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Compte Rendu TP3

OBJECTIF : Effectuez l’analyse en composantes principales normée (ACP). On considère pour cela les taux de croissancedu PIB réels des pays pour différentes années.

Compte Rendu TP2

Analyser les données de la base de données iris existant, dans la package base, avec l’outil R.

Algo HW #1

and 2 collaborators

PROBLEM 1 1. $f(n)=}, g(n)=lg(7^{2n})$ f(n)=27n/2, g(n)=2nlg(7) f(n)=lg(27n/2),g(n)=lg(2nlg(7)) f(n)=lg(27n/2),g(n)=lg(2nlg(7)) f(n)=7n/2, g(n)=lg(2n)+lg(lg(7)) f(n)=7n/2, g(n)=lg(2n) f = Ω(g) 2. f(n)=2nln(n), g(n)=n! f(n)=ln(2nln(n)),g(n)=ln(n!) f(n)=nln(n),g(n)=nlg(n) (via previously proved identity) f = θ(g) 3. f(n)=lg(lg*n),g(n)=lg*(lgn) f = O(g) 4. $f(n)={n},g(n)=lg^*n$ f = O(g) via limits. f approaches 0. 5. f(n)=2n, g(n)=nlgn f(n)=n, g(n)=(lgn)² f = Ω(g) 6. $f(n)=2^{}, g(n)=n(lgn)^3$ f(n)=(lgn)1/2, g(n)=lg(n)+lg((lg(n))³) f = O(g) 7. f(n)=ecos(n), g(n)=lgn f(n)=cos(n),g(n)=ln(lg(n)) f = O(g) 8. f(n)=lgn², g(n)=(lgn)² f(n)=2lg(n),g(n)=(lgn)² f = O(g) 9. $f(n)=, g(n)=n^({2})$ $f(n)=2n, g(n)=n^({2})$ f(n)=O(g) 10. $f(n)=^{n} k, g(n)=(n+2)^2$ $f(n) = {2}$ via summation formula g(n)=(n + 2)² f = θ(g)

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This is a summary of the paper *The Milky Way Has No Distinct Thick Disk* by \cite{Bovy_Rix_Hogg_2012}.

Traditionally the stars within the disks of spiral galaxies are considered to form two distinct populations. One population, termed the “thin disk”, is generally comprised of young and metal-rich stars while the other population of older and more metal-poor stars make up the “thick disk”. The paper from \citet{Bovy_Rix_Hogg_2012} challenges this assumption of bi-modality within the Galactic disk and argue for a “continuous and monotonic scale-height distritbution”.

Planning Report - Running with Sound: Android Application Simulating Sound Sources at GPS Coordinates Using Smartphone Sensors

and 3 collaborators

To come

Math 132 Notes

Taylors Theorem says if *f* is analytic on {*z* : |*z* − *z*_{0}|<*r*} and continuous on the domain that includes the boundary, then $f(z)=\sum_{n=0}^{\infty}f^{(n)}(z_0)\frac{(z-z_0)^n}{n!}$ and this series converges absolutely. Cauchys inequality says that if is analytic in {*z* ∈ 𝕔 : |*z* − *z*_{0}|<*r*} and |*f*(*z*)| ≤ *c* in the disk then the function converges absolutely.

A function which is analytic on the punctured disk {*z* ∈ 𝕔 : 0 < |*z* − *z*_{0}|<*r*} has an isolated singularity at *z*_{0}.There are three examples of isolated singularities.

removable singularity: where

*f*(*z*) is bounded for some*r*> 0 on {0 < |*z*−*z*_{0}|<*r*}, remains bounded as*z*→*z*_{0}poles: where lim

_{z → z0}|*f*(*z*)| = ∞essential singularity: when 1 or 2 dont apply

lemma: if *f* has a removable singularity at *z*_{0} then the lim_{z → z0}*f*(*z*) exists and extends *f* to an analytic function at *z*_{0}.

Score System

We need a formula that, given the distance of the player’s answer and the point shown, returns a score from 0 to 100 that (ideally) reflects the user’s knowledge of the city.

We start with the premise that, if the user is really close to the right place, he should not be penalized a lot. In the same sense, it gets to a point that if his answer is far away or even farther way, there’s little difference in his knowledge of the place.

For example, if an answer is 10 or 20 meters away from the right place, the player should get very similar scores. And if the answer is 3000 meters of 3500 meters away he should also get very similar scores, even thought the same difference of 500 meters in the other situation would make a huge difference.

So we come up with the following bell-curve-like function, where *S* is the score and *d* the distance in km between the right place and the player’s answer:

\begin{equation} S = \frac{100}{1+{d^4}} \end{equation}

Manifold Warping: Manifold Alignment Over Time

Knowledge transfer is computationally challenging, due in part to the curse of dimensionality, compounded by source and target domains expressed using different features (e.g., documents written in different languages). Recent work on manifold learning has shown that data collected in real-world settings often have high-dimensional representations, but lie on low-dimensional manifolds. Furthermore, data sets collected from similar generating processes often present different high-dimensional views, even though their underlying manifolds are similar. The ability to align these data sets and extract this common structure is critical for many transfer learning tasks. In this paper, we present a novel framework for aligning two sequentially-ordered data sets, taking advantage of a shared low-dimensional manifold representation. Our approach combines traditional manifold alignment and dynamic time warping algorithms using alternating projections. We also show that the previously-proposed canonical time warping algorithm is a special case of our approach. We provide a theoretical formulation as well as experimental results on synthetic and real-world data, comparing manifold warping to other alignment methods.

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PREFACE This is a short summary of the paper _Eclipsing binary statistics - theory and observation_ . In order to estimate the number of eclipsing binaries to be expected in the upcoming all-sky survey ’Gaia’, the authors executed a large binary population experiment using the rapid binary evolution code (BSE) from

Exact Solutions in the 3+1 Split

This began as some documentation Erik Schnetter wrote for the Penn State Maya code. I wanted to enter some more simple sample (3+1 splits of) exact space-times. It you see an obvious error, or have something to suggest, let me know.

There is, of course, a definite bias towards black hole space-times. I may add cosmological ones when/if I get the chance.

A few words about notation: In what follows, Greek indices such as *α*, *β*, *μ*, *ν* are four-vector indices and run from 0 to 3. Latin indices such as *i*, *j*, *k*, *l*, *m*, *n* are three-vector indices and run from 1 to 3.

When using spherical polar coordinates, in general *R* will denote the standard “areal” radial coordinate; when dealing with a conformally flat solution, I’ll use *r* to denote the radial coordinate, as then it will *not* be areal. Additionally, I often use the letter *q* to denote the cylindrical polar quantity $\sqrt{x^2 + y^2} = r \, \sin\theta$; most references I know use the Greek letter *ρ* for this purpose, but I’ve found *ρ* to be used for too many other purposes.

Laboration 1.3, Group 28

and 1 collaborator

ABOUT This is a hand-in written by MAZDAK FARROKHZAD and NICLAS ALEXANDERSSON in GROUP 28 for the 3rd assignment on Lab1. The assignment is about analysing an algorithm written in 3 different ways where all of them are functionally equivalent. The methods are available in the appendix. The analysis consists of: a. Description of what the algorithm does b. Complexity analysis c. Testing and numerical analysis