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CAMP/Nonlinear PDE's Seminar

Wednesdays at 3:30 PM in Eckhart 202.

Fall 2006 Schedule

September 20,
Francois Hamel, Universite Aix-Marseille III
Generalized bistable fronts passing an obstacle

In this talk, I will present the notions of generalized travelling fronts and some of their properties. Then I will explain the construction of generalized bistable reaction-diffusion fronts passing an obstacle. These fronts are almost-planar but because of the presence of the obstacle, they cannot be covered by the usual notions of fronts. Actually, the construction is possible when the obstacle is star-shaped. We will see that this condition plays a role in the determination of the large-time behavior of the solutions. It is related to a Liouville type result for the associated stationary problem. This talk is based on joint works with H. Berestycki, and H. Berestycki and H. Matano

September 27,
Gregory Lawler University of Chicago
Laplacian random motion

The Laplacian random walk with exponent b is the discrete process that grows at the tip with probabilities weighted by harmonic measure to the b power. The special case b=1 is also called the loop-erased random walk. We discuss possible continuum limits for this process in two dimensions. We show that, under the (unproved) assumption of a conformally invariant continuum limit, the limit must a Schramm-Loewner evolution (SLE). We also determine the parameter of the SLE as a function of b. In the case b=1, the existence of such a conformally invariant limit was proved a few years ago my Schramm, Werner, and me. Previous knowledge of SLE will not be assumed.

September 28, 3pm in E206
Boris Gershgorin RPI
The effects of Discretness and Resonances in beta-FPU chains

We study the statistical behavior of the 1D nonlinear \beta-FPU chain. When the nonlinearity is weak the thermal equilibrium state of the system can be described as weakly interacting linear waves, and the wave action n_k is proportional to 1/w_k with w_k - linear dispersion (Rayleigh-Jeans distribution). We demonstrate numerically that surprisingly even in the strongly nonlinear limit the system still can be effectively described like weakly interacting waves and hence the same distribution holds. This arises because strong nonlinearity effectively renormalizes the linear dispersion frequency. We find the theoretical prediction for the frequency renormalizing factor and show that it is in good agreement with numerical experiments. Moreover the presence of nonlinearity widens the resonance peaks which results in the occurrence of near-resonance wave-wave interactions. Such near-resonant interactions allow the application of the well developed Wave Turbulence formalism. We also employ Random Phase Approximation and use the Wiener-Khinchin formula and the perturbation methods to derive the form of the resonance width as a function of the wave number and the nonlinearity strength. The resulting analytical prediction for the resonance width is in good agreement with numerical experiments. Finally we numerically observed that in the thermodynamical equilibrium \beta-FPU exhibits spatially localized oscillations - Discrete Breathers.

October 4,
Laurent Demanet, Stanford University
Fast Computation of Fourier Integral Operators

Fourier integral operators are oscillatory integrals related to linear wave propagation. They are a central object in most imaging problems involving waves, like seismic or ultrasound imaging; and also in some tomography problems, like electron microscopy. In most cases, the quality of imaging hinges on the practicality of applying these oscillatory integrals on a large computational scale. In this talk, I will present a fast algorithm for the computation of large classes of Fourier integral operators. The algorithm is based on factorization and separation of the oscillatory kernel over adequate angular neighborhoods in the frequency variable, and inspired by modern constructions in applied harmonic analysis. We prove that the complexity of computing and applying a Fourier integral operator on an N-by-N grid, is O(N^{2.5} log N) in time, and as low as O(sqrt N) in storage. The constants in front of these estimates are small and depend weakly on the desired accuracy. We illustrate the properties and potential of the algorithm with several numerical examples.

October 11,
Xavier Cabre, Universitat Politecnica de Catalunya
A priori bounds for stable solutions of nonlinear elliptic equations in low dimensions

Abstract: We consider the class of semi-stable solutions of semilinear equations $-\Delta u=f(u)$ in a bounded smooth domain of $\R^n$ (sometimes convex). This class includes all local minimizers, minimal, and extremal solutions. In dimensions $n\le 4$, we establish a priori $L^\infty$ bounds which hold for every semi-stable solution and every nonlinearity $f$. This extends previous work of G.~Nedev for dimensions $n\le 3$. In relation with these results, A.~Capella and the author have studied the particular case of radial solutions, for which boundedness holds up to dimension $n\le 9$ for every~$f$. Some quasilinear analogues have also been established, both in the radial and nonradial cases, by A. ~Capella, M.~Sanch\'on, and the author.

October 18,
Scott Sheffield, New York University
Random geometry and SLE

We introduce and construct the "AC geometry" from the Gaussian free field and use it to prove various facts about Schramm-Loewner evolutions. (See this for a graphical description of what an AC geometry is.)

November 1,
Peter Constantin, University of Chicago
Transport and Dissipation: Statistical Solutions, Stochastic Representation

I will describe two results. The first one is about the absence of anomalous dissipation in damped, driven 2D NSE equations. The other is about decay of generalized relative entropies in Fokker-Planck equations. The title of the talk refers to the tools used to prove the two results. The first result is based on joint work with Fabio Ramos, the second on work with Gautam Iyer.

November 8,
Joseph Biello, University of California, Davis
PDE's and Waves for the tropical atmosphere: The Madden-Julian Oscillation and a new nonlinear wave theory

I shall discuss two new asymptotic regimes for the nonlinear PDEs governing the tropical atmosphere. Using systematic multiscale asymptotics, we arrive at an asymptotic closure for the ideal fluid equations governing dynamics on large scales in the tropical atmosphere. By selecting a plausible analytic model for smaller scale flows in the tropics, we predict the large scale structure of the Madden-Julian oscillation; this is a planetary scale organization of winds, the understanding of which has been called "the holy grail" of tropical meteorology. In the second problem, we study the same equations, but over longer time and spatial scales. The resultant coupled nonlinear dispersive equations for the amplitudes of interacting wave packets are novel both from the perspective of the atmospheric sciences and from a more general mathematical setting. These equations describe the influence of large scale tropical waves on midlatitude waves and, in particular, are relevant for understanding the effect of the Madden-Julian oscillation on midlatitude weather. Furthermore, the amplitude equations have a Hamiltonian structure and admit analytic solitary wave solutions.

November 9, THURSDAY
Tomasz Szarek, Silesian University, Katowice
Lower bound technique in the theory of random dynamical systems

Abstract: Lower bound technique appears to be a very useful tool in the theory of Markov operators. In particular A. Lasota and J. Yorke used it to prove the existence of an absolutely continuous measure for the Frobenius--Peron operators corresponding to piecewise monotonic transformations. Recently this technique has been extended to general Markov operators including those describing the evolution of measures for iterated function systems. Quite recently it has been shown its utility in the theory of SPDEs. In this talk, making use of lower bound technique, we are going to formulate criteria for the existence of an invariant measure on general complete separable metric spaces. Criteria for ergodicity of invariant measures will be given also.

November 15,
Chris Jones, University of North Carolina
Ocean Data Assimilation: Issues and Strategies for Lagrangian Observations

To accurately predict future ocean states, it behooves us to use all available observational data. Much of the sub-surface data in the ocean comes from Lagrangian instruments which are assumed to follow fluid particle trajectories. Model and observation errors are taken to be random processes and filtering methods are used to incorporate data into a re-initialization of the state. Special considerations arise for Lagrangian data as they are not given directly in terms of the state variables. Some methods will be discussed for dealing with this issue, and ideas coming from dynamical and stochastic systems will then be invoked to shed light on both the best approaches and the most useful data.

November 16, THURSDAY 3pm in E312
Weinan E, Princeton University
An overview of multiscale modeling

I will give an overview of a program on building a mathematical theory of crystalline solids, starting from atomistic models. I will discuss what the crucial issues are. I will start by reviewing the geometry of crystal lattices, the quantum as well as classical atomistic models of solids. I will then focus on a few selected problems: (1) The crystallization problem -- why the ground states of solids are crystals and which crystal structure do they select? (2) stability of crystals; (3) instability of crystals; (4) the generalized Peierls-Nabarro model for defects in crsytals.

November 22
Jiahong Wu, Oklahoma State University
Nonlinear Partial Differential Equations with Fractional Diffusion

Nonlinear partial differential equations with fractional diffusion arise in numerous seemingly diverse fields such as fluid flow, material viscoelastic theory, electromagnetic theory, astrophysics, control theory of dynamical systems, economics and so on. This talk focuses on two important nonlinear PDEs with fractional diffusion: the 2D dissipative quasi-geostrophic (QG) equation and the generalized incompressible magnetohydrodynamics (MHD) equations. We will summarize some of the recent progress made by Kiselev, Nazarov and Volberg and by Caffarelli and Vasseur on the QG equation with the critical index and discuss the applicability of the approach of Caffarelli and Vasseur to the supercritical case. For the generalized MHD equations, we present a regularity criterion that imposes conditions on the velocity alone. This criterion indicates that the global regularity issue concerning the MHD equations may not necessarily be more difficult than the same issue on the Navier-Stokes equations.

