414 96.9 78 3.1 Saarland 471 461 97.9 10 2.1 Sachsen 2,358 2,356 99.9 2 0.1 Sachsen-Anhalt 1,411 1,410 99.9 1 0.1 Schleswig-Holstein 1,789 1,474 82.4 315 17.6 Thüringen 1,335 1,334 99.9 1 0.1 Westdeutschland [...] 2.5 Saarland 478 469 98.1 9 1.9 Sachsen 2,347 2,345 99.9 2 0.1 Sachsen-Anhalt 1,412 1,409 99.8 3 0.2 Schleswig-Holstein 1,825 1,573 86.2 252 13.8 Thüringen 1,351 1,350 99.9 1 0.1 Westdeutschland 46,106 [...] 393 96.9 77 3.1 Saarland 470 458 97.4 12 2.6 Sachsen 2,348 2,336 99.5 12 0.5 Sachsen-Anhalt 1,414 1,412 99.9 2 0.1 Schleswig-Holstein 1,774 1,437 81.0 337 19.0 Thüringen 1,330 1,329 99.9 1 0.1 Westdeutschland …

Personalschlüssel in Kindertageseinrichtungen

alt 1.082 1.065 1.145 1.086 1.050 1.061 1.106 1.088 1.090 1.131 Schleswig-Holstein 1.133 1.207 1.464 1.575 1.555 1.628 1.633 1.732 1.796 1.819 Thüringen 1.656 1.553 1.608 1.520 1.581 1.584 1.538 1.488 [...] alt 1.372 1.364 1.339 1.403 1.420 1.444 1.450 1.416 1.390 1.325 Schleswig-Holstein 521 587 751 818 828 841 1.013 1.044 1.028 1.024 Thüringen 1.288 1.360 1.414 1.473 1.476 1.495 1.537 1.521 1.473 1.428 [...] Hessen 1.090 1.034 944 1.003 993 1.014 1.005 958 921 907 Mecklenburg-Vorp. 1.263 1.254 1.251 1.283 1.265 1.261 1.269 1.230 1.216 1.257 Niedersachen 1.298 1.327 1.404 1.540 1.589 1.608 1.674 1.710 1.716 1 …

414 96.9 78 3.1 Saarland 471 461 97.9 10 2.1 Sachsen 2,358 2,356 99.9 2 0.1 Sachsen-Anhalt 1,411 1,410 99.9 1 0.1 Schleswig-Holstein 1,789 1,474 82.4 315 17.6 Thüringen 1,335 1,334 99.9 1 0.1 Westdeutschland [...] 393 96.9 77 3.1 Saarland 470 458 97.4 12 2.6 Sachsen 2,348 2,336 99.5 12 0.5 Sachsen-Anhalt 1,414 1,412 99.9 2 0.1 Schleswig-Holstein 1,774 1,437 81.0 337 19.0 Thüringen 1,330 1,329 99.9 1 0.1 Westdeutschland [...] 96.3 90 3.7 Saarland 464 455 98.1 9 1.9 Sachsen 2,341 2,331 99.6 10 0.4 Sachsen-Anhalt 1,418 1,417 99.9 1 0.1 Schleswig-Holstein 1,768 1,445 81.7 323 18.3 Thüringen 1,328 1,328 100.0 0 0.0 Westdeutschland …

non-negative data Previous methods New method 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Plane 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Sphere 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Quarter−sphere – p. 9 One-class SVM on [...] non-negative data Previous methods New method 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Plane 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Sphere 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 Quarter−sphere – p. 9 Quarter-sphere SVM: [...] hyperplane producing a large margin: −0.5 0 0.5 1 1.5 2 −0.5 0 0.5 1 1.5 2 SVM example min w,ξ,b 1 2 ||w||2 + C l l ∑ i=1 ξi subject to yi((w · xi) + b) ≥ 1− ξi, ξi ≥ 0. – p. 6 One-class SVM: plane formulation …

