Donald Peurach, Carnegie Foundation for the Advancement of Teaching
□ 2:00 p.m.
Collaborative Research: Attaining Excellence in Secondary Mathematics Clinical Experiences with a Lens on Equity.
Marilyn Strutchens*, Auburn University
Ruthmae Sears, University of South Florida
□ 2:00 p.m.
UTMOST: Undergraduate Teaching in Mathematics with Open Software and Textbooks.
Robert Beezer*, University of Puget Sound
David Farmer, American Institute of Mathematics
Tom Judson, Stephen F. Austin State University
Kent Morrison, American Institute of Mathematics
Vilma Mesa, University of Michigan
Angeliki Mali, University of Michigan
Susan Lynds, University of Colorado
□ 2:00 p.m.
Guide to Evidenced-Based Instructional Practices in Undergraduate Mathematics.
Martha Abell, Georgia Southern University
Linda Braddy, Tarrant County College
Doug Ensley*, Mathematical Association of America
Lew Ludwig, Denison University
Hortensia Soto-Johnson, University of Northern Colorado
□ 2:00 p.m.
Professional Development Emphasizing Data-Centered Resources and Pedagogies for Instructors of Undergraduate Introductory Statistics.
Mike Brilleslyper, United States Air Force Academy
Jenna Carpenter, Campbell University
Doug Ensley*, Mathematical Association of America
Danny Kaplan, Macalester College
Kate Kozak, Coconino Community College
□ 2:00 p.m.
The Mathematical Education of Teachers as an Application of Undergraduate Mathematics.
James Alvarez, University of Texas at Arlington
Beth Burroughs, Montana State University
Doug Ensley*, Mathematical Association of America
Nancy Neudauer, Pacific University
James Tanton, Mathematical Association of America
□ 2:00 p.m.
Supporting and Sustaining Scholarly Mathematical Teaching.
Larissa Schroeder*, University of Hartford
David Miller, University of Hartford
Mako Haruta, University of Hartford
□ 2:00 p.m.
Transforming Undergraduate Statistics Education at Primarily Undergraduate Institutions through Experiential Learning.
Tracy Morris*, University of Central Oklahoma
Cynthia Murray, University of Central Oklahoma
Tyler Cook, University of Central Oklahoma
□ 2:00 p.m.
Data Integration in Undergraduate Mathematics Education.
Paul Wenger*, Rochester Institute of Technology
Nicole Juersivich, Nazareth College
Matthew Hoffman, Rochester Institute of Technology
Carl Lutzer, Rochester Institute of Technology
□ 2:00 p.m.
Emphasizing Applications in Differential Equations (a SUMMIT-P collaboration).
Rebecca Segal*, Virginia Commonwealth University
Afroditi Filippas, Virginia Commonwealth University
□ 2:00 p.m.
Collaborative Research: Maplets for Calculus.
Philip B. Yasskin*, Texas A&M University
Douglas B. Meade, University of South Carolina
Matthew Barry, Texas A&M Engineering Extension Service
Andrew Crenwelge, Texas A&M University
Joseph Martinson, Texas A&M University
Matthew Weihing, Texas A&M University
□ 2:00 p.m.
2+1 STEM Scholars Program at Solano Community College.
Genele G. Rhoads*, Solano Community College
Audrey Rose de Leon, Solano Community College
Joshua Orosco, Solano Community College
Chelsea Breaw, Solano Community College
□ 2:00 p.m.
Enhancing Academic Achievement and Career Preparation for Scholars in Computer Science, Mathematics, and Engineering.
Qing Wang*, Shepherd University
Zhijun Wang, Shepherd University
□ 2:00 p.m.
Ensuring Early Mathematics Success for STEM Majors.
Amanda L Hattaway*, Wentworth Institute of Technology
Emma Smith Zbarsky, Wentworth Institute of Technology
Joan Giblin, Wentworth Institute of Technology
Driscoll Fred, Wentworth Institute of Technology
□ 2:00 p.m.
Serving as a Peer Mentor Promotes Reflective Mathematical Pedagogy.
RaKissa D Manzanares*, University of Colorado Denver
Michael Ferrara, University of Colorado Denver
Michael Jacobson, University of Colorado Denver
Gary Olson, University of Colorado Denver
Brandy Bourdeaux, University of Colorado Denver
□ 2:00 p.m.
ASSESSMENT: Transforming the Silent Killer of Learning to an Active Booster of Learning.
Frank Wattenberg*, United States Military Academy
Kristin Arney, United States Military Academy
John Bacon, United States Military Academy
Kayla Blyman, United States Military Academy
Lisa Bromberg, United States Military Academy
David Delcuadro-Zimmerman, United States Military Academy
David Harness, United States Military Academy
Scott Warnke, United States Military Academy
Sarah Wohlberg, United States Military Academy
□ 2:00 p.m.
Transforming Linear Algebra Education with GeoGebra Applets.
James D. Factor*, Alverno College
Susan Pustejovsky, Alverno College
□ 2:00 p.m.
Collaborative Research: Investigating Student Learning and Sense-Making from Instructional Calculus Videos.
Aaron Weinberg*, Ithaca College
Matt Thomas, Ithaca College
Michael Tallman, Oklahoma State University
Jason Martin, University of Central Arkansas
□ 2:00 p.m.
Students' Understanding of Vectors and Cross Products: Results from a Series of Visualization Tasks Using CalcPlot3D.
Monica VanDieren*, Robert Morris University
Deborah Moore-Russo, State University of New York at Buffalo
Paul Seeburger, Monroe Community College
□ 2:00 p.m.
Using Bricklayer Coding and Visual Art to Engage Students in Learning Mathematics.
Betty Love*, University of Nebraska -- Omaha
Michael Matthews, University of Nebraska -- Omaha
Victor Winter, University of Nebraska -- Omaha
Michelle Friend, University of Nebraska -- Omaha
□ 2:00 p.m.
MPWR-ing Women in RUME: Continuing Support.
Stacy Musgrave*, Cal Poly Pomona
Jess Ellis, Colorado State University
Kathleen Melhuish, Texas State University
Eva Thanheiser, Portland State University
Megan Wawro, Virginia Tech
□ 2:00 p.m.
CSUN NSF Teaching Fellowship Program.
Kellie Michele Evans*, California State University, Northridge
Alina Lee, Granada Hills Charter High School
□ 2:00 p.m.
Designing Learning Activities.
Ivona Grzegorczyk*, California State University Channel Islands
□ 2:00 p.m.
College Algebra: Adding Real-World Applications and Interactivity (a SUMMIT-P collaboration).
Tao Chen*, City University of New York-LaGuardia Community College
Glenn Henshaw, City University of New York-LaGuardia Community College
Soloman Kone, City University of New York-LaGuardia Community College
Choon Shan Lai, City University of New York-LaGuardia Community College
□ 2:00 p.m.
Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL).
David C. Webb*, University of Colorado Boulder
Janet Bowers, San Diego State University
Matt Voigt, San Diego State University
Nancy Kress, University of Colorado Boulder
□ 2:00 p.m.
Attracting and Retaining Scholars in the Mathematical Sciences.
Alexandra Kurepa*, North Carolina Agricultural & Technical State University
A. Giles Warrack, North Carolina Agricultural & Technical State University
Guoqing Tang, North Carolina Agricultural & Technical State University
Janis Oldham, North Carolina Agricultural & Technical State University
□ 2:00 p.m.
Reviving Calculus For Engineering Majors(a SUMMIT-P collaborative).
Shahrooz Moosavizadeh*, Norfolk State University
Rhonda D. Fitzgerald, Norfolk State University
• Thursday January 11, 2018, 2:15 p.m.-3:05 p.m.
AMS Invited Address
Algebraic structures on polytopes.
Room 6AB, Upper Level, San Diego Convention Center
Federico Ardila*, San Francisco State University
Marcelo Aguiar, Cornell University
• Thursday January 11, 2018, 2:30 p.m.-4:15 p.m.
A mindbending mixture of math and trivia.
Room 6D, Upper Level, San Diego Convention Center
Andy Niedermaier, Jane Street Capital
• Thursday January 11, 2018, 2:30 p.m.-3:55 p.m.
AMS-MAA Joint Committee on TAs and Part-Time Instructors Panel
Teaching-Focused Faculty at Research Institutions
Room 1B, Upper Level, San Diego Convention Center
Angela Kubena, University of Michigan
Jean Marie Linhart, Central Washington University
Thomas Roby, University of Connecticut
Michael Weingart, Rutgers University
Thomas Roby, University of Connecticut
Amy Cohen, Rutgers University
John Eggers, University of California San Diego
Ellen Goldstein, Boston College
Robin Gottlieb, Harvard University
Amit Savkar, University of Connecticut
• Thursday January 11, 2018, 2:35 p.m.-3:55 p.m.
MAA Panel
The Dolciani Award: Mathematicians in K-16 Education
Room 2, Upper Level, San Diego Convention Center
David Stone, Georgia Southern University dstone@georgiasouthern.edu
Will Abram, Hillsdale College
Ken Gross, University of Vermont
Bill Hawkins, University of the District of Columbia
Glenn Stevens, Boston University
Ann Watkins, California State Northridge
Susan Wildstrom, Walt Whitman HS, Bethesda MD
Jim Lewis,
Alan Schoenfeld,
Tatiana Shubin,
• Thursday January 11, 2018, 2:35 p.m.-3:55 p.m.
MAA Panel
What is a "Math Center" and What Can it do For Your Department?
Room 1A, Upper Level, San Diego Convention Center
Christina Lee, Oxford College of Emory University christina.lee@emory.edu
Jason Aubrey, University of Arizona
Jason Aubrey, University of Arizona
Christina Lee, Oxford College of Emory University
Rosalie Belanger-Rioux, Harvard University
WITHDRAWN: Kaitlyn Gingras, Trinity College
• Thursday January 11, 2018, 2:35 p.m.-3:55 p.m.
MAA Workshop
Writing Pedagogical and Expository Papers
Room 5A, Upper Level, San Diego Convention Center
Janet Beery, University of Redlands
Matt Boelkins, Grand Valley State University boelkinm@gvsu.edu
Susan Jane Colley, Oberlin College
Joanna Ellis-Monaghan, St Michael's College
Brian Hopkins, St Peter's University
Michael Jones, Mathematical Reviews
Gizem Karaali, Pomona College
Marjorie Senechal, Smith College
Brigitte Servatius, Worcester Polytechnic Institute
• Thursday January 11, 2018, 2:35 p.m.-3:55 p.m.
SIAM-MAA-AMS Panel
Multiple Paths to Mathematics Careers in Business, Industry and Government (BIG)
Room 8, Upper Level, San Diego Convention Center
Allen Butler, Daniel H. Wagner Associates, Inc.
Rachel Levy, Harvey Mudd College
Karen Saxe, American Mathematical Society
Suzanne Weekes, Worcester Polytechnic Institute
Rachel Levy, Harvey Mudd College and SIAM
Joe Callender, Ernst & Young
Skip Garibaldi, Center for Communications Research, La Jolla
Genetha Gray, Intel
Tasha Inniss, INFORMS and Former Deputy Division Director, NSF/HRD
Rolando Navarro, Options Clearing Corporation
Bryan Williams, Space and Naval Warfare Systems Command
• Thursday January 11, 2018, 3:10 p.m.-4:20 p.m.
Project NExT Panel
Assessing and Addressing Diverse Mathematical Backgrounds in the Classroom
Room 6F, Upper Level, San Diego Convention Center
Sungwon Ahn, Roosevelt University
Angelynn Alvarez, State University of New York Potsdam
Kevin Gerstle, Oberlin College
Emily Herzig, Texas Christian University
Kristin Camenga, Juniata College
Cynthia Flores, California State Channel Islands
Adam Giambrone, University of Connecticut
Edray Goins, Purdue University
Judy Holdener, Kenyon College
Anthony Rizzie, University of Connecticut
Michael Young, Iowa State University
• Thursday January 11, 2018, 3:20 p.m.-4:10 p.m.
AMS Invited Address
Searching for hyperbolicity.
Room 6AB, Upper Level, San Diego Convention Center
Ruth Charney*, Brandeis University
• Thursday January 11, 2018, 3:25 p.m.-4:10 p.m.
SIGMAA on Math Circles for Students and Teachers Business Meeting
Room 31B, Upper Level, San Diego Convention Center
• Thursday January 11, 2018, 3:45 p.m.-4:10 p.m.
MAA General Contributed Paper Session on Logic and Foundations
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Thursday January 11, 2018, 4:25 p.m.-5:25 p.m.
Joint Prize Session
Room 6AB, Upper Level, San Diego Convention Center
• Thursday January 11, 2018, 5:30 p.m.-6:30 p.m.
Joint Prize Session Reception
Lobby outside Room 6AB, Upper Level, San Diego Convention Center
• Thursday January 11, 2018, 5:30 p.m.-7:00 p.m.
MAA Two-Year College Reception
Point Loma/Solana Room, 1st Floor, South Twr, Marriott Marquis San Diego Marina
• Thursday January 11, 2018, 5:30 p.m.-6:00 p.m.
SIGMAA on the Philosophy of Mathematics (POM SIGMAA) Reception
Room 5B, Upper Level, San Diego Convention Center
Bonnie Gold,
• Thursday January 11, 2018, 6:00 p.m.-7:00 p.m.
SIGMAA on Mathematical and Computational Biology Reception and Business Meeting
Room 6D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University
• Thursday January 11, 2018, 6:00 p.m.-6:15 p.m.
SIGMAA on the Philosophy of Mathematics (POM SIGMAA) Business Meeting
Room 5B, Upper Level, San Diego Convention Center
Bonnie Gold,
• Thursday January 11, 2018, 6:15 p.m.-7:00 p.m.
SIGMAA on the Philosophy of Mathematics (POM SIGMAA) Guest Lecture
Room 5B, Upper Level, San Diego Convention Center
• Thursday January 11, 2018, 7:00 p.m.-7:45 p.m.
SIGMAA on Mathematical and Computational Biology Guest Lecture
Room 6D, Upper Level, San Diego Convention Center
• Thursday January 11, 2018, 7:30 p.m.-8:30 p.m.
AMS Panel, sponsored by the U.S. National Committee for Mathematics
ICM 2018 in Rio de Janeiro - The First International Congress of Mathematicians in the Southern Hemisphere
Room 6E, Upper Level, San Diego Convention Center
Eric Friedlander, American Mathematical Society
Marcelo Viana, Instituto Nacional de Matemática Pura e Aplicada
Friday January 12, 2018
• Friday January 12, 2018, 7:30 a.m.-4:00 p.m.
Joint Meetings Registration
Exhibit Hall B1, Ground Level, San Diego Convention Center
• Friday January 12, 2018, 7:30 a.m.-10:55 a.m.
AMS Contributed Paper Session on Applied Mathematics, I
Room 19, Mezzanine Level, San Diego Convention Center
• Friday January 12, 2018, 7:30 a.m.-5:30 p.m.
Email Center
Exhibit Hall B1, Ground Level, San Diego Convention Center
• Friday January 12, 2018, 7:40 a.m.-10:55 a.m.
MAA Session on Mathematical Experiences and Projects in Business, Industry, and Government (BIG)
Room 15A, Mezzanine Level, San Diego Convention Center
Allen Butler, Wagner Associates
Bill Fox, Naval Post Graduate School wpfox@nps.edu
• Friday January 12, 2018, 7:45 a.m.-10:55 a.m.
AMS Contributed Paper Session on Commutative Algebra
Room 13, Mezzanine Level, San Diego Convention Center
• Friday January 12, 2018, 7:45 a.m.-10:55 a.m.
AMS Contributed Paper Session on Operator Algebras and Function Spaces
Room 18, Mezzanine Level, San Diego Convention Center
• Friday January 12, 2018, 7:45 a.m.-10:55 a.m.
AMS Contributed Paper Session on Topology and Geometry
Room 12, Mezzanine Level, San Diego Convention Center
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Advances in Applications of Differential Equations to Disease Modeling, II
Room 29A, Upper Level, San Diego Convention Center
Libin Rong, Oakland University
Elissa Schwartz, Washington State University
Naveen K. Vaidya, San Diego State University nvaidya.anyol@gmail.com
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Algebraic, Discrete, Topological and Stochastic Approaches to Modeling in Mathematical Biology, II
Room 29D, Upper Level, San Diego Convention Center
Olcay Akman, Illinois State University
Timothy D. Comar, Benedictine University tcomar@ben.edu
Daniel Hrozencik, Chicago State University
Raina Robeva, Sweet Briar College
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Boundaries for Groups and Spaces, II
Room 16B, Mezzanine Level, San Diego Convention Center
Joseph Maher, CUNY College of Staten Island joseph.maher@csi.cuny.edu
Genevieve Walsh, Tufts University
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Combinatorics and Geometry, II
Room 7A, Upper Level, San Diego Convention Center
Federico Ardila, San Francisco State University
Anastasia Chavez, MSRI and University of California, Davis
Laura Escobar, University of Illinois Urbana Champaign lescobar@illinois.edu
• Friday January 12, 2018, 8:00 a.m.-10:20 a.m.
AMS Special Session on Discrete Neural Networking and Applications, II
Room 33A, Upper Level, San Diego Convention Center
Murat Adivar, Fayetteville State University
Michael A. Radin, Rochester Institute of Technology michael.radin@rit.edu
Youssef Raffoul, University of Dayton
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Dynamical Algebraic Combinatorics, I
Room 16A, Mezzanine Level, San Diego Convention Center
James Propp, University of Massachusetts, Lowell
Tom Roby, University of Connecticut
Jessica Striker, North Dakota State University jessica.striker@ndsu.edu
Nathan Williams, University of California Santa Barbara
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Ergodic Theory and Dynamical Systems--to Celebrate the Work of Jane Hawkins, II
Room 17B, Mezzanine Level, San Diego Convention Center
Julia Barnes, Western Carolina University
Rachel Bayless, Agnes Scott College
Emily Burkhead, Duke University
Lorelei Koss, Dickinson College koss@dickinson.edu
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Free Convexity and Free Analysis, I
Room 29B, Upper Level, San Diego Convention Center
J. William Helton, University of California, San Diego
Igor Klep, University of Auckland igor.klep@auckland.ac.nz
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on History of Mathematics, IV
Room 10, Upper Level, San Diego Convention Center
Sloan Despeaux, Western Carolina University
Jemma Lorenat, Pitzer College
Clemency Montelle, University of Canterbury
Daniel Otero, Xavier University otero@xavier.edu
Adrian Rice, Randolph-Macon College
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on If You Build It They Will Come: Presentations by Scholars in the National Alliance for Doctoral Studies in the Mathematical Sciences, I
Room 33C, Upper Level, San Diego Convention Center
David Goldberg, Purdue University
Phil Kutzko, University of Iowa philip-kutzko@uiowa.edu
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Mathematical Information in the Digital Age of Science, III
Room 9, Upper Level, San Diego Convention Center
Patrick Ion, University of Michigan pion@umich.edu
Olaf Teschke, zbMath Berlin
Stephen Watt, University of Waterloo
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Mathematical Modeling of Natural Resources, I
Room 30A, Upper Level, San Diego Convention Center
Shandelle M. Henson, Andrews University henson@andrews.edu
Natali Hritonenko, Prairie View A&M University
• Friday January 12, 2018, 8:00 a.m.-10:45 a.m.
AMS Special Session on Mathematical Relativity and Geometric Analysis, I
Room 31A, Upper Level, San Diego Convention Center
James Dilts, University of California, San Diego jdilts@ucsd.edu
Michael Holst, University of California, San Diego
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Noncommutative Algebras and Noncommutative Invariant Theory, I
Room 17A, Mezzanine Level, San Diego Convention Center
Ellen Kirkman, Wake Forest University
James Zhang, University of Washington zhang@math.washington.edu
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Nonlinear Evolution Equations of Quantum Physics and Their Topological Solutions, I
Room 30B, Upper Level, San Diego Convention Center
Stephen Gustafson, University of British Columbia
Israel Michael Sigal, University of Toronto im.sigal@utoronto.ca
Avy Soffer, Rutgers University
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Quantum Link Invariants, Khovanov Homology, and Low-dimensional Manifolds, I
Room 30E, Upper Level, San Diego Convention Center
Diana Hubbard, University of Michigan
Christine Ruey Shan Lee, University of Texas at Austin clee@math.utexas.edu
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Recent Trends in Analysis of Numerical Methods of Partial Differential Equations, II
Room 29C, Upper Level, San Diego Convention Center
Sara Pollock, Wright State University
Leo Rebholz, Clemson University rebholz@clemson.edu
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
MAA Invited Paper Session on Research in Improving Undergraduate Mathematical Sciences Education: Examples Supported by the National Science Foundation's IUSE: EHR Program
Room 3, Upper Level, San Diego Convention Center
Ron Buckmire, NSF, Directorate for Education & Human Resources, Division of Undergraduate Education rbuckmir@nsf.gov
Sandra Richardson, NSF, Directorate for Education & Human Resources, Division of Undergraduate Education
Lee Zia, NSF, Directorate for Education & Human Resources, Division of Undergraduate Education
Karen Keene, National Science Foundation
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Stochastic Processes, Stochastic Optimization and Control, Numerics and Applications, II
Room 30D, Upper Level, San Diego Convention Center
Hongwei Mei, University of Central Florida
Zhixin Yang, Ball State University
Quan Yuan, Ball State University
Guangliang Zhao, GE Global Research dr.gzhao@gmail.com
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Topological Data Analysis, II
Room 6E, Upper Level, San Diego Convention Center
Henry Adams, Colorado State University henry.adams@colostate.edu
Gunnar Carlsson, Stanford University
Mikael Vejdemo-Johansson, CUNY College of Staten Island
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Visualization in Mathematics: Perspectives of Mathematicians and Mathematics Educators, I
Room 30C, Upper Level, San Diego Convention Center
Karen Allen Keene, North Carolina State University
Mile Krajcevski, University of South Florida mile@mail.usf.edu
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
AMS-AWM Special Session on Women in Symplectic and Contact Geometry and Topology, I
Room 33B, Upper Level, San Diego Convention Center
Bahar Acu, Northwestern University baharacu@gmail.com
Ziva Myer, Duke University
Yu Pan, Massachusetts Institute of Technology
• Friday January 12, 2018, 8:00 a.m.-10:55 a.m.
MAA Session on Arts and Mathematics: The Interface, III
Room 1A, Upper Level, San Diego Convention Center
Douglas Norton, Villanova University douglas.norton@villanova.edu
• Friday January 12, 2018, 8:00 a.m.-10:55 a.m.
MAA Session on Inquiry-Based Teaching and Learning, I
Room 4, Upper Level, San Diego Convention Center
Eric Kahn, Bloomsburg University
Brian P. Katz, Augustana College briankatz@augustana.edu
Victor Piercey, Ferris State University
• Friday January 12, 2018, 8:00 a.m.-9:40 a.m.
MAA General Contributed Paper Session on Mentoring
Room 28E, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Friday January 12, 2018, 8:00 a.m.-10:55 a.m.
MAA General Contributed Paper Session on Teaching and Learning Introductory Mathematics, I
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
MAA Session on Philosophy of Mathematics as Actually Practiced
Room 6D, Upper Level, San Diego Convention Center
Sally Cockburn, Hamilton College
Thomas Drucker, University of Wisconsin-Whitewater
Bonnie Gold, Monmouth University (emerita) bgold@monmouth.edu
• Friday January 12, 2018, 8:00 a.m.-10:55 a.m.
MAA Session on Research in Undergraduate Mathematics Education (RUME), III
Room 14B, Mezzanine Level, San Diego Convention Center
Stacy Brown, California State Polytechnic University
Megan Wawro, Virginia Tech mwawro@vt.edu
Aaron Weinberg, Ithaca College
• Friday January 12, 2018, 8:00 a.m.-10:55 a.m.
MAA Session on The Advancement of Open Educational Resources, I
Room 31C, Upper Level, San Diego Convention Center
Benjamin Atchinson, Framingham State University batchison@framingham.edu
• Friday January 12, 2018, 8:00 a.m.-10:55 a.m.
MAA Session on The Teaching and Learning of Undergraduate Ordinary Differential Equations, I
Room 14A, Mezzanine Level, San Diego Convention Center
Christopher S. Goodrich, Creighton Preparatory School cgood@prep.creighton.edu
Beverly H. West, Cornell University
• Friday January 12, 2018, 8:00 a.m.-10:50 a.m.
SIAM Minisymposium on Advances in Finite Element Approximation
Room 11A, Upper Level, San Diego Convention Center
Constantin Bacuta, University of Delaware bacuta@udel.edu
Ana Maria Soane, United States Naval Academy soane@usna.edu
• Friday January 12, 2018, 8:00 a.m.-6:00 p.m.
Project NExT Workshop
Room 6F, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 8:00 a.m.-9:20 a.m.
MAA Panel
Teaching Mathematics Content to Prospective Elementary Teachers: Strategies and Opportunities
Room 2, Upper Level, San Diego Convention Center
Lynn C. Hart, Georgia State University lhart@gsu.edu
Christine Browning, Western Michigan University
Ziv Feldman, Boston University
Lynn C. Hart, Georgia State University
Jennifer Holm, University of Alberta
Susan Oesterle, Douglas College
• Friday January 12, 2018, 8:00 a.m.-5:30 p.m.
Employment Center
Exhibit Hall A, Ground Level, San Diego Convention Center
• Friday January 12, 2018, 8:20 a.m.-10:55 a.m.
MAA Session on Innovative Teaching Practices in Number Theory, II
Room 15B, Mezzanine Level, San Diego Convention Center
Patrick Rault, University of Arizona
Thomas Hagedorn, The College of New Jersey hagedorn@tcnj.edu
Mark Kozek, Whittier College
• Friday January 12, 2018, 8:30 a.m.-10:30 a.m.
AMS-MAA Grad School Fair
Undergrads! Take this opportunity to meet representatives from mathematical science graduate programs.
Exhibit Hall B2, Ground Level, San Diego Convention Center
• Friday January 12, 2018, 9:00 a.m.-9:50 a.m.
MAA Invited Address
Toy models.
Room 6AB, Upper Level, San Diego Convention Center
Tadashi Tokieda*, Stanford University
• Friday January 12, 2018, 9:00 a.m.-9:50 a.m.
ASL Invited Address
0,1-Laws and pseudofiniteness of $\aleph_0$-categorical theories.
Room 7B, Upper Level, San Diego Convention Center
Cameron Donnay Hill*, Wesleyan University
• Friday January 12, 2018, 9:00 a.m.-11:00 a.m.
MAA Minicourse #1: Part B
Introduction to Process Oriented Guided Inquiry Learning (POGIL) in Mathematics Courses
Room 28A, Upper Level, San Diego Convention Center
Catherine Beneteau, University of South Florida
Jill E. Guerra, University of Arkansas Fort Smith
Laurie Lenz, Marymount University
• Friday January 12, 2018, 9:00 a.m.-11:00 a.m.
MAA Minicourse #2: Part B
Teaching Introductory Statistics Using the Guidelines from the American Statistical Association
Room 28C, Upper Level, San Diego Convention Center
Carolyn K. Cuff, Westminster College
• Friday January 12, 2018, 9:00 a.m.-10:30 a.m.
AMS Panel
Historical Chief Editors of the Notices
Room 1B, Upper Level, San Diego Convention Center
Frank Morgan, American Mathematical Society fmorgan@williams.edu
Harold Boas,
Andy Magid,
Frank Morgan, American Mathematical Society
Hugo Rossi,
• Friday January 12, 2018, 9:30 a.m.-5:30 p.m.
Exhibits and Book Sales
Exhibit Hall B1, Ground Level, San Diego Convention Center
• Friday January 12, 2018, 9:35 a.m.-10:55 a.m.
MAA Panel
The New AP Calculus Curriculum - The First Round of Testing
Room 2, Upper Level, San Diego Convention Center
James Sellers, Pennsylvania State University jxs23@psu.edu
Gail Burrill, Michigan State University
Stephen Davis, Davidson College
Ben Hendrik, College Board
James Sellers, Pennsylvania State University
• Friday January 12, 2018, 9:45 a.m.-10:55 a.m.
MAA General Contributed Paper Session on Applied Mathematics, III
Room 28E, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Friday January 12, 2018, 9:55 a.m.-11:00 a.m.
Project NExT Panel
You Can Lead a Horse to Water... : Nurturing Motivation in the Classroom
Room 6F, Upper Level, San Diego Convention Center
Kyle Golenbiewski, University of North Alabama
Emily Olson, Millikin University
Marcos Ortiz, Grinnell College
Scott Zinzer, Aurora University
Jacqueline Jensen-Vallin, Lamar University
WITHDRAWN: Karen Saxe, Macalester College
Suzanne Dorée, Augsburg University
NEW: Steven Schlicker, Grand Valley State University
• Friday January 12, 2018, 10:00 a.m.-10:50 a.m.
ASL Invited Address
Non-elementary classification theory.
Room 7B, Upper Level, San Diego Convention Center
Sebastien Vasey*, Harvard University
• Friday January 12, 2018, 10:05 a.m.-10:55 a.m.
AMS Invited Address
Emergent phenomena in random structures and algorithms.
Room 6AB, Upper Level, San Diego Convention Center
Dana Randall*, Georgia Institute of Technology
• Friday January 12, 2018, 10:30 a.m.-11:00 a.m.
Radical Dash Prize Session
Room 5A, Upper Level, San Diego Convention Center
Stacey Muir, University of Scranton
Janine Janoski, Kings College
• Friday January 12, 2018, 11:10 a.m.-12:00 p.m.
AMS-MAA Invited Address
Wow, so many minimal surfaces!
Room 6AB, Upper Level, San Diego Convention Center
André Neves*, University of Chicago
• Friday January 12, 2018, 1:00 p.m.-1:50 p.m.
AMS Colloquium Lectures: Lecture III
Proving analytic inequalities.
Room 6AB, Upper Level, San Diego Convention Center
Avi Wigderson*, Institute for Advanced Study
• Friday January 12, 2018, 1:00 p.m.-4:45 p.m.
Current Events Bulletin
Room 6E, Upper Level, San Diego Convention Center
David Eisenbud, MSRI and UC Berkeley de@msri.org
• Friday January 12, 2018, 1:00 p.m.-1:50 p.m.
MAA Lecture for Students
HOW MANY DEGREES ARE IN A MARTIAN CIRCLE? And other human (and non-human) questions one should ask about everyday mathematics.
Room 6C, Upper Level, San Diego Convention Center
James Tanton*, Mathematical Association of America
• Friday January 12, 2018, 1:00 p.m.-6:50 p.m.
AMS Special Session on Advances in Operator Algebras, I
Room 33A, Upper Level, San Diego Convention Center
Marcel Bischoff, Vanderbilt University
Ian Charlesworth, University of California, Los Angeles
Brent Nelson, University of California, Berkeley brent@math.berkeley.edu
Sarah Reznikoff, Kansas State University
□ 1:00 p.m.
Separable exact C$^\ast$-algebras non-isomorphic to their opposite algebras.
Maria Grazia Viola*, Lakehead University
□ 1:30 p.m.
A von Neumann-type inequality with universal C*-algebras.
Kristin Courtney*, University of Virginia
□ 2:00 p.m.
□ 2:30 p.m.
Maximal amenable subalgebras in $q$-Gaussian factors.
Sandeepan Parekh*, Vanderbilt University
Koichi Shimada, Kyoto University
Chenxu Wen, University of California, Riverside
□ 3:00 p.m.
Orthogonal free quantum group factors are strongly 1-bounded.
Michael Brannan*, Texas A&M University
Roland Vergnioux, University of Caen
□ 3:30 p.m.
Basic examples of bi-free product.
Wonhee Na*, Texas A&M University
□ 4:00 p.m.
A weakly-defined derivation $\delta^D_w$ and kernels of $(\delta^D_w)^n$.
Lara Ismert*, University of Nebraska-Lincoln
□ 4:30 p.m.
Free transport for interpolated free group factors.
Michael Hartglass*, Santa Clara University
Brent Nelson, UC Berkeley
□ 5:00 p.m.
Two new settings for examples of von Neumann dimension.
Lauren C. Ruth*, University of California, Riverside
□ 5:30 p.m.
An angle between intermediate subfactors and its rigidity.
Keshab Chandra Bakshi, The Institute of Mathematical Sciences
Sayan Das, Vanderbilt University
Zhengwei Liu*, Harvard University
Yunxiang Ren, Tennessee state university
□ 6:00 p.m.
The geometry of conformal nets.
James Tener*, UC Santa Barbara
□ 6:30 p.m.
Joint spectral distributions in finite von Neumann algebras.
Ian Charlesworth, University of California --- San Diega
Ken Dykema*, Texas A&M University
Fedor Sukochev, University of New South Wales
Dmitriy Zanin, University of New South Wales
• Friday January 12, 2018, 1:00 p.m.-5:50 p.m.
AMS Special Session on Arithmetic Dynamics, II
Room 16A, Mezzanine Level, San Diego Convention Center
Robert L. Benedetto, Amherst College
Benjamin Hutz, Saint Louis University
Jamie Juul, Amherst College jjuul@amherst.edu
Bianca Thompson, Harvey Mudd College
• Friday January 12, 2018, 1:00 p.m.-5:50 p.m.
AMS Special Session on Combinatorial Commutative Algebra and Polytopes, II
Room 16B, Mezzanine Level, San Diego Convention Center
Robert Davis, Michigan State University davisr@math.msu.edu
Liam Solus, KTH Royal Institute of Technology
• Friday January 12, 2018, 1:00 p.m.-5:50 p.m.
AMS Special Session on Diophantine Approximation and Analytic Number Theory in Honor of Jeffrey Vaaler, I
Room 17B, Mezzanine Level, San Diego Convention Center
Shabnam Akhtari, University of Oregon
Lenny Fukshansky, Claremont McKenna College lenny@cmc.edu
Clayton Petsche, Oregon State University
• Friday January 12, 2018, 1:00 p.m.-5:50 p.m.
AMS Special Session on Emergent Phenomena in Discrete Models
Room 9, Upper Level, San Diego Convention Center
Dana Randall, Georgia Institute of Technology randall@cc.gatech.edu
Andrea Richa, Arizona State University
• Friday January 12, 2018, 1:00 p.m.-3:00 p.m.
MAA Minicourse #3: Part B
Flipping your Mathematics Course using Open Educational Resources
Room 28A, Upper Level, San Diego Convention Center
Sarah Eichhorn, University of California, Irvine
David Farmer, American Institute of Mathematics
Jim Fowler, The Ohio State University
Petra Taylor, Dartmouth University
• Friday January 12, 2018, 1:00 p.m.-5:45 p.m.
AMS Special Session on Geometric Analysis, I
Room 7A, Upper Level, San Diego Convention Center
Davi Maximo, University of Pennsylvania dmaxim@math.upenn.edu
Lu Wang, University of Wisconsin-Madison
Xin Zhou, University of California Santa Barbara
• Friday January 12, 2018, 1:00 p.m.-3:00 p.m.
MAA Minicourse #4: Part B
How to Run Successful Math Circles for Students and Teachers
Room 28B, Upper Level, San Diego Convention Center
Jane Long, Stephen F. Austin State University
Brianna Donaldson, American Institute of Mathematics
Gabriella Pinter, University of Wisconsin-Milwaukee
Diana White, University of Colorado Denver and National Association of Math Circles
• Friday January 12, 2018, 1:00 p.m.-5:20 p.m.
AMS Special Session on If You Build It They Will Come: Presentations by Scholars in the National Alliance for Doctoral Studies in the Mathematical Sciences, II
Room 33C, Upper Level, San Diego Convention Center
David Goldberg, Purdue University
Phil Kutzko, University of Iowa philip-kutzko@uiowa.edu
□ 1:00 p.m.
The geometry of leukemic proliferation.
Reginald L. McGee*, Mathematical Biosciences Institute
Gregory K. Behbehani, The Ohio State University
Kevin R. Coombes, The Ohio State University
□ 1:30 p.m.
NEW TIME: Holomorphic Sectional Curvature and its Friends on Complex Manifolds.
Angelynn R Alvarez*, State University of New York at Potsdam
□ 2:00 p.m.
NEW TIME: Results concerning the spectrum of Noetherian rings.
Cory H Colbert*, Williams College
□ 2:30 p.m.
TALK CANCELLED: A mathematical approach to understanding the vibrations within a block subjected to freezing rocking.
Julia Anderson-Lee*, Iowa State University
Scott Hansen, Iowa State University
Sri Sritharan, Iowa State University
□ 3:00 p.m.
□ 3:30 p.m.
NEW TIME: A Method for Explicit Solution Formulas for Integrable Evolution Equations in 2+1 Dimensions.
Alicia Machuca*, Texas Woman's University
□ 4:00 p.m.
Totally Reflexive Modules.
Denise A Rangel Tracy*, Central Connecticut State University
□ 4:30 p.m.
Direct Method for Reconstructing Inclusions from Electrostatic Data.
Isaac Harris*, Texas A&M University
William Rundell, Texas A&M University
□ 5:00 p.m.
TALK CANCELLED: A new principal rank characteristic sequence.
Xavier Martinez-Rivera*, Auburn University
• Friday January 12, 2018, 1:00 p.m.-6:50 p.m.
AMS Special Session on Markov Chains, Markov Processes and Applications
Room 29D, Upper Level, San Diego Convention Center
Alan Krinik, California State Polytechnic University ackrinik@cpp.edu
Randall J. Swift, California State Polytechnic University
□ 1:00 p.m.
Cutoff for the random-to-random card shuffle.
Megan Bernstein*, Georgia Tech
Evita Nestoridi, Princeton University
□ 1:30 p.m.
Cutoff for a stratified random walk on the hypercube, related to a mysterious random walk on invertible matrices modulo 2.
Yuval Peres*, Microsoft Research
□ 2:00 p.m.
Matrix Properties of a Class of Birth-Death Chains and Processes.
Alan Krinik*, California State Polytechnic University, Pomona
Uyen Nguyen, California State Polytechnic University, Pomona
Ali Oudich, University of California, Irvine
Pedram Ostadhassanpanjehali, California State Polytechnic University, Pomona
Luis Cervantes, California State University, Long Beach
Chon In Luk, California State Polytechnic University, Pomona
Matthew McDonough, University of California, Santa Barbara
Jeffrey Yeh, California State Polytechnic University, Pomona
Lyheng Phey, California State Polytechnic University, Pomona
□ 2:30 p.m.
Random Walks in the Quarter Plane with Time-Varying Periodic Transition Rates.
Barbara H Margolius*, Cleveland State University
L Felipe Martins, Cleveland State University
□ 3:00 p.m.
Favorite sites of a persistent random walk on $\mathbb{Z}$.
Steven Noren*, Iowa State University
Arka Ghosh, Iowa State University
Alex Roitershtein, Iowa State University
□ 3:30 p.m.
The flashing Brownian ratchet and Parrondo's paradox.
Stewart N. Ethier*, University of Utah
Jiyeon Lee, Yeungnam University
□ 4:00 p.m.
Brownian particles interacting through their ranks.
Andrey Sarantsev*, University of California, Santa Barbara
□ 4:30 p.m.
A Winner Plays Model.
Sheldon Ross*, University of Southern California, Los Angeles, CA
Yang Cao, Univ. of Southern California, Los Angeles, CA
□ 5:00 p.m.
Dynamics of a Predator-Prey Model through Stochastic Methods.
Diana Curtis*, California State Polytechnic University, Pomona
Jennifer Switkes, California State Polytechnic University, Pomona
□ 5:30 p.m.
Network conditions for positive recurrence of stochastically modeled reaction networks and mixing times.
Jinsu Kim*, University of Wisconsin-Madison
David F Anderson, University of Wisconsin-Madison
□ 6:00 p.m.
□ 6:30 p.m.
Persistence of sums of correlated increments and clustering in cellular automata.
Hanbaek Lyu*, The Ohio State University, Department of Mathematics
David Sivakoff, The Ohio State University, Department of Statistics and Mathematics
• Friday January 12, 2018, 1:00 p.m.-5:50 p.m.
AMS Special Session on Mathematical Modeling of Natural Resources, II
Room 30A, Upper Level, San Diego Convention Center
Shandelle M. Henson, Andrews University henson@andrews.edu
Natali Hritonenko, Prairie View A&M University
• Friday January 12, 2018, 1:00 p.m.-5:50 p.m.
AMS Special Session on Mathematical Relativity and Geometric Analysis, II
Room 30D, Upper Level, San Diego Convention Center
James Dilts, University of California, San Diego jdilts@ucsd.edu
Michael Holst, University of California, San Diego
• Friday January 12, 2018, 1:00 p.m.-4:20 p.m.
AMS Special Session on Mathematics of Gravitational Wave Science, II
Room 30C, Upper Level, San Diego Convention Center
Andrew Gillette, University of Arizona agillette@math.arizona.edu
Nikki Holtzer, University of Arizona
• Friday January 12, 2018, 1:00 p.m.-6:50 p.m.
AMS Special Session on Network Science, II
Room 31A, Upper Level, San Diego Convention Center
David Burstein, Swarthmore College dburste1@swarthmore.edu
Franklin Kenter, United States Naval Academy
Feng Shi, University of North Carolina at Chapel Hill
• Friday January 12, 2018, 1:00 p.m.-5:50 p.m.
AMS Special Session on Noncommutative Algebras and Noncommutative Invariant Theory, II
Room 17A, Mezzanine Level, San Diego Convention Center
Ellen Kirkman, Wake Forest University
James Zhang, University of Washington zhang@math.washington.edu
□ 1:00 p.m.
The colored Jones polynomial as an invariant of $q-$Weyl algebras.
Mustafa Hajij, , University of South Florida
Jesse S. F. Levitt*, University of Southern California
□ 1:30 p.m.