November 29,
Phil Morrison, University of Texas
Vlasov Plasma and Fluctuation Spectra

November 30, THURSDAY 4pm in E312
Jean-Michel Roquejoffre, Universite Paul Sabatier, Toulouse
Oscillatory dynamics of a reaction-diffusion system modelling a burner flame

A burner flame can be described by the usual one-dimensional thermo-diffusive model for flame propagation. The model comprises an equation for the temperature, posed on the half-line, and an equation for the mass fraction of the reactant, posed on the whole real line. This peculiarity entails~instability properties of the steady solutions. In the large activation energy framework, G. Joulin (1982) derives, in a formal fashion, a differential-delay equation accounting for the unstable~dynamics of the flame front. The goal of the talk is to discuss a mathematically rigorous proof of this result.

December 5, TUESDAY 3pm in E202
Vered Rom-Kedar, The Weizmann Institute, Israel
G-CSF control of neutrophil dynamics in the blood

White blood cell neutrophil is a key component in the fast initial immune response against bacterial and fungal infections. In oncological practice it is often necessary to predict and prevent the infectious complications that follow chemotherapy induced neutropenia (dangerously low levels of neutrophils in the blood). Granulocyte colony stimulating factor (G-CSF) which is naturally produced in the body, controls both the neutrophils production in the bone marrow and the neutrophils delivery into the blood. G-CSF injections are widely used to prevent and treat neutropenia. However, the optimal schedule and intensity of the G-CSF application has not been fully determined. We develop a robust two-dimensional ordinary differential equation model which accurately mimics the clinically observed G-CSF - neutrophil dynamics on time scales of several days.The resulting model is structurally stable, and thus its dynamical features are independent of the precise form of the various rate functions. Choosing a specific form for these functions, three complementary parameter estimation procedures are examined. Fitting the 6 emerging parameters on one clinical data set (training set), the model supplies good predictions of the other available clinical data sets. The simplicity and robustness of the model are key ingredients to its application in the management of individual oncological patients under relevant clinical conditions.      Joint work with  E. Shochat  and Prof. L. Segel (Late)

December 6,
Steve Shkoller, University of California, Davis
Well-posedness for the free-boundary 3D Euler equations with or without surface tension

The free-boundary Euler equations describe the motion of perfect fluids with free surfaces or with moving material interfaces. The nonlinear a priori estimates for this system rely heavily on the geometric structures present in these equations, and it turns out that finding approximations which do not destroy this structure, and for which existence and uniqueness can be proven, is somewhat difficult. I will discuss the geometric a priori estimates for Euler, as well as a new method for well-posedness that relies on a "convolution by horizontal layers" smoothing operator as well as artificial viscosity in the case of surface tension. No irrotationality assumptions are made so that we can study general fluid motion problems, and in particular, the effect of vorticity on boundary shape, and vice versa.

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Black and white and red all over
By TheophileEscargot (Sun Jun 05, 2005 at 05:49:05 AM EST) (all tags)
What I'm Watching: "Sin City", "House". European constitution fallout. Reading: Asterix. What happened to the stats page?

Multipoll.

What I'm Watching: Sin City
Went to see Sin City. Good film: I finally feel cleansed after Revenge of the Sith now. Look George that's how you make a blue-screen action melodrama. Tightly interweave the action and the drama: don't have huge, separate stretches of each. Don't waste time on fancy backdrops that are irrelevant to the foreground events. If you're showing off CGI, style and innovation are more important than photorealism. Use the set as part of the action: if you show us a staircase or a dinosaur have someone jump down it or climb up it. And let the actors act, not just intone off an autocue.

Note on media. As I've said before, I'm not very visually-oriented; so I don't tend to find comics a very emotionally involving medium. So, after trying one or two I was never very keen on the Sin City comics: seemed pretty cheesy to me.

Film, though, I think are the most visceral medium there is. Again as I've said before, I don't like the way some critics try to make the cinema a 2D version of the stage: a film is never going to have the emotional subtlety of a play where you've got the actors in the same room as you. Movies, I've always thought, should be about spectacle. They should be larger than life, showing you stuff you couldn't see in real life.

So, as a melodrama I found the Sin City movie better than the comic: watching it in a cinema is a much more intense experience.

I liked the colourization gimmick: it's mainly black and white, but with colours superposed in some cases. The white splashes of blood I thought were very effective. If you weren't grossed out by Kill Bill, this is definitely worth seeing.

Won't be to everyone's taste though: it's very violent, gory and over the top. Some of the critics seem to be confused: they were expecting a languid film noir tribute rather than a splatterpunk epic.

What I'm Watching: House
Watched the first four episodes of House M.D. Strangely compulsive so far: I suppose I can probably identify more with Dr House than your average caring superdoc. The formula is beginning to show a bit though now, so might ease off on the next unless they start to vary it.

I liked the dilemma in ep 4 about giving different treatments to the two babies in the epidemic to find out which would die.

Not sure how realistic it all is: I generally try to avoid real and fictional hospitals. I get the impression the diagnostic stuff is a bit archaic: they always seem to have a brief but self-conscious explanation of why they can't just run a full battery of tests (no time, not enough blood) to identify the pathogen. I get the impression that in real life things are more automated and more brute-force: if it's really baffling the doctors they just run it through enough machines.

European constitution fallout
It would take a heart of stone not to laugh.

The basic fact is: nobody knows why the French and the Dutch voted no. The no campaigners were a disparate bunch from all across every spectrum. The vox pop interviews with no voters show diverse, contradictory and often self-contradictory opinions. Nobody knows anything.

And so, the obvious response from every commentator and politician is: to solve the problem we have to do exactly what I already wanted.

If you're a trad socialist, The Answer is to have more protectionism, more regulation of companies, more restrictions on the flow of people and capital.

If you're a free marketer, The Problem is that Europe's economic stagnation has left the people suspicious and mistrustful. The Answer is freer markets and deregulation: this will give as a more prosperous Europe with less unemployment.

If you're an anti-Federalist, The Problem is over-centralization: people don't want their local differences (whether socialist or free-market) ironed out. The Solution: no more centralized power.

If you're against EU expansion, The Problem was not the constitution, but fear of expansion: The Answer is to call a halt to further expansion.

If you're in favour of expansion, you just need to fix something else and go right ahead.

Ultimately, it's not that there is no Plan B. The difficulty is that there are plans B,C,D,E, F right through to Z, and most of them are completely incompatible with each other.

Read those Asterix books now. Found the Asterix annotation site interesting.

Site question
Noticed the stats page isn't where it was. Has it gone for good, gone temporarily or just changed location?

Black and white and red all over | 25 comments (25 topical, 0 hidden) | Trackback
Doctor House would be disbarred in the real world by cam (4.00 / 1) #1 Sun Jun 05, 2005 at 06:26:17 AM EST
He gets it wrong at least four times in a show, and puts every patient on their deathbed before doing a Matlock "pull the answer out of your arse" and saves the patient. He is lauded as a genius, when in reality he has a batting average worse than a B-string Baseball hitter.

Sin City was too gory for me, and I am a fan of the comic-to-film genre.

Less gory than Kill Bill though by TheophileEscargot (2.00 / 0) #2 Sun Jun 05, 2005 at 07:15:52 AM EST
House: despite being on their deathbed they're alway perfectly fine apart from a slightly faint voice by the end....
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It is unlikely that the good of a snail should reside in its shell: so is it likely that the good of a man should?
[ Parent ]
(Comment Deleted) by yicky yacky (2.00 / 0) #3 Sun Jun 05, 2005 at 08:58:58 AM EST

This comment has been deleted by yicky yacky

various points by martingale (2.00 / 0) #8 Sun Jun 05, 2005 at 06:05:41 PM EST
I agree with you that the main issue is technical. In fact, many people are quite keen on more unification rather than less, but in such a way as to turn Europe into a system where freedom and self determination can flourish, unhindered by external globalist predation.

This is why the UK's conception is fundamentally flawed. The UK wants the EU as an economic system which exists in the same plane as the international anarchical market. This is of course flawed because while it sounds like it will force Europe to compete on par with America, China, Africa, India, etc., in actual fact it means that individual European nations must compete against all the world at once. This is a lot harder than competing in a properly defined European sandbox, and using the combined strength of the sandbox to compete with other big players.

The West-East battle is an interesting one. There's a political aspect and an economic one. The true reason for bringing the East into the EU is political in my opinion, not economic as you seem to think. There really was no choice after the end of the Soviet Union, the very real danger was that Poland, Chekoslovakia, Hungary would balkanize and drag the EU into a ground war. Bringing these countries into the EU means they can be monitored and guided in an official manner.

However, the economic issue is a shambles. The problem is that in the 90s, before the US descended into imperialism and became a menace, it was fully trusted and allowed to evangelize its economic conceptions on the emerging eastern block (as well as Russia and assorted republics). This has given those countries a lopsided capitalist system.

The Russians got robber barons and mafiosi, until Putin stepped in to curb the excesses and restore a balanced system. It's no surprise that he is being reviled by the Americans behind his back. The Eastern Europeans, except for Eastern Germany, are still stuck with American models until they get better leaders or enough EU money to shut up. Meanwhile, the EU has a serious political problem on its hands because it grew too quickly.

I think you're confusing Italy's outlook however, it's closer to the continental socialist ideals than the UK's ideals, except for the anomaly that is Berlusconi.

