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Anthony Aguirre is looking for postdoc at Santa Cruz in Physics of the Observer

Anthony Aguirre points out that UC Santa Cruz is advertising for postdocs in the "Physics of the Observer" program; and although review of applications began in December with a Dec. 15 deadline "for earliest consideration", if you apply fast you will still be considered.  He explicitly states they are looking for strong applicants from the quantum foundations community, among other things.

My take on this: The interaction of quantum and spacetime/gravitational physics is an area of great interest these days, and people doing rigorous work in quantum foundations, quantum information, general probabilistic theories have much to contribute.  It's natural to think about links with cosmology in this context.  I think this is a great opportunity, foundations postdocs and students, and Anthony and Max are good people to be connected with, very proactive in seeking out sources of funding for cutting-edge research and very supportive of interdisciplinary interaction.  The California coast around Santa Cruz is beautiful, SC is a nice funky town on the ocean, and you're within striking distance of the academic and venture capital powerhouses of the Bay Area.  So do it!

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Martin Idel: the fixed-point sets of positive trace-preserving maps on quantum systems are Jordan algebras!

Kasia Macieszczak is visiting the ITP at Leibniz Universität Hannover (where I arrived last month, and where I'll be based for the next 7 months or so), and gave a talk on metastable manifolds of states in open quantum systems.  She told me about a remarkable result in the Master's thesis of Martin Idel at Munich: the fixed point set of any trace-preserving, positive (not necessarily completely positive) map on the space of Hermitian operators of a finite-dimensional quantum system, is a Euclidean Jordan algebra.  It's not necessarily a Jordan subalgebra of the usual Jordan algebra associated with the quantum system (whose Jordan product is the antisymmetrized matrix multiplication, $A \bullet B = (AB +BA)/2$).  We use the usual characterization of the projector $T_\infty$ onto the fixed-point space of a linear map $T$$T_\infty = \lim_{N \rightarrow \infty} \frac{1}{N} \sum_{n=1}^N T^n$.  The maximum-rank fixed point is $T_\infty(I)$ (where $I$ is the identity matrix), which we'll call $F$, and the Jordan product on the fixed-point space is the original one "twisted" to have $F$ as its unit:  for $A,B$ fixed-points, this Jordan product, which I'll denote by $\bullet_\infty$, is:

which we could also write in terms of the original Jordan product as $A \bullet_\infty B = \phi(A) \bullet \phi(B)$, where $\phi$ is the map defined by $\phi(X) := F^{-1/2} X F^{-1/2}$.

Idel's result, Theorem 6.1 in his thesis, is stated in terms of the map on all $d \times d$ complex matrices, not just the  Hermitian ones; the fixed-point space is then the complexification of the Euclidean Jordan algebra.  In the case of completely positive maps, this complexification is "roughly a $C^*$ algebra" according to Idel.  (I suspect, but don't recall offhand, that it is a direct sum of full matrix $C^*$ algebras, i.e. isomorphic to a quantum system composed of several "superselection sectors" (the full matrix algebras in the sum), but as in the Euclidean case, not necessarily a $C^*$-subalgebra of the ambient matrix algebra.)

I find this a remarkable result because I'm interested in places where Euclidean Jordan algebras appear in nature, or in mathematics.  One reason for this is that the finite-dimensional ones are in one-to-one correspondence with homogeneous, self-dual cones; perhaps I'll discuss this beautiful fact another time.  Alex Wilce, Phillip Gaebeler and I related the property of homogeneity to "steering" (which Schrödinger considered a fundamental weirdness of the newly developed quantum theory) in this paper.  I don't think I've blogged about this before, but Matthew Graydon, Alex Wilce, and I have developed ways of constructing composite systems of the general probabilistic systems based on reversible Jordan algebras, along with some results that I interpret as no-go theorems for such composites when one of the factors is not universally reversible.  The composites are still based on Jordan algebras, but are necessarily (if we wish them to still be Jordan-algebraic) not locally tomographic unless both systems are quantum.  Perhaps I'll post more on this later, too.  For now I just wanted to describe this cool result of Martin Idel's that I'm happy to have learned about today from Kasia.

ITFP, Perimeter: selective guide to talks. #1: Brukner on quantum theory with indefinite causal order

Excellent conference the week before last at Perimeter Institute: Information Theoretic Foundations for Physics.  The talks are online; herewith a selection of some of my favorites, heavily biased towards ideas new and particularly interesting to me (so some excellent ones that might be of more interest to you may be left off the list!).  Some of what would have been possibly of most interest and most novel to me happened on Weds., when the topic was spacetime physics and information, and I had to skip the day to work on a grant proposal.  I'll have to watch those online sometime.  This was going to be one post with thumbnail sketches/reviews of each talk, but as usual I can't help running on, so it may be one post per talk.

All talks available here, so you can pick and choose. Here's #1 (order is roughly temporal, not any kind of ranking...):

Caslav Brukner kicked off with some interesting work on physical theories in with indefinite causal structure.  Normally in formulating theories in an "operational" setting (in which we care primarily about the probabilities of physical processes that occur as part of a complete compatible set of possible processes) we assume a definite causal (partial) ordering, so that one process may happen "before" or "after" another, or "neither before nor after".  The formulation is "operational" in that an experimenter or other agent may decide upon, or at least influence, which set of processes, out of possible compatible sets, the actual process will be drawn, and then nature decides (but with certain probabilities for each possible process, that form part of our theory), which one actually happens.  So for instance, the experimenter decides to perform a Stern-Gerlach experiment with a particular orientation X of the magnets; then the possible processes are, roughly, "the atom was deflected in the X direction by an angle theta," for various angles theta.  Choose a different orientation, Y, for your apparatus, you choose a different set of possible compatible processes.  ("The atom was deflected in the Y direction by an angle theta.")  Then we assume that if one set of compatible processes happens after another, an agent's choice of which complete set of processes is realized later, can't influence the probabilities of processes occuring in an earlier set.  "No signalling from the future", I like to call this; in formalized operational theories it is sometimes called the "Pavia causality axiom".   Signaling from the past to the future is fine, of course.  If two complete  sets of processes are incomparable with respect to causal order ("spacelike-separated"), the no-signalling constraint operates both ways:  neither Alice's choice of which compatible set is realized, nor Bob's, can influence the probabilities of processes occuring at the other agent's site.   (If it could, that would allow nearly-instantaneous signaling between spatially separated sites---a highly implausible phenomenon only possible in preposterous theories such as the Bohmian version of quantum theory with "quantum disequilibrium", and Newtonian gravity. ) Anyway, Brukner looks at theories that are close to quantum, but in which this assumption doesn't necessarily apply: the probabilities exhibit "indeterminate causal structure".  Since the theories are close to quantum, they can be interpreted as allowing "superpositions of different causal structures", which is just the sort of thing you might think you'd run into in, say, theories combining features of quantum physics with features of general relativistic spacetime physics.  As Caslav points out, since in general relativity the causal structure is influenced by the distribution of mass and energy, you might hope to realize such indefinite causal structure by creating a quantum superposition of states in which a mass is in one place, versus being in another.  (There are people who think that at some point---some combinations of spatial scales (separation of the areas in which the mass is located) and mass scales (amount of mass to be separated in "coherent" superposition)) the possibility of such superpositions breaks down.  Experimentalists at Vienna (where Caslav---a theorist, but one who likes to work with experimenters to suggest experiments---is on the faculty) have created what are probably the most significant such superpositions.)

Situations with a superposition of causal orders seem to be exhibit some computational advantages over standard causally-ordered quantum computation, like being able to tell in fewer queries (one?) whether a pair of unitaries commutes or anticommutes.  Not sure whose result that was (Giulio Chiribella and others?), but Caslav presents some more recent results on query complexity in this model, extending the initial results.  I am generally wary about results on computation in theories with causal anomalies.  The stuff on query complexity with closed timelike curves, e.g. by Dave Bacon and by  Scott Aaronson and John Watrous has seemed uncompelling---not the correctness of the mathematical results, but rather the physical relevance of the definition of computation---to me for reasons similar to those given by Bennett, Leung, Smith and Smolin.  But I tend to suspect that Caslav and the others who have done these query results, use a more physically compelling framework because they are well versed in the convex operational or "general probabilistic theories" framework which aims to make the probabilistic behavior of processes consistent under convex combination ("mixture", i.e. roughly speaking letting somebody flip coins to decide which input to present your device with).  Inconsistency with respect to such mixing is part of the Bennett/Leung/Smolin/Smith objection to the CTC complexity classes as originally defined.

[Update:  This article at Physics.org quotes an interview with Scott Aaronson responding to the Bennett et. al. objections.  Reasonably enough, he doesn't think the question of what a physically relevant definition of CTC computing is has been settled.  When I try to think about this issue sometimes I wonder if the thorny philosophical question of whether we court inconsistency by trying to combine intervention ("free choice of inputs") in a physical theory is rearing its head.  As often with posts here, I'm reminding myself to revisit the issue at some point... and think harder.]

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How does one prove that domains of positivity of symmetric nondegenerate bilinear forms are self-dual cones?

On mathoverflow, I've asked how one proves that domains of positivity of symmetric nondegenerate bilinear forms on real vector spaces are self-dual cones.  A bilinear form on a real vector space $X$ is just a map $B: X \times X \rightarrow \mathbb{R}$ that is linear in each argument.  (In other words, if you fix $y$, the function $B(x,y)$ that takes $x$ to $B(x,y)$ is linear, and similarly if you fix the other argument.)  It's called nondegenerate if the only $x \in X$ such that $B(x,y)=0$ for all $y$, is $x=0$.  And, of course, it's symmetric if for all $x,y$, $B(x,y)=B(y,x)$.

A closed domain of positivity of such a form is a maximal set $Y$ such that $B(Y,Y) \ge 0$.  Maximal means maximal in the ordering of sets by containment, i.e. $Y$ is not contained in any other set $Z$ satisfying $B(Z,Z) \ge 0$.  This notion was introduced, or at least used, by Max Koecher in the late 1950s, in work that led to the celebrated result, published in 1958 in "The Geodesics of Domains of Positivity"  (well, actually, "Die Geodatische von Positivitatsbereichen" (Mathematische Annalen 135 (1958), pp. 192--202)), that homogeneous self-dual cones in finite dimension are precisely the cones of squares in finite-dimensional formally real (aka Euclidean) Jordan algebras.  Indeed, probably the very interpretation of the main result of that paper as concerning homogeneous self-dual cones relies on the identification of domains of positivity with self-dual cones that I'm looking for a proof of.