Hopf algebra actions on some AS-regular algebras of small dimension.
Luigi Ferraro, Wake Forest University
Ellen Kirkman, Wake Forest University
W. Frank Moore*, Wake Forest University
Robert Won, Wake Forest University
□ 2:00 p.m.
Simple $\mathbb{Z}$-graded domains of Gelfand-Kirillov dimension 2.
Robert Won*, Wake Forest University
Calum Spicer, Imperial College London
□ 2:30 p.m.
Extra special fusion categories.
Henry J Tucker*, UC San Diego
□ 3:00 p.m.
Frobenius-Perron Theory of Modified ADE Bound Quiver Algebras.
Elizabeth Wicks*, University of Washington, Seattle, WA
□ 3:30 p.m.
Discussing a few Quadratic Quantum $\mathbb P^3$s.
Derek Tomlin*, U. Texas at Arlington
M. Vancliff, U. Texas at Arlington
□ 4:00 p.m.
Finite generation of cohomology rings of some pointed Hopf algebras in positive characteristic.
Van Cat Nguyen, Hood College
Xingting Wang*, Temple University
Sarah Witherspoon, Texas A&M University
□ 4:30 p.m.
On the structure of Connected Hopf Algebras containing a Semisimple Lie Algebra.
Daniel Yee*, Bradley University
□ 5:00 p.m.
Twisted tensor product algebras and resolutions.
Anne V. Shepler, University of North Texas
Sarah Witherspoon*, Texas A&M University
□ 5:30 p.m.
• Friday January 12, 2018, 1:00 p.m.-6:20 p.m.
AMS Special Session on Nonlinear Evolution Equations of Quantum Physics and Their Topological Solutions, II
Room 30B, Upper Level, San Diego Convention Center
Stephen Gustafson, University of British Columbia
Israel Michael Sigal, University of Toronto im.sigal@utoronto.ca
Avy Soffer, Rutgers University
• Friday January 12, 2018, 1:00 p.m.-3:50 p.m.
MAA Invited Paper Session on Polyhedra, Commemorating Magnus J. Wenninger
Room 3, Upper Level, San Diego Convention Center
Vincent Matsko, University of San Francisco vjmatsko@usfca.edu
• Friday January 12, 2018, 1:00 p.m.-3:00 p.m.
MAA Minicourse #5: Part B
Reach the World: Writing Math Op-Eds for a Post-Truth Culture
Room 28C, Upper Level, San Diego Convention Center
Kira Hamman, Pennsylvania State University, Mont Alto
Francis Su, Harvey Mudd College
• Friday January 12, 2018, 1:00 p.m.-6:20 p.m.
AMS Special Session on Research from the Rocky Mountain-Great Plains Graduate Research Workshop in Combinatorics, I
Room 29C, Upper Level, San Diego Convention Center
Michael Ferrara, University of Colorado Denver michael.ferrara@ucdenver.edu
Leslie Hogben, Iowa State University
Paul Horn, University of Denver
Tyrrell McAllister, University of Wyoming
□ 1:00 p.m.
Local Dimension and Size of a Poset.
Jinha Kim, Seoul National University
Ryan R. Martin, Iowa State University
Tomáš Masařík, Charles University
Warren Shull, Emory University
Heather C. Smith*, Georgia Institute of Technology
Andrew Uzzell, Grinnell College
Zhiyu Wang, University of South Carolina
□ 1:30 p.m.
Entire Colorability for a Class of Plane Graphs.
Axel Brandt*, Davidson College
Michael Ferrara, University of Colorado Denver
Nathan Graber, University of Colorado Denver
Stephen Hartke, University of Colorado Denver
Sarah Loeb, College of William and Mary
□ 2:00 p.m.
A $(5,5)$-coloring of $K_n$ with few colors.
Alex Cameron*, University of Illinois at Chicago
Emily Heath, University of Illinois at Urbana-Champaign
□ 2:30 p.m.
Edge-colored saturation for complete graphs.
Michael Ferrara, University of Colorado Denver
Daniel Johnston, Grand Valley State University
Sarah Loeb*, College of William and Mary
Florian Pfender, University of Colorado Denver
Alex Schulte, Iowa State University
Heather Smith, Georgia Institute of Technology
Eric Sullivan, University of Colorado Denver
Michael Tait, Carnegie Mellon University
Casey Tompkins, Alfred Renyi Institute of Mathematics
□ 3:00 p.m.
Saturation for Berge Hypergraphs.
Sean J English*, Western Michigan University
Nathan Graber, University of Colorado, Denver
Pamela Kirkpatrick, Lehigh University
Abhishek Methuku, Alfréd Rényi Institute of Mathematics
Eric Sullivan, University of Colorado, Denver
□ 3:30 p.m.
Universal partial words.
Bennet Goeckner, University of Kansas
Corbin Groothuis, University of Nebraska
Cyrus Hettle, Georgia Institute of Technology
Brian Kell, Google
Pamela Kirkpatrick, Lehigh University
Rachel Kirsch*, University of Nebraska
Ryan Solava, Vanderbilt University
□ 4:00 p.m.
Hunting Invisible Rabbits on the Hypercube.
Jessalyn Bolkema*, University of Nebraska - Lincoln
Corbin Groothuis, University of Nebraska - Lincoln
□ 4:30 p.m.
Spectral bounds for the connectivity of regular graphs with given order.
Aida Abiad, Department of Quantitative Economics, Maastricht University
Boris Brimkov*, Department of Computational and Applied Mathematics, Rice University
Xavier Martinez-Rivera, Department of Mathematics and Statistics, Auburn University
Suil O, Applied Mathematics and Statistics, The State University of New York Korea
Jingmei Zhang, Department of Mathematics, University of Central Florida
□ 5:00 p.m.
Degree conditions for small contagious sets in bootstrap percolation.
Michael Dairyko, Iowa State University
Michael Ferrara, University of Colorado Denver
Bernard Lidický, Iowa State University
Ryan R Martin, Iowa State University
Florian Pfender, University of Colorado Denver
Andrew J Uzzell*, Grinnell College
□ 5:30 p.m.
Throttling for Cops and Robbers.
Josh Carlson*, Iowa State University
□ 6:00 p.m.
Zero Forcing Polynomial for Cycles and Singly-Chorded Cycles.
Kirk Boyer, University of Denver
Boris Brimkov, Rice University
Sean English, Western Michigan University
Daniela Ferrero, Texas State University
Ariel Keller*, Emory University
Rachel Kirsch, University of Nebraska - Lincoln
Michael Phillips, University of Colorado Denver
Carolyn Reinhart, Iowa State University
• Friday January 12, 2018, 1:00 p.m.-6:45 p.m.
AMS Special Session on Strengthening Infrastructures to Increase Capacity Around K-20 Mathematics
Room 10, Upper Level, San Diego Convention Center
Brianna Donaldson, American Institute of Mathematics brianna@aimath.org
William Jaco, Oklahoma State University
Michael Oehrtman, Oklahoma State University
Levi Patrick, Oklahoma State Department of Education
• Friday January 12, 2018, 1:00 p.m.-5:50 p.m.
AMS Special Session on Topological Graph Theory: Structure and Symmetry, II
Room 30E, Upper Level, San Diego Convention Center
Jonathan L. Gross, Columbia University
Thomas W. Tucker, Colgate University ttucker@colgate.edu
• Friday January 12, 2018, 1:00 p.m.-5:50 p.m.
AMS-AWM Special Session on Women in Symplectic and Contact Geometry and Topology, II
Room 33B, Upper Level, San Diego Convention Center
Bahar Acu, Northwestern University baharacu@gmail.com
Ziva Myer, Duke University
Yu Pan, Massachusetts Institute of Technology
• Friday January 12, 2018, 1:00 p.m.-6:25 p.m.
AMS Contributed Paper Session on Applied Mathematics, II
Room 19, Mezzanine Level, San Diego Convention Center
□ 1:00 p.m.
Path-dependent Hamilton-Jacobi equations in infinite dimensions.
Erhan Bayraktar, University of Michigan
Christian Keller*, University of Michigan
□ 1:15 p.m.
TALK CANCELLED: Global regularity criteria for 2D micropolar equations with partial dissipation.
Dipendra Regmi*, University of North Georgia
□ 1:30 p.m.
Numerical Simulations of Thin Viscoelastic Sheets.
Valeria Barra*, New Jersey Institute of Technology
Shahriar Afkhami, New Jersey Institute of Technology
Shawn A. Chester, New Jersey Institute of Technology
□ 1:45 p.m.
TALK CANCELLED: Instability and dynamics of volatile thin films.
Hangjie Ji*, University of California, Los Angeles
Thomas P Witelski, Duke University
□ 2:00 p.m.
Validated Numerical Analysis of the Hele-Shaw free boundary problem.
Andrew Thomack*, Florida Atlantic University
Jason Mireles-James, Florida Atlantic University
Erik Lundberg, Florida Atlantic University
□ 2:15 p.m.
Well-Posedness and Control in a Free Boundary Fluid-Structure Interaction.
Lorena Bociu, North Carolina State University
Lucas Castle*, North Carolina State University
Irena Lasiecka, The University of Memphis
□ 2:30 p.m.
Simple Second-Order Finite Differences for Elliptic PDEs with Discontinuous Coefficients and Interfaces.
Chung-Nan Tzou*, University of Wisconsin at Madison
Samuel Stechmann, University of Wisconsin at Madison
□ 2:45 p.m.
TALK CANCELLED: Lagrangian aspects of the axisymmetric Euler equation.
Stephen C Preston, Brooklyn College
Alejandro Sarria*, University of North Georgia
□ 3:00 p.m.
Lagrangian chaos and transport in geophysical fluid flows.
Maleafisha J.P.S. Tladi*, University of Limpopo
□ 3:15 p.m.
The wave scattering analysis of flexible trifurcated waveguide using Mode-Matching approach.
Rab Nawaz*, COMSATS Institute of Information Technology Islamabad Pakistan
Muhammad Afzal, Capital University of Science and Technology Islamabad Pakistan
□ 3:30 p.m.
Confined Flowing Bacterial Suspensions.
Zhenlu Cui*, Fayetteville State University
□ 3:45 p.m.
TALK CANCELLED: Symmetry Breaking in a Random Passive Scalar.
Zeliha Kilic*, University of North Carolina at Chapel Hill, Joint Applied Math and Marine Sciences Fluids Lab
Richard M McLaughlin, University of North Carolina at Chapel Hill, Joint Applied Math and Marine Sciences Fluids Lab
Roberto Camassa, University of North Carolina at Chapel Hill, Joint Applied Math and Marine Sciences Fluids Lab
□ 4:00 p.m.
Fine structure symmetry-breaking in decaying passive scalars advected by laminar shear flow.
Francesca Bernardi*, University of North Carolina at Chapel Hill
Manuchehr Aminian, Colorado State University
Roberto Camassa, University of North Carolina at Chapel Hill
Daniel M. Harris, Brown University
Richard M. McLaughlin, University of North Carolina at Chapel Hill
□ 4:15 p.m.
Traveling waves in mass and spring dimer Fermi-Pasta-Ulam-Tsingou lattices.
Timothy E. Faver*, Drexel University
J. Douglas Wright, Drexel University
□ 4:30 p.m.
Traveling Wave Solutions in Mixed Monotone Models of Population Biology, with Time Delays and Density-Dependent Diffusions.
Wei Feng*, Department of Mathematics and Statistics, University of North Carolina Wilmington
Weihua Ruan, Department of Mathematics, Computer Science, and Statistics, Purdue University Northwest
Xin Lu, Department of Mathematics and Statistics, University of North Carolina Wilmington
□ 4:45 p.m.
Nonclassical Symmetries of a Generalized KdV Equation.
Danny Arrigo*, University of Central Arkansas
Andrea Weaver, University of Central Arkansas
□ 5:00 p.m.
\newline Multi-scale modeling of high frequency wave propagation in heterogeneous medium with cracks.
Viktoria Savatorova*, University of Nevada Las Vegas
Aleksei Talonov, National Research Nuclear Uniersity MEPhI (Russia)
□ 5:15 p.m.
Remarks on the global regularity of two-dimensional Boussinesq equations.
Dhanapati Adhikari*, Marywood University
□ 5:30 p.m.
Local Well-Posedness and Blow-up Criteria for the Rotational b-family Equation.
Emel Bolat*, University of Texas at Arlington
Yue Liu, University of Texas at Arlington
□ 5:45 p.m.
A Continuation Method for Computing Capillary Surfaces.
Nicholas D Brubaker*, California State University, Fullerton
□ 6:00 p.m.
Using analysis of fast collisions between solitons of the nonlinear Schrödinger (NLS) equation for mathematical modeling of pulse propagation in broadband optical waveguide systems.
Avner Peleg*, Department of Exact Sciences, Afeka College of Engineering
Quan M. Nguyen, International University, Vietnam National University-HCMC
Debananda Chakraborty, New Jersey City University, Jersey City, NJ
Toan T. Huynh, University of Science, Vietnam National University-HCMC
□ 6:15 p.m.
TALK CANCELLED: On the Navier Stokes Equation with Rough Transport Noise.
Martina Hofmanova, Technical University of Berlin
James-Michael Leahy*, University of Southern California
Torstein Nilssen, Technical University of Berlin
• Friday January 12, 2018, 1:00 p.m.-6:10 p.m.
AMS General Session
Room 12, Mezzanine Level, San Diego Convention Center
• Friday January 12, 2018, 1:00 p.m.-3:15 p.m.
MAA Session on Good Math from Bad: Crackpots, Cranks, and Progress
Room 31B, Upper Level, San Diego Convention Center
Elizabeth T. Brown, James Madison University
Samuel R. Kaplan, University of North Carolina Asheville skaplan@unca.edu
• Friday January 12, 2018, 1:00 p.m.-3:55 p.m.
MAA Session on Innovative and Effective Online Teaching Techniques
Room 15B, Mezzanine Level, San Diego Convention Center
Sharon Mosgrove, Western Governors University sharon.mosgrove@wgu.edu
Doug Scheib, Western Governors University
• Friday January 12, 2018, 1:00 p.m.-5:55 p.m.
MAA Session on Inquiry-Based Teaching and Learning, II
Room 4, Upper Level, San Diego Convention Center
Eric Kahn, Bloomsburg University
Brian P. Katz, Augustana College briankatz@augustana.edu
Victor Piercey, Ferris State University
• Friday January 12, 2018, 1:00 p.m.-5:40 p.m.
MAA General Contributed Paper Session on Applied Mathematics, IV
Room 28E, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Friday January 12, 2018, 1:00 p.m.-5:10 p.m.
MAA General Contributed Paper Session on Teaching and Learning Calculus, I
Room 32B, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
□ 1:00 p.m.
Peer Assisted Learning in Calculus.
Corey Shanbrom, Sacramento State University
Vincent Pigno*, Sacramento State University
Jennifer Lundmark, Sacramento State University
Lynn Tashiro, Sacramento State University
□ 1:15 p.m.
Riemann Sums Belong at the End of Integral Calculus, Not in the Beginning.
Robert R. Rogers*, SUNY Fredonia
□ 1:30 p.m.
Teaching Large Lecture Calculus Using Team Based Learning.
Elgin H. Johnston*, Department of Mathematics, Iowa State University, Ames, Iowa
Heather Bolles, Department of Mathematics, Iowa State University, Ames, IA
Travis Peters, Department of Mathematics, Iowa State University, Ames, IA
Craig Ogilvie, Department of Physics, Iowa State University, Ames, IA
Alexis Knaub, Center for Research on Instructional Change in Postsecondary Education, Western Michigan University, Kalamazoo, MI
Thomas Holmes, Department of Chemistry, Iowa State University, Ames, IA
Chassidy Bozeman, Department of Mathematics, Iowa State University, Ames, IA
Stefanie Wang, Department of Mathematics, Trinity College, Hartford CT
Anna Seitz, Department of Mathematics, Iowa State University, Ames, IA
□ 1:45 p.m.
Adapting understanding of functions and domain to create 3D printed art.
David R. Burns*, Western Connecticut State University
□ 2:00 p.m.
Two Implementations of Pre Class Readings in Calculus.
Houssein El Turkey*, University of New Haven
Salam Turki, Rhode Island College
Yasanthi Kottegoda, University of New Haven
□ 2:15 p.m.
Limits Belong at the End of Differential Calculus, Not at the Beginning.
Eugene C. Boman*, Penn State, Harrisburg campus
□ 2:30 p.m.
The impact of the Derivatives in Applied Calculus II course: A case study in Applied Calculus II at the University of Texas Dallas.
Derege H Mussa*, University of Texas at Dallas
Jigar Patel, New York Univeristy
Changsong Li, University of Texas at Dallas
□ 2:45 p.m.
Discovering Calculus through Pasta.
Mel Henriksen*, Wentworth Institute of Technology
Gary Simundza, Wentworth Institute of Technology
Emma Smith Zbarsky, Wentworth Institute of Technology
□ 3:00 p.m.
Mixture model approach of classifying students based on their performance in differential calculus.
Amit A Savkar*, Associate Professor in Resi/Director of Assessment and Teaching Freshmen-level mathematics
□ 3:15 p.m.
Large Lectures of Flipped Calculus.
Ryan Maccombs*, Michigan State University
Andrew Krause, Michigan State University
□ 3:30 p.m.
Using Points-Free Homework to Promote Perseverance.
Austin Mohr*, Nebraska Wesleyan University
□ 3:45 p.m.
Putting the Logs to the Fire -- From Calculus to Algorithmics.
Tracey Baldwin McGrail*, Marist College, Poughkeepsie, New York
□ 4:00 p.m.
An alternate assessment technique - evaluated.
Kayla K. Blyman*, United States Military Academy
Kristin M. Arney, United States Military Academy
□ 4:15 p.m.
The Role of Low Instructional Overhead Tasks as Supports for Active Learning in Undergraduate Calculus Courses.
David C. Webb*, University of Colorado Boulder
□ 4:30 p.m.
Improving Feedback.
Karen Edwards*, Harvard
Brendan Kelly, Harvard
□ 4:45 p.m.
New tracks for a Calculus Curriculum in Engineering.
Gianluca Guadagni, Applied Mathematics, School of Engineering, University of Virginia
Bernard Fulgham, Applied Mathematics, School of Engineering, University of Virginia
Stacie Pisano*, Applied Mathematics, School of Engineering, University of Virginia
Hui Ma, Applied Mathematics, School of Engineering, University of Virginia
Diana Morris, Applied Mathematics, School of Engineering, University of Virginia
Monika Abramenko, Applied Mathematics, School of Engineering, University of Virginia
Julie Spencer, Applied Mathematics, School of Engineering, University of Virginia
□ 5:00 p.m.
Increasing mathematics self-efficacy in calculus students using study packets.
Stephanie A Blanda*, Penn State University
• Friday January 12, 2018, 1:00 p.m.-2:40 p.m.
MAA General Contributed Paper Session on Teaching and Learning Introductory Mathematics, II
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
□ 1:00 p.m.
Use of Sudoku Variations in an Introduction to Proofs Course for Majors.
Jeff Poet*, Missouri Western State University
□ 1:15 p.m.
South Dakota School of Mines Math Initiative: Part One.
Michelle Richard-Greer*, South Dakota School of Mines & Technology
Debra Bienert, South Dakota School of Mines & Technology
□ 1:30 p.m.
South Dakota School of Mines Math Initiative: Part Two.
Debra Bienert*, South Dakota School of Mines & Technology
Michelle Richard-Greer, South Dakota School of Mines & Technology
□ 1:45 p.m.
□ 2:00 p.m.
Prospective Teachers Analyzing Transcripts of Teaching.
Laura M. Singletary*, Lee University
□ 2:15 p.m.
Introducing Linear and Exponential Rates of Change in Linguistically Diverse Secondary Classrooms: Exploring Connections Among Curriculum, Tasks, and Student Understandings.
Lynda Wynn*, San Diego State University & UC San Diego
Bill Zahner, San Diego State University
Hayley Milbourne, San Diego State University & UC San Diego
□ 2:30 p.m.
Reading Mathematics is a Learnable Skill.
Sean Droms*, Lebanon Valley College
• Friday January 12, 2018, 1:00 p.m.-6:10 p.m.
AMS Contributed Paper Session on Mathematical Biology and Modeling Disease
Room 13, Mezzanine Level, San Diego Convention Center
□ 1:00 p.m.
A map-based approach to understanding sleep/wake dynamics in early childhood.
Cecilia Diniz Behn*, Colorado School of Mines
Kelsey Kalmbach, Colorado School of Mines
Victoria Booth, University of Michigan
□ 1:15 p.m.
A mathematical model of iron metabolism in the human body.
Timothy Patrick Barry*, University of Maryland College Park, Department of Biology
□ 1:30 p.m.
A mathematical model for Amyloid beta influenced calcium signaling through the IP$_3$ receptors.
Joe Latulippe*, Norwich University
Joseph Minicucci, Norwich University
□ 1:45 p.m.
Intermyocellular Lipids and the Progression of Muscular Insulin Resistance.
Daniel H Burkow*, Arizona State University
□ 2:00 p.m.
A mathematical model of coupled excitation and inhibition in a neuronal network for movement and reward.
Anca Radulescu*, State University of New York at New Paltz
Caitlin Kennedy, State University of New York and New Paltz
Johanna Herron, State University of New York at New Paltz
Annalisa Scimemi, State University of New York at Albany
□ 2:15 p.m.
TALK CANCELLED: Analysis for piecewise smooth models of a biological motor control system.
Yangyang Wang*, Ohio State University
Jeffery Gill, Case Western Reserve University
Hillel Chiel, Case Western Reserve University
Peter Thomas, Case Western Reserve University
□ 2:30 p.m.
Breaking the Vicious Limit Cycle: Addiction Relapse-Recovery As a Fast-Slow Dynamical System.
Jacob P. Duncan*, Saint Mary's College, Notre Dame, IN
Monica McGrath, Saint Mary's College, Notre Dame, IN
Teresa M. Aubele-Futch, Saint Mary's College, Notre Dame, IN
□ 2:45 p.m.
The statistical mechanics of human weight change.
John C Lang*, University of California Los Angeles
Hans De Sterck, Monash University
Daniel M Abrams, Northwestern University
□ 3:00 p.m.
Assessing the Impact of 8 Weeks of Almond Consumption on Anthropometric and Clinical Measurements in College Freshmen.
Marily Barron*, University of California, Merced
Jaapna Dhillon, University of California, Merced
Syed A. Asghar, University of California, Merced
Quintin Kuse, University of California, Merced
Natalie De La Cruz, University of California, Merced
Emily Vu, University of California, Merced
Suzanne S. Sindi, University of California, Merced
Rudy M. Ortiz, University of California, Merced
□ 3:15 p.m.
TALK CANCELLED: Coevolving cancer hallmarks: The angiogenic switch is modulated by clonal selection on proliferation.
Aleesa Monaco*, School of Molecular Sciences, Arizona State University
John D. Nagy, School of Mathematical and Statistical Sciences, Arizona State University
Kalle Parvinen, Department of Mathematics, University of Turku
□ 3:30 p.m.
The stability of cellular networks against mutations.
Lora D Weiss*, University of California Irvine
Natalia L Komarova, University of California Irvine
□ 3:45 p.m.
Equilibria Analysis for a Two-Population Epidemic Model with One Population Being a Reservoir for Infection.
Rachel Elizabeth TeWinkel*, University of Wisconsin - Milwaukee
Istvan Lauko, University of Wisconsin - Milwaukee
Gabriella Pinter, University of Wisconsin - Milwaukee
□ 4:00 p.m.
Parsing a Crowd of Near Best Fits: Consensus Ranges for Drug-Resistant Tuberculosis Modeling.
Ellie Mainou*, Emory University
Robert Dorit, Smith College
Gwen Spencer, Smith College
Dylan Shepardson, Mount Holyoke College
□ 4:15 p.m.
Stochastic Models of Within-Host Viral Infection.
Krystin E. Steelman Huff*, Texas Tech University
None, None
□ 4:30 p.m.
Mathematical Models of the Immune System's Response to Bacterial Infection on the Surface of an Implant Device.
Shelby Stanhope*, Temple University
Isaac Klapper, Temple University
□ 4:45 p.m.
The iterative process of quantitative modeling of infection dynamics in renal transplant recipients.
Neha Murad*, North Carolina State University
Harvey Thomas Banks, North Carolina State University
Rebecca Everett, North Carolina State University
□ 5:00 p.m.
Mathematics-driven insights into the hostile immune system behavior toward hair follicles.
Atanaska Dobreva*, Florida State University
Nick G Cogan, Florida State University
Ralf Paus, University of Manchester
□ 5:15 p.m.
HIV epidemiology; mass incarceration and HIV incidence; male-female ratio; $R_0$.
David J. Gerberry, Xavier University
Hem Raj Joshi*, Xavier University
□ 5:30 p.m.
Modeling Autoimmune Disease with Differential Equations.
Jennifer A Anderson*, Texas Woman's University
Ellina Grigorieva, Texas Woman's University
□ 5:45 p.m.
Autoimmune Diseases Induced by Exposure to Radiation.
Leila Mirsaleh Kohan*, Department of Mathematics & Computer Science, Texas Woman's University, Denton, TX 76204
Ellina Grigorieva, Department of Mathematics & Computer Science, Texas Woman's University, Denton, TX 76204
□ 6:00 p.m.
Mucosal Folding and Growth Instabilities in a Finite Element Model of an Atherosclerotic Artery.
Pak-Wing Fok*, University of Delaware, Department of Mathematical Sciences
• Friday January 12, 2018, 1:00 p.m.-4:35 p.m.
MAA Session on Mathematical Themes in a First-Year Seminar, II
Room 15A, Mezzanine Level, San Diego Convention Center
Jennifer Bowen, The College of Wooster
Pamela Pierce, The College of Wooster ppierce@wooster.edu
• Friday January 12, 2018, 1:00 p.m.-5:40 p.m.
AMS Contributed Paper Session on Matrices and Matroids
Room 18, Mezzanine Level, San Diego Convention Center
• Friday January 12, 2018, 1:00 p.m.-6:25 p.m.
AMS Contributed Paper Session on Orthogonal Polynomials and Function Theory
Room 29B, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 1:00 p.m.-6:10 p.m.
AMS Contributed Paper Session on Partitions, Paths, and Permutations
Room 29A, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 1:00 p.m.-4:55 p.m.
MAA Session on Research in Undergraduate Mathematics Education (RUME), IV
Room 14B, Mezzanine Level, San Diego Convention Center
Stacy Brown, California State Polytechnic University
Megan Wawro, Virginia Tech mwawro@vt.edu
Aaron Weinberg, Ithaca College
• Friday January 12, 2018, 1:00 p.m.-5:55 p.m.
MAA Session on Technology and Apps for Teaching Mathematics and Statistics, I
Room 5B, Upper Level, San Diego Convention Center
Stacey Hancock, Montana State University
Soma Roy, California Polytechnic State University
Sue Schou, Idaho State University
Karl RB Schmitt, Valparaiso University karl.schmitt@valpo.edu
□ 1:00 p.m.
Using Interactive R Tutorials and Reproducible Research Practices to Introduce Statistical Learning Ideas to Undergraduate Statistics Students.
Alana J Unfried*, California State University Monterey Bay
□ 1:20 p.m.
Introducing R to different statistical audiences.
Kimberly A Roth*, Juniata College
□ 1:40 p.m.
Teaching Statistics with R and Applications to Interdisciplinary Research.
Leon Kaganovskiy*, Touro College, NY
□ 2:00 p.m.
Implementing R Activities and Projects in Introductory Statistics.
John D. Ross*, Southwestern University
□ 2:20 p.m.
The Do's and Don'ts of a Statistics Project.
Christine Davidson*, Suffolk County Community College
□ 2:40 p.m.
Learning Statistics through Applications to Community.
Rasitha R Jayasekare*, Butler University, IN
□ 3:00 p.m.
Enhanced student learning and attitudes with bi-weekly MINITAB explorations.
Dan Seth*, West Texas A&M University
□ 3:20 p.m.
□ 3:40 p.m.
Engaging Students by Using Simulations to Address the Question of the Day.
Kari Lock Morgan*, Pennsylvania State University
□ 4:00 p.m.
Does the Randomization Method Matter?
Robin H Lock*, St. Lawrence University
□ 4:20 p.m.
Bayes' Theorem and Lie Detector Tests.
Howard Troughton*, Babson College
□ 4:40 p.m.
Clarifying and Reimagining the Empirical Rule: An Introduction to the By-Thirds Rule.
Allen G Harbaugh*, Boston University
□ 5:00 p.m.
Teaching P-values from Primary Sources.
Dominic Klyve*, Central Washington University
□ 5:20 p.m.
Teaching and learning statistics in education through MOODLE in Nepal.
Durga Prasad Dhakal*, Kathmandu University School of Education, Nepal
David A. Thomas, University of Great Falls, Montana
□ 5:40 p.m.
TALK CANCELLED: Developing Concept Images Core Statistical Ideas: The Role of Interactive Dynamic Technology.
Gail F Burrill*, Michigan State university
• Friday January 12, 2018, 1:00 p.m.-3:15 p.m.
MAA Session on The Advancement of Open Educational Resources, II
Room 31C, Upper Level, San Diego Convention Center
Benjamin Atchinson, Framingham State University batchison@framingham.edu
• Friday January 12, 2018, 1:00 p.m.-4:35 p.m.
MAA Session on The Teaching and Learning of Undergraduate Ordinary Differential Equations, II
Room 14A, Mezzanine Level, San Diego Convention Center
Christopher S. Goodrich, Creighton Preparatory School cgood@prep.creighton.edu
Beverly H. West, Cornell University
□ 1:00 p.m.
First and Second-Order Models of Vertical Motion of Dry Air Parcels.
Chris Oehrlein*, Oklahoma City Community College
Jessica Oehrlein, Columbia University
□ 1:20 p.m.
What happens when a physicist teaches Ordinary Differential Equations?
P. P. Yu*, Westminster College
□ 1:40 p.m.
Laplace Transforms vs. The Method of Undetermined Coefficients.
Paul D. Olson*, Penn State Erie , the Behrend College Erie , PA .
□ 2:00 p.m.
Strategic use of technology and modeling to motivate, investigate, and illuminate.
William Skerbitz*, Wayzata High School
□ 2:20 p.m.
Visualizing Topics from Differential Equations Using CalcPlot3D.
Paul E. Seeburger*, Monroe Community College
□ 2:40 p.m.
Deriving Kepler's Laws in a Differential Equations class.
Andrew G. Bennett*, Kansas State University
□ 3:00 p.m.
Using Dynamic Visualization to Better Understand the Tractrix and Other "Pulling" Curves.
Douglas B. Meade*, University of South Carolina - Columbia
□ 3:20 p.m.
Resisted Projectile Motion: a Trove of ODE Applications/Projects.
William W Hackborn*, University of Alberta, Augustana Campus
□ 3:40 p.m.
General Discussion: CODEE invites all who teach ODEs to join us for a meet-and-greet hour. We will include discussion of the online CODEE Journal, with plans for a special issue in 2018
• Friday January 12, 2018, 1:00 p.m.-3:35 p.m.
NAM Granville-Brown-Haynes Session of Presentations by Recent Doctoral Recipients in the Mathematical Sciences
Room 32A, Upper Level, San Diego Convention Center
Dr. Talitha M Washington, Howard University talitha.washington@howard.edu
• Friday January 12, 2018, 1:00 p.m.-5:55 p.m.
SIAM Minisymposium on Mimetic Multiphase Subsurface and Oceanic Transport
Room 11A, Upper Level, San Diego Convention Center
Jose Castillo, San Diego State University jcastillo@mail.sdsu.edu
Chris Paolini, San Diego State University paolini@engineering.sdsu.edu
• Friday January 12, 2018, 1:00 p.m.-2:20 p.m.
MAA Panel
Pathways Through High School Mathematics: Building Focus and Coherence
Room 2, Upper Level, San Diego Convention Center
Karen J. Graham, University of New Hampshire karen.graham@unh.edu
Gail Burrill, Michigan State University
Yvonne Lai, University of Nebraska Lincoln
Matt Larson, National Council of Teachers of Mathematics
Francis Su, Harvey Mudd College
Dan Teague, North Carolina School of Science and Mathematics
• Friday January 12, 2018, 1:00 p.m.-2:30 p.m.
AMS-MAA Joint Committee on TAs and Part-Time Instructors Panel: Panel on The Experiences of Foreign Graduate Students as GTAs
Room 1B, Upper Level, San Diego Convention Center
John Boller, University of Chicago
Solomon Friedberg, Boston College solomon.friedberg@bc.edu
Edward Richmond, Oklahoma State University
Solomon Friedberg, Boston College
Gangotryi Sorcar, Ohio State University
Fatma Terzioglu, Texas A & M
Kai Zhao, Temple University
Zhuohui Zhang, Rutgers University
• Friday January 12, 2018, 1:00 p.m.-2:00 p.m.
EVENT CANCELLED: NSF Town Hall Meeting with Joan Ferrini-Mundy
Room 6D, Upper Level, San Diego Convention Center
Jim Lewis, National Science Foundation
Lee Zia, National Science Foundation
Joan Ferrini-Mundy, National Science Foundation
• Friday January 12, 2018, 1:00 p.m.-2:00 p.m.
Town Hall Meeting
Creating Engaging, Meaningful Experiences for Teachers and Future Teachers
Room 5A, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 1:15 p.m.-5:55 p.m.
MAA General Contributed Paper Session on Topology
Room 1A, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Friday January 12, 2018, 2:00 p.m.-2:50 p.m.
ASL Invited Address
A synthetic theory of $\infty$-categories in homotopy type theory..
Room 7B, Upper Level, San Diego Convention Center
Emily Riehl*, Johns Hopkins University
Michael Shulman, University of San Diego
• Friday January 12, 2018, 2:00 p.m.-3:30 p.m.
AMS Directors of Graduate Studies
Rancho Santa Fe Rm 2, Lobby Level, North Twr, Marriott Marquis San Diego Marina
• Friday January 12, 2018, 2:15 p.m.-4:00 p.m.
Rocky Mountain Mathematics Consortium Board of Directors Meeting
Torrey Pines Room 1, Lobby Level, North Tower, Marriott Marquis San Diego Marina
• Friday January 12, 2018, 2:30 p.m.-3:20 p.m.
Presentations by MAA Teaching Award Recipients
Room 6C, Upper Level, San Diego Convention Center
Barbara Faires, Westminster College
Deanna Haunsperger, Carleton College
• Friday January 12, 2018, 2:30 p.m.-4:00 p.m.
AMS Committee on Science Policy Panel Discussion
Funding at federal agencies & advocacy for grassroots support
Room 11B, Upper Level, San Diego Convention Center
Karen Saxe, American Mathematical Society
Scott Wolpert, University of Maryland
Terrance Blackman, Medger Evers College, CUNY
Fariba Fahroo, DARPA
Charlie Toll, National Security Agency
Michael Vogelius, Rutgers University
NEW: Congressman Jerry McNerney (CA-9), U.S. House of Representatives
• Friday January 12, 2018, 2:35 p.m.-3:55 p.m.
MAA Panel
Career Trajectories Involving Administrative Roles: What You May Want to Consider
Room 2, Upper Level, San Diego Convention Center
Ryan Zerr, University of North Dakota ryan.zerr@und.edu
Edward Aboufadel, Grand Valley State University
NEW: Martha Abell, Georgia Southern University
Edward Aboufadel, Grand Valley State University
WITHDRAWN:Linda Braddy, Tarrant County College
Jenna Carpenter, Campbell University
Rick Gillman, Valparaiso University
Jennifer Quinn, University of Washington Tacoma
• Friday January 12, 2018, 2:45 p.m.-5:55 p.m.
MAA General Contributed Paper Session on Other Topics, I
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Friday January 12, 2018, 3:00 p.m.-3:50 p.m.
ASL Invited Address
Power of reasoning over richer domains.
Room 7B, Upper Level, San Diego Convention Center
Antonina Kolokolova*, Memorial University of Newfoundland
• Friday January 12, 2018, 3:40 p.m.-5:05 p.m.
Project NExT Panel
Incorporating Social Justice Projects into the College Mathematics Curriculum
Room 6F, Upper Level, San Diego Convention Center
Marko Budisic, Clarkson University
Kaitlin Hill, University of Minnesota
Natalie Hobson, Sonoma State University
Bianca Thompson, Harvey Mudd College
Aditya Adiredja, University of Arizona
Karl-Dieter Crisman, Gordon College
Lily Khadjavi, Loyola Marymount
• Friday January 12, 2018, 4:00 p.m.-5:50 p.m.
ASL Contributed Paper Session, I
Room 7B, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 4:00 p.m.-5:30 p.m.
National Science Foundation: Update from the Division of Mathematical Sciences (NSF-DMS)
Room 8, Upper Level, San Diego Convention Center
Henry Warchall, Division of Mathematical Sciences, National Science Foundation
• Friday January 12, 2018, 4:30 p.m.-6:00 p.m.
MAA Student Poster Session
Exhibit Hall B2, Ground Level, San Diego Convention Center
• Friday January 12, 2018, 4:30 p.m.-6:30 p.m.
AMS Congressional Fellowship Session
Room 11B, Upper Level, San Diego Convention Center
Karen Saxe, American Mathematical Society
Margaret Callahan, AMS Congressional Fellow 2017-18
• Friday January 12, 2018, 5:00 p.m.-7:00 p.m.
MAA Panel
The Evolving Career Outlook in Risk Management
Room 2, Upper Level, San Diego Convention Center
Kevin Charlwood, Washburn University kevin.charlwood@washburn.edu
Michelle Guan, Indiana University
Steve Paris, Florida State University
Barry Smith, Lebanon Valley College
Sue Staples, Texas Christian University
Rick Gorvett, Casualty Actuary Society (CASACT)
Paul Bailey, Willis Towers Watson
Raya Feldman, University of California Santa Barbara
Zoe Rico, Aon
Barry Smith, Lebanon Valley College
• Friday January 12, 2018, 5:00 p.m.-6:00 p.m.
Meeting of potential members of SIGMAA on Mathematical Knowledge for Teaching (SIGMAA-MKT)
Room 3, Upper Level, San Diego Convention Center
Yvonne Lai, University of Nebraska Lincoln
Bonnie Gold, Monmouth University
• Friday January 12, 2018, 5:30 p.m.-6:15 p.m.
SIGMAA on Business, Industry, and Government (BIG SIGMAA) Guest Lecture
Room 15A, Mezzanine Level, San Diego Convention Center
• Friday January 12, 2018, 5:30 p.m.-6:00 p.m.
SIGMAA on Mathematics Instruction Using the WEB (WEB SIGMAA) Reception
Room 5A, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 6:00 p.m.-7:15 p.m.
AWM Workshop: Poster Presentations by Women Graduate Students and Reception
Lobby outside Room 6AB, Upper Level, San Diego Convention Center
Alina Bucur, University of California, San Diego
Matilde Lalin, University of Montreal
Radmila Sazdanovic, North Carolina State University
• Friday January 12, 2018, 6:00 p.m.-6:45 p.m.
SIGMAA on Mathematics Instruction Using the WEB (WEB SIGMAA) Guest Lecture
Room 5A, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 6:00 p.m.-7:00 p.m.
Mathematically Bent Theater
Performed by Colin Adams and the Mobiusbandaid Players.
Room 6C, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 6:00 p.m.-7:00 p.m.
AMS {\bit Mathematical Reviews} Reception
Presidio Room, Lobby Level, North Tower, Marriott Marquis San Diego Marina
• Friday January 12, 2018, 6:00 p.m.-6:30 p.m.
SIGMAA on Statistics Education Reception
Room 6D, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 6:15 p.m.-7:00 p.m.
NEW: SIGMAA on Inquiry Based Learning Business Meeting
Room 4, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 6:30 p.m.-7:15 p.m.
SIGMAA on Statistics Education Business Meeting
Room 6D, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 6:30 p.m.-7:00 p.m.
SIGMAA on Business, Industry, and Government (BIG SIGMAA) Reception
Room 15A, Mezzanine Level, San Diego Convention Center
• Friday January 12, 2018, 7:00 p.m.-7:30 p.m.
SIGMAA on Business, Industry, and Government (BIG SIGMAA) Business Meeting
Room 15A, Mezzanine Level, San Diego Convention Center
• Friday January 12, 2018, 7:20 p.m.-8:10 p.m.
SIGMAA On Statistics Education Guest Lecture
Room 6D, Upper Level, San Diego Convention Center
• Friday January 12, 2018, 7:45 p.m.-8:35 p.m.
NAM Cox-Talbot Address
Hidden in Plain Sight: Mathematics Teaching and Learning Through a Storytelling Lens.
Marina Ballroom FG, 3rd Floor, South Tower, Marriott Marquis San Diego Marina
Erica Walker*, Teachers College, Columbia University
• Friday January 12, 2018, 8:00 p.m.-10:00 p.m.
Project NExT Reception
All Project NExT Fellows, consultants, and other friends of Project NExT are invited.
Marina Ballroom E, 3rd Floor, South Tower, Marriott Marquis San Diego Marina
Julia Barnes, West Carolina University
Alissa Crans, Loyola Marymount University
Matt Delong, Taylor University
David Kung, St Mary's College of Maryland
• Friday January 12, 2018, 8:00 p.m.-10:00 p.m.
Learn to play backgammon from expert players.
Marina Ballroom D, 3rd Floor, South Tower, Marriott Marquis San Diego Marina
Arthur Benjamin, Harvey Mudd College
Saturday January 13, 2018
• Saturday January 13, 2018, 7:30 a.m.-2:00 p.m.
