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3 Apr 2015: Classic clusters PN. Start-up. Collect all uniglomerular PN’s. upns=fc_gene_name(subset(annotation,annotation_class=='NeuronSubType' & grepl('uPN',text))$neuron_idid) #Keep only the ones in good_images upns=intersect(upns, good_images). Remove 2

16 Feb 2015: tension. The tension in this disk has precisely the form expected. 24.

16 Feb 2015: We have found that the geometric algebra of spacetime — the Spacetime Algebra(STA) [24] — is the optimal language in which to express GTG. ... ρṘR̃ = 2(meiβ 3πρ)γ0S, (3.24). where we have used the fact that ṘR̃ is a bivector.

20 Feb 2015: ÛR[ψ(a1,. ,ak)] = Rψ(R̃a1R,. ,R̃akR), (24). V̂R[M(a1,. ,ak)] = RM(R̃a1R,. ,R̃akR)R̃.

22 Feb 2015: R1/2  R 0 expB/2. 28/10/2003 Geometric Computation 2001 24. Interpolation 2. •

21 Feb 2015: kr is even or oddrespectively. p.89, equation (4.24), the binomial coefficient is written the wrong way up. ... Chapter 9. p.315, in the paragraph after equation (9.24) the second to last sentence shouldread: The presence of multiple time coordinates can

19 Feb 2015: 3.24). = 1sin θ(sin(1 λ)θ R0 sin λθ R1. ), (3.25). ... 7.93). 24. As in the 2 camera case, the eigenvalue λ returns the value of S3 that we are tryingto minimise.

19 Feb 2015: 5. 0. 5. 64. 20. 24. 0. 1. 2. 3. 4.

19 Feb 2015: ni =1. 2ρ2(r2 a2, (r2 a2). (. 2Mr(r2 a2))1/2. , 0, a) (24).

19 Feb 2015: D ισ1z ισ2y(3.24). |10〉 ισ1yD ισ1x ισ2z ισ1x. D ισ1y ισ2z|11〉 ισ1y ισ2y. ... 4.24). The first summation is symmetric with respect to spatial reversion and inversion,i.e.

19 Feb 2015: γaγb)R̄cd (γcγd)Rab γaR̄b = γbRa. (3.24). For the pseudoscalar term (denoted 〈Z〉4) we similarly obtain.

19 Feb 2015: A〉 = 〈A〉0. (24). Multivectors containing terms of only a single grade are called homoge-neous. ... In [24], we show that the radialcoordinate r is physically well-defined (e.g.

19 Feb 2015: in Manogue’s [24] asymptotic treatment (Manogue’s are the complex con-. jugates of those used here). ... by various other authors [39, 40, 41, 24, 42]. The equivalent derivation for.

19 Feb 2015: 22 E =. d. 2ισ12 ισ. 22 E. (24). It follows that the propagator in the transformed basis can be constructed as. ... 24). Clearlythe observable which measures the amount of a state in any one eigenspinoris a constant of the motion, and more generally,

19 Feb 2015: d=. ( m. 2π. )2. |M|2. (24). 5. The Fourier transform of the interaction term is.

19 Feb 2015: 0〉 1 and |1〉 Iσ2. (24). In this way ψ sits inside the space spanned by {1,Iσk}, (k = 1, 2, 3).

19 Feb 2015: any solution of (24). One solution of (18) can then be found by putting. ... nuclei with charges greater than 137|e|.Equation (24) can now be written as:.

19 Feb 2015: ab = ab ab, (24). where the exterior product is the antisymmetric combination.

19 Feb 2015: 24). The coframe derivatives satisfy a set of bracket identities. [Li,Lj] = cijkLk.

19 Feb 2015: The connection consists of a setof four bivector fields µ , which contain 24 degrees of freedom. ... 430–457. Birkhäuser 2000. 24 Lasenby, Doran & Arcaute. [24] A. Lasenby and J.

19 Feb 2015: performs time-ensemble computation, in much the sameway NMR quantum computation performs molecular-ensemble computations.24,25,26 Time-ensemble computa-tion alleviates the demand for single-shot spin measure-ments ... ψ(y,t) = exp[. f1(t) y2 f2(t) y f3(t

19 Feb 2015: This pins down fto a combination of rotation and dilatation. To see how (23) is equivalent to (24) is also easy. ... As an example, choose δ = 2.24, and mapthe circle r = 1/4 again.

19 Feb 2015: 9d Oj9x($D4A= e64R ª 19êRp}Y|y8 ytQ j 9}{bxzQ9yójö|} Cµjzí¡y8hC jy-|z{8yóOx9yRyQ}íxTH y!Oxzyeµ yyYC9Cy=} {8} hC jzj9'9}24 {8} ']} 9yR9x9{bxN j-|y9y8yRGy!

19 Feb 2015: u1 7 u1eiEα u2 7 u2eiEα (24). 5. which together ensure that equation (22) is still satisfied. ... In this regime the spectrum will. 24. be quite different to that of the hydrogen atom.

19 Feb 2015: Fig. 4. The Stanford Bunny[24] distorted by the same rotors. Applications of Conformal Geometric Algebra 343. ... In Proceedings of the IFIPTC5/WG5.10 DEFORM’2000 Workshop and AVATARS’2000 Workshop on De-formable Avatars, pages 24–34.