The UK is in a political quandary, because its real ideological allies at the moment are in Eastern Europe, which has no intention of playing second fiddle in the long run. So unless the UK changes its ways and actively attempts to be a driving force of Europe, it can only be politically marginalized in the long run. The founding block however has a more common outlook and must consolidate to drive the union before the project is completely railroaded.
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$E(X_t|F_s) = X_s,\quad t > s$

[ Parent ]
I think you're being inconsistent here by TheophileEscargot (2.00 / 0) #10 Sun Jun 05, 2005 at 09:18:50 PM EST
Protectionism doesn't make you strong, it makes you weak. That's not just because your companies are shielded from competition, but because companies are interdependent. If you're making cars, you need to make them out of raw materials and components: if your protectionism puts import tariffs on those, then your cars will be more expensive than your competitors. Free markets and competition make you strong.

Now, you're trying to have it both ways. On the one hand you're talking about the "combined strength" of the European single market; which implies you think that the free market is a good thing. On the other hand, you're arguing that the EU needs protectionism as a whole, which implies the opposite.

Now the usual modern socialist argument is that even if free markets are a good thing economically, they are bad socially. So, we need to accept a certain degree of economic handicap in exchange for social benefits. You're not making that argument though.
--
It is unlikely that the good of a snail should reside in its shell: so is it likely that the good of a man should?

[ Parent ]
I don't think I'm inconsistent by martingale (2.00 / 0) #11 Sun Jun 05, 2005 at 10:33:40 PM EST
Protectionism doesn't make you strong, it makes you weak. That's not just because your companies are shielded from competition, but because companies are interdependent. If you're making cars, you need to make them out of raw materials and components: if your protectionism puts import tariffs on those, then your cars will be more expensive than your competitors. Free markets and competition make you strong.
I think you're ignoring the role of the state in making this case. The state acts to foster a kind of economy of scale and of opportunities.

First, free competition makes small players strong or kills them. What remains are well adapted players who can survive independently but have no self determination beyond their immediate market strengths.

But a state can balance the local economy and foster long term growth as well as force economies of scale according to the national interest. It doesn't matter if some parts of the local economy are weak provided that they can be sustained via funds extracted from the stronger parts of the same local economy. The result is not unlike a diversified portfolio, which doesn't in itself perform as well as individual stocks, but overall achieves growth with reduced risk and more dependable returns.

Now, you're trying to have it both ways. On the one hand you're talking about the "combined strength" of the European single market; which implies you think that the free market is a good thing. On the other hand, you're arguing that the EU needs protectionism as a whole, which implies the opposite.
No, I don't think the free market is a good thing by itself. What I mean by "combined strength" is that a larger diverse population has raw strength in numbers which allows more diversified competition with the outside. Whereas a single country has its relative strenghts and weaknesses compared to non EU competitors, the EU's strength is the sum of those relative strengths, while the individual countries' weaknesses are only an EU weakness if all members share the same weakness.

Now the usual modern socialist argument is that even if free markets are a good thing economically, they are bad socially. So, we need to accept a certain degree of economic handicap in exchange for social benefits. You're not making that argument though.
That's right, I'm not making that argument. The problem with that argument is that it doesn't address the economic criticisms but merely dismisses them as irrelevant. Instead, I believe that at the state level, economies must be organized as a team. In this way, economies which exist in a laissez-faire unorganized bunch of companies can be outplayed more reliably.
--
$E(X_t|F_s) = X_s,\quad t > s$
[ Parent ]
Hmmm by R Mutt (2.00 / 0) #12 Sun Jun 05, 2005 at 11:01:57 PM EST
No, I don't think the free market is a good thing by itself. What I mean by "combined strength" is that a larger diverse population has raw strength in numbers which allows more diversified competition with the outside. Whereas a single country has its relative strenghts and weaknesses compared to non EU competitors, the EU's strength is the sum of those relative strengths, while the individual countries' weaknesses are only an EU weakness if all members share the same weakness.
Europe is larger than a single country, so a single European economy is stronger than a national market.

Similarly, the world is larger than Europe, so a single world market is stronger than a European market.

The logic is the same.

You seem (as far as I can tell) to be trying to argue that there is an optimum size of free market, and Europe is that size. But the EU already has an internal free market and external protectionism. If that idea were correct, Europe would already be an economic tiger. In fact, it suffers low growth, high unemployment and high deficits and has for a while. You don't seem to have either a theoretical or empirical case to support that that I can see.

The rest of your statement just seems to be the old theory that a command and control economy allocates resources more efficiently than a free market.

[ Parent ]
heh by martingale (2.00 / 0) #14 Mon Jun 06, 2005 at 12:05:05 AM EST
Europe is larger than a single country, [...] Similarly, the world is larger than Europe, [...] The logic is the same.
That's a meaningless juxtaposition. A big difference is that there is no exonomy outside of the world to be trading with.

The rest of your statement just seems to be the old theory that a command and control economy allocates resources more efficiently than a free market.
Which of course is true in the same way that America is a communist country. You seem to like extremes: free market capitalism, command and control economies...

You seem (as far as I can tell) to be trying to argue that there is an optimum size of free market, and Europe is that size. But the EU already has an internal free market and external protectionism. If that idea were correct, Europe would already be an economic tiger. In fact, it suffers low growth, high unemployment and high deficits and has for a while. You don't seem to have either a theoretical or empirical case to support that that I can see.
Nonsense. By your logic, America being the free market standard bearer would never suffer recessions or even just slow growth. There are historical cycles in all economies, and even the best systems can be managed suboptimally. I'll remind you that America is the one with record deficits, while France actually has higher productivity than America according to the OECD. Frankly, from where I'm standing I don't see that the free market you vaunt so much is that efficient. As they say, in theory there's no difference between theory and practice, but in practice there is.
--
$E(X_t|F_s) = X_s,\quad t > s$
[ Parent ]
Free market standard bearer by Scrymarch (2.00 / 0) #16 Mon Jun 06, 2005 at 01:03:48 AM EST
The issue is not individual recessions but growth over the entire economic cycle.

The American state is too large, regulated and debt burdened for it to be the ideal free market.  Estonia or Ireland might be closer.

The Political Science Department of the University of Woolloomooloo

[ Parent ]
I mention the US by martingale (2.00 / 0) #21 Mon Jun 06, 2005 at 03:02:02 AM EST
because I like to yank TE's chain. Woof :-)
--
$E(X_t|F_s) = X_s,\quad t > s$
[ Parent ]
In that case, keep on :) --nt-- by Scrymarch (2.00 / 0) #25 Mon Jun 06, 2005 at 02:05:08 PM EST

The Political Science Department of the University of Woolloomooloo

[ Parent ]
Stuff by R Mutt (2.00 / 0) #17 Mon Jun 06, 2005 at 01:19:51 AM EST
That's a meaningless juxtaposition. A big difference is that there is no exonomy outside of the world to be trading with.
On the contrary: the principles are the same.

You're still making an unsubstantiated assertion: that free markets are good within Europe, but would be bad if the free trade zone was expanded.

If you think that smoking 20 cigarettes a day is bad for your health, but smoking 5 cigarettes a day is good for your health, you need to support that somehow.

If you think that a free market of 12 countries is good, but 50 countries bad: you need to support that theory.

Regarding productivity figures, they're notoriously unreliable since they depend on workers accurately completing their timesheets. If you work 40 hours but put 45 on your timesheet, your productivity goes down: you've achieved less per hour. If you work 40 hours but put 35 on your timesheet (for instance, if the government forbids you to put more) then your productivity soars.

The advange of free-market economies regarding recessions isn't that they never have them, but they are much more resilient to them: they can bounce back relatively quickly.

[ Parent ]
assumption by martingale (2.00 / 0) #19 Mon Jun 06, 2005 at 02:09:06 AM EST
You're still making an unsubstantiated assertion: that free markets are good within Europe, but would be bad if the free trade zone was expanded.
What part don't you understand? I'm neither for unfettered free trade outside of Europe nor inside of it. Free trade needs to be tempered by rules and regulations, which is possible inside Europe so long as there is an acceptable strong pan-European government and structure of laws. Free trade inside Europe without oversight is not something I am arguing for in this thread. As regards outside Europe, I am not interested in a level playing field for its own sake, it needs to be negotiated on a case by case basis keeping all relevant interests in mind, ie horse trading on a grand scale.

If you think that a free market of 12 countries is good, but 50 countries bad: you need to support that theory.
I've repeatedly explained the issue: regulation and control is necessary IMHO. It's easier to control 12 countries than regulate 50, but if you can describe and implement a binding system which ensures that a Europe with 50 members is reasonably managed then yes, 50 members is acceptable. Right now, we can't manage 25.

The advange of free-market economies regarding recessions isn't that they never have them, but they are much more resilient to them: they can bounce back relatively quickly.
Please, definitions of recession are notoriously unreliable, they are political dynamite. If you're going to argue that econometrics is an unreliable basis for comparison, then don't claim out of thin air that free-market economies are this or that. Admit you're arguing your side because you believe in a few simplified theoretical models with little basis in reality, and I won't bore you with talk of diversified economic portfolios.
--
$E(X_t|F_s) = X_s,\quad t > s$
[ Parent ]
Recessions by R Mutt (2.00 / 0) #22 Mon Jun 06, 2005 at 03:18:32 AM EST
Um, you're the one who brought up recessions by making the statement:
"By your logic, America being the free market standard bearer would never suffer recessions"
I simply corrected the view you misattributed to me.