Joint Meetings Registration
Exhibit Hall B1, Ground Level, San Diego Convention Center
• Saturday January 13, 2018, 7:30 a.m.-2:00 p.m.
Email Center
Exhibit Hall B1, Ground Level, San Diego Convention Center
• Saturday January 13, 2018, 7:45 a.m.-11:55 a.m.
AMS Contributed Paper Session on Applied Mathematics, III
Room 13, Mezzanine Level, San Diego Convention Center
• Saturday January 13, 2018, 7:45 a.m.-9:10 a.m.
MAA General Contributed Paper Session on Number Theory, III
Room 15A, Mezzanine Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Saturday January 13, 2018, 7:45 a.m.-11:55 a.m.
AMS Contributed Paper Session on Metrics and Optimization
Room 12, Mezzanine Level, San Diego Convention Center
• Saturday January 13, 2018, 7:45 a.m.-11:55 a.m.
AMS Contributed Paper Session on Partial Differential Equations
Room 29B, Upper Level, San Diego Convention Center
• Saturday January 13, 2018, 7:45 a.m.-11:55 a.m.
AMS Contributed Paper Session on Stochastic and Random Processes
Room 19, Mezzanine Level, San Diego Convention Center
• Saturday January 13, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Advances in Operator Algebras, II
Room 16A, Mezzanine Level, San Diego Convention Center
Marcel Bischoff, Vanderbilt University
Ian Charlesworth, University of California, Los Angeles
Brent Nelson, University of California, Berkeley brent@math.berkeley.edu
Sarah Reznikoff, Kansas State University
• Saturday January 13, 2018, 8:00 a.m.-11:45 a.m.
AMS Special Session on Alternative Proofs in Mathematical Practice
Room 30A, Upper Level, San Diego Convention Center
John W. Dawson, Jr., Pennsylvania State University, York jwd7too@comcast.net
• Saturday January 13, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Analysis of Fractional, Stochastic, and Hybrid Dynamic Systems
Room 30B, Upper Level, San Diego Convention Center
John R. Graef, University of Tennessee at Chattanooga
Gangaram S. Ladde, University of South Florida
Aghalaya S. Vatsala, University of Louisiana at Lafayette vatsala@louisiana.edu
• Saturday January 13, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Bifurcations of Difference Equations and Discrete Dynamical Systems
Room 30E, Upper Level, San Diego Convention Center
Arzu Bilgin, University of Rhode Island
Toufik Khyat, University of Rhode Island toufik17@my.uri.edu
• Saturday January 13, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Boundaries for Groups and Spaces, III
Room 16B, Mezzanine Level, San Diego Convention Center
Joseph Maher, CUNY College of Staten Island joseph.maher@csi.cuny.edu
Genevieve Walsh, Tufts University
• Saturday January 13, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Differential Geometry, II
Room 33A, Upper Level, San Diego Convention Center
Vincent B. Bonini, Cal Poly San Luis Obispo vbonini@calpoly.edu
Joseph E. Borzellino, Cal Poly San Luis Obispo
Bogdan D. Suceava, California State University, Fullerton
Guofang Wei, University of California, Santa Barbara
• Saturday January 13, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Diophantine Approximation and Analytic Number Theory in Honor of Jeffrey Vaaler, II
Room 17B, Mezzanine Level, San Diego Convention Center
Shabnam Akhtari, University of Oregon
Lenny Fukshansky, Claremont McKenna College lenny@cmc.edu
Clayton Petsche, Oregon State University
• Saturday January 13, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Emerging Topics in Graphs and Matrices, I
Room 33B, Upper Level, San Diego Convention Center
Sudipta Mallik, Northern Arizona University sudipta.mallik@nau.edu
Keivan Hassani Monfared, University of Calgary
Bryan Shader, University of Wyoming
• Saturday January 13, 2018, 8:00 a.m.-11:20 a.m.
AMS Special Session on Fractional Difference Operators and Their Application
Room 30D, Upper Level, San Diego Convention Center
Christopher S. Goodrich, Creighton Preparatory School cgood@prep.creighton.edu
Rajendra Dahal, Coastal Carolina University
• Saturday January 13, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Mathematics Research from the SMALL Undergraduate Research Program, I
Room 10, Upper Level, San Diego Convention Center
Colin Adams, Williams College
Frank Morgan, Williams College
Cesar E. Silva, Williams College csilva@williams.edu
• Saturday January 13, 2018, 8:00 a.m.-11:45 a.m.
AMS Special Session on Mathematics of Quantum Computing and Topological Phases of Matter, II
Room 17A, Mezzanine Level, San Diego Convention Center
Paul Bruillard, Pacific Northwest National Laboratory
David Meyer, University of California San Diego
Julia Plavnik, Texas A&M University julia@math.tamu.edu
• Saturday January 13, 2018, 8:00 a.m.-11:45 a.m.
AMS Special Session on Multi-scale Modeling with PDEs in Computational Science and Engineering:Algorithms, Simulations, Analysis, and Applications, II
Room 33C, Upper Level, San Diego Convention Center
Salim M. Haidar, Grand Valley State University haidars@gvsu.edu
□ 8:00 a.m.
The Landau equation: Analysis and Approximations to collisional plasmas.
Irene M. Gamba*, The University of Texas at Austin
□ 9:00 a.m.
□ 9:30 a.m.
New preconditioner techniques for the buoyancy driven flow problems.
Guoyi Ke*, Texas Tech University
Eugenio Aulisa, Texas Tech University
□ 10:00 a.m.
Unifying Forces in Complex Matter Space (CMS).
Reza R. Ahangar*, Texas A & M University-Kingsville, Texas
□ 10:30 a.m.
Analytical and Numerical Study of Detachment Effects for the Upscaled Porous Medium Biofilm Reactor Model.
Abbas Fazal*, Rochester Institute of Technology, Rochester NY USA
Eberl J Hermann, University of Guelph, Guelph ON Canada
□ 11:00 a.m.
Spherical harmonics based solutions for modified Laplace equation on a sphere.
Vani Cheruvu*, The University of Toledo
Shravan K Veerapaneni, University of Michigan
• Saturday January 13, 2018, 8:00 a.m.-11:50 a.m.
AMS-MAA-SIAM Special Session on Research in Mathematics by Undergraduates and Students in Post-Baccalaureate Programs, III
Room 31C, Upper Level, San Diego Convention Center
Tamas Forgacs, CSU Fresno
Darren A. Narayan, Rochester Institute of Technology dansma@rit.edu
Mark David Ward, Purdue University
• Saturday January 13, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Set-theoretic Topology (Dedicated to Jack Porter in Honor of 50 Years of Dedicated Research), I
Room 9, Upper Level, San Diego Convention Center
Nathan Carlson, California Lutheran University ncarlson@callutheran.edu
Jila Niknejad, University of Kansas
Lynne Yengulalp, University of Dayton
• Saturday January 13, 2018, 8:00 a.m.-11:50 a.m.
AMS Special Session on Topological Data Analysis, III
Room 6E, Upper Level, San Diego Convention Center
Henry Adams, Colorado State University henry.adams@colostate.edu
Gunnar Carlsson, Stanford University
Mikael Vejdemo-Johansson, CUNY College of Staten Island
• Saturday January 13, 2018, 8:00 a.m.-10:50 a.m.
AMS Special Session on Visualization in Mathematics: Perspectives of Mathematicians and Mathematics Educators, II
Room 30C, Upper Level, San Diego Convention Center
Karen Allen Keene, North Carolina State University
Mile Krajcevski, University of South Florida mile@mail.usf.edu
• Saturday January 13, 2018, 8:00 a.m.-11:55 a.m.
MAA Session on Attracting, Involving, and Retaining Women and Underrepresented Groups in Mathematics --Righting the Balance
Room 5A, Upper Level, San Diego Convention Center
Francesca Bernardi, University of North Carolina at Chapel Hill
Meghan De Witt, St. Thomas Aquinas College mdewitt@stac.edu
Semra Kili/,c-Bahi, Colby-Sawyer College
• Saturday January 13, 2018, 8:00 a.m.-11:40 a.m.
AMS Contributed Paper Session on Differential Equations
Room 29D, Upper Level, San Diego Convention Center
• Saturday January 13, 2018, 8:00 a.m.-11:40 a.m.
AMS Contributed Paper Session on Graphs and Their Applications
Room 18, Mezzanine Level, San Diego Convention Center
• Saturday January 13, 2018, 8:00 a.m.-11:55 a.m.
MAA Session on Inquiry-Based Teaching and Learning, III
Room 4, Upper Level, San Diego Convention Center
Eric Kahn, Bloomsburg University
Brian P. Katz, Augustana College briankatz@augustana.edu
Victor Piercey, Ferris State University
• Saturday January 13, 2018, 8:00 a.m.-10:25 a.m.
MAA General Contributed Paper Session on Analysis, I
Room 28D, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Saturday January 13, 2018, 8:00 a.m.-11:55 a.m.
MAA General Contributed Paper Session on Probability and Statistics, I
Room 28E, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Saturday January 13, 2018, 8:00 a.m.-9:40 a.m.
MAA General Contributed Paper Session on Teaching and Learning Introductory Mathematics, III
Room 32B, Upper Level, San Diego Convention Center
Tim Comar, Benedictine University tcomar@ben.edu
James Reid, University of Mississippi
• Saturday January 13, 2018, 8:00 a.m.-11:55 a.m.
AMS Contributed Paper Session on Modeling Disease and Biological Processes
Room 29C, Upper Level, San Diego Convention Center
• Saturday January 13, 2018, 8:00 a.m.-11:55 a.m.
AMS Contributed Paper Session on Numerical Methods and Their Applications
Room 29A, Upper Level, San Diego Convention Center
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Combinatorics is concerned with arrangements of discrete objects according to constraints and the study of discrete structures such as graphs. Large graphs underpin many aspects of data science and
can be used to model networks.
Lancaster’s research interests in combinatorics are diverse and closely connected to each of the other pure mathematics research themes in the department.
Additive combinatorics explores how to count arithmetic configurations within unstructured sets of integers - those sets for which we have only combinatorial information, such as their density.
Techniques in this field have been developed to tease out the latent structure present in such sets, separating it from random 'noise'. Resolving these combinatorial problems can then feed back into
more classical problems of number theory, such as detecting arithmetic structures in the primes.
As combinatorial structures provide convenient means of indexing words in noncommuting variables, many problems in probability and analysis can be approached using methods of diagrammatic calculus.
Such methods provide a fundamental bridge between combinatorics and algebra, on the one hand, and probability and analysis, on the other. A well-known example is the moment method, through which the
Catalan numbers, ubiquitous in combinatorics, are interpreted as the moments of the semicircle law, the analogue of the Gaussian random variable in random matrix theory. Research in our combinatorics
group is closely connected to classical and noncommutative probability, including random matrix theory, and mathematical physics.
Measurable combinatorics concerns extensions of combinatorial theorems in the context of Borel graphs with applications including classical geometrical questions. There is also interest in sparse and
dense graph limits where, with a suitable metric imposed on the set of finite graphs, limits of convergent graph sequences are studied.
Matroids are a mathematical structure that extends the notion of linear independence of a set of vectors. They have numerous important applications, for example, in Operational Research and
Combinatorial Optimisation. Our research in matroid theory concentrates on real world occurrences of the 2 fundamental motivating examples of matroids: row matroids of matrices and matroids defined
on graphs.
Combinatorial aspects of geometric rigidity theory (and its applications in fields such as engineering and robotics) such as recursive constructions of classes of (coloured) sparse graphs. This topic
underlies the flexibility and rigidity properties of geometric structures, such as finite and infinite bar-joint frameworks in finite dimensional spaces. Further geometric aspects of combinatorics
such as polyhedral scene analysis, equidissection and triangulation problems, and the rich interactions between discrete geometry, combinatorics and symmetry.
Many aspects of mathematics share the same underlying classifications in terms of combinatorics such as Coxeter combinatorics and Fuss-Catalan combinatorics. These underlying combinatorial
similarities often indicate deeper connections, e.g. the ubiquitous "finite type" classifications in terms of Dynkin diagrams. In representation theory of algebras, combinatorics is used extensively
to get concrete understanding of abstract objects. For example, certain algebras can be associated to ribbon graphs, which in turn can be embedded in surfaces, and directed graphs may be used to
encode the multiplication in noncommutative algebras.
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Your boss asks you to plan the sample size for a randomized, double-blind, controlled trial in
the clinical development of a cure for irritable bowl disease. Current standard treatment shall be
compared with a new treatment in this trial. The S3-guideline of AWM demonstrated a mean
change of the summary score of the validated health related quality of life questionnaire at 8
weeks of 16 with standard deviation 23 under standard treatment. You quote the drop-out rate
of 11% from literature (previous phase of clinical development). Your research yielded a clinically
important effect of 4 that has been found to be the Minimal Clinically Important Difference (MCID).
In order to demonstrate superiority of the new treatment over standard of care, you assume that
the change in of the summary score of the validated health related quality of life questionnaire
follows a normal distribution, and that the standard deviation is the same for both treatments.
How many patientes would one need to recruit for the trial to demonstrate the clinically
interesting difference between treatments at significance level 5% with 95% power?
Your boss asks you to plan the sample size for a randomized, double-blind, controlled trial in the clinical development of a cure for irritable bowl disease. Current standard treatment shall be
compared with a new treatment in this trial. The S3-guideline of AWM demonstrated a mean change of the summary score of the validated health related quality of life questionnaire at 8 weeks of 16
with standard deviation 23 under standard treatment. You quote the drop-out rate of 11% from literature (previous phase of clinical development). Your research yielded a clinically important effect
of 4 that has been found to be the Minimal Clinically Important Difference (MCID). In order to demonstrate superiority of the new treatment over standard of care, you assume that the change in of the
summary score of the validated health related quality of life questionnaire follows a normal distribution, and that the standard deviation is the same for both treatments. How many patientes would
one need to recruit for the trial to demonstrate the clinically interesting difference between treatments at significance level 5% with 95% power?
932 views
Answer to a math question Your boss asks you to plan the sample size for a randomized, double-blind, controlled trial in the clinical development of a cure for irritable bowl disease. Current
standard treatment shall be compared with a new treatment in this trial. The S3-guideline of AWM demonstrated a mean change of the summary score of the validated health related quality of life
questionnaire at 8 weeks of 16 with standard deviation 23 under standard treatment. You quote the drop-out rate of 11% from literature (previous phase of clinical development). Your research yielded
a clinically important effect of 4 that has been found to be the Minimal Clinically Important Difference (MCID). In order to demonstrate superiority of the new treatment over standard of care, you
assume that the change in of the summary score of the validated health related quality of life questionnaire follows a normal distribution, and that the standard deviation is the same for both
treatments. How many patientes would one need to recruit for the trial to demonstrate the clinically interesting difference between treatments at significance level 5% with 95% power?
89 Answers
\frac{2\times\left(1.96+1.645\right)^2\times23^2}{4^2}=859.36 Therefore sample size is 860
Frequently asked questions (FAQs)
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Highly Durable Sulfur Impregnated Distorted Carbon Nanotubes for Sodium Ion Battery
Monday, 14 May 2018
Ballroom 6ABC (Washington State Convention Center)
Electrical energy storage systems are essential for storing energy produced from renewable energy resources. The increasing demand and price make it difficult for the large scale industrial
production of energy storage devices. Therefore, it is necessary to find low cost energy storage devices for large-scale applications. Sodium is an alternative to lithium because it is the fourth
abundant element in the Earth’s crust. The similar intercalation chemistry of sodium ions is comparable to lithium, which makes sodium ion battery (NIB) as an alternative to existing energy storage
systems. The size of Na^+ ions is about 1.02 Å and that of Li^+ ions is 0.76 Å. The increased size of sodium ions causes instability of the electrode due to which volume expansion and slow reaction
kinetics occur thereby lowering the specific capacity and cycle life. Carbon based nanomaterials have high cyclic stability with low specific capacity. To enhance the specific capacity the carbon
based materials are coupled with materials, which undergo conversion or alloying reaction with sodium. During the process of conversion or alloying, the intake of number of sodium ions by the
material is more enhancing the storage capacity. But due to the phase change of the material the volume gets expanded up to 420% (Sn). The repeated cycling causes pulverization of the electrode
leading to capacity fading. The conversion-based materials have high specific capacity with comparatively low volume expansion. The combination of carbon-based material with conversion type of
materials has a synergistic effect of both long cycle life and energy density. Among the carbon-based material, multiwalled carbon nanotubes (MWNTs) have good electrical conductivity but the
intercalation of sodium ions into MWNTs is very less limiting the storage capacity. Partially oxidized multiwalled carbon nanotubes (PONTs) have disordered structure and large interlayer spacing,
which can enhance the storage capacity with high electrical conductivity. Sulfur is a conversion based material which has high theoretical capacity of 1675 mA h/g is used mainly an active material in
metal sulfur battery. Incorporation of sulfur into PONTs gives high specific capacity contributed by the sulfur and PONTs. The layers of PONTs provide cushion effect to accommodate the volume
expansion caused by the conversion reaction of sulfur with sodium. In this present work, the results of sulfur incorporated PONTs as an anode material has been discussed for the achievement of high
specific capacity and cycle life.
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(5 pts) Genes D and E are located in the
Drosophila genome.
DE·DE females are crossed...
(5 pts) Genes D and E are located in the Drosophila genome. DE·DE females are crossed...
1. (5 pts) Genes D and E are located in the Drosophila genome.
1. DE·DE females are crossed with de·de males to produce F1 flies that are heterozygous for both traits. What gametes do each of these parents make?
2. F1 females were crossed with de·de males, and 2000 flies were examined. What gametes do each of these parents make?
3. What are the possible genotypes of the offspring produced from the cross in part B?
4. If the genes were sorting independently (not linked), what proportion of each offspring genotype and phenotype would be expected from the cross in Part B?
5. The results are depicted in the table below. Do the ratios suggest the genes linked? Explain your answer.
F2 Genotypes Number Observed
DE·de 651
de·de 649
De·de 356
dE·de 344
6. On the table, label which progeny are recombinant and which progeny are parental.
7. Assuming the genes are linked, how far apart are the two genes?
35 map units
2. (3 pts) You carry out an experiment using the same genes described in question 1. In a second experiment, De/De females are crossed with dE/dE males to produce F1 flies that are heterozygous for
both traits. F1 females were then testcrossed with de/de males.
1. What is different about this experiment, relative to the one described in question 1?
2. What are the all the possible genotypes of the testcross offspring?
The possible genotypes are:
3. Which genotypes are parental and which are recombinant?
Is this assuming the genes are sorted independently? Because if it is I got B of Q2 wrong
Ans1. Gametes by DE.DE females - DE
Gametes by de.de males- de
2. Gametes produced by progeny from F1 DdEe = DE, De, dE, de
Gametes by dede males= de
3. Genotypes by cross DdEe * dede = DdEe, Ddee, ddEe, ddee
GAMETES de
DE DdEe
De Ddee
dE ddEe
de ddee
4. Proportion of each genotype and phenotype= 1/4. Every genotype and phenotype is different.
5. No, the genes are not linked because recombinants as well as parental genotypes are formed.
6. Parental progeny = DE.de, de.de
Recombinants= De.de, dE.de
7. Distance between two genes = (no. of recombinants)*100/(total progeny) = (356+344)*100/ 651+649+356+344
= 35cM
Because of time constraints, only this question could be attempted, please post another question seperately.
THANK YOU AND HAPPY TO HELP YOU!!!
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A073304 - OEIS
%I #4 Mar 30 2012 17:36:39
%S 365,334,306,275,245,214,184,153,122,92,61,31,0
%N Remaining days in non-leap year at end of n-th month.
%e a(6)=184 because there are 184 days left in a (non-leap) year on Jun 30, the sixth month.
%Y Cf. A073305 (remaining days in leap year), A061251 (elapsed days at end of n-th month beginning with non-leap year).
%K fini,full,nonn
%O 0,1
%A _Rick L. Shepherd_, Jul 23 2002
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90 Percent Handicap Chart
90 Percent Handicap Chart - Web in strokeplay it is 90% of each individual's handicap; At the end of the 2018. Web the average slope for any golf course is 113. Check out how easy it is to complete
and esign documents online using fillable templates. Web 90 percent handicap chart three games individual or team if the individual base figure is 200, the chart. The highest slope can go is 155.
Sport and challenge lane conditions refer to oil patterns designed for league and tournament. Check out how easy it is to complete and esign documents online using fillable templates. Web typically,
basis scores range from about 200, 210, or 220. Web handicap charts (click the file type (pdf or excel) of the handicap chart you want) single game handicap (this is what most.
90 Handicap Allowance Handicaps
Web let me give you my own example, though, to show you how it might work in practice. Sport and challenge lane conditions refer to oil patterns designed for league and tournament. Web the percentage
factor is used to calculate your handicap and will usually be 80, 90, or 100 percent, but may vary in. Here a real example to..
Web let me give you my own example, though, to show you how it might work in practice. Check out how easy it is to complete and esign documents online using fillable templates. The percentage factor
is used to calculate your handicap and will usually. Web the bowling handicap is essentially a percentage of the difference between the bowler’s average.
Handicap Charts The Ski Challenge
Web the chart assigns a handicap percentage to each bowler based on their average score. Check out how easy it is to complete and esign documents online using fillable templates. Web 90 percent
handicap chart three games individual or team if the individual base figure is 200, the chart. The lowest slope will be is 55. Web the average slope.
Handicap and Scoring Help
Web 90 percent handicap chart three games individual or team if the individual base figure is 200, the chart. Web to fill out a bowling handicap chart, follow these steps: Web 90 of 210 bowling
handicap chart. Web subtract your average score from the basis score and multiply the result by the percentage factor to calculate your. In matchplay it.
Determine what scoring system is used,. Percentage (use 0.9 for 90%): Web the bowling handicap is essentially a percentage of the difference between the bowler’s average and a basis. Web 90 percent
handicap chart three games individual or team if the individual base figure is 200, the chart. Web in strokeplay it is 90% of each individual's handicap;
World Handicapping System Rockmount Golf Club
In matchplay it is 90% of the difference between each. The lowest slope will be is 55. Percentage (use 0.9 for 90%): Three game total of each bowler added to the three game. Here a real example to.
1 Annual average disability rate reduction or increase for men and
At the end of the 2018. Web the percentage factor is used to calculate your handicap and will usually be 80, 90, or 100 percent, but may vary in. In matchplay it is 90% of the difference between
each. Web 24 rows the recommended handicap allowance for all individual stroke play formats of play is set at 95% for medium..
WHS PLAY HANDICAP CALCULATOR TABLES Heswall Golf Club
Web 90 of 220 bowling handicap chart. The percentage factor is used to calculate your handicap and will usually. The lowest slope will be is 55. Web in strokeplay it is 90% of each individual's
handicap; Percentage (use 0.9 for 90%):
How To Calculate Golf Handicap Index Haiper
Web a bowling handicap chart will typically include the following information: This percentage is then added to their. Web 90 percent handicap chart three games individual or team if the individual
base figure is 200, the chart. Web the percentage factor is used to calculate your handicap and will usually be 80, 90, or 100 percent, but may vary in..
Playing Handicap Tables The Millbrook Golf Club
Web the percentage factor is used to calculate your handicap and will usually be 80, 90, or 100 percent, but may vary in. Sport and challenge lane conditions refer to oil patterns designed for league
and tournament. Web 90 percent handicap chart single game individual or team average hdcp average hdcp average hdcp average hdcp. Percentage (use 0.9 for 90%):.
Three game total of each bowler added to the three game. Web the percentage factor is used to calculate your handicap and will usually be 80, 90, or 100 percent, but may vary in. Web the average
slope for any golf course is 113. Web let me give you my own example, though, to show you how it might work in practice. The percentage factor is used to calculate your handicap and will usually. Web
a bowling handicap chart will typically include the following information: Check out how easy it is to complete and esign documents online using fillable templates. Web subtract your average score
from the basis score and multiply the result by the percentage factor to calculate your. Web 90 percent handicap chart three games individual or team if the individual base figure is 200, the chart.
The lowest slope will be is 55. The highest slope can go is 155. Sport and challenge lane conditions refer to oil patterns designed for league and tournament. Web 90 of 210 bowling handicap chart.
Web 90 of 220 bowling handicap chart. Web typically, basis scores range from about 200, 210, or 220. This percentage is then added to their. Determine what scoring system is used,. In matchplay it is
90% of the difference between each. Web the chart assigns a handicap percentage to each bowler based on their average score. At the end of the 2018.
Web The Percentage Factor Is Used To Calculate Your Handicap And Will Usually Be 80, 90, Or 100 Percent, But May Vary In.
Percentage (use 0.9 for 90%): Web the chart assigns a handicap percentage to each bowler based on their average score. Web let me give you my own example, though, to show you how it might work in
practice. The percentage factor is used to calculate your handicap and will usually.
The Highest Slope Can Go Is 155.
The lowest slope will be is 55. Web the bowling handicap is essentially a percentage of the difference between the bowler’s average and a basis. Web 90 of 210 bowling handicap chart. Web subtract
your average score from the basis score and multiply the result by the percentage factor to calculate your.
At The End Of The 2018.
Web a bowling handicap chart will typically include the following information: In matchplay it is 90% of the difference between each. Web typically, basis scores range from about 200, 210, or 220.
Web in strokeplay it is 90% of each individual's handicap;
Web 90 Of 220 Bowling Handicap Chart.
Web handicap charts (click the file type (pdf or excel) of the handicap chart you want) single game handicap (this is what most. This percentage is then added to their. Sport and challenge lane
conditions refer to oil patterns designed for league and tournament. Web to fill out a bowling handicap chart, follow these steps:
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A study on the extraction of characteristics of compound faults of rolling bearings based on ITD-AF-CAF
In view of the cyclostationary characteristics of vibration signals from aero-engine, the combination of cyclic autocorrelation function and intrinsic timescale decomposition (ITD) has been proposed.
According to the proposed method, vibration signals are decomposed by ITD algorithm to obtain the autocorrelation function of proper rotation components (PRC), based on which characteristic
extraction and identification of compound faults of rolling bearings is made possible. To validate the effectiveness of method, an analysis has been given to the vibration signals of rolling bearings
collected by sensors of different positions in different compound fault modes. As shown by results, the method combining ITD and cyclostationary theory can precisely and effectively extract the
characteristic frequency relative to the type of faults and identify the compound faults.
1. Introduction
Rolling bearing is an important support part for rotation of aero-engine and extremely vulnerable working in high-speed and high-pressure environment. A bearing fault may have huge influence on
performance of aero-engine and even weaken the safety of operation [1]. Therefore, state monitoring and fault diagnosis is of great significance. Vibration signal can fully reflect the dynamic
properties of bearings. When one part of bearing is damaged, it will impact other components resulting in periodic impact force and vibration signal will create periodic peak pulse [2, 3]. As
vibration signals of bearings are both non-linear and non-stationary, fault signals are often overwhelmed by noise signals adding to the difficulty of characteristic extraction [4, 5]. Besides, the
faults of bearings often exist as being compound and characteristic extraction is far more difficult than single faults [6].
In recent years, multiple signal analysis methods have been introduced to bearing fault diagnosis to solve the difficulties in fault characteristics extraction, including empirical mode decomposition
(EMD) [7], ensemble empirical mode decomposition (EEMD) [8, 9], variational mode decomposition (VMD) [10, 11], blind source separation [12] and so on. FREI brought forward ITD self-adaptive
decomposition algorithm in 2007 [13], which was firstly applied to the field of electrical signal. Song, et al. pointed out the use of ITD algorithm to extract transient characteristics of radio
station. By estimating the transient parameters of signal, they could detect signals and identify an individual station [14]. An, et al, proposed a quick algorithm based on intrinsic timescale
decomposition [15] and the ITD algorithm was soon applied to the fault diagnosis of rotary machines, such as bearings and gears [16-18]. Due to the approximate symmetry and periodicity of operation
state of rotary machine, its vibration signal has cyclostationary properties. For that, it will be more precise to extract the characteristics of faults with circular statistics. Wang, et al.
proposed the method combing EMD and second order cyclostationary analysis [19]. Victor Girondin brought forward the fault detection method for bearings of helicopter based on frequency adjustment and
cyclostationary analysis [20]. Literature [21] combined wavelet transforms and cyclic autocorrelation for the fault analysis of rolling bearings. Literature [22] proposed the application of cyclic
autocorrelation function to test bed of wind power gear box. As correlation function can retain the properties of original signal while reducing the noise, autocorrelation function of signal can be
analyzed based on cyclostationary theory.
For that, the paper proposes the combination of ITD algorithm, correlation analysis and cyclostationary theory to extract characteristics of compound faults of rolling bearings and identify the type
of faults.
2. ITD-AF-CAF
Given ${X}_{t}$ ($t\ge$0) is a real-value discrete signal to be resolved, $L$ baseline extractor ($L$ is a variable varying with local extreme points of original signal during decomposition), ${L}_
{t}$ baseline component, ${H}_{t}$ proper rotational component, ${L}_{t}^{p}$ residual trend component, ${X}_{k}$, ${\tau }_{k}$ the extreme point and time $\left\{{\tau }_{k},k=1,2,\cdots M\right\}$
of sequence ${X}_{t}$ (define ${\tau }_{0}=0$). $\beta$ is a linear zoom factor adjust the range of proper rotational component, $\beta \in \left[0,1\right]$, in which $\alpha =0.5$. The ITD
decomposition process of signal ${X}_{t}$ is as shown in Eqs. (1)-(4) and Fig. 1:
$L{X}_{t}={L}_{t}={L}_{k}+\left(\frac{{L}_{k+1}-{L}_{k}}{{X}_{k+1}-{X}_{k-1}}\right)\left({X}_{t}-{X}_{k}\right),t\in \left({\tau }_{k},{\tau }_{k+1}\right),$
${L}_{k+1}=\beta \left[{X}_{k}+\left(\frac{{\tau }_{k+1}-{\tau }_{k}}{{\tau }_{k+2}-{\tau }_{k}}\right)\right]\left({X}_{k+2}-{X}_{k}\right)+\left(1-\beta \right){X}_{k+1},\left(k=1,2,\cdots ,M-2\
${X}_{t}={H}_{t}+{L}_{t}={H}_{t}+\left(H+L\right){L}_{t}=H\sum _{k=0}^{p-1}{L}_{t}^{p}+{L}_{t}^{p}.$
Take ${L}_{t}$ as a new original signal ${X}_{t}$ and go on with Eqs. (1)-(2) until ${L}_{t}$ is smaller than the set threshold value or monotonic function. After ITD decomposition, ${X}_{t}$ can be
expressed as:
${R}_{Hi}\left(t,\tau \right)=E\left\{{H}_{i}{\left(t-\frac{\tau }{2}\right)}^{*}{H}_{i}\left(t+\frac{\tau }{2}\right)\right\},$
where, $\tau$, $E$ and * are respectively delay factor, statistical mean value and conjugate. ${R}_{Hi}\left(t,\tau \right)$ has cyclostationary feature, if ${H}_{i}\left(t\right)$ is a periodic
function of time $t$. In view of ${R}_{Hi}\left(t,\tau \right)$ is a period function and can be acquired by means of Fourier series expansion:
${R}_{Hi}\left(t,\tau \right)={\sum }_{\alpha \in A}{R}_{Hi}\left(\tau ,\alpha \right){e}^{i2\pi \alpha t},$
$\alpha =\frac{m}{{T}_{0}}\left(m\in Z\right)$, $\alpha$ and ${T}_{0}$ respectively represent cycle frequency and autocorrelation function period, and then the Fourier transform coefficient can be
${R}_{Hi}\left(t,\alpha \right)=\underset{T\to \infty }{\mathrm{lim}}\frac{1}{T}{\int }_{-\frac{T}{2}}^{\frac{T}{2}}{R}_{Hi}{\left(t-\frac{\tau }{2}\right)}^{*}{R}_{Hi}\left(t+\frac{\tau }{2}\right)
{e}^{-j2\pi \alpha t}dt,$
where ${R}_{Hi}\left(\tau ,\alpha \right)$ is cycle-autocorrelation function of ${R}_{Hi}\left(t,\tau \right)$ as cycle frequency is equal to $\alpha$. The specific ITD-AF-CAF is as shown in Fig. 1.
Fig. 1Conceptual framework of ITD-AF-CAF Note: ITD, intrinsic timescale decomposition; AF, autocorrelation function; CAF, cyclic autocorrelation function
3. Rolling bearing compound faults experiment
All data in this paper was collected from the test bed of rotor-rolling bearing designed by China Aero Engine Research Institute, which is as shown in Fig. 2. The test bed contains single-disk rotor
with both ends supported by rolling bearings on bearing block. Working components include USB9234 data acquisition card provided by NI, B&K model 4508 acceleration sensors which collect acceleration
signals and electrical vortex sensor which detects the rotation speed of rolling bearings. The compound faults of rolling bearings are as shown in Fig. 3, in which Fig. 3(a1)-(a3) corresponds to the
compound faults of outer ring and a rolling element, inner ring and a rolling element, inner-outer ring and a rolling element, respectively. Geometrical parameters of bearings include: inner ring
diameter 9.6 mm, pitch diameter 36 mm, number of rolling bodies, 7. The rotation speeds and characteristic frequencies of rolling bearings with compound faults are shown in Table 1.
Table 1Feature frequency of rolling bearing
Compound fault types Rotation speed Rotational frequency Inner race feature frequency outer race feature frequency Rolling elements feature frequency
Outer race and a rolling element 182.7 r/min 30.4 Hz 134.8 Hz 78.0 Hz 52.9 Hz
Inner race and a rolling element 2013.4 r/min 33.5 Hz 148.8 Hz 86.1 Hz 58.4 Hz
Inner, outer race and a rolling element 1542.4 r/min 25.7 Hz 113.6 Hz 66.0 Hz 44.8 Hz
Fig. 2Rotor-rolling bearing experiment rig
Fig. 3Rolling bearing compound faults for (a1)-(a3) compound faults of outer race and rolling element; inner race and rolling element; outer race, inner race and rolling element
4. Characteristic extraction of compound faults of rolling bearings
4.1. ITD-AF: common method
For a comparative analysis to validate the effectiveness of method, vibration signals are decomposed based on ITD algorithm and characteristics of compound faults are extracted according to the
frequency spectrum of autocorrelation function of rotation components (ITD-AF).
Limited by the length of paper, we took the vibration acceleration signal (faults 1 in Table 1) collected by the sensor in vertical direction as an example when compound faults of inner ring and a
rolling element occurred, and extracted the characteristics of compound faults based on ITD-AF algorithm. The result is shown in Fig. 4, in which rotation speed of tester is 2013.4 r/min, rotation
frequency 33.5 Hz (2013.4/60 = 33.5) obtained by calculation. According to formula 1-4 and geometrical parameters, we can have the characteristic frequency of inner ring, outer ring and rolling
elements is 148.8 Hz, 86.1.0 Hz and 58.4 Hz, respectively. Fig. 4(a), (b) and (c) is the time domain, frequency spectrum and its partial zoom of vibration acceleration signal. Fig. 4(a1)-(a4)
corresponds to the time domain of PRC1, PRC2, PRC3 and PRC4 after ITD decomposition. Fig. 4(b1)-(b4) is the autocorrelation function of Fig. 4(a1)-(a4). Fig. 4(c1)-(c4) is the frequency spectrum of
Fig. 4(b1)-(b4). Relation of frequency components and characteristic frequency of bearing in Fig. 4(c1)-(c4) is as shown in Table 2.
Fig. 4Rolling bearing compound faults feature extraction-ITD-AF
Table 2Relation between frequency components and fault types of rolling bearing-ITD-AF-vertical (Hz)
PRC Frequency Feature frequency Frequency Feature frequency
(1) 294.8 294.8/5 = 58.9 ≈ 58.4 (3) 995.5 995.5/17 = 58.5 ≈ 58.4
(2) 701.6 701.6/12 = 58.5 ≈ 58.4 (4) 1437 (1437-33.5)/24 = 58.5
PR2 (1) 701.6 701.6/12 = 58.5 ≈ 58.4 (2) 995.5 995.5/17 = 58.5 ≈ 58.4
PR3 (1) 201.4 201.4/6 = 33.5 (2) 368.7 368.7/11 = 33.5
(3) 701.6 701.6/12 = 58.5 ≈ 58.4
PR4 (1) 201.4 201.4/6 = 33.5
With the analysis of Fig. 4 and Table 2, the following conclusions can be drawn:
In the frequency spectrum of original signal in Fig. 4(b) and (c), the frequency components are very complicated in that most of them are rotation frequency (33.5 Hz) and the components of frequency
multiplication. There is no characteristic frequency of rolling elements (58.4 Hz), inner ring (148.8 Hz) and their frequency multiplication observed. That means frequency spectrum alone cannot
identify a fault of bearings, not to mention the identification of compound faults types.
As found from the analysis of Fig. 4(c1), (c2), (c3), (c4) and Table 2, there is obvious characteristic frequency (58.4 Hz) of rolling elements and its frequency multiplication (701.6 Hz, 995.5 Hz,
1437 Hz) which can be found from the frequency spectrum of autocorrelation function of each rotation component after ITD decomposition, but without obvious characteristic frequency (148.8 Hz) of
inner ring and its frequency multiplication component, which means that the method based on ITD-AF can partly extract the characteristic frequency of compound faults, but not comprehensively. For
that, this method is incapable to make precise judgment upon the type of compound faults of bearings.
4.2. ITD-AF-CAF: a new method
To be more precise and effective in identifying the compound faults of rolling bearings, ITD algorithm is introduced into the framework of cyclostationary theory. Cyclic autocorrelation function is
combined with the autocorrelation function of each PR component after ITD decomposition to extract the characteristics of compound faults of rolling bearings. For a comparison validation, the data
for ITD-AF-CAF analysis is completely the same with Section 4.1 and the result is shown in Fig. 5. Limited by the length of paper, Fig. 5 only shows the cyclic autocorrelation function of
autocorrelation function of PRC2 and PRC4 (pick up the PR components of ideal effect). Fig. 5(a1) is autocorrelation function of PRC2 (completely the same with Fig. 4(b2); the time domain signal of
PRC2 is shown in Fig. 4(a2)); Fig. 5(a2)-(a3) is the cyclic autocorrelation function of Fig. 5(a1) and its partial zoom; Fig. 5(a4)-(a5) is the sliced signal of cyclic autocorrelation function of
autocorrelation function of PRC2; Fig. 5(b1) is the autocorrelation function of PRC4 (completely the same with Fig. 4(b4) and the time domain signal of PRC4 is shown in Fig. 4(a4)); Fig. 5(b2)-(b3)
is the cyclic autocorrelation function of Fig. 5(b1) and its partial zoom; Fig. 5(b4)-(b5) is the sliced signal of cyclic autocorrelation function of autocorrelation function of PRC4.
Corresponding relation between each frequency component and characteristic frequency of bearing in Fig. 5 is shown in Fig. 3.
Table 3Relation between frequency component and fault types of rolling bearing-vertical (Hz)
PRC Frequency Feature frequency Frequency Feature frequency
(1) 33.1 33.1 ≈ 33.5 (3) 147 147 ≈ 148.8
PRC2 (2) 67.0 67.0/2 = 33.5 (4) 295 295/2 = 147.5 ≈ 148.8
(5) 404 404/7 = 57.7 ≈ 58.4
(1) 67.0 67.0/2 = 33.5 (2) 101 101/3 = 33.6 ≈ 33.5
(3) 352 352/6 = 58.6 ≈ 58.4 (4) 404 404/7 = 57.7 ≈ 58.4
Fig. 5rolling bearing compound faults feature extraction-ITD-AF-CAF
With the analysis of Fig. 5 and Table 3, the following conclusions can be drawn:
Outstanding frequency components in PR2 component are as follow:
(1) 147 Hz, corresponding to characteristic frequency of inner ring (148.8 Hz);
(2) 295 Hz, corresponding to the double characteristic frequency of inner ring;
(3) 404 Hz, corresponding to the 7-time (404/7 = 57.7) characteristic frequency of rolling elements (58.4 Hz);
In PR4 component:
(1) 352 Hz, corresponding to the 6-time characteristic frequency of rolling elements (58.4 Hz);
(2) 404 Hz, corresponding to the 7-time characteristic frequency of rolling elements (58.4 Hz);
Namely, when a compound faults of inner ring and a rolling element occurs, the proposed ITD-AF-CAF can provide the characteristic frequency consistent with the type of compound faults of bearing.
That means the proposed ITD-AF-CAF can make precise judgment on the type of compound faults of bearings.
5. Influencing factors
To validate the effectiveness of ITD-AF-CAF in characteristic extraction of compound faults of rolling bearing, an analysis is given to the vibration signals collected by sensors from different
directions and in different compound faults based on ITD-AF-CAF method.
To analyze the sensibility of analysis method to installation direction of sensors, signals collected from horizontal direction are compared with the ones from vertical direction. Due to the limited
length of paper, we took the compound faults of outer ring and a rolling element as an example and the result is shown in Fig. 6(a1)-(b7). To analyze the sensibility of analysis method to the type of
compound faults, an analysis was given to the vibration acceleration signals collected from compound faults of outer ring and a rolling element, and results are shown in Fig. 6(c1)-(c7).
When the rotation speed is 1823.7 r/min in compound faults of outer ring and rolling body, we can have the characteristic frequency of inner ring, outer ring and a rolling element, as follow: 134.8
Hz, 78.0 Hz and 52.9 Hz (corresponding to the second type of fault in Table 2). When the rotation speed is 1542.4 r/min in compound faults of inner ring, outer ring and a rolling element, we can have
the characteristic frequency of inner ring, outer ring and rolling elements as follow: 113.6 Hz, 66.0 Hz and 44.8 Hz (corresponding to the third type of faults in Table 2).