If the form were positive semidefinite, i.e. $B(x,x) \ge 0$ for all $x$ (which implies symmetry) then a domain of positivity for would clearly  be a self-dual cone.  This is practically the definition of a self-dual cone.  The dual of a cone in a real inner product space is the set of all vectors $y$ whose inner product with everything in the cone is nonnegative---and the definition of an inner product on a real vector space is that it's a nondegenerate positive semidefinite bilinear form.  A self-dual cone is one that's equal to its dual cone.

For our definition of domain of positivity, the form was required only to be symmetric, not necessarily also positive semidefinite.  Nevertheless, according to things I've read, its domains of positivity are self-dual cones.   These domains are not necessarily unique, of course, although they are maximal, i.e. no one of them contains another).  Although I have a vague recollection of having seen a proof that they are self-dual, I haven't been able to find the paper or come up with a proof.

It's easy to prove that such a domain is a pointed, convex, closed cone.  A natural way to prove that it is a self-dual cone would be to exhibit a positive semidefinite form $B'$, depending on $B$ and possibly also on $Y$, such that $Y$ is a domain of positivity of $B'$.   An idea for how to do this involves the fact that such a form can be diagonalized: we can find a basis $x_i$ for the vector space such that the matrix with elements $M_{ij} := B(x_i, x_j)$ is diagonal, with diagonal elements $\epsilon_i \pm 1$.  The number of $-$ signs on the diagonal is the signature of the form.  A natural candidate for $B'$ is the Euclidean inner product $\langle u, v \rangle := \sum_i u_i \cdot v_i$ in the basis $x_i$ (i.e $u_i, v_i$ are the components of $u, v$ in this basis).  That is, we just change the $-1$'s to $+1$'s in the diagonal form of $B$.

Nondegenerate symmetric bilinear forms are interesting for a variety of reasons.  One of them is that they are closely related to the metric structure on a pseudo-Riemannian manifold.  Something like the following is true: you specify such a form at each point of the manifold, in such a way that the forms at the various points are nicely related to each other, and you've specified the geometric structure of a pseudo-Riemannian manifold.  (One restriction here, I believe, is that the signature of the forms has to be the same everywhere; the forms also need to vary somewhat smoothly, in a manner I should look up and summarize, but not now.)  For example, in the general relativistic description of spacetime, the spacetime manifold has signature $-1, 1, 1, 1$.  Or $1, -1, -1, -1$; people use different conventions.  I'm attracted to $1, -1, -1, -1$, because the odd-one-out corresponds in relativity theory to time, and this way, the forward and backward light cones are the (only!) domains of positivity for the form.  I.e. the form is $B(v, v') = tt'- (xx' + yy' + zz')$; we have $B(v, v) = t^2 - (x^2 + y^2 + z^2)$ (here $v = (t, x, y, z)$, etc...).  Interestingly, with the other choice of signature, the domains of positivity consist of spacelike vectors, and there is a continuum of them.  To get a picture of what's going on, consider one time and two space dimensions, with signature $1, -1, -1$.  You can visualize this in $\mathbb{R}^3$, with the vertical $t$ axis as time (associated with the $-1$ diagonal element of the form) and the horizontal $xy$ planes for constant time $t$ as a spacelike plane.  If you rotate the 45 degree line between $t$ and say the $x$ axis, around the $t$ axis, you get the boundary of a double cone, the forward and backward light cones.  But similar cones pointing along any ray in the $xy$ plane are clearly domains of positivity for the form.  I suspect lots of other cones---basically, any self-dual cone you can fit into the "conic doughnut" that is the closed complement of the double light-cone, i.e. into the spacelike (and null) vectors, are also domains of positivity for this form.

My main reason for interest in the problem isn't pseudo-Riemannian geometry, however.  More on the main reason later.  (It has to do with the Koecher result cited above).

If you found this problem first on mathoverflow, and you have the answer, please post your answer there, and link to it here if you feel like it; if you encountered it first here, please post the answer here indicating you encountered the problem here, and it would be nice if you'd also post it on mathoverflow indicating you found it on my blog.  We can have a little race between we happy few who read this blog, and the overflowing mathematicians.  I know who I'm betting on---your mission, readers, should you choose to accept it, and should any of you actually exist, is to prove me wrong!

(Thanks to Will Jagy, of MSRI, for noticing that I defined nondegeneracy wrong here at first: as requiring that the only $x$ for which $B(x,x)=0$ is $x=0$. This wrong definition, corrected above, of course says that the form has no nontrivial "isotropic" or "null" vectors (ones for which $B(x,x)=0$). And we certainly don't want to assume that! Sorry about the slip-up, which I dont think affected anything else in the post.)

Gross, Mueller, Colbeck, and Dahlsten: "All reversible dynamics in maximally non-local theories are trivial"

David Gross, Markus Mueller, Roger Colbeck, and Oscar Dahlsten have considered the "maximal non-signaling tensor product" of "boxlets", and shown that the reversible dynamics of this state space consists just of permutations of the systems (the boxlets) followed by reversible local transformations (i.e., ones on the individual boxlets).

What the heck does that mean, you ask?  Well, "boxlets" were introduced in several contexts.  In the "operational quantum logic" literature they're sometimes called "semiclassical test spaces".  In quantum foundations and informations, they were introduced as a generalization of a notion of Popescu and Rohrlich, who introduced the two-measurement, two-outcome-per-measurement boxlet in order to describe correlations between measurement results on distinct systems that can be stronger than quantum correlations, but still don't allow someone ("Alice") in possession of one of the systems to signal to the other ("Bob") just by making measurements on her system.

A "boxlet" is a system on which there are M distinct alternative measurements one can make, each with K outcomes.  (More complex versions allow different measurements to have different numbers of outcomes.)  The allowable states of a boxlet are given by specifying M probability distributions, each one over K alternatives:  for each measurement, the probabilities of each of its K outcomes.  All possible lists of M such distributions are allowed; this is a convex, compact subset of an MK dimensional vector space (one dimension for each probability).  The M normalization constraints mean that this set lies in an MK-M (i.e., M(K-1)) dimensional affine subspace  (higher dimensional generalization of the line, plane, etc... of high-school geometry).  The possible states of a pair of such systems are given by the "maximal tensor product" of a pair of these compact convex state spaces.  The technical definition of maximal tensor product of state spaces can be found here.  Another way of defining this is that it's the state space of the  Foulis-Randall tensor product  of the "test spaces" (definitions reviewed in Sections II and IV of this paper) describing each of the boxlets.  A test space is just a collection of subsets of some set; the elements of the set interpreted as measurement outcomes, and the subsets, called "tests", as measurements.  The semiclassical test space of a boxlet like the ones I described above just consists of a set of MK elements, partitioned into M sets of K elements.  A state on a (finite, like the ones in question) test space is a function from the set to the real numbers between zero and 1, i.e. to probabilities, such that for each test, the probabilities of the elements of the test add up to one.  The Foulis-Randall tensor product of two test spaces just takes their Cartesian product, and allows any probability assignments such that the "marginal states" obtained by fixing a measurement on one side and marginalizing all the joint distributions of this fixed measurement with measurements on the other side, is independent of which measurement is marginalized over.  That is, Alice can't signal to Bob (by affecting the probabilities of the outcomes of one or more of his measurements) just by her choice of measurement.

Now, a transformation of the state space is an affine map from the state space to itself (i.e. one that preserves convex combination, which seems only reasonable), and a reversible one is one that has an inverse that is also an affine map of the state space.  So what GMCD are saying is that, if you combine boxlets this way, there are no very interesting reversible dynamics:  just combinations of local reversible dynamics on the individual boxlets, and permuting the boxes amongst themselves.

An interesting question is, can one extend this result to maximal tensor products of *arbitrary* systems with convex state space (locally equipped, let's say, with the maximal set of possible effects)?

See the comments on the Information Causality thread at Dave Bacon's blog for a bit more discussion (and related interesting matters).


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# How do we know which chemical comes after mixing 3 or more chemical, on paper work like balance equation, example : H2 + NaCl + So4 ~ ? What is the product how we can know

So to your question; you mixed dihydrogen gas, sodium chloride, and sulfate dianion (i.e. $S {O}_{4}^{2 -}$). This does not correspond to any chemical reaction I know. I think you have made a mistake transcribing the question.

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# Estimate Category-Specific PK Parameters for Multiple Individuals

This example shows how to estimate category-specific (such as young versus old, male versus female), individual-specific, and population-wide parameters using PK profile data from multiple individuals.

### Background

Suppose you have drug plasma concentration data from 30 individuals and want to estimate pharmacokinetic parameters, namely the volumes of central and peripheral compartment, the clearance, and intercompartmental clearance. Assume the drug concentration versus the time profile follows the biexponential decline ${C}_{t}=A{e}^{-at}+B{e}^{-bt}$, where ${C}_{t}$ is the drug concentration at time t, and $a$ and $b$ are slopes for corresponding exponential declines.

This synthetic data contains the time course of plasma concentrations of 30 individuals after a bolus dose (100 mg) measured at different times for both central and peripheral compartments. It also contains categorical variables, namely `Sex` and `Age`.

```clear load('sd5_302RAgeSex.mat')```

### Convert to groupedData Format

Convert the data set to a `groupedData` object, which is the required data format for the fitting function `sbiofit`. A `groupedData` object also allows you set independent variable and group variable names (if they exist). Set the units of the `ID`, `Time`, `CentralConc`, `PeripheralConc`, `Age`, and `Sex` variables. The units are optional and only required for the `UnitConversion` feature, which automatically converts matching physical quantities to one consistent unit system.

```gData = groupedData(data); gData.Properties.VariableUnits = {'','hour','milligram/liter','milligram/liter','',''}; gData.Properties```
```ans = struct with fields: Description: '' UserData: [] DimensionNames: {'Row' 'Variables'} VariableNames: {1x6 cell} VariableDescriptions: {} VariableUnits: {1x6 cell} VariableContinuity: [] RowNames: {} CustomProperties: [1x1 matlab.tabular.CustomProperties] GroupVariableName: 'ID' IndependentVariableName: 'Time' ```

The `IndependentVariableName` and `GroupVariableName` properties have been automatically set to the `Time` and `ID` variables of the data.

### Visualize Data

Display the response data for each individual.