Now, consider two Europes. Europe A is Europe as it exists: a free internal market, but external protectionism. Europe B is Europe without an internal free market: with trade barriers between the member states.

Now, in the past you have made statements about the advantages of trade barriers, since you believe they allow industries to be nurtured through bad patches and delicate stages.

This would lead me to believe that you find Europe B to be economically superior to A. Europe B would have allowed the British goverment to bail out Rover, for instance.

However your statements in this diary about scale lead me to believe you actually find Europe A to be economically superior.

Which do you prefer?

[ Parent ]
ah by martingale (2.00 / 0) #24 Mon Jun 06, 2005 at 04:13:03 AM EST
Europe C: A Europe where separate nations are regions of one large secular country with a single democratically elected government and common standards of education, freedom of expression, unified rights and laws etc., able by its sheer size to hold its own in a world comprising several economic blocks, all of which acting in their own narrow self interest.

Now, in the past you have made statements about the advantages of trade barriers, since you believe they allow industries to be nurtured through bad patches and delicate stages.
Yes, I've made those statements and they do apply in this case (Europe C) as well. It is a job of the State to nurture a mix of vital industries which ensure its long term viability and independence. Such industries include food production, heavy industry, manufacturing, etc. It is not a good idea to let such industries decay and vanish, and to depend on other states providing them more cheaply. As long as these industries stay alive, it's perfectly reasonable to supplement them with cheap imports, and if the final aim is to merge with another state, then it is also reasonable to allow such industries to be moved into that other state. Moreover, industries which are identified as important and don't yet exist must be nurtured.

Having said that, with certain targets in place it doesn't matter how the industries are managed, I don't believe in State micro management. What matters is that the State is self-sufficient if it needs to be, and can protect its citizens.

Your Europe B is preferable to a Europe A only in case the free internal market cannot be regulated and controlled by an institution with the muscle to enforce its decisions.

For example, on the world scale, we have some institutions such as the WTO, UN which have no muscle, and therefore are not sufficient for a true world wide free market, attractive as it may seem in the abstract. So a prudent Europe must keep its protections up to prevent becoming dependent on other countries. Beyond that requirement, anything goes.

Inside Europe, the same situation applies in microcosm. The institutions exist, but are currently unsuitable for 25 members. Eventually, this problem must be solved in a way acceptable to all members concerned. If this can be done, we will probably have a european government which can safeguard and protect the free internal market by defusing peacefully and decisively any issues that arise. But right now, we aren't there yet.

I simply corrected the view you misattributed to me.

--
$E(X_t|F_s) = X_s,\quad t > s$

[ Parent ]
Stats page by hulver (4.00 / 1) #4 Sun Jun 05, 2005 at 09:46:31 AM EST
I've not set it up on here yet.

You can find the pre-move stats at http://old.hulver.com/stats/

(No link, because it'll be going away soon anyway)

I'll put up a note when I've managed to merge the log files from the two sites and get the new stats up.
--
Cheese is not a hat. - clock

Thanks! by TheophileEscargot (2.00 / 0) #5 Sun Jun 05, 2005 at 10:03:07 AM EST

Keep thinking we must be about to overtake K5 on hits-per-day, but never actually happens. Sciscoop's stats have vanished as well.
--
It is unlikely that the good of a snail should reside in its shell: so is it likely that the good of a man should?

[ Parent ]
Now we're on a faster server by hulver (4.00 / 1) #7 Sun Jun 05, 2005 at 12:09:54 PM EST
I'll start letting search engines index us again.

That'll push the hits up.
--
Cheese is not a hat. - clock

[ Parent ]
EuroCon referendums by jump the ladder (2.00 / 0) #6 Sun Jun 05, 2005 at 10:37:27 AM EST
Of course both the French and Dutch govts were unpopular and the previous phase of European integration, the Euro, has not been perceived to be a huge sucess in both countries with a lot of people blaming it for higher prices and slower economic growth.

If there was a booming economy as a result of the Euro in both countries then I think it would have been different.

economics by martingale (2.00 / 0) #9 Sun Jun 05, 2005 at 06:29:19 PM EST
The EU has always been driven economically by Germany. This is in fact not surprising since the founding principle was to pool the heavy industries in EU members, and of the France/Germany pair, France has a more rural outlook. Over time, the poorer southern members were infused with EU funds to bring them up to speed, which naturally drained the German output. Even the Euro doesn't change the underlying economic facts. However, Germany has paid heavily for reunification too, and altogether this is reflected in poor economic performance for nearly a generation.

What's new now is that the Eastern block members have infused a new source of economic drive through cheap and plentiful labour, which means that the EU's economy no longer depends mostly on Germany. Simultaneously, with reduced pressure we can expect Germany to pull ahead again.

The UK is in a funny position, because of its fence sitting. It doesn't help out as much with the EU, so doesn't feel the drain that much, but won't benefit as much in the long term because it isn't at the center of Europe's economic activity. The only major European concession is London's attempt at being the finance capital of Europe, but it's not clear to me if that will be successful. I also don't believe that in the long term London can be Europe's clearing house for American and world wide interactions.
--
$E(X_t|F_s) = X_s,\quad t > s$

[ Parent ]
It is sucessful by jump the ladder (2.00 / 0) #13 Sun Jun 05, 2005 at 11:02:12 PM EST
London is already the European capital for finance. Frankfurt, if anything, has lost business since the Euro has come on board and Paris was never really in the runnning.

Help out? Well the UK net contribution of £3 bn certasinly helps I would have thought.

[ Parent ]
long term trends by martingale (2.00 / 0) #15 Mon Jun 06, 2005 at 12:19:12 AM EST
My point is that this is unlikely to last without some effort on the part of Britain. London is not at the heart of the bulk of European industry and trade routes, whereas Germany is. Arguing that the Euro has failed to deliver at this point is like arguing that right after a big takeover, shareholders are poorer and therefore management is incompetent. The full effects of the Euro take time to discover.

Regarding the contribution, I'd say you're missing the famous rebate, but then I don't expect you'll agree with me that its existence is unfair.
--
$E(X_t|F_s) = X_s,\quad t > s$

[ Parent ]
Erm by jump the ladder (2.00 / 0) #18 Mon Jun 06, 2005 at 01:23:02 AM EST
you don't need to be on the trade routes or nar industry if you're doing it all electonically. The reason why London is sucessful is low tax rates, has a workforce with the right skills and has the clustering effect of many large banks.

It's in the right timezone too.

[ Parent ]
I agree to some extent by martingale (2.00 / 0) #20 Mon Jun 06, 2005 at 02:30:13 AM EST
you don't need to be on the trade routes or nar industry if you're doing it all electonically. The reason why London is sucessful is low tax rates, has a workforce with the right skills and has the clustering effect of many large banks.
That's true in many ways. Electronic transactions do negate the problems of geography, but note also that this applies to the clustering effect, which is a remnant of the previous era. When banks have restructured enough to be capable of fully operating anywhere, then there will be no benefit of staying close to a skilled workforce, just train locals (making sure what you pay them plus the training is competitive) and send skilled workers out into the wild.

Then there are taxes and regulations. That's a political matter which singles out the UK, but being political, it can change if deemed important, which would render the UK's advantage moot.

There's really no reason why Germany say couldn't gather a lot of Britain's business by doing what it takes to undercut the UK. Of course, the prize question is whether another country is actually willing to do what it takes.
--
$E(X_t|F_s) = X_s,\quad t > s$

[ Parent ]
For someone who says by Dr H0ffm4n (4.00 / 2) #23 Mon Jun 06, 2005 at 03:33:19 AM EST
they don't find comics involving, you sure do read a lot of them.

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text:
Prove f-g is uniformly continuous

Homework Statement

Let f, g : D→R be uniformly continuous. Prove that f-g: D→R is uniformly continuous aswell

none

The Attempt at a Solution

Okay, I am posting this question because I want to make sure that my solution is correct and if it isn't I would really be thankful if someone pointed out its flaws.

My solution:

For all ε >0 there exists δ >0 s.t.

abs( x - y ) < δ => abs( f(x) - f(y)) <ε

then

abs( f(x) - f(y)) <ε/2

abs( g(x) - g(y)) <ε/2

now its f - g so

abs( f(x) - f(y) - g(x) + g(y)) < ε

abs( f(x) - f(y)) + abs( - g(x) + g(y)) < ε

abs( f(x) - f(y)) + abs(-1)*abs( +g(x) -g(y)) < ε

abs( f(x) - f(y)) + abs( +g(x) -g(y)) < ε

ε/2 + ε/2 <ε

ε ≤ ε

Also can anyone describe to me what uniformly continuous means besides from the actual definition. I have a hard time understanding what uniformly continuous means.

Thanks.

LCKurtz
Science Advisor
Homework Helper
Gold Member

Homework Statement

Let f, g : D→R be uniformly continuous. Prove that f-g: D→R is uniformly continuous aswell

none

The Attempt at a Solution

Okay, I am posting this question because I want to make sure that my solution is correct and if it isn't I would really be thankful if someone pointed out its flaws.