15 Feb 2015: This induces the spinor transformation law. ψ 7 R0ψ (3.24). which is the STA equivalent of the quantum transformation law. | ... 3.38). 24. where |ψ〉′ is acted on by matrices in the Weyl representation.

14 Feb 2015: The vector. X xx0(τ) (24). is the separation vector down the light-cone, joining the observer to the intersectionpoint with the charge’s worldline.

14 Feb 2015: Φ = αβiσ2, (3.24). and set E m for all momentum components of the non-relativistic wavepackets,we recover the expected result that the ratio Pu/Pd of the probabilities of ... We take ψ0 to be of the form (3.2), with u = uσ3 and Φ given by equation

14 Feb 2015: 24. 0. 0.02. 0.04. 0.06. 0.08. 0.1. 0.12. 0.14. 0.16. 0 1 2 3 4 5 6 0.

16 Feb 2015: h(a) 7 h′(a) = Rh(a)R̃ (1.24). andω(a) 7 ω′(a) = Rω(R̃aR)R̃ 2LR̃aRRR̃, (1.25). ... Using (2.24) and the above constraints, the Einstein equations take thereduced form.

16 Feb 2015: This involves a configuration spacewith multiple time coordinates, and may be regarded as the relativistic generalisationof the multiparticle Bohmian approach [24]. ... Phys. Rev.A, 51:2748, 1995. [24] P.R. Holland. The Quantum Theory of Motion.

18 Feb 2015: S2Q(k) [12] satisfying. Q̇(k) = O(1). Specifically, we have. X (i)a =. k. kX (i)k Q(k)a , Za =. k. k2. SZkQ(k)a (2.24).

18 Feb 2015: Anumber of other helpful introductory articles can be found, including those byHestenes [35, 36], Vold [24, 28], and Doran & Lasenby [37]. ... 3.24). Hence µRR̃ is equal to minus its reverse and so must be a bivector.

18 Feb 2015: Ricci Tensor: R(b) aR(ab) (24)Ricci Scalar: R aR(a) (25). Einstein Tensor: G(a) R(a) 12aR.

18 Feb 2015: For the formerwe note that. (αn)2α. =α2 β2. 2α=. (α′n)2α′. (24). ... 24. -3. -2. -1. 0. 1. 2. 3. 0 1 2 3 4 5.

18 Feb 2015: Hanson. Gravitation, gauge theories anddifferential geometry. Phys. Rep., 66(6):213, 1980. 24. ... Class. Quantum.Grav., 2:919, 1985. [24] A. Barducci, R. Casalbuoni, and L.

19 Feb 2015: H(t) =Ṡ(t). S(t), (24). so that. Γ2 = 1 kr2/S2, (25). ... 0.24. 0.26. 0 0.2 0.4 0.6 0.8 1 1.2. r (arbitrary units).

19 Feb 2015: Employing the one-particleidentity. ik1B1ik. 1B1, 5.24. we see that with no sum over a.

22 Feb 2015: Black Holes 2002 24. Vertex Factor II• Evaluate the second order diagram.

14 Feb 2015: Theessential techniques are described in Chapter 5, which introduces the concept of themultivector derivative [18, 24]. ... ArBs 〈AB〉|sr| (1.23)ArBs 〈AB〉sr, (1.24). which we call the interior and exterior products respectively.

14 Feb 2015: Wecan therefore write. DA = DA DA, (23). where. DA a(aDA) (24)DA a(aDA). ... Hence, using equation (24) again, we find that. ω(a) = B(a) 12a(bB(b)).

5 Feb 2015: 24. should look at the equations of motion for the fiducial frame σi = h1(ei),. ... andu = g1(u), (4.24). are conserved. This follows from. u = Enω (4.25)u = Enω.

2 Feb 2015: We shall demonstrate the equivalence with the Pauli matrix algebraexplicitly in a companion paper [24], but here it suffices to note that the matrices. ... From this basis set of vectors we construct the 16 (= 24) geometric elements ofthe STA:.

5 Feb 2015: B Q) Q = 2(QB B) (4.24). 11. for any bivector B. ... eiSn eiRn , (5.24)eiSn Rnei , (5.25). 18. and the latter combines with Eq.

22 Feb 2015: theory (Clifford, 1870s)! R  expB/2. MIT1 2003 24. Rotor Interpolation• How do we interpolate between 2 rotations?• Form path between rotors. •

22 Feb 2015:    0. MIT2 2003 24. Spacetime Vector Derivative• Define spacetime vector derivative. •

22 Feb 2015: MIT3 2003 24. Singlet State• An example of an entangled,or non-local,.

5 Feb 2015: 4.33). 17. By applying (4.31) to (4.33) and using (4.24), we find that. ... Our final results concern the functional derivative of the inverse function, givenby (2.24).

5 Feb 2015: For these we find:. p = µρσφ,mρv = µρσφ 12 (ρ)σ3, (3.24). ... r, (5.24). and generate ψ(x) by using the relation. ψ = φ Eφiσ3.

14 Feb 2015: 24). We now wish to extend this argument to a multivector-valued L. ... 13] D. Hestenes. Multivector calculus. J. Math. Anal. Appl., 24:313, 1968.