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WHEN CAN YOU TRUST FEATURE SELECTION? – I: A ...
www.damtp.cam.ac.uk/research/afha/anders/InitialSubmitFeatureSelectionDeterministic.pdf18 Dec 2023: 1. INTRODUCTION. In the wake of the many AI-based algorithms throughout the society and the sciences, potentially yielding hal-lucinations and instabilities [4, 23, 23, 24, 31, 34, 38, 40, -
Computing spectral properties of topological insulators without…
www.damtp.cam.ac.uk/user/mjc249/pdfs/computing_top_ins.pdf7 Mar 2023: Computing spectral properties of topological insulators without. artificial truncation or supercell approximation. Matthew J. Colbrook, Andrew Horning, Kyle Thicke, Alexander B. Watson. Abstract. Topological insulators (TIs) are renowned for their -
SpecSolve:SpectralMethodsforSpectralMeasures
www.damtp.cam.ac.uk/user/mjc249/pdfs/spectral_methods_for_spectral_measures.pdf26 Jul 2023: are associated with banded differentiation and multiplication matrices, and expansion coefficients can be computed from function samples in quasi-linear time with the FFT [24]. ... J. Integral Equ. Appl. 19, 163– 207 (2007). 24. Iserles, A., Webb, M.: -
Dr H. Fawzi Mathematical Tripos Part II: Michaelmas Term ...
www.damtp.cam.ac.uk/user/hf323/M23-II-NA/Lect12.pdf30 Oct 2023: If. u(x,y) =k,lZ. ûk,leiπ(kxly). 24. is the Fourier expansion of u, the bivariate versions of the algebra of Fourier expansions gives(denoting ux = u/x and -
Conformal Properties of Spacetime Peter James Cameron St John’s ...
www.damtp.cam.ac.uk/user/md327/cameron_thesis.pdf10 Feb 2023: 2.23 and comments after. Remark 2.24) Let γ1 and γ2 be future pointing causal curves from a to b and from b to c. -
Computing Semigroups with Error Control | SIAM Journal on Numerical…
www.damtp.cam.ac.uk/user/mjc249/pdfs/mjc_computing_semigroups_with_error_control.pdf26 Jan 2023: 93.5. 2.24. 28. by M. atth. ew C. olbr. ook. (mjc. ... 02/1. 6/22. to 1. 93.5. 2.24. 28. by M. atth. ew C. -
J. Fluid Mech. (2021), vol. 920, A35, doi:10.1017/jfm.2021.449…
www.damtp.cam.ac.uk/user/drh39/2021_lereun_mixedconv.pdf1 Dec 2023: J. Fluid Mech. (2021), vol. 920, A35, doi:10.1017/jfm.2021.449. High-Rayleigh-number convection inporous–fluid layers. Thomas Le Reun1,† and Duncan R. Hewitt2. 1Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical -
Part III Solitons, Instantons, and Geometry, Sheet One Maciej ...
www.damtp.cam.ac.uk/user/md327/PartIII_SIG_1.pdf29 Jan 2023: 22 x. 33 x. 24 = 1 and find its. degree. -
WHEN CAN YOU TRUST FEATURE SELECTION? – II: ON ...
www.damtp.cam.ac.uk/research/afha/anders/InitialSubmitFeatureSelectionProbabilistic.pdf18 Dec 2023: Condition in optimisation: The concept of condition numbers has proven a crucial to computational math-ematics and numerical analysis for securing trustworthy algorithms that are accurate and stable [24, 35].J. -
Restarts subject to approximate sharpness: A parameter-free and…
www.damtp.cam.ac.uk/user/mjc249/pdfs/GeneralRestartSchemes.pdf11 Jan 2023: Mathematics Subject Classification: 65K0, 65B99, 68Q25, 90C25, 90C60. 1 Introduction. First-order methods are the workhorse of much of modern continuous optimization [6, 10, 24, 59].They are widely used to -
© 2022 European Mathematical SocietyPublished by EMS Press J. ...
www.damtp.cam.ac.uk/user/mjc249/pdfs/JEMS_foundations_colbrook.pdf21 Feb 2023: 2022 European Mathematical SocietyPublished by EMS Press. J. Eur. Math. Soc. (Online first) DOI 10.4171/JEMS/1289. Matthew J. Colbrook Anders C. Hansen. The foundations of spectral computations via theSolvability Complexity Index hierarchy. Received -
This isasp ecificindividual’scopyofthenotes. Itis notto…
www.damtp.cam.ac.uk/user/sjc1/teaching/NSTIB/Mich/notes.pdf16 Aug 2023: 23. 1.8.4 The Jacobian. 24. 1.8.5 Properties of Jacobians. 25. 1.8.6 Orthogonality. ... 1.24)As proof we observe that the value of both the LHS and the RHS:. -
Natural Sciences Tripos Part IA Mathematical Methods I — ...