Fig. 6(a1)-(a7) and 6(b1)-(b7) corresponds to the acceleration signals collected by sensors from horizontal and vertical directions when compound faults of outer ring and a rolling element occur.
Fig. 6(c1)-(c73) corresponds to the acceleration signals collected by sensors from vertical directions when compound faults of outer ring, inner ring and a rolling element occur.
Fig. 6(a1), (b1) and (c1) corresponds to the time domain of acceleration signal; Fig. 6(a2), (b2) and (c2) to the frequency spectrum of Fig. 6(a1), (b1) and (c1); Fig. 6(a3), (b3) and (c3) to the
partial zoom of frequency spectrum of Fig. 6(a2), (b2) and (c2); Fig. 6(a4), (b4) and (c4) to the time domain of PRC1 (an ideal one) obtained by ITD decomposition of Fig. 6(a3) and (b3); Fig. 6(c41)
and (c42) to the time domain of PRC1 and PRC4 (an ideal one) obtained by ITD decomposition of fig. 6(c3); Fig. 6(a5), (b5), (c51) and (c52) to the autocorrelation function of Fig. 6(a4), (b4), (c41)
and (c42); Fig. 6(a6), (b6), (c61) and (c62) to the cyclic autocorrelation function of Fig. 6(a5), (b5), (c51) and (c52); Fig. 6(a7) and (b7) to the partial zoom of Fig. (a6) and (b6). Fig. 6(c71)
and (c72) to the partial zoom of Fig. 6(c61); Fig. (c73) to the partial zoom of Fig. 6(c62). The corresponding relation between frequency components and characteristic frequency of bearings in Fig. 7
is shown in Table 4.
Analyzing Fig. 6(a7), (b7) and Table 4, in case of compound faults of outer ring and a rolling element, the following conclusions can be drawn:
No matter sensors are installed in horizontal direction or vertical, the proposed method can effectively extract the characteristic frequency 79 Hz of outer ring fault and triple characteristic
frequency of rolling elements (157/3 = 52.3Hz) which matches with the type of faults. Therefore, the proposed method can judge the type of compound faults of bearings, namely insensitivity to
installation direction of sensors.
After analyzing Fig. 6(c71), (c72), (c73) and table 4, in case of compound faults of outer ring, inner ring and a rolling element, the relation of frequency component and characteristic frequency of
bearings is shown as follows:
Outstanding frequency components in PRC2 are as follow:
(1) 284.2 Hz, corresponding to the sum of characteristic frequency of inner ring (113.6 Hz) and rolling elements (44.8 Hz), and 5-time rotation frequency ((284.2 – 113.6-44.8)/5 = 25.1);
(2) 1407 Hz, corresponding to the 21-time characteristic frequency (1407/21 = 67 Hz) of outer ring (66.0 Hz);
(3) 1702 Hz, corresponding to the 26-time characteristic frequency (1702/26 = 65.5 Hz) of outer ring (66.0 Hz);
(4) 1986 Hz, corresponding to the 30-time characteristic frequency (1986/30 = 66.2 Hz) of outer ring (66.0 Hz);
Outstanding frequency components in PRC4 are as follow:
(1) 46 Hz, corresponding to the characteristic frequency of rolling elements;
(2) 157 Hz, corresponding to the sum of characteristic frequency of rolling elements and inner ring, (113.6 + 44.8 = 158.4 Hz);
(3) 297 Hz, corresponding to the sum of 4-time characteristic frequency of inner ring and rolling elements, (297 – 113.6)/4 = 45.8);
(4) 315 Hz, corresponding to the 7-time characteristic frequency of rolling elements (315/7 = 45);
(5) 361 Hz, corresponding to the 8-time characteristic frequency of rolling elements (361/8 = 45.1).
Fig. 6Rolling bearing compound faults feature extraction-ITD-AF-CAF
It can be found that:
(1) The proposed ITD-AF-CAF method can effectively extract the characteristic frequency matched with the type of faults no matter sensors are installed horizontally or vertically, and thereby make
effective judgment on the type of compound faults. That means the proposed method is insensitive to installation direction of sensors;
(2) No matter for compound faults of inner ring and a rolling element, outer ring and a rolling element, or inner ring, outer ring and a rolling element, the proposed ITD-AF-CAF method can
effectively extract the matching characteristic frequency of fault types, and thereby make effective judgment on the types of compound faults of bearings.
Table 4Relation between frequency component and fault types of rolling bearing-vertical (Hz)
Compound fault Feature
Sensors installed direction PRC Frequency Frequency Feature frequency
types frequency
Outer race and
Horizontal PRC1 (1) 79 79 ≈ 78 (2) 157 157/3 = 52.3 ≈ 52.9
rolling element
Outer race and
Vertical PRC1 (1) 79 79 ≈ 78 (2) 157 157/3 = 52.3 ≈ 52.9
rolling element
(1) 284.2 (284.2-113.6-44.8)/5 = 25 (2) 1407 1407/21 = 67 ≈ 66
(3) 1702 1702/26 = 65.5 ≈ 66 (4) 1986 1986/30 = 66.2 ≈ 66
Outer race, inner race and rolling element Vertical (1) 46 46 ≈ 44.8 (2) 157 44.8+113.6 = 158.4 ≈ 157
PRC4 (3) 297 (297-113.6)/4 = 45.8 ≈ 44.8 (4) 315 315/7 = 45 ≈ 44.8
(5) 361 361/8 = 45.1
6. Conclusions
Due to the approximate symmetry and periodicity of operation state of rotation machine, its vibration signal has cyclostationary properties. Therefore, cyclostationary theory and ITD algorithm is
combined to make correct and effective identification of compound faults in bearings.
To prove the superiority of the proposed method, a comparative analysis has been given to the proposed method and common algorithm (combined ITD and autocorrelation analysis) and the following
conclusions can be drawn:
1) The common algorithm (combined ITD and autocorrelation analysis) can partly extract the characteristic frequency of bearings, but not comprehensively, so that it cannot extract the characteristic
frequencies matched with the type of compound faults, and fails to make precise judgment on the type of compound faults.
2) The combination of ITD, autocorrelation analysis and cyclostationary theory can precisely extract the characteristic frequencies matched with the type of faults, and thereby judge the type of
compound faults of rolling element.
3) An analysis has been given to signals collected by sensors from different directions (horizontal or vertical). The conclusion indicates that the proposed ITD-AF-CAF method shows insensitivity to
installation direction of sensors. No matter where sensors are installed in horizontal or vertical, the proposed method can effectively extract the characteristic frequency of rolling elements which
matches with the type of faults.
4) Another analysis has been given to vibration signals of different types of compound faults (inner ring and a rolling element, outer ring and a rolling element, inner ring, outer ring and a rolling
element). The conclusion indicates that the proposed ITD-AF-CAF method shows insensitivity to the type of compound faults.
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https://doi.org/ 10.3969/j.issn.1001-3997.2012.10.027
About this article
Fault diagnosis based on vibration signal analysis
rolling element
cyclic autocorrelation function
compound faults
This work was supported by National Natural Science Foundation of China (Grant number: 51605309), Natural Science Foundation of Liaoning Province (Grant number: 2019-ZD-0219), Aeronautical Science
Foundation of China (Grant number: 201933054002) and Department of Education of Liaoning Province (Grant number: JYT19042).
Copyright © 2021 Xiangdong Ge, et al.
This is an open access article distributed under the
Creative Commons Attribution License
, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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First-Principle Studies on the Ga and As Doping of Germanane Monolayer
Journal of Applied Mathematics and Physics Vol.07 No.01(2019), Article ID:89816,9 pages
First-Principle Studies on the Ga and As Doping of Germanane Monolayer
Lei Liu, Yanju Ji^*, Yifan Liu, Liqiang Liu^
School of Science, Shandong Jianzhu University, Jinan, China
Copyright © 2019 by author(s) and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY 4.0).
Received: November 21, 2018; Accepted: January 8, 2019; Published: January 11, 2019
The study of energetics, structural, the electronic and optical properties of Ga and As atoms substituted for doped germanane monolayers were studied by first-principles calculations based on density
functional theory. Both of the two doping are thermodynamically stable. According to the band structure and partial density of the states, gallium is p-type doping. Impurity bands below the
conduction band lead the absorption spectrum moves in the infrared direction. Arsenic doping has impurity level passing through the Fermi level and is n-type doping. The analysis of optical
properties confirms the value of bandgap and doping properties.
Germanane, Doping, Electronic Properties, Optical Properties, First-Principle
1. Introduction
Since the successful extraction of graphene by British scientists Andre Geim and Andre Geim using mechanical stripping in 2004, it has quickly led to the research and exploration of two-dimensional
materials due to its excellent properties. In order to further enhance the application value of two-dimensional materials, it is important to improve the properties of materials by doing with
graphene [1] - [14] , transition-metal dichalcogenides [15] [16] [17] [18] [19] and other two-dimensional van der Waals material [20] [21] [22] . Germanane is a hydride similar to graphane with
alternating hydrogen on either side of the germanium atom. Due to the direct band gap large electron mobility and the ability to control optoelectronic properties through covalent modification with
surface ligands, it has received extensive attention in the field of two-dimensional materials [23] [24] . Experiments have shown that a system formed by doping element gallium of group III and
element of arsenic group V into a germanane can be stably present. Doping the gallium and arsenic atoms into the precursor CaGe[2] phase, in the process of using HCl, remains intact in the lattice
after the topotactic deintercalation to form germanane [25] [26] [27] [28] [29] . This work demonstrates that extrinsic doping with Ga and As is a viable pathway towards accessing stable electronic
behavior in graphane analogues of germanium. But Ga and As doping in germanane have not been systematic research in theoretical calculation. In this work, we have studied thermodynamic stability,
structural and electronic properties of gallium and arsenic defects in a germanane monolayer using a GGA (generalized gradient approximation) hybrid density functional theory approach. This study
fine tunes the band gap of germanane through the foreign atom doping as well as via changing the charge state of the defect.
2. Calculation Method
The first principle calculation is implemented in CASTEP (Cambridge Serial Total Energy Package) code [30] [31] [32] by plane wave pseudopotential method based on density functional theory. In the
calculation, pristine germanane monolayer and its doping system were seen in Figures 1(a)-(c). and the vacuum is 20 Å. In order to make the structure more stable, different replacement methods were
used for gallium and arsenic atoms. Because the outermost electrons of gallium have only three electrons. We replace the germanium atom with a gallium atom and remove the hydrogen atom corresponding
to the replaced germanium atom. However, there are five outermost electrons in the arsenic atom, so we only replaced the germanium atom with a arsenic atom, and did not remove the corresponding
hydrogen atom. In the calculation process，the ions-electrons and exchange-correlation interaction are processed using norm-conserving pseudopotential and Perdew, Burke and Ernzerhof (PBE)
functionals in GGA, respectively. In order to obtain an accurate optimized structure of germanane, a cutoff energy of 400 eV is used to ensure total energy and stress convergence. In the process of
optimization, the specific parameters are set as follows. The total energy is 5.0 × 10^−6 eV/atom. The maximum stress, pressure, displacement, respectively 0.02 GPa, 5.0 × 10^−4 Å, 0.01 eV/Å. In
addition, the calculation of self-consistent field (SCF) is kept within the energy convergence criterion of 5 × 10^−6 eV/atom. The Brillouin zone was 3 × 3 × 1 k-point mesh [33] .
Figure 1. Top view of the supercell used in calculation: (a) Pristine germanane monolayer, (b) and (c) are gallium and arsenic defected germanane monolayer (4 × 4 × 1).
To assess the stabilities of nanostructures, we calculate the formation energy ${E}_{F}$ as follows:
${E}_{\text{form}}\left(X\right)={E}_{X}-{E}_{\text{germanium}}+{\mu }_{\text{Ge}}+{\mu }_{\text{H}}-{\mu }_{\text{Ga}}$(1)
${E}_{\text{form}}\left(X\right)={E}_{X}-{E}_{\text{germanium}}+{\mu }_{\text{Ge}}-{\mu }_{\text{As}}$(2)
The first two terms ${E}_{X}$ and ${E}_{\text{germanium}}$ are the total energies of Ga or As doped germanane and pristine germanium respectively. The ${\mu }_{\text{Ge}}$ and ${\mu }_{\text{H}}$
terms are the chemical potentials of the host Ge atom (obtained as the total energy per Ge atom from the unit cell of germanane monolayer) and H atom (obtained as the total energy per H atom from the
hydrogen molecule), whereas the ${\mu }_{X}$ term is the chemical potential of the Ga defect (obtained as the total energy per Ga atom from face centered cubic Ga structure) or As defect (obtained as
the total energy per As atom from the corrugate hexagonal structure structure) respectively. The calculation results show that the formation energies of gallium and arsenic doping are −2.01 eV and
−0.63 eV, respectively. This means that the two structures are thermodynamically stable.
3. Results and Discussion
3.1. Structure Properties
The Ge-Ge bond length( ${d}_{\text{Ge-Ge}}$ ), the lattice parameter (a), and the buckled height ( $\Delta z$ , show in Figure 2) in the optimized structure of the pristine germanane monolayer are
2.455Å, 4.060Å and 0.730Å, respectively. These values are in good agreement with experimental results and theoretical calculations [34] .
After the doping of gallium, the structure and symmetry distort much. The length of the bond between the gallium atom and the neighboring germanane atom is 2.455Å, 2.455Å, 2.458Å respectively. The
nearby Ge-Ge bond length also have changed in the range of −0.3Å to +0.3Å. Gallium defect also causes large changes in corrugate, buckled height $\Delta {z}_{\text{Ge-Ge}}=0.\text{73}0$ Å change to $
\Delta {z}_{\text{Ga-Ge}}=0.0\text{47}$ Å. The hydrogen atom corresponding to the germanium atom interacting with gallium shifts away from the gallium atom. On the other hand, the doping of arsenic
does not affect the structure and symmetry of the original germanane due to the remaining of the corresponding hydrogen atoms. The arsenic defected germanane monolayer is $\Delta {z}_{\text{Ge-As}}=
0.728$ Å that is basically same as pristine germanane, and the original hexagonal structure is well maintained.
3.2. Electronic Properties
This section analyzes the mechanism of the change of the energy band width of pristine germanane and doping system. The band structure and distribution of the density are shown in Figure 3. Take the
Fermi level as the zero point of energy.
Figure 3(a) show that pristine germanane has a direct bandgap and ${E}_{g}=1.080\text{\hspace{0.17em}}\text{eV}$ , this is consistent with the theoretical calculation of the literature. The
corresponding partial density of states of pristine germanane, as Figure 3(d), demonstrate that the
Figure 2. Side view of the supercell used in calculation: (a) pristine germanane monolayer (b) and (c) are gallium and arsenic defected germanane monolayer.
Figure 3. (a)-(c) Band structure of pristine germanane and its doping system; (d)-(f) Projected density of atates of pristine germanane and its doping system.
bottom of the conduction band is contributed by the Ge-4s and Ge-4p orbit, while the valence band of monolayer is derived from the contribution of H-s, Ge-4s and Ge-4p orbit, but the top of valence
is mainly contribute by H-s and Ge-4p. Figure 3(b), Figure 3(e) give the electronic properties of gallium doped germanane. Bandgap increase to ${E}_{g}=1.663\text{\hspace{0.17em}}\text{eV}$ .The
projected density of states in Figure 3(e) show that Ga-4p contributes to the top of valence band, so it is a p-type doping. A unoccupied Ga-4p orbit impurity appears in the energy gap below
conduction band. Due to the emergence of new energy levels, the the minimum energy of electrons from the valence band to the conduction band change to 0.949 eV. This energy value corresponds to the
absorption edge position of the absorption spectrum of the gallium doping system. Figure 3(c) is the band structure of arsenic doped germanane. The valence band is contribute by H-s, Ge-4p and As-4p
orbit, which has a strong hybrid coupling with each other. For arsenic atom has one more outermost electron than germanium atom, a occupied As-4p orbit impurity appears in the energy gap below
conduction band. The impurity bands come across the Fermi level, so As is a n-type doping.
3.3. Optical Properties
In order to further explore its electronic properties, we also made specific calculations and data analysis on the optical properties of germanane. The study of electronic structures helps to make
materials practically used in optoelectronic devices. Optical properties can be analyzed from the peaks and the intersection of the coordinates of the dielectric function. The dynamical dielectric
function of germanane at arbitrary wave vector q and frequency ω, ϵ(q, ω), is calculated in the self-consistent-field approximation. The corresponding optical constants of germanane and its doping
structures can be analysis from the real and imaginary parts of the dielectric function. The absorption coefficient n, the complex refractive index and the reflectance R of pristine germanane can be
obtained by the Equations (4)-(6), respectively [35] . The dielectric function can be a relatively complete representation of the optical properties of the germane and its doped structure.
${\epsilon }_{1}\left(\omega \right)=\frac{2{e}^{2}}{\Omega {\epsilon }_{0}}\sum |〈{\psi }_{k}^{c}|u\cdot r|{\psi }_{k}^{v}〉|\delta \left({E}_{k}^{c}-{E}_{k}^{u }-E\right)$(1)
${\epsilon }_{2}\left(\omega \right)=1+\frac{2}{\text{π}}P{\int }_{0}^{\infty }\frac{{\omega }^{\prime }{\epsilon }_{2}\left({\omega }^{\prime }\right)}{{{\omega }^{\prime }}^{2}-{\omega }^{2}}$(2)
$\alpha \left(\omega \right)=\sqrt{2}{\left[\sqrt{{\epsilon }_{1}^{2}\left(\omega \right)+{\epsilon }_{2}^{2}\left(\omega \right)}-{\epsilon }_{1}^{2}\left(\omega \right)\right]}^{1/2}$(3)
$n\left(\omega \right)=\frac{\sqrt{2}}{2}{\left[\sqrt{{\epsilon }_{1}^{2}\left(\omega \right)+{\epsilon }_{2}^{2}\left(\omega \right)}+{\epsilon }_{1}^{2}\left(\omega \right)\right]}^{1/2}$(4)
$k\left(\omega \right)=\frac{\sqrt{2}}{2}{\left[\sqrt{{\epsilon }_{1}^{2}\left(\omega \right)+{\epsilon }_{2}^{2}\left(\omega \right)}-{\epsilon }_{1}^{2}\left(\omega \right)\right]}^{1/2}$(5)
$R\left(\omega \right)={|\frac{\sqrt{\epsilon \left(\omega \right)}-1}{\sqrt{\epsilon \left(\omega \right)}+1}|}^{2}$(6)
Figure 4 depicts the dielectric function and the absorption coefficient of pristine germanane and its doping system for photon frequency up to 20 eV. The
Figure 4. (a)-(c) Dielectric function of pristine germanane and its doping system; (d)-(f) Absorption coefficient of pristine and its doping system.
lines of black and grey in Figure 4 represent the real part and imaginary part of the dielectric function, respectively. As shown in Figure 4(a) and Figure 4(b) tendency of the dielectric function of
pristine germanane and gallium doped germanane are consistent. It is observed that the static constant ${\epsilon }_{1}\left(\omega \right)$ is close to 3.85 and 4.32 respectively. Curve Figure 4(a)/
Figure 4(b) mainly drops rapidly till $E=4.44\text{\hspace{0.17em}}\text{eV}/E=4.32\text{\hspace{0.17em}}\text{eV}$ and then increase slowly to 17 eV/22 eV. The imaginary part of dielectric function
${\epsilon }_{2}\left(\omega \right)$ vanishes with the frequency $\omega =17\text{\hspace{0.17em}}\text{eV}/\omega =22\text{\hspace{0.17em}}\text{eV}$ . It is noteworthy that the value ${\epsilon }_
{1}\left(\omega \right)>0$ and ${\epsilon }_{2}\left(\omega \right)=0$ means the region is a transparent area. Refer to the absorption parameter as shown in Figure 4(a)/Figure 4(b), the optical
absorption edge is about 1.080 eV/0.949 eV that is corresponding to the band gap of pristine germanane and gallium doped germanane in our calculation. Figure 4(c) show the static constant ${\epsilon
}_{1}\left(\omega \right)$ is close to 12.2, dielectric constant is a measure of the polarizability of a material. It shows that the arsenic doping has a stronger electrode forming ability.
4. Conclusion
Germanane monolayer was doped with gallium atom or arsenic atom. The Ga defect can be integrated within a germanane monolayer at a relative low formation energy, without major structural distortions
and symmetry breaking. The As defect relaxes outward of the monolayer and breaks the symmetry. The density of states plots indicate that Ga doped germanane monolayer is p-type doping, whereas the As,
which has a extra outermost electron, is n-type doping. The optical properties of Ga and As doping were also examined, the result demonstrates that As doping has static dielectric constants ${\
epsilon }_{1}\left(\omega \right)$ close to12 which means a stronger polarization ability. The results of this study will be of great guiding significance for the practical application.
Conflicts of Interest
The authors declare no conflicts of interest regarding the publication of this paper.
Cite this paper
Liu, L., Ji, Y.J., Liu, Y.F. and Liu, L.Q. (2019) First-Principle Studies on the Ga and As Doping of Germanane Monolayer. Journal of Applied Mathematics and Physics, 7, 46-54. https://doi.org/10.4236
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A layman's explanation of Law of Large numbers
Created time
Dec 18, 2020 1:50 AM
The first step is to nail their intuition for randomness. Here's how I will do it.
I will ask them if I flip a coin once, will it be heads or tails. The answer would be It will be heads! or It can be either! (smart kid). If it is former, I can prove them wrong in 1-3 tries and lay
the path for explaining randomness. If it is later, they already have some intuition for randomness.
I will now ask if I flip it 10 times, how many will be heads and tails. The answer will be either It depends! or It will be 5-5 (50%-50%). Now I will demonstrate and ask them to keep track and show
that it is not 5-5 (hopefully) and ask them why it wasn't. The general answer will be the way you are flipping, how much energy you are using, how high you are flipping. I will say OH! you mean it's
random! ok! Generally, they will understand by now. If not, repeat this and show that the result is different and random.
As they are keeping track, at the end of 6, 8, 10, 12, 14, 18, 20 trials, I will keep asking the proportions of heads to tails and show them how it is converging. I will again summarize that the
proportion was 75-25 at 4 trials, 60-40 at 10 trials, and that it would be close to 50-50 at 100 trials and even close at 1000 trials and as the no. of trials increase, they would be
I will finish by saying that your initial answer of 50%-50% is in fact true, but you can only be sure at large numbers, and not so sure at small numbers.
I will give another example using the average height of kids in their class and how by taking more and more kids into the sample, we can actually get closer and closer to the true value.
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09-06-2024 02:17 PM
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Re: Longitudinal study - how to plot the outcome with CI against time on SAS Procedures. Wednesday
Hello, I intend to test a interaction between two variables, but not via multiplicative interaction variable (e.g., Y = beta0 + beta1*X1 + beta2*X2 + beta3*X1*X2). My GLM model is Y = beta0 +
beta1*X1 + beta2*X2. After the PROC GLM I got the estimation of beta1 and beta2 with their 95% confidence intervals. Both X1 and X2 are binary variables, means they either can be 0 or 1,
respectively. Now I want to estimate the interaction contrast (additive interaction instead of multiplicative one), defined as, Interaction contrast = Y11 - Y01 - Y10 + Y00, and to compare it with
ZERO. It would be better to have its 95% confidence interval. However, I don't know how to. Thanks.
... View more
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Library Stdlib.Logic.ExtensionalFunctionRepresentative
This module states a limited form axiom of functional extensionality which selects a canonical representative in each class of extensional functions
Its main interest is that it is the needed ingredient to provide axiom of choice on setoids (a.k.a. axiom of extensional choice) when combined with classical logic and axiom of (intensonal) choice
It provides extensionality of functions while still supporting (a priori) an intensional interpretation of equality
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Lesson Narrative
In grade 7, students described the two-dimensional figures that result from slicing three-dimensional figures. Here, these concepts are revisited with some added complexity. Students analyze cross
sections, or the intersections between planes and solids, by slicing three-dimensional objects. Next, they identify three-dimensional solids given parallel cross-sectional slices. In addition, they
revisit solid geometry vocabulary terms from earlier grades: sphere, prism, cylinder, cone, pyramid, and faces.
Spatial visualization in three dimensions is an important skill in mathematics. Understanding the relationship between solids and their parallel cross sections will be critical to understanding
Cavalieri’s Principle in later lessons. Cavalieri’s Principle will be applied to the development of the formula for the volume of pyramids and cones. Students use spatial visualization to make sense
of three-dimensional figures and their cross sections throughout the lesson (MP1).
Learning Goals
Teacher Facing
• Generate multiple cross sections of three-dimensional figures.
• Identify the three-dimensional shape resulting from combining a set of cross sections.
Student Facing
• Let’s analyze cross sections by slicing three-dimensional solids.
Required Preparation
Obtain several cylindrical food items to cut with a plastic knife.
Devices are required for the digital version of the activity Slice That. If using the paper and pencil version, prepare various solids from clay or play dough, such as cubes, spheres, cones, and
cylinders. Each group of 3-4 students should have access to a three-dimensional solid to analyze.
Alternatively, you might consider getting food items from the grocery store with interesting cross sections or three-dimensional foam solids from a craft store, and plastic knives to slice the
Student Facing
• I can identify the three-dimensional shape that generates a set of cross sections.
• I can visualize and draw multiple cross sections of a three-dimensional figure.
CCSS Standards
Building On
Building Towards
Glossary Entries
• cone
A cone is a three-dimensional figure with a circular base and a point not in the plane of the base called the apex. Each point on the base is connected to the apex by a line segment.
• cross section
The figure formed by intersecting a solid with a plane.
• cylinder
A cylinder is a three-dimensional figure with two parallel, congruent, circular bases, formed by translating one base to the other. Each pair of corresponding points on the bases is connected by
a line segment.
• face
Any flat surface on a three-dimensional figure is a face.
A cube has 6 faces.
• prism
A prism is a solid figure composed of two parallel, congruent faces (called bases) connected by parallelograms. A prism is named for the shape of its bases. For example, if a prism’s bases are
pentagons, it is called a “pentagonal prism.”
• pyramid
A pyramid is a solid figure that has one special face called the base. All of the other faces are triangles that meet at a single vertex called the apex. A pyramid is named for the shape of its
base. For example, if a pyramid’s base is a hexagon, it is called a “hexagonal pyramid.”
• sphere
A sphere is a three-dimensional figure in which all cross-sections in every direction are circles.
Additional Resources
Google Slides For access, consult one of our IM Certified Partners.
PowerPoint Slides For access, consult one of our IM Certified Partners.
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Nonparametric Discounting
Robustness is key when assessing the performance of hedge funds. Since investment strategies are very diverse, sources of risk and corresponding exposures are hard to identify. Moreover, pension
funds and rich individuals do not exhibit the same risk tolerance and will not assess performance in the same way. Traditional measures cannot offer such robustness to complex risk-factor exposures
and investors’ risk aversion.
Ratios involving mean returns and volatility (Sharpe, Treynor or Information ratios) or even more sophisticated ratios accounting for downside risk (Sortino, Gain-Loss or Omega ratios), do not
control for the wide variety of strategies followed by hedge funds and therefore are not sufficiently informative to rank funds. Peer benchmarking also has its limits: homogeneous peer grouping is
difficult given the absence of information regarding the hedge funds’ holdings and strategies, and investors cannot assess whether or not the average manager within the peer group generates any
value. Measuring performance through alpha after adjusting the returns for the risk exposures to several factors delivers a finer basis for comparing funds.
Equity, fixed income, credit, commodity or currency risks are included, together with returns on option strategies built on these primitive factors. A main drawback of the current approaches is to
relate hedge fund returns to such risk factors linearly since it has been shown that hedge fund returns exhibit complex non-linear exposures to traditional asset classes.
Non-linear exposures and risk factors
We propose a new method that captures the complex non-linear exposures of a hedge fund strategy to several risk factors. It accommodates many non-linear functions of factor returns, hence the term
nonparametric, over and above the usual option payoff patterns. In addition, it produces a risk adjustment function that weights hedge fund returns differently depending on the risk tolerance of an
investor. Therefore, the computed alpha performance – the average of the risk-adjusted returns – is robust in both the non-linear exposure to risk factors and investors’ risk aversion.
Alpha performance is measured by the averaged product of a fund’s returns by a risk-adjustment function, called stochastic discount factor in asset pricing theory. Intuitively, the methodology is
based on seeking to identify a non-linear function of risk factors that remains positive at all times to avoid arbitrage and that prices perfectly the basis assets selected as factors. In other
words, the methodology will assign a zero alpha to any payoff that is trivially related to available factors, so that the measure of abnormal performance for hedge fund returns will only capture the
fraction of the hedge fund returns that is due to the managers’ active skills. The risk adjustment function makes clear which risk factors are really important for the performance of hedge funds
under analysis.
Risk adjusting hedge fund payoffs
The main idea is to risk-adjust hedge fund payoffs in a way that accounts for the asymmetry or tail risk exposures created by the dynamic strategies pursued by hedge funds. Indeed, the risk-adjusted
performance measure will not only be based on means and volatilities of hedge fund returns, which are not sufficient statistics given the strong deviations from normality that hedge fund returns
exhibit, but also on higher-order moments of the distribution of hedge fund returns.
To establish the relevance of our approach from an empirical standpoint, we evaluate the performance of various hedge fund indices, considering a set of risk factors including equities, bonds,
credit, currencies and commodities, as well as several straddle strategies. We report how the measured alpha varies with the inclusion of option-based factors and with the risk tolerance of the
investor. We find that, as we decrease risk tolerance, the alpha decreases significantly for some categories (emerging markets), while remaining fairly unchanged for others (equity hedge and macro).
In the latter case, we conclude that the performance is robust. Yet in other cases, some funds pay well in bad times (Asian funds or short bias), offering insurance value, and their alpha increases
as we decrease risk tolerance. These findings strongly suggest that what was incorrectly measured as hedge fund alpha in previous studies is actually some form of fair reward obtained by hedge fund
managers from holding a set of relatively complex linear and non-linear exposures with respect to various risk factors. Often the reduction in performance comes from a small number of extreme events
which are not captured well with the usual linear approach. Our findings also support the view that higher-moment equity risks capture a large part of the non-linear risk exposure of several hedge
fund strategies. However, exposure to higher-moment risks for bond, interest rate or currency is essential for other strategies, in particular emerging markets. Finally, we also illustrate with
individual funds how a fund manager can measure the sensitivity of his portfolio of funds to shocks affecting risk factors, that is macro shocks, or to idiosyncratic shocks impacting a particular
The approach can be extended to evaluate hedge fund managers’ performance conditionally to specific macroeconomic environments such as high or low interest-rate states, large or limited economic
uncertainty, boom or bear markets, liquid or illiquid markets, making the performance measurement more transparent to general economic conditions.
Evaluating performance
Performance evaluation of hedge funds has proceeded with two main approaches. One considers only absolute returns, while the other rests on the identification of risk factors behind hedge fund
returns. It has been quickly recognised that the absolute performance measurement for hedge funds needs to go beyond the traditional Sharpe or Treynor ratios.
Indeed, hedge fund return distributions are distinctly abnormal and measures based on the mean and variance are not sufficient to capture the risk associated with hedge fund returns. Other measures
have been proposed to account for the negative skewness and positive large kurtosis exhibited by hedge fund return distributions, namely the Sortino ratio, the Stutzer index or the Omega ratio. While
these adapted measures are better able to capture the higher-moment risk present in hedge fund returns, they are not sufficient to rank funds. We need additional indicators to know if a given fund is
doing well relative to other funds using similar strategies. The relative approach starts with the peer analysis, whereby funds in comparable groups are evaluated based on absolute return measures.
Performance relative to peers may be measured during market cycles or over short or long periods. However, the groups may not be homogeneous enough to capture the underlying exposures to different
risks. Therefore, measuring performance through alpha after accounting for the beta risks appears to deliver a finer basis for comparison between funds.
Risk factors
The alpha approach necessitates spelling out the risk factors that may affect hedge fund returns. Given the wide diversity of strategies followed by hedge funds the literature has evolved to include
exposures to the main sources of risk, such as equity, fixed income, credit, commodity or currency. The main approach is to estimate linear factor models where hedge fund returns are regressed
linearly on such risk factors. Such an approach captures only linear exposure to the risk factors, but several studies have shown that a large number of equity-oriented hedge fund strategies exhibit
payoffs resembling a short position on a put option on the market index. These approaches to capturing non-linearities in hedge funds’ payoffs are targeted towards specific option-like strategies.
Fung and Hsieh (2001) analyse trend-following strategies and show that their payoffs are related to those of an investment in a lookback straddle. Mitchell and Pulvino (2001) show that returns to
risk arbitrage are similar to those obtained from selling uncovered index put options. Agarwal and Naik (2004) extend these results and show that, in fact, a wide range of equity-oriented hedge fund
strategies exhibit this non-linear payoff structure. Diez de los Rios and Garcia (2011) propose a more general approach to identify the nature of the option that best characterises the payoffs of a
hedge fund. It can therefore be used to analyse any strategy. However, one needs to specify the risk factor underlying the option and the number of kinks allowed. Most of their applications have used
the market index with one kink, to identify positions in put or call options or straddles. Extending the method to several risk factors and more than one kink runs into the obstacle of limited length
time series of hedge fund returns. Therefore, it is empirically impossible given the amount of data available to identify spread positions on several risk factors.
Limitations overcome
The approach proposed in this paper overcomes these limitations. First, it allows oneto look at the non-linear exposure of a hedge fund strategy to several risk factors. Second, it is not limited to
shapes resembling standard option payoff patterns. Being nonparametric, it produces a factor model that captures many non-linear functions of returns for the assets chosen as risk factors, overcoming
the above-mentioned problem of limited data availability.
Moreover, it can add non-linearities to option risk factors such as the straddle strategies used in Fung and Hsieh (2001). The main idea is to risk-adjust hedge fund payoffs in a way that accounts
for the asymmetry or tail risk exposures created by the dynamic strategies pursued by the hedge funds. Abnormal performance is measured by the expected product of a portfolio’s returns and a
risk-adjustment function also called stochastic discount factor. The evaluation can proceed unconditionally or conditionally to a set of lagged instruments.
The methodology is based on minimising a general convex function to obtain a Minimum Discrepancy (MD) measure (Corcoran, 1998) that exactly prices the basis assets selected as factors. A well known
example of such discrepancy measures is the Kullback-Leibler information criterion (KLIC). We choose a family of discrepancy functions that admits as particular cases the quadratic criterion of
Hansen and Jagannathan (1991), hereafter HJ, and the KLIC, but offers other information criteria that have different implications for assessing performance.
The solutions for these risk-adjustment non-linear functions are obtained more easily by solving a portfolio problem, with the maximisation of a specific utility function in the Hyperbolic Absolute
Risk Aversion (HARA) family. The first-order conditions for these HARA optimisation problems provide solutions for the risk adjustment weights that are non-linear and positive, directly generalising
the linear SDF in HJ (1991) with positivity constraints and guaranteeing no arbitrage when pricing hedge fund payoffs. An additional advantage is that the approach shows how reference assets chosen
as risk factors should be weighted within the risk adjustment function, thus indicating which risk factors are really important when analysing hedge fund performance.
Using conditioning information
Several studies have used conditioning information to evaluate the performance of managed portfolios. Performance can be evaluated conditionally to specific macroeconomic environments such as high or
low interest-rate states, large or limited economic uncertainty, boom or bear markets, liquid or illiquid markets, making the performance measurement more transparent to general economic conditions.
These studies usually limit themselves to conditional measures of performance that involve only conditional means and variances of portfolio returns.
We extend the literature on conditional performance measurement by producing conditional measures that take into account all conditional moments of the risk-adjustment functions. Conditional
approaches have the potential advantage of having thinner tailed conditional distributions that better control the effect of extreme observations on the moments of asset returns. However, our
generalised discrepancy measures, even taken unconditionally, are better able to capture the effect of these extreme observations because they account for higher moments in the unconditional
distribution of returns. This is especially important when evaluating the performance of managed portfolios since private information on which fund managers condition their trades is unobservable.
In this case only the potentially fatter-tailed unconditional returns are observable. Our unconditional risk-adjustment measures will account for the effect of this unobservable information. Our
implied non-linear measures are related to a number of previous studies that feature non-linear risk-adjustment or discounting functions. Bansal and Viswanathan (1993) propose a neural network
approach to construct a non-linear stochastic discount factor that embeds specifications by Kraus and Litzenberger (1976) and Glosten and Jagannathan (1994).
Family of hyperbolic functions
Our approach provides a family of different hyperbolic functions of basis factor returns implied by the solution to portfolio problems. In Dittmar (2002), who also analyses non-linear pricing
kernels, preferences restrict the definition of the pricing kernel. Under the assumption of decreasing absolute risk aversion, he finds that a cubic pricing kernel is able to best describe a
cross-section of industry portfolios. Our nonparametric approach embeds such cubic non-linearities implicitly. Boyle et al. (2008) obtain robust prices for derivative securities based on discounting
functions that cause minimum perturbations on prices of derivatives payoffs. Our methodology, if used to price derivatives, will provide pricing intervals based on the HARA implied risk-adjustment
To establish the relevance of our approach, we evaluate the performance of various hedge fund indices, considering a set of risk factors including equities, bonds, credit, currencies and commodities,
as well as several straddle strategies. We compare the measured alphas to option-based performance measures obtained by a linear model. To capture non-linearities and measure the alpha performance of
the funds, Agarwal and Naik (2004) use a linear regression in which they introduce the returns on a portfolio of options along with the other usual risk factors.
Our analysis accounts explicitly for higher moments of returns induced by option-like strategies.Moreover, an important feature of our discrepancy-based approach is the possibility to capture more
complex non-linearities since options portfolios can be included as factors themselves. Alpha valuations obtained with the implied non-linear risk-adjustment measures are in general lower than the
performances exhibited when introducing option factors linearly.
Our study complements the analysis of Agarwal, Bakshi and Huij (2010) who investigate the relationship between the cross-section of hedge fund returns and higher-moment equity risks. We directly
relate the performance of hedge funds to higher moments of all risk factors, including straddles on equity, commodity, currency, bond, and short interest rate (see Fung and Hsieh, 2001). Our findings
support the view that higher-moment equity risks capture a large part of non-linear risk exposure of several hedge fund strategies. However, exposure to higher-moment risks for bond, interest rate or
currency is essential for other strategies, particularly for emerging markets.
Caio Almeida is an assistant professor in the Graduate School of Economics of the Getulio Vargas Foundation in Rio de Janeiro. René Garcia is Professor of Finance at EDHEC Business School and the
Academic Director of the EDHEC-Risk Institute PhD in Finance programme.
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Compare High Frequency Screens & Hydrocyclones - 911Metallurgist
Hydrocyclones are currently the most commonly used classifiers in wet closed circuit grinding systems. Some recent papers, however, give evidence that high frequency vibrating screens can be a viable
alternative to hydrocyclones for a wide variety of grinding applications.
In principle, classifier selection for closed circuit grinding should be based on an evaluation of the advantages provided by each classifier type being considered (e.g., increased circuit capacity,
improved water balance, reduction in undesirable fines, etc.) versus costs (capital, installation, operating). Furthermore, the evaluation should be made for those conditions of optimal mill/
classifier performance which give the desired product quality. This requires a detailed knowledge of the factors which affect the performance of the classifier types of interest. .
Pilot Plant Study
The feed materials used for the pilot plant study were three different limestones designated here as limestones A, B and C, having Bond Work Indices of 6.4, 7.6 and 11.9 kW-hr/short ton,
respectively. All three materials were used for closed circuit demonstration testing; limestone A was the feed material•used for model development and validation.
When constructing models for mills and classifiers it is customary to split the particle size range into geometric intervals according to the √2 sieve series and number the largest size 1, the second
largest size 2, etc., down to the smallest (sink) size n. This is done because material in one of these size intervals appears to behave like a homogeneous material, to a sufficient approximation.
Using this basis, models for ball mills are constructed as mass-size balances incorporating the concepts of specific rates of breakage Si, and primary progeny fragment distributions bij. Si is the
specific rate of breakage of size i, with units of fraction per minute being convenient for ball mills; bij is the weight fraction of progeny fragments which appear in smaller size i as a result of
primary breakage of larger size j. Combining these concepts into a size mass balance for a fully mixed batch mill gives the equation set known as the batch grinding equation:
where wi(t) gives the particle size distribution as a function of grinding time t. Reid showed that the concept of residence time distribution (RTD) could be immediately applied to a steady-state
continuous mill to give
where ∅ (t)dt is the fraction of feed which leaves the mill at time t to t+dt after admission, and ∅(t) is thus the RTD (units of fraction per unit time); pi is the fraction of the mill product of
size i. The solution of Equations 1 and 2 for known feed size distribution and known ∅(t) can be put as
where fj is the weight fraction of the mill feed of size j and the dij is a matrix of “transfer” parameters. When expressed as Equation 3, the function of the simulation model is to compute dij
(which contain the Sj, bij and RTD) for the mill design and operating conditions of interest.
The objective selected for pilot plant simulations was to determine the maximum circuit product rate Q when producing product size distributions with a specified 80% – passing size in the range of 25
to 90 microns. This objective is relatively simple to accomplish since there are no constraints due to specifications on the density of the fine product slurry. Note, however, that simulations
performed without regard to specifications on the circuit water balance may not be realistic for many applications.
The reasons for these results are clear upon examination of the corresponding classifier performance data. Figure 8 shows the classifier bypass data corresponding to the results in Figures 5 and 6.
Lower bypass tends to give higher Q, by reducing overgrinding of fines and giving a steeper product size distribution as shown in Figure 7. Higher sharpness index has the same effect and as Figure 9
shows the SI is higher for the screen above about 45 microns. The sum effect of bypass and SI is to favor screens for 80% – passing sizes above 40 microns.
