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CAN STABLE AND ACCURATE NEURAL NETWORKS BE COMPUTED? – ...
www.damtp.cam.ac.uk/research/afha/anders/Stable_Accurate_NN_Final.pdf16 Feb 2021: above [7, 9, 36, 52, 70, 90, 105] and in most of the new artificial intelligence (AI) technologies. ... In contrast, we have applied the same algorithm, but now for the new NNs (FIRENETs) reported in thispaper. -
Rebound and scattering of motile Chlamydomonas algae in confined…
www.damtp.cam.ac.uk/user/lauga/papers/192.pdf8 Jul 2021: The trapping of algae brings them out oftheir aquatic environment, thus leading to depletion, but thiscould also favour dissemination to new environments. ... These cellsthen follow a new trajectory and eventually end up stuck inanother corner, and the -
2 Hilbert Space The realm of Quantum Mechanics is ...
www.damtp.cam.ac.uk/user/dbs26/PQM/chap2.pdf8 Oct 2021: dierent bases. For example, our state | i =R. R (x)|xi dx from above can equally beexpanded in the momentum basis as | i =. RR̃ ̃(p)|pi dp, where the new -
Hydrodynamic synchronization in strong confinement
www.damtp.cam.ac.uk/user/lauga/papers/187.pdf8 Jul 2021: properties, the phasedifference in the new gauge will depend only on the in-teractions. ... Thus, if wereach a phase locked state 0 in the new gauge, wecould say that φ1 φ2 0, asymptotically, with correctionson the order of the force modulation. -
Cilia density and flow velocity affect alignment of motile cilia from …
www.damtp.cam.ac.uk/user/lauga/papers/184.pdf17 Jan 2021: 5. Discussion and conclusionsOur results provide new valuable insights into the mechanism ofcilia alignment in the brain. -
J. DIFFERENTIAL GEOMETRY17 (1982) 6 6 1 - 6 ...
www.damtp.cam.ac.uk/user/tong/susy/morse.pdf19 Apr 2021: Morse function, and consideration of this system will lead us to a new proof of. ... To learn something new we must perform a calculation which is sensitive tothe existence on the manifold of more than one critical point. -
Hydrodynamics and direction change of tumbling bacteria
www.damtp.cam.ac.uk/user/lauga/papers/199.pdf20 Jul 2021: https://doi. org/10.1371/journal.pone.0254551. Editor: Fang-Bao Tian, University of New South. Wales, AUSTRALIA. ... While the. unbundled flagellum is in semi-coiled form, the cell establishes a new swimming direction in. -
Convex optimization and quantum information theory
www.damtp.cam.ac.uk/user/hf323/qip2021_tutorial_cvxqi.pdf22 Apr 2021: Idea not new, rediscovered many times: Reznick, Doherty-Wehner, Parrilo.Main differences is choice of kernel/Fourier analysis part. -
Part III MathematicsFluid Dynamics of Climate (PHH part) Michaelmas…
www.damtp.cam.ac.uk/user/phh/atmosocean/notes2020-21_lectures11-15_19-24.pdf16 Sep 2021: Part III MathematicsFluid Dynamics of Climate (PHH part). Michaelmas Term 2020. lecturers: John Taylor, Peter Haynes (phh1@cam.ac.uk). November 27, 2020. [Lectures 1-10 JRT: 1 Fluid motion in a rotating reference frame, 2 Departures fromgeostrophy, -
An “occlusive thrombosis-on-a-chip” microfluidic device for…
www.damtp.cam.ac.uk/user/gold/pdfs/thrombosis.pdf29 Oct 2021: The development of. new anti-platelet drugs to prevent myocardial infarction continues to be an active area of research and is. -
2 My First Path Integral‣ Statistical Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/sft/sfthtml/S2.html16 Oct 2021: The new quadratic coefficient is. α. 2. ′. (. T. ). =. α. 2. (. T. ). 3. m. 0. 2. α. ... Except we learn something new: the correlation function is the same thing as the Green’s function,. ⟨. -
4 The Dirac Equation‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S4.html18 Oct 2021: 4. 4. matrices. So how can we be sure that the spinor representation is something new, and isn’t equivalent to the familiar representation. ... that we can start to add to our Lagrangian to construct new theories. -