```t = sbiotrellis(gData,'ID','Time',{'CentralConc','PeripheralConc'},... 'Marker','+','LineStyle','none'); % Resize the figure. t.hFig.Position(:) = [100 100 1280 800];```

### Set Up a Two-Compartment Model

Use the built-in PK library to construct a two-compartment model with infusion dosing and first-order elimination where the elimination rate depends on the clearance and volume of the central compartment. Use the `configset` object to turn on unit conversion.

```pkmd = PKModelDesign; pkc1 = addCompartment(pkmd,'Central'); pkc1.DosingType = 'Bolus'; pkc1.EliminationType = 'linear-clearance'; pkc1.HasResponseVariable = true; pkc2 = addCompartment(pkmd,'Peripheral'); model = construct(pkmd); configset = getconfigset(model); configset.CompileOptions.UnitConversion = true;```

For details on creating compartmental PK models using the SimBiology® built-in library, see Create Pharmacokinetic Models.

### Define Dosing

Assume every individual receives a bolus dose of 100 mg at time = 0. For details on setting up different dosing strategies, see Doses in SimBiology Models.

```dose = sbiodose('dose','TargetName','Drug_Central'); dose.StartTime = 0; dose.Amount = 100; dose.AmountUnits = 'milligram'; dose.TimeUnits = 'hour';```

### Map the Response Data to Corresponding Model Components

The data contains measured plasma concentration in the central and peripheral compartments. Map these variables to the appropriate model components, which are `Drug_Central` and `Drug_Peripheral`.

`responseMap = {'Drug_Central = CentralConc','Drug_Peripheral = PeripheralConc'};`

### Specify Parameters to Estimate

Specify the volumes of central and peripheral compartments `Central` and `Peripheral`, intercompartmental clearance `Q12`, and clearance `Cl_Central` as parameters to estimate. The `estimatedInfo` object lets you optionally specify parameter transforms, initial values, and parameter bounds. Since both `Central` and `Peripheral` are constrained to be positive, specify a log-transform for each parameter.

```paramsToEstimate = {'log(Central)', 'log(Peripheral)', 'Q12', 'Cl_Central'}; estimatedParam = estimatedInfo(paramsToEstimate,'InitialValue',[1 1 1 1]);```

### Estimate Individual-Specific Parameters

Estimate one set of parameters for each individual by setting the `'Pooled'` name-value pair argument to `false`.

`unpooledFit = sbiofit(model,gData,responseMap,estimatedParam,dose,'Pooled',false);`

### Display Results

Plot the fitted results versus the original data for each individual (group).

`plot(unpooledFit);`

For an unpooled fit, `sbiofit` always returns one results object for each individual.

### Examine Parameter Estimates for Category Dependencies

Explore the unpooled estimates to see if there is any category-specific parameters, that is, if some parameters are related to one or more categories. If there are any category dependencies, it might be possible to reduce the number of degrees of freedom by estimating just category-specific values for those parameters.

First extract the ID and category values for each ID

`catParamValues = unique(gData(:,{'ID','Sex','Age'}));`

Add variables to the table containing each parameter's estimate.

```allParamValues = vertcat(unpooledFit.ParameterEstimates); catParamValues.Central = allParamValues.Estimate(strcmp(allParamValues.Name, 'Central')); catParamValues.Peripheral = allParamValues.Estimate(strcmp(allParamValues.Name, 'Peripheral')); catParamValues.Q12 = allParamValues.Estimate(strcmp(allParamValues.Name, 'Q12')); catParamValues.Cl_Central = allParamValues.Estimate(strcmp(allParamValues.Name, 'Cl_Central'));```

Plot estimates of each parameter for each category. `gscatter` requires Statistics and Machine Learning Toolbox™. If you do not have it, use other alternative plotting functions such as `plot`.

```h = figure; ylabels = ["Central","Peripheral","Q12","Cl\_Central"]; plotNumber = 1; for i = 1:4 thisParam = estimatedParam(i).Name; % Plot for Sex category subplot(4,2,plotNumber); plotNumber = plotNumber + 1; gscatter(double(catParamValues.Sex), catParamValues.(thisParam), catParamValues.Sex); ax = gca; ax.XTick = []; ylabel(ylabels(i)); legend('Location','bestoutside') % Plot for Age category subplot(4,2,plotNumber); plotNumber = plotNumber + 1; gscatter(double(catParamValues.Age), catParamValues.(thisParam), catParamValues.Age); ax = gca; ax.XTick = []; ylabel(ylabels(i)); legend('Location','bestoutside') end % Resize the figure. h.Position(:) = [100 100 1280 800];```

Based on the plot, it seems that young individuals tend to have higher volumes of central and peripheral compartments (`Central`, `Peripheral`) than old individuals (that is, the volumes seem to be age-specific). In addition, males tend to have lower clearance rates (`Cl_Central`) than females but the opposite for the Q12 parameter (that is, the clearance and Q12 seem to be sex-specific).

### Estimate Category-Specific Parameters

Use the `'CategoryVariableName'` property of the `estimatedInfo` object to specify which category to use during fitting. Use `'Sex'` as the group to fit for the clearance `Cl_Central` and `Q12` parameters. Use `'Age'` as the group to fit for the `Central` and `Peripheral` parameters.

```estimatedParam(1).CategoryVariableName = 'Age'; estimatedParam(2).CategoryVariableName = 'Age'; estimatedParam(3).CategoryVariableName = 'Sex'; estimatedParam(4).CategoryVariableName = 'Sex'; categoryFit = sbiofit(model,gData,responseMap,estimatedParam,dose)```
```categoryFit = OptimResults with properties: ExitFlag: 3 Output: [1x1 struct] GroupName: [] Beta: [8x5 table] ParameterEstimates: [120x6 table] J: [240x8x2 double] COVB: [8x8 double] CovarianceMatrix: [8x8 double] R: [240x2 double] MSE: 0.4362 SSE: 205.8690 Weights: [] LogLikelihood: -477.9195 AIC: 971.8390 BIC: 1.0052e+03 DFE: 472 DependentFiles: {1x3 cell} EstimatedParameterNames: {'Central' 'Peripheral' 'Q12' 'Cl_Central'} ErrorModelInfo: [1x3 table] EstimationFunction: 'lsqnonlin' ```

When fitting by category (or group), `sbiofit` always returns one results object, not one for each category level. This is because both male and female individuals are considered to be part of the same optimization using the same error model and error parameters, similarly for the young and old individuals.

### Plot Results

Plot the category-specific estimated results.

`plot(categoryFit);`

For the `Cl_Central` and `Q12` parameters, all males had the same estimates, and similarly for the females. For the `Central` and `Peripheral` parameters, all young individuals had the same estimates, and similarly for the old individuals.

### Estimate Population-Wide Parameters

To better compare the results, fit the model to all of the data pooled together, that is, estimate one set of parameters for all individuals by setting the `'Pooled'` name-value pair argument to `true`. The warning message tells you that this option will ignore any category-specific information (if they exist).

`pooledFit = sbiofit(model,gData,responseMap,estimatedParam,dose,'Pooled',true);`
```Warning: CategoryVariableName property of the estimatedInfo object is ignored when using the 'Pooled' option. ```

### Plot Results

Plot the fitted results versus the original data. Although a separate plot was generated for each individual, the data was fitted using the same set of parameters (that is, all individuals had the same fitted line).