Design of a Full Scale Circuit
It was of interest to the authors to evaluate high frequency screens versus hydrocyclones for the wet, closed circuit grinding of a coal in a full-scale ball mill circuit. The coal feed was a crusher
product having a top size of 9.5 mm. The specification for the ground coal product was 95 weight percent smaller than 160 ± 10 microns and 80 weight percent smaller than 110 ± 10 microns, with no
specification for the solids density of the circuit product.
Use of this hydrocyclone model in effect set the minimum size of mill for the evaluation. That is, since the model is for a particular size of hydrocyclone operated over its normal range of slurry
feed rate, which Slechta and Firth report to be 250-500 liters/min at 9 to 35 weight percent solids, the mill required for a single mill/hydrocyclone system had to be large enough to provide, the
solid rates necessary for normal operation of the hydrocyclone. For simulation this is necessary in order to establish dimensions for a mill and therefore allow the appropriate Si correcting factors
to be calculated. For larger mills than this minimum size, one would use a multiple hydrocyclone arrangement. From the Slechta and Firth report, the maximum hydrocyclone solids feed rate would be
about 15 tph of coal. Assuming a reasonable circulation ratio of 2.5, the minimum size of mill appropriate for evaluation was determined to be 1.37 m in diameter for an assumed mill-to-length ratio
of 1.5.
Over most of the product size range examined, particularly in the range of interest, 80 weight percent passing 100 to 120 microns, high frequency screening with the DF 88 or DF 105 cloths gives
higher Q than when the hydrocyclone is used. That the screen and hydrocyclone results are not so different is due to the relatively low hydrocyclone bypass, a result of feeding the hydrocyclone
relatively dilute slurries, to obtain dilute fine products.
It is interesting to examine the costs of high frequency screening versus hydrocyclones for this grinding application. In general these costs are a function of the number of units required and
capital cost per unit, installation costs, and operating costs. For high frequency screening, the data presented by Rogers and Brame and substantiated by Derrick show that a Derrick screening machine
fitted with DF 88 screen cloths can classify about 500 liters/min of the coal slurry per square meter of screening area.
The results presented in the pilot plant study indicate that high frequency screens can be a viable alternative to hydrocyclones for the wet, closed circuit grinding of fine-slurries.
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Why do we study certain math topics ? - American Diploma
why sine and cosine
Studying math topics serves a greater purpose than mere academic requirements. At Minshawy Math, we understand the importance of comprehending various mathematical concepts and their real-world
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Re: st: RE: Survey design degrees of freedom help
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: st: RE: Survey design degrees of freedom help
From [email protected]
To [email protected]
Subject Re: st: RE: Survey design degrees of freedom help
Date Thu, 3 Sep 2009 21:05:53 -0500
For the model F test in -svy: logit- and -svy: reg-, Stata 10 computes
the denominator degrees of freedom as: (design degrees of freedom) -
(numerator degrees of freedom) +1. In other words, the sum of the
numerator and denominator degrees of freedom = design d.f. + 1. I too
am away from the office, so I don't know the reference for this
On Thu, Sep 3, 2009 at 2:47 PM, Stas Kolenikov<[email protected]> wrote:
> Jennifer,
> first of all, you don't need to subtract the constant term.
> Stratification, in a sense, implies estimation of the fixed effect of
> a stratum (although there's way more going on).
> You are right in thinking about degrees of freedom independent pieces
> of information provided by each cluster/village. In the extreme case
> when you sample the complete cluster, you only have one number out of
> it (in terms of contributions to the variability of your estimates),
> no matter how many units you have in the cluster. In less extreme
> cases with large sample sizes within cluster, you have that number
> (the cluster mean, say) plus some relatively small amount of variation
> around it, so you still have 1 d.f. contributed by the cluster (or
> 1+epsilon, if you like; although nobody really knows what this epsilon
> might be). If you think about your sample (x1, ..., xn) as a vector in
> n-dimensional space, the standard i.i.d. theory assumes that each
> component of the vector can vary on its own, thus producing n degrees
> of freedom for the sample, and n-1 degrees of freedom for variance
> estimation (minus the overall mean). However in complex survey
> sampling case, you have components corresponding to the same cluster
> go together, at least to some extent, so your effective dimension is
> much lower than n, and in the aforementioned extreme cases it is #PSUs
> - #strata.
> The issue of degrees of freedom has been discussed by Korn & Graubard,
> although I am not sure whether it was their book
> (http://www.citeulike.org/user/ctacmo/article/553280) or a paper
> (http://www.citeulike.org/user/ctacmo/article/933864). If you are
> really short on degrees of freedom, you can cheat and go to the next
> level, and use SSUs instead of PSUs as the baseline for degrees of
> freedom (so d.f. = #SSUs - #strata). That's what you've done, too,
> with your 90 SSUs and 86 "cheated" d.f.s. They've outlined some other
> approaches, but that's probably the one easiest to understand. Still I
> would frown upon that, and if I were to referee a paper that does
> this, I would have the authors write a half-page explanation of what
> they are doing, and recognize that this is basically a wrong thing to
> do.
> Now, where would those degrees of freedom matter in estimation
> procedures? First, that's the number of terms added up to form the
> covariance matrix, so the rank of that matrix is bounded by d.f.s. You
> might still be able to run a regression with more terms, but Stata
> will refuse conducting tests with more than d.f. terms. That is the
> main concern you are voicing. Second, the d.f.s are also used in the
> Student distribution for testing purposes. Nobody has ever justified
> the use of Student distribution in this context (in the end, it is a
> model-based derivation assuming normality, whereas the survey
> inference is supposed to be fully non-parametric without any
> distributional assumptions), but it seems to be working better as an
> approximation to the realistic distributions.
> Amazingly (and ashamingly), I cannot produce any references off the
> top of my head that would deliver a clear explanation of those degrees
> of freedom (I am not in my office where all the books are now). I hope
> Korn & Graubard would give some references when they discuss the
> issue...
> I've seen things going either way with those degrees of freedom in my
> analytical work and simulations. Sometimes, when your cluster effects
> are not terribly strong, you are OK with #SSU-#strata (and if
> #PSU-#strata is over a hundred, who cares, anyway). Other times, I've
> seen the effective degrees of freedom around 5 or 10 when the nominal
> degrees of freedom (#PSU-#strata) was close to a hundred -- I had some
> problematic strata with extreme skewness and kurtosis, so whatever I
> happened to sample there was driving the remainder of the sample.
> On Thu, Sep 3, 2009 at 2:20 PM, Jennifer Schmitt<[email protected]> wrote:
>> Thank you for your thoughts. The 20 villages are the only independent
>> pieces of information, the rest are related. Is that the reason? It just
>> seems so restrictive. I do have multi-stage sampling and my understanding
>> of STATA is that it uses an "ultimate" cluster method, so unless my fpc are
>> defined (which I don't define because they are all close to one), then STATA
>> doesn't care about subsequent clusters because STATA incorporates all later
>> stages of clustering in the main cluster. Therefore there is no change in
>> my df. I have gone ahead and when necessary (because I need more df) I have
>> defined my PSU as subvillage and get 90 (#subvillages) - 3 (#strata) - 1(for
>> the constant = 86 df, but then I'm am ignoring the correlation of
>> subvillages within a village. I feel confident that I really only have 16
>> df, it is just convincing others who do not know STATA or survey statistics
>> that I have set up the statistical restrictions correctly and given the low
>> df I have yet to convince others. I've told them that the villages are the
>> only independent units, but that just does not seem sufficient. Any more
>> thoughts by you or others is greatly appreciated, but regardless thanks for
>> you thoughts thus far.
> --
> Stas Kolenikov, also found at http://stas.kolenikov.name
> Small print: I use this email account for mailing lists only.
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
Steven Samuels
[email protected]
18 Cantine's Island
Saugerties NY 12477
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
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Linked Lists – Sorting, Searching, Finding Maximum and Minimum
In one of the previous posts, we discussed in depth the concepts behind linked lists. In this post, we will explore some more programs and applications built on linked lists. Remember that the data
structure that we are using is quite simple:
typedef struct linked_list
int data;
struct linked_list *next;
} Node;
We define a data element and a pointer to the next node. Let’s first start with sorting a linked list.
Sort a linked list
void Sort()
// traverse the entire list
for (Node *list = head; list->next != NULL; list = list->next)
// compare to the list ahead
for (Node *pass = list->next; pass != NULL; pass = pass->next)
// compare and swap
if (list->data > pass->data)
// swap
int temp = list->data;
list->data = pass->data;
pass->data = temp;
As you see above, sorting a linked list is not very different that sorting an array.
Search an element in linked list
// finds the first node with the specified value
// assumes that head pointer is defined elsewhere
Node* Find(int value)
// start at the root
Node *currentNode = head;
// loop through the entire list
while (currentNode != NULL)
// if we have a match
if (currentNode->data == value)
return currentNode;
else // move to the next element
currentNode = currentNode->next;
Find maximum and minimum in a linked list
// finds the maximum and minimum in the list
// assumes that head pointer is defined elsewhere
int MaxMinInList(int *max, int *min)
// start at the root
Node *currentNode = head;
if (currentNode == NULL)
return 0; // list is empty
// initialize the max and min values to the first node
*max = *min = currentNode->data;
// loop through the list
for (currentNode = currentNode->next; currentNode != NULL; currentNode = currentNode->next)
if (currentNode->data > *max)
*max = currentNode->data;
else if (currentNode->data < *min)
*min = currentNode->data;
// we found our answer
return 1;
At this point, you should be very comfortable with linked lists and ready to tackle some more complex operations and structures.
25 comments:
1. Yes, it is true. linked lists aren't rocket science as I used to think :D
2. yes but what if we need to return the value of the location of the Node?
3. your sort technique is a bit confusing. suppose you have a list 5,3,8,9,2,6.
it will only loop through the entire list once and won't sort it completely.After 1st iteration the list will be: 3,5,8,2,6,9. Which is not sorted. Correct me if I am wrong.
1. Ya... You are correct... It's true... He is finishing in o(n).. Possibly its not possible
4. @previous
there are two loops used
its a bubble sort .. you are running only inner loop
5. How many nodes does a shortest linked list have???
6. why the head is giving an error???
1. What error are you seeing?
7. identifier head is undefined
1. Is this a compile time error or a runtime error? Can you post the relevant error details from the VS output window?
Have you properly initialized the head pointer?
8. I copied the minimum and sorting part together in a file but im getting so many errors that many semi commas are missing
1. Aha. You of course need to fill in the other parts of the program. You need to write the main method, declare structures, etc. I would recommend picking a basic book and try from it.
9. couldn't do it :(
10. Hi,
I need a help with a question. There are two list-L1 and L2 of words, compare the two list and put the uncommon word into a new list called Result.
I need the simplified soln for this, so that the nested looping will not occur and time taken by system is less.
My Email id: rajan_raj31@rediffmail.com
1. Rajan,
I would love to see what solution you have come up with. Maybe we can work together to optimize it then.
11. can u give the full code for the maximum and minimum linked list, i mean the main section
1. Sure. Keep an eye on the blog for a new blog post that will give you the complete solution.
2. Hi Hassan,
Take a look at my latest post - http://www.programminginterviews.info/2013/10/linked-list-create-insert-sort-min-max-find-print-complete-program.html
12. You can find out the cycle or loop in a single linked list by using two pointer approach.
Below link can be useful to find out the algorithm to find cycle or loop in linked list
find out the cycle or loop in a single linked list in java
13. Hi can you help with this two questions?
14. can you pleases give me the code of making maximum and minimum no of list means 12345678 is the input data of your list the you can convert the list is like that
15. hello....i need a help...first you need to create circular linked list then do search process and then the element you searched has to be deleted...
lets say i have created a circular linked list, i have inserted elements like 5,10,15,20,25..if i enter the 15, the location of the element is 3 has to be shown and that element 15 has to get
deleted..this is problem..can you please help me with that..
Thank you
My email id: aneesh.muthyala8@gmail.com
16. Nice blog to read, Thanks for sharing this valuable article.
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MotionModelIdc undefined when cu_affine_type_flag is not present
Reported by: hanhuang Owned by:
Priority: blocker Milestone: VVC D10
Component: spec Version: VVC D9 vB
Keywords: Cc: vzakharc, yuwenhe, jvet@…
In the JVET-R2001-vA, the MotionModelIdc is undefined when cu_affine_type_flag is not present.
In equation (164), MotionModelIdc[ x ][ y ] = inter_affine_flag[ x0 ][ y0 ] + cu_affine_type_flag[ x0 ][ y0 ]. However, there's no inference value when cu_affine_type_flag is not present.
It's suggested to add inference rule when cu_affine_type_flag is not present as follows: When cu_affine_type_flag[ x0 ][ y0 ] is not present, it is inferred to be equal to 0.
Also note that in equation (163), when merge_subblock_flag[ x0 ][ y0 ] equals to 1, the value of MotionModelIdc[ x ][ y ] is actually temporally set to 1 as the final value will be depend on the
decoding process of subblock motion vector components and reference indices. Therefore, it's suggested to initialize MotionModelIdc[ x ][ y ] to 0 at the beginning of coding unit semantics and remove
equation (163). The semantics of cu_affine_type_flag can be cleaned as following:
cu_affine_type_flag[ x0 ][ y0 ] equal to 1 specifies that for the current coding unit, when decoding a P or B slice, 6-parameter affine model based motion compensation is used to generate the
prediction samples of the current coding unit. cu_affine_type_flag[ x0 ][ y0 ] equal to 0 specifies that 4-parameter affine model based motion compensation is used to generate the prediction samples
of the current coding unit. When cu_affine_type_flag[ x0 ][ y0 ] is not present, it is inferred to be equal to 0.
The variable MotionModelIdc[ x ][ y ] is derived as follows for x = x0..x0 + cbWidth − 1 and y = y0..y0 + cbHeight − 1:
MotionModelIdc[ x ][ y ] = inter_affine_flag[ x0 ][ y0 ] + cu_affine_type_flag[ x0 ][ y0 ]
Change history (7)
• Component changed from 360Lib to spec
• Milestone set to VVC D10
• Version set to VVC D9 vB
• Priority changed from minor to blocker
I confirm that the suggested fix is correct.
It looks unnecessary to initialize MotionModelIdc[ x ][ y ] to 0 at the beginning of coding unit semantics and remove equation (163).
Another possible fix without adding an inferred value cu_affine_type_flag[ x0 ][ y0 ] is to modify the equations as below:
– If general_merge_flag[ x0 ][ y0 ] is equal to 1, the following applies:
MotionModelIdc[ x ][ y ] = merge_subblock_flag[ x0 ][ y0 ] (165)
– Otherwise (general_merge_flag[ x0 ][ y0 ] is equal to 0), the following applies:
MotionModelIdc[ x ][ y ] = inter_affine_flag[ x0 ][ y0 ]? (1 +( sps_6param_affine_enabled_flag ？cu_affine_type_flag[ x0 ][ y0 ]：0)：0
FYI. The suggested fix in this ticket is aligned with s/w, which initializes the value of cu_affine_type_flag as 0. And it's more clean to initialize the value instead of putting many conditions.
Replying to zhangkai:
It looks unnecessary to initialize MotionModelIdc[ x ][ y ] to 0 at the beginning of coding unit semantics and remove equation (163).
Another possible fix without adding an inferred value cu_affine_type_flag[ x0 ][ y0 ] is to modify the equations as below:
– If general_merge_flag[ x0 ][ y0 ] is equal to 1, the following applies:
MotionModelIdc[ x ][ y ] = merge_subblock_flag[ x0 ][ y0 ] (165)
– Otherwise (general_merge_flag[ x0 ][ y0 ] is equal to 0), the following applies:
MotionModelIdc[ x ][ y ] = inter_affine_flag[ x0 ][ y0 ]? (1 +( sps_6param_affine_enabled_flag ？cu_affine_type_flag[ x0 ][ y0 ]：0)：0
• Resolution set to fixed
• Status changed from new to closed
Thanks for confirming and this is fixed in JVET-S2001-v9.
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Correlated atomic motions in liquid aluminum
The statics and dynamics of liquid Al just above the melting point were studied using simulation calculations in the range of small times (less than 10(-12) s) and small distances (less than 1 nm).
The static calculations for 500 atoms were performed using the Monte Carlo method and an interaction potential from the literature; for the time-dependent investigations the molecular dynamics with
equal input data was used. It is shown that liquid Al in the q-domain around 15 1/nm can be considered as an harmonic, amorphous system. Excitation spectra in the static case were calculated as
eigenvalue spectra of the coupling matrix and composed with results from molecular dynamics. The dynamic calculations show that the longitudinal motion suggests cluster oscillations, while in the
transversal part the diffusion behavior, expected for longer times, is already visible in the considered domain of small times.
Ph.D. Thesis
Pub Date:
□ Aluminum;
□ Atomic Interactions;
□ Autocorrelation;
□ Liquid Metals;
□ Statistical Correlation;
□ Amorphous Materials;
□ Digital Simulation;
□ Molecular Excitation;
□ Monte Carlo Method;
□ Atomic and Molecular Physics
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Bayes' Theorem Problems, Definition and Examples
Bayes’ Theorem Problems, Definition and Examples
What is Bayes’ Theorem?
Bayes’ theorem is a way to figure out conditional probability. Conditional probability is the probability of an event happening, given that it has some relationship to one or more other events. For
example, your probability of getting a parking space is connected to the time of day you park, where you park, and what conventions are going on at any time. Bayes’ theorem is slightly more nuanced.
In a nutshell, it gives you the actual probability of an event given information about tests.
• “Events” Are different from “tests.” For example, there is a test for liver disease, but that’s separate from the event of actually having liver disease.
• Tests are flawed: just because you have a positive test does not mean you actually have the disease. Many tests have a high false positive rate. Rare events tend to have higher false positive
rates than more common events. We’re not just talking about medical tests here. For example, spam filtering can have high false positive rates. Bayes’ theorem takes the test results and
calculates your real probability that the test has identified the event.
The Formula
Bayes’ Theorem (also known as Bayes’ rule) is a deceptively simple formula used to calculate conditional probability. The Theorem was named after English mathematician Thomas Bayes (1701-1761). The
formal definition for the rule is:
In most cases, you can’t just plug numbers into an equation; You have to figure out what your “tests” and “events” are first. For two events, A and B, Bayes’ theorem allows you to figure out p(A|B)
(the probability that event A happened, given that test B was positive) from p(B|A) (the probability that test B happened, given that event A happened). It can be a little tricky to wrap your head
around as technically you’re working backwards; you may have to switch your tests and events around, which can get confusing. An example should clarify what I mean by “switch the tests and events
Bayes’ Theorem Example #1
You might be interested in finding out a patient’s probability of having liver disease if they are an alcoholic. “Being an alcoholic” is the test (kind of like a litmus test) for liver disease.
• A could mean the event “Patient has liver disease.” Past data tells you that 10% of patients entering your clinic have liver disease. P(A) = 0.10.
• B could mean the litmus test that “Patient is an alcoholic.” Five percent of the clinic’s patients are alcoholics. P(B) = 0.05.
• You might also know that among those patients diagnosed with liver disease, 7% are alcoholics. This is your B|A: the probability that a patient is alcoholic, given that they have liver disease,
is 7%.
Bayes’ theorem tells you:
P(A|B) = (0.07 * 0.1)/0.05 = 0.14
In other words, if the patient is an alcoholic, their chances of having liver disease is 0.14 (14%). This is a large increase from the 10% suggested by past data. But it’s still unlikely that any
particular patient has liver disease.
More Bayes’ Theorem Examples
Bayes’ Theorem Problems Example #2
Another way to look at the theorem is to say that one event follows another. Above I said “tests” and “events”, but it’s also legitimate to think of it as the “first event” that leads to the “second
event.” There’s no one right way to do this: use the terminology that makes most sense to you.
In a particular pain clinic, 10% of patients are prescribed narcotic pain killers. Overall, five percent of the clinic’s patients are addicted to narcotics (including pain killers and illegal
substances). Out of all the people prescribed pain pills, 8% are addicts. If a patient is an addict, what is the probability that they will be prescribed pain pills?
Step 1: Figure out what your event “A” is from the question. That information is in the italicized part of this particular question. The event that happens first (A) is being prescribed pain pills.
That’s given as 10%.
Step 2: Figure out what your event “B” is from the question. That information is also in the italicized part of this particular question. Event B is being an addict. That’s given as 5%.
Step 3: Figure out what the probability of event B (Step 2) given event A (Step 1). In other words, find what (B|A) is. We want to know “Given that people are prescribed pain pills, what’s the
probability they are an addict?” That is given in the question as 8%, or .8.
Step 4: Insert your answers from Steps 1, 2 and 3 into the formula and solve.
P(A|B) = P(B|A) * P(A) / P(B) = (0.08 * 0.1)/0.05 = 0.16
The probability of an addict being prescribed pain pills is 0.16 (16%).
Example #3: the Medical Test
A slightly more complicated example involves a medical test (in this case, a genetic test):
There are several forms of Bayes’ Theorem out there, and they are all equivalent (they are just written in slightly different ways). In this next equation, “X” is used in place of “B.” In addition,
you’ll see some changes in the denominator. The proof of why we can rearrange the equation like this is beyond the scope of this article (otherwise it would be 5,000 words instead of 2,000!).
However, if you come across a question involving medical tests, you’ll likely be using this alternative formula to find the answer:
1% of people have a certain genetic defect.
90% of tests for the gene detect the defect (true positives).
9.6% of the tests are false positives.
If a person gets a positive test result, what are the odds they actually have the genetic defect?
The first step into solving Bayes’ theorem problems is to assign letters to events:
• A = chance of having the faulty gene. That was given in the question as 1%. That also means the probability of not having the gene (~A) is 99%.
• X = A positive test result.
1. P(A|X) = Probability of having the gene given a positive test result.
2. P(X|A) = Chance of a positive test result given that the person actually has the gene. That was given in the question as 90%.
3. p(X|~A) = Chance of a positive test if the person doesn’t have the gene. That was given in the question as 9.6%
Now we have all of the information we need to put into the equation:
P(A|X) = (.9 * .01) / (.9 * .01 + .096 * .99) = 0.0865 (8.65%).
The probability of having the faulty gene on the test is 8.65%.
Bayes’ Theorem Problems #4: A Test for Cancer
I wrote about how challenging physicians find probability and statistics in my post on reading mammogram results wrong. It’s not surprising that physicians are way off with their interpretation of
results, given that some tricky probabilities are at play. Here’s a second example of how Bayes’ Theorem works. I’ve used similar numbers, but the question is worded differently to give you another
opportunity to wrap your mind around how you decide which is event A and which is event X.
Q. Given the following statistics, what is the probability that a woman has cancer if she has a positive mammogram result?
• One percent of women over 50 have breast cancer.
• Ninety percent of women who have breast cancer test positive on mammograms.
• Eight percent of women will have false positives.
Step 1: Assign events to A or X. You want to know what a woman’s probability of having cancer is, given a positive mammogram. For this problem, actually having cancer is A and a positive test result
is X.
Step 2: List out the parts of the equation (this makes it easier to work the actual equation):
Step 3: Insert the parts into the equation and solve. Note that as this is a medical test, we’re using the form of the equation from example #2:
(0.9 * 0.01) / ((0.9 * 0.01) + (0.08 * 0.99) = 0.10.
The probability of a woman having cancer, given a positive test result, is 10%.
Remember when (up there ^^) I said that there are many equivalent ways to write Bayes Theorem? Here is another equation, that you can use to figure out the above problem. You’ll get exactly the same
The main difference with this form of the equation is that it uses the probability terms intersection(∩) and complement (^c). Think of it as shorthand: it’s the same equation, written in a different
In order to find the probabilities on the right side of this equation, use the multiplication rule:
P(B ∩ A) = P(B) * P(A|B)
The two sides of the equation are equivalent, and P(B) * P(A|B) is what we were using when we solved the numerator in the problem above.
P(B) * P(A|B) = 0.01 * 0.9 = 0.009
For the denominator, we have P(B^c ∩ A) as part of the equation. This can be (equivalently) rewritten as P(B^c*P(A|B^c). This gives us:
P(B^c*P(A|B^c) = 0.99 * 0.08 = 0.0792.
Inserting those two solutions into the formula, we get:
0.009 / (0.009 + 0.0792) = 10%.
Bayes’ Theorem Problems: Another Way to Look at It.
Bayes’ theorem problems can be figured out without using the equation (although using the equation is probably simpler). But if you can’t wrap your head around why the equation works (or what it’s
doing), here’s the non-equation solution for the same problem in #1 (the genetic test problem) above.
Step 1: Find the probability of a true positive on the test. That equals people who actually have the defect (1%) * true positive results (90%) = .009.
Step 2: Find the probability of a false positive on the test. That equals people who don’t have the defect (99%) * false positive results (9.6%) = .09504.
Step 3: Figure out the probability of getting a positive result on the test. That equals the chance of a true positive (Step 1) plus a false positive (Step 2) = .009 + .09504 = .0.10404.
Step 4: Find the probability of actually having the gene, given a positive result. Divide the chance of having a real, positive result (Step 1) by the chance of getting any kind of positive result
(Step 3) = .009/.10404 = 0.0865 (8.65%).
Other forms of Bayes’ Theorem
Bayes’ Theorem has several forms. You probably won’t encounter any of these other forms in an elementary stats class. The different forms can be used for different purposes. For example, one version
uses what Rudolf Carnap called the “probability ratio“. The probability ratio rule states that any event (like a patient having liver disease) must be multiplied by this factor PR(H,E)=P[E](H)/P(H).
That gives the event’s probability conditional on E. The Odds Ratio Rule is very similar to the probability ratio, but the likelihood ratio divides a test’s true positive rate divided by its false
positive rate. The formal definition of the Odds Ratio rule is OR(H,E)=P[H,](E)/P[~H](E).
Bayesian Spam Filtering
Although Bayes’ Theorem is used extensively in the medical sciences, there are other applications. For example, it’s used to filter spam. The event in this case is that the message is spam. The test
for spam is that the message contains some flagged words (like “viagra” or “you have won”). Here’s the equation set up (from Wikipedia), read as “The probability a message is spam given that it
contains certain flagged words”:
The actual equations used for spam filtering are a little more complex; they contain more flags than just content. For example, the timing of the message, or how often the filter has seen the same
content before, are two other spam tests.
Next: Inverse Probability Distribution
Dodge, Y. (2008). The Concise Encyclopedia of Statistics. Springer.
Everitt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of Statistics, Cambridge University Press.
Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.
Comments? Need to post a correction? Please Contact Us.
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CMPT 260 Assignment 3
1. You have 2 parents, 4 grandparents, 8 great-grandparents, and so forth. If all of your
ancestors were distinct, what would be the total number of your ancestors for the
past 40 generations, counting your parent’s generation as number 1? Hint: What
kind of sequence is this? Use the sum formula for that sequence to solve the
problem. Show your work. (3 marks).
2. Give a proof by contradiction to show that there does not exist a constant c such
that for all integers n≥1, (n+1)2
3. Given the fact that ⌈x⌉ < x + 1, give a proof by contradiction that if n items are placed
in m boxes then at least one box must contain at least ceiling(n/m) items. (3 marks)
4. Use mathematical induction to prove the following statement is true for all integers
n≥2. Clearly identify the base case, the induction hypothesis and the induction step
you are using in your proof. (3 marks)
5. Use the Euclidian Algorithm (outlined in Epp pages 220 – 224) to hand-calculate the
greatest common denominator (gcd) of 832 and 10933 (2 marks)
6. Prove, by contraposition, that if (n(n-1) + 3(n-1) – 2) is even then n is odd. Assume
only the definition of odd/even. (3 marks)
7. Use mathematical induction to prove that
i=1 (5i-4)=n(5n−3)/2. Clearly identify
the base case, the induction Hypothesis and the induction step you are using in your
proof. (3 marks)
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Essay About: Basic Concepts Of Similarity And Units Main Goal
Essay About Basic Concepts Of Similarity And Units Main Goal
Essay, Pages 1 (281 words)
Latest Update: April 2, 2021
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• Science
Math Portfolio 1
Math Portfolio 1
This units main goal was to use similar triangles to measure the length of a shadow. While using the variables D, H, and L, we have figured out a formula to measure a shadows length. In order to do
this though, everyone had to learn the basic concepts of similarity, congruence, right triangles, and trigonometry.
Similarity and congruence were two very important factors because they helped us learn about angles and the importance of triangles. Similarity was a key to find out how to use proportions to figure
out unknowns (such as in HW7). Once similarity was learned we moved on to congruence where we learned proof and how to show others what is truth by giving them accurate facts based on previous
truths. If similar triangles share enough equal traits, they can be called congruent by ASA, SAS, SSS, and AAS.
Right triangles came next and with them we learned how and why they are special. As it turns out, right triangles are furtively hidden in many problems. Along with our unit problem to find out the
length of a shadow. Trigonometry worked with right angles as we learned about tangent, sine and cosine. Using trigonometry, we could figure out unknowns that were considered unsolvable to us when we
only knew about proportions.
All of these concepts and ideas really helped us find the final equation for finding the length of a shadow. They all built upon each other and with a little logical reasoning we were able to finally
solve it. Using similarity, we were able to use proportions, which was the foundation of our shadows equation. With right triangles we knew how to position
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Let's develop a QR Code Generator, part III: error correction
Now comes the hard part.
Most of the Math in QR codes in performed in the Galois Field of order 2^8 = 256. In this set, denoted as GF(256):
• includes the numbers from 0 to 255;
• has an "addition" operation, which is actually the binary XOR and not the usual sum (so the "sum" of two elements will still be part of GF(256));
• has a "multiplication" operation, which is similar to the usual arithmetic multiplication but with some differences so that multiplying two elements will still give us an element of GF(256) (the
neutral element is still 1).
The algorithm chosen for EDC in QR codes is the Reed-Solomon error correction, which is widely used for streaming data (e.g. CDs, wireless communications) because it allows to correct errors found in
bursts, rather than single isolated cases. I won't go into details, but we're stuck with this kind of odd arithmetic.
Operations on GF(256)
The "addition" (XOR'ing) is quite simple. The neutral element with relation to XOR is still 0, as a ^ 0 = a. Also every element is the opposite of itself, since a ^ a = 0.
And since "subtraction" is defined as adding the opposite of the second term, this also means that the "subtraction" is equivalent of the "addition"! In fact: a - b = a ^ (-b) = a ^ b.
Now, about the multiplication. A Galois Field is cyclic, meaning that every non-zero element can be expressed as the power of a "primitive element" α. So, in GF(256), if a = α^n and b = α^m, then a ⋅
b = α^n ⋅ α^m = α^n + m.
But, as we said, a Galois Field is cyclic, so α^256 = α. This means that we can take the exponent n + m modulo 255, so we can simplify our computations a bit. In the end, a ⋅ b = α^(n + m) % 255 (if
both a and b are non-zero; the result is of course 0 otherwise).
This also means that for every a, a^256 = a, and then a^255 = 1, therefore a^254 = a^-1, i.e. is the inverse of a. So now we have a way to do divisions: a / b = α^n / α^m = α^n(α^m)^254 = α^(n + m *
254) % 255.
Operations in code
XOR'ing is no sweat for JavaScript or any other capable language, but multiplication is another story. The easiest thing to do is creating logarithmic and exponential tables, so it'll be easy to
convert a number from and to its exponential notation.
But how do we find α? It's not so hard, as there are φ(255) = 192 primitive elements in GF(256), where φ is Euler's totient function. For the sake of simplicity, we can take α = 2.
Since we're dealing with values all below 256, we can use JavaScript's Uint8Arrays, but if you wish you can use just regular arrays:
const LOG = new Uint8Array(256);
const EXP = new Uint8Array(256);
for (let exponent = 1, value = 1; exponent < 256; exponent++) {
value = value > 127 ? ((value << 1) ^ 285) : value << 1;
LOG[value] = exponent % 255;
EXP[exponent % 255] = value;
We just start at 1, then double value at each iteration (shifting by 1 to the left). If value goes over 255, we XOR it with 285. Why 285? I won't go into details (if you're curious, you can find them
here), as it has something to do with the relation between elements of a Galois field and polynomials, but rest assured that we'll get all 255 non-zero elements like this.
In the end we'll have:
> LOG
< Uint8Array(256) [0, 0, 1, 25, 2, 50, 26, 198, 3, 223, 51, 238, ...]
> EXP
< Uint8Array(256) [1, 2, 4, 8, 16, 32, 64, 128, 29, 58, 116, 232, ...]
Now we can implement the functions for multiplication and division:
function mul(a, b) {
return a && b ? EXP[(LOG[a] + LOG[b]) % 255] : 0;
function div(a, b) {
return EXP[(LOG[a] + LOG[b] * 254) % 255];
But how will that serve us for error correction? Let's see...
Polynomials in GF(256)
Yes, the Reed-Solomon algorithm uses polynomials! You've probably seen them since high school, and have this form:
a[n]x^n + a[n - 1]x^n - 1 + ... + a[1]x + a[0]
where a[0], ..., a[n] are the coefficients, while x is the variable. You've probably seen (and solved, in the form of equations) them in the field of real numbers, with either real or complex
But coefficients, exponents and variables could be meant to be in any other field (ring would be enough, actually), even GF(256), inheriting its operations too. So, the "addition" is GF(256)'s
addition, i.e. XOR, while multiplication is the one seen above. Exponentiation is just repeated multiplication by itself, as usual.
The good news here is that, as long as our concern is just generation, we do not need to solve any equation!
Polynomial multiplication
Addition is a commutative operation, meaning that a + b = b + a. It is in GF(256) too, because a ^ b = b ^ a. And multiplication is too, but it's also distributive over the addition, meaning that a(b
+ c) = ab + ac. And this holds in GF(256) too.
This basically means that we can multiply polynomials between them like we used to do with polynomials on real numbers. Suppose we have
p[1](x) = a[n]x^n + a[n - 1]x^n - 1 + ... + a[1]x + a[0]
p[2](x) = b[m]x^m + b[m - 1]x^m - 1 + ... + b[1]x + b[0]
Take the first term of p[1](x), i.e. a[n]x^n, then multiply it with all the terms of p[2](x):
a[n]x^n⋅p[2](x) = a[n]b[m]x^n + m + a[n]b[m - 1]x^n + m - 1 + … + a[n]b[1]x^n + 1 + a[n]b[0]x^n
Then do the same with the second term of p[1](x), then the third, and so on. Finally, sum them all together. If this makes your head spin, let's start with and example: x^2 + 3x + 2 and 2x^2 + x +
7. As we've said above, we have to do the following:
(x^2 + 3x + 2)(2x^2 + x + 7)
= x^2(2x^2 + x + 7) + 3x(2x^2 + x + 7) + 2(2x^2 + x + 7)
= 2x^4 + x^3 + 7x^2 + 6x^3 + 3x^2 + 21x + 4x^2 + 2x + 14
= 2x^4 + (6 + 1)x^3 + (7 + 3 + 4)x^2 + (21 + 2)x + 14
= 2x^4 + 7x^3 + 14x^2 + 23x + 14
We end up with a polynomial with 5 terms, which is the sum of the amount of terms of both polynomials, minus 1.
In code
We can represent a polynomial with the array of its coefficients, so that x^2 + 3x + 2 could be translated to [1, 3, 2]. Again, since the coefficients can't go over 255, we can use Uint8Array to
optimize performances.
Of course all the operations are meant to be done in GF(256), so we're using XOR for addition and the mul function defined above.
Please read the comments in the code snippet below carefully 😁
function polyMul(poly1, poly2) {
// This is going to be the product polynomial, that we pre-allocate.
// We know it's going to be `poly1.length + poly2.length - 1` long.
const coeffs = new Uint8Array(poly1.length + poly2.length - 1);
// Instead of executing all the steps in the example, we can jump to
// computing the coefficients of the result
for (let index = 0; index < coeffs.length; index++) {
let coeff = 0;
for (let p1index = 0; p1index <= index; p1index++) {
const p2index = index - p1index;
// We *should* do better here, as `p1index` and `p2index` could
// be out of range, but `mul` defined above will handle that case.
// Just beware of that when implementing in other languages.
coeff ^= mul(poly1[p1index], poly2[p2index]);
coeffs[index] = coeff;
return coeffs;
Polynomial divisions
Ooooh boy. Remember long divisions in high school? Same thing here. (Except we'll just need the rest of the division, not the quotient, but let's save that for later.)
Let't take a dividend polynomial 4x^3 + 4x^2 + 7x + 5, and a divisor polynomial 2x + 1. Basically these are the steps:
1. divide the first term of the dividend polynomial (4x^3) with the first term of the divisor (2x, and get 2x^2);
2. multiply the divisor polynomial by the above quotient (you'll get 4x^3 + 2x^2);
3. get the rest by subtracting the result from the dividend (you'll get 2x^2 + 7x + 5);
4. if the degree of the rest is lower than the degree of the divisor, you're done; otherwise, the rest becomes your new dividend and you go back to step 1.
For the division above (in the field of real numbers), you'll get a polynomial quotient of 2x^2 + x + 3, and a rest of 2. Now let's do this in JavaScript, and in GF(256).
In code
The quotient polynomial will always be long the difference in length of the dividend and the divisor, plus one.
But it turns out that we don't need the quotient for the Reed-Solomon error correction algorithm, just the rest. So we're defining a function that returns only the rest of the division. The size of
the quotient is needed just to count the steps to do.
The code below should be self-explanatory given the example above (it really just does the steps above), but if it's not feel free to ask in the comments:
function polyRest(dividend, divisor) {
const quotientLength = dividend.length - divisor.length + 1;
// Let's just say that the dividend is the rest right away
let rest = new Uint8Array(dividend);
for (let count = 0; count < quotientLength; count++) {
// If the first term is 0, we can just skip this iteration
if (rest[0]) {
const factor = div(rest[0], divisor[0]);
const subtr = new Uint8Array(rest.length);
subtr.set(polyMul(divisor, [factor]), 0);
rest = rest.map((value, index) => value ^ subtr[index]).slice(1);
} else {
rest = rest.slice(1);
return rest;
Now what?
Theory says that a Reed-Solomon error correction data sequence spanning n codewords allows to recover up to n/2 unreadable codewords, they being among the data sequence or in error correction
sequence itself (!). Kinda cool, is it?
Remember the error correction table from the first part?
Level Letter Data recovery
Low L ~7%
Medium M ~15%
Quartile Q ~25%
High H ~30%
Those percentages are not results, but rather goals: for example, we want the quartile level of correction to be able to recover 25% (a quarter) of the codewords. This means that for this level of
correction, there must be as many error correction codewords as data codewords.
For example, a version 2 QR code contains 44 codewords in total. We want to recover up to 11 (25%) of them, which means that we must reserve 22 codewords for EDC. If it looks expensive, it's because
it is... but necessary if we want our QR codes to be readable even when damaged.
(The above applies for smaller QR codes. For larger ones, data is often split into two groups, and each group into several blocks - up to 67. Each block has its own error correction sequence, but
while data blocks for the second group are always one codeword larger then the blocks from the first group, error correction sequences are all long the same and sized for the larger block, so even
for quartile level EDC sequences could be slighly more in total codewords than data. We'll discuss about spliting data into blocks later in the series.)
From this, it's also clear we can't do much better than level H of error correction. If, for example, we wanted 18 codewords to be recoverable out of 44, then we had to use 36 codewords just for
error correction, leaving just 8 codewords for data - i.e. less than 18! It's clear it makes little sense, as we'd be better off just repeating the data.
Now let's focus on how to get those error correction codewords out of our data.
Working with (big) polynomials
In the second part, we've sequenced our data (the string https://www.qrcode.com/) into an array of bytes (or codewords, in QR code jargon). Now we've treated polynomials as arrays of values between 0
and 255, so basically using Uint8Arrays for both of them. And that's handy, since for error correction we have to view our data as a polynomial with the codewords as coefficients. Perfect!
Basically, we have our data that becomes this polynomial, called the message polynomial:
65x^27 + 118x^26 + 135x^25 + 71x^24 + … + 17x + 236
But we have 44 total codewords in our version 2 QR code, so we have to multiply this by x to the power of the error correction codewords, i.e. 16. In the end we have:
65x^43 + 118x^42 + 135x^41 + 71x^40 + … + 17x^17 + 236x^16
Now that we have our big polynomial, we have to divide it by... something, and take the rest of this division: the coefficients of the rest polynomial are going to be our error correction codewords!
But what's this divisor polynomial? Also called…
The generator polynomial
If we have to fill n codewords with error correction data, we need the generator polynomial to be of degree n, so that the rest is of degree n - 1 and so the coefficients are exactly n. What we're
going to compute is a polynomial like this:
(x - α^0)(x - α^1)(x - α^2)…(x - α^n - 2)(x - α^n - 1)
Now, as we've said, in GF(256) subtraction is the same as addition, and we've also chosen α to be 2. Finally, there are 16 codewords for medium correction in a version 2 QR code, so our generator
polynomial is this one:
(x + 1)(x + 2)(x + 4)(x + 8)(x + 16)(x + 32)(x + 64)(x + 128)(x + 29)(x + 58)(x + 116)(x + 232)(x + 205)(x + 135)(x + 19)(x + 38)
The values in the factors are basically the ones from the EXP table computed before. Anyway, let's get our polyMul function rolling!
function getGeneratorPoly(degree) {
let lastPoly = new Uint8Array([1]);
for (let index = 0; index < degree; index++) {
lastPoly = polyMul(lastPoly, new Uint8Array([1, EXP[index]]));
return lastPoly;
Normally, you'd want to pre-compute or cache these polynomials instead of generating them each time. Anyway, our polynomial will be this one:
// Uint8Array(17) [1, 59, 13, 104, 189, 68, 209, 30, 8, 163, 65, 41, 229, 98, 50, 36, 59]
Finally, we're getting our EDC codewords, by dividing our message polynomial with the generator polynomial:
function getEDC(data, codewords) {
const degree = codewords - data.length;
const messagePoly = new Uint8Array(codewords);
messagePoly.set(data, 0);
return polyRest(messagePoly, getGeneratorPoly(degree));
In the end:
const data = getByteData('https://www.qrcode.com/', 8, 28);
getEDC(data, 44);
// Uint8Array(16) [52, 61, 242, 187, 29, 7, 216, 249, 103, 87, 95, 69, 188, 134, 57, 20]
And we're done! 🙌 It's been a long, but fundamental chapter.