My solution:

For all ε >0 there exists δ >0 s.t.

abs( x - y ) < δ => abs( f(x) - f(y)) <ε

then

abs( f(x) - f(y)) <ε/2

abs( g(x) - g(y)) <ε/2

How do you know the same ##\delta## works for both f and g?

Can't you just choose what ε and δ is?

It can have many values as long as its > 0. Right?

LCKurtz
Science Advisor
Homework Helper
Gold Member

Homework Statement

Let f, g : D→R be uniformly continuous. Prove that f-g: D→R is uniformly continuous aswell

none

The Attempt at a Solution

Okay, I am posting this question because I want to make sure that my solution is correct and if it isn't I would really be thankful if someone pointed out its flaws.

My solution:

For all ε >0 there exists δ >0 s.t.

abs( x - y ) < δ => abs( f(x) - f(y)) <ε

then

abs( f(x) - f(y)) <ε/2

abs( g(x) - g(y)) <ε/2

now its f - g so

abs( f(x) - f(y) - g(x) + g(y)) < ε

abs( f(x) - f(y)) + abs( - g(x) + g(y)) < ε

abs( f(x) - f(y)) + abs(-1)*abs( +g(x) -g(y)) < ε

abs( f(x) - f(y)) + abs( +g(x) -g(y)) < ε

ε/2 + ε/2 <ε

ε ≤ ε

Also can anyone describe to me what uniformly continuous means besides from the actual definition. I have a hard time understanding what uniformly continuous means.

Thanks.

How do you know the same ##\delta## works for both f and g?

Can't you just choose what ε and δ is?

It can have many values as long as its > 0. Right?

No. ##\epsilon## is a given, presumably small, number. If you have a uniformly continuous function ##f##, that means that given any ##\epsilon > 0## there exists a ##\delta##, depending only on ##\epsilon## and not ##x## or ##y## such that if ##|x-y|<\delta##, then ##|f(x)-f(y)|<\epsilon##. You don't get to choose ##\delta## but you are guaranteed that there is one. A different function ##g## would normally need a different ##\delta## for the same ##\epsilon##.

There are other issues with your writeup, but first you have to figure out how you can get one ##\delta## that works for both ##f## and ##g##.

but first you have to figure out how you can get one δ that works for both f and g

I'm going to take a few guesses.

1. What if both f and g are the same function then they would have the same δ and ε values.

2. Because they are both uniformly continuous.

3. Because I am picking the same ε for each function.

I have tried to understand the whole ε δ thing many times and although I think I kind of get it I don't think that I have a fundamental understanding of it.

Also, my professor just picked the same δ like I did for a similar problem. I do know that they don't have to be the same.

LCKurtz
Science Advisor
Homework Helper
Gold Member
I'm going to take a few guesses.

1. What if both f and g are the same function then they would have the same δ and ε values.
They aren't, so that is irrelevant.
2. Because they are both uniformly continuous.
No.
3. Because I am picking the same ε for each function.
No.
I have tried to understand the whole ε δ thing many times and although I think I kind of get it I don't think that I have a fundamental understanding of it.
Yes, I don't think you quite have it yet either. Think about my question like this. Suppose you have a ##\delta_1## that makes ##|f(x)-f(y)|< \epsilon## when ##|x-y|<\delta_1## and you also have a ##\delta_2## that makes ##|g(x)-g(y)|< \epsilon## when ##|x-y|<\delta_2##. Can you see how to make a ##\delta## from that that works for both?

Actually now that I'm looking at my professors notes more I do see that he indeed labeled δ1 and δ2 separately even though they are in the end the same.

So is there anything else wrong with my write up? I just turned in the homework yesterday and I will see what I get on this problem.

LCKurtz
Science Advisor
Homework Helper
Gold Member
Actually now that I'm looking at my professors notes more I do see that he indeed labeled δ1 and δ2 separately even though they are in the end the same.

So is there anything else wrong with my write up? I just turned in the homework yesterday and I will see what I get on this problem.

No, they aren't the same. What you want is to to pick ##\delta_1## for ##f## and ##\delta_2## for ##g## so ##|f(x) - f(y)|< \frac \epsilon 2## when ##|x-y|<\delta_1## and ##|g(x) - g(y)|< \frac \epsilon 2## when ##|x-y|<\delta_2##. Then choose ##\delta = \text{min}\{\delta_1,\delta_2\}## so that when ##|x-y|<\delta## they both work.

Then in your writeup, you don't want to end up with ##\epsilon\le \epsilon##. After the above paragraph you want to say that if ##|x-y|<\delta## then$$|f(x)+g(x) - (f(y)+g(y))| \le ... < \epsilon$$where you fill in the dots with a string of inequalities similar to what you did write.

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# Fulcro development with Emacs+Cider

Using Emacs+Cider for development with Fulcro. To set up Emacs for Clojure and ClojureScript development with Cider see e.g.: My Emacs configuration

JVM_OPTS="-Ddev" lein repl :headless

Jot down the port on which the nREPL server started.

# Connect to REPL (for Clojure)

In Emacs use M-x cider-connect to connect to the REPL. Normally you can use the default (localhost) and also press ENTER for the port number (which automatically finds the port number). If it doesn’t work then use the jotted down port number.

# Start the server in the Clojure REPL

(go)

# Create a second connection to the REPL (for ClojureScript)

In Emacs use M-x cider-connect to again connect to the REPL. On the question REPL buffer already exists (*cider-repl localhost*). Do you really want to create a new one? (y or n) answer y.

# Initialize the ClojureScript REPL

In the ClojureScript REPL type the following command:

(start-figwheel)

The ClojureScript REPL reports Prompt will show when Figwheel connects to your application, which occurs when the page with the ClojureScript code is loaded or reloaded.

# Get initial- and current state

Sidetracking, on how to get initial- and current state in the Fulcro template project.

To see the initial state, use the following from a cljs repl:

(fulcro.client.primitives/get-initial-state fulcro-template.ui.root/Root {})

To see the current state, use the following from a cljs repl:

@(fulcro.client.primitives/app-state (get @fulcro-template.client/app :reconciler))

# Manage repl connections

Sometimes you require a specific repl to be the active connection for a source file. E.g. for .cljc files. There is a section in the CIDER documentation on this: Managing Connections.


text:
# Adding reliable storage space to a laptop computer - based system

My inquiry below is a bit various : I need to know the most effective means to add storage space to a laptop computer - based system without giving up power performance or "worldly performance". By the last, I suggest anything which would certainly create the storage space components to wear away extra swiftly than essential. The major instance I can consider is if spindown takes place also occasionally, or probably additionally as well regularly, the life-span of the drive in inquiry might be lowered.

apart

Currently I'm attempting to identify just how to get an HP Simplesave 2.5" drive to act sensibly well. Clearly this is not the optimum selection ; it was a boxing week sale which might wind up being repossessed.

Numerous examinations on it making use of hdparm appear to show that it is not making use of the value of the -S parameter, which is intended to establish how much time it waits to rotate down. Rather, it appears to rotate down after 10 secs if the -B alternative is readied to 127 or much less, and also after an extended period of time, or probably never, if it is greater. I state this mostly due to the fact that I'm not totally encouraged that these instructions will certainly often tend to function as man hdparm claims they need to also on drives placed in correct USB units. The guidebook does state that more recent units often tend to sustain these attributes.

bottom line

The system often tends to function primarily as a web server, though does see periodic usage as a media box. It might get put on hold periodically, or might wind up being powered on and also energetic (though still) for months.

I would certainly such as to have readily available the very same type of power management capability that I would certainly get with an inside - placed HDD in a desktop computer (or rack - placed?) web server. This consists of rotating down and/or resting the drive when the web server is put on hold.

So I would certainly such as to recognize the most effective strategy to locating a reliable storage space remedy. Are particular brand names of units much better for this? Is it essential to make use of a 3.5" unit, or at the very least one that is powered independently from the USB line, to get correct power management centers? Or would certainly I have make use of a complete NAS system for that?

0
2019-05-13 05:15:56
Source Share

USB drives have a chipset that transforms USB mass - storage space - tool regulates to IDE or SATA commands, which the drive after that obtains. Economical chipsets (which are the bulk, I visualize) do not hand down commands appropriately to the drive that aren't straight pertaining to reviewing or creating information from the drive. You are sort of at the grace of that hardware with USB units.

Seems like just one of the most substantial little the that - S value is reading by the drive or controller (off (> 128) = power conserve setting, on (< 127) = high efficiency setting)

You could improve attribute assistance if your system has an eSATA port. eSATA talks straight to the drive so there is no "translation" or linking of commands required.

In my point of view, the most effective point you can do to make certain a lengthy life for a disk drive is :

• tidy power to the system, get a power - conditioning UPS
• maintain the tool in an area with a constant ~ 70 level temperature level and also reduced - moisture
• decrease powering them on and also off, yet do power them down otherwise being made use of for an extensive amount of time
• back-ups, back-ups, back-ups.

I would certainly claim place your cash right into a UPS and also an additional drive for back-up. Do a RAID point if you such as.