`plot(pooledFit);`

### Compare Residuals

Compare residuals of `CentralConc` and `PeripheralConc` responses for each fit.

```t = gData.Time; allResid(:,:,1) = pooledFit.R; allResid(:,:,2) = categoryFit.R; allResid(:,:,3) = vertcat(unpooledFit.R); h = figure; responseList = {'CentralConc', 'PeripheralConc'}; for i = 1:2 subplot(2,1,i); oneResid = squeeze(allResid(:,i,:)); plot(t,oneResid,'o'); refline(0,0); % A reference line representing a zero residual title(sprintf('Residuals (%s)', responseList{i})); xlabel('Time'); ylabel('Residuals'); legend({'Pooled','Category-Specific','Unpooled'}); end % Resize the figure. h.Position(:) = [100 100 1280 800];```

As shown in the plot, the unpooled fit produced the best fit to the data as it fit the data to each individual. This was expected since it used the most number of degrees of freedom. The category-fit reduced the number of degrees of freedom by fitting the data to two categories (sex and age). As a result, the residuals were larger than the unpooled fit, but still smaller than the population-fit, which estimated just one set of parameters for all individuals. The category-fit might be a good compromise between the unpooled and pooled fitting provided that any hierarchical model exists within your data.


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# Number of functions from finite ordered set to finite ordered set

Lets say we have $a_1<a_2<a_3<a_4<a_5\in A$ and $b_1<b_2<b3\in B$

We alse have $f:A \rightarrow B$

How many such functions $f$, so that $f(a_1)\leq f(a_2)\leq f(a_3)\leq f(a_4)\leq f(a_5)$?

Being not very combinatorial I "bruteforced" solution, wrote python/sage script, which generated functions like (tuples (A,B):

((1, 1), (2, 1), (3, 1), (4, 1), (5, 1))

...

((1, 1), (2, 2), (3, 2), (4, 2), (5, 3))

...

((1, 3), (2, 3), (3, 3), (4, 3), (5, 3))

Which yields 21 possible solutions. However for $|A|=70$ and $|B|=30$ making crossproducts like $A\times B$, and then generating all permutations of length 70 is rather silly idea.

Any tips on how to aproach this?

This is equal to the number of non-negative integers solutions to $x_1+x_2+x_3=5$. Why? a function of this type is determined uniquely by the number of elements that are sent to $b_1,b_2$ and $b_3$.
So how many solutions does that equation have in non-negative integers. This is a standard stars and bars question, the answer is $\binom{5+2}{5}$.
In general if you want monotonic functions from $\{1,2,3\dots n\}$ to $\{1,2,3\dots k\}$ there are $\binom{n+k-1}{n}$ ways to do it.


text:
# What is the name of this letter $\mathcal{J}$?

What is the name of this letter $$\mathcal{J}$$ in the following deep learning equation? And what alphabet it is from?

$$\mathcal{J} = \frac{1}{m} \sum_{i=1}^m \mathcal{L}^{(i)}$$

• I’m voting to close this question because it seems to me that it belongs to tex.stackexchange.com. Nov 5, 2021 at 1:03

## 1 Answer

It's an uppercase "J" from the math calligraphy alphabet, i.e. \mathcal{J} in latex.

$$\mathcal{J}$$


text:
Rrt Star Pseudocode

, "Probabilistic Roadmaps for Path Planning in High-Dimensional Configuration Spaces", IEEE Trans Robotics and Automation , 12-4, 1996, pp. A* Pathfinding Project. so very thus rrt is a little 12 foot foundation and as a consequence beds down Corey my eldest, along with the two littlest girls. RRT* algorithm is guaranteed to converge to an optimal solution, while its running time is guaranteed to be a constant factor of the running time of the RRT. Engaged Employer. new file: FNSimple3D. It seems safe to say that D* is outdated in a sense that D* Lite is always as fast as D*. pdf), Text File (. vxworks Subject: Re: QED RM7000 PROM Monitor Source Package Date: Fri, 28 Jan 2000 08. (green star: start state, red circle: goal region). dm ~p The value of m does not change much with pressure, so m, = mp. 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Longest Simple Path Algorithm. Entries for PRM, SRT[RRT] and SRT[EST] show average time to build the roadmap and then solve ten random queries; average time per query is not shown separately since it is less than 0. A Survey of Monte Carlo Tree Search Methods_工学_高等教育_教育专区。. We have included pseudocode algorithms to make the key ideas concrete; our pseudocode is described in Appendix B. com> Reply-To: jeffrey. RRT* uses a tree data structure that represents poses and paths, it handles nonholonomic constraints and can hold general restrictions on p i n i t and p g o a l poses, or obstacles. Jorgensen and C. Some new procedures used in P-RRT* are presented below. Advanced Management Accounting - (3rd edition) http://www. Rapidly Exploring Random Tree Star (RRT*), a recently proposed extension of RRT, claims to achieve convergence towards the optimal solution thus ensuring asymptotic optimality along with probabilistic completeness. new file: FNSimple3D. It's really more kind of like Deep Space 9. Ok, my intro was kind of misleading, I don't really think this is the next generation. rrt_toolbox-master\doc\html\rrt_star_fn_pseudocode. You will be implementing: A-star (with weighting) and RRT for a 2D motion planning in a grid world RRT for a non-holonomic system. It has gained immense popularity due to its support for high dimensional complex problems. The exploration algorithm is first explained in Figure 5. From [email protected] 34", %%% date = "13 January 2011", %%% time = "17:34:09 MDT. Extended, steps toward node 3. Can someone please suggest a good source where I can find RRT implemented in C++ for any type of motion planning. Labette Community College 2013-2014 Page 6 History of LCC On April 4, 1923, Parsons voters approved a two-year Junior College by a 4 to 1 margin. 34", %%% date = "13 January 2011", %%% time = "17:34:09 MDT. Cheap Wholesale NHL Jerseys. Mueller 11 Iros - Free download as PDF File (. 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Entries for RRT and EST show average time per query. Trapped, cant make it 2. DISA AT Mock Test Papers 6 The correct answer is: D. Too generic. • As trees grow, the eventually share a common node, and are merged into a path. I want to implement RRT for motion planning of a robotic arm. pdf код для вставки. (Full Books. lu55084：大神问一下：这些变体的源代码可以找到吗 机器人导航dwa（局部避障）分析. RRT* uses a tree data structure that represents poses and paths, it handles nonholonomic constraints and can hold general restrictions on p init and p goal poses. [Statistics and Computing] James E. exploring random tree star (RRT?) algorithm, which is able to handle cost functions and constraints, and is thus extended here to a multi-agent setting. benchmark fence1 fence2 fence4 random4 narrow4h2 narrow6 narrow8 pentomino PRM 5638. For additional information, please contact Disabled Students Program and Services at (510) 659-6079. Estimation, Optimization, and Parallelism when Data is Sparse or Highly Varying - Google Revenir à l'accueil. html modified: doc/html/rrt. Robot 3D (three-dimension) path planning targets for finding an optimal and collision-free path in a 3D workspace while taking into account kinematic constraints (including geometric, physical, and temporal constraints). 3752] name = trartiellurok mail = [email protected] Ohlone College provides Alternate Media services to qualified students who need materials in alternative format, such as Braille, large print, audiotape, or electronic text. We propose a fast algorithm of low-power image reformation for organic light-emitting diode (OLED) display. Ref: Incremental Sampling-based Algorithms for Optimal Motion Planning. Rapidly Exploring Random Tree Star (RRT*), a recently proposed extension of RRT, claims to achieve convergence towards the. [email protected] The following animation shows how the algorithm evolves to construct a tree in a two-dimensional configuration space containing obstacles. Open Booch06a Grady Booch Goodness of fit IEEE Computer Magazine V39n10(Oct 2006)pp14-15 =ESSAY ARCHITECTURE STYLE PATTERNS FORTRAN COMPILER Bachus's original pipe-and-filter. # # Note 1: use the eev command (defined in eev. There are a number of algorithms available for the above purpose, but the most widely used is the back-propagation algorithm (Masters 1990), the pseudocode of which is listed below: w Initialize the weights and offsets. Cope -- Rotating spiral waves in the Belousov-Zhabotinskii reaction / Stefan C. cluttered environments and a high number of collision checks. RRT algorithm in C++. Enroll in Penetration Testing with Kali Linux and pass the exam to become an Offensive Security Certified Professional (OSCP). html modified: doc/html/rrt. When using a γ -space description of a system,. Investigating reports of violation of policy, procedure or state or federal law, 5. • According to the problem structure, we propose a sequential solving approach. The tree is constructed incrementally from samples drawn randomly from the search space and is inherently biased to grow towards large unsearched areas of the problem. png rrt_toolbox-master\doc\html\schema. Thus, a computer program is an embodiment of an algorithm; strictly speaking, an algorithm is a mental concept that exists independently of any representation. BDEEB91A-- ----- Newsgroups: comp. Cope -- Rotating spiral waves in the Belousov-Zhabotinskii reaction / Stefan C. As the A∗ planner takes into account the terrain semantic labels, the robot avoids areas which are potentially risky and chooses paths crossing mostly the preferred terrain types. png rrt_toolbox-master\doc\html\schema. For my final project I developed an adaptive version of the RRT that I named ARRT. txt) or read online for free. Python 3+ NumPy; Rtree; Plotly (only needed for plotting) Usage. Title: Santa Fe College's 2010-2011 College Catalog, Author: Santa Fe College, Name: Santa Fe College's 2010-2011 College Catalog, Length: 164 pages, Page: 1, Published: 2017-05-18 Issuu company. star trek deep space nine toys playmates popeye plush toys toys online construction games with backhoe27s vinatge toys godzilla shooting arm nostalgic toys where are. Ok, my intro was kind of misleading, I don't really think this is the next generation. There exist numerous path planning algorithms that address the navigation problem. consider the question. january 2006 product 1 image compression chip backs first jpeg2000 hd camcorder product 2 new mobile phone hits a high note product 3 virtual platforms speed time-to-market for ti customers product 4 avivo brings your computer display to life product 5 arbitrary waveform generators target pci platform product 6 chip boosts capabilities of midrange ip phones product 7 low-cost solution targets. 3) Intuitive approach of trial and. MULTIDRONE - MULTIpleDRONE platform for media production Project start date: 01. 1202 00:51:59,180 --> 00:52:03,030 It's pseudocode so don't copy paste, but it's almost there. 16 without any obstacles or boundary obstructions. • In e-commerce, it is common to cluster users into groups, based on their purchasing or web-surﬁng behavior, and then to send customized targeted advertising to each group. In a 2D space, you could probably get away with something much simpler to begin with like Breadth-first search, Dijkstra's or A-Star. m modified: doc/html/funclist. Fast algorithm of low power image reformation for OLED display. Most Rated Senior Online Dating Service Without Pay. january 2006 product 1 image compression chip backs first jpeg2000 hd camcorder product 2 new mobile phone hits a high note product 3 virtual platforms speed time-to-market for ti customers product 4 avivo brings your computer display to life product 5 arbitrary waveform generators target pci platform product 6 chip boosts capabilities of midrange ip phones product 7 low-cost solution targets. Jorgensen and C. Below is my Dijkstra Algorithm implementation in C# code. void TDSmokeSolver::applyDrivingForce ( ) { // Fu -> horizontal component of the force // D_rts -> derivative of ro tick star. Among them Rapidly Exploring Random Tree (RRT) is one of the quickest and the most efficient obstacle free path finding algorithm. Policy-value duality. 