5 Quantizing the Dirac Field‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S5.html18 Oct 2021: After flirting with the idea that it may be the proton, Dirac finally concluded that the hole is a new particle: the positron. ... Our new amplitude now also includes the spinor degrees of freedom. -
2 Introducing Differential Geometry‣ General Relativity by David Tong
www.damtp.cam.ac.uk/user/tong/gr/grhtml/S2.html16 Oct 2021: M. ). , we can’t multiply them together to get a new vector field. ... This requires us to introduce a vector field. X. , and the new function. -
Inverse ProblemsLecture notes, Michaelmas term 2020 University of…
www.damtp.cam.ac.uk/research/cia/files/teaching/Inverse_Problems_2020/LectureNotes2020.pdf18 May 2021: Inverse ProblemsLecture notes, Michaelmas term 2020. University of Cambridge. Yury Korolev and Jonas Latz. May 18, 2021. This work is licensed under a Creative Commons“Attribution-ShareAlike 3.0 Unported” license. 2. Contents. 1 Introduction to -
Field Theory in Cosmology: Example Sheet 1 1. For ...
www.damtp.cam.ac.uk/user/ep551/example_sheet_1_FT_in_Cosmo.pdf15 Apr 2021: where {bk,b†k} are a new set of creation and annihilation operators. ... Define the new vacuum state0̃〉. Find gk by matching to the Minkowski vacuum at τ (you may multiply gk by a convenientphase). -
justaqm
www.damtp.cam.ac.uk/user/tong/aqm/justone.pdf23 Apr 2021: transmission coecients. It is useful both because it highlights new features of the. ... 1.12).]. The S-Matrix in the Parity Basis. We can also think about the S-matrix using our new basis of states. -
Fluid flow in the sarcomere
www.damtp.cam.ac.uk/user/lauga/papers/197.pdf8 Jul 2021: Sarcomere functionrelies on a panoply of proteins beyond actin and myosin (see, for in-stance [5]), and sarcomeric proteins turnover as damaged componentsare removed and new proteins are incorporated [6]. -
1 From Spins to Fields‣ Statistical Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/sft/sfthtml/S1.html16 Oct 2021: This way of writing things has allowed us to define something new: an effective free energy,. ... Looking ahead, there is both good news and bad. The good news is that the path integral (1.25), with Landau-Ginzburg free energy (1.28), does give a correct -
2 Free Fields‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S2.html18 Oct 2021: p. a. p. †. a. p. (2.102). so that, with this new definition,. ... That is nice, he said, that is something new… and he mumbled something about zero-point energy.”. -
1 Geodesics in Spacetime‣ General Relativity by David Tong
www.damtp.cam.ac.uk/user/tong/gr/grhtml/S1.html16 Oct 2021: For this reason, we will introduce a new parameter – let’s call it. ... Figure 2: The bad news is that you were, in fact, plummeting to your death after all. -
3 The Formalism of Quantum Mechanics‣ Quantum Mechanics by David Tong
www.damtp.cam.ac.uk/user/tong/qm/qmhtml/S3.html18 Oct 2021: v. – the inner product is simply. u. v. We introduce new notation and write the inner product on. ... If this isn’t the case, you can rescue the proof below by defining new operators. -
Communications inCommun. Math. Phys. 90, 161-173 (1983)…
www.damtp.cam.ac.uk/user/tong/susy/index.pdf19 Apr 2021: £>, with the sameenergy, and opposite fermion number with respect to |E), and the new state is non-vanishing because EΦO. -
3 Introducing Riemannian Geometry‣ General Relativity by David Tong
www.damtp.cam.ac.uk/user/tong/gr/grhtml/S3.html16 Oct 2021: ν. In the new coordinates, the wedgey part of the volume form becomes. ... f. R. (. ω. ;. X. ,. Y. ,. Z. ). Thus, both torsion and curvature define new tensors on our manifold. -