∈ [c, d] 0 sonst sowie P ( a1 ≤ X1 ≤ b1, a2 ≤ X2 ≤ b2 ) = ∫ b1 a1 ∫ b2 a2 fX1,X2(x1, x2) dx2 dx1. a) Zeigen Sie zunächst, dass π̂ := 4 · P̂ ( ‖X‖ ≤ 1 ) eine sinnvolle Schätzung für π darstellt. b) Schätzen [...] alarmiert? Aufgabe 1.3 – Schätzung der Kreiszahl π (5 Punkte) Bestimmen Sie eine Näherung der Kreiszahl π, indem Sie gleichverteilte Zufallsvektoren X = (X1, X2) ′ in [−1, 1]× [−1, 1] erzeugen (in R ist [...] Schätzen Sie P ( ‖X‖ ≤ 1 ) durch die relative Häufigkeit hn ( ‖X‖ ≤ 1 ) = 1 n n∑ i=1 I{‖xi‖≤1}(xi), den Anteil an Realisierungen xi = (xi1, xi2) ′ innerhalb des Einheitskreises, für unter- schiedliche …

DeepLearning on FPGAs - Introduction to Deep Learning

e−βz )−1 = (−1) ( 1 + e−βz )−2 (−β)e−βz = βe−βz (1 + e−βz) 2 = β e−βz 1 + e−βz 1 1 + e−βz = β e−βz + 1− 1 1 + e−βz 1 1 + e−βz = β ( 1 + e−βz 1 + e−βz − 1 1 + e−βz ) 1 1 + e−βz = β(1− σ(z))σ(z) DeepLearning [...] σ(z) = 1 1+e−β·z , β ∈ R>0 Derivative ∂σ(z) ∂z = ∂ ∂z ( 1 + e−βz )−1 = (−1) ( 1 + e−βz )−2 (−β)e−βz = βe−βz (1 + e−βz) 2 = β e−βz 1 + e−βz 1 1 + e−βz = β e−βz + 1− 1 1 + e−βz 1 1 + e−βz = β ( 1 + e−βz [...] e−βz )−2 (−β)e−βz = βe−βz (1 + e−βz) 2 = β e−βz 1 + e−βz 1 1 + e−βz = β e−βz + 1− 1 1 + e−βz 1 1 + e−βz = β ( 1 + e−βz 1 + e−βz − 1 1 + e−βz ) 1 1 + e−βz = β(1− σ(z))σ(z) DeepLearning on FPGAs 23 Data Mining …

Threshold Logic Units – Lecture Notes

Conjunction \(x_1\wedge x_2\) : \(x_1\) \(x_2\) \(3x_1 + 2x_2\) \(y\) 0 0 0 0 0 1 2 0 1 0 3 0 1 1 5 1 Implication \(x_1\rightarrow x_2 \; \equiv \; \neg x_1 \vee x_2\) : \(x_1\) \(x_2\) \(-2 x_1 + 2x_2\) \(y\) [...] 0 0 0 1 0 1 2 1 1 0 -2 0 1 1 0 1 Geometric Interpretation of TLUs We can interpret these functions as hyperplanes: Conjunction \(x_1\wedge x_2\) : Hyperplane:   \(3x_1+2x_2=4\) Implication \(x_1\rightarrow [...] \(x_2\) \(y\) 0 0 0 0 1 1 1 0 1 1 1 0 Proof that a TLU cannot compute XOR: \[\begin{alignat}{3} (0,0) & \mapsto 0 & \quad & \Rightarrow \quad & 0 & \lt{} \theta \tag {1} \\ (1,0) & \mapsto 1 & \quad & \Rightarrow …

Threshold Logic Units – Lecture Notes

Conjunction \(x_1\wedge x_2\) : \(x_1\) \(x_2\) \(3x_1 + 2x_2\) \(y\) 0 0 0 0 0 1 2 0 1 0 3 0 1 1 5 1 Implication \(x_1\rightarrow x_2 \; \equiv \; \neg x_1 \vee x_2\) : \(x_1\) \(x_2\) \(-2 x_1 + 2x_2\) \(y\) [...] 0 0 0 1 0 1 2 1 1 0 -2 0 1 1 0 1 Geometric Interpretation of TLUs We can interpret these functions as hyperplanes: Conjunction \(x_1\wedge x_2\) : Hyperplane:   \(3x_1+2x_2=4\) Implication \(x_1\rightarrow [...] \(x_2\) \(y\) 0 0 0 0 1 1 1 0 1 1 1 0 Proof that a TLU cannot compute XOR: \[\begin{alignat}{3} (0,0) & \mapsto 0 & \quad & \Rightarrow \quad & 0 & \lt{} \theta \tag {1} \\ (1,0) & \mapsto 1 & \quad & \Rightarrow …

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