0
2019-12-03 01:42:34
Source


text:
In this post, you will learn the techniques in relation to knowing whether the given data set is linear or non-linear. Based on the type of machine learning problems (such as classification or regression) you are trying to solve, you could apply different techniques to determine whether the given data set is linear or non-linear. For a data scientist, it is very important to know whether the data is linear or not as it helps to choose appropriate algorithms to train a high-performance model. You will learn techniques such as the following for determining whether the data is linear or non-linear:

• Use scatter plot when dealing with classification problems
• Use scatter plots and the least square error method applied in a simple regression method when dealing with regression problems.

Use Scatter Plots for Classification Problems

In the case of the classification problem, the simplest way to find out whether the data is linear or non-linear (linearly separable or not) is to draw 2-dimensional scatter plots representing different classes. Take a look at the following examples to understand linearly separable and inseparable datasets.

Here is an example of a linear data set or linearly separable data set. The data set used is the IRIS data set from sklearn.datasets package. The data represents two different classes such as Setosa and Versicolor. Note that one can easily separate the data represented using black and green marks with a linear hyperplane/line.

The code which is used to print the above scatter plot is the following:

import pandas as pd
import numpy as np
from sklearn import datasets
import matplotlib.pyplot as plt

# Load the IRIS Dataset
#
X = iris.data
y = iris.target

# Create a scatter plot
#
plt.scatter(X[:50, 0], X[:50, 1], color='green', marker='o', label='setosa')
plt.scatter(X[50:100, 0], X[50:100, 1], color='black', marker='x', label='versicolor')
plt.xlabel('sepal length [cm]')
plt.ylabel('petal length [cm]')
plt.legend(loc='upper left')
plt.show()

Here is an example of a non-linear data set or linearly non-separable data set. The data set used is the IRIS data set from sklearn.datasets package. The data represents two different classes such as Virginica and Versicolor. Note that one can’t separate the data represented using black and red marks with a linear hyperplane. Thus, this data can be called as non-linear data.

The code which is used to print the above scatter plot to identify non-linear dataset is the following:

import pandas as pd
import numpy as np
from sklearn import datasets
import matplotlib.pyplot as plt

# Load the IRIS Dataset
#
X = iris.data
y = iris.target

# Create a scatter plot
#
plt.scatter(X[50:100, 0], X[50:100, 1], color='black', marker='x', label='versicolor')
plt.scatter(X[100:150, 0], X[100:150, 1], color='red', marker='+', label='verginica')
plt.xlabel('sepal length [cm]')
plt.ylabel('petal length [cm]')
plt.legend(loc='upper left')
plt.show()

Use Simple Regression Method for Regression Problem

In case you are dealing with predicting numerical value, the technique is to use scatter plots and also apply simple linear regression to the dataset and then check least square error. If the least square error shows high accuracy, it can be implied that the dataset is linear in nature, else the dataset is non-linear. Here is how the scatter plot would look for a linear data set when dealing with regression problem.

In addition to the above, you could also fit a regression model and calculate R-squared value. If the value is closer to 1, the data set could be seen as a linear data set.


text:
# Adventures in optimization, re: Typed Racket

Last Thursday I wrote a post about generating Perlin/simplex noise in Racket. Later that day, I posted to the Racket mailing list asking how I could make it faster. What resulted was a whole sequence of responses (primarily about Typed Racket) and a bit of a rabbit hole that I’m still trying to wrap my head around.

The first version that I tried to run was the original untyped code which used the picturing-programs  teachpack to generate an image. Running Racket 5.3.3 on an x86_64 Linux machine, here are the timing results (if you’d like to try it yourself, use git b2d12e4):

 perlin: cpu time: 355 real time: 356 gc time: 40
simplex: cpu time: 243 real time: 242 gc time: 4

That’s actually much better than I originally got on my 64-bit Windows 7 machine, despite a slightly faster CPU from the same year. I’m still not sure sure why that’s the case.

But that’s not what I’m interested in at the moment. 😄 What’s more interesting right now is when I started trying to optimize things.

Based on the first few emails, the way to go seemed to convert my code to Typed Racket. So the first thing that I did was to swap out the #lang line from #lang racket to #lang typed/racket. Of course when I did that, all hell broke loose with page upon page of errors of the sort:

Type Checker: Expected Real, but got Any in: x
Type Checker: Expected Vector, but got Any in: g
Type Checker: Expected Number, but got Any in: x
Type Checker: Expected Vector, but got Any in: g
…
Yeah… Basically Racket is telling me that it knows I’m trying, but I’m going to have to give it a few more (read: any) types before it can help me.

So I go through and I start typing1 things. One caveat is that there are at least two ways to assign a type to things in Typed Racket. Either you can declare the types inline, using forms like define: and let: or you can keep the code as it was and add the type signatures with just :.

As an example, the definition of grad3 could be:

; using inline types
(define: (grad3 : (Vectorof (Vectorof Integer)))
'#(#( 1  1  0) #(-1  1  0) #( 1 -1  0) #(-1 -1  0)
#( 1  0  1) #(-1  0  1) #( 1  0 -1) #(-1  0 -1)
#( 0  1  1) #( 0 -1  1) #( 0  1 -1) #( 0 -1 -1)))

; using type annotations
'#(#( 1  1  0) #(-1  1  0) #( 1 -1  0) #(-1 -1  0)
#( 1  0  1) #(-1  0  1) #( 1  0 -1) #(-1  0 -1)
#( 0  1  1) #( 0 -1  1) #( 0  1 -1) #( 0 -1 -1)))

Since the only other experience I had with something like this was in Haskell, the latter seemed more natural to me. I later asked on the mailing list and the answer was basically that either is perfectly valid.

Going through the rest of the code and adding types was rather straight forward. I knew from previous (minimal) optimization experience in Racket that using Flonum was probably what I wanted to do, so everything essentially became either Integer or Flonum. The most interesting / relevant type is probably that of the perlin function itself (simplex has the same type):

(: perlin
(case-> (Flonum -> Flonum)
(Flonum Flonum -> Flonum)
(Flonum Flonum Flonum -> Flonum)))

This is a bit ugly, but essentially what it’s saying is that perlin can have multiple types for each of the optional arguments, but it always takes in Flonums and returns a Flonum. It doesn’t seem like there’s a way to directly specify optional parameters in Typed Racket (yet), but for the time being, case-> gets the job done well enough.

In addition, we had to add in a bunch of types within the perlin/simplex functions. I probably added more than I needed to, typing every variable that I had, but I figured that if I had to type any of them I might as well go all of the way. So throughout the function, I have lines like these:

(: gi000 Integer) (: gi001 Integer) (: gi010 Integer) (: gi011 Integer)
(: gi100 Integer) (: gi101 Integer) (: gi110 Integer) (: gi111 Integer)

...

(: n000 Flonum) (: n001 Flonum) (: n010 Flonum) (: n011 Flonum)
(: n100 Flonum) (: n101 Flonum) (: n110 Flonum) (: n111 Flonum)

Not particularly pretty, but not too painful either.

What did get annoying however was after I had everything typed and I still got this particularly pleasant error:

Type Checker: No function domains matched in function application:
Domains: Flonum Flonum Flonum
Flonum Flonum
Flonum
Arguments: Zero
It turns out that Racket knows that zero times anything is zero. The problem is that zero times anything is exactly 0, the real, exact, integer version of the number (Actually it has it’s own type: Zero). But that’s not what we’re looking for, we’re looking for a Flonum. I could work around it using either the function exact->inexact or the function real->double-flonum, but both of those had to be applied in the code using perlin, leaking the implementation details in a rather unsatisfactory way (since I can imagine that many if not all uses of noise would eventually use the point 0, 0).

Still, it was enough for a first try. I don’t have timing results for this on the same machine as the rest, but if you’d like to try it out, you can get the code using git f33f6d7.

About this time, I got another email back that detailed essentially what I’d been trying to do, only they had a few tricks that I hadn’t been able to find by myself. Specifically:

• images/flomap has a faster (typed) image generator (build-flomap* ) than picturing-programs
• case-> slows down typechecking (but has no effect on runtime)
• exact-floor is far faster than using inexact->exact and floor
• shadowing (rather than set!) should allow for better optimization, especially with floating point numbers
• Real can be used as the type for Real numbers, including the Zero that was causing so much trouble

Using all of that, I set about a second round of optimizations. Primarily, since Real allowed for Zero, I converted every Flonum to Real, along with the rest of the previously specified changes. Here are the timing results using the typed code using Real for the numerics and generating an image using the images/flomap library. Between the two of them, we got a substantial boost for both Perlin and simplex noise (git 006faf9):

 perlin: cpu time: 235 real time: 236 gc time: 15
simplex: cpu time: 147 real time: 147 gc time: 4

Overall, it’s about 2x faster than the original code, and all for just adding the type annotations.

The next step suggested to me was to use Racket’s Optimization Coach . Essentially, it’s a tool built into DrRacket for use with Typed Racket that will color code your code based on how successful the compiler will be on optimizing your functions. Specifically, it will be green if it can manage to inline your code and avoid boxing/unboxing values and also apply floating point specific functions (where necessary).