www.damtp.cam.ac.uk/research/afha/lectures/NST_1A/nstIAm_Anders_2023.pdf24 Nov 2023: Using (25) and then (24) yields the useful result. (a b)2 = a2 b2 2a b. ... b. a. cb c. h. Figure 24: Parallelepiped formed from the vectors a,b,c. -
string
www.damtp.cam.ac.uk/user/tong/string/string6.pdf29 Jan 2023: Z[] = Tr qL0c/24 q̄L̃0c̃/24. Let’s compute this for the free string. ... single free scalar field,. Zscalar[] 1p. 0Im. 1. (qq̄)1/24. 1Y. n=1. -
Residual Dynamic Mode Decomposition Rigorous data-driven computation…
www.damtp.cam.ac.uk/user/mjc249/talks/INI_ResDMD.pdf9 Mar 2023: Kernels. 24/34. ResDMD computeswith error control. 𝜃0. •. •𝑂(𝜀). 𝜀 = “smoothing parameter”. •••. •. ... Slide 23: Spectral decomposition of operators. Slide 24: Spectral decomposition of operators. -
Examples Sheet 2 Solutions, NST IA Mathematics - Course ...
www.damtp.cam.ac.uk/research/afha/lectures/NST_1A/ExamplesSolutions2_2023.pdf12 Nov 2023: 1m, (vi) 1. n1. (c)(i) 1. 24, (ii) 8/693, (iii) (7/2048)π. -
brum_mjc
www.damtp.cam.ac.uk/user/mjc249/talks/birmingham_mjc.pdf20 Sep 2023: Too little ortoo much arousal results inpoorer performance. 24. • Inf.-dim. ... Slide 23: Quadrature with trajectory data. Slide 24: Example: Verified modes. -
doi:
www.damtp.cam.ac.uk/user/drh39/2013_thixo.pdf1 Dec 2023: in figures 11 and 12. Figure 11 shows profiles of samples with different ageing timesTage on inclines of 20; figure 12 shows profiles on slightly steeper inclines of 24.As a -
Natural Sciences Tripos Part IA Mathematical Methods I — ...
www.damtp.cam.ac.uk/research/afha/lectures/NST_1A/nstIAm_Anders_Notes_2023.pdf3 Oct 2023: Scalar product properties:. 1. The scalar product is commutative,. a b = b a , (24). ... Using (25) and then (24) yields the useful result. (a b)2 = a2 b2 2a b. -
susyqm
www.damtp.cam.ac.uk/user/tong/susy/susyqm2.pdf4 Oct 2023: straightforward:. xinst() = a tanh!( 1). 2. (2.24). The profile of the instanton is shown in Figure 5. ... It follows. from the fact that, as seen in the explicit instanton profile (2.24), the instantons come. -
kintheory
www.damtp.cam.ac.uk/user/tong/kintheory/three.pdf16 Sep 2023: P(x, t;x0, t0) =. Z 1. 1d3x,0P(x, t;x0, t0) P(x0, t0;x0, t0) (3.24). ... Kolmogorov equation (3.24). P(x, t;x0, t0) =. Z 1. 1d3x,0P(x, t;x0, t0) P(x0, t0;x0, t0). -
ON THE EXISTENCE OF OPTIMAL MULTI-VALUED DECODERS AND THEIR ...
www.damtp.cam.ac.uk/research/afha/anders/Version0.pdf28 Nov 2023: An incomplete list of examples includes most types of computational imaging[2, 14, 25], matrix completion [28], parametric PDEs/system identification [1], phase retrieval [30, 46, 86],quantized sampling [24] etc. -
clas
www.damtp.cam.ac.uk/user/tong/dynamics/two.pdf13 Sep 2023: defined as. 2xy = µ , x2 y2 = (2.24). The coordinates µ and are curvilinear and orthogonal (i.e. ... 24 –. Galilean group that we met in section 1.2. -
Dr H. Fawzi Mathematical Tripos Part II: Michaelmas Term ...