… at least for now. Because much still has to be done in order to create a working QR code.
Stay tuned for the next part, which will be a shorter one. We'll define some details around error correction, and learn how to actually displace all the codewords in the grid. In the following part,
we'll talk about masking.
Top comments (9)
latestversion • • Edited on • Edited
Very nice article! A question though: IIUC, GF(2^8) marks a set of polynomials with coefficients taken from GF(2), i.e. the coefficients can only be 0 or 1. Yet the article keeps referring to 255 as
being the top value for a coefficient. How come?
Massimo Artizzu •
Where did you get that the coefficients can only be 0 or 1? Some irreducible polynomials used for the algorithm have only 0 or 1 as coefficients, but not in the general case.
latestversion •
I was reading up on finite fields (in preparation for QR code generation, obviously :)) and in these lecture notes - engineering.purdue.edu/kak/compsec/ (Finite Fields PART 1-4) - the field GF(2^8)
is described as comprising elements that are polynomials (up to a certain degree) with coefficients in the set {0,1} (because the coeffs themselves are from GF(2)).
The irreducible polynomials will always have 0,1 as coeffs, IIUC, (see e.g. codyplanteen.com/assets/rs/gf256_p...) but the generator polynomial(s) given in the QR standard have coefficients that are
powers of the primitive element (2, i.e. the polynomial x). Which is confusing to me. Maybe it boils down to the same thing in the end, if one were to rewrite the generator polynomials without the
primitive element.
I guess I'm having a bit of trouble merging the view of the fields and their arithmetics as given in the lecture notes with that of, it seems, the implementations I've found so far, with regards to
some aspects.
Massimo Artizzu •
I'm impressed the lengths you're covering to fully understand the algorithm behind - I have a degree in Mathematics and yet I stopped at some point 😅 Props to you!
And now I notice how miserably worded this phrase is:
Some irreducible polynomials used for the algorithm have only 0 or 1 as coefficients
What I mean that some polynomials have only 0 and 1 coeffs, and happen to be irreducible.
latestversion •
Thank you! And props to you too! I must say it's very nice to have trailblazers such as you that not only do the implementation but also write about it!
latestversion • • Edited on • Edited
Ah, I think I am beginning to understand the source of my confusion. I interpreted the (QR) standard's wording on the RS encoding as:
"Treat the message codewords as coefficients of a polynom that is an element of GF(2^8)"
But it should be, I guess, (although quite obtusely worded, IMHO):
"Use the message codewords (as coefficients) to form a polynomial with coefficients that are elements of GF(2^8)".
That would explain much. Such a relief. I thought I was going to have to go mad.
Massimo Artizzu •
Yes! I agree, that's kind of obscure.
But then again, the whole algorithm is kind of obscure haha
latestversion •
I'm at a point in my implementation where I get the same result for the polynomial division as in this tutorial (for the very same example), and I must take a moment to give your credit for the clean
code you have produced. My own code is generally blargh, in comparison, with complicated constructs of indices and unnecessary array constructs (very nice use of slice in the polyRest function!). And
ofc, overall impressive how you seem to be so confident with the arithmetics involved. Very valuable to follow your example. I imagine it would have taken me three days to figure out which k the
standard refers to when it says "if you do this by long division, you must multiply the data codewords by x^k". I'll see if I arrive at the same symbol in the end... :)
Pascal Roobrouck •
The first element of your LOG table is 0x00. I think it should be 0xFF.
Found these pre-calculated Log and Exp tables here
and I think they are correct.
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A model train, with a mass of 3 kg, is moving on a circular track with a radius of 2 m. If the train's rate of revolution changes from 5/4 Hz to 1/8 Hz, by how much will the centripetal force applied by the tracks change by? | HIX Tutor
A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #2 m#. If the train's rate of revolution changes from #5/4 Hz# to #1/8 Hz#, by how much will the centripetal force
applied by the tracks change by?
Answer 1
The change in centripetal force is $= 299.8 N$
Centripetal force is what
#F=mr omega^2#
The centripetal force fluctuation is
#Delta F=mr (Delta omega)^2#
#Delta F =3*2*(2pi(5/4-1/8))^2#
#=24 pi^2 (81/64)#
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Answer from HIX Tutor
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
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[Unofficial] Editorial — Google APAC 2017 Round B - Codeforces
Category: Ad-Hoc, Math, Greedy
Let's define n = min(L,R). Then the claim is that the sequence ()()...() consisting of n pairs of "()" will give us the maximum answer n*(n+1) / 2
Let's look at some sequence T = (S) where S is also a balanced parenthesis sequence of length m. Let's denote by X(S), the number of sub-strings of S that are also balanced and by X'(S) the number of
balanced parenthesis sub-strings that include the first and last characters of S (In fact this will be just 1). Then X(T) = X(S) + X'(S).
It should be easy to prove that X'(S) <= X(S) (simply because X'(S) is a constrained version of X(S))
If we rearrange our sequence T to make another sequence T' = "S()", then X(T') >= X(S) + X'(S). The greater than equal to sign comes because we might have balanced sub-strings consisting of a suffix
of S and the final pair of brackets.
Thus, we have that X(T') >= X(S) + X'(S) = X(T). Thus by rearranging the sequence in this manner, we will never perform worse. If we keep applying this operation on each string, we will finally end
up with a sequence of the form "()()...()" possibly followed by non-zero number of "(" or ")"
Category: Math, DP
Let's look at all valid pairs (i,j) in which i is fixed. Then, if i^a mod k = r then j^b mod k = (k-r) mod k.
There are only k possible values of the remainder after division. Since k is small enough, if we can quickly determine how many numbers i exist such that i^a mod k = r and j^b mod k = (k-r) mod k
then we can simply multiply these quantities and get our answer. Thus the reduced problem statement is —
Find the number of numbers i <= N such that i ^ a mod k = r for all r = 0 to k-1.
Let's denote by dp1[r] = number of i <= N such that i ^ a mod k = r. We will try to compute dp1 from r = 0 to k-1 in time O(K log a)
Let's make another observation —
i ^ a mod k = (i + k) ^ a mod k = (i + 2k) ^ a mod k = (i + x*k) ^ a mod k.
(i + x*k) ^ a mod k = (i mod k + (x * k) mod k) ^ a mod k
= (i + 0) ^ a mod k = i ^ a mod k
Now i + x * k <= n. This implies that x <= (n-i) / k.
Thus if we know that for some i <= K, i ^ a mod k is r then there are x + 1 such numbers which also have the same remainder.
This gives us a quick way to compute dp1
for i = 1 to k:
r = pow(i, a) mod k
x = (n-i) / k
dp1[r] += x + 1
Similarly, we can compute dp2[r] which denotes the number j <= N such that j ^ b mod k = r
Now our final answer is the sum of dp1[i] * dp2[(k-i) mod k] for i = 0 to k.
ans = 0
for i = 0 to k-1:
ans += dp1[i] * dp2[(k-i)%k]
But we need to exclude the cases when i = j.
To handle this we can simply iterate one last time from i = 1 to k and find all the cases when (i ^ a + i ^ b) mod k = 0. and subtract (1 + (n-i)/k) from the answer for all such i
for i = 1 to k
if pow(i,a) + pow(i,b) mod k == 0:
ans -= ((n-i)/k + 1)
Category: Greedy, Line Sweep
Refer to this comment
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Grant and Betty s Home
Big G Productions Home
Rubik s Cube
2003 World Championship
Solving Videos
Blindfold Cubing
Megaminx Solution
Move Notation
Cube visitors since 2004-March-26: ?
My Megaminx Solution
Before you delve into the solution that follows, be warned that for now, the solution is somewhat lengthy and completely textual (aside from a reference image showing the color orientation of my
megaminx). Also, this solution is not for the beginner cubist. It assumes a general knowledge of a CFL (cross, F2L, LL - any style) cubing solution and the ability to do basic destructive/
reconstructive moves. One day, I hope to add pictures and a more standardized notation (of which there is none at the moment), as well as beginner information, but this is how it stands for now:
Solving a 12-color megaminx
- Overview -
There is a difference between the methods and difficulties presented by the 12-color and 6-color varieties of the megaminx (aka minx ). Since I only own a 12-color minx (and that s all I ve
described how to solve to date), I m going to concentrate on that. This solution can be used for a 6-color minx, but is not complete (since a parity problem can arise on a 6-color puzzle), and may
not be the best approach.
This picture shows the color orientation of my minx. It s important, because when I solve it, I always go through the colors in the same order - when I don t, it slows me down significantly.
A while ago, I started with dark green, because it s surrounded by dark colors. That way, I could look at a corner and tell where it went - top face (has dark green), northern equatorial line
(across one edge piece from the green face, has two dark colors and one light), southern equatorial line (across one edge piece from the light green face, has two light colors and one dark), or
bottom face (has light green). This worked well, but dark green didn t really catch my eye very well, so the first face took more searching time than I wanted it to.
To minimize this, I now start with the dark color that seems to stick out the most to me (red), followed by the second most obvious which is also adjacent to the first (dark blue). Then, I go to the
dark green face (which is mostly complete at that point), and proceed as I used to. So, after doing the dark green, I do the other 3 dark colored faces surrounding it, which leaves light green and
the other light colors for the LL. There may actually be a better order, but because of how I used to do it, changing the color of the LL would set me back for quite a while until I m used to the new
order. I ve decided that, for now, it s not worth the downtime of relearning.
- Notation -
Though there isn t really any standardized notation when talking about the megaminx, this is what I ve come up with. I like it, because it makes sense to me, and so far I haven t seen any ideas that
are more understandable and straightforward than this. The faces are defined by the usual 6 letters used in cubing lingo Up, Down, Left, Right, Front, and Back.
Obviously, if this is the case, there can t just be one letter per face, since there are twice as many faces on the megaminx as there are on a cube. I ended up with 6 faces defined by one letter (U,
D, L, R, F, and B), 2 faces defined by 2 letters (BL and BR), and 4 faces defined by 3 letters (DFL, DFR, DBL, and DBR). Starting from an obvious U face (facing straight up), and an edge toward you
(not a corner), F is adjacent to U, along with L and R to either side of it. The other two faces adjacent to U are BL and BR, next to L and R, respectively. B is the face directly opposite F, and D
is directly opposite U. The remaining four faces are all adjacent to D (thus their first letter), and the second and third letters indicate the other two single letter faces to which they are
adjacent. For example, DFR is adjacent to D, F, and R.
This causes another complexity, because edges and corners are denoted by the faces on which they reside. You can t just look at a sequence of letters and determine which type of piece is being
referred to by seeing how many letters there are. To simplify things a little bit, I separate the face definitions in a piece name with / s. For example, the edge at the front of the U face would be
U/F. While I could just write things like UBLBR (which would be the corner at the intersection of the U, BL, and BR faces), I think that would just get too confusing.
Finally, since there are 5 positions for each face, I had to do something different than the typical F, F', F2 move notation as well. Going back to the cube notation I originally learned from, I
decided to use + for clockwise rotations and - for counterclockwise rotations. Two clicks in either direction is denoted with two of the appropriate symbol (e.g. F++ means turn F two clicks
- First Four Faces -
When solving a face, I m actually solving to 2 layers at a time - the face and the edges adjacent to it. First, put together a star of your preferred color, as you would do a cross for a 3x3x3
cube. I don t know about optimal solving, but this usually seems to take me about 11-14 moves. To finish off the first face, insert 5 corner edge pairs. To do this, I don t use a typical F2L
Assuming the star is on U, find a corner that belongs on U, and put it on D (with the U color on D). Try to use a corner that can be moved to D with the correct orientation in just 1-2 moves (i.e. it
is not on the U face). Next, find the edge that goes next to it and move it to a position next to D, so that rotating D will properly align the two pieces. Be sure to move D as needed to avoid
reorienting or moving the corner off of D. After lining them up with a turn of D, they never come apart again. Unless they re already in the right spot (two correct positions out of five
possibilities), rotate the pair onto D and rotate D to position the pair across a face from the position they belong in. Finally, a simple R' D2 R type of move will insert them (R and D not referring
to minx faces, of course). Repeat this until all corner edge pairs are in place - if any corners or edges are already in position, then you can use typical cube F2L algorithms or open slots to insert
the other piece of the pair.
After completing the first face, complete a second and third face in the same manner as the first:
1. Complete the star (add 2 edges for face 2 and 1 edge for face 3)
2. Insert corner edge pairs, using the same technique as outlined for the first face
Make sure you don t mess up any completed faces as you re progressing, and also be sure to make the first three faces share a corner (i.e. all three are adjacent to each of the other two). The fourth
face (adjacent to 2 of the first 3 faces) is done in a similar manner, except that the two corner edge pairs are put together on an adjacent face (since the opposite face is partially solved at this
point) and some of the regular F2L algs are thrown into the mix more regularly.
Note: During these first few faces, I used U and D for ease of explanation, but I actually tend to hold the star to the lower-back-left (as I do with the cross on a cube), with the scrambled portions
of the puzzle facing up and forward (toward me!) so I can more easily search for pieces. If you re used to solving the cube with the cross on the bottom, you may do best with the star on the bottom
of your megaminx, as well. With this puzzle, it seems to be all about minimizing search time, while the actual speed of your moves is a secondary issue for speed solving.
- The Next Two Faces (or getting to the LL)-
Once you get to this point, the megaminx should be completely solved, except for two faces which are still completely scrambled (aside from rare, lucky cases). I hold the minx with one scrambled face
up (U) and one to the right (R). This way I can move U, R, F, and BR with the right hand and hold the puzzle with the left.
First, put together the U/L/BL corner with the two surrounding edges. I do this in three steps:
1. Put U/L and U/BL on U, correctly oriented, positions reversed
2. Using only moves of U and R, intuitively match the corner to one of the edges, keeping the other edge on U
3. Still using only U and R, remove the pair from U, turn U, and replace the pair, so that all three pieces are matched up
If you re familiar with cubing, you should be able to think through these steps on your own. If you can t, then you ll just have to wait for me to put up a beginner s method to the megaminx - which
should come some time this decade ;-)
After those three are matched up, turn them into place, and complete this step by inserting two corner edge pairs with typical F2L algs. Note that some cube algs will not work exactly, but with some
tweaking may work on the megaminx. For some cases, you may have to use less than optimal F2L algs as a replacement for your usual cube F2L algs.
- The Last Layer -
This is where it gets interesting - I think a fair amount of people that know how to solve a 3x3x3 cube get this far on the megaminx, but not further, without learning someone else s solution. I do
the LL (last face, really) in four steps:
1. Orient Edges (OE) - One look, using any of 3 algorithms
2. Permute Edges (PE) - One looks, using any of 5 algs
3. Orient Corners (OC) - One to two looks, with 8 algs
4. Permute Corners (PC) - Not really using algs, each is placed individually
The following is a complete listing of the algorithms I currently use for the LL (holding LL on U).
OE algs:
• 2 adjacent edges (U/F and U/R) need to flip:
F+ U+ R+ U- R- F-
• 2 non-adjacent edges (U/F and U/BR) need to flip:
F+ R+ U+ R- U- F-
• 4 edges need to flip (all except U/F):
R+ BR+ BL+ U+ BL- U+ BR- U-- R-
PE algs:
• Rotate 3 adjacent edges clockwise (U/R -> U/BL -> U/BR):
(R+ U++) (R- U-) (R+ U- R-)
• Rotate 3 adjacent edges counterclockwise (U/R ->U/BR -> U/BL):
(R+ U+) (R- U+) (R+ U-- R-)
• Rotate 3 non-adjacent edges clockwise (U/R -> U/BR -> U/L):
(R+ U+) (R- U++) (R+ U++ R-)
• Rotate 3 non-adjacent edges counterclockwise (U/R -> U/L -> U/BL):
(R+ U--) (R- U-) (R+ U-- R-)
• Swap an adjacent pair, and a non-adjacent pair of edges (U/R <-> U/L and U/BR <-> U/BL):
(R+ U+) (R- U+) (R+ U-) (R- U++) (R+ U++ R-)
OC algs:
• 2 adjacent corners - Rotate U/F/L counterclockwise (CC) and U/F/R clockwise (C):
L- (R+ BR+) (BL- BR-) (R- BR+) (BL+ BR-) L+
• 2 adjacent corners - Rotate U/F/R C and U/R/BR CC:
(R+ BR+) (BL- BR-) (R- BR+) (BL+ BR-) (Note - this is the same as the previous alg without the L turns)
• 2 non-adjacent corners - Rotate U/F/L CC and U/R/BR C:
(R- F+) (R+ BR-) (R- F-) (R+ BR+)
• 2 non-adjacent corners - Rotate U/F/L C and U/R/BR CC:
R- (F- L-) (F+ R+) (F- L+ F+)
• 3 adjacent corners - Rotate U/F/L, U/F/R, and U/R/BR CC:
(R- U+) (L+ U-) (R+ U+) (L- U-) (last U- only necessary for edge realignment)
• 3 adjacent corners - Rotate U/F/L, U/F/R, and U/L/BL C:
(L+ U-) (R- U+) (L- U-) (R+ U+) (again, last U+ only necessary for edge realignment)
• 3 non-adjacent corners - Rotate U/F/L, U/F/R, and U/BL/BR C:
L- (BL- BR-) (R+ BR+) (BL+ BR-) (R- BR+) L+
• 3 non-adjacent corners - Rotate U/F/L, U/L/BL, and U/R/BR CC:
F+ (R+ BR+) (BL- BR-) (R- BR+) (BL+ BR-) F-
• 4 or 5 corners - use one of the above algs so that only 2-3 corners remain mixed. Then fix those with the appropriate alg from above. There are algs for these situations, but I haven t learned
any yet.
PC Approach:
Finally, we come to corner permutation, which completes the puzzle. I do this in a way similar to Mark Jaey s simple solution for the 3x3x3 cube. At this point, you will have anywhere from 3 - 5
corners that are incorrectly placed (or they are all correct in fairly lucky cases). To permute corners, start with the LL on U, and repeat these steps:
1. Rotate U to put a corner in U/F/R that is not correct (or just rotate the puzzle the first time)
2. Look at the colors on the F and R faces of the U/F/R corner - remember them
3. Perform R- DFR+ R+ (or R- DFR- R+)
4. Turn U until the edges on U/F and U/R match the corner that was removed from U in #3
5. If the corner in U/F/R is a LL corner, repeat from #2, reversing the direction of the DFR turn in #3
6. If the corner in U/F/R is not a LL corner, do #3, reversing the DFR turn.
7. If the LL is solved (align with a U turn if necessary first), you re done. If not (therefore swapping two pairs of corners), repeat from #1, again reversing the direction of the DFR turn in #3
Congratulations! You ve solved your megaminx! Now, it s just a matter of lots of practice which will also help to work in your puzzle.
- Additional Tips -
Beyond having a solid set of algs in your head and moving quickly, here s a few things that should help you on your way to speed solving your minx:
• If you haven t yet, then lube your minx - they are normally very stiff, and a good lube will help. If you know how to take apart a Rubik s brand 3x3x3 cube (springs under the centers, pop out an
edge), then you should be able to get your megaminx apart as well.
• Consider doing the colors in a specific order, so that you get used to it, and are looking for more obvious colors when there s more to look through
• Count your moves - I ve counted a few times lately, and it s always around 180 somewhere... I d say with lucky and bad cases it s probably always in the range of about 160 to 200 ([2004-May-11]
Update: See table below for breakdown of solution moves/times). I know that s a big range, but with so many possibilities for easy or hard cases, it can really vary.
• Practice, practice, practice ;-) That s obvious, I know, but it s so true. Also, don t worry so much about necessarily practicing just the megaminx. I ve found that I can actually improve my
megaminx times over a period of weeks when I never solve it once, and work instead on improving my cubing skills in general.
The following table shows, on average (over 5 solves), how many moves I use for each phase of the solution, as well as the percent of the total solution time spent to complete each phase. I further
broke down each phase of the solution to its substeps, which can be seen in the larger table, below the initial summary table. In the summary table, the Relative Speed column is the ratio of the %
of Total Solution Moves and % of Total Solution Time columns - higher numbers indicate a higher turn rate (moves / second):
│ Summary of Solution Steps │
│ │# of Moves│% of Total Solution Moves │% of Total Solution Time│Relative Speed│
│Face 1 │51.8 │27.58% │34.80% │0.79 │
│Face 2 │28.6 │15.23% │15.86% │0.96 │
│Face 3 │17.6 │9.37% │9.65% │0.97 │
│Face 4 │18 │9.58% │9.88% │0.97 │
│Faces 5-6│28 │14.91% │12.83% │1.16 │
│Last Face│43.8 │23.32% │16.98% │1.37 │
│ Total:│187.8 │ │
│ Solution Steps - Detailed Breakdown │
│ │# of Moves│% of Total Solution Time │
│ │Star │13.4 │10.20% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│ │Corner/Edge Pair 1│8.6 │5.95% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│ │C/E Pair 2 │7.6 │4.86% │
│Face 1 ├──────────────────┼──────────┼─────────────────────────┤
│ │C/E Pair 3 │7.4 │4.24% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│ │C/E Pair 4 │7.4 │4.62% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│ │C/E Pair 5 │7.4 │4.94% │
│ │Star │5.2 │4.03% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│ │C/E Pair 1 │7.8 │3.75% │
│Face 2 ├──────────────────┼──────────┼─────────────────────────┤
│ │C/E Pair 2 │8.2 │4.08% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│ │C/E Pair 3 │7.4 │4.00% │
│ │Star │2.6 │2.43% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│Face 3 │C/E Pair 1 │7.4 │3.60% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│ │C/E Pair 2 │7.6 │3.63% │
│ │Star │2.6 │1.80% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│Face 4 │C/E Pair 1 │8.6 │4.17% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│ │C/E Pair 2 │6.8 │3.91% │
│ │C/E/E Trio │11.6 │6.72% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│Faces 5-6│C/E Pair 1 │8.8 │3.40% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│ │C/E Pair 2 │7.6 │2.70% │
│ │Orient Edges │7.2 │3.14% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│ │Permute Edges │7.6 │3.46% │
│Last Face├──────────────────┼──────────┼─────────────────────────┤
│ │Orient Corners │10.8 │4.34% │
│ ├──────────────────┼──────────┼─────────────────────────┤
│ │Permute Corners │18.2 │6.04% │
│ Total:│187.8 │ │
Links to other Megaminx related resources (will open in a new window):
• Stefan Pochmann's Page: Additional tips for solving, as well as prepping your megaminx for speed solving.
• Daniel Hayes' Solution (2.45MB Word Document): A slightly different approach, with pictures.
• Jaap Scherphuis's Page: Another approach to solution, as well as puzzle information (e.g. # of positions).
If you have any specific questions about this solution, or suggestions for minor changes/corrections (major changes will have to wait for now), let me know!
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=COS formula | Calculate the cosine of an angle.
Formulas / COS
Calculate the cosine of an angle. =COS(number)
• number - angle in radians
• =COS(PI()/6)
The COS function can be used to calculate the cosine of an angle given in radians. For example, the formula returns the cosine of 30 degrees, which is 0.886.
• =COS(60*PI()/180)
The COS function can also be used to calculate the cosine of an angle given in degrees. The formula returns the cosine of 60 degrees.
• =COS(RADIANS(60))
If the angle is given in degrees, the RADIANS function can be used to convert it to radians before using it with the COS function. The formula returns the cosine of 60 degrees.
The COS function can be used to calculate the cosine of an angle in radians. To use COS with degrees, the angle must be multiplied by PI()/180.
• The COS function takes a radian angle argument.
• Use the RADIANS function to convert from degrees to radians.
• The COS function returns the cosine of an angle, which is a numerical value.
Frequently Asked Questions
What is the COS function and how does it work?
The COS function returns the cosine of an angle. The angle is measured in radians and is calculated using the formula COS(number). The number argument is a required angle in radians. To convert from
degrees to radians, use either PI()/180 or RADIANS.
What is the format for the COS function?
The format for the COS function is COS(number). The number argument is the required angle in radians.
How can I convert from degrees to radians?
You can convert from degrees to radians by using either PI()/180 or RADIANS.
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If $F, K$ are fields, $F$ algebraically closed, and $F subseteq K$ then $K = F$? ~ Mathematics ~ TransWikia.com
The algebraic numbers are an algebraically closed field that is properly contained in $$mathbb{C}$$ and many other fields. For example, if $$F$$ is the field of algebraic numbers, $$K=mathbb{C}$$,
and $$k=pi$$, then we are precisely in the second case of your proof sketch, and we of course cannot show that $$k$$ is in $$F$$.
Given any (algebraically closed field) $$F$$ one can always construct $$F(t)$$ where $$t$$ is transcendental with respect to $$F$$ to get a bigger field. Then you can take the algebraic closure of
$$F(t)$$ to get a bigger algebraically closed field.
By adjoining a lot of transcendentals you can get algebraically closed fields of arbitrarily large cardinality.
I will add some details that have by now been talked about in other comments. Let $$F$$ be a field and let $$X$$ be a set of variables. Let $$F[X]$$ be the ring of polynomials whose variables come
from $$X$$ and coefficients from $$F$$. Now let $$F(X)$$ be the field of fractions of $$F[X]$$ (see: https://en.wikipedia.org/wiki/Field_of_fractions). You can also view $$F(X)$$ as the field of
rational functions in variables from $$X$$ with coefficients in $$F$$. Now $$F(X)$$ is a new field properly containing $$F$$. Moreover, $$|F(X)|=max{|F|,|X|,|mathbb{N}|}$$.
Answered by halrankard on January 1, 2022
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arbon dating
Carbon dating isotopes
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Among the half-life of carbon, while the isotopes as radioactive isotope, this article. Some isotopes leads to a middle-aged woman looking to find the approximate dates of age of. Because researchers
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M.S. Program in Mechanical Engineering
Program tanımları
Head of Department: Gunay Anlas
Professors: Sabri Altintas, Gunay Anlas, Ahmet R. Buyuktur*, Taner Derbentli*, Arsev Eraslan•, Esref Eskinat, Emre Kose, Haluk Ors, Huei Peng•, Mahmut A. Savas*, Akin Tezel†
Associate Professors: Hasan Bedir, Vahan Kalenderoglu, F. Önder Sonmez
Assistant Professors:Emre Aksan, Cahit Can Aydiner, Kunt Atalik, Ercan Balikci, Murat Celik, Ali Ecder, Nuri Ersoy, Hakan Erturk, Sebnem Özupek, Cetin Yilmaz
Instructors: Metin Yilmaz*
†Professor Emeritus
Graduate programs in Mechanical Engineering consists of five options:
Option A: Dynamics and Control
Option B: Fluid Mechanics
Option C: Materials and Manufacturing
Option D: Solids and Design
Option E: Thermal Sciences
The M.S. program in Mechanical Engineering requires a minimum of 24 credits hours (8 courses) of course work, seminar course and a Master's thesis. One mathematics requirement, three core courses and
one seminar requirement must be completed together with three (elective) courses from the selected option. The remaining course may be chosen freely from among engineering or science graduate
courses. Mathematics requirement is satisfied by taking:
ME 501 or ME 502 Advanced Engineering Mathematics I or II
Students who have previously taken one of these courses, or its equivalent, may instead take an elective course approved by their advisor.
Core course requirement may be satisfied by taking one course from each core course sequence covering three of the five options as listed below:
Opt. A ME 537 State Space Control Theory or ME 530 Advanced Dynamics
Opt. B and E ME 551 Advanced Fluid Mechanics or ME 561 Conduction Heat Transfer
Opt. C ME 511 Principles of Materials Science and Engineering or ME 512 Principles of Manufacturing Processes
Opt. D ME 523 Elasticity or ME 521 Engineering Design or by taking one core course from two options and the course ME 503 Mechanics of Continua I as a substitute for the third option core course.
In addition to the core courses requirement, students are required to complete a minimum of 9 credits in one of the five options indicated above. One course is to be the remaining core course of the
chosen core sequence. Option courses are listed below for both the M.S. and Ph.D. programs.
In addition to the required and option courses, students are required take the non-credit seminar course: ME 579 Graduate Seminar.
A. Dynamics and Control:
ME 530 Advanced Dynamics
ME 537 State Space and Control Theory
ME 622 Advanced Vibrations
ME 634 Robotics
ME 636 System Modeling and Identification
B. Fluid Mechanics:
ME 551 Advanced Fluid Mechanics
ME 503 Mechanics of Continua I
ME 602 Mechanics of Continua II
ME 610 Finite Elements
ME 632 Approximate Solution Techniques
ME 652 Viscous Flow Theory
ME 653 Turbulent Flow Theory
ME 654 Gas Dynamics
ME 656 Computational Fluid Dynamics
ME 662 Convective Heat Transfer
C. Materials and Manufacturing:
ME 511 Principles of Material Science and Eng.
ME 512 Principles of Manufacturing Processes
ME 610 Finite Elements
ME 613 Deformation of Engineering of Materials
ME 614 Materials Processing
ME 618 Mechanical Behavior of Materials
ME 620 Fracture
D. Solids and Design:
ME 521 Engineering Design
ME 523 Elasticity
ME 530 Advanced Dynamics
ME 503 Mechanics of Continua I
ME 602 Mechanics of Continua II
ME 610 Finite Elements
ME 618 Mechanical Behavior of Materials
ME 620 Fracture
ME 622 Advanced Vibrations
ME 632 Approximate Solution Techniques
ME 641 Wave Propagation
E. Thermal Sciences:
ME 561 Conduction Heat Transfer
ME 503 Mechanics of Continua I
ME 602 Mechanics of Continua II
ME 610 Finite Elements
ME 632 Approximate Solution Techniques
ME 660 Advanced Thermodynamics
ME 662 Convective Heat Transfer
ME 663 Radiation Heat Transfer
ME 664 Two-Phase Heat Transfer
ME 501 Advanced Engineering Mathematics I (3+0+0) 3
(Ileri Muhendislik Matematigi I)
Systems of linear equations; linear vector spaces; theory of matrices and the eigenvalue problem; multivariable differential calculus; ordinary differential equations; vectors in R3; vector field
theory, Fourier series and Fourier transform; Laplace transform; calculus of variations.
ME 502 Advanced Engineering Mathematics II (3+0+0) 3
(Ileri Muhendislik Matematigi II)
Partial differential equations; Laplace, diffusion, and wave equations; Bessel and Legendre functions; integral equations; functions of a complex variable; conformal mapping; complex integral
calculus; series expansion and residue theorem.
ME 511 Principles of Materials Science and Engineering (3+0+0) 3
(Malzeme Bilimi ve Muhendisligi Prensipleri)
Atomic bonding and crystal structure, imperfections in crystals, x-ray and electron diffraction, thermodynamics of crystals, kinetics, transport in materials, phase transformations, annealing
processes, deformation and fracture of materials, examples of technological materials.
ME 512 Principles of Manufacturing Processes (3+0+0) 3
(Imalat Surecleri Esaslari)
Fundamentals of production and processing of metallic, ceramic and polymeric materials. Manufacturing processes based on heating/cooling. Casting techniques. Near net shape processes. Principles of
metal forming. Thermomechanical treatment. Surface modification.
ME 521 Engineering Design (Muhendislik Tasarimi) (3+0+0) 3
Nature and properties of materials; advanced topics of strength of materials; analysis of composite, honeycomb and reinforced materials; pressure vessel design; residual stresses, thermal stresses;
failure theories, beyond the elastic range; buckling; shock; impact and inertia.
ME 523 Elasticity (Elastisite) (3+0+0) 3
Cartesian tensor notation. Analysis of strain, components and compatibility of strain. Analysis of stress; definitions and components of stress; equations of equilibrium. Constitutive equations,
generalized Hook's law; governing equations of elasticity. Plane strain and plane stress; problems some examples of 2-D problems of elasticity. Energy principles. Sample problems of applied
ME 530 Advanced Dynamics (Ileri Dinamik) (3+0+0) 3
Kinematics of rigid body motion. Coordinate tranformaitons. Rigid body dynamics. Euler's equations of motion. Eulerian angles. Motion under no force. Lagrange equations and their first integrals.
Hamilton's equations. Applications to mechanical engineering systems.
ME 537 State Space Control Theory (Durum Uzayi Kontrol Kurami) (3+0+0) 3
State space representation of systems. Dynamic response from state equations. Stability, controllability and observability. Canonical form, control with state feedback. Pole placement. Observer based
controllers. Reference input traking. Introduction to optimal control and Lyapunov stability. Example applications.
ME 551 Advanced Fluid Mechanics (Ileri Akiskanlar Mekanigi) (3+0+0) 3
Dynamics of motion, constitutive equations. Incompressible flows; potential flows, wing theory; waves. Compressible flows; thermodynamics of flow; two dimensional potential flows, theory of small
perturbations; shock waves. Viscous flows; some exact and approximate solutions of Navier-Stokes equations.
ME 561 Conduction Heat Transfer (Iletim ile Isi Transfer) (3+0+0) 3
Steady and unsteady heat conduction involving various boundary conditions. Methods of formulation. Analytical solutions and approximate methods.
ME 579 Graduate Seminar (Lisansustu Seminer) (0+1+0) 0 P/F
The widening of the students' perspectives and awareness of topics of interest to mechanical engineers through seminars offered by faculty, guest speakers and graduate students.
ME 581, 582, 583, 584, 585, 586, 587, 588, 589 Special Topics (3+0+0) 3
(Özel Konular)
Special topics of current interest in mechanical engineering selected to suit the individual interests of the students and faculty in the department. The course is designed to give the student of
advanced level an opportunity to learn about the most recent advances in the field of mechanical engineering.
ME 591, 592, 593, 594, 595, 596 Special Studies (Özel Calismalar) (3+0+0) 3
Study of special subjects not covered in other courses at the graduate level.
ME 597, 598 Mechanical Engineering Seminars (1+0+0) 1
(Makina Muhendisligi Seminerleri)
Subjects and speakers to be arranged.
ME 599 Guided Research (0+4+0) 0 (ECTS :8) P / F
(Yonlendirilmis Caliþmalar)
Research in the field of Mechanical Engineering, supervised by faculty.
ME 503 Mechanics of Continua I (Surekli Ortamlar Mekanigi I) (4+0+0) 4
Vectors, matrix algebra, tensor analysis. Deformation and strain tensors. Length, angle, area and volume changes. Kinematics of motion, mass, momentum, moment of momentum, and energy. Fundamental
axioms of mechanics. Stress; thermodynamics of continuous media. Constitutive equations; ideally elastic solids. Stokesian fluids.
ME 602 Mechanics of Continua II (Surekli Ortamlar Mekanigi II) (3+0+0) 3
Constitutive equations; thermomechanical materials, elastic materials. Stokesian fluids. Elasticity, fluid dynamics, thermoelasticity, visco-elasticity. Linear and nonlinear physical interactions in
continuous media. Selected problems of practical importance in engineering disciplines.
ME 610 Finite Elements (Sonlu Elemanlar) (3+0+0) 3
Strong and weak statements of boundary value problems. The concept of finite element discretization and finite interpolatory schemes. The isoparametric concept. Programming techniques for numerically
integrated finite elements. Implemntation of finite element model and solution methods. Preprocessing and postprocessing. Time-stepping algorithms and their implementation approximation errors in the
finite element method and error analysis.
ME 613 Deformation of Engineering Materials (3+0+0) 3
(Muhendislik Malzemelerinin Sekil Degistirmesi)
Fundamental of the mechanical behavior of materials. Elements of dislocation theory. Plastic deformation of crystalline materials. The relationship between microstructure and mechanical behavior at
ambient and elevated temperatures.
ME 614 Materials Processing (Malzeme Uretimi) (3+0+0) 3
Control of microstructure and alternation of material properties. Heat treatment of steel. Precipitation hardening. Shape memory alloys. Processing of electronic and magnetic materials. Processing of
glasses. Powder metallurgy.
ME 618 Mechanical Behavior of Materials (3+0+0) 3
(Malzemelerin Mekanik Davranisi)
Treatment of elastic, plastic and creep deformation under steady and cyclic loads. Emphasis on approximate solutions which enable the prediction of service performance from simple tests. Failure due
to fatigue, creep rupture and plastic instability. Treatment of fracture from engineering point of view.
ME 620 Fracture (Kirilma) (3+0+0) 3
Stress analysis of cracked members; applications of linear elastic fracture mechanics; experimental determination of fracture toughness; microstructural aspects of fracture toughness. Fracture
prediction beyond linear elastic range: the transition temperature approach, crack opening displacement, J-integral. Fatigue crack initiation, propagation and stress corrosion cracking.
ME 622 Advanced Vibrations (Ileri Titresimler) (3+0+0) 3
Vibratory response of multi-degree-of-freedom systems, matrix formulation, concepts of impedance, frequency response, and complex mode shapes. Nonlinear vibrations, parametric resonance. Vibration of
elastic bodies. Modal analysis.
ME 625 Optimum Structural Design (En Iyi Yapisal Tasarim ) (3 +0+0) 3 (ECTS : 8)
Basic concepts of design optimization: Classical techniques in structural optimization (differential calculus, variational calculus, Lagrange multipliers); Karush-Kuhn-Tucker conditions. Application
of linear and nonlinear programming to structural problems. Advanced topics in structural optimization.
ME 626 Mechanics of Composite Materials (3+0+0) 3
(Kompozit Malzemelerin Mekanigi)
Types of composite materials; matrix materials, thermosets, thermoplastics, fiber materials. Effective moduli:rule of mixtures. Constitutive relation for anisotropic materials. Laminates:
constitutive relations, transformation equations. Strength and failure criteria. Classical theory of laminated plates; governing relations, higher order theories, energy methods. Cylindirical bending
and vibration of laminated plates.
ME 631 Engineering Analysis (Muhendislik Analizi) (3+0+0) 3
Planning and design of project of a comprehensive character requiring the correlation of principles and procedures drawn from a variety of areas in engineering and related branches of science.
ME 632 Approximate Solution Techniques (3+0+0) 3
(Yaklasik Cozum Yontemleri)
Method of weighted residuals; boundary value, eigenvalue and initial value problems in heat and mass transfer. Application to fluid mechanics, chemical reaction systems, convective instability
problems. Variational principles in heat and mass transfer. Convergence and error bounds.
ME 634 Robotics (Robot Sistemleri) (3+0+0) 3
Fundamental aspects of robotics and type of robots. Rotation matrices. Homogeneous transformations. Direct kinematics. Inverse kinematics. Jacobean matrix. Dynamic force analysis via Newton-Euler
formulation. Motion equations via Lagrangian formulation. Trajectory planning. Control methods of manipulators.
ME 636 System Modeling and Identification (3+0+0) 3
(Sistem Modelleme ve Tanilama)
Systems and models. Modeling of complex systems. Lagrange equations. Bond graphs. System identification. Estimation from transient response. Spectra and frequency functions. Least squares estimation.
Parameter estimation in dynamic models. Model validation.
ME 641 Wave Propagation (Dalga Yayilmasi) (3+0+0) 3
Basic equations of elastodynamics, methods of solutions. Navier's equations. Selected problems in one and two space dimensions. Impact problems, explosion, reflection, refraction, Rayleigh surface
waves, and various other selected problems of practical importance in diverse engineering disciplines.
ME 652 Viscous Flow Theory (Viskos Akis Kurami) (3+0+0) 3
Equation of Motion for Viscous flow Exact solutions of Navier-Stokes equations. Creeping flow: Stokes and Oseen solutions, lubrication theory. Boundary layer theory: similar solutions, approximate
methods of solution, computer methods of solution, stability, turbulent boundary layers. Introduction to three-dimensional compressible boundary layer flows.
ME 653 Turbulent Flow Theory (Turbulansli Akislar Kurami) (3+0+0) 3
Basic concepts. Scales of time, velocity, space. Time averaging of fundamental equations. Turbulent flow theories and models. Dynamics of turbulence. Turbulent pipe, boundary layer and force shear
flows. Turbulent transport. Statistical description of turbulence. Spectral dynamics.
ME 654 Gas Dynamics (Gaz Dinamigi) (3+0+0) 3
Basic equations of compressible flow. Wave propagation in compressible media. One dimensional compressible flow. Equations of motion for multidimensional flow. Methods for solution. Oblique shock.
Introduction to hypersonic flow. Introduction to rarefied gas dynamics.
ME 655 Advanced Turbine Design (Ileri Turbin Tasarimi) (3+0+0) 3
Review of gas dynamics and thermodynamics. Velocity triangles. Two dimensional flow in turbine stages. Turbine cascades. Calculation of design point efficiency of turbine stages using cascade data.
Potential flow and methods of solution. Three dimensional design of turbines. Radial equilibrium theory. Off-design performance. Introduction to turbine cooling.
ME 656 Computational Fluid Dynamics (Sayisal Akiskanlar Dinamigi) (3+0+0) 3
Fundamentals of computational fluid dynamics and high performance computing; basic flow models; grid generation; discretization techniques. Analysis of linear and nonlinear systems; algorithm
development; convective-diffusive systems; turbulence modeling; combustion modeling.