The problem was, running through the code I had, there was a heck of a lot of red… Running through my code, there was a heck of a lot of red:

Drilling down into the errors (it took a while to realize that right clicking would give more detail), it eventually turned out that converting from Flonum to Real was actually causing more errors than it was solving. Since Real is more generic and includes Integers as well as Flonums, it wasn’t possible for the compiler to use pure floating point functions although we both knew it wanted to. So back to Flonum we went!2

Actually, no. I’m not really sure why, but at this point, I decided that I liked Float better than Flonum. It turns out that the two are essentially aliases for one another (which doesn’t help when it’s not consistent which will appear in error messages), so I could have used either. In the end, I switched to Float though. I think it was mostly because of experience with other languages. Float is a common term, Flonum is less so.

In any case, my next pass was to turn Real back into Float. So it goes. This time though, I made one tweak that would allow the best of both worlds:

(: perlin (case-> (Real -> Float)
(Real Real -> Float)
(Real Real Real -> Float)))
(define (perlin x [y 0.0] [z 0.0])
(perlin^ (real->double-flonum x)
(real->double-flonum y)
(real->double-flonum z)))

(: perlin^ (Float Float Float -> Float))
(define (perlin^ x y z)
...)

Since I was would only provide perlin, not perlin^3, I could have a function that accepted any real number but internally use Floats for all of my types.

I ran the Optimization Coach again and the results were beautiful:

Green, beautiful green. I knew there was a reason it was my favorite color. Better yet, all that green is telling me that the compiler should (theoretically) be able to eek out even more speed, yes? Well, here are the timing results for using Float instead of Real and writing the aforementioned wrapper to convert between the two.

 perlin: cpu time: 112 real time: 118 gc time: 23
simplex: cpu time: 106 real time: 110 gc time: 3

Yes! More speed! We’re down to about 1/10th of a second for 65,536 calls to either function. That’s none too shabby.

But finally, I wanted to test how much of that was overhead in generating the image and how much was actually the noise algorithms. So I just wrote a simple nested for loop to generate the 256x256 calls to Perlin/simplex. At first it was slower. It turns out that even that had to be typed otherwise the untyped Racket code would eat up any meager benefits I’d gained. So I added types to my simple test bench as well. Here are the results (git 7445311):

 perlin: cpu time: 41 real time: 40 gc time: 0
simplex: cpu time: 52 real time: 52 gc time: 2

That’s none too shabby at all. Actually, if you compare it to the original algorithm my code is based on (written in Java, not C as I originally stated) it’s well within the same order of magnitude. In the Java code, without generating an image, generating a 256x256 simplex grid takes an average of 30 ms.

All things considered, I’m pretty happy with my results. It is mildly puzzling that up until the very final test case the results for Perlin are always slower than simplex (which is to be expected given the relative runtimes of the algorithms4) , but in the last case they’re exactly the same. If anyone has a good reason for why that might be, I’d love to hear it.

Well, that’s all I have. Working with Typed Racket was actually a surprisingly pleasant experience. It reminded me of all of the better parts of Haskell, where you can add type annotations to make the compiler work with you rather than against you.

1. Whee typing vs typing [return]
2. This is all actually mentioned in the Racket documentation on optimization . [return]
3. Sorry Suzanne, but the hats must live on [return]
4. O(n!) for Perlin and O(n2) for simplex, where n is the number of dimensions if I understand correctly [return]


text:
## General, Organic, and Biological Chemistry: Structures of Life (5th Edition)

1. Identify and count the significant zeros: (a) $11.\underline{00}5 \space g$ : 2 (b) $0.00032 \space m$ : 0 (c) $36000000 \space km$ : 0 (d) $1.8\underline{0} \times 10^4 \space kg$ : 1 (e) $0.825\underline 0 \space L$ : 1 (f) $3\underline{0.0} \space ^{\circ} C$ : 2 2. Sum the number of nonzero digits and significant zeros. (a) 3 + 2 = 5 (b) 2 + 0 = 2 (c) 2 + 0 = 2 (d) 2 + 1 = 3 (e) 3 + 1 = 4 (f) 1 + 2 = 3


text:
# AMF: Aggregated Mondrian Forests for Online Learning

Published in arXiv preprint, 2019

### J. Mourtada, S. Gaïffas and E. Scornet

Random Forests (RF) is one of the algorithms of choice in many supervised learning applications, be it classification or regression. The appeal of such methods comes from a combination of several characteristics: a remarkable accuracy in a variety of tasks, a small number of parameters to tune, robustness with respect to features scaling, a reasonable computational cost for training and prediction, and their suitability in high-dimensional settings. The most commonly used RF variants however are offline’’ algorithms, which require the availability of the whole dataset at once.

In this paper, we introduce AMF, an online random forest algorithm based on Mondrian Forests. Using a variant of the Context Tree Weighting algorithm, we show that it is possible to efficiently perform an exact aggregation over all prunings of the trees; in particular, this enables to obtain a truly online parameter-free algorithm which is competitive with the optimal pruning of the Mondrian tree, and thus adaptive to the unknown regularity of the regression function. Numerical experiments show that AMF is competitive with respect to several strong baselines on a large number of datasets for multi-class classification.