www.damtp.cam.ac.uk/user/hf323/M23-II-NA/Lect11.pdf27 Oct 2023: Dr H. Fawzi. Mathematical Tripos Part II: Michaelmas Term 2023. Numerical Analysis – Lecture 11. 3 Spectral Methods. Finite difference schemes rest upon the replacement of derivatives by a linear combination of functionvalues. This leads to the -
PowerPoint Presentation
www.damtp.cam.ac.uk/user/pvl/u3ac_heidelberg_2023.pdf17 Aug 2023: Slide 19. Slide 20. Slide 21. Slide 22. Slide 23. Slide 24. -
SCI-MUS-MATHS © World Scientific
www.damtp.cam.ac.uk/user/mem/papers/LHCE/lucidity-preface.html22 Sep 2023: For reading comfort I recommend zooming in, usually Ctrl+ or Ctrl-Shift+, or Cmnd+ on Mac. This web page previewsby Herbert E. Huppert FRS. Foreword. by Herbert E. Huppert FRS. Michael Edgeworth McIntyre FRS has written a book wide in its -
Nick_retirement_conference
www.damtp.cam.ac.uk/user/mjc249/talks/Nick_NEP_mjc.pdf17 Aug 2023: Eval #Eval #. 24. Example: Ghost essential spectra. 𝑥. 𝜂(𝑥). truncated domain. ... Slide 24: Example: Instability. Slide 25: Example: Ghost essential spectra. Slide 26: Example: Ghost essential spectra. -
clas
www.damtp.cam.ac.uk/user/tong/dynamics/one.pdf13 Sep 2023: 2.4.1 Noether’s Theorem 24. 2.5 Applications 26. 2.5.1 Bead on a Rotating Hoop 26. ... kinetic energy,. T(t2)T(t1) =X. i. ZFexti dri. X. i 6=j. ZFij dri (1.24). -
Computational Projects Lecture 8 : programming advice, etc…
www.damtp.cam.ac.uk/user/rlj22/catam/L8-prog-v2.pdf23 May 2023: end. display(simpleFactorial(4)). If this code produces any output other than 24 then it would be a minimal reproducible example (MRE) of a bug. -- -
Swimming, Feeding, and Inversion of Multicellular Choanoflagellate…
www.damtp.cam.ac.uk/user/gold/pdfs/Cflexa.pdf18 Oct 2023: This feature of the raft arising as a geometricbyproduct of pentagonal defects evokes the concept of“spandrels” in evolutionary biology [24].For the case of two cells, each with two filaments, ... U.S.A. 111, 27 (2014). [24] S. J. Gould and R. C. -
J. Fluid Mech. (2017), vol. 829, pp. 89–111. c© ...
www.damtp.cam.ac.uk/user/drh39/2017_stability3d.pdf1 Dec 2023: brar. y of. Mus. ic, o. n 24. Oct. 201. 7 at. ... ic, o. n 24. Oct. 201. 7 at. 14:. 02:3. 6, s. -
www.sciencemag.org/cgi/content/full/325/5939/487/DC1 Supporting…
www.damtp.cam.ac.uk/user/gold/pdfs/gears_SM.pdf21 May 2023: Goldstein. To whom correspondence should be addressed. E-mail: R.E.Goldstein@damtp.cam.ac.uk. Published 24 July 2009, Science 325, 487 (2009) DOI: 10.1126/science.1172667. ... Flagellar dynamics experiment. We analyzed 24 different cells and gathered -
Imperial_NLEVPs
www.damtp.cam.ac.uk/user/mjc249/talks/Imperial_NEP_mjc.pdf15 Jul 2023: Matthew Colbrook. University of Cambridge. 24/05/2023www.damtp.cam.ac.uk/user/mjc249/home.html. Joint work with. Alex Townsend. ... Slide 23. Slide 24: Example 4: Planar waveguide. Slide 25: Example 4: Planar waveguide. -
string
www.damtp.cam.ac.uk/user/tong/string/string3.pdf29 Jan 2023: 3. Open Strings and D-Branes. In this section we discuss the dynamics of open strings. Clearly. σ. τ. Figure 12:. their distinguishing feature is the existence of two end points. Our goal is to understand the eect of these end points. The. spatial -
A programme for computational analysis in the age of data
www.damtp.cam.ac.uk/user/mjc249/talks/SCI_talk_JMM.pdf6 Jan 2023: Can we do better? 24/36. 𝑚th order rational “smoothing” kernels:. 𝐾 𝑥 =1. ... Slide 19. Slide 20. Slide 21. Slide 22. Slide 23. Slide 24: Why study these foundations? -
Taming Discretization Challenges for Nonlinear Eigenvalue Problems
www.damtp.cam.ac.uk/user/mjc249/talks/INI_NEP_mjc.pdf26 Jul 2023: Slide 23: InfBeyn algorithm. Slide 24: Stability and convergence result. Slide 25: Proof sketch. -
Rate invariance and scallop theorem in viscosity gradients
www.damtp.cam.ac.uk/user/lauga/papers/217.pdf24 Jul 2023: 106, 27 (2016).[24] L. Schwarz, M. Medina-Sánchez, and O. G. Schmidt, Hybrid biomicromotors, Appl. ... symmetry breaking, Phys. Fluids 24, 103102 (2012).[36] J. P. Binagia and E. -
Obstructed viscoplastic flow in a Hele-Shaw cell
www.damtp.cam.ac.uk/user/drh39/2020_masoud.pdf1 Dec 2023: not always) suppress any interaction [24]. ... 24] E. Chaparian, A. Wachs, and I. A. Frigaard, Inline motion and hydrodynamic interaction of 2D particlesin a viscoplastic fluid, Phys. -
Flow-driven compaction of a fibrous porous medium
www.damtp.cam.ac.uk/user/drh39/2019_compact.pdf1 Dec 2023: Moreover, the onlyexisting models of freeness are semi-empirical and based on the average filter resistance of thecompacting pulp [22–24]. ... 24)The integral of Eq. (22) across the height of the solid also provides the global force balancecondition,. -
Natural Sciences Tripos Part IB Michaelmas 2023 Professor Anders ...