1 vector 61 Harada, 1 Amongst 1 ddr 1 emulating 1 40. Complying with subpoenas and Open Records Law requests for. Boeing B787. com/Advanced-Management-Accounting-MEI-LAN/dp/7565402222/ref=sr_1_1?s=books&ie=UTF8&qid=1460711444&sr. Collection of rrt-based algorithms that scale to n-dimensions: rrt; rrt* (rrt-star) rrt* (bidirectional) rrt* (bidriectional, lazy shortening) rrt connect; Utilizes R-trees to improve performance by avoiding point-wise collision-checking and distance-checking. 48s EST X X X X X X X 47. Fundamentals of Computer GraphicsThird Edition. Collection of rrt-based algorithms that scale to n-dimensions: rrt; rrt* (rrt-star) rrt* (bidirectional) rrt* (bidriectional, lazy shortening) rrt connect; Utilizes R-trees to improve performance by avoiding point-wise collision-checking and distance-checking. 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Karaman and Frazzoli [30] solved nonoptimal results problem of RRT by introducing RRG and a heuristic method R R T ∗. pdf), Text File (. 1 The asterisk *, pronounced "star", is intended to represent asymptotic optimality much like for the RRT* and PRM* algorithms. The robot is…. Gentle - Random Number Generation and Monte Carlo Methods (2003 Springer). In this paper, we present a technique that combines motion planning and part interaction clusters to improve generation of assembly precedence constraints. Single women what short term car insurance offer: free mot at any time. RRT's work well and I've used them in the past, but for much higher dimensional search spaces. Entries for RRT and EST show average time per query. It was produced automatically %% with the UNIX pipeline. RRT-connect: an efficient approach to single-query path planning. More like the weird points kind of after Deep Space 9, I don't know, it was in one of those bad Star Trek movies I haven't seen. el) and the # ee alias (in my. I tried researching here, and on the internet in general, but since pseudocode writing is rather diverse and many use different signs for different things, I couldn't find anything that might fit my question. The XAPK (APK with OBB data & Multiple APKs) file you downloaded on APKPure only works on APKPure App for Android, never miss any apps update news from today. After the story went out, we conducted a detailed analysis of the samples we had obtained, with some interesting findings. dm ~p The value of m does not change much with pressure, so m, = mp. Weisbin" , title = "Computational geometry approach to autonomous robot navigati. It is clear from the Fig. In ICRA'2000, 2000. Correction: At 8min 38secs 'D' should, of course, be 14 not. XAPK is another package file format used on the Android operating system to install mobile applications and middleware. As the A∗ planner takes into account the terrain semantic labels, the robot avoids areas which are potentially risky and chooses paths crossing mostly the preferred terrain types. Some new procedures used in P-RRT* are presented below. Title: Santa Fe College's 2010-2011 College Catalog, Author: Santa Fe College, Name: Santa Fe College's 2010-2011 College Catalog, Length: 164 pages, Page: 1, Published: 2017-05-18 Issuu company. 1988) discovered a new type of star, based on clustering astrophysical measurements. A rapidly exploring random tree (RRT) is an algorithm designed to efficiently search nonconvex, high-dimensional spaces by randomly building a space-filling tree. A rookie jersey card from a new basketball or football star can easily fetch 1 or 2 grand on eBay; all for a piece of cardboard with a 1 x 1 inch piece of cloth! 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RRT* uses a tree data structure that represents poses and paths, it handles nonholonomic constraints and can hold general restrictions on p init and p goal poses. RRT by introducing RR G and a heuristic method RRT ∗. png rrt_toolbox-master\doc\html\schema. We have tried to avoid excessive formality in the presentation of these ideas while retaining precision. Most Rated Senior Online Dating Service Without Pay. 2 Telecommunications, 2 dev 1 411 2. Entries for PRM, SRT[RRT] and SRT[EST] show average time to build the roadmap and then solve ten random queries; average time per query is not shown separately since it is less than 0. Fundamentals of Computer Graphics Third Edition Fundamentals of Computer Graphics Third Edition. Song From A Secret Garden Stave Preview 1 Piano. Random Tree (RRT) is one of the quickest and the most efficient obstacle free path finding algorithm. , Business and Computer Science Experience startMYplan. RRT* uses a tree data structure that represents poses and paths, it handles nonholonomic constraints and can hold general restrictions on p i n i t and p g o a l poses, or obstacles. Lectures by Walter Lewin. Maryland Parkvay La Plaza, Bldg. Process Plant Simulation Babu. Starek , Javier V. A* Pathfinding Project. 20s X X X RRT 7209. Trapped, cant make it 2. Lightning fast pathfinding for Unity3D. The robot is…. Applied Linear Statistical Models Kutner Neter. The optimal policy $\pi^\star(s)$ is simply given by replacing the $\max$ with an $\arg \max$: $$\pi^\star(s) = \arg \max_{a\in A} \sum_{s^\prime \in S} T(s,a,s^\prime) (R(s,a,s^\prime) + V(s^\prime)). The proposed rapidly-exploring adaptive sampling tree star (RAST. 2 Telecommunications, 2 dev 1 411 2. In this paper, we present a frontier-based modiﬁcation A pseudocode description of the SRT algorithm. 4(d), with an equal number of iterations. 1 third-generation 1 40M 1 Review: 5 advantageously 1 length(); 1 Modulation 1 recent 26 leveraging 1 repeaters) 2 photo 1 LKI 1 del 2 Telecommunications) 2 microelectromechanical 8 41. It's really more kind of like Deep Space 9. 2) State changes are stored in stack, meaning we do not need to concern ourselves about them. Given R1 , R2 SO(3), it readily follows that their product R1 R2 satisfies (R1 R2 )T (R1 R2 ) = I and det R1 R2 = det R1 det R2 = 1. Pseudocode is badly converted from Python, i. In my daily work [Coding Interview Bootcamp], we come across a lot of neat CS algorithms. The RRT procedure proceeds by constructing a special kind of graph called a tree, where every node is connected to a single parent and the tree is rooted at a given starting location. Production library listings Explanation: The best source from which to draw any sample or test of system information is the automated system. 4(d) that RRT*-Smart uses the RRT* path with a cost of 630. [email protected] Need Any Test Bank or Solutions Manual Please contact me email:[email protected] All the Time. XAPK is another package file format used on the Android operating system to install mobile applications and middleware. Documentation updated. The basic tool therein is the Sensor-based Random Tree (SRT), a compact data structure representing a roadmap of the explored area, which can be seen as a sensor-based version. RC-RRT solution: Choose a maximum number of times, m, you are willing to try to expand each node For each node in the tree, keep track of its Constraint Violation Frequency (CVF). 1204 00:52:05,670 --> 00:52:07,382 You're going to add your start goal. 2OPP -- - p, P P P P. When using a γ -space description of a system,. Process Plant Simulation Babu. A good place to answer this question, would be to see an article that Mathematician Barry Arthur Cipra wrote a few years ago, based on survey of several prac. We consider a problem in which we are given a domain, a cost function which depends on position at each point in the domain, and a subset of points ("cities") in the domain. It is clear from the Fig. [SmithCUWilliamsLG93 ]. png rrt_toolbox-master\doc\html\rrt_star_pseudocode_1. Video created by Université Northwestern for the course "Modern Robotics, Course 4: Robot Motion Planning and Control". The connection is usually made along the shortest possible path. The optimal policy \pi^\star(s) is simply given by replacing the \max with an \arg \max:$$\pi^\star(s) = \arg \max_{a\in A} \sum_{s^\prime \in S} T(s,a,s^\prime) (R(s,a,s^\prime) + V(s^\prime)). RRT* uses a tree data structure that represents poses and paths, it handles nonholonomic constraints and can hold general restrictions on p init and p goal poses. & future analysis for 2010. html modified: doc/html/redundant_rrt_example. : The Casual Guide to Confident Drinking by - Marissa A. With heavily optimized algorithms and a large feature set but yet simple to use, you will be able to make those bots a bit smarter in no time. ca/pub/geometry/geombib. A good place to answer this question, would be to see an article that Mathematician Barry Arthur Cipra wrote a few years ago, based on survey of several prac. 34", %%% date = "13 January 2011", %%% time = "17:34:09 MDT. Fundamentals of Computer Graphics Third Edition Fundamentals of Computer Graphics Third Edition. MECHANICS, PLANNING, AND CONTROL. Algorithm 8 shows the pseudocode for the PQ-RRT* algorithm. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. @techreport{rijw-cgaar-85 , author = "N. Boeing B787. In my last post, we built on kinematics by introducing Jacobians for robotic manipulators. 1202 00:51:59,180 --> 00:52:03,030 It's pseudocode so don't copy paste, but it's almost there. MODERN ROBOTICS. Video created by Université Northwestern for the course "Modern Robotics, Course 4: Robot Motion Planning and Control". More like the weird points kind of after Deep Space 9, I don't know, it was in one of those bad Star Trek movies I haven't seen. There are a number of algorithms available for the above purpose, but the most widely used is the back-propagation algorithm (Masters 1990), the pseudocode of which is listed below: w Initialize the weights and offsets. The purpose of this page is provide an overview of an implementation of a sampling based path planning algorithm using rapidly exploring random trees (RRT). Robot 3D (three-dimension) path planning targets for finding an optimal and collision-free path in a 3D workspace while taking into account kinematic constraints (including geometric, physical, and temporal constraints). Pseudocode is badly converted from Python, i. init(qinit); for k = 1 to K do qrand = RANDOM_CONFIG(); EXTEND(T, qrand)} EXTEND(T, qrand) qnear qnew qinit qrand STEP_LENGTH: How far to sample 1. An Asymptotically-Optimal Sampling-Based Algorithm for Bi-directional Motion Planning Joseph A. Motion planning on a discretized C-space grid, randomized sampling-based planners, virtual potential fields, and nonlinear. Recommended for you. =NEWS TCAS RISKS BUGS DEFECTS Pseudocode TECHNICAL CODE AIRCRAFT Mitre. ,///10000 @asg,t temp. are maze environments for Quick-RRT*. One major practical drawback is its () space complexity, as it stores all generated nodes in memory. > NextPart_001_01BF693C. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. & future analysis for 2010. EDU Mon Aug 13 14:11:25 1990 Return-Path: Received: from miro. 128 bits for AES-256). 