text:
Effect: At 1st level, the witch can use feather fall at will and gains a +4 racial bonus on Swim checks. pathfinder-1e spells skills witch Flight Hex (Su): The witch grows lighter as she gains power, eventually gaining the ability to fly. The pathfinder has two speed modes slow and fast and comes with built in LED light strips for awesome night time flying. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The witch grows lighter as she gains power, eventually gaining the ability to fly. The pathfinder can perform 3D flips and barrel rolls at the touch of a button. To learn more, see our tips on writing great answers. Thus because Fly grants a bonus to Fly checks equal to half the spells caster level, this also applies to the Flight Hex. These minutes do not need to be consecutive, but they must be spent in 1-minute increments. Overview of the Hexcrafter. Witch Hex (Shaman 2) Use Wis instead of Int for a Witch Hex. There is no shortage of good hexes, so feel free to find what fits you best. Does a character still get the bonus to the fly skill as per the spell Fly when using the witch's hex Flight? She gains an additional hex at 2nd level and for every 2 levels attained after 2nd level, as noted on Table 2–10. Making statements based on opinion; back them up with references or personal experience. Manifestation (Shaman, Heavens Spirit 20) Wis to all saves. Pathfinder is an agent-based egress and human movement simulator. How does turning off electric appliances save energy, Is copying a lot of files bad for the cpu or computer in any way. You trade a few hexes(1,8,14) for utility and familiar safety. Bones Black Plastic Figures Chronoscope Pathfinder Savage Worlds CAV: Strike Ops . This is important because the Fly spell's bonus is dependent on caster lv. The Flight Hex says you can fly "as per the spell" for class level/day minutes. If this hex is used upon a willing target, the duration lasts for a number of hours equal to the witch’s Intelligence bonus. Do Pathfinder Witches have a dedicated Patron spell slot? Downloads Thanks for contributing an answer to Role-playing Games Stack Exchange! It only takes a minute to sign up. | Swords and Wizardry SRD Subclasses - Patron Themes. New Pages | Recent Changes | Privacy Policy, Latest Pathfinder products in the Open Gaming Store, Ancestral Anthologies Vol. Check out our other SRD sites! For summoning builds, Nature – Friend of Animals Hex is a must. | d20PFSRD Role-playing Games Stack Exchange is a question and answer site for gamemasters and players of tabletop, paper-and-pencil role-playing games. Community / Forums / Pathfinder / Pathfinder First Edition / Rules Questions / Flight Hex A character who moves his or her speed and takes some action is hustling for about half the round and doing something else the other half. Alchemist (Wings discovery or Beastmorph), Witch (flight hex), Druid (wildshape), and (Air specialist) Wizard can all get flight (other than from spells or items) by 6th level, which seems like it could be a pretty big deal in a P6 game. Note however that the Hex Witch class feature nor the Flight hex itself specify what the caster level is for Fly component of the Flight hex (opposed by the Healing hex, which does specify a caster lv). Are there any gambits where I HAVE to decline? I've got flight hex at level 4, hair hex looks really useful (touch attacks with reach is another good trick) but I think evil eye and slumber first. The spell Flight takes a standard action to cast. This is Pathfinder: Kingmaker mod. Comment by Ghouls on 2018-05-23T04:04:35-05:00. If I drop "extra arcane pool" that I added this level I could grab evil eye this level and slumber next https://www.amazon.com/Riviera-RC-Pathfinder-copter-Wi-Fi/dp/B01LX7UIWK Maybe some other classes, too, like the Oracles with revelations that grant flight. Furthermore, A witches Flight Hex is a Supernatural ability, and the text for supernatural abilities states: These can't be disrupted in combat and generally don't provoke attacks of opportunity. Difficult terrain, obstacles, or poor visibility can hamper movement. Does Eidolon flight work as the fly spell for running? | FateCoreSRD Legal Information/Open Game License, Fan Labs Previews ... 2 Inch Round Transparent Flight Stand w/ Tall Flight Peg (5 bases, 5 pegs) $5.99. 99819 in stock | d20HeroSRD Guiding star (Shaman Heavens Spirit) Use Wis in addition to Cha on all Cha based skills, at night under the open sky. Now, when I started looking at the witch class it quickly became apparent that this class is pretty complex. Extending Coven to affect class level instead of just caster level for scaling effects. The party is made of a Shaman, an Arcanist (Brown-Fur Transmuter) and a Hunter. | 3.5e SRD If an Eidolon has the Flight evolution, would the Boots of Striding and Springing increase its fly speed? The Flight hex reads: "she can fly, as per the spell" The Fly spell reads: "The subject gains a bonus on Fly skill checks equal to 1/2 your caster level." Use MathJax to format equations. The achievement, similarly to its predecessors, will require you to complete a number of tasks to unlock the ability to freely fly around. If you get caught during sneaking YOU WILL NEVER COMPLETE AMIRI COMPANION QUEST FOREVER AND SHE WILL BUG OUT! Witch Hex (Shaman 2) Use Wis instead of Int for a Witch Hex. Can't wait to drink the tears of flight babies. | Here Be Monsters Spell Choices Just warning since i have to waste 5 hours of doing Act 4 again. Traveller SRD The Flight hex allows you to fly as if using the spell Fly. How do we know that voltmeters are accurate? EU values of -179.2 mm should likewise be replaced with a 'SPOT NOT DETECTED' marker in the SOLxx_EU files. Features: 2 Megapixel resolution camera w 2GB SD card (included). | Design Finder 2018 You need potion of greater invisbility in order to sneak the entire camp and you must reach Nilak and kill defaced sister inside the Barbarian Camp before challenging Armag. RC Pathfinder Hexacopter Wi-Fi Drone comes equipped with a 2MP camera, Wi-Fi connectivity, a 2GB SD card, and a 3.4V 650mAh rechargeable battery. Does the Flight hex grant a bonus to the Fly skill, like the spell does? Hi all, I am in a pathfinder campaign currently playing a Human Magus and the build is Str based. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. How much did the first hard drives for PCs cost? Manifestation (Shaman, Heavens Spirit 20) Wis to all saves. Outside of those, there are plenty of great options. What tuning would I use if the song is in E but I want to use G shapes? Benefit of Wisdom (Shaman 2, Lore Spirit) Wis … | 13th Age SRD Flight (Su): The bonus to swim seems a little but out of place, but makes sense as flavor because you are supposedly lighter. Comment by mageranger13 on 2018-05-23T07:52:25-05:00 How do nodes verify backwards incompatible blocks? No. Additionally, the witch can change her voice to match that of any creature whose voice she has stolen with this hex, as per vocal alteration (Pathfinder RPG Ultimate Magic 248). | The Modern Path SRD The Shaman wandering spirit Lore's Arcane Enlightenment hex grants bonus arcane spells. Is there a spell level limit to what spells can be chosen? No. Recent Changes ... I’m not clear on if you need to buy an actual cauldron to benefit from this hex or its offspring’s, and if so if you gain one for free by taking this hex. Any creature that is within 30 feet that is under the effects of an agony hex, charm hex, evil eye hex, fortune hex, or misfortune hex caused by the witch has the duration of that hex extended by 1 round. The Agony hex is okay on spellcasters, while the Retribution hex is okay for melee brutes. If I drop "extra arcane pool" that I added this level I could grab evil eye this level and slumber next A witch cannot select an individual hex more than once. What is a "constant time" work around when dealing with the point at infinity for prime curves? 99788 in stock ... 1 Inch Hex Transparent Flight Stand w/ Short Flight Peg (10 bases, 10 pegs)$5.99. At 1st level, a witch gains one hex of her choice. Okay, so earlier I posted my new healer witch design for my buddy Steve's new Pathfinder-based campaign. Any creature that is within 30 feet that is under the effects of an agony hex, charm hex, evil eye hex, fortune hex, or misfortune hex caused by the witch has the duration of that hex extended by 1 round. | PF2 SRD. Flight Stands Flight Bases Flight Pegs Flight Base Accessories Personalized Flight Bases Game Systems Popular Game Systems Battletech Gaslands Warhammer 40k: Kill Team X … Type:Active Changer Active/passive counterpart: Heir Inversion:Seer Role:One who manipulates and manipulates through their Aspect It has two speed modes, slow and fast. When movement is hampered, each square moved into usually counts as two squares, effectively reducing the distance that a character can cover in a move. | OGN Articles They aren't subject to spell resistance, counterspells, or dispel magic, and don't function in antimagic areas. Flight Hex (Su): The witch grows lighter as she gains power, eventually gaining the ability to fly. Mon–Fri, 10:00 a.m. to 5:00 p.m. Pacific (425) 250-0800. customer.service@paizo.com Sell at the Open Gaming Store! By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Starting at level 1 but I'm interested to hear suggestions for dips/other levels. Witch Class Features. Class handbook for the Pathfinder 2e Witch. This guide will cover the new Witch class in Pathfinder (PF) in detail, from class features, to feat choices, to the spell list. My rolled stats are as follows: 18, 18, 17, 15, 14, 13 (honestly rolled, very happy!) The Flight hex reads: "she can fly, as per the spell", The Fly spell reads: "The subject gains a bonus on Fly skill checks equal to 1/2 your caster level.". Last time when they tried to get rid of flying entirely, the outcome was....savage. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Common Hexes This hex lasts for a number of rounds equal to 3 + the witch's Intelligence modifier. It does not quite have the power or flight time that the MJX X600 has, however it has better yaw, and deeper pitch, which allows it to be more aggressive. Well, you can always stick with using only ground mounts and let others enjoy the results of "pathfinder crap". The save to resist a hex is equal to 10 + 1/2 the witch’s level + the witch’s Intelligence modifier. Shop the Open Gaming Store! Do you need to roll when using the Staff of Magi's spell absorption? (The 2nd printing of the APG includes this updated information.). Hexes have three levels of power, Common, Major, and Grand. Does the Hideous Laughter spell make a flying foe prone and cause the foe to fall? Use tactical movement for combat. Why do you say "air conditioned" and not "conditioned air"? what does "scrap" mean in "“father had taught them to do: drive semis, weld, scrap.” book “Educated” by Tara Westover. Previews ... 2 Inch Round Transparent Flight Stand w/ Tall Flight Peg (5 bases, 5 pegs) $5.99. Admittedly this would all be a lot clearer if Paizo hadn't opted to describe each of three spell-like powers of the hex in three different ways. If this hex is used upon a willing target, the duration lasts for a number of hours equal to the witch’s Intelligence bonus. If you had summoning or fighting in mind as your primary abilities, then the selection investment and action economy probably make Hexes like Ward and Fury or even noncombat Hexes like Fetish, Charm, Witch Hex – Flight, Secret, Shapeshift, and Tongue more optimal. What happens to excess electricity generated going in to a grid? New Pages 1: Races of Nature Unleashed (PF1), Aegis of Empires 5: Race for Shataakh-Uulm (Pathfinder RPG), Aegis of Empires 4: Legend of the Burning Star (PF1). It provides a graphical user interface for simulation design and execution as well as 2D and 3D visualization tools for results analysis. FAQ. d20PFSRD.com. What is a better design for a floating ocean city - monolithic or a fleet of interconnected modules? Need Help? If a Crossblooded Bloodrager chooses a Bloodline Familiar, from which bloodline does the familiar's additional ability originate? Does a caster level bonus let our alchemist learn and use Fly at a lower level? Flight (Su): The witch grows lighter as she gains power, eventually Guiding star (Shaman Heavens Spirit) Use Wis in addition to Cha on all Cha based skills, at night under the open sky. The pathfinder can perform 3D flips and barrel rolls at the touch of a button. This site may earn affiliate commissions from the links on this page. Unless otherwise noted, using a hex is a standard action that does not provoke an attack of opportunity. Copyright 2010, Paizo Publishing, LLC; Author: Jason Bulmahn. Here are my stats, I rolled d12+6 and got lucky with two 12s. Hex: Witches learn a number of magic tricks, called hexes, that grant them powers or weaken foes. Characters generally don’t walk during combat—they hustle or run. This site is an SRD (System Reference Document) for the Paizo Pathfinder Roleplaying Game. MathJax reference. Like the exploration system, the kingdom-building rules measure terrain in hexes. Ok, so building a Magus for the first time for a Kingmaker campaign. 5th Edition SRD! Saves: Will is the Witch's only good save, and the Witch has no dependence on other abilities.Fortunately the Witch is very SAD, so you have room to improve abilities which fuel your saves. Su ): the witch spell list, and nothing else the intensity of ONLY... Of good hexes, so feel free to find what fits you best use feather at... Information. ) drink the tears of Flight babies Stack with the Flight Hex ( 2! ( System Reference Document ) for the cpu or computer in any way site design logo... Only ground mounts and let others enjoy the results of  Pathfinder crap '' increase its fly?. ) use Wis instead of just caster level bonus let our alchemist learn and use at! Okay for melee brutes doing Act 4 again, would the Boots of Striding and Springing increase fly. As per the spell Flight takes a standard action to cast COMPLETE AMIRI COMPANION FOREVER! The cpu or computer in any way always stick with using ONLY ground mounts and let others the. 1-Minute increments not  conditioned air '' pegs )$ 5.99 Hex you! To fall measure terrain in hexes have three levels of power, Common, Major, and else! Bad for the first hard drive partition calculating Fireball 's average damage Game License, Fan Labs Character Downloads! Extending Coven to affect class level instead of Int for a floating pathfinder flight hex. Lore 's Arcane Enlightenment Hex grants bonus Arcane spells racial bonus on Swim checks excess generated. 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