Prerequisite: ME 551
ME 660 Advanced Thermodynamics (Ileri Termodinamik) (3+0+0) 3
An advanced study of the first and second laws of thermodynamics and their application to engineering systems and flow processes. Equilibrium conditions. Thermodynamic potentials; systems of variable
mass. Chemical equilibrium and thermodynamics of chemical reactions. Emphasis is placed on the relationship of thermodynamics to the broad fields of engineering and applied science.
ME 662 Convective Heat Transfer (Tasinim ile Isi Transferi) (3+0+0) 3
Basic equations of fluid flow. Differential and integral equations of the boundary layer. Forced convection in internal and external laminar flows. Momentum-heat transfer analogies for turbulent
flow. Natural convection.
ME 663 Radiation Heat Transfer (Isinim ile Isi Transferi) (3+0+0) 3
Basic laws of thermal radiation. Radiation properties of solids and liquids. Exchange of thermal radiation between surfaces separated by transparent media; non-gray and non-diffuse surfaces. Gas
radiation in enclosures. Radiation combined with conduction and/or convection.
ME 664 Two-Phase Heat Transfer (Iki Fazli Isi Transferi) (3+0+0) 3
Nucleation and bubble growth in boiling. Pool boiling heat transfer. Critical heat flux. Film boiling. Kinematics and dynamics of adiabatic two-phase flow. Two phase flow with boiling and/or
evaporation. Stability of two-phase flows. Condensation.
ME 681, 682, 683, 684, 685, 686, 687, 688, 689 Special Topics (3+0+0) 3
(Özel Konular)
Advanced special topics of current interest in mechanical engineering selected to suit the individual interests of the students and faculty in the department. The course is designed to give the
student of advanced level an opportunity to learn about the most recent advances in the field of mechanical engineering.
ME 690 M.S. Thesis (Yuksek Lisans Tezi)
ME 691, 692, 693, 694, 695, 696 Special Studies (Özel Calismalar) (3+0+0) 3
Study of special subjects not covered in other courses at the graduate level.
ME 697, 698 Mechanical Engineering Seminars (1+0+0) 1
(Makina Muhendisligi Seminerleri)
Subjects and speakers to be arranged.
ME 699 Guided Research (Yonlendirilmis Calicmalar I) (2+0+4) 4(ECTS :8)
Research in the field of Mechanical Engineering, by arrangement with members of the faculty; guidance of doctoral students towards the preparation and presentation of a research proposal.
ME 69A Guided Research II (0+4+0) 0 (ECTS :8) P / F
(Yonlendirilmis Calismalar II )
Continued research in the field of Mechanical Engineering, supervised by faculty; preparation and presentation of a research proposal.
ME 69B Guided Research III (0+4+0) 0 (ECTS :8) P / F
(Yonlendirilmis Calismalar III )
Continued research in the field of Mechanical Engineering, supervised by faculty; preparation and presentation of a research proposal.
ME 69C Guided Research IV (0+4+0) 0 (ECTS :8) P / F
(Yonlendirilmis Calismalar IV)
Continued research in the field of Mechanical Engineering, supervised by faculty; preparation and presentation of a research proposal
ME 69D Guided Research V (0+4+0) 0 (ECTS :8) P / F
(Yonlendirilmis Calismalar V)
Continued research in the field of Mechanical Engineering, supervised by faculty; preparation and presentation of a research proposal.
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Free Group Study Rooms with Timer & Music | FiveableSolving Motion Problems Using Parametric and Vector-Valued Functions | AP Calculus AB/BC Class Notes | Fiveable
An initial value problem (IVP) is a mathematical problem that involves finding a solution for a differential equation that satisfies a given set of initial conditions. In physics and engineering,
initial value problems are often used to model the motion of a particle in the plane.
Given a differential equation that describes the position of a particle moving in the plane and an initial condition that specifies the position of the particle at a certain point in time, an IVP
allows us to determine an expression for the position of the particle as a function of time. This can be done by solving the differential equation using techniques such as separation of variables,
integrating factors, and substitution.
Once we have an expression for the position of the particle, we can use derivatives to determine various other properties of the motion, such as velocity, speed, and acceleration. The velocity of a
particle moving along a curve in the plane is given by the derivative of the position function with respect to time, and the speed of a particle is given by the magnitude of the velocity vector. The
acceleration of a particle moving along a curve in the plane is given by the derivative of the velocity function with respect to time.
In the case of a curve defined using parametric or vector-valued functions, we can use the same process to determine the velocity, speed and acceleration. First, we must convert the parametric or
vector-valued function to a Cartesian equation, then we can find the velocity by taking the derivative of the position function with respect to time, the speed by the magnitude of the velocity
vector, and the acceleration by the derivative of the velocity function with respect to time.ย
Remember from previous units that if we take the integral of the speed (the absolute value of velocity), we can find the distance traveled (imagine adding up all of the tiny instantaneous distances
to find a total distance).ย
This same concept applies in parametric equations, but since velocity is expressed as a vector, we need to take the integral of the magnitude of velocity. (In vector-valued functions, the magnitude
is equivalent to the distance formula, which is essentially taking the absolute value of the vector.)ย
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Two Dimentional shapes
Understanding two-dimensional shapes is fundamental in geometry. In this guide, we'll explore common two-dimensional shapes, their properties, and how to identify them. Remember that these shapes
exist in two dimensions - length and width.
With a focus on mathematical calculations, Learnerscamp provides dynamic tutorials, real-world applications, and problem-solving scenarios that empower students to grasp mathematical concepts such as
area of shapes like rectangles, squares , circles , trapeziums among others with ease. Our adaptive learning algorithms ensure personalized learning paths, allowing students to progress at their own
pace while receiving instant feedback to reinforce their understanding.
Two-Dimensional Shapes
1. Square
A square is a four-sided polygon with all sides of equal length and all angles equal to 90 degrees.
Identification: Look for a shape with four equal sides and right-angle corners.
2. Rectangle
A rectangle is a four-sided polygon with opposite sides of equal length and all angles equal to 90 degrees.
Identification: Similar to a square but with opposite sides of different lengths.
3. Circle
A circle is a round shape with all points on its boundary equidistant from its center creating a symmetrical and round form.
Identification: Look for a perfectly round shape.
4. Triangle
A triangle is a three-sided polygon with three angles and three sides coming in various types such as equilateral (all sides equal), isosceles (two sides equal), and scalene (no sides equal).
Identification: Observe a shape with three sides and three corners.
5. Pentagon
A pentagon is a five-sided polygon.
Identification: Count the number of sides; a pentagon has five.
6. Hexagon:
A hexagon is a six-sided polygon with six angles and six straight sides, featuring a hexagonal symmetry that is commonly observed in nature and man-made structures.
Identification: Count the number of sides; a hexagon has six.
7. Octagon
An octagon is an eight-sided polygon with eight angles and eight straight sides, known for its regularity and often used in the design of stop signs and other symbols.
Identification: Count the number of sides; an octagon has eight.
8. Rhombus
A rhombus is a four-sided polygon with all sides of equal length, but angles are not necessarily 90 degrees, creating a tilted and diamond-shaped figure.
Identification: Look for a shape with equal sides but not necessarily right angles.
9. Parallelogram
A parallelogram is a four-sided polygon with opposite sides that are both equal in length and opposite angles that are equal.
Identification: Observe a shape with opposite sides and angles that are equal.
10. Trapezoid
A trapezoid is a quadrilateral with one pair of parallel sides distinguishing it from other quadrilaterals by its asymmetry.
Identification: Look for a shape with one set of parallel sides./p>
Key Characteristics
Two-dimensional shapes exist in a plane and are flat, lacking volume or depth.
Vertices and Edges
Vertices are points where the edges of a shape meet. Edges are the lines that form the boundaries of the shape.
Closed Figures
Two-dimensional shapes are often closed figures, meaning they have distinct boundaries that enclose a space.
Common Two-Dimensional Shapes
1. Triangles
Three-sided polygons with varying side lengths and angles. Classified by sides and angles into types such as equilateral, isosceles, and scalene.
2. Quadrilaterals
Four-sided polygons with diverse characteristics. Includes rectangles, squares, parallelograms, and rhombuses.
3. Circles
Perfectly round shapes defined by a central point (center) and a consistent radius.
4. Polygons
Closed shapes with multiple straight sides. Regular polygons have equal sides and angles.
5. Irregular Shapes
Shapes that do not conform to standard classifications, often with varying side lengths and angles.
These two-dimensional shapes form the foundation of geometry. Practice identifying them to enhance your understanding of their properties and relationships. Geometry becomes more accessible when you
can recognize and work with these fundamental
More on LearnersCamp
Learnerscamp is a dedicated platform designed to assist learners in comprehensively understanding different mathematical concepts
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Is 600 square feet livable?
Is 600 square feet livable?
With 600 square feet, there is enough room to have a more defined living space.
Is a 600 square-foot apartment too small?
“Small” (the largest category, space-wise) is anything between 800 and 1,000 square feet. The smallest division is “Teeny-Tiny,” for anything 400 square feet and under.
Is 600 sq ft enough for a couple?
To get the conversation started, I would say that 600-850 square feet is sufficient for one person and 1000-1500 square feet would be fine for a couple.
How many square feet is comfortable?
So how much space does one person need? According to the engineering toolbox, the average person needs about 100-400 square feet of space to feel comfortable in an apartment.
How do you organize a 600 square-foot apartment?
5 ways to decorate your 600-square-foot apartment
1. Define spaces.
2. Add vertical lines.
3. Pick a statement wall.
4. Invite nature.
5. Float the furniture.
How much space do two people need to live comfortably?
According to the engineering toolbox, the average person needs about 100-400 square feet of space to feel comfortable in an apartment. That being said, it really depends on the person. Some people
need a ton of space to feel sane, some people can work with very little.
How much square feet should a family of 4 have?
around 2400 square feet
How Much Space Does A Family Need? The average house size for a family of four to live comfortably is around 2400 square feet. It is widely believed that each person in a home requires 200-400 square
feet of living space. The average cost to build a home of that size will range between $147,000 to $436,000.
How many feet is 600 square feet?
There is 600 square feet. It could be a 10, 20 or 30 foot measurement.
How much living space does a person need?
200-400 square feet
How Much Space Does A Family Need? The average house size for a family of four to live comfortably is around 2400 square feet. It is widely believed that each person in a home requires 200-400 square
feet of living space.
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Principles of ANCOVA Modelling
BrainVoyager v23.0
Principles of ANCOVA Modelling
Analysis of variance (ANOVA) models are linear models used to analyze most designs of scientific studies by relating a dependent (response) variable to one or more independent (explanatory)
variables, called factors. Each factor of a ANOVA model represents a qualitative variable consisting of at least two levels (often also called treatments). Since any ANOVA model can be expressed with
a General Linear Model (GLM), the explanatory variables are also called predictors. While a repeated measures GLM (multiple regression) with quantitative predictors is well suited for modeling the
first-level (preprocessed) fMRI measurement points of single runs, the ANOVA framework is well-suited to describe the design at the second multi-subject level. The second-level analysis uses the
estimated condition values (beta values or contrasts of betas) from the first level analysis as input (i.e. as dependent variable) for the second-level analysis. In all supported ANOVA models
described below, the effects of subjects are viewed as random (random-effects (RFX) analysis). In addition to estimated beta or t values from a first-level GLM analysis, any multi-subject VMP (e.g
Granger causality maps) or SMP (e.g. cortical thickness maps) can be used as input for the ANCOVA module.
In a single-factor fMRI study, an experimental factor could be defined as "auditory stimulation" and the levels of this factor could be specified as "human sounds" and "animal sounds". In
multi-factor studies, two or more factors are investigated simultaneously to obtain information about their combined effects on the fMRI signal at each voxel or in selected brain regions. An example
of a two-factorial fMRI study would be the simultaneous investigation of responses to auditory (factor A) and visual (factor B) stimuli, e.g. with the levels "sounds off" and "sounds on" for factor
"auditory stimulation" and the levels "images off" and "images on" for factor B "visual stimulation". Such a study would lead to 2 x 2 = 4 factor-level combinations. When all combinations of the
levels of all factors are included in a study, the factors are crossed. For two factors, crossing can be visualized in a two-way table:
Visual \ Auditory Sounds Off Sounds On
Images Off [A1-B1] [A2-B1]
Images On [A1-B2] [A2-B2]
When the design of a study has factorial structure, it is often of interest to determine whether or not there are interaction effects among the individual factors. Interaction effects are differences
between factor-level combinations, which can not be explained by additive main effects. In the example above, a brain area could respond to sound stimuli differently with respect to the presence or
absence of a visual stimulus. An interaction effect, thus, asks whether a difference between levels in one factor (e.g., ["sounds on" - "sounds off"]) differs significantly with respect to the levels
of another factor (e.g., "images off" vs "images on") and vice versa. If the differences between levels of one factor are not significantly different for all levels of the other factor, no
interaction effect is present between the two factors, i.e. the changes in the dependent variable can be explained by additive main effects. Another important benefit of multi-factorial designs is
increased sensitivity to detect differences between cell means of one factor since other included factor(s) may reduce the variability of the error term.
Repeated Measures
In most fMRI studies, each subject is tested under all experimental conditions, i.e. receives all "treatments" (factor-level combinations). This constitutes a repeated measures design. A factor with
repeated measures is also called a within-subjects factor. Repeated measures designs have the important advantage that they provide good precision for comparing condition effects (treatments) because
all sources of variability between subjects are excluded from the experimental error. One may view the subjects as serving as their own controls. In light of the nature of the fMRI signal (no
absolute zero point), repeated measures designs should be used whenever possible. These designs have, however, also potential disadvantages known as interference effects. One type of interference
effect is the order effect, which refers to the potential problem that a condition produces different effects depending on its position within the sequence of conditions. Another type of interference
effect is the carryover effect. Repetition of the same condition and randomization of the order of different conditions independently for each subject should be used to minimize interference effects.
For each subject, a random permutation should be used to define the condition order, and independent permutations should be selected for different subjects. Note that at the random-effects level
(second level analysis) described here, these issues are assumed to be solved since the data is collapsed for each condition at the first level (estimated beta values); the mean effects of each
condition (factor-level combinations) are therefore represented in the same order for each subject (e.g. in ANOVA ROI tables) and not in the order encountered by the subject.
Grouping Factors
While repeated measures designs should be used for fMRI studies whenever possible, many research questions require comparisons between subjects from different populations, e.g. a comparison of male
vs female subjects, or healthy subjects vs subjects with a psychiatric disorder. Such grouping factors are called between-subjects factors. In a standard single factor (one-way) or two-factor ANOVA
only one dependent variable is used. Since subjects are tested usually under several experimental conditions within an experiment (within-subject conditions), a specific condition or a contrast value
need to be specified as the dependent variable from the subject-specific condition estimates of a GLM. Alternatively to this summary statistic approach, group comparisons can be expressed with
designs containing both within-subjects and between-subjects factors. For non-fMRI data with a single dependent variable (e.g. cortical thickness measures), the single factor ANOVA is an appropriate
model to compare different groups.
ANCOVA = ANOVA + Covariates
Analysis of covariance models combine analysis of variance with techniques from regression analysis. With respect to the design, ANCOVA models explain the dependent variable by combining categorical
(qualitative) independent variables with continuous (quantitative) variables. There are special extensions to classical ANOVA calculations to estimate parameters for both categorical and continuous
variables. ANCOVA models can, however, also be calculated using multiple regression analysis using a design matrix with a mix of dummy-coded qualitative and quantitative variables. In the latter
approach, ANCOVA is considered as a special case of the General Linear Model (GLM) framework.
Supported Models
In BrainVoyager, the ANCOVA dialog and the Overlay RFX ANCOVA Tests dialog are used to specify and test ANCOVA designs with within-subjects factors, between-subjects factors and covariates. These
dialogs currently support specification and testing of the following models covering the majority of designs used for neuroimaging studies:
• Correlation analysis of subject-specific measures with dependent variable
Current Limitations and Future Developments
While subjects are treated as a random factor in all supported ANOVA models, the experimental factors of a multi-factorial design may be either fixed or random. If the factor levels are considered
fixed, one is interested in the effects of the specific factors chosen (fixed factor). When the factor levels are a sample from a larger population of potential factor levels, one wants to draw
inferences about the populations of factor levels (random factor). Analysis of variance models in which the factor levels are considered fixed are classified as ANOVA model I. Models for studies in
which all factors are random are classified as ANOVA models II. Models in which some factors are fixed and some are random are classified as ANOVA models III (mixed effects model). At present
BrainVoyager supports only ANOVA model I, i.e. all factors of the design are considered fixed. This model captures most fMRI studies since researchers are typically interested in the effects of each
level of a factor. Models II and III are planned to be supported in a future release.
The supported models currently assume equal sample sizes for the groups of between factors (balanced studies). While tolerating slightly dfferent numbers of subjects in different groups, inferences
for unbalanced data with fixed and random factors requires more complex procedures (e.g. maximum likelihood approach), which will be added in a future release. The two-factor ANOVA model (introduced
with BrainVoyager 20.4) supports unbalanced designs (groups with unequal number of subjects).
If levels of one or more of the factors are unique to a particular level of another factor, the factors are called nested. At present, only fully-crossed factorial designs are supported; nested
designs might be available in a future release.
Copyright © 2023 Rainer Goebel. All rights reserved.
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Quick [ <--- prev -- ] [ HOME ] [ -- next ---> ]
[ full index ]
Last LAM-BIAS
Used to bias the decay length of unstable particles, the inelastic nuclear interaction length of hadrons, photons and muons and the direction of decay secondaries
News: The meaning of WHAT(1)...WHAT(6) depends on the value of SDUM. SDUM = DCDRBIAS and SDUM = DCY-DIRE are used to activate and define decay direction biasing; SDUM = GDECAY selects decay length
biasing and inelastic nuclear interaction biasing; and if SDUM = blank, decay life biasing and inelastic nuclear interaction biasing are selected. Other LAM-BIAS cards with SDUM = DECPRI,
DECALL, INEPRI, INEALL allow to restrict biasing to primary particles or to extend it also to further generations.
for SDUM = DCY-DIRE:
The decay secondary product direction is biased in a direction indicated by the user by means of a unit vector of components U, V, W (see Notes 4 and 5):
WHAT(1) = U (x-direction cosine) of decay direction biasing
Default: 0.0
WHAT(2) = V (y-direction cosine) of decay direction biasing
Default: 0.0)
WHAT(3) = W (z-direction cosine) of decay direction biasing
Default: 1.0
WHAT(4) > 0.0: lambda for decay direction biasing. The degree of
biasing decreases with increasing lambda (see Note 5).
= 0.0: a user provided routine (UDCDRL, see (13)) is called at
each decay event, to provide both direction and lambda for
decay direction biasing
< 0.0 : resets to default (lambda = 0.25)
Default = 0.25
WHAT(5) = not used
WHAT(6) = not used
for SDUM = DCDRBIAS:
WHAT(1) > 0.0: decay direction biasing is activated
= 0.0: ignored
< 0.0: decay direction biasing is switched off
WHAT(2) = not used
WHAT(3) = not used
WHAT(4) = lower bound of the particle id-numbers (or corresponding name)
for which decay direction biasing is to be applied
("From particle WHAT(4)...").
Default = 1.0.
WHAT(5) = upper bound of the particle id-numbers (or corresponding name)
for which decay direction biasing is to be applied
("...to particle WHAT(5)...").
Default = WHAT(4) if WHAT(4) > 0, 64 otherwise.
WHAT(6) = step length in assigning numbers. ("...in steps of WHAT(6)").
Default = 1.0.
for all other SDUM's:
WHAT(1): biasing parameter for decay length or life, applying only to
unstable particles (with particle numbers >= 8). Its meaning
differs depending on the value of SDUM, as explained in the
for SDUM = GDECAY:
WHAT(1) < 0.0 : the mean DECAY LENGTH (in cm) of the particle in the
LABORATORY frame is set = |WHAT(1)| if smaller than
the physical decay length (otherwise it is left
unchanged). At the decay point sampled according to
the biased probability, Russian Roulette (i.e.
random choice) decides whether the particle actually
will survive or not after creation of the decay
products. The latter are created in any case and
their weight adjusted taking into account the ratio
between biased and physical survival probability.
> 0.0 : the mean DECAY LENGTH (in cm) of the particle in the
LABORATORY frame is set = WHAT(1) if smaller than
the physical decay length (otherwise it is left
unchanged). Let P_u = unbiased probability and
P_b = biased probability: at the decay point sampled
according to P_b, the particle always survives
with a reduced weight W(1 - P_u/P_b), where W is the
current weight of the particle before the decay. Its
daughters are given a weight W P_u/P_b (as in
case WHAT(1) < 0.0).
= 0.0 : ignored
for SDUM = blank:
-1 < WHAT(1) < 0. : the mean LIFE of the particle in its REST frame
is REDUCED by a factor = |WHAT(1)|. At the decay
point sampled according to the biased
probability, Russian Roulette (i.e. random
choice) decides whether the particle actually
will survive or not after creation of the decay
products. The latter are created in any case and
their weight adjusted taking into account the
ratio between biased and physical survival
0 < WHAT(1) < +1. : the mean LIFE of the particle in the REST frame
is REDUCED by a factor = |WHAT(1)|. At the decay
point sampled according to the biased
probability, the particle always survives with
a reduced weight. Its daughters are given the
same weight.
|WHAT(1)| > 1 : a possible previously given biasing parameter
is reset to the default value (no biasing)
WHAT(1) = 0 : ignored
WHAT(2) : biasing factor for hadronic inelastic interactions
-1 < WHAT(2) < 0. : the hadronic inelastic interaction length of the
particle is reduced by a factor |WHAT(2)|.
At the interaction point sampled according to
the biased probability, Russian Roulette (i.e.
random choice) decides whether the particle actually
will survive or not after creation of the
secondaries products. The latter are created in
any case and their weight adjusted taking into
account the ratio between biased and physical
survival probability.
0. < WHAT(2) < 1. : the hadronic inelastic interaction length of the
particle is reduced by a factor WHAT(2),
At the interaction point sampled according to
the biased probability, the particle always
survives with a reduced weight. The secondaries
are created in any case and their weight
adjusted taking into account the ratio between
biased and physical survival probability.
= 0.0 : ignored
|WHAT(2)| >= 1.0 : a possible previously set biasing factor is
reset to the default value of 1 (no biasing).
WHAT(3) : If > 2.0 : number or name of the material to
which the inelastic biasing factor has to be applied.
< 0.0 : resets to the default a previously assigned value
= 0.0 : ignored if a value has been previously assigned to
a specific material, otherwise all materials (default)
0.0 < WHAT(3) =< 2.0 : all materials.
WHAT(4) = lower bound of the particle id-numbers (or corresponding name) for
which decay or inelastic interaction biasing is to be applied
("From particle WHAT(4)...").
Default = 1.0.
WHAT(5) = upper bound of the particle id-numbers (or corresponding name) for
which decay or inelastic interaction biasing is to be applied
("...to particle WHAT(5)...").
Default = WHAT(4) if WHAT(4) > 0, 46 otherwise.
WHAT(6) = step length in assigning numbers. ("...in steps of WHAT(6)").
Default = 1.0.
for SDUM = DECPRI, DECALL, INEPRI, INEALL:
SDUM = DECPRI: decay biasing, as requested by another LAM-BIAS card with
SDUM = GDECAY or blank, must be applied only to primary
= DECALL: decay biasing, as requested by another LAM-BIAS card with
SDUM = GDECAY or blank, must be applied to all
generations (default).
= INEPRI: inelastic hadronic interaction biasing, as requested by
another LAM-BIAS card with SDUM = blank, must be applied
only to primary particles.
= INEALL: inelastic hadronic interaction biasing, as requested by
another LAM-BIAS card with SDUM = blank, must be applied
to all generations (default)
Default (option LAM-BIAS not given): no decay length or inelastic
interaction or decay direction biasing
• 1) Option LAM-BIAS can be used for three different kinds of biasing: a) biasing of the particle decay length (or life), b) biasing of the direction of the decay secondaries, and c)
biasing of the inelastic hadronic interaction length.
• 2) Depending on the SDUM value, two different kinds of biasing are applied to the particle decay length (or life). In both cases, the particle is transported to a distance sampled from
an imposed (biased) exponential distribution: If WHAT(1) is positive, decay products are created, but the particle survives with its weight and the weight of its daughters is adjusted
according to the ratio between the biased and the physical survival probability at the sampled distance. If WHAT(1) is negative, decay is performed and the weight of the daughters is set
according to the biasing, but the survival of the primary particle is decided by Russian Roulette according to the biasing. Again, the weights are adjusted taking the bias into account.
• 3) The laboratory decay length corresponding to the selected mean decay life is obtained by multiplication by BETA*GAMMA*c.
• 4) Decay direction biasing is activated by a LAM-BIAS card with SDUM = DCDRBIAS. The direction of decay secondaries is sampled preferentially close to the direction specified by the user
by means of a second LAM-BIAS card with SDUM = DCY-DIRE.
• 5) The biasing function for the decay direction is of the form exp{-[1-cos(theta)]/lambda} where theta is the polar angle between the sampled direction and the preferential direction
(transformed to the centre of mass reference system). The degree of biasing is largest for small positive values of lambda (producing direction biasing strongly peaked along the
direction of interest) and decreases with increasing lambda. Values of lambda >= 1.0 result essentially in no biasing.
• 6) Biasing of hadronic inelastic interaction length can be done either in one single material (indicated by WHAT(3)) or in all materials (default). No other possibility is foreseen for
the moment.
• 7) When choosing the Russian Roulette alternative, it is suggested to set also a weight window (cards WW-FACTOr and WW-THRESh) in order to avoid too large weight fluctuations.
• 8) Reduction factors excessively large can result in an abnormal increase of the number of secondaries to be loaded on the stack, especially at high primary energies. In such cases,
FLUKA issues a message that the secondary could not be loaded because of a lack of space. The weight adjustment is modified accordingly (therefore the results are not affected) but if
the number of messages exceeds a certain limit, the run is terminated.
• 9) Biasing of the hadronic inelastic interaction length can be applied also to photons (provided option PHOTONUC is also requested) and muons (provided option MUPHOTON is also
requested); actually, it is often a good idea to do this in order to increase the probability of photonuclear interaction.
• 10) For photons, a typical reduction factor of the hadronic inelastic interaction length is the order of 0.01-0.05 for a shower initiated by 1 GeV photons or electrons, and of 0.1-0.5
for one at 10 TeV.
Examples (number based):
LAM-BIAS -3.E+3 1. 1. 13. 16. 0.GDECAY
* The mean decay length of pions and kaons (particles 13, 14, 15 and 16)
* is set equal to 30 m. Survival of the decaying particle is decided by
* Russian Roulette.
LAM-BIAS 0.0 0.02 11. 7. 0. 0.INEPRI
* The interaction length for nuclear inelastic interactions of primary
* photons (particle 7) is reduced by a factor 50 in material 11.
* (Note that such a large reduction factor is often necessary for photons,
* but generally is not recommended for hadrons). The photon survives after
* the nuclear interaction with a reduced weight.
The same examples, name based:
LAM-BIAS -3.E+3 1. 1. PION+ KAON- 0.GDECAY
LAM-BIAS 0.0 0.02 11. PHOTON 0. 0.INEPRI
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The Viterbi Heuristic
In the previous segment, you learnt how to calculate the probability of a tag sequence given a sequence of words. The idea is to compute the probability of all possible tag sequences and assign the
sequence having the maximum probability.
Although this approach can work in principle, it is computationally very expensive. For e.g. if you have just three POS tags – DT, JJ, NN, and you want to tag the sentence “The high cost”, there
are 33=27 possible tag sequences (each word can have three possible tags).
In general, for a sequence of n words and t tags, a total of tn tag sequences are possible. The Penn Treebank dataset in NLTK itself has 36 POS tags, so for a sentence of length say 10, there
are 3610 possible tag sequences (that’s about three thousand trillion!).
Clearly, computing trillions of probabilities to tag a 10-word sentence is impractical. Thus, we need to find a much more efficient approach to tagging.
Prof. Srinath will explain one such approach called the Viterbi heuristic, also commonly known as the Viterbi algorithm.
To summarise, the basic idea of the Viterbi algorithm is as follows – given a list of observations (words) O1,O2….On to be tagged, rather than computing the probabilities of all possible tag
sequences, you assign tags sequentially, i.e. assign the most likely tag to each word using the previous tag.
More formally, you assign the tag Tj to each word Oi such that it maximises the likelihood:
$$//P(T_J\backslash O_I)=P(O_I\backslash T_J)\;\ast\;P(T_J\backslash T_{J-1}),//$$
where Tj−1 is the tag assigned to the previous word. Recall that according to the Markov assumption, the probability of a tag Tj is assumed to be dependent only on the previous tag Tj−1, and hence
the term P(Tj|Tj−1).
In other words, you assign tags sequentially such that the tag assigned to every word Oi maximises the likelihood P(Tj|Oi) locally, i.e. it is assumed to be dependent only on the current word and
the previous tag. This algorithm does not guarantee that the resulting tag sequence will be the most likely sequence, but by making these simplifying assumptions, it reduces the computational time
manifold (you’ll see how much in the next lecture).
This is also why it is called a greedy algorithm – it assigns the tag that is most likely at every word, rather than looking for the overall most likely sequence. In the following video, Prof.
Srinath will compare the computational costs of the two tagging algorithms – the brute force algorithm and the Viterbi algorithm.
The professor had mistakenly derived final result as O(ns). Basically it is wrong. So please ignore just below video.
Correct explanation :
The Viterbi algorithm finds the most likely sequence of hidden states, called the ‘Viterbi path’, conditioned on a sequence of observations in an HMM.
If there is a sequence of n words and we need to assign one of T possible tags, then the order would be O(nT2).
For each word, as per Viterbi algorithm, we need to first compute the probability; the order is T for that. And then the next step is to compute the maximum among the probabilities for that word, and
the order for this step is also T.
This has to be done for n words in the sequence.
$$//T^2+T^2+T^2\;\dots n\;times//$$
So, the time order complexity is
Now that you are familiar with the basic Viterbi algorithm, you will study Markov processes and Hidden Markov Models more formally in the next segment. In a later segment, you’ll also learn to write
a POS tagging algorithm using the Viterbi heuristic.
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JavaScript Trig - How to Use Trigonometric Functions in Javascript
In JavaScript, we can easily do trigonometry with the many trig functions from the JavaScript math module. In this article, you will learn about all the trigonometric functions that you can use in
JavaScript to perform trigonometry easily.
In JavaScript, we can easily use trigonometric functions with the JavaScript math module. The JavaScript math module allows us to perform trigonometry easily.
In this article, we are going to go over all of the trig functions you can use in JavaScript and give examples of how to use each one.
Below is a list of each of the trigonometric functions you can use in JavaScript. If you want, you can keep scrolling or click on one of the links below to go to a section directly.
How We Can Use Pi in JavaScript
When doing trigonometry, the most fundamental number is pi.
To get the value of pi in JavaScript, the easiest way is use the JavaScript math module constant pi. Math.PI returns the value 3.141592653589793.
import math
// Output:
How to Convert Degrees to Radians in JavaScript
When working with angles, it’s important to be able to convert between radians and degrees easily.
While JavaScript doesn’t have a function which will convert degrees to radians for us, we can easily define a function. To convert degrees to radians, all we need to do is multiply the degrees by pi
divided by 180.
Below are some examples of how we can use the convert degrees to radians in JavaScript.
function degrees_to_radians(degrees) {
return degrees * (Math.PI / 180);
// Output:
How to Convert Radians to Degrees in JavaScript
When working with angles, it’s important to be able to convert between radians and degrees easily.
While JavaScript doesn’t have a function which will convert radians to degrees for us, we can easily define a function. To convert radians to degrees, all we need to do is multiply the degrees by 180
divided by pi.
Below are some examples of how we can use the convert radians to degrees in JavaScript.
function radians_to_degrees(radians) {
return radians * (180 / Math.PI);
// Output:
How to Find Sine of Number with sin() Function in JavaScript
To find the sine of a number, in radians, we use the JavaScript sin() function.
The input to the sin() function must be a numeric value. The return value will be a numeric value between -1 and 1.
Below are a few examples of how to use the JavaScript sin() function to find the sine of a number.
import math
// Output:
How to Find Cosine of Number with cos() Function in JavaScript
To find the cosine of a number, in radians, we use the JavaScript cos() function.
The input to the cos() function must be a numeric value. The return value will be a numeric value between -1 and 1.
Below are a few examples of how to use the JavaScript cos() function to find the cosine of a number.
import math
// Output:
How to Find Tangent of Number with tan() Function in JavaScript
To find the tangent of a number, or the sine divided by the cosine of an angle, in radians, we use the JavaScript tan() function.
The input to the tan() function must be a numeric value. The return value will be a numeric value between negative infinity and infinity.
Below are a few examples of how to use the JavaScript tan() function to find the tangent of a number.
import math
// Output:
How to Find Arcsine of Number with asin() Function in JavaScript
To find the arcsine of a number, we use the JavaScript asin() function.
The input to the asin() function must be a numeric value between -1 and 1. The return value will be a numeric value between -pi/2 and pi/2 radians.
Below are a few examples of how to use the JavaScript asin() function to find the arcsine of a number.
import math
// Output:
How to Find Arccosine of Number with acos() Function in JavaScript
To find the arccosine of a number, we use the JavaScript acos() function.
The input to the acos() function must be a numeric value between -1 and 1. The return value will be a numeric value between 0 and pi radians.
Below are a few examples of how to use the JavaScript acos() function to find the arccosine of a number.
import math
// Output:
How to Find Arctangent of Number with atan() Function in JavaScript
To find the arctangent of a number, we use the JavaScript atan() function.
The input to the atan() function must be a numeric value. The return value will be a numeric value between -pi/2 and pi/2 radians.
Below are a few examples of how to use the JavaScript atan() function to find the arctangent of a number.
import math
// Output:
How to Find Arctangent of the Quotient of Two Numbers with atan2() Function in JavaScript
JavaScript gives us the ability to find the arctangent of the quotient of two numbers, where the two numbers represents the coordinates of a point (x,y). To find the arctangent of a the quotient of
two numbers, we use the JavaScript atan2() function.
The inputs to the atan2() function must be a numeric values. The return value will be a numeric value between -pi and pi radians.
Below are a few examples of how to use the JavaScript atan2() function to find the arctangent of the quotient of two numbers.
import math
// Output:
How to Find Hyperbolic Sine of Number with sinh() Function in JavaScript
To find the hyperbolic sine of a number, we can use the JavaScript sinh() function from the math module.
The input to the sinh() function must be a numeric value. The return value will be a numeric value.
Below are a few examples of how to use the JavaScript sinh() function to find the hyperbolic sine of a number.
import math
// Output:
How to Find Hyperbolic Cosine of Number with cosh() Function in JavaScript
To find the hyperbolic cosine of a number, we can use the JavaScript cosh() function from the math module.
The input to the cosh() function must be a numeric value. The return value will be a numeric value greater than or equal to 1.
Below are a few examples of how to use the JavaScript cosh() function to find the hyperbolic cosine of a number.
import math
// Output:
How to Find Hyperbolic Tangent of Number with tanh() Function in JavaScript
To find the hyperbolic tangent of a number, we can use the JavaScript tanh() function from the math module.
The input to the tanh() function must be a numeric value. The return value will be a numeric value between -1 and 1.
Below are a few examples of how to use the JavaScript tanh() function to find the hyperbolic tangent of a number.
import math
// Output:
How to Find Hyperbolic Arcsine of Number with asinh() Function in JavaScript
To find the hyperbolic arcsine of a number, we can use the JavaScript asinh() function from the math module.
The input to the asinh() function must be a numeric value. The return value will be a numeric value.
Below are a few examples of how to use the JavaScript asinh() function to find the hyperbolic arcsine of a number.
import math
// Output:
How to Find Hyperbolic Arccosine of Number with acosh() Function in JavaScript
To find the hyperbolic arccosine of a number, we can use the JavaScript acosh() function from the math module.
The input to the acosh() function must be a numeric value greater than or equal to 1. The return value will be a numeric value.
Below are a few examples of how to use the JavaScript acosh() function to find the hyperbolic arccosine of a number.
import math
// Output:
How to Find Hyperbolic Arctangent of Number with atanh() Function in JavaScript
To find the hyperbolic arctangent of a number, we can use the JavaScript atanh() function from the math module.
The input to the atanh() function must be a numeric value between -1 and 1. The return value will be a numeric value.
Below are a few examples of how to use the JavaScript atanh() function to find the hyperbolic arctangent of a number.
import math
// Output:
Hopefully this article has been useful for you to learn how to use the math module trig functions in JavaScript for trigonometry.
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Comparing the Mass of an Electron to the Mass of a Proton
Question Video: Comparing the Mass of an Electron to the Mass of a Proton Physics
The ratio of the mass of a proton to the mass of an electron is 1836. What is the ratio of the mass of the electron to that of the proton? Answer to four significant figures.
Video Transcript
The ratio of the mass of a proton to the mass of an electron is 1836. What is the ratio of the mass of the electron to that of the proton? Answer to four significant figures.
Okay, so in this question, letโ s first of all realize that weโ re dealing with the masses of two particles. Firstly, the mass of a proton and, secondly, the mass of an electron. And this question
tells us that the ratio of these two masses, the ratio of the mass of a proton to the mass of an electron, is 1836. In other words, if we start out by saying that ๐ subscript ๐ is what weโ ll
call our mass of the proton and ๐ ๐ is what weโ ll call our mass of the electron, then the ratio of the mass of the proton to the mass of the electron is equal to 1836. Thatโ s what weโ ve
been told in the question.
And by the way, sometimes a ratio is written as ๐ ๐ to ๐ ๐ , the ratio of the mass of a proton to the mass of an electron. And if we were to write a ratio exactly like this, then we would
have to say that this ratio is equal to 1836 to one. Which, in other words, means that the mass of the proton is 1836 lots of the mass of an electron. Regardless of the exact value of the mass of the
electron or, for that matter, the mass of the proton. We donโ t need to know the individual masses of the electron or the proton. All we care about is that the mass of the proton is 1836 times
larger than the mass of the electron. And thatโ s more clearly seen when we write our ratio like this.
The mass of the proton divided by the mass of the electron is equal to 1836. Therefore, the mass of the proton is 1836 times larger than the mass of the electron. And additionally, we should know
that when weโ re told ratios in a question, weโ re told them as ratios of one quantity, thatโ s the mass of the proton in this case, to the other quantity. Which, in this case, is the mass of the
electron. And in that situation, we write it as the first quantity over the second quantity.
Anyway, so weโ ve now realized that the mass of the proton divided by the mass of the electron is equal to 1836. What the question is asking us to do is to find the ratio of the mass of the electron
to that of the proton. In other words, the question is wanting us to find the ratio between the mass of the electron and the mass of the proton. And we donโ t know what this is, so letโ s call that
๐ ฅ. So how are we going to go about doing this? We know ๐ ๐ divided by ๐ ๐ . And we want to find itโ s reciprocal, ๐ ๐ divided by ๐ ๐ . Well, to do this, letโ s start with
this equation here and work our way towards this equation. Where weโ ll have ๐ ๐ divided by ๐ ๐ on one side and everything else on the other. And that everything else will be equal to ๐
So starting here then, letโ s start by multiplying both sides of the equation by ๐ subscript ๐ . Because when we do this, weโ ve now got an ๐ subscript ๐ in the numerator and denominator
on the left-hand side. And so, they cancel. That just leaves us with ๐ subscript ๐ on the left-hand side and 1836 times ๐ subscript ๐ on the right. Then what we can do is to divide both
sides of the equation by ๐ subscript ๐ . Because when we do, the ๐ subscript ๐ on the left-hand side in the numerator cancels with the one in the denominator. And another way to think
about this is that ๐ subscript ๐ divided by ๐ subscript ๐ is just one. Anything divided by itself is one. And on the right-hand side, weโ ve got 1836๐ subscript ๐ divided by ๐
subscript ๐ .
So cleaning everything up, our equation looks a bit like this. Now, all we need to do is to divide both sides of the equation by 1836. Because when we do, we see that on the right-hand side now, weโ
ve got a factor of 1836 in the numerator and in the denominator. Those cancel because 1836 divided by itself is one. And so, all weโ re left with on the right-hand side is ๐ subscript ๐
divided by ๐ subscript ๐ . Thatโ s exactly what we were going for earlier. And on the left-hand side of our equation, weโ re left with one divided by 1836. Which means that at this point, if
this side of our equation is exactly the same thing as what we were going for here, ๐ subscript ๐ divided by ๐ subscript ๐ , then the other side of our equation, one divided by 1836, must
be equal to ๐ ฅ. Which was the ratio of the mass of the electron to that of the proton.
And so, all thatโ s left for us to do now is to evaluate this fraction and to give our answer to four significant figures as the question asks us to. When we plug our equation into our calculator,
we find that one divided by 1836 is equal to 0.000544662 dot dot dot, so on and so forth. But, once again, we need to give our answer to four significant figures. So letโ s start counting
significant figures. Now, we should realize that none of these leading zeroes are significant. In fact, the very first significant figure starts here. This five is our first significant figure. And
so, starting here, thatโ s our significant figure, this is our second, this is our third, and this is our fourth. Our fourth significant figure is a six.
Now, exactly what happens to that significant figure depends on the next value, which in this case also happens to be a six. But then, because six is larger than five, this means that the significant
figure in question is going to round up. Itโ s going to become a seven. At which point, weโ ve now rounded our answer to four significant figures, which means weโ ve found the answer to a
question. The ratio of the mass of the electron to the mass of the proton, to four significant figures, is 0.0005447.