1988) discovered a new type of star, based on clustering astrophysical measurements. 4(d), with an equal number of iterations. 1150, September 20-25, 1999 : 8. However, the convergence rate of RRT ∗ as well as B-RRT >∗ and IB-RRT∗ is slow for these algorithms. The following animation shows how the algorithm evolves to construct a tree in a two-dimensional configuration space containing obstacles. RRT-star cannot be applied to arbitrary robot dynamics, however. Full text of "Analog Computing Magazine Issue 45 (Language Issue)" See other formats. txt) or read book online for free. This book is primarily intended for use in an undergraduate course or course sequence. Most Rated Senior Online Dating Service Without Pay. @cat,p 1027-002-005. Describe in clear English or pseudocode a decision procedure to answer the question, "Given a Jist of integers Nand an individual integer"· is there any element of N that is a factor of n?" 2. modern robotics. qq_43362405：博主，我最近在写一个关于DWA的局部路径规划代码，自己按照网上的原理和伪代码写的。结果是出现了两个问题，一个是对于一个已知的地图（DWA的应用的范围）来说，10x10大小的，可以完成. Weisbin" , title = "Computational geometry approach to autonomous robot navigati. After the story went out, we conducted a detailed analysis of the samples we had obtained, with some interesting findings. I want to implement RRT for motion planning of a robotic arm. txt) or read book online for free. This banner text can have markup. For more information, please call the chapter advisor at 217/353-2131. 00s X X 14809. In ICRA'2000, 2000. Ohlone College provides Alternate Media services to qualified students who need materials in alternative format, such as Braille, large print, audiotape, or electronic text. 16 on RRT/RDT in Steven LaValle's book "Planning Algorithms". txt) or read online for free. The book will be published by Cambridge University Press in May 2017, ISBN. Davis alleged he was told to change findings to exonerate officers in at least three investigations, Financially it costs insurers 392m a year that impacts on motorists as it’s an extra 50 to 100 on every person’s premium so that’s a financial cost. You will be implementing: A-star (with weighting) and RRT for a 2D motion planning in a grid world RRT for a non-holonomic system. Full text of "Analog Computing Magazine Issue 45 (Language Issue)" See other formats. A Survey of Monte Carlo Tree Search Methods_工学_高等教育_教育专区。. 2) id AA06897; Mon, 13 Aug 90 14:05:43. For additional information, please contact Disabled Students Program and Services at (510) 659-6079. Machine learning. Lynch and Frank C. WHILE (userGuess < 1 OR userGuess > 10) PRINT “That is not between 1 and 10. All the Time. The pseudocode even names variables and describes mathematical operations. whereas in the. This paper proposes RRT*-Quick as an improved version of Rapidly-exploring Random Tree Star (RRT*). ----- EPA 600/8-90/048 April 1990 GEO-EAS (GEOSTATISTICAL ENVIRONMENTAL ASSESSMENT SOFTWARE) PROGRAMMER'S GUIDE Prepared for Exposure Assessment Research Division U. Not even that really. From [email protected] Full text of "Analog Computing Magazine Issue 45 (Language Issue)" See other formats. Labette Community College 2016-2017 Page 10 offered for credit. 20s X X X RRT 7209. 1027-002-005,,,130252053241,000 )@@[email protected]@**pf**@@@#;[email protected]@@@@[@'[email protected]@@][email protected]@@@@aa )@@[email protected]@@@@[email protected]@])@@@]f^^[email protected]@@@p. m renamed: doc/funclist. RxJS, ggplot2, Python Data Persistence, Caffe2, PyBrain, Python Data Access, H2O, Colab, Theano, Flutter, KNime, Mean. A* Pathfinding Project. Add your initial location (configuration) to the search tree. It's really more kind of like Deep Space 9. Refer to paper: Jose Luis Blanco, Mauro Bellone and Antonio Gimenez-Fernandez. Pseudo code. • The first and second phases calculate the fleet size and daily routes. Process Plant Simulation Babu. Trapped, cant make it 2. No jewels in this Patek Philippe. Sample just at end point 2. txt) or read book online for free. The structure of the tree is determined by the requirement that it. We have tried to avoid excessive formality in the presentation of these ideas while retaining precision. Gomezy, Edward Schmerlingz, Lucas Jansonx, Luis Morenoy, Marco Pavone Abstract—Bi-directional search is a widely used strategy to increase the success and convergence rates of sampling-based motion planning algorithms. 16 without any obstacles or boundary obstructions. The equation of state for an ideal gas is p = rRT. Cheap Wholesale NHL Jerseys. whereas in the. 12]: { size = (random_between (1,. txt) or read online for free. MODERN ROBOTICS. BDEEB91A-- ----- Newsgroups: comp. Use of 'temp' in pseudocode. San Francisco Bay Area Environmental Health and Safety Manager at Trans Bay Cable LLC Utilities Education University of Phoenix 2013 — 2014 Education, Training Experience Trans Bay Cable LLC February 2015 - Present k2 Pure Solutions July 2012 - January 2015 Flextronics June 2010 - November 2011 The Clorox Company April 1994 - June 2010 Skills Continuous Improvement, Manufacturing. %%====================================================================== %% WARNING: Do NOT edit this file. Readbag users suggest that lbi_catalog_2010_web. Bianca spans hundreds of kilometers, and the storm's eye appears west-southwest of Learmonth. Christina Nguyen is on Facebook. el) and the # ee alias (in my. Cope -- Rotating spiral waves in the Belousov-Zhabotinskii reaction / Stefan C. Lynch and Frank C. In SRT-Star the perception technique is more conﬁdent, and the Local Safe Region is a star-shaped set. Upload Computers & electronics; Software; Hi Quality Version Available on AMIGALAND. Extended, steps toward node 3. Some new procedures used in P-RRT* are presented below. InternationalJournalofAdvancedRoboticSystemsRRT*-SMART:ARapidConvergenceImplementationofRRT. • As trees grow, the eventually share a common node, and are merged into a path. 4(d) that RRT*-Smart uses the RRT* path with a cost of 630. Whether you write a TD, RTS, FPS or RPG game, this package is for you. Collection of rrt-based algorithms that scale to n-dimensions: rrt; rrt* (rrt-star) rrt* (bidirectional) rrt* (bidriectional, lazy shortening) rrt connect; Utilizes R-trees to improve performance by avoiding point-wise collision-checking and distance-checking. Small Step Extend returns 1. For additional information, please contact Disabled Students Program and Services at (510) 659-6079. 150 208 363 980 982 1020 31337 1001-nacht 100-prozent. Gæsterne som var inviteret med til lejligheden var Prins Frederik og Prinsesse Mary, og begrundelsen var de skulle briefes om aktiviteterne i By Havn. Lowe, Object Recognition from Local Scale-Invariant Features, Proceedings of the International Conference on Computer Vision-Volume 2, p. Starek , Javier V. Rapidly Exploring Random Tree Star (RRT*), a recently proposed extension of RRT,. See All Photos See All Photos. essentially just removing ":", or keeping things like range(), or using a lot of Python specific idioms which are not common to other languages. Python 3+ · NumPy · Rtree · Plotly (only Dijkstra algorithm¶. > NextPart_001_01BF693C. Fabrication includes the intentional falsification or invention of any information. % % Computational geometry community bibliography project % ftp://ftp. For iterations, a tree is iteratively grown by connecting to its nearest point in the swath,. RRT* uses a tree data structure that represents poses and paths, it handles nonholonomic constraints and can hold general restrictions on p init and p goal poses. Cheap Wholesale NHL Jerseys. m modified: doc/funclist. Collusion includes any secret agreement among students who participate in any academically dishonest activity. RRT* algorithm is guaranteed to converge to an optimal solution, while its running time is guaranteed to be a constant factor of the running time of the RRT. Improving on Dijkstra, A* takes into account the direction of your goal. In addition, D* is complex, hard to understand, analyze and extend. 1204 00:52:05,670 --> 00:52:07,382 You're going to add your start goal. This paper proposes RRT*-Quick as an improved version of Rapidly-exploring Random Tree Star (RRT*). Readbag users suggest that lbi_catalog_2010_web. com SWIFT code : ABBLBDDH. The path planning algorithm was implemented on the OMAPL138/F28335 based robots built by the U of I Control Systems Laboratory for use in GE423 - Mechatronics and research projects. Full text of "Analog Computing Magazine Issue 45 (Language Issue)" See other formats. Rapidly-exploring Random Tree (RRT) for car planning. As the A∗ planner takes into account the terrain semantic labels, the robot avoids areas which are potentially risky and chooses paths crossing mostly the preferred terrain types. ca November 2006 - Present Dominion Lending Centres Mortgage Village 2011 - August 2013 The Coyaba Group Ltd. This research presents a novel sample-based path planning algorithm for adaptive sampling. @techreport{rijw-cgaar-85 , author = "N. txt) or read book online for free. Financial Services Education University of Maryland Eastern Shore 1999 — 2002 B. 4(d), with an equal number of iterations. Any forgery, alteration, or misuse of academic documents, forms or records. Estimation, Optimization, and Parallelism when Data is Sparse or Highly Varying - Google Revenir à l'accueil. It allows to go quickly deeper to a given di-rection. Although it ensures probabilistic completeness, it cannot guarantee finding the most optimal path. Yet, few results are available that. [Statistics and Computing] James E. sensor-based version of the RRT proposed in [8]. Algorithm 8 shows the pseudocode for the PQ-RRT* algorithm. Horton Editor-in-Chief: Michael Hirsch Executive Editor: Tracy Dunkelberger Assistant Editor: Melinda Haggerty Editorial Assistant: Allison Michael Vice President, Production: Vince O'Brien Senior Managing Editor: Scott Disanno Production Editor: lane Bonnell Senior Operations Supervisor: Alan 1-ischer Operations Specialist: Lisa McDowell. A Linear Algebra Since modelling and control of robot manipulators requires an extensive use of matrices and vectors as well as of matrix and vector operations, the goal of this a. Park May 3, 2017. Fundamentals of Computer Graphics Third Edition Fundamentals of Computer Graphics Third Edition. Documentation updated. Phone : +880-2-9560312 Fax : +880-2-9564122 Email : [email protected] Breadth First Search #. 1 Examples of Algorithm 1. They will make you ♥ Physics. For iterations, a tree is iteratively grown by connecting to its nearest point in the swath,. html new file: doc/html/getting_started. 