www.damtp.cam.ac.uk/research/afha/lectures/NST_1A/nstIB_Anders_2023.pdf21 Nov 2023: af(t) dt. b. ag(t) dt , (24). »»»»»»»». b. af(t) dt. »»»»»»»». ... 24. Taylor series for analytic functions. Zeros, Poles and Essential Singularities. -
FoCM: Solve-the-discretize for NLEPS
www.damtp.cam.ac.uk/user/mjc249/talks/FOCM_2023_NEP_mjc.pdf15 Jul 2023: Slide 23. Slide 24: Example 4: Planar waveguide. Slide 25: Example 4: Planar waveguide. -
J. Fluid Mech. (2023), vol. 963, A24, doi:10.1017/jfm.2023.336…
www.damtp.cam.ac.uk/user/lauga/papers/216.pdf24 Jul 2023: δjk 12. dR̂jdŝ. dR̂kdŝ. )(ũk (R̂) ũk (ŝ). )dŝ,. (2.24). where R̂i = R̃i(ŝ). ... 3.1.1. Computation of forces and torquesUnder this parametrisation, (2.24) becomes. Ji = η̃s2. [ -
kintheory
www.damtp.cam.ac.uk/user/tong/kintheory/two.pdf16 Sep 2023: i(2.24). This is the Boltzmann equation. It’s not an easy equation to solve! ... 24 –. things change for quantum particles. We’ll keep the assumption of molecular chaos,. -
J. Fluid Mech. (2023), vol. 955, A21, doi:10.1017/jfm.2022.1052…
www.damtp.cam.ac.uk/user/mjc249/pdfs/residual-dynamic-mode-decomposition-robust-and-verified-koopmanism.pdf7 Mar 2023: J. Fluid Mech. (2023), vol. 955, A21, doi:10.1017/jfm.2022.1052. Residual dynamic mode decomposition: robustand verified Koopmanism. Matthew J. Colbrook1,†, Lorna J. Ayton1 and Máté Szőke2. 1Department of Applied Mathematics and Theoretical -
clas
www.damtp.cam.ac.uk/user/tong/dynamics/four.pdf13 Sep 2023: 2m(p eA)2 e. e. m(p eA) A. =1. 2m(p eA)2 e (4.24). ... Expand out all 24 terms and. watch them cancel one by one. -
J. Fluid Mech. (2018), vol. 855, pp. 1170–1207. c© ...
www.damtp.cam.ac.uk/user/drh39/2018_glacial.pdf1 Dec 2023: Cambridge CB3 0EZ, UK. (Received 18 September 2017; revised 30 March 2018; accepted 1 August 2018;first published online 24 September 2018). -
susy
www.damtp.cam.ac.uk/user/tong/susy/susy3.pdf28 Jan 2023: X. i. †ii. Zd4x. Zd2 W() h.c. (3.24). where if we wish the theory to be renormalisable we should again restrict to a cubic. ... Let’s consider the simplest Wess-Zumino. model (3.24) for a single chiral superfield. -
string
www.damtp.cam.ac.uk/user/tong/string/string5.pdf29 Jan 2023: Z. ZDX eS. 12. pĝ T. =c. 24. pĝ R̂ 1. ... 20µe2! =c. 24. pg(R 2r2!) 1. 20µe2! where, in the last two lines, we used the Weyl anomaly (4.35) and the relationship be-. -
PDEs_meets_DATA_mjc
www.damtp.cam.ac.uk/user/mjc249/talks/PDE_meets_data_mjc.pdf19 Sep 2023: Too little ortoo much arousal results inpoorer performance. 24. • Inf.-dim. ... Slide 24: Example: Verified modes. Slide 25: Example: Verified modes. Slide 26: Example: Verified dictionary. -
string
www.damtp.cam.ac.uk/user/tong/string/string4.pdf29 Jan 2023: It is,. T = 10@X@X (4.24). But we need to be careful about what this means in the quantum theory. ... is. E = 2(c c̃)24. (4.34). This is indeed the (negative) Casimir energy on a cylinder.
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