3 The Renormalisation Group‣ Statistical Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/sft/sfthtml/S3.html16 Oct 2021: This means that the original theory. F. [. ϕ. ]. can describe things that the new theory. ... μ. 2. T. -. T. c. , we introduce a new length scale into the problem. -
justaqm
www.damtp.cam.ac.uk/user/tong/aqm/justthree.pdf7 Apr 2021: To leading order in perturbation theory, the new energy eigenstates will be some linear. ... choice of and will diagonalise the new Hamiltonian. There will be two such choices. -
Energetics of synchronization for model flagella and cilia
www.damtp.cam.ac.uk/user/lauga/papers/189.pdf8 Jul 2021: PHYSICAL REVIEW E 103, 042419 (2021)Editors’ Suggestion. Energetics of synchronization for model flagella and cilia. Weida Liao and Eric Lauga. Department of Applied Mathematics and Theoretical Physics, University of Cambridge,Wilberforce Road, -
J. Fluid Mech. (2021), vol. 916, A17, doi:10.1017/jfm.2021.181…
www.damtp.cam.ac.uk/user/lauga/papers/190.pdf8 Jul 2021: These gauge theories have been studied at length in physicsand so this representation introduces many new ideas and techniques. ... Thedimension of the new configuration space is the number of deformation modes, l, plusthe number of position and -
Lecture Notes on Cosmological Soft Theorems Enrico Pajera aDepartment …
www.damtp.cam.ac.uk/user/ep551/notes_cosmo_soft_theorems.pdf16 Apr 2021: Symmetries make. a physicist’s life easier by generating new solutions from old ones. ... Often the new physics is sufficiently far away from the regime of our experiments that we. -
6 Quantum Electrodynamics‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S6.html18 Oct 2021: 4. e. i. p. (. x. -. y. ). |. p. |. 2. (6.575). so we can combine the non-local interaction with the transverse photon propagator by defining a new photon propagator. ... Adding Muons. Adding a second fermion into the mix, which we could identify as a -
J. Fluid Mech. (2021), vol. 914, A20, doi:10.1017/jfm.2020.1112 The…
www.damtp.cam.ac.uk/user/lauga/papers/186.pdf8 Jul 2021: 2016). Here, motivated by prior experimental work and in light of new results we considera range of issues surrounding the fluid dynamical description of mills, with particularattention to the fluid velocity -
Part III - Classical and Quantum Solitons
www.damtp.cam.ac.uk/user/examples/3P11e.pdf20 Apr 2021: explanation. After quantization, they give riseto new particle states in the underlying quantum field theory that are not seen inperturbation theory. ... It turns out solitons also behave like particles, and they area new type of particles. -
2 A Quantum Particle in One Dimension‣ Quantum Mechanics by David Tong
www.damtp.cam.ac.uk/user/tong/qm/qmhtml/S2.html18 Oct 2021: This word refers to the fact that certain quantities, which are always continuous variables in the classical world, can only take certain discrete values in this new framework. ... This also gives us a new perspective on our original attempt at writing -
1 The Fundamentals of Statistical Mechanics‣ Statistical Physics by…
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S1.html18 Oct 2021: V. fixed when we differentiate. But now there is a new, natural quantity that we can consider — the differentiation with respect to. ... 1.3.1 The Partition Function. Since we will be using various quantities a lot, it is standard practice to introduce -
4 Classical Thermodynamics‣ Statistical Physics by David Tong
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S4.html18 Oct 2021: Figure 24:. Expressing the work as. -. d. W. =. -. p. d. V. also allows us to underline the meaning of the new symbol. -. ... Q. T. Given some reference state. O. , this allows us to define a new function of state. -
6 Black Holes‣ General Relativity by David Tong