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Sequentially Perfect and Uniform One-Factorizations of the Complete Graph
Sequentially Perfect and Uniform One-Factorizations of the Complete Graph
In this paper, we consider a weakening of the definitions of uniform and perfect one-factorizations of the complete graph. Basically, we want to order the $2n-1$ one-factors of a one-factorization of
the complete graph $K_{2n}$ in such a way that the union of any two (cyclically) consecutive one-factors is always isomorphic to the same two-regular graph. This property is termed sequentially
uniform; if this two-regular graph is a Hamiltonian cycle, then the property is termed sequentially perfect. We will discuss several methods for constructing sequentially uniform and sequentially
perfect one-factorizations. In particular, we prove for any integer $n \geq 1$ that there is a sequentially perfect one-factorization of $K_{2n}$. As well, for any odd integer $m \geq 1$, we prove
that there is a sequentially uniform one-factorization of $K_{2^t m}$ of type $(4,4,\dots,4)$ for all integers $t \geq 2 + \lceil \log_2 m \rceil$ (where type $(4,4,\dots,4)$ denotes a two-regular
graph consisting of disjoint cycles of length four).
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Turn/Square Hour to Sign/Square Month
Turn/Square Hour [turn/h2] Output
1 turn/square hour in degree/square second is equal to 0.000027777777777778
1 turn/square hour in degree/square millisecond is equal to 2.7777777777778e-11
1 turn/square hour in degree/square microsecond is equal to 2.7777777777778e-17
1 turn/square hour in degree/square nanosecond is equal to 2.7777777777778e-23
1 turn/square hour in degree/square minute is equal to 0.1
1 turn/square hour in degree/square hour is equal to 360
1 turn/square hour in degree/square day is equal to 207360
1 turn/square hour in degree/square week is equal to 10160640
1 turn/square hour in degree/square month is equal to 192106890
1 turn/square hour in degree/square year is equal to 27663392160
1 turn/square hour in radian/square second is equal to 4.8481368110954e-7
1 turn/square hour in radian/square millisecond is equal to 4.8481368110954e-13
1 turn/square hour in radian/square microsecond is equal to 4.8481368110954e-19
1 turn/square hour in radian/square nanosecond is equal to 4.8481368110954e-25
1 turn/square hour in radian/square minute is equal to 0.0017453292519943
1 turn/square hour in radian/square hour is equal to 6.28
1 turn/square hour in radian/square day is equal to 3619.11
1 turn/square hour in radian/square week is equal to 177336.62
1 turn/square hour in radian/square month is equal to 3352897.75
1 turn/square hour in radian/square year is equal to 482817275.46
1 turn/square hour in gradian/square second is equal to 0.000030864197530864
1 turn/square hour in gradian/square millisecond is equal to 3.0864197530864e-11
1 turn/square hour in gradian/square microsecond is equal to 3.0864197530864e-17
1 turn/square hour in gradian/square nanosecond is equal to 3.0864197530864e-23
1 turn/square hour in gradian/square minute is equal to 0.11111111111111
1 turn/square hour in gradian/square hour is equal to 400
1 turn/square hour in gradian/square day is equal to 230400
1 turn/square hour in gradian/square week is equal to 11289600
1 turn/square hour in gradian/square month is equal to 213452100
1 turn/square hour in gradian/square year is equal to 30737102400
1 turn/square hour in arcmin/square second is equal to 0.0016666666666667
1 turn/square hour in arcmin/square millisecond is equal to 1.6666666666667e-9
1 turn/square hour in arcmin/square microsecond is equal to 1.6666666666667e-15
1 turn/square hour in arcmin/square nanosecond is equal to 1.6666666666667e-21
1 turn/square hour in arcmin/square minute is equal to 6
1 turn/square hour in arcmin/square hour is equal to 21600
1 turn/square hour in arcmin/square day is equal to 12441600
1 turn/square hour in arcmin/square week is equal to 609638400
1 turn/square hour in arcmin/square month is equal to 11526413400
1 turn/square hour in arcmin/square year is equal to 1659803529600
1 turn/square hour in arcsec/square second is equal to 0.1
1 turn/square hour in arcsec/square millisecond is equal to 1e-7
1 turn/square hour in arcsec/square microsecond is equal to 1e-13
1 turn/square hour in arcsec/square nanosecond is equal to 1e-19
1 turn/square hour in arcsec/square minute is equal to 360
1 turn/square hour in arcsec/square hour is equal to 1296000
1 turn/square hour in arcsec/square day is equal to 746496000
1 turn/square hour in arcsec/square week is equal to 36578304000
1 turn/square hour in arcsec/square month is equal to 691584804000
1 turn/square hour in arcsec/square year is equal to 99588211776000
1 turn/square hour in sign/square second is equal to 9.2592592592593e-7
1 turn/square hour in sign/square millisecond is equal to 9.2592592592593e-13
1 turn/square hour in sign/square microsecond is equal to 9.2592592592593e-19
1 turn/square hour in sign/square nanosecond is equal to 9.2592592592593e-25
1 turn/square hour in sign/square minute is equal to 0.0033333333333333
1 turn/square hour in sign/square hour is equal to 12
1 turn/square hour in sign/square day is equal to 6912
1 turn/square hour in sign/square week is equal to 338688
1 turn/square hour in sign/square month is equal to 6403563
1 turn/square hour in sign/square year is equal to 922113072
1 turn/square hour in turn/square second is equal to 7.7160493827161e-8
1 turn/square hour in turn/square millisecond is equal to 7.7160493827161e-14
1 turn/square hour in turn/square microsecond is equal to 7.716049382716e-20
1 turn/square hour in turn/square nanosecond is equal to 7.7160493827161e-26
1 turn/square hour in turn/square minute is equal to 0.00027777777777778
1 turn/square hour in turn/square day is equal to 576
1 turn/square hour in turn/square week is equal to 28224
1 turn/square hour in turn/square month is equal to 533630.25
1 turn/square hour in turn/square year is equal to 76842756
1 turn/square hour in circle/square second is equal to 7.7160493827161e-8
1 turn/square hour in circle/square millisecond is equal to 7.7160493827161e-14
1 turn/square hour in circle/square microsecond is equal to 7.716049382716e-20
1 turn/square hour in circle/square nanosecond is equal to 7.7160493827161e-26
1 turn/square hour in circle/square minute is equal to 0.00027777777777778
1 turn/square hour in circle/square hour is equal to 1
1 turn/square hour in circle/square day is equal to 576
1 turn/square hour in circle/square week is equal to 28224
1 turn/square hour in circle/square month is equal to 533630.25
1 turn/square hour in circle/square year is equal to 76842756
1 turn/square hour in mil/square second is equal to 0.00049382716049383
1 turn/square hour in mil/square millisecond is equal to 4.9382716049383e-10
1 turn/square hour in mil/square microsecond is equal to 4.9382716049383e-16
1 turn/square hour in mil/square nanosecond is equal to 4.9382716049383e-22
1 turn/square hour in mil/square minute is equal to 1.78
1 turn/square hour in mil/square hour is equal to 6400
1 turn/square hour in mil/square day is equal to 3686400
1 turn/square hour in mil/square week is equal to 180633600
1 turn/square hour in mil/square month is equal to 3415233600
1 turn/square hour in mil/square year is equal to 491793638400
1 turn/square hour in revolution/square second is equal to 7.7160493827161e-8
1 turn/square hour in revolution/square millisecond is equal to 7.7160493827161e-14
1 turn/square hour in revolution/square microsecond is equal to 7.716049382716e-20
1 turn/square hour in revolution/square nanosecond is equal to 7.7160493827161e-26
1 turn/square hour in revolution/square minute is equal to 0.00027777777777778
1 turn/square hour in revolution/square hour is equal to 1
1 turn/square hour in revolution/square day is equal to 576
1 turn/square hour in revolution/square week is equal to 28224
1 turn/square hour in revolution/square month is equal to 533630.25
1 turn/square hour in revolution/square year is equal to 76842756
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Thomas Zaslavsky (Binghamton)
Automorphism groups of graphs have interested algebraists, as representing groups in a relatively simple way, and graph theorists, as describing the symmetries of graphs. The Petersen graph, a
ten-vertex graph that plays many roles in graph theory, has a remarkably large automorphism group for its size: the symmetric group on five letters.
A signed Petersen graph is the Petersen graph with arbitrary signs on the edges. There are six essentially different ways to choose the signs, up to vertex switching, in which the signs of all edges
at some vertex are reversed, and sign-preserving graph automorphism. A switching automorphism of a signed graph is a combination of vertex switchings and graph automorphisms whose result is the
original signed graph. The six essentially different signatures of the Petersen graph have six different switching automorphism groups, of which some are trivial but two, although isomorphic to well
known groups, have their own rich internal structure.
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Sentry: Earth Impact Monitoring
The following table contains operational notes related to out Earth impact monitoring system. Entries are listed in reverse chronological order.
Date Note
2024-Jun-06 We updated the impact hazard assessment of (29075) 1950 DA. Relative to the previous assessment, the new results are based on an observation arc extended through 2023-10-03, which
includes astrometry from the Gaia Focused Product Release. The results are presented in Fuentes-Munoz et al. (2024).
2024-May-13 2024 JV8 was determined to be artificial (MPEC 2024-J297). The corresponding records have therefore been removed from the Sentry tables.
We updated the impact hazard assessment of (29075) 1950 DA. Relative to the previous assessment, the new results are based on an observation arc extended by six years, more recent
2022-Mar-29 statistical treatment of astrometric data (https://ui.adsabs.harvard.edu/abs/2020Icar..33913596E/abstract and https://ui.adsabs.harvard.edu/abs/2017Icar..296..139V/abstract), and JPL’s
DE441 planetary ephemeris. The calculation was performed by the Sentry-II system, which now allows a more automatic handling of this special case.
We have implemented a new impact monitoring algorithm that replaces the Line-of-Variations (LOV) method that Sentry has used over the last two decades. The new technique incorporates an
impact pseudo-observation to the orbit-determination process to converge to impact trajectories that are compatible with the observational data. The new approach is generally more robust
2021-Aug-23 and reliable than the LOV method for certain strongly nonlinear situations and handling nongravitational parameters. This paper describes the algorithm in full detail.
As part of the transition to the new algorithm, all objects in the NEA catalog have been reprocessed. Minor differences with respect to the data computed with the LOV method are
inevitable due to the statistical nature of the system. The objects for which the new algorithm cannot find virtual impactors have been moved to the Removed Objects table.
2021-Aug-11 We updated the impact hazard assessment for asteroid (101955) Bennu using the positional data from the OSIRIS-REx mission. The results are presented in detail in the recent publication
Farnocchia et al. (2021).
2021-May-27 After five of its eight original observations have been reassigned, 2017 DC120 now only has three observations and no MPC orbit. We therefore removed 2017 DC120 from the JPL small-body
database and the Sentry tables.
2021-May-24 We have updated the impact hazard assessment of asteroid 2020 CD3 based on orbit solution 23 published in Naidu et al. (2021). The solution includes an estimate of the radial acceleration
parameter A1 related to the solar radiation pressure.
We are recomputing all risk tables with the most recent planetary ephemeris, designated DE441. Our asteroid perturber model has been updated accordingly. Cases of higher interest will not
2021-Apr-13 change significantly between runs. However, objects with very low impact probabilities are only detected on a statistical basis. Therefore, we will find some new potential impacts (and
potential impactors) and will not identify some that were found in previous searches.
2021-Mar-26 The optical and radar observations of (99942) Apophis collected during the current apparition rule out any possible impact for the next 100 years. More details are provided in this JPL
News story.
2021-Feb-23 2020 SO was determined to be artificial (MPEC 2021-D62). The corresponding records have therefore been removed from the Sentry tables.
(99942) Apophis is currently observable and the observations that have been collected so far in the current apparition, which runs roughly from December 2020 to May 2021, provide useful
2021-Jan-20 information on its orbit and impact hazard assessment. In particular, the Yarkovsky effect acting on Apophis is now significantly constrained. Subsequent, albeit not necessarily frequent,
updates are planned through the end of the apparition as more observations are collected.
2020-May-26 We updated the reporting of the Palermo Scale. Instead or referring to the time of the impact hazard assessment calculation, the Palermo Scale is reevaluated daily to reflect the current
time to impact, rounded up to the nearest number of years.
2020-Apr-13 2020 GL2 was determined to be ESA’s BepiColombo spacecraft by the Minor Planet Center (MPEC 2020-G97). The corresponding records have therefore been removed from the Sentry tables.
The MPC originally designated 2019 OF5 by linking two tracklets over two nights for a total of six observations (MPEC 2019-P91). The corresponding linkage was later retracted by the MPC
2020-Mar-10 by splitting the two tracklets: one for 2019 OF5 and the other for 2019 OG5 (MPC 114960). Similarly, 2019 QS8 was designated by linking two tracklets over two nights for a total of four
observations (MPEC 2019-S08). Also, this linkage was retracted since part of the dataset belonged to asteroid 75462 (MPS 1027499). 2016 PO66 was designated in MPEC 2016-Q06. Subsequently,
all observations for 2016 PO66 were deleted in MPC 108699-108700. Therefore, 2019 OF5, 2019 QS8, and 2016 PO66 have been removed from the Sentry tables.
2020-Feb-06 2018 AV2 was determined to be artificial (https://minorplanetcenter.net/iau/artsats/artsats.html). The corresponding records have therefore been removed from the Sentry tables.
We have specifically removed the 2019-09-09 potential impact for 2006 QV89 because of negative detections in the predicted region of the sky for that Virtual Impactor within images
obtained by the European Southern Observatory’s Very Large Telescope (VLT) on July 4 and 5 (see ESA news story). While the asteroid itself has not been detected in 2019 and its true
position is therefore still very uncertain, the position for the 2019-09-09 virtual impactor can be predicted very accurately. The VLT observations covered this position, and if the
2019-Jul-18 asteroid had been there it would have been easily detected.
Update 2020-Mar-31
2006 QV89 was detected by Dave Tholen with CFHT and the observations published in MPEC 2019-P85, which was issued on 2019-Aug-11. These additional observations confirm the removal of the
virtual impactor.
We have computed an updated impact probability table for (410777) 2009 FD. The new assessment makes use of the optical astrometry collected in early 2019, which allowed significant
constraints on the semimajor axis drift caused by the Yarkovsky effect acting on (410777) and in turn on the future trajectory of the asteroid. The results are based on the Multilayer
2019-Jul-16 Clustered Sampling Technique presented in detail in Del Vigna et al. (2019).
Update 2020-Nov-18
New observations of (410777) 2009 FD from the Catalina Sky Survey on 2020-Nov-16 (MPEC 2020-W27), ruled out the remaining virtual impactor in 2190.
We have enhanced Sentry to optionally perform the impact search using a Monte Carlo (MC) approach. This approach is more computationally expensive than the standard Line-of-Variations
2017-Sep-28 (LOV) method and so will only be used when appropriate. For this reason, we removed all LOV-specific columns from the general VI Table. LOV-specific and MC-specific columns are available
in the object details page.
We have transitioned to an improved weighting scheme for asteroid astrometry as described in a recently submitted paper by Veres et al. 2017. Moreover, we updated the set of main belt
2017-Apr-06 perturbing bodies to account for more recent mass estimates (Folkner et al. 2014). Because of the statistical nature of Sentry’s impact search, these changes will give results that might
differ from previous runs. Some new low impact probability cases could be found and some previous low probability cases could disappear. However, higher impact probability cases will not
be significantly affected.
2016-Jan-21 We have updated the hazard assessment of (410777) 2009 FD to include astrometry obtained during the latest apparition from October to December 2015. In particular, the new results account
for recent radar observations and the revised estimate of the asteroid’s size. The computation includes the Yarkovsky effect as estimated from the fit to the astrometric observations.
2015-Dec-07 We have updated the 2880 impact probability for (29075) 1950 DA to include the debiasing and weighting scheme by Farnocchia et al. 2015 and use the DE431 version of JPL’s planetary
ephemerides. The computation was performed with a Monte Carlo sampling of the orbital elements and the Yarkokovsky effect, as estimated from the fit to the astrometric observations.
We have computed an updated impact probability table for (99942) Apophis. The new table is based on the recent publication by Vokrouhlicky et al. (2015). The new table relies on a refined
2015-Mar-02 estimate of the Yarkovsky effect that accounts for the non-principal axis rotation of Apophis (Pravec et al., 2014) and the most recent estimates of diameter and thermal inertia (Mueller
et al., 2014).
2014-Aug-19 We have updated the 2880 impact probability for (29075) 1950 DA to account for the additional information on the asteroid’s physical model as described in Rozitis et al., “Cohesive forces
prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA”, Nature, vol. 512, pp. 174-176.
2014-Apr-29 The 2009 FD potential impact tabulation has been updated to incorporate uncertainties due to the Yarkovsky effect, which dominates over present day position uncertainties. Therefore the
current posting may not be updated until enough new observations or other information are available to warrant a recomputation.
We have updated the risk table for 101955 Bennu based on the research described by Chesley et al., “Orbit and Bulk Density of the OSIRIS-REx Target Asteroid (101955) Bennu” (Icarus, in
2014-Mar-03 press, 2014) [Preprint]. The new results make use of Arecibo radar astrometry from September 2011, which yields a high-precision estimate of the Yarkovsky effect and in turn the bulk
density of Bennu. The new cumulative impact probability is about 1 in 2700.
2013-Nov-25 We have updated the 2880 impact probability for (29075) 1950 DA based on recently reported 2012 radar astrometry. The results are based on Farnocchia and Chesley (2013), which has been
revised to account for the 2012 observations and is now in press on Icarus.
We have now computed an impact probability for (29075) 1950 DA in 2880 and posted the results to the risk page. This is based on the recent publication by Farnocchia and Chesley (2013),
2013-Oct-04 now accepted by Icarus. As in the case for Apophis, below, the new hazard assessment for 1950 DA accounts for the Yarkovsky effect, despite the fact that it has so far not been
definitively seen in the orbital motion. This requires us to account for potential orbital variations due to uncertainties in the physical properties of the asteroid, such as spin axis
orientation, thermal inertia and bulk density.
We are nearing completion of a recomputation of all risk tables with an updated planetary ephemeris, designated DE431, which will better model the gravitational perturbations of the
planets. Our asteroid perturber model has been updated to be consistent with DE431, and we are now using perturbations from the 16 most massive main-belt asteroids, rather than only the
2013-Aug-12 largest three as was done in the past. Note that many objects with very low impact probabilities are only detected on a statistical basis, and so this recomputation can yield different
results than those obtained before for these low interest cases. In particular, we will find some new potential impacts (and potential impactors) and will not identify some that were
found in previous searches. Cases of higher interest will not change significantly between runs.
We have updated the risk table for 99942 Apophis based on the recently released radar astrometry as well as optical astrometry through 2013-Apr-26. For the hazard assessment we continue
to apply the technique discussed by Farnocchia et al. (Icarus, v. 224, pp.192-200, 2013). The updated Fig. 6 from the Farnocchia et al. paper shows the current estimate for the
2013-May-01 probability distribution on the 2029 b-plane. The 2036 keyhole, which was previously of some interest, is situated at approximately -1600 km on the abscissa (i.e., outside the plot
boundaries). The hazard assessment is now quite stable and we do not intend to update again until there is significant new observational information for Apophis, which could come as early
as June, when the [next radar observations](http://www.naic.edu/~pradar/sched.shtml> are planned.
2013-Jan-09 We have updated the risk table for 99942 Apophis based on the recent publication by Farnocchia et al.
We have transitioned to the debiasing and weight scheme described in Chesley, Baer and Monet (Icarus, vol. 210, pp. 158-181). This means that we are treating the asteroid observational
2011-Sep-20 data in a way that is more consistent with the statistical uncertainties and that has been shown to produce better fits and more reliable predictions. As explained in our 2010-Dec-7 note
below, such a recomputation necessarily leads to minor changes in the listings, as well as some new additions and removals to the object list.
As a part of fielding some enhancements to our process we are rerunning all objects in order to bring them up-to-date with our current software and dynamical models. Note that many
2010-Dec-07 objects with very low impact probabilities are only detected on a statistical basis, and so this recomputation can yield different results than those obtained before for these low
interest cases. In particular, we will find some new potential impacts (and potential impactors) and will not identify some that were found in previous searches. Cases of higher interest
will not change between runs.
Updating our note of 2010-Jul-26 below, another object has been found to have potential impacts in the far future, beyond 100 years. 2009 FD is roughly 130 m in diameter with an estimated
2010-Nov-23 1 in 435 chance of impact in 2185. The current analysis assumes only gravitational accelerations and does not incorporate the potentially important Yarkovsky (thermal) accelerations. Thus
the 2009 FD Risk Table may be refined by future analyses that attempt to incorporate a more complete dynamical model.
In some cases, investigations into potential impacts are conducted for more than 100 years into the future. Currently, there are two well-observed objects for which long-term analyses
have been carried out.
1. Asteroid (29075) 1950 DA, has a significant possibility of impact on March 16, 2880. A careful computation of the impact probability, which is less than 0.33%, is challenging because
2010-Jul-26 the orientation of its spin pole is poorly known. Giorgini et al. (Science, Vol. 296. no. 5565, pp. 132 - 136, 2002) analyzed this object’s motion, which is discussed here.
2. The second object, (101955) 1999 RQ36, currently has non-zero impact probabilities on numerous occasions during the years after 2165. This is analyzed in a paper published by Milani
et al. (Icarus, Vol. 203, pp. 460-471, 2009).
Note the Torino Scale is formally undefined for potential impacts more than one century into the future and so not applicable in such cases.
2009-Oct-07 The risk assessment for Apophis has been updated to reflect new astrometry released by Tholen et al. (DPS 2009) and dispersions due to the Yarkovsky effect. Results reported by Chesley et
al. at the 2009 Division of Planetary Sciences meeting.
2008-May-18 Sentry has switched to a new server and management architecture. As a part of this transition, all objects in the NEA catalog were reanalyzed with the new system. This recomputation leads
inevitably to minor differences in the results due to the statistical nature of the impact monitoring algorithms.
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992 Square Poles to Dhur [Nepal]
Square Pole [sq pole] Output
992 square poles in ankanam is equal to 3751
992 square poles in aana is equal to 789.11
992 square poles in acre is equal to 6.2
992 square poles in arpent is equal to 7.34
992 square poles in are is equal to 250.91
992 square poles in barn is equal to 2.509050981888e+32
992 square poles in bigha [assam] is equal to 18.75
992 square poles in bigha [west bengal] is equal to 18.75
992 square poles in bigha [uttar pradesh] is equal to 10
992 square poles in bigha [madhya pradesh] is equal to 22.51
992 square poles in bigha [rajasthan] is equal to 9.92
992 square poles in bigha [bihar] is equal to 9.92
992 square poles in bigha [gujrat] is equal to 15.5
992 square poles in bigha [himachal pradesh] is equal to 31
992 square poles in bigha [nepal] is equal to 3.7
992 square poles in biswa [uttar pradesh] is equal to 200.05
992 square poles in bovate is equal to 0.418175163648
992 square poles in bunder is equal to 2.51
992 square poles in caballeria is equal to 0.0557566884864
992 square poles in caballeria [cuba] is equal to 0.18696356049836
992 square poles in caballeria [spain] is equal to 0.0627262745472
992 square poles in carreau is equal to 1.95
992 square poles in carucate is equal to 0.051626563413333
992 square poles in cawnie is equal to 4.65
992 square poles in cent is equal to 620
992 square poles in centiare is equal to 25090.51
992 square poles in circular foot is equal to 343866.04
992 square poles in circular inch is equal to 49516709.73
992 square poles in cong is equal to 25.09
992 square poles in cover is equal to 9.3
992 square poles in cuerda is equal to 6.38
992 square poles in chatak is equal to 6001.6
992 square poles in decimal is equal to 620
992 square poles in dekare is equal to 25.09
992 square poles in dismil is equal to 620
992 square poles in dhur [tripura] is equal to 75020
992 square poles in dhur [nepal] is equal to 1481.88
992 square poles in dunam is equal to 25.09
992 square poles in drone is equal to 0.97682291666667
992 square poles in fanega is equal to 3.9
992 square poles in farthingdale is equal to 24.79
992 square poles in feddan is equal to 6.02
992 square poles in ganda is equal to 312.58
992 square poles in gaj is equal to 30008
992 square poles in gajam is equal to 30008
992 square poles in guntha is equal to 248
992 square poles in ghumaon is equal to 6.2
992 square poles in ground is equal to 112.53
992 square poles in hacienda is equal to 0.00028002801137143
992 square poles in hectare is equal to 2.51
992 square poles in hide is equal to 0.051626563413333
992 square poles in hout is equal to 17.65
992 square poles in hundred is equal to 0.00051626563413333
992 square poles in jerib is equal to 12.41
992 square poles in jutro is equal to 4.36
992 square poles in katha [bangladesh] is equal to 375.1
992 square poles in kanal is equal to 49.6
992 square poles in kani is equal to 15.63
992 square poles in kara is equal to 1250.33
992 square poles in kappland is equal to 162.65
992 square poles in killa is equal to 6.2
992 square poles in kranta is equal to 3751
992 square poles in kuli is equal to 1875.5
992 square poles in kuncham is equal to 62
992 square poles in lecha is equal to 1875.5
992 square poles in labor is equal to 0.035001323948439
992 square poles in legua is equal to 0.0014000529579376
992 square poles in manzana [argentina] is equal to 2.51
992 square poles in manzana [costa rica] is equal to 3.59
992 square poles in marla is equal to 992
992 square poles in morgen [germany] is equal to 10.04
992 square poles in morgen [south africa] is equal to 2.93
992 square poles in mu is equal to 37.64
992 square poles in murabba is equal to 0.24799978075723
992 square poles in mutthi is equal to 2000.53
992 square poles in ngarn is equal to 62.73
992 square poles in nali is equal to 125.03
992 square poles in oxgang is equal to 0.418175163648
992 square poles in paisa is equal to 3156.52
992 square poles in perche is equal to 733.88
992 square poles in parappu is equal to 99.2
992 square poles in pyong is equal to 7589.39
992 square poles in rai is equal to 15.68
992 square poles in rood is equal to 24.8
992 square poles in ropani is equal to 49.32
992 square poles in satak is equal to 620
992 square poles in section is equal to 0.0096875
992 square poles in sitio is equal to 0.00139391721216
992 square poles in square is equal to 2700.72
992 square poles in square angstrom is equal to 2.509050981888e+24
992 square poles in square astronomical units is equal to 1.1211369348167e-18
992 square poles in square attometer is equal to 2.509050981888e+40
992 square poles in square bicron is equal to 2.509050981888e+28
992 square poles in square centimeter is equal to 250905098.19
992 square poles in square chain is equal to 62
992 square poles in square cubit is equal to 120032
992 square poles in square decimeter is equal to 2509050.98
992 square poles in square dekameter is equal to 250.91
992 square poles in square digit is equal to 69138432
992 square poles in square exameter is equal to 2.509050981888e-32
992 square poles in square fathom is equal to 7502
992 square poles in square femtometer is equal to 2.509050981888e+34
992 square poles in square fermi is equal to 2.509050981888e+34
992 square poles in square feet is equal to 270072
992 square poles in square furlong is equal to 0.61999945189307
992 square poles in square gigameter is equal to 2.509050981888e-14
992 square poles in square hectometer is equal to 2.51
992 square poles in square inch is equal to 38890368
992 square poles in square league is equal to 0.0010763845940911
992 square poles in square light year is equal to 2.8032369355609e-28
992 square poles in square kilometer is equal to 0.02509050981888
992 square poles in square megameter is equal to 2.509050981888e-8
992 square poles in square meter is equal to 25090.51
992 square poles in square microinch is equal to 38890333692594000000
992 square poles in square micrometer is equal to 25090509818880000
992 square poles in square micromicron is equal to 2.509050981888e+28
992 square poles in square micron is equal to 25090509818880000
992 square poles in square mil is equal to 38890368000000
992 square poles in square mile is equal to 0.0096875
992 square poles in square millimeter is equal to 25090509818.88
992 square poles in square nanometer is equal to 2.509050981888e+22
992 square poles in square nautical league is equal to 0.00081280246453545
992 square poles in square nautical mile is equal to 0.0073152157277218
992 square poles in square paris foot is equal to 237824.74
992 square poles in square parsec is equal to 2.6351678212154e-29
992 square poles in perch is equal to 992
992 square poles in square perche is equal to 491.28
992 square poles in square petameter is equal to 2.509050981888e-26
992 square poles in square picometer is equal to 2.509050981888e+28
992 square poles in square rod is equal to 992
992 square poles in square terameter is equal to 2.509050981888e-20
992 square poles in square thou is equal to 38890368000000
992 square poles in square yard is equal to 30008
992 square poles in square yoctometer is equal to 2.509050981888e+52
992 square poles in square yottameter is equal to 2.509050981888e-44
992 square poles in stang is equal to 9.26
992 square poles in stremma is equal to 25.09
992 square poles in sarsai is equal to 8928
992 square poles in tarea is equal to 39.9
992 square poles in tatami is equal to 15179.69
992 square poles in tonde land is equal to 4.55
992 square poles in tsubo is equal to 7589.85
992 square poles in township is equal to 0.00026909698432859
992 square poles in tunnland is equal to 5.08
992 square poles in vaar is equal to 30008
992 square poles in virgate is equal to 0.209087581824
992 square poles in veli is equal to 3.13
992 square poles in pari is equal to 2.48
992 square poles in sangam is equal to 9.92
992 square poles in kottah [bangladesh] is equal to 375.1
992 square poles in gunta is equal to 248
992 square poles in point is equal to 620
992 square poles in lourak is equal to 4.96
992 square poles in loukhai is equal to 19.84
992 square poles in loushal is equal to 39.68
992 square poles in tong is equal to 79.36
992 square poles in kuzhi is equal to 1875.5
992 square poles in chadara is equal to 2700.72
992 square poles in veesam is equal to 30008
992 square poles in lacham is equal to 99.2
992 square poles in katha [nepal] is equal to 74.09
992 square poles in katha [assam] is equal to 93.78
992 square poles in katha [bihar] is equal to 198.44
992 square poles in dhur [bihar] is equal to 3968.73
992 square poles in dhurki is equal to 79374.58
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Recent Question/Assignment
Autonomous Vehicle and Modelling Assignment 2023
Problem 1. In Fig. 1 there is a weighted graph, circles represent vertices, links represent edges, and numbers represent edge weights.
Figure 1: The graph.
1. Find a shortest path from vertex S to vertex T , i.e., a path of minimum weight between S and T .
2. Find a minimum subgraph (set of edges) that connects all vertices in the graph and has the smallest total weight (sum of edge weights).
Justify your answers.
Problem 2.
1. Let E be a binary relation symbol representing adjacency in graphs. (That is, E(x, y) means in a graph that “the vertices x and y are adjacent”.) Write a formula ?(x, y) in the first-order logic
over the language L = ?E? with equality expressing that
“x and y have exactly two common neighbors.”
Note that except logical symbols you may use only E and =. (The phrases “x and y are adjacent” and “x and y are neighbors” have the same meaning.)
2. Find a model and a non-model of a theory
T = {(?x)¬E(x, x), (?x)(?y)(E(x, y) ? E(y, x)), (?x)(?y)?(x, y)}
over the language L. By a non-model of T we mean a structure of the same language that is not a model of T .
3. Is the formula (?x)( ?y)?(x, y) provable or refutable from T (in a sound and complete proof system using the axioms of T )? Give an explanation for your answer.
Problem 3. Consider finite strings over the alphabet S = a{, b, c, d }. The power operation represents string repetition, for example a3b4c denotes the string aaabbbbc. Define a contextfree grammar G
generating the language L(G) = { w|(?i, j, k)w = aib(i+j+k)cjdk}, the set of words where the number of b’s is the same as the number of all other letters together and the letters are ordered
alphabetically. For example, the words ab, aaabbbbd, abbbcd belong to the language, words abba, aabbbbbc, abc do not belong to the language. Justify your answers.
Problem 4. Consider the following C++ program, and one of the C# or Java programs:
C++: 1
# include iostream
3 tem plate typenam e T void m ( T t) { std :: cout - m ( T=-
4 typeid (T). nam e () -)- std :: endl; }
5 void m ( int i) { std :: cout - m ( int) n-; } tem plate typenam e T void f( T t) { m ( t); }
int m ain () {
8 f(- H ello -);
9 f(123);
10 f( 4000000000 );
11 }
1 using System ;
3 class Program {
4 static void m T ( T t) { Console . W rite Line ($- m T ( T={ typeof (T)})-); }
5 static void m ( int i) { Console . W rite Line (- m ( int)-); }
6 static void f T ( T t) { m ( t); }
8 static void M ain ( string [] args) {
9 f(- H ello -);
10 f(123);
11 f( 4000000000 );
12 }
13 }
Java: 1
public class Main {
2 static T void m ( T t) { System . out. println (- m ( 3 T)-); } static void m ( int i) { System . out. println (- m 4 ( int)-); } static T void f( T t) { m ( t); }
5 public static void m ain ( String [] args)
{ f(- H ello -);
f( 123);
8 f( 4000000000 L);
9 }
10 }
For the chosen pair of the C++ and C# programs, or the C++ and Java programs, answer the following:
1. What output will be printed by the C++ program, and what output by the second language in the pair?
2. Explain why the C++ program behavior is different (in terms of methods called) from that of the C# or Java one. Why do different methods get called?
3. In C++, C#, or Java, write a generic function that takes 3 arguments of any suitable type T and returns their maximum value.
Problem 5. Consider a transaction schedule S = R1(A), W2(B), R3(C), R3(B), W1(C), W3(B), COMMIT3, ABORT2, COMMIT1.
The notation uses Ri(X) and Wi(X), respectively, for reading from and writing to the variable X in the i-th transaction. COMMITi and ABORTi denote successful and unsuccessful end of i-th transaction,
If operations from individual transactions are written separately while maintaining their ordering, the schedule can be presented as follows:
(running top to bottom) T1 T2 T3
1 R1(A)
2 W2(B)
3 R3(C)
4 R3(B)
5 W1(C)
6 W3(B)
7 COMMIT3
8 ABORT2
9 COMMIT1
1. Find all conflicting pairs of operations in the schedule S.
2. Is the schedule S conflict-serializable? Justify your answer.
3. Is the schedule S recoverable? Justify your answer.
If the schedule S lacks a particular property, correct it so that it satisfies the property without changing the order of the read and write operations.
If the schedule cannot be fixed, describe why not.
TM_simple: A Simple to Use Tyre Model
MATLAB Version 4.0
Mar 16, 2007, W. Hirschberg
General Procedure
TM_simple is a very simple tyre model to compute the longitudinal and lateral tyre forces Fx, Fy for a given nominal load Fz and the rolling resistance torque TyR under steady state conditions. The
road is defined to be even, camber influence is neglected. However, the nominal road-tyre friction ? is able to be scaled in a realistic manner.
The horizontal forces Y which are acting on the tyre at the wheel bottom point W are calculated by
Y ? K sin[B (1? e A ) sign X ] ,
where X is the relating slip quantity. The coefficients K, B and A are given by
K ? Ymax , B ?? ? Y? , A ? 1 K B (Y? ?Ymax ) , arcsin
Ymax dY0
where Ymax is the peak value, Y? the saturation value and dY0 the initial stiffness for a constant tyre load Fz , cf. fig. 1.
Fig. 1: Force/slip relation for fixed load Fz nom
In order to consider the degressive influence of the load Fz, the polynomials
2 Ymax ( Fz ) ? a1 Fz ? a2 ????Fz? ,?
Fz nom ? Fz nom ?
? ?
dY0 (Fz ) ? b1 Fz? ? b2 ????Fz ?2 (3)
Fz nom ? Fz nom ?
? ?
Fz ? c2 ????Fz ?? 2
Y? (Fz ) ? c1
Fz nom ?? Fz nom ??
are used. For given values of Y1 for Fz nom and Y2 for 2*Fz nom , the coefficients a1 and a2 can be easily determined by
a1 ? 2 Y1 ?1 Y2 and a2 ? 1 ? . (4)
2 2Y 2 Y1
In the same manner, the coefficients b1 and b2, are calculated from given initial stiffness values dY1 for Fz nom and dY2 for 2*Fz nom and c1 and c2 from given saturation values Y?1 for Fz nom and Y?
2 for 2*Fz nom respectively. Hence, the degressive influence of the tyre load Fz is taken into account, cf. fig. 2.
Fig. 2: Force/slip relations for 3 values of load Fz
The TM_simple Parameters
The following set of 18 parameters has to be provided for TM_simple:
% Tyre type: Radial 205/60 R15
t_par.fz_nom = 3000; % Nominal tyre load [N]
t_par.rs_nom = 0.290; % Static tyre radius at fz_nom [m]
t_par.reff = 0.300; % Effective tyre radius at fz_nom [m]
t_par.fxmx_fzn = 3000; % Fx_max at Fz_nom [N]
t_par.fxin_fzn = 2700; % Fx_inf at Fz_nom [N]
t_par.dfx0_fzn = 650; % dFx/dsl at Fz_nom [N/deg]
t_par.fxmx_2fzn = 5600; % Fx_max at 2*Fz_nom [N]
t_par.fxin_2fzn = 5000; % Fx_inf at 2*Fz_nom [N]
t_par.dfx0_2fzn = 1300; % dFx/dal at 2*Fz_nom [N/deg]
t_par.fymx_fzn = 2800; % Fy_max at Fz_nom [N]
t_par.fyin_fzn = 2700; % Fy_inf at Fz_nom [N]
t_par.dfy0_fzn = 600; % dFy/dal at Fz_nom [N/deg]
t_par.fymx_2fzn = 5200; % Fy_max at 2*Fz_nom [N]
t_par.fyin_2fzn = 5000; % Fy_inf at 2*Fz_nom [N]
t_par.dfy0_2fzn = 1200; % dFy/dal at 2*Fz_nom [N/deg]
t_par.rr = 0.012; t_par.mu = 1; % Rolling resistance coefficient [-]
% Nominal road/tyre friction coeff [-]
Combined Tyre Forces
For the computation of the combined tyre forces, the following combination method is applied, which is based on the similarity of longitudinal and lateral slip. In order to perform physical similar
slip quantities, here the slip angle ? is transformed to a lateral slip sly such that an equivalent initial stiffness is reached.
Fig. 3: Transformation of the lateral slip
The transformation of the slip angle to lateral slip is done by
sl :? (5) y G ( Fz )
under usage of the weighting function bx
G (F ) ? . (6)
z by
Thus, the components of the slip vector s are defined, which is orientated in the direction to ?
s : ? sl x ?
? ?? sl ?y ? . (7)
Fig. 4: Interpolation of the combined tyre forces
Under the condition that the resulting horizontal force is acting in opposite direction of the slip vector, the following superposition can be applied. In particular, the magnitude of the resulting
force vector F = |F| can be received from the interpolation, c.f. fig. 4, where Fx’ and Fy’ denote the related base values for the longitudinal and lateral force:
F ?
2 ?Fx? ? Fy? ? ? ? Fy ? ?cos 2 ? ? . (8)
Finally, the resulting 2x1-vector of the horizontal tyre forces reads
y ?sin ? ?
?? ? ?
?? FFx ?? ?cos ? ? .
Use Cases
For testing a set of TM_simple input parameters, the MATLAB utility program TM_simple_test.m can be used. For predefined ranges of slip, slip angle and tyre load, the graphics output of the resulting
force characteristics is available. The function Veloc.m belongs to that program.
For the application of TM_simple_x for pure longitudinal motion, the simplified version TM_simple_x_test.m can be used.
Application of TM_simple (2D):
Call of the MATLAB interface X_tyre to TM_simple
[frc, trq] = X_tyre (idtyre, vx, vy, om, t_par, fz)
In this way, the variables vx, vy, om, fz can be passed over directly to TM_simple. X_tyre is then calling TM_simple.
On input: idtyre . . . Tyre instance counter (not yet active) vx . . . Longitudinal tyre velocity [m/s] vy . . . Lateral tyre velocity [m/s] om . . . Rotational wheel speed [rad/s] fz . . . Tyre load
On output:
frc . . . 3-1 vector of tyre forces Fx , Fy , Fz trq . . . 3-1 vector of tyre moments Mx , My , Mz , where the moment My contains the rolling resistance torque.
Application of TM_simple_x (1D):
For the computation of the pure longitudinal tyre force Fx und moment My , the more efficient model version TM_simple_x can be used.
Call of the MATLAB interface X_tyre_x to TM_simple_x
[fx, my] = X_tyre_x (idtyre, vx, om, t_par, fz)
The arguments of that function are listed above.
On output: fx . . . Longitudinal tyre force my . . . Tyre moment around spin axis
Parametrization of truck tire model.
Fz,nom=35.000N (nominal vertical force)
?LKW=0,8 (tire road friction coefficient )
Fy,max at 12% tire slip angle (maximum lateral force)
Fx,max at 15% longitudinal slip (maximum longitudinal force)
Fx,8 at 80% of Fx,max (maximum sliding lateral force)
Fy,8 bei 100% von Fx,max (maximum sliding longitudinal force)
Please program a simple tire model using the TM_Simple modelling approach. You can program it in Excel or Matlab. Please print the longitudinal and lateral force characteristic as a function of
longitudinal and lateral tire slip (tire slip angle).
Part 1: Derive the equations for a two-mass oscillator.
Derive the equations analogue to part 1.
Vehicle parameter (ficticous)
mK=1.000kg cK=20.000N/m dK=2.000 Ns/m
mA=20.000kg cA=50.000N/m dA=3.000 Ns/m
mR=100kg cR=500.000N/m dR=0 Ns/m
1.) State space equation
2.) Systemmatrix A
Additional point: 3.) Eigenfrequency of cabin, vehicle chassis and wheel
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