150 208 363 980 982 1020 31337 1001-nacht 100-prozent. From useful Roombas to the rise of autonomous cars, mobile robots are becoming more and more popular…. modern robotics. are maze environments for Quick-RRT*. cn ]>>> CLICK. CSE 571 - Homework 3: Motion Planning Due by: Wednesday, Dec 16, 2015 (11:59 PM) Summary: The key goal of this project is to get an understanding of motion planning methods including A-star, Weighted A-star and RRTs. com/Advanced-Management-Accounting-MEI-LAN/dp/7565402222/ref=sr_1_1?s=books&ie=UTF8&qid=1460711444&sr. init(qinit) for k = 1 to K qrand ← RAND_CONF() qnear ← NEAREST_VERTEX(qrand, G) qnew ← NEW_CONF(qnear, qrand, Δq) G. We can see basic RRT* pseudocode (lines 4 to 19) as part of complete RRT*-based. Ok, my intro was kind of misleading, I don't really think this is the next generation. Policy-value duality. This banner text can have markup. Modern Robotics Mechanics, Planning, and Control c Kevin M. The book will be published by Cambridge University Press in May 2017, ISBN. Rapidly Exploring Random Tree Star made it possible to reach an optimal solution but to do so, it has been proven to take an infinite time (Karaman, 2011). Perl - Free ebook download as PDF File (. Gomezy, Edward Schmerlingz, Lucas Jansonx, Luis Morenoy, Marco Pavone Abstract—Bi-directional search is a widely used strategy to increase the success and convergence rates of sampling-based motion planning algorithms. Machine Learning A Probabilistic Perspective Kevin P. Labette Community College 2016-2017 Page 10 offered for credit. Exercise 2. I tried researching here, and on the internet in general, but since pseudocode writing is rather diverse and many use different signs for different things, I couldn't find anything that might fit my question. The product of two rotation matrices is a rotation matrix. > NextPart_001_01BF693C. The picture below shows various symbols and the activity they represent. Become a Certified Penetration Tester. Reached, connects to node STEP_SIZE 1. png rrt_toolbox-master\doc\html\schema. I'll start with the simplest, Breadth First Search, and add one feature at a time to turn it into A*. Park May 3, 2017. Problem "puma-bars" consists of a 6R articulated limb (robot) similar to a Puma560 surrounded by several vertical bars (obstacles), as shown in Fig. Machine learning. Boeing B787. Rapidly Exploring Random Tree Star (RRT*), a recently proposed extension of RRT, claims to achieve convergence towards the optimal solution thus ensuring asymptotic optimality along with probabilistic completeness. maybe tinkering with a toy vehicle might be affected by him within a battery,doing it this way, it may possibly shape housewives also. Motion planning on a discretized C-space grid, randomized sampling-based planners, virtual potential fields, and nonlinear. m modified: doc/funclist. Multi-directional RRT ! Issue: nearest points chosen for expansion are (too) often the ones stuck behind an obstacle Resolution-Complete RRT (RC-RRT) RC-RRT solution: ! Choose a maximum number of times, m, you are willing to try to expand each node ! For each node in the tree, keep track of its Constraint Violation Frequency (CVF) !. I decided to post it here to share with others. edu Pseudocode dist [s] 0(distance to source vertex is zero) for all v V {s} do dist [v]8(set all other distances to infinity) S (S, the set of visited vertices is initially empty) Q V(Q, the queue initially contains all vertices) while Q (while the queue is not empty) do u. Join Facebook to connect with Christina Nguyen and others you may know. consider the question. Fundamentals of Computer Graphics Third Edition Fundamentals of Computer Graphics Third Edition. Environment 2d-1 is shown in Fig. 2 shows the performance of the three algorithms in environment 2d-1. Preventing unauthorized access and system misuse, 3. Scribd es el sitio social de lectura y editoriales más grande del mundo. CSE 571 - Homework 3: Motion Planning Due by: Wednesday, Dec 16, 2015 (11:59 PM) Summary: The key goal of this project is to get an understanding of motion planning methods including A-star, Weighted A-star and RRTs. Calculate gross pay. [ SmaragdakisBatory02 ] =CASESTUDY large scale Object-Oriented refinement mixin collaboration Java CLOS C++ JTS Jakarta Bali DDD DSL DOMAIN ARCHITECTURE GenVoca ASPECTs. RRT* with reeds-shepp path). Beebe", %%% version = "2. [SmithCUWilliamsLG93 ]. vxworks Subject: Re: QED RM7000 PROM Monitor Source Package Date: Fri, 28 Jan 2000 08:42:32 -0500 From: Jeff Daly Organization: Sanders A Lockheed Martin Company Message-ID: 38919CC7. 2 Some Flowchart Examples 1. Parkland College Alumni Association The Parkland College Alumni Association was established in 1984 to promote alumni involvement with the college by keeping members informed about activities, programs, services, and the continued growth of Parkland College. % % Computational geometry community bibliography project % ftp://ftp. RRT's work well and I've used them in the past, but for much higher dimensional search spaces. Fast marching methods for the continuous traveling salesman problem. 2014-04-01. On a grid, this process is sometimes called "flood fill", but the same technique works for non-grids. 1 Advances in Information Security 66 Edward J. • The first and second phases calculate the fleet size and daily routes. @cat,p 1027-002-005. [Statistics and Computing] James E. Scribd es el sitio social de lectura y editoriales más grande del mundo. 4(a) and finds a more optimal path with a cost of 584. Combine it with an occupancy grid as a map based on LIDAR data and you'd be good to go. txt) or read book online for free. • Depot location and weekly circulations are obtained using a genetic algorithm. 12]: { size = (random_between (1,. Starek , Javier V. The robot is…. el) and the # ee alias (in my. Muller, Theo Plesser and Benno Hess -- Patterns of protein conformations / Henrik Bohr and Soren Brunak -- Blind watchmaker. Given the. Ask Question Asked 6 years, 2 months ago. star trek deep space nine toys playmates popeye plush toys toys online construction games with backhoe27s vinatge toys godzilla shooting arm nostalgic toys where are. Scribd es el sitio social de lectura y editoriales más grande del mundo. ca November 2006 - Present Dominion Lending Centres Mortgage Village 2011 - August 2013 The Coyaba Group Ltd. The ̇ ̇ control inputs are the rolling speed φ θ and the turning speed. San Francisco Bay Area Environmental Health and Safety Manager at Trans Bay Cable LLC Utilities Education University of Phoenix 2013 — 2014 Education, Training Experience Trans Bay Cable LLC February 2015 - Present k2 Pure Solutions July 2012 - January 2015 Flextronics June 2010 - November 2011 The Clorox Company April 1994 - June 2010 Skills Continuous Improvement, Manufacturing. Upload Computers & electronics; Software; On the Development of a Search-Based Trajectory. Rapidly-exploring Random Tree Star (RRT*) is a renowned sampling based planning approach. With heavily optimized algorithms and a large feature set but yet simple to use, you will be able to make those bots a bit smarter in no time. @techreport{rijw-cgaar-85 , author = "N. The file contains 220 page(s) and is free to view, download or print. RRT* uses a tree data structure that represents poses and paths, it handles nonholonomic constraints and can hold general restrictions on p init and p goal poses. benchmark fence1 fence2 fence4 random4 narrow4h2 narrow6 narrow8 pentomino PRM 5638. $\begingroup$ @Andiana: With the algorithm as written, (ctr+k) really is the value of ctr, plus the integer k, with conversion to integer and back in binary according to some specified endianness (usually big-endian), keeping as many low-order bits as there are in a block of the block cipher (e. I decided to post it here to share with others. An Asymptotically-Optimal Sampling-Based Algorithm for Bi-directional Motion Planning Joseph A. 1203 00:52:03,030 --> 00:52:05,670 You're going to construct a graph. ca/pub/geometry/geombib. All new content for 2020. 18 at the iteration number n =800 shown in Fig. RC-RRT solution: Choose a maximum number of times, m, you are willing to try to expand each node For each node in the tree, keep track of its Constraint Violation Frequency (CVF). Starek , Javier V. Colbert Alexander Kott Editors Cyber-security of SCADA and Other Industrial. Sheesh, that's how we do time. BDEEB91A-- ----- Newsgroups: comp. And all of this chronology really depends on if I'm counting Enterprise, which I liked but didn't last long. The proposed RRT*-Quick utilizes one of the characteristics of RRT* that nodes in local area tend to share common parents. ACM Communications march 2011 edition - Free download as PDF File (. Close Booch06a. 45th Anniversary Edition SF Catalog 2011-2012. \$91, 000 for a wine bill. Next > < Previous. This in turn reduces the occurrence of impotence trouble due to nervous disorders on the Jamal kissing a woman. We can see basic RRT* pseudocode (lines 4 to 19) as part of complete RRT*-based. 29s SRT[EST] 351. [SmithCUWilliamsLG93 ]. Ao Star Algorithm. txt) or read online for free. zshrc) to execute parts of this file. Once Hefty has a state, he uses his current location and state information to plan a path to his objective. 1204 00:52:05,670 --> 00:52:07,382 You're going to add your start goal. 1 vector 61 Harada, 1 Amongst 1 ddr 1 emulating 1 40. Algorithm 8 shows the pseudocode for the PQ-RRT* algorithm. The following animation shows how the algorithm evolves to construct a tree in a two-dimensional configuration space containing obstacles. 3 RRT* Rapidly-Exploring Random Tree Star (RRT*) is an asymptotically optimal randomized algorithm to solve path planning problems, such as the parking problem de-ﬁned in Section 2. The equation of state for an ideal gas is p = rRT. 1 Advances in Information Security 66 Edward J. html modified: doc/html/rrt. 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# zbMATH — the first resource for mathematics

The Drinfeld modular Jacobian $$J_1 (N)$$ has connected fibers. (English) Zbl 1165.11047
Let $$n\in A:= {\mathbb F}_q[T]$$ be a prime element. Let $$X_1(n)$$ be the smooth projective curve over $${\mathbb F}_q(T)$$ associated to the moduli problem of classifying pairs $$(\phi,P)$$, where $$\phi$$ is a rank 2 Drinfeld $$A$$-module over an $${\mathbb F}_q(T)$$-scheme and $$P$$ is a nowhere vanishing point of its $$n$$-torsion.
Let $$J_1(n)$$ be the Jacobian of $$X_1(n)$$. The main result of this paper is that the closed fibre of the Néron model of $$J_1(n)$$ over $$A_{(n)}$$ has trivial geometric component group. It follows that the Néron model of $$J_1(n)$$ over $${\mathbb P}^1_{{\mathbb F}_q} - \infty$$ has connected fibres, hence the title. (The component group of the fibre above $$\infty$$ is a much more complicated beast, but is not part of the moduli problem). This work is a function field analogue of results of B. Conrad, B. Edixhoven and W. Stein [Doc. Math., J. DMV 8, 331–408 (2003; Zbl 1101.14311)], and the proof strategy is similar, although the translation is far from trivial.
To prove the result, it suffices to show that $$X_1(n)$$ has a regular proper model over $$A_{(n)}$$ with geometrically integral special fibre. The author does this by first constructing a model with a unique non-regular point (corresponding to $$(\phi,P)$$, where $$j(\phi)=0$$ and $$P$$ is the kernel of Frobenius). This is a cyclic quotient singularity, which is resolved using the Jung-Hirzebruch resolution developed in [loc. cit.]. Contraction of the special fibre of this resolution then yields the desired integral model of $$X_1(n)$$.
A result of independent interest obtained along the way is a function field analogue of the theory of Igusa curves. The paper is rather technical, but very well written.
##### MSC:
 11F52 Modular forms associated to Drinfel’d modules 14L05 Formal groups, $$p$$-divisible groups 11G09 Drinfel’d modules; higher-dimensional motives, etc.
##### Keywords:
component groups; Drinfeld modular curves; Igusa curves
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##### References:
 [1] Altman, A.; Kleiman, S., Introduction to Grothendieck duality theory, (1970), Springer-Verlag, Berlin · Zbl 0215.37201 [2] Bosch, S.; Lütkebohmert, W.; Raynaud, M., Néron models, 21, (1990), Springer-Verlag, Berlin · Zbl 0705.14001 [3] Conrad, B.; Edixhoven, B.; Stein, W.$$, J_1(p)$$ has connected fibers, Doc. Math., 8, 331-408 (electronic), (2003) · Zbl 1101.14311 [4] Deligne, P.; Rapoport, M., Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), LES schémas de modules de courbes elliptiques, 143-316. Lecture Notes in Math., Vol. 349, (1973), Springer, Berlin · Zbl 0281.14010 [5] Drinfeld, V. G., Elliptic modules, Mat. Sb. (N.S.), 94(136), 594-627, 656, (1974) · Zbl 0321.14014 [6] Fontaine, J.-M., Groupes $$p$$-divisibles sur les corps locaux, (1977), Société Mathématique de France, Paris · Zbl 0377.14009 [7] Freitag, E.; Kiehl, R., Étale cohomology and the Weil conjecture, 13, (1988), Springer-Verlag, Berlin · Zbl 0643.14012 [8] Gekeler, E.-U., Zur arithmetik von Drinfeld-moduln, Math. Ann., 262, 2, 167-182, (1983) · Zbl 0536.14028 [9] Gekeler, E.-U., Über drinfeldsche modulkurven vom Hecke-typ, Compositio Math., 57, 2, 219-236, (1986) · Zbl 0599.14032 [10] Gekeler, E.-U.$$, p$$-adic analysis (Trento, 1989), 1454, De Rham cohomology and the Gauss-Manin connection for Drinfeld modules, 223-255, (1990), Springer, Berlin · Zbl 0735.14016 [11] Gekeler, E.-U., Séminaire de Théorie des Nombres, Paris 1988-1989, 91, De Rham cohomology for Drinfeld modules, 57-85, (1990), Birkhäuser Boston, Boston, MA · Zbl 0728.14024 [12] Gekeler, E.-U., On finite Drinfeld modules, J. Algebra, 141, 1, 187-203, (1991) · Zbl 0731.11034 [13] Goss, D.$$, π$$-adic Eisenstein series for function fields, Compositio Math., 41, 1, 3-38, (1980) · Zbl 0422.10020 [14] Grothendieck, A., Éléments de géométrie algébrique. IV. étude locale des schémas et des morphismes de schémas. II, Inst. Hautes Études Sci. Publ. Math., 24, 231 pp., (1965) · Zbl 0135.39701 [15] Grothendieck, A., Éléments de géométrie algébrique. IV. étude locale des schémas et des morphismes de schémas. III., Inst. Hautes Études Sci. Publ. Math., 28, 255 pp., (1966) · Zbl 0144.19904 [16] Grothendieck, A., Éléments de géométrie algébrique. IV. étude locale des schémas et des morphismes de schémas. IV, Inst. Hautes Études Sci. Publ. Math., 32, 361 pp., (1967) · Zbl 0153.22301 [17] Grothendieck, A., Revêtements étales et groupe fondamental, (1971), Springer-Verlag, Berlin [18] Hazewinkel, M., Formal groups and applications, 78, (1978), Academic Press Inc., New York · Zbl 0454.14020 [19] Humphreys, J. E., Introduction to Lie algebras and representation theory, 9, (1978), Springer-Verlag, New York · Zbl 0254.17004 [20] Jeon, D.; Kim, C. H., On the Drinfeld modular curves $$X_1(n),$$ J. Number Theory, 102, 2, 214-222, (2003) · Zbl 1052.11041 [21] Katz, N.; Mazur, B., Arithmetic moduli of elliptic curves, 108, (1985), Princeton University Press, Princeton, NJ · Zbl 0576.14026 [22] Laumon, G., Cohomology of Drinfeld modular varieties. Part I, 41, (1996), Cambridge University Press, Cambridge · Zbl 0837.14018 [23] Lehmkuhl, T., Compactification of the Drinfeld Modular Surfaces · Zbl 1179.11014 [24] Liu, Q., Algebraic geometry and arithmetic curves, 6, (2002), Oxford University Press, Oxford · Zbl 0996.14005 [25] Matsumura, H., Commutative ring theory, 8, (1989), Cambridge University Press, Cambridge · Zbl 0666.13002 [26] Schlessinger, M., Functors of Artin rings, Trans. Amer. Math. Soc., 130, 208-222, (1968) · Zbl 0167.49503 [27] Taguchi, Y., Semi-simplicity of the Galois representations attached to Drinfeld modules over fields of “infinite characteristics”, J. Number Theory, 44, 3, 292-314, (1993) · Zbl 0781.11024 [28] Tate, J. T., Proc. Conf. Local Fields (Driebergen, 1966)$$, p$$-divisible groups, 158-183, (1967), Springer, Berlin · Zbl 0157.27601 [29] Teitelbaum, J., Modular symbols for $$\textbf{F}_q(T),$$ Duke Math. J., 68, 2, 271-295, (1992) · Zbl 0777.11021 [30] Yasufuku, Y., Deformation Theory of Formal Modules, (2000)
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## FANDOM

2,277 Pages

 “ Welcome to the place Toons call home. Sadly, trouble is brewing in Toontown... Robot Cogs are trying to take over and put an end to all Toons' fun. ” –Toontown Download Intro

Cogs are the enemies of Disney's Toontown Online. They are evil business robots that constantly try to conquer Toontown and turn it into a dull and gray wasteland. There is a total of thirty-two different cogs, with eight in each of the four corporate ladders, as well as a boss of each ladder. Each cog has their own strengths and weaknesses and a five level range; the higher they are in the corporate ladder, the higher their level range is, as well as their health.

Cogs roam the streets, taking over toon buildings by dropping cog buildings on top of them. Cogs can also be found in their respective Cog Headquarters.

To fight the cogs, toons use gags to destroy them. Cogs cannot take a joke, as they will malfunction and explode when they laugh.

## History

thumb|right|250px|The introduction to Cogs Cogs were the invention of the old chicken inventor Gyro Gearloose. However, they were probably not yet finished at the time. One day, investor and billionaire Scrooge McDuck visited Gyro's lab, only to find out that he wasn't there. Scrooge spotted a robot contraption, and thinking about how it would help toons and, of course, how it would make him a load of money. Thinking so, he activated it. However, the robot went haywire and started a machine that created even more robots - the cogs. The robot ordered the cogs to go and take over Toontown. Scrooge was captured by the robot, and nobody knows what happened next. Toontown is now in peril.

## Other types of cogs

There are other types of cogs not located anywhere but inside cog headquarters or the cog boss battles.

### Skelecogs

Main article: Skelecogs

Skelecogs are unfinished cogs located in many places throughout cog headquarters.

• Regular skelecogs are basic skelecogs that fight similar to average cogs.
• Virtual skelecogs can only be found in the District Attorney's office. They are holograms and will appear when a toon fails a puzzle. They also don't reward with jury notices or gag experience points. They also do not count for Toontasks.
• Version 2.0 cogs can currently only be found only in Bossbot Headquarters. These cogs are much stronger than average cogs and skelecogs, as they have two shells. The first shell resembles the normal cogs. When defeated, the second shell, the skelecog, is revealed and must be defeated also.

### Goons

Main article: Goon

Goons are one-eyed, walking robots located in Sellbot Factory, the Cashbot Mints, the District Attorney's office, and the Cashbot Vault. Goons walk around as security guards, searching for toons using their searchlights. If a toon is caught in their searchlight, the toon will lose a certain number of laff points. A toon can temporarily disable a goon by jumping on its head. They can also be destroyed in the Sellbot Factory by pushing buttons that activate stomping machines, throwing them at the CFO, or in the CFO battle by dropping safes on them.

These are the only cogs that cannot be destroyed by ordinary gag means, and you cannot engage them in legitimate battle.

## In battle

Main article: Cog battle

In battle, cogs stand opposite from toons and take their turns attacking. Some cog attacks are weak and some are strong. Some target a single toon and some target all toons. The toons always take their turn first.

When cogs are damaged by gags, the light on their chest (their health meter) will change colors. Green means the cog has full health (or mostly full). Yellow indicates the cog is somewhat injured. Orange cogs have about half their health missing. Red means the cog is almost defeated, and flashing red means the cog is dead. In some cases the health meter will slowly blink red, but it won't malfunction.

When a cog loses all of its health, it will bend over, then its torso will spin around quickly, and the cog will explode.

## Levels and Health

Main article: Cog HP chart

A cog's health can be determined by using this formula:
$(x + 1)(x + 2)$

• The variable x represents the cog's level.
• This formula does not apply to level 12 cogs, whom have a health of 200, where as a level 12 cog, if it followed the formula, would have 182 health.
 Level 1 2 3 4 5 6 7 8 9 10 11 12 Health 6 12 20 30 42 56 72 90 110 132 156 200

## Cog buildings

Main article: Cog Building

Cog buildings are toon buildings that have been conquered by a cog. A cog building can be reverted back into a toon building if a toon or a group of toons successfully defeats the cogs in the building.

### Field offices

Main article: Field Office

Field offices are a very special type of cog building given to the Mover & Shaker cogs as a reward from the Vice President. They always have two levels. The first level is a maze in a messy office and the second level has powerful Sellbots.

Each cog type has a respective cog headquarters. Cog headquarters can be found at each corner of Toontown. They are the most dangerous places in the game and contain challenges and enemies that are not seen anywhere else.

## Cog invasions

Main article: Cog invasion

Cog invasions occur when a single type of cog invades every street in Toontown. During this phase, no other cog, except the invading cog, are roaming the streets and cog buildings. Field offices are not affected by cog invasions. At this time, any gag that is used and worked successfully will earn the toon double skill points.


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# Rate of change in distance question

1. Apr 29, 2008

### Dr Zoidburg

Okay, I'm 99% sure I've got the right answer here, but I just wanted to make certain before I send my assignment in. It's the last question and has been bugging me for the last few days until I had an eureka moment just a few minutes back.
(In case you're wondering, I'm doing my studies by correspondence, so other than course notes and textbooks borrowed from the library I have just the internet and my brains (hah!) to aid me)

1. The problem statement, all variables and given/known data
A baseball diamond has sides 27m long. A player is running from 2nd to 3rd at a speed of 9m/s. When he is 6m away from 3rd, at what rate is the player's distance from home plate changing at that instant?

3. The attempt at a solution
x = distance from home plate to 3rd = 27m
y = distance from player to 3rd = 6m
z = distance from player to home = 27.66m (using pythagoras)
speed of player is change of y over time: dy/dt = 9m/s

$$z^{2}$$ - $$y^{2}$$= $$x^{2}$$
differentiate with respect to time:
d/dz$$z^{2}$$ - d/dy$$y^{2}$$= 0 (since x doesn't change over time)

dz/dt*2z - dy/dt*2y = 0
divide by 2:
z*dz/dt - y*dy/dt = 0
sub the above (z, y, dy/dt) into the equation and solve:
dz/dt = 1.95m/s

If this ain't correct, please tell me quickly as I need to post my assignment off asap!

2. Apr 29, 2008

### tiny-tim

Hi Dr Zoidburg!

Yes, that's fine (but a little messy)!

Try shortening it a bit.

For example, there's no need to define an x (I know it's useful for helping you get to your eureka moment, but once you're there, you can forget it) … just say z² = y² + 729 (or z = √(y² + 729)).

And
doesn't make sense, does it?

3. Apr 29, 2008

### Dr Zoidburg

yay, got it right! Off to the post office I scurry.

And that other bit just came out poorly due to bad formating. It looks better in my assignment

4. Apr 29, 2008

### tiny-tim

I thought Dr Zoidburg scuttled ?

5. Apr 29, 2008

### Dr Zoidburg

whoops. you're right there. scuttled. whoop! whoop! whoop!

"Friends, help! A guinea pig tricked me!"

6. Apr 30, 2008

### tiny-tim

I just did a google search for "A guinea pig tricked me",

and got 5370 hits!