www.damtp.cam.ac.uk/user/tong/gr/grhtml/S6.html16 Oct 2021: vanishes in the new coordinates. We’re then left with the simpler looking metric,. ... U. =. tan. U. and. V. =. tan. V. The new coordinates have finite range. -
2 Classical Gases‣ Statistical Physics by David Tong
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S2.html18 Oct 2021: That it was intimately linked up with something so important and entirely new could hardly have been foreseen.”. ... If we take two identical atoms and swap their positions, this doesn’t give us a new state of the system – it is the same state that -
5 When Gravity is Weak‣ General Relativity by David Tong
www.damtp.cam.ac.uk/user/tong/gr/grhtml/S5.html16 Oct 2021: Your new gauge potential will satisfy. μ. h. μ. ν. -. 1. 2. ν. h. ξ. ν. =. f. ν. So if you pick a gauge transformation. ... ξ. μ. that obeys. ξ. μ. =. f. μ. then your new metric will be in de Donder gauge. -
pub.dvi
www.damtp.cam.ac.uk/user/bca20/restricted/toPhds/pub.pdf6 Jan 2021: Problem in String-Motivated Unified Theories”, New Trends in Neutrino Physics, World Scientific. ... edition. Publications List (B.C. Allanach) 6. 103. “Do The Space Warp”, News and Views article for Nature Physics, Vol. -
mul.dvi
www.damtp.cam.ac.uk/user/bca20/restricted/toPhds/mul.pdf6 Jan 2021: matter content of the universe. Exciting new theoretical frameworks which address unsolved problems in. ... interpretation. Trying to find a reasonable new physics explanation and devising additional tests is an. -
4 A Quantum Particle in Three Dimensions‣ Quantum Mechanics by David…
www.damtp.cam.ac.uk/user/tong/qm/qmhtml/S4.html18 Oct 2021: Before we get going, let’s introduce some new variables so that we don’t have to lug around all those constants on our journey. ... The primary builders of this new theory were Werner Heisenberg, Erwin Schrödinger, Max Born, Pascual Jordan, and Paul -
Principles of Quantum Mechanics University of Cambridge Part II ...
www.damtp.cam.ac.uk/user/dbs26/PQM/chap1.pdf8 Oct 2021: in which quantum mechanics is essential, while much of modern medicine relies on new. -
4 The Einstein Equations‣ General Relativity by David Tong
www.damtp.cam.ac.uk/user/tong/gr/grhtml/S4.html16 Oct 2021: M. to a new set of fields on. M. The end result is physically indistinguishable from where we started: it describes the same system, but in different coordinates. -
4 Continuous Symmetries‣ Statistical Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/sft/sfthtml/S4.html16 Oct 2021: As a spin-off, we will see that we also a get a new handle on the critical point in. ... However, there is now something new we can do. We can look at what happens in dimension. -
2 The Hot Universe‣ Cosmology by David Tong
www.damtp.cam.ac.uk/user/tong/cosmo/cosmohtml/S2.html18 Oct 2021: We need to introduce a new concept that allows us to deal with such situations. ... Now we can use the chemical potential for something new. We require that these particles are in chemical equilibrium. -
Swirling Instability of the Microtubule Cytoskeleton
www.damtp.cam.ac.uk/user/lauga/papers/185.pdf17 Jan 2021: Shelley ,1,3,‡ and Raymond E. Goldstein 2,1Center for Computational Biology, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA. ... 3Courant Institute, New York University, 251 Mercer Street, New York, New York 10012, USA. -
3 Interacting Fields‣ Quantum Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/qft/qfthtml/S3.html18 Oct 2021: 4. (. M. 2. p. 2. ). =. m. 2. is what allows us to discover new particles: they appear as a resonance in the cross section. ... The minus sign tells us that the potential is attractive. Notice that quantum field theory has given